advances in chromatography: volume 48

VOLUME 48

Advances inCHROMATOGRAPHY

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VOLUME 48

Advances inCHROMATOGRAPHYEDITORS:

ELI GRUSHKAHebrew University of JerusalemJerusalem, Israel

NELU GRINBERGBoehringer-Ingelheim Pharmaceutical, Inc.Ridgefield, Connecticut, U.S.A.

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v

ContentsContributors .............................................................................................................vii

1 Chapter Understanding the Retention Mechanism in Reversed-Phase Liquid Chromatography: Insights from Molecular Simulation ............1

Jake L. Rafferty, J. Ilja Siepmann, and Mark R. Schure

2 Chapter Thermodynamic Modeling of Chromatographic Separation ............. 57

Jørgen M. Mollerup, Thomas Budde Hansen, Søren S. Frederiksen, and Arne Staby

3 Chapter Ultra-Performance Liquid Chromatography Technology and Applications .................................................................................99

Uwe D. Neue, Marianna Kele, Bernard Bunner, Antonios Kromidas, Tad Dourdeville, Jeffrey R. Mazzeo, Eric S. Grumbach, Susan Serpa, Thomas E. Wheat, Paula Hong, and Martin Gilar

4 Chapter Biointeraction Affinity Chromatography: General Principles and Recent Developments ....................................................................... 145

John E. Schiel, K. S. Joseph, and David S. Hage

5 Chapter Characterization of Stationary Phases in Supercritical Fluid Chromatography with the Solvation Parameter Model .................... 195

Caroline West and Eric Lesellier

6 Chapter Silica Hydride—Chemistry and Applications .................................. 255

Joseph J. Pesek and Maria T. Matyska

7 Chapter Multidimensional Gas Chromatography .......................................... 289

Peter Quinto Tranchida, Danilo Sciarrone, and Luigi Mondello

8 Chapter Sample Preparation for Chromatographic Analysis of Environmental Samples ................................................................... 329

Tuulia Hyötyläinen

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vi Contents

9 Chapter Sample Preparation for Gas Chromatography Using Solid-Phase Microextraction with Derivatization ................................................ 373

Nicholas H. Snow

Index ...................................................................................................................... 389

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vii

Bernard BunnerCore TechnologyWaters CorporationMilford, Massachusetts

Tad DourdevilleCore TechnologyWaters CorporationMilford, Massachusetts

Søren S. FrederiksenDiabetes API, Modelling &

OptimisationNovo Nordisk A/SBagsværd, Denmark

Martin GilarBiopharmaceutical OperationsWaters CorporationMilford, Massachusetts

Eric S. GrumbachChemical OperationsWaters CorporationMilford, Massachusetts

David S. HageDepartment of ChemistryUniversity of Nebraska–LincolnLincoln, Nebraska

Thomas Budde HansenProtein Separation & VirologyNovo Nordisk A/SGentofte, Denmark

Paula HongChemical OperationsWaters CorporationMilford, Massachusetts

Tuulia HyötyläinenMaj and Tor Nessling FoundationHelsinki, Finland

K. S. Joseph Department of ChemistryUniversity of Nebraska–LincolnLincoln, Nebraska

Marianna KeleChemical OperationsWaters CorporationMilford, Massachusetts

Antonios KromidasChemical OperationsWaters CorporationMilford, Massachusetts

Eric LesellierInstitute of Organic and Analytical

Chemistry University of OrleansOrléans, France

Maria T. MatyskaDepartment of ChemistrySan Jose State UniversitySan Jose, California

Jeffrey R. MazzeoBiopharmaceutical OperationsWaters CorporationMilford, Massachusetts

Jørgen M. MollerupPrepchromKlampenborg, Denmark

Contributors

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viii Contributors

Luigi MondelloDepartment of PharmacochemistryUniversity of MessinaMessina, Italy

Uwe D. NeueChemical OperationsWaters CorporationMilford, Massachusetts

Joseph J. PesekDepartment of ChemistrySan Jose State UniversitySan Jose, California

Jake L. RaffertyDepartment of ChemistryUniversity of MinnesotaMinneapolis, Minnesota

John E. SchielDepartment of ChemistryUniversity of Nebraska–LincolnLincoln, Nebraska

Mark R. SchureTheoretical Separation Science

LaboratoryThe Dow Chemical CompanySpring House, Pennsylvania

Danilo Sciarrone Department of PharmacochemistyUniversity of MessinaMessina, Italy

Susan SerpaChemical OperationsWaters CorporationMilford, Massachusetts

J. Ilja SiepmannDepartment of Chemistry and

Department of Chemical Engineering and Materials Science

University of MinnesotaMinneapolis, Minnesota

Nicholas H. SnowDepartment of Chemistry and

BiochemistrySeton Hall UniversitySouth Orange, New Jersey

Arne StabyCMC Project Planning & Management Novo Nordisk A/SGentofte, Denmark

Peter Quinto TranchidaDepartment of PharmacochemistryUniversity of MessinaMessina, Italy

Caroline WestInstitute of Organic and Analytical

Chemistry University of OrleansOrléans, France

Thomas E. WheatChemical OperationsWaters CorporationMilford, Massachusetts

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1

1 Understanding the Retention Mechanism in Reversed-Phase Liquid Chromatography: Insights from Molecular Simulation

Jake L. Rafferty, J. Ilja Siepmann, and Mark R. Schure

Contents

1.1 Introduction ......................................................................................................21.2 Thermodynamic-Based Models of Reversed-Phase Liquid

chromatography (RPLC) ..................................................................................31.2.1 Solvophobic Theory ..............................................................................41.2.2 Lattice and Self-Consistent Field Theories...........................................81.2.3 Group Contribution Methods ................................................................81.2.4 Lipophilic View Based on Comparison to

n-Hexadecane Transfer .........................................................................91.3 Outstanding Problems in Understanding the Reversed-Phase Liquid

Chromatography (RPLC) Retention Mechanism ........................................... 111.3.1 The Simulation Approach ................................................................... 121.3.2 The Driving Forces for Reversed-Phase Liquid Chromatography

(RPLC): Solvophobic or Lipophilic? .................................................. 121.3.3 Do Chains Lie Extended Away or Cover the Surface? ....................... 151.3.4 Where Is the Solvent? .........................................................................201.3.5 Partition or Adsorption?...................................................................... 211.3.6 Effects of Embedded Polar Groups ....................................................251.3.7 Determination of the Phase Volumes .................................................261.3.8 Pressure and Pore Curvature Effects ..................................................271.3.9 General Observations for the Bonded-Phase–Solvent–Solute

Environment .......................................................................................27

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2 Advances in Chromatography: Volume 48

1.1 IntroduCtIon

The search for the retention mechanism of reversed-phase liquid chromatography (RPLC) has had a long and interesting history. The mechanism appears to be elusive [1–4] because retention measurements of model compounds on retentive phases have mostly been utilized to infer the mechanism. For example, if one injects a series of compounds, the elution order generally reflects the extent of molecular interactions with the stationary phase: more favorable interactions with the retentive phase take place for molecules with longer retention times. In this review, we refer to the station-ary phase interchangeably as a retentive phase and to the mobile phase as a solvent phase; it makes no difference to the thermodynamics of retention whether a phase is moving or not. As one may expect, but is not necessarily true in all cases, larger molecules usually have longer retention times and it has been rationalized that the magnitude of the solute’s interactions with the retentive phase is simply a function of its size. As we will discuss shortly, this guideline is riddled with problems as it is does not take into account specific interactions of the solute with both the retentive phase and the solvent components.

The term reversed-phase appears to be first used by Howard and Martin [5] where these pioneers described the surface derivatization of a siliceous material with dichlo-rodimethyl silane to chemically bind a hydrophobic moiety to the support surface. Further refinement of the bonding chemistry has been a continual process and has been documented recently by Kirkland [6] and the history of the terminology has been given by Melander and Horváth [7]. We loosely use the term RPLC here as liquid chroma-tography with a waxy hydrophobic phase, typically C18, and polar solvents that are

1.4 Simulation Methodology ................................................................................281.4.1 Simulation and the Theory of Liquids ................................................281.4.2 Previous Molecular Simulations of Reversed-Phase Liquid

Chromatography (RPLC) Systems .....................................................291.4.2.1 Transferable Potentials for Phase Equilibria

Force Field ........................................................................... 311.4.2.2 Monte Carlo Methods for Molecular Simulation .................341.4.2.3 Gibbs Ensemble Method ......................................................361.4.2.4 Configurational-Bias Monte Carlo ....................................... 381.4.2.5 Application of the CBMC Method in the Gibbs

Ensemble to Simulating Reversed-Phase Liquid Chromatography (RPLC) .................................................... 42

1.4.3 Analysis and Presentation of Data ...................................................... 451.4.3.1 Gauche Defect Statistics ...................................................... 451.4.3.2 Order Parameter ................................................................... 451.4.3.3 Heterogeneity in System Composition .................................461.4.3.4 Solute Distribution Coefficients and Transfer

Free Energies .......................................................................461.5 Reflections ...................................................................................................... 47Acknowledgments ....................................................................................................48References ................................................................................................................48

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Retention Mechanism in Reversed-Phase Liquid Chromatography 3

generally a binary mixture of water and an organic modifier. Many different solvent systems have been utilized for RPLC but most common are aqueous mixtures with methanol, acetonitrile, or tetrahydrofuran. With this description it is easy to see that normal phase chromatography utilizes polar moieties on/in the retentive medium, such as bare silanols, bonded amino groups or cyano groups, etc., and the mobile phase con-sists of less polar solvents of varying degrees, such as n-hexane, although methanol–water or acetonitrile–water mixtures can also be utilized.

The majority of separations conducted with high performance liquid chromatog-raphy (HPLC) are carried out using RPLC columns [8–10]. This point was made over 25 years ago where authors stated [11] “It has become quite trivial to write that reversed-phase liquid chromatography (RPLC) is certainly the most popular chro-matographic technique.” Refinements in this technique drove researchers to make models of the retention process and to refine these models. The early work in this area was thermodynamic in nature with models utilizing lumped interactions. As time passed these interactions became more explicitly detailed. A number of these approaches have been reviewed in detail [12]. The most popular of these, the sol-vophobic theory of Horváth and coworkers, [3,7,13–16] which will be discussed in detail below, took the center stage in the development of a theory of RPLC. It would take nearly 30 years after the initial presentation of this theory for the evolution of particle-based simulation methodology to allow the a priori determination of the RPLC mechanism [17] without invoking a predetermined mechanism; a necessity and limitation of any thermodynamic theory.

In this chapter we review some of the salient features of past theoretical attempts at describing the RPLC process. We then highlight the results of our RPLC investigations that utilize advanced molecular simulation methods and provide a molecular-level detail of the retention mechanism that is currently not attainable through experiment or theory. We present our simulation approach, configurational-bias Monte Carlo in the Gibbs ensemble using transferable force fields, which is the method of choice for these investigations. We also discuss the future aspects of molecular simulation in RPLC and liquid chromatography to solve outstanding questions in retention mecha-nisms. In this regard, this chapter is a continuation of ideas, concepts, and techniques illustrated in a chapter published in Advances in Chromatography by one of us (MRS) ten years ago, entitled “Particle Simulation Methods in Separation Science” [18]. However, our main emphasis here is on the RPLC mechanism and how simula-tion allows a detailed understanding of this extraordinary separation technique. We intend this chapter to be useful as a teaching tool for those interested in this mecha-nism and as a brief historical account as to how the research of this mechanism has evolved. This is not intended to be a comprehensive review of the older theoretical work, but should serve as an indication as to where this field is moving.

1.2 thermodynamIC-based models of reversed-phase lIquId Chromatography (rplC)

The intention of RPLC model development from the late 1970s through to the early 1990s was two-fold: one was to elucidate the retention mechanism and thereby aid in the development of novel RPLC systems and the other was to predict retention order and

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thereby provide the ability of solute identification through retention time measurement. Today this latter goal is largely irrelevant because of the power of mass spectrometry and the ease with which LC and mass spectrometry are integrated, enabling the identi-fication of small and medium-size molecules with very few assumptions.

One of the common ways to model RPLC was one where empirical values were fitted to equations with predetermined forms. This style of lumped constant thermodynamic model can be effective within a certain homologous series of sol-utes and with very well defined constraints. These models have been reviewed by Kaliszan [12] for work done up to 1987. However, these models can never be rigorous because they neglect a number of physical and chemical facts:

1. The interactions between solvent and bonded-phase chains are represented at a highly empirical and structureless level that neglects specific interac-tions that may result in an enrichment of one of the solvent components at the bonded-phase–solvent interface, near the silica substrate, or within the bonded-phase region.

2. These models are not atomistic; any change in the solute structure cannot reflect the complex interactions with the solvent and retentive phase (such as specific steric hindrance) but rather some parameter is expected to change within the model. These parameters may have been previously parameterized from experimental data. This is especially critical with molecules that pos-sess complex shapes, with chain branching and multiple functional groups. Orientation effects due to the anisotropic nature of the retentive phase cannot be taken into account.

3. Secondary interactions of the solute with the support material, typically sil-ica, are mimicked on an empirical level with no ability to properly account for the competition between the solvent and the solute for these sites.

Nonetheless, a great deal of experimental data was generated and is still being generated that has been useful in recognizing how chromatographic parameters and analyte structure affect retention. We will now discuss a few of the most successful and recognized theories from the thermodynamic model era.

1.2.1 Solvophobic theory

Of all of the theories proposed for RPLC, the solvophobic theory is the most well known. Rather than review this theory [3,7,13–16], the highlights will be given here with emphasis on the resulting limitations of this and other thermodynamic theo-ries of retention in RPLC. However, it needs to be stressed that in the absence of a molecular-detailed view of the RPLC process, these simpler thermodynamic theo-ries offered some interesting insights and served for many years as a valuable guide for RPLC development.

It must be realized that thermodynamic models are bookkeeping systems. This is why thermodynamics is versatile and can be used to describe anything from traffic flow [19] to flowing liquids [20]. But there is almost no way to describe molecular systems that have complex interactions in a detailed thermodynamic model. In the

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bookkeeping domain, the RPLC models have attempted to isolate each effect by phase and by accounting for solvent–solute, retentive phase–solvent, and retentive phase–solute interactions. This is nearly impossible to do quantitatively for complex systems in the liquid domain and this is why most fundamental studies of liquids have utilized molecular simulation [21–23] as a method to study many-body systems.

The solvophobic theory in essence predicts that the most favorable free energy contribution driving the solute retention process is the decrease in the solvent–solute interaction when the solute transfers into the retentive phase. The descriptor “most favorable” here refers to the most negative free energy change within the process [24,25], and a negative free energy change refers to one that increases the retention time. The process is described by a thermodynamic cycle, shown in Figure 1.1, which is essential in any thermodynamic theory for accounting purposes.

The solvophobic theory of Horváth and coworkers is based on Sinanoglu’s theory [26,27]. This theory was adapted by Horváth and coworkers for use in liquid chro-matography applications although its potential utilization is much wider than this; its use [26,27] is oriented toward liquid–liquid partitioning processes particularly in biologically relevant applications. The thermodynamic calculation of Δ G°retention is accomplished by accounting for the other free energies in Figure 1.1 such that:

∆ ∆ ∆G G Gretention mobile stationary = − (1.1)

where the superscript ° denotes a standard state. Here is should be noted that the use of a standard state is only a choice of a particular reference system, but that chro-matographic separation usually takes place at concentrations far away from the usual standard state of unit molar concentration. Hence, the standard state notation is not used in many subsequent equations.

The RPLC solvophobic theory further invokes a thermodynamic model where the two free energy terms on the right hand side (rhs) of Equation 1.1 are expanded such that:

∆ ∆ ∆ ∆

∆

G G G G

G

mobile cav AL cav A cav L

int

= − −

+

, , ,( )

( ,, , ,− −

+ + −

AL int A int L

mix red

∆ ∆

∆∆ ∆

G G

G G RTRTVE

)

ln

(1.2)

Gas phase

Mobile phase Stationary phase

∆Gmobile

∆Gretention

−∆Gstationary

fIgure 1.1 The thermodynamic cycle which identifies the process of solute retention, solvation, and the ideal vapor reference state in RPLC.

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where ΔGcav,AL is the free energy change of cavity formation for the solute– retentive phase complex, ΔGcav,A is the free energy of cavity formation for the solute, and ΔGcav,L is the free energy of cavity formation for the bonded retentive phase. The term ΔGint,AL is the free energy for the solute–retentive phase complex with the solvent, ΔGint,A is the free energy for the solute–solvent complex, and ΔGint,L is the free energy of the solvent–retentive phase interaction. The term ΔΔGmix is the free energy of mixing of solute and solvent molecules of different sizes, ΔGred is the reduction of ΔG°vapor due to the presence of the solute, R is the gas constant, T is absolute temperature, and VE is the molar volume of the solvent [15]. The last term in the above equation represents the volume change for the process.

The solvation process for each solute consists of two steps; the cavity formation of a solute molecule in the solvent system and the interaction of the solute with the surrounding solvent. This model assumes that these free energies are independent; i.e., these terms are separable. As stated by Horváth et al. [15], the energy of cavity formation is dependent on the size of the solute molecule and the cohesive energy of the solute–solvent interaction. As is the usual case with thermodynamic theories, there is a lack of an explicit description of the molecular geometry and structure. Furthermore, the authors of this theory assume that the change in free volumes for the solute-chain interaction and the unbound chain cancel each other out [15].

Combining Equations 1.1 and 1.2 yields:

∆ ∆ ∆ ∆

∆

G G G G

G

retention cav AL cav A cav L = − −

+

, , ,( )

( iint AL int A int L

mix red

, , ,− −

+ + −

∆ ∆

∆∆ ∆

G G

G G RTR

)

lnTT

VG

E

+ ∆ vapor

(1.3)

The solvophobic theory of RPLC continues to define these free energy terms individually using simple equations that attempt to tie these individual terms with experimentally measurable parameters. For example, ΔGcav,A, the free energy of cavity formation of the solute, is equated to:

∆ ∆G AgE Acav A, = κ γE (1.4)

where κ Eg is the curvature correction to the surface tension of the solute, γE, and ΔAA

is the molecular surface area of the solute.These types of equations have no easily measurable analog. For example, κ E

g and ΔAA are used throughout the solvophobic theory of RPLC but there is no easy way to make these measurements. The free energy expansions of other terms are given in the original papers.

One advantage of this theory is that these equations can imply the retention order of compounds in homologous series. For example, as ΔAA increases, the free energy of retention decreases causing retention to increase, as implied in Equations 1.3

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and 1.4 and explicitly stated in the well-known relations used in chromatography [28,29]:

KGRT

= −

exp∆ retention (1.5)

and

′ =k Kφ (1.6)

where k′ is the commonly used retention measure that gives the number of column volumes after the void volume of a retained solute, K is the distribution coefficient in units of molar concentrations (or number densities), and φ is the phase ratio of the column, i.e., the ratio of the mobile (solvent) phase volume to the retentive phase volume. We will show below that the retentive phase volume is ill-defined in this problem and may be very difficult to measure.

Molecular surface areas can be calculated with molecular modeling tools [23]. However, there exists a similar equation for the free energy of cavity formation for the solute–retentive phase complex, and this implies that there is an average value for this in spite of the fact that there may be a host of different locations and geometries for the solute complex in the retained state due to the anisotropic and microhetero-geneous nature of the retentive phase. The average value of this may suffice but it is this lack of detail that makes these types of theories semi-empirical at best.

Another example where the theory shows useful trends is that the surface tension shows up as a multiplicative term in the cavity expressions and in general the higher the bulk surface tension between the solute and the solvent, the more retained will be the solute. A number of examples for simple solutes and solvent systems show this trend. For example, an increase in the methanol content of the solvent will decrease the retention factor because the surface tension between a solute and the solvent decreases with increasing methanol content. However, it should be noted here that these surface tensions can only be measured for planar surfaces of bulk phases and that preferential solvation in solvent mixtures [30–33] and curvature induced micro-phase segregation in solvent mixtures [34] can lead to significant differences between the molecular-scale and its macroscopic analog. This greatly hampers the usefulness of bulk surface tensions for thermodynamic models of the retention process.

The solvophobic theory, however, has a number of deficiencies. The most impor-tant deficiency is that there is a distinct lack of detail about the influence of the reten-tive phase on retention. Experimentally, it has been known for years that the solvent composition can alter properties of the retentive phase [35–39], such as the amount of sorbed solvent. The theory cannot accommodate this observation nor predict this a priori. The solvophobic theory of RPLC is focused on the mobile (solvent) phase in determining the retentive properties and disregards the retentive phase. Since it is well known that embedded polar groups (EPGs) [40–43] significantly modify the retention properties of solutes, this seems to invalidate the solvophobic theory of RPLC. It is also well known that the length of the bonded-phase alkyl chains influences retention. It has often been said that it would be possible to include the

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retentive phase in free energy-like equations. However, this was perhaps the best attempt at explaining chromatographic retention at the time of its development. As we will show shortly, simulation is much better suited for the purpose of determining the mechanism of RPLC. The parameters required to apply a theory, which may not be measurable experimentally, need not be explicitly defined in a simulation.

1.2.2 lattice and self-ConSiStent field theorieS

Lattice theories are used to simplify certain statistical mechanics problems by forcing a molecular architecture into structural constraints which occupy vertices on a lattice. Configurational statistics are then utilized to determine chain conformation and solute retention. This approach was taken for RPLC by Martire and Boehm [44]. Other applications of this approach include studying liquid crystal problems. This theory has the simplifying assumption that the retentive phase has liquid crystalline, rather than interfacial, organization [2]. Solvent properties are defined through semi-empirical energy interactions. This theory leads typically to broad-brush learnings regarding chain ordering although for the short chains used in chromatography the theory has been criticized because the model tends to overestimate the ordering of chains [2]. Ben-Naim [45] has recently stated: “Today, lattice theories have almost disappeared from the scene of the study of liquids and liquid mixtures.”

In another form of theory, but closer to a simulation, Böhmer, Koopal, and Tijssen [46], and Tijssen and coworkers [47], used a lattice theory adopted from the self-consistent field theory for adsorption (SCFA) developed by Scheutjens and Fleer [48]. Both aliphatic and amphiphilic solute molecules are predicted to be distributed non- uniformly in the grafted layer and are accumulated in the interfacial region between the chains and solvent, respectively. It is quite interesting that such detail can be obtained in a lattice theory of this kind. However, it is not clear what parameters should be cho-sen for such important variables as the Flory–Huggins χ parameters. It is common to build polymer theories using such coarse-grain parameters and then express the results over ranges of these parameters. To our knowledge, no further work has been done using the SCFA approach to study the RPLC mechanism. Specific molecular structure is difficult to graft into a theoretical or simulation approach which is inherently coarse-grained. However, it is well known in polymer physics and chemistry that this theoreti-cal approach is quite useful for studying polymer adsorption where atomic-level detail is not essential to describe trends driven by changes in χ or the chain length.

1.2.3 Group Contribution methodS

Many of the past attempts at the theory of RPLC have grouped terms such that homolo-gous series of a certain molecular structure can be calculated once the retention factor of the primary molecule is determined. A number of methods have been explored but the most interesting application [49–51] of this uses the UNIFAC model. UNIFAC is an abbreviation of UNIversal Functional Activity Coefficient, which is a semi-empirical system, used for estimating activity coefficients of mixtures. UNIFAC uses the functional groups present on the solute to attempt to predict the equilibrium prop-erties of a mixture. For such a simple approach, the accurate prediction of retention

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is a tall order but this approach should give the correct retention order when solutes contain different group contributions. In fact, when plots are made of the logarithm of the retention factor k′, as a function of the volume percent of the organic modifier acetonitrile, the agreement for certain solutes is adequate [51]. However, there are no mechanistic insights that can be gleaned from this form of study; the numbers involved are entirely thermodynamic and offer little detail.

1.2.4 lipophilic view baSed on CompariSon to n-hexadecane tranSfer

Carr and coworkers [52,53] conducted some key experimental work that shed light on the thermodynamic driving force of RPLC retention. These studies used a bulk liquid n-hexadecane phase as an analog to the typical RPLC stationary phase because this avoids the difficult measurement of the phase ratio, φ. We will discuss the pit-falls of measuring the volume of the retentive chains or the phase ratio below. Their first paper [52] measured the distribution coefficient, K, of a homologous series of alkylbenzenes, from benzene through n-butylbenzene, between n-hexadecane and various solvent phases, including methanol–water, acetonitrile–water, isopropanol–water, and tetrahydrofuran–water systems. Head-space gas chromatography was used to obtain partition and distribution coefficients.

Carr and coworkers realized that they must use a thermodynamic cycle, shown in Figure 1.1, to interpret their results. Furthermore, they focused on the incremental free energy of transfer of a methylene group, ∆GCH2

, to negate any dependence on the phase ratio in these n-hexadecane–solvent distribution coefficient measurements via:

∆G RT K Kn nCH2 1 = − /+ln( ) (1.7)

where Kn + 1 is the distribution coefficient of an alkylbenzene having one more methylene group than the alkylbenzene yielding Kn. Using what these authors called an energy level diagram, they were able to construct the free energy of transfer of a methylene group between a methanol–water solvent of varying composition and the n-hexadecane phase (see Figure 1.2). This figure shows that the partitioning from a gas phase into liquid n-hexadecane is favorable (i.e., possesses a negative free energy of transfer) and is much larger in magnitude than the incremental free energy of par-titioning into the solvent for all solvent compositions. Only for water-rich solvents (≤ 20% methanol by volume) is the transfer of the methylene increment from the gas phase to the solvent phase unfavorable, but the magnitude of this solvophobic effect is quite small. For solvent compositions with volume fraction of methanol fMeOH ≥ 30% commonly used in RPLC, the transfer of a methylene group is favorable from gas to solvent, i.e., not solvophobic, but the free energy difference between the n-hexadecane and the gas phase is much more favorable than the transfer from gas to solvent. Even for neat water solvent, the unfavorable transfer of a methylene group from gas to sol-vent is associated with only a relatively small free energy change of ≈ + 0.6 kJ/mol.

This suggests that the driving force for the partitioning of nonpolar molecules such as the alkylbenzenes is the lipophilic interaction with n-hexadecane and not the usu-ally solvophilic interaction with the solvent phase (for fMeOH ≥ 30%). This observation

84534.indb 9 11/5/09 12:24:16 PM


is contrary to the solvophobic theory and has been referred to as the revisionist view. Furthermore, Carr and coworkers compared this data to certain RPLC experiments and showed that the magnitude of the transfer free energies is very similar. They were also cautionary about suggesting that polar molecules would have the same driving forces. In the case of benzene, the vapor to water free energy of transfer is favorable, but the transfer to hexadecane from the vapor phase is ≈ 4 times more favorable. This study shed new light on the driving force for nonpolar molecule solutes and was in stark disagreement with the solvophobic theory which deemphasized the role of the retentive phase. In fact, other studies [54,55] (the second reference is from Carr’s own laboratory) suggested that the solvent controlled the energetics of retention. The good agreement found for methylene group partitioning into a bulk n-hexadecane and for the RPLC transfer process has been used to argue that, in a thermodynamic sense, the RPLC retention mechanism appears to be well described by a partition process.

In a following study from Carr’s laboratory [53], the free energies of transfer were broken down into the enthalpy and entropy components that make up the free energy through the well-known relationship: ΔG° = ΔH°−TΔS°. The authors again used n- hexadecane as a model for a retentive phase material noting that n- octadecane is a solid at room temperature whereas n-hexadecane is a liquid. Their results indicated that favorable enthalpic contributions were much larger for the transfer of solutes from gas to n-hexadecane than were the unfavorable entropic part of the free energy. The gas to solvent transfer was enthalpically favorable as the entropic part was minimally unfavor-able. The transfer from solvent to the hexadecane retentive phase was also enthalpically favorable for nonpolar solutes with a small unfavorable component from the entropic part. Hence, the entropic component appears to reduce the favorability of retention but is rather small in magnitude. These authors also suggested based on these data that lipophilic forces are the driving force for retention and that the retention mechanism is

Water

Gas

C16

1020

304050

6070

8090

100

% MeOH

–0.6

–0.4

–0.2

Free

ene

rgy

of tr

ansf

er o

f a –

CH

2 gro

up o

fal

kylb

enze

nes (

25°C

. kC

al/m

ol)

0.2

0.0

fIgure 1.2 Carr and coworkers measured incremental transfer free energy diagram for a methylene group between bulk methanol–water solvent, n-hexadecane, and gas phase. (From Carr, P. W., Li, J., Dallas, A. J., Eikens, D. I., and Tan, L. C., J. Chromatogr. A, 656, 113–133, 1993. With permission.)

84534.indb 10 11/5/09 12:24:17 PM


more like a partitioning effect than an adsorption effect. This is most difficult to prove, however, because these thermodynamic free energies cannot be used to infer a mecha-nism (but only to disprove a mechanism), let alone that most of these measurements were made on a system that is a liquid and may differ from the anisotropic environment of chemically bonded chains [56]. Comparison with RPLC measurements was made and the numbers are of a similar trend. However, it was suggested that the lack of good phase ratio measurements have hindered making good direct comparisons.

Perhaps the most important point made in the studies from Carr’s laboratory [52,53] is that the use of a vapor-phase standard state for these measurements is of tantamount importance. Others [57–60] have emphasized this point; in one study [54] Martire and coworkers used the pure solute liquid as the reference state. As Carr and coworkers have stated [53]: “The use of such excess thermodynamic quantities inevitably ‘bury’ the interactions that are common to the initial and final states.” Although Carr and coworkers solved the driving force mystery for liquid n-hexadecane retentive phases, the mecha-nism of RPLC was only established by inference and only for nonpolar solutes.

1.3 outstandIng problems In understandIng the reversed-phase lIquId Chromatography (rplC) retentIon meChanIsm

None of the thermodynamic-based theoretical approaches discussed above can answer the most basic question of whether a molecule adsorbs or partitions into the retentive phase. Here it should be noted that adsorption and partition contributions can be separated by investigating the dependence of the retention factor on the inter-facial or surface area or on the thickness of the retentive phase. Although this is pos-sible for gas–liquid chromatography [61–63], it is obviously not possible for RPLC, where the thickness of the retentive phase cannot be varied without changing the nature of the bonded chains. Thus, partition and adsorption can only be determined from knowledge of the solute location. To be clear, adsorption occurs when the solute lies at the interface between bonded chains and solvent (albeit one may argue that a secondary adsorption site would be a location near the silica substrate). Partition in RPLC refers to the solute occupying a space within the bonded phase (neither close to the substrate nor the interface with the solvent).

It is well known that n-octadecane itself is virtually insoluble in water with its solu-bility estimated to be approximately 7 ppb by volume [64] and 4.3 × 10−10 by molfraction [65], but the solubility of water in a liquid alkane is much higher and does not depend as strongly on the chain length of the solvent [66,67]. Nevertheless, it is reasonable to sus-pect that water will not be found in significant concentration within the bonded-phase layer. We will see shortly, through the use of simulation in which one can pinpoint the location and the spatial concentration, that the solvent penetration into a bonded octade-cyl silane (ODS) phase differs markedly from a bulk n-octadecane phase.

Furthermore, the thermodynamic theories are incapable of pinpointing the driving forces of retention. This is most unfortunate because this has been an outstanding problem for many years. Fortunately, simulation can also solve this problem without an a priori biasing of the problem, i.e., without first constructing a set of equations that presuppose a mechanism.

84534.indb 11 11/5/09 12:24:17 PM


In addition, a number of workers have speculated on whether the bonded chains lie flat on the surface (i.e., phase collapse) or whether the chains stand up. Again, simulation can provide precise information on the overall bonded-phase distribution and the conformation of individual grafted silanol chains.

We have used modern simulation methods to study the problems described above and hope that the reader will agree that simulation has resolved many of the mys-teries of the RPLC retention mechanism. The following subsections review some of our most important findings. Following these insights we will present a detailed description of the simulation methodology, thereby allowing the reader to understand why certain methodologies are particularly suited to unraveling the RPLC retention mechanism.

1.3.1 the simulation approach

We have recently examined the chain conformation, solvent penetration, and reten-tion thermodynamics [17,68–73] of various RPLC systems via particle-based simu-lations using efficient sampling Monte Carlo algorithms and accurate force fields. These studies investigated the effects of mobile (solvent) phase composition for methanol–water [17,68,69] and acetonitrile–water mixtures [73], of the grafting den-sity of dimethyl octadecylsilane bonded phases [71,72], of the inclusion of embedded ether and amide functionalities in the bonded-phase chains [70], of the chain lengths for bonded alkyl chains [74,75], and of pore curvature [74]. Most of these studies utilized bonded-phase chains with dimethyl side chains and a main chain with a backbone consisting of 18 carbon, nitrogen, or oxygen atoms grafted onto a planar slit pore with exposed (1 1 1) surfaces of a slab of β-cristobalite [76] and at a column pressure of 1 atm. Further details on the system setup are given in Section 1.4.2.5 and our works referenced in this paragraph.

We will now present selected results of these studies in a form that provides the answers to the outstanding questions in RPLC mechanism research described in the previous section. Specifically, results will be shown for a 2.9 μmol/m2 ODS phase in contact with pure water, 33% mol fraction methanol, 67% molfraction methanol, and 33% molfraction acetonitrile (denoted hereafter as systems ODS-2.9/WAT, ODS-2.9/33M, ODS-2.9/67M, and ODS-2.9/67A, respectively), 1.6 and 4.2 μmol/m2 ODS phases in contact with 50% methanol (systems ODS-1.6/50M and ODS-4.2/50M), and 2.9 μmol/m2 EPG phases in contact with 33% methanol (systems Amide-2.9/33M and Ether-2.9/33M). Some of the quantities presented in the discussion of these sys-tems may be somewhat foreign to the reader. For this reason we include, toward the end of this chapter, Section 1.4.3 dealing with the definitions of these quantities and how they are computed from the simulation data.

1.3.2 the drivinG forceS for reverSed-phaSe liquid chromatoGraphy (rplc): Solvophobic or lipophilic?

The thermodynamic cycles (or free energy diagrams) for RPLC systems consisting of an ODS bonded phase with a grafting density of 2.9 μmol/m2 in contact with both methanol–water and water–acetonitrile solvent mixtures are compared in Figure 1.3

84534.indb 12 11/5/09 12:24:17 PM


to those involving partitioning between the same solvent phases and a bulk liquid n-hexadecane phase.* We prefer to provide the solvent concentrations in mole frac-tion units because this measure is independent of temperature and pressure and lends itself better to an analysis of the local concentration in subregions of the RPLC system.

The meaning of these free energy diagrams is as follows. First, we choose a helium gas (i.e., an ideal gas) phase as our reference state and assign the Gibbs free energy of a solute to zero in this state, although this choice of a reference state energy is entirely arbitrary. This reference state is used for both the alkane incremental free energy and the alcohol incremental free energy. The need for this reference state was first recognized by Carr and coworkers [52], as discussed above, and later used by Vailaya and Horváth [15]. Incremental transfer free energies are used here because they can be determined with very high precision and allow direct comparison to experimental data without knowledge of the phase ratio. A homologous series of n-alkane solutes is used to determine the incremental transfer free energy of a meth-ylene group, and comparison of the n-alkane and primary alcohol solutes with the same number of carbon atoms allows one to determine the incremental transfer free energy of the hydroxyl group. The use of the incremental free energy of retention

* A description of how these free energies are computed is given in Section 1.4.3.4.

–3 –3

–2 –2

–1 –1

∆GC

H2 (k

J/m

ol)

–30 –30

–20 –20

–10 –10

00

11

00

∆GO

H (k

J/m

ol)

WAT

WAT

33M

33M

67M

67M

MET

MET

ODS

ODS

C16

C16

ODS

ODS

C16

C16

ODS

ODS

C16

C16

ODS

ODS

C16

C16

Vapor

Vapor

33A

33A

fIgure 1.3 Computed incremental transfer free energy diagrams for a methylene group (top) and a hydroxyl group (bottom) between methanol–water (solid black lines) and ace-tonitrile–water (solid gray lines) solvent mixtures, solvent saturated bulk n-hexadecane (C16) and bonded ODS phases, and gas phase. For comparison of the simulated data to experiment, the data of Barman is shown as dashed lines. (From Barman, B. N., A thermodynamic inves-tigation of retention and selectivity in reversed-phase liquid chromatographic systems, PhD thesis, Georgetown University, 1985.)

84534.indb 13 11/5/09 12:24:18 PM


further takes the solute chain length out of the problem but also implies that the Martin equation is valid for the methylene increment:

∆ ∆G n n G C( -alkane) CH= +2 0 (1.8)

where n is the number of methylene segments in an n-alkane solute, ∆GCH2 is the

incremental transfer free energy per methylene group, and C0 is a constant. This rela-tionship states that there is a linear relationship between the free energy of retention and solute carbon length. Indeed, for the solutes we have utilized so far this relation-ship holds true. Similarly it is assumed that the hydroxyl increment is independent of chain length and given by

∆ ∆ ∆G G G n( ) (1-alkanol -alkane)OH= + (1.9)

where both solutes posses the same number of carbon atoms.In the case of the alkane solutes, shown in the top of Figure 1.3, we note that

only the incremental transfer free energy of a methylene group from the reference vapor phase into pure water is positive. A positive free energy is often referred to as unfavorable because it describes a transfer process that yields an equilibrium con-centration higher in the “from” phase than the “to” phase [24,25]. In the special case of a transfer from a vapor phase to a solvent phase, this type of unfavorable process is also referred to as solvophobic (i.e., expulsion from the solvent to a vapor phase is a favorable process). All other transfer processes observed for the methylene increment in the RPLC thermodynamic cycle (see Figure 1.3) possess negative free energies of transfer for the solute going from the vapor phase to the solvent, to the ODS bonded phase, and to the n-hexadecane phase. We say these interactions are favorable due to the negative free energies of transfer. Note that the magnitude of the transfer free energy of the methylene group to the retentive phases (both the ODS bonded phase and the liquid n-hexadecane phases) is always larger than those to the solvent phase. This denotes that the lipophilic interaction is driving retention, i.e., the interaction of the solute with the retentive phase is more favorable (or alternatively the free energy of transfer is more negative) for retention than is interaction with the solvent phase.

This lipophilic interaction is the driving force for nonpolar molecules in RPLC. Interestingly, the transfer thermodynamics are very similar for acetonitrile–water solvents and methanol–water solvents on a mole fraction basis, which is used for comparison here. Also note that the incremental free energy of transfer to the bonded ODS phase and to the liquid n-hexadecane phase are quite similar and appears to be insensitive to the solvent composition. We will return to this point shortly as this similarity could be used to infer that the solute-ODS interaction may be similar to the bulk partitioning to a liquid n-hexadecane phase (at least for small alkane sol-utes). We will show shortly that this is not the case. But this highlights the problem with inferring mechanism from thermodynamic values; we will show that this mode of inference is incorrect.

Now we look at the lower panel in Figure 1.3 for the thermodynamics of the trans-fer of a hydroxyl group. The free energy map for the hydroxyl group differs from that for the methylene group in many important ways. First, the transfer free energy is favorable for a hydroxyl group going from the vapor reference state to any solvent

84534.indb 14 11/5/09 12:24:19 PM


phase and the process is most favorable for the transfer to neat water solvent. Second, for all solvent compositions, this free energy of transfer to the solvent is more favor-able than transferring to the ODS bonded phase and far more favorable than to the liquid n-hexadecane phase. In other words, the free energy diagram indicates that the hydroxyl group would much rather be in the solvent than in either chain system, i.e., there is a solvophilic contribution of the hydroxyl group to retention. On a molecular level what would drive the hydroxyl group to favor the solvent over the chain? An analysis of the hydrogen bonding of alcohol solutes in the various phases demonstrates that the formation of hydrogen bonds govern the transfer thermodynamics [17].

It should also be noted that an increase of the methanol content makes the hydroxyl group’s interaction with the solvent-saturated ODS bonded phase less favorable, whereas the opposite is true for the solvent-saturated n-hexadecane phase [17]. This is also explained by the number of hydrogen bonds per alcohol solute that decreases with increasing methanol concentration in the ODS bonded phase while it increases in the n-hexadecane phase due to clustering of methanol for higher methanol mol-fractions [77]. The number of hydrogen bonds in the ODS bonded phase exceeds the number of hydrogen bonds in the n-hexadecane phase by factors of 36 to 1.5 for phases in contact with neat water and neat methanol, respectively [17]. It should be noted that these differences only hold for an ODS bonded phase without endcapping and at intermediate grafting density.

The striking differences between the methylene group and hydroxyl group transfer make it clear that RPLC retention cannot be reduced to a single mecha-nism that holds for all analytes. Furthermore, the striking differences between an ODS bonded phase and a liquid n-hexadecane phase for the hydroxyl group make it clear that the anisotropic chain grafting and the presence of substrate-ODS and ODS-solvent interfaces cannot be neglected in a description of the RPLC thermodynamics.

In closing this section, we also note that the computed incremental free energies for the transfer from the mobile phase to the ODS phase are in excellent agreement with experimental retention data of Barman [78]. The numerical values of these incremental free energies have been previously reported by us [17]. The agreement provides validation of the accuracy of the force field used in our Monte Carlo simula-tions (see Section 1.4.2.1) and gives confidence for the microscopic-level analysis.

1.3.3 do ChainS lie extended away or Cover the surface?

Spectroscopic techniques have long been used to probe the bonded chain conforma-tion and the solvent environment [79–82]. However, spectroscopic techniques usually involve averaging over time and space and hence offer only limited insight into the conformation of individual grafted chains, the penetration of solvent into various regions of the retentive phase, and the spatial and orientational preferences of solute molecules within and near the retentive phase. We have examined the structure of the bonded chains in a number of publications [17,68–73] and will present some of the salient results of these studies here.

One of the primary advantages of molecular simulation is that knowledge of the explicit positions of all atomic (or interaction) sites allows one to produce highly

84534.indb 15 11/5/09 12:24:19 PM


detailed snapshots of a complex chemical system. However, for non-crystalline sys-tems, such as in RP liquid chromatography, one should always keep in mind that the properties of the system are described by ensemble averages over millions of config-urations and that snapshots are a visualization aid. In principle, every configuration visited during the production period of a Monte Carlo or molecular dynamics simu-lation contributes equally to the ensemble average. Since system sizes used typically in molecular simulations are quite small (containing a few thousand molecules), fluc-tuations between different snapshots can be quite large and a given snapshot will not be able to represent the ensemble averages of all important properties.

Snapshots of eight RPLC systems spanning a range of mobile phase composi-tions and grafting densities for ODS bonded phases and for two bonded phases with EPGs are shown in Figure 1.4. These snapshots were taken toward the end of the production simulations. In this section, we will focus on the six systems with bonded ODS chains and the results for the EPG chains will be discussed in Section 1.3.6. As can be seen, the ODS chains are in a disordered conformational state and, with the exception of the system with the lowest grafting density, the chain backbone shows a preferential orientation closer to the substrate normal than parallel to the substrate. The conformational disorder allows for some back folding of individual chains and a rough interface between the ODS chains and the solvent region. For the lowest grafting density (1.6 μmol/m2) or for high methanol concentration (67% MeOH), sig-nificant solvent penetration is evident. Please also note in Figure 1.4 the coordinate z, which will used in subsequent discussion, is given below the snapshots. The value z = 0 Å is the position of the silica surface (defined as the outermost silicon substrate atom) and z increases as one moves away from this silica surface.

One can look at many different statistical quantities with this type of simulation and a representative set is discussed below. One of the most revealing statistics to characterize the retentive phase structure is density profiles, as shown in Figure 1.5. These profiles show the density of stationary phase CHx segments and solvent mol-ecules as a function of z (see Section 1.4.3.3). When moving from z = 0 Å to larger z, for the intermediate ODS grafting density, the interior part of the bonded-phase region shows very little change with solvent composition, but the density in the tail region softens somewhat with increasing methanol concentration or for replacing methanol with acetonitrile at the same concentration. As subtle as the chain density profile appears to respond to changes in the solvent composition, changes in the grafting density lead to significant differences. The lower grafting density results in a decrease of both the thickness and the carbon density, whereas the higher grafting density mostly leads to an increase of the bonded-phase thickness caused by steric effects. Complementary information can be gleaned from the average z location of the terminal methyl group, as shown in Table 1.1. Overall, it is clear that the ODS chains do not lie flat when in contact with neat water nor approach an all-trans posi-tion when the organic modifier content is increased.

Another important conformational measure is the fraction of gauche defects (defined in Section 1.4.3.1). As can be seen in Figure 1.6, the fraction of gauche defects along the backbone is quite insensitive to changes in the solvent compo-sition; a result that is not unexpected given that the conformation of an isolated n-octadecane chain also shows little dependence on solvent (including solvation in

84534.indb 16 11/5/09 12:24:19 PM


0 012 1224 24 36z (Å) z (Å)

fIgure 1.4 (See color insert following page 248.) Simulation snapshots of stationary phase configurations taken from simulations of various RPLC systems. The left column, from top to bottom, shows snapshots for systems ODS-2.9/WAT, ODS-2.9/33M, ODS-2.9/67M, and ODS-2.9/33A. The right column, from top to bottom, shows snapshots for systems ODS-1.6/50M, ODS-4.2/50M, Amide-2.9/33M, and Ether-2.9/33M. The silica substrate and grafted alkyl chains are shown as tubes with oxygen in orange, silica in yellow, and CHx groups in gray. Methanol, acetonitrile, and water are shown in the ball and stick representation with oxygen in red, hydrogen in white, nitrogen in green, and methyl groups in blue. Solutes are shown as large spheres with CHx groups in cyan, oxygen in red, and hydrogen in white.

84534.indb 17 11/5/09 12:24:26 PM


a bulk n-octadecane phase) [30,31]. Changes in the ODS grafting density lead to different conformational distributions for the first few dihedral angles closest to the silanol linker [71]. The fractions of gauche defects averaged over all dihedral angles are compared in Table 1.1 and, again, it is clear that this quantity is not significantly altered for the range of chromatographic parameters considered here.

0

0.4

0.8

1.2

0

0.4

0.8

0

0.4

0.8

ρ (z

) (g/

mL)

z (Å) z (Å)

0

0.4

0.8

0 12 24 0 12 24 36

ODS-2.9/WAT

ODS-2.9/33M

ODS-2.9/67M

ODS-2.9/33A

ODS-1.6/50M

ODS-4.2/50M

Amide-2.9/33M

Ether-2.9/33M

fIgure 1.5 (See color insert following page 248.) The density profiles for the grafted chains (black), water (red), methanol (blue), and acetonitrile (green) in the retentive phase. The eight panels depict ensemble averages for the same eight systems shown in Figure 1.4. The total system density, computed as the sum of bonded phase and solvent densities, is shown in purple. The interfacial region (all panels), defined by the range where the total solvent density falls between 10 and 90% of its bulk value, is shaded in gray while the Gibbs dividing surface fitted to the total solvent density is shown by the dashed orange vertical line. The location of z = 0 Å corresponds to the silica surface.

84534.indb 18 11/5/09 12:24:27 PM


0.00

0.25

0.50

0.75

1.00

f gauc

he

ODS-2.9/WATODS-2.9/33MODS-2.9/67MODS-2.9/33A

ODS-1.6/50MODS-4.2/50MAmide-2.9/33MEther-2.9/33M

Dihedral angle or 1−3 vector index

–0.50

0.00

0.50

S

0 4 8 12 16 4 8 12 16

fIgure 1.6 The ensemble average fraction of gauche defects (top two panels) and the ori-entational order parameter (bottom two panels) as a function of the location along the chain backbone.

table 1.1summary of some average stationary phase structural and Interfacial propertiesa

system f bgauche Snc z dgds δ eint

ODS-2.9/WAT 0.251 −0.142 14.51 3.74

ODS-2.9/33M 0.271 −0.101 14.82 5.34

ODS-2.9/67M 0.281 −0.082 14.74 101

ODS-2.9/33A 0.271 −0.022 14.93 6.33

ODS-1.6/50M 0.262 −0.101 12.41 7.68

ODS-4.2/50M 0.274 0.142 18.81 5.93

Amide-2.9/33M 0.291 0.171 18.06 7.04

Ether-2.9/33M 0.311 0.071 16.76 7.64

a Subscripts indicate the standard error of the mean in the final digit as computed from four inde-pendent simulations.

b Fraction of gauche defects averaged over all 15 backbone torsions.c Order parameter averaged over all sixteen 1–3 backbone vectors.d Location of the Gibbs dividing surface relative to the silica surface (Å).e Width of the interfacial region (Å).

84534.indb 19 11/5/09 12:24:27 PM


Another measure of the chain conformation is the orientational order parameter, S, which is defined in Section 1.4.3.2. At the intermediate grafting density, the lower part of the ODS chain prefers backbone orientations perpendicular to the substrate S > 0, whereas the upper part prefers orientation parallel to the substrate S < 0. However, the magnitude of the order parameters is relatively small and, hence, indicates that these preferences are relatively weak. Nevertheless, it is clear that a decrease in the solvent polarity (increase of methanol concentration or replacing methanol with acetonitrile) is reflected by an increase of S along the entire backbone. Steric hindrance leads to a significantly more erect ODS backbone orientation at a coverage of 4.2 μmol/m2, whereas little orientational ordering is observed for the lower part of the ODS chains at a coverage of 1.6 μmol/m2.

One of the former mysteries of RPLC has been how retention appears to be lost once a pure water mobile phase is utilized and the column depressurized [83]. It was thought that water would force the chains to flatten out on the surface and lose the ability to retain solute. However, the decrease in retention was shown to be a problem in pore wetting [83], a classic and well-known problem in surface chemistry [84]. Researchers have speculated that chains must be in an unsolvated collapsed state since the void volume changes little with a change in the solvent composition and that only an adsorption mechanism is possible for chains in this state [85,86].

The chain orientation has been controversial, but here we have shown that molec-ular simulation can clarify many of the questions about microscopic detail that are impossible to obtain from theory and experiment.

1.3.4 where IS the solvent?

Although the chain conformation is hardly affected by the solvent composition, the extent of solvent penetration, preferential adsorption of the organic species, and the properties of the bonded chain/solvent interface are quite sensitive to both solvent composition and grafting density. Some of these effects are best represented through density profiles, shown in Figure 1.5. First, the extent of solvent penetration increases as the polarity of the mobile phase decreases (increase in methanol concentration or replacing methanol with acetonitrile) and as the grafting density decreases. Second, with the exception of the system at low grafting density, only the organic modifier shows a significant density in the central region of the bonded ODS phase, but a significant amount of both water and methanol is found to form hydrogen bonds with residual silanols on the substrate (see sharp peak near z = 3 Å). Third, the interfacial region, which we define as the range where the total solvent density falls between 10% and 90% of its bulk value, becomes thicker as the methanol concentration increases or the grafting density decreases. In contrast, the location of the Gibbs dividing surface (GDS, a plane defining a border between the mobile and stationary phases) is nearly invariant to solvent composition. Fourth, partial dewetting (as indi-cated by a minimum in the total density profile) is found for all systems, but is most pronounced at the sharp interface with neat water solvent and increases slightly with increasing grafting density for constant solvent composition.

One of the earliest studies of the RPLC problem using molecular dynamic simu-lations [87] highlighted that the methanol concentration is enhanced and water is

84534.indb 20 11/5/09 12:24:28 PM


depleted in the vicinity of a single isolated decane chain. More recently, similar behavior was observed for an isolated n-octadecane chain solvated in methanol– water [30] and in acetonitrile–water mixtures [31] using Monte Carlo simulation. This behavior can be explained by water having to alter its structure near the hydrophobic chain, resulting in strained or lost hydrogen bonds. The same thermodynamic forces contribute to the partial dewetting mentioned above.

Concomitant with the depletion of water near the interface with the hydrophobic bonded phase, we observe an enhancement of the organic modifier density near the interface. In particular, for the solvent mixtures for which the organic modifier is the minority component (33% methanol and 33% acetonitrile), the density of the organic modifier increases as the interface is approached from the solvent region and shows a maximum at the outer edge of the interfacial region. A more dramatic measure of the preferential ODS chain solvation by the organic modifier is the local molfraction enhancement depicted in Figure 1.7, as defined in Section 1.4.3.3. About 6 Å above the location of the GDS, the solvent composition starts to deviate from the bulk solvent composition, and enhancements by factors of 2 and 3 are observed at zGDS and in the central region of the ODS bonded phase for solvent mixtures with 33% organic modifier. The enhancement is still present but much smaller in magnitude for 67% methanol.

1.3.5 partition or adSorption?

One of the outstanding questions about RPLC is whether solutes partition or adsorb. As discussed above, adsorption in RPLC refers to a solute being located in the inter-facial region (with a potential secondary adsorption mode near substrates with resid-ual silanols), and partition refers more to a liquid–liquid-like transfer process where the solute is found mostly in the central region of the bonded phase. The problem here is that neither spectroscopic probes nor simple retention measurements can pro-vide detailed information regarding the spatial distribution of the solute. However,

z (Å) z (Å)

0

1

2

3

4x lo

cal/x

bulk

ODS-2.9/33MODS-2.9/67MODS-2.9/33A

0 12 24 0 12 24 36


fIgure 1.7 The organic modifier molfraction enhancement. Left panel: The location of the Gibbs dividing surface is indicated by the vertical lines (with same line styles as for the enhancement).

84534.indb 21 11/5/09 12:24:29 PM


simulation can provide a detailed view of this distribution by statistical analysis of the trajectory files. Given that an RPLC system is inherently microheterogeneous, the solute distribution is neither constant along the surface normal (as one should expect from the chain and solvent density profiles) nor is it constant within a given plane parallel to the substrate because of the specific grafting location of the chains and the resulting in-plane distribution of residual silanols. In this review, we limit the discussion to the distribution coefficient profiles along the surface normal, K(z), but note that the in-plane distribution is also of interest and has been previously dis-cussed as function of ODS grafting densities [72].

The K(z) profiles for n-butane and 1-propanol for the various ODS systems are shown in Figure 1.8, while this quantity is defined in Section 1.4.3.4. (Please note the different independent variable scales for the different panels.) With the exception of the ODS chains at low grafting density, the K(z) profile for n-butane shows two peaks for all ODS systems. One of these peaks is located about 2 Å below the GDS and the other peak is located at z ≈ 7 Å, i.e., deep in the interior of the ODS chains but above the dimethyl side chains and the region where water and methanol solvent are bound to residual silanols. The fact that this profile shows a strong z-dependence instead of being uniform for the entire bonded-phase region demonstrates that the retention mechanism for n-butane, a small prototypical nonpolar molecule, is significantly more complex than one would infer from the good agreement of the transfer thermody-namics for a methylene group to either the ODS phase or a bulk liquid n-hexadecane phase (see Figure 1.3). The peak at z ≈ 7 Å may be classified as partition-like, but additional analysis shows that both the solute and the chain backbone possess a pref-erence for alignment along the surface normal [17], i.e., it has some similarity to par-titioning into a liquid crystalline phase compared to an isotropic liquid phase.

The peak near the lower bound of the interfacial region may be classified as adsorption, but it does not necessarily represent the solute lying on top of the chain region because the latter region extends well beyond the GDS for all cases. A likely explanation for this adsorptive peak is the depletion in the overall density near the interface that leads to a reduction in the entropic cost of cavity formation. Hence, the retention mechanism for n-butane has two modes of interaction: partition and adsorption for all the systems with at least intermediate ODS grafting density. Only the adsorptive mode remains at the lowest grafting density.

It should also be noted that the K(z) profile for 33% acetonitrile falls in between the profiles for 33% and 67% methanol, a reflection of the lower polarity of ace-tonitrile that makes it a better solvent for n-butane. It should be noted that this obser-vation is not in conflict with the good agreement of the transfer free energies from a reference gas phase to the solvent saturated ODS phases (see Figure 1.3) because the K(z) profiles reflect the mobile-to-retentive part of the thermodynamic cycle, shown in Figure 1.1.

The K(z) profiles for 1-propanol show that this polar molecule resides primarily in the interfacial region, i.e., an adsorptive mode of retention. Orientational analysis for the alcohol solute in the interfacial region indicates relatively strong alignment with the surface normal and the hydroxyl group pointing towards the solvent phase [17]. For most systems, there is also a minor peak near z ≈ 5 Å where the 1- propanol

84534.indb 22 11/5/09 12:24:29 PM


0

800

1600

2400

0

40

80

120

0

5

10

15

0

1

2

3

0

30

60

0

2

4

0

12

24

0

1

2

0

4

8

K (z

)

0

1

2

0

15

30

0

2

4

K (z

)

z (Å)

0

10

20

0

1

2

0 12 24 36 0 12 24 36z (Å)

0

6

12

0

1

2

ODS-2.9/WAT

ODS-2.9/33M

ODS-2.9/67M

ODS-2.9/33A

Amide-2.9/33M

Ether-2.9/33M

ODS-4.2/50M

ODS-1.6/50M

fIgure 1.8 (See color insert following page 248.) The distribution coefficient profiles for n-butane (blue) and 1-propanol (red). The eight panels depict ensemble averages for the same eight systems shown in Figure 1.4. The interfacial region (all panels) is shaded in gray while the Gibbs dividing surface is shown by the dashed orange vertical lines. The blue axis labels correspond to n-butane and the red to 1-propanol.

84534.indb 23 11/5/09 12:24:30 PM


molecules form hydrogen bonds to solvent molecules bound to residual silanol groups [17]. As the methanol concentration is increased or the ODS grafting density is decreased, the 1-propanol solutes are found in more diffuse regions across the available space because of the greater extent of solvent penetration (see Figure 1.5). Because the hydroxyl group prefers to reside in the solvent phase and the alkyl tail prefers the ODS phase, the retention of 1-propanol is quite weak, with the distribu-tion coefficients being less than 5 with the exception of the ODS phase in contact with neat water.

We can also examine the incremental free energy of transfer for methylene and hydroxyl groups as a function of z as an indicator of where the most favor-able interactions occur. This is shown in Figure 1.9 and defined in Section 1.4.3.4. These profiles not only indicate that the most favorable interactions for methylene groups, i.e., lipophilic interactions, take place within the interior of the bonded phase near z ≈ 8 Å, but that the solvent effects, while affecting the magnitude of the transfer free energies, do not change the shape of these spatial profiles. For the hydroxyl groups, these incremental free energy profiles demonstrate that locations near the substrate (where direct binding to residual silanols or to water and methanol molecules can occur) are about as favorable as solvation in the bulk solvent phase. This is in contrast to the interior region of the bonded ODS phase, which is deeply unfavorable with a free energy barrier close to +15 kJ/mol at z ≈ 8 Å. This is the same location that is most favorable for the methylene group

–4

–2

0

2∆G

CH

2 (kJ/

mol

)

ODS-2.9/WATODS-2.9/33MODS-2.9/67MODS-2.9/33A


z (Å) z (Å)

–10

0

10

∆GO

H (k

J/m

ol)

0 12 24 0 12 24 36

fIgure 1.9 Incremental free energies of transfer for methylene (top panels) and hydroxyl groups (bottom panels) as a function of z.

84534.indb 24 11/5/09 12:24:31 PM


for the ODS phases at intermediate and high grafting densities. This free energy barrier is somewhat lower for the solvent phase with high methanol content and for the low grafting density, because of the reduced solvent strength for hydroxyl groups in the former case and because of the enhanced solvent penetration in the latter case.

Our results suggest that a local solubility model could explain the location where the solutes are found. However, the transfer free energies are dependent on solvent penetration which in turn depends on solvent composition and grafting density, and it would be very challenging for a local solubility model to account for these effects and also the solute structure. Hence, the simulations provide a detailed picture that, currently, cannot be obtained through theory or experiment.

1.3.6 effectS of embedded polar groupS

We discussed in the previous sections that the traditional ODS phase presents a hydrophobic surface to the solvent that leads to partial dewetting in the interfacial region. To increase wetting and reduce peak tailing, a number of stationary phases have become popular with chromatographers which incorporate EPGs into the bonded chains [40–43,88,89]. These polar moieties include ethers, amides, carbam-ates, and carbamides, amongst others. We have investigated phases with embedded ether and amide groups, but with the same backbone length as the ODS chains, i.e., substituting an amide group for carbons at the 4 and 5 positions above the silicon atom and a di-ether functionality in position 4 and 7 of the C18 chain [70]. It should be noted here that both the amide and the ether phase provide four hydrogen-bonding sites per chain (three acceptor and one donor for the amide, and four acceptor for the di-ether).

The snapshots and the density profiles (see Figures 1.4 and 1.5) show significantly enhanced solvent penetration for the amide and ether phases compared to the ODS phase in contact with a 33% methanol solvent phase. In particular, the methanol con-centration near the amide group is very much enhanced compared to the ODS phase, whereas the ether groups lead to a larger enhancement for the water density. The latter is also reflected in the local mole fraction enhancement profile (see Figure 1.7) that shows a very small enhancement in the region near the ether functionalities, but larger enhancements near the chain anchor point and the interface. The solvent pen-etration leads to some swelling of the EPG bonded phases as reflected in the outward shifts of the average position of the terminal methyl group and the location of the GDS. In addition, the interfacial thickness is increased for the EPG phases compared to the ODS phase. An analysis of the structural aspects of EPG phases in contact with other solvent compositions can be found in [70].

One of the most advantageous properties of EPG phases is that these are known to reduce the tailing of basic compounds when the silanol groups are not end-capped. Based on the free energy profile of the hydroxyl group, shown in Figure 1.9, we have suggested that the presence of the EPG groups and the solvent molecules near them allow for more favorable interactions with the solute’s polar groups via hydrogen bonding and dipole-dipole interactions. Thereby, the free energy barrier for the transfer of a polar group to the silanols is lowered and the presence of EPGs

84534.indb 25 11/5/09 12:24:31 PM


acts like a bridge to enhance the transport to and from the silanols and, hence, reduce tailing [70]. There is currently little molecular-level information on the mechanism of tailing for basic compounds interacting with silanols. Modeling the solute-silanol interactions for basic compounds is extremely challenging because of the potential for charge transfer or even proton transfer. Thus, we did not attempt to simulate basic solutes and this hypothesis is indirect.

It is known that solute retention is affected by EPG phases [40–43,88,89]. Again, K(z) profiles can be employed to analyze the retention mechanism of nonpolar and polar analytes (see Figure 1.8). For n-butane, the K(z) profiles for the two EPG phases retain the bimodal distribution also observed for the ODS, but the peak heights are reduced by factors of ≈ 3 and ≈ 6 for the amide and ether phases, respectively, due to greater solvent penetration compared to the ODS phase with the same grafting density in contact with 33% methanol. This difference between the two EPG phases for nonpolar solutes is likely due to the ether phase having greater affinity for water and the amide phase having greater affinity for methanol, coupled with the greater affinity of the butane solute for methanol [70].

For the 1-propanol solute, the main peak in the K(z) profile is still found near the GDS, but the presence of the EPGs leads to a second peak at z ≈ 9 Å, i.e., close to the location of the polar groups. In particular, for the amide phase this region is nearly as favorable for 1-propanol as the interfacial region. In contrast to the ODS phase, the peak near the silanol groups is greatly reduced for both EPG phases. Thus, to some extent the EPGs change the retention mechanism for 1-propanol from purely adsorp-tive for the ODS phases to a combined adsorption/partition for the EPG phases.

1.3.7 determination of the phaSe volumeS

From the molecular-level information that we have discussed in the previous sections it should be apparent that measurement of the solvent (i.e., mobile) phase and reten-tive phase volumes would be extremely difficult because of the roughness of the interface and the potential for solvent penetration. Knowledge of the phase volumes would be desirable, so that studies of retained compounds could be easily expressed as a transfer free energy, as shown in Equations 1.5 and 1.6, from measurement of the retention factor, k′. Since the extent of solvent penetration (for a given grafting den-sity and chemical nature of the bonded chains) depends on the solvent composition, the phase ratio is also affected by changes in the solvent composition. Hence, adsorp-tion measurements on dry columns or combustion measurements of the carbon mass may not reflect the volume of the retentive phase under chromatographic conditions. These and other difficulties have been discussed in the literature [90].

The situation is further complicated by the fact that both polar and nonpolar analytes can be found in the interfacial region and such an adsorptive mode may depend more on the interfacial area than the volume of the retentive phase. Most importantly, the simulations clearly indicate that K is not constant within the retentive phase, whereas Equation 1.6 does not account for any molecular-level heterogeneity of the retentive phase. For our simulations it is possible to obtain a GDS for the sol-vent density (see Section 1.4.3.3), thereby offering a thermodynamic definition of the volume of the mobile phase. However, it should be noted that this definition results

84534.indb 26 11/5/09 12:24:31 PM


in a fraction of the solvent molecules (e.g., those binding to residual silanols) being counted as part of the retentive phase. For systems with significant solvent penetration (e.g., ODS at low grafting density or the two EPG phases), the solvent density does not decay smoothly when entering the stationary phase so there is some ambiguity in the location of the GDS. Another option open to the simulation would be to count the average number of solvent molecules in the RPLC system and use the molar vol-umes of a bulk solvent phase of the same composition to determine the volume of the mobile phase, but this approach assumes that the solubility of the solvent in the reten-tive phase is zero; an assumption that is clearly incorrect due to solvent penetration.

To some extent, one may also be able to experimentally determine the thermody-namic or the absolute volume of the mobile phase, as given by the GDS or the total amount of solvent. However, neither approach would lead to a K(z) profile. Thus, the use of incremental transfer free energies may be most advantageous for thermody-namics measurements because the phase ratio (or the volume to interfacial area ratio) will simply cancel when comparing two analytes.

1.3.8 preSSure and pore Curvature effectS

There are other effects which have been modeled by our group, which we mention in passing as they are also part of the RPLC mechanism story. Simulations can also be used to elucidate the effects of pressure. A preliminary account of our simulations to investigate pressure and pore curvature effects [74] has recently been given. Although these effects have been studied by experimental means, they are difficult to probe because they are not large effects for typical RPLC conditions. For example, the pres-sure effect not only exists as a physicochemical effect within the retentive chains, but also manifests itself on column hardware, packing material, solvent compressibility, and most importantly pore wetting. Isolating one effect from another is most diffi-cult. The simulations indicate that pressure has only a minor effect on the structural and thermodynamic properties of the retentive phase (as long as the pore is wetted over the entire pressure range) [74].

Precisely controlling the surface curvature of silica-based packings (i.e., a silica matrix with a very narrow distribution of pore diameters) is nearly impossible by synthetic means and determining the distribution of pore curvatures from adsorption experiments involves severe approximations. This is where simulation may be consid-ered the only mode of investigation rather than as a last resort, because the simulation, of course, allows for exact control of the pore curvature and shape. Simulations for an RPLC system consisting of ODS chains grafted on the surface of a cylindrical pore with a diameter of 70 Å indicate significant changes compared to the slit pores discussed here because the curvature leads to more accessible residual silanols, enhanced steric hindrance of the upper part of the ODS chains, and different wetting properties [74].

1.3.9 General obServationS for the bonded-phaSe–solvent–solute environment

Under typical chromatographic conditions, the bonded-chain structures are disor-dered with a significant fraction of gauche defects and weak orientational preferences

84534.indb 27 11/5/09 12:24:31 PM


of the backbone that change from preferentially perpendicular to the substrate for the lower part of the chains to random near the terminal group (and a slight preference for parallel orientations for the backbone from carbon 8 to 12 for ODS chains at low to intermediate grafting densities). That is, under none of the chromatographic con-ditions discussed in this study would it be appropriate to classify the chains as either being in a fully extended all-trans conformation or being in a collapsed state.

In all cases, some water and methanol solvent molecules are found to form hydro-gen bonds with residual silanols. The extent of solvent penetration increases with increasing concentration of the organic modifier, decreasing grafting density, and in the presence of EPGs. The solvent composition changes gradually as one approaches the retentive phase with an increase of the molfraction of the organic modifier starting already well before the GDS is reached. This mole fraction enhancement peaks in the center of the bonded-phase region for ODS chains, but its smaller size and the steric hindrance of the dimethyl side chains allows water to be enriched near the silanols.

The distribution coefficients for polar and nonpolar solutes are not uniform in the retentive phase. Alkane solutes exhibit a bimodal K(z) profile indicating contributions from partition and adsorption toward retention. Alcohol solutes show a strong prefer-ence for adsorption and the bonded-chain–solvent interface where they can form hydro-gen bonds with solvent molecules and embed their tail segments in the bonded chains.

The driving forces for the retention of alkane solutes are lipophilic interactions which are present both in the central part of the bonded-chain region and near the interface (where a reduction of the cavity entropy compensates for a partial loss of solute-chain interactions). The incremental transfer free energy of a methylene group from a reference gas phase to the solvent is favorable (solvophilic) for solvent com-positions typically used in RPLC, but the solvophilic free energy is much smaller in magnitude than the lipophilic free energy. The incremental transfer free energy of the hydroxyl group is favorable for both the ODS and the solvent phase, but the latter is larger in magnitude and, hence, a hydroxyl group decreases retention. An increase in the organic modifier concentration reduces the magnitude of both the favorable interactions with the solvent and the ODS phase for the hydroxyl group.

1.4 sImulatIon methodology

1.4.1 Simulation and the theory of liquidS

One of the most challenging areas of physical chemistry has been a quantitatively accurate theory of liquids. This is because of their disordered structure and the significant strength of the intermolecular interactions. The situation is further com-plicated when (micro-) heterogeneity is introduced in the form of a multicomponent mixture or the presence of interfaces, or when the interactions are anisotropic (e.g., dipole–dipole interactions). Analytical theories of complex liquids require signifi-cant approximations for solving the statistical mechanical phase space integrals. Particle-based simulations can overcome these mathematical difficulties and, in the limit of infinite computer time, will provide the exact solution for a given statistical mechanical problem. However, since computer time is always finite, one needs to employ sampling algorithms that can locate the more important states of the system,

84534.indb 28 11/5/09 12:24:32 PM


i.e., those that have a low energy and, hence, contribute significantly to the system’s average properties. These sampling schemes have become ever-more sophisticated [21,22] and allow many new properties of liquids, including mixtures and interfacial systems, to be determined with excellent precision. Nevertheless, large amounts of computer time, memory and storage are needed for simulations of complex systems. The cost of molecular simulations has decreased dramatically over the past 20 years because of the development of more efficient sampling algorithms, but also due to increases in computer speed. Molecular simulation has increased the understanding of the chemistry and physics of the liquid state in invaluable ways. We feel that the same is true for the understanding of RPLC and liquid chromatography in general, as these are just special cases of the physical chemistry of liquids.

In addition to overcoming the sampling problem that allows the computation of precise ensemble averages, the other main challenge for the simulation of real chemical systems is the development of force fields that describe the interactions in the model systems and, hence, control the accuracy of the simulations. These force fields allow particles to interact via nonbonded electrostatic and dispersion (i.e., van der Waals) forces and bonded stretching, bending, and dihedral terms at the level of individual atoms or small groups of atoms (e.g., a methylene group).

1.4.2 previouS molecular simulationS of reverSed-phaSe liquid chromatoGraphy (rplc) syStemS

The use of molecular simulations for the RPLC problem goes back about 15 years. Many studies [87,91–107] have used the molecular dynamics (MD) simulation tech-nique [18,23] where the classical equations of motion are solved via finite-difference methods with a time increment of about one femtosecond and total simulation lengths rarely exceeding a few nanoseconds in these studies. With very few exceptions, these MD simulations focused on structural properties of the RPLC system described at varying levels of sophistication. Many of these studies do not include the solvent [92–96,102,103] which greatly hampers their fidelity of describing the RPLC sys-tem. Some of the early and most of the more recent MD simulations have utilized explicit solvent [87,91,97–101,104,107] and provided some structural (and less often dynamical) information for the solvated bonded phase. Unfortunately, some of these simulations yielded rather conflicting data and some showed a dependence on the initial configuration used for the simulations. This highlights one of the difficulties in the utilization of the MD technique: the total amount of physical time that can be simulated is limited and is generally, under the best of conditions, less than fractions of a microsecond. Hence, with MD there is a good chance that the final structure(s) may have been determined by the initial starting chain conformation.

In only two of these cases [91,97] were attempts made to compute the free energy profile for the transfer of a solute (methane in both cases) from the mobile phase to the retentive phase. Although these studies provided some indication of the com-plexity of the transfer free energy profile, the choice of methane as solute and some of the other simulation parameters prevented a direct comparison to experimental retention data. Very recently, an MD simulation was used to explore the location and orientation of an acridine orange solute [107], a probe molecule that has also been

84534.indb 29 11/5/09 12:24:32 PM


used in spectroscopic studies of chain orientation [108–112]. However, in this MD simulation the solute only transfers once from the mobile phase to the bonded phase and, thereafter, remains stuck for the remainder of the few-nanosecond trajectory. Being stuck would correspond to a retention time of infinity, clearly not a valuable comparison to experimental retention data. A very interesting recent MD study is an exploration of the chiral recognition in the Whelk-O1 stationary phase, where sepa-ration factors are estimated from multiple trajectories and calculations of the binding (not free) energy [105,106].

In chromatography, we discuss retention measurements as being very near or at equilibrium [28,29]; the zone broadening that takes place is a so-called nonequilib-rium process [28,29]. This is one of the reasons we did not pursue the MD technique after 1994; the interesting part of the simulation needed to connect directly to the retention experiment is the phase equilibrium problem, not the chain dynamics. It is essential when doing mechanism studies by simulation that one has access to equi-librium data where possible. For RPLC, comparison of incremental free energies to test simulation against experiment is a good bridge between the two paradigms. We note that a host of experimental studies measuring incremental free energies are available [52,54,78,113].

For the past twenty years, the computational chemical engineering community has very strongly favored the Monte Carlo approach for the computation of phase equi-libria because the stochastic Monte Carlo procedure can: (1) overcome the time-scale problem through smart moves that sample events occurring over long timescales in a single step, and (2) exploit open ensembles where the particle numbers are allowed to fluctuate and the chemical potential (molar free energy) can either be specified or the transfer free energies be computed from ensemble averaged number densities. In those regards, the Monte Carlo method is clearly the method of choice for research-ing the RPLC problem. Furthermore, the high precision of Monte Carlo simulations for phase equilibria has allowed the development of a new class of transferable force fields that are parameterized and validated against phase equilibrium data over a wide range of state points (temperatures, pressures, and often also compositions of multi-component systems). A detailed description of the advanced Monte Carlo methods and transferable force fields employed by us is provided in subsequent sections.

Our philosophy leans heavily on the argument that RPLC is a separation technique and, hence, the most valuable comparison to RPLC experiments and route to valida-tion of the simulation approach must be a comparison to retention data. Spectroscopic data lends itself only to indirect comparison because the direct computation of infra-red, Raman, or NMR spectra for complex RPLC systems (that cannot be described by a single static configuration) is well beyond the reach of current simulation techniques. Nevertheless, this is not to suggest that simulations which agree with experimental retention data have to be correct, but that simulations without such agreement have very limited value for describing the retention mechanism.

In closing this section, we also want to briefly address whether quantum mechani-cal methods can be applied to investigate the RPLC retention mechanism. The tradi-tional quantum mechanical approach [114] is a static one where the binding energy for the solute is computed from the difference between a system consisting of solute and host and a system consisting solely of the host molecule(s). In many cases, the

84534.indb 30 11/5/09 12:24:32 PM


structural optimization is first performed for individual molecules and these molecules are treated as rigid for the computation of the binding energy. In some cases, medium effects are included via continuum solvation models and the binding free energy is estimated using the harmonic approximation [114]. However, as should be clear from the preceding discussion, these static quantum mechanical methods are not appropri-ate for describing retention in RPLC because of the inherent disorder and microhetero-geneity that cannot be captured in one static calculation. The alternative is to carry out first principles simulations that usually employ Kohn–Sham density functional theory to represent the interacting system. Applications of first principles simulations suffer from the high expense of the energy/force calculation that limits the system size to a few hundred atoms and very short simulation length (typically less than 50 picosec-onds) [115], and a lack of accuracy for non-bonded interactions that does not yet permit the satisfactory prediction of fluid phase equilibrium problems [116,117]. Hence, first principles simulations have not yet been applied to RPLC systems.

1.4.2.1 transferable potentials for phase equilibria force fieldJust as with experimental measurements, there are two principal challenges that must be overcome in a simulation. The first is to attain results that are precise and the second is to attain results that are accurate. In a simulation, precision depends solely on the efficient sampling of the important configurations of the system (the relevant regions of phase space) and accuracy depends solely on the model used to describe inter- and intramolecular interactions. In this section we describe how this accuracy is accomplished. The following sections on Monte Carlo simulation methods will show how efficient sampling of phase space is achieved.

The interactions between most molecules in our model chromatographic system are described by the united-atom version of the transferable potentials for phase equilibria (TraPPE-UA) force field [118–125].*

The united-atom term is used to denote that all CHx segments are represented as one interaction site rather than, for example, using four interaction sites to describe a methyl (CH3) group. This drastically reduces the time spent computing molecular interactions and sacrifices little in the way of accuracy. All atoms in other types of functional groups (for example, OH, NHx, and C = O) are accounted for explicitly.

There are two components to the TraPPE force field, an intermolecular (nonbonded) and an intramolecular (bonded) part. The nonbonded interactions are described by a combination of Lennard-Jones and Coulombic potentials. The for-mer describes repulsive (overlap) and dispersive, or van der Waals interactions, and the latter describes first-order electrostatic interactions between sites bearing partial charges. The general intermolecular potential energy function is as follows:

Ur r

i

N

j i

N

ijij

ij

ij

ij

( )rN = −=

−

= +∑ ∑

1

1

112 6

4εσ σ

+

q q

ri j

o ij4πε (1.10)

* The exceptions are that the TIP4P model [126] is used for water and the silica substrate is described by a zeolite potential [127–129].

84534.indb 31 11/5/09 12:24:32 PM


where rN is the set of coordinates for all interaction sites in the system, N is the number of interactions sites, rij is the distance between sites i and j, and ε0 is the per-mittivity of free space. The remaining variables are related to parameters fit to each type of interaction site. In the Lennard-Jones portion of the potential, each interaction site is described by a well-depth, εi, and diameter σi. For interactions between two sites i and j, the Lorentz–Berthelot combining rules are applied ε ε εij i j= and σij = (σi + σj)/2. In our RPLC simulations, the Lennard-Jones interactions are trun-cated at 10 Å. For the Coulombic portion of the potential, each interaction site is describe by a partial charge qi and the Ewald summation technique [21] is applied with a direct space cutoff of 10 Å and a convergence parameter of κ = 0.28.

The functional form for the intramolecular portion of the potential is

U r uk

( ) ( ) ( )N

= + −∑ ∑dihedrals

tor

angles

eqφ θ θθ

22 (1.11)

where the first sum runs over all possible dihedral (torsional) angles φ and the second over all possible bond angles θ, with force constants kθ and equilibrium angles θeq. The torsional potential utor varies, but is usually in the form of a cosine series. In the TraPPE force field, bond lengths are held fixed at their equilibrium values. These bond lengths, and torsional and bond-bending potentials, are usually fit to poten-tial energy surfaces generated using high-level quantum mechanical calculations. In addition, sites separated by four or more bonds in a molecule interact via the non-bonded potential described above. A diagram depicting this intramolecular potential is shown in Figure 1.10.

The parameters in the nonbonded portion of the potential (ε, σ, and q) are fit in order to reproduce experimental vapor-liquid coexistence curves (VLCCs, a plot of temperature versus the vapor and liquid phase densities) for single component systems. We choose to fit to this data as it (1) covers a wide range of temperatures and pressures, (2) is extremely sensitive to small differences in the parameters, and (3) allows us to simulate processes that involve phase equilibria.

To fit the force field parameters for different molecules a building-up strategy is employed, as shown in Figure 1.11. This process ensures that parameters from functional groups in one molecule are transferable to another and that very few new parameters need to be fit when new molecules with different functional groups need

1

2

3

4

5

Fixedbond

length

Harmonicbond

bending

Cosineseries

torsion

Nonbondedinteraction

θ

fIgure 1.10 Diagram of the TraPPE intramolecular potential.

84534.indb 32 11/5/09 12:24:34 PM


to be described. We will demonstrate this process for n-alkanes and n-alkanols. First we start with ethane, which is modeled as two CH3 groups. Since ethane is a nonpolar molecule, there are no partial charges and only two parameters need to be fit, σCH3

and εCH3

. Vapor–liquid equilibrium (VLE) simulations of the molecule, which will be described in a following subsection, with multiple parameter sets, allows one to find the best parameter set that reproduces the experimental data. Next we move on to larger linear alkanes, for example, butane. The parameters for the methyl group, σCH3

and εCH3, can be transferred from ethane and now only two new parameters

need to be fit for the methylene group, σCH2 and εCH2

, and again VLE simulations are employed for this purpose.

At this point we have a parameter set that can describe any linear alkane. However, we are interested in more than just alkanes, so we extend this technique to include different functional groups. To describe methanol, we take the σCH3

and εCH3 param-

eters from ethane. Now we need to fit σ0 and ε0 for the oxygen (no σ and ε are needed for hydrogen due to its small size) and optimize a set of partial charges since metha-nol is a polar molecule. These partial charges are located on the methyl, oxygen, and hydrogen sites. We will denote them as q1, q2, and q3, respectively. After these param-eters are optimized to fit the VLE data, any linear alkanol can be described. For example, to describe propanol, we would take the needed Lennard-Jones parameters from butane and methanol and the three partial charges from methanol (see Figure 1.11). At this point it is easy to envision the extension of this technique to additional functional groups. This extension has already been made and the TraPPE-UA force field is capable of describing the vast majority of functional groups important for organic molecules [118–125].

To demonstrate the robustness of this fitting process two plots are shown in Figure 1.12. The first shows the VLE curves for a series of alcohols in comparison to experiment, and the agreement is excellent. In this plot, the only molecule to which parameters were fit is methanol. The parameters for the other alcohols were trans-ferred from methanol and the alkanes as described above. In addition, the second

CH3 CH3

CH3 CH2

CH3

CH3

CH2

H

O

q3

q2q1

CH2

H

O

q3

q2q1

CH3 CH2

fIgure 1.11 Diagram of the TraPPE parameterization philosophy.

84534.indb 33 11/5/09 12:24:37 PM


plot in this figure shows the force field is capable of reproducing the experimentally observed x-ray scattering intensities for the liquid phase of these alcohols. At no point was any structural data used in the fitting process, therefore this is a great testa-ment to the transferability of the force field.

In addition to single component property prediction, the TraPPE force field has been successfully applied to numerous multicomponent systems. As described in this chapter, it can accurately predict free energies of retention (retention times) in RPLC and has done the same for previous work with gas chromatography [63,130–135]. Additionally and among other things, it has been applied to accu-rately predict solute partitioning in a variety of other systems [32,77,136,137], phase diagrams in binary and ternary systems [138–141], viscosities [142], Hildebrand solubility parameters [143], and phenomena involving nucleation and aggregation [138,144–146].

1.4.2.2 monte Carlo methods for molecular simulationIn a liquid system, a wide range of molecular states, or configurations, can be accessed. Each possible state in this system is characterized by a set of coordinates r and p that describe the position and momenta of every atom in the system. The entire

0.0 0.3 0.6 0.9ρ (g/mL)

200

300

400

500

600T

(K)

0

20

40

60

0 1 432q (1/Å)

I(q)

(e.u

.)

fIgure 1.12 Validation of the TraPPE parameterization philosophy. Left: vapor–liquid coexistence curves from experiment and simulation. The simulation data is shown as symbols with methanol depicted as triangles, ethanol as circles, 1-pentanol as squares, and 1-octanol as diamonds. Right: x-ray scattering intensities for the liquid phase (at 293 K and 1 atm). Simulation data is shown with symbols: methanol (triangles-up), ethanol (circles), 1-propanol (squares), 1-butanol (diamonds), and 1-octanol (triangles-down). In both plots the experimen-tal data is shown as lines. (Vahvaselka, R. S. K. S. and Torkkel, M., J. Appl. Cryst., 28, 189–195, 1995; Smith B. and Srivastava, R., Thermodynamic Data for Pure Compounds: Part B Halogenated Hydrocarbons and Alcohols, Elsevier, Amsterdam, 1986.)

84534.indb 34 11/5/09 12:24:38 PM


set of possible states is called phase space, while a given set of r and p is called a point in phase space. Under a set of macroscopic constraints, for example, constant temperature, pressure, and number of molecules (i.e., a canonical ensemble), the probability of the system visiting any one of these states j is

ρβ

jjE

Q=

−exp( ) (1.12)

where Ej is the energy of the system, β = 1/kT, k is Boltzmann’s constant, and T is tem-perature. In the denominator we have Q, the canonical ensemble partition function

Q Ej

j= −∑ exp( )β (1.13)

and the above sum runs over all possible states of the system. The average of any property of interest in the system can be expressed as [147]

⟨ ⟩ =−∑

AA E

Qj

j jexp( )β (1.14)

where Aj is the value of the property for state j.At this point we have some seemingly simple equations that allow us to compute

average properties for our system as long as one knows how to compute the energy (which we described in the previous section). However, in practice things are not that simple. Even for relatively small systems the number of terms in the summation in Equation 1.14 is enormous, i.e., of magnitude 10N where N is the number of molecules [147]. Clearly, even with today’s vast computational resources, we cannot visit all of these states and directly compute the average. We can, however, estimate the average in Equation 1.14. Most of the states in a system are of significantly high energy so that they contribute very little to the average (Ej is large, so exp(−β Ej) is small). Thus, if we can find a way to sample only those states which contribute significantly to the average, then the problem is truncated greatly. To accomplish this, we need some means of generating these higher probability configurations of our system, and this is where molecular simulation comes in.

Molecular simulations are carried out via two principle methods, molecular dynamics (MD) and Monte Carlo (MC). The former is a deterministic method with an explicit dependence on time while the latter is a stochastic method with no depen-dence on time. However, both methods depend on a well-defined way to describe the energy of the system, i.e., a potential energy function, and both methods generate configurations of the system based on their statistical mechanical probabilities as described above.

In an MD simulation one starts with the system in some initial state described by the position and momenta of all particles. Forces between the particles (the

84534.indb 35 11/5/09 12:24:39 PM


derivative of the potential energy) are computed in predetermined increments of time. With these forces and the current particle positions and momenta, the posi-tion and momenta of each particle at the next time increment can be computed via Newton’s equations of motion [21–23]. The process is repeated some number of times and, thus, the system evolves with time. The average properties for the system can then be computed by averaging the properties at each individual time step.

The application of the MC simulation method is most easily demonstrated in the canonical ensemble. For simplicity, we will show the process here for an atomic system (only translational degrees of freedom) but an analogous procedure can be demonstrated for molecular systems with rotational and conformational degrees of freedom. In an MC simulation, one starts with the system in some initial state described by the position of all of the particles. With these coordinates, the initial potential energy of the system, Eold, can be computed. Next, a trial move is attempted by randomly picking a particle in the system. This particle is then moved in a random direction by a distance between zero and an arbitrary maximum displacement. The new potential energy, Enew, of the system is then computed. If the energy of this sys-tem is lowered, the move is immediately accepted. Otherwise, the move is accepted with a probability of

P E Eaccept new old= − −exp[ ( )]β (1.15)

When a move is accepted, the new configuration is kept and its properties are counted toward the averages for the system. When a move is rejected, the old coor-dinates of the system are restored and the properties of this old configuration are counted again toward the averages of the system. It can be shown that this technique samples configurations with exact probability prescribed by Equation 1.12 above. The MC technique described above was originally described by Metropolis and coworkers in 1953 [148].

In the above examples, it appears that the MD method is much more intuitive (envision computing the position of the balls after a player shoots in a billiards game) while the MC method is much more abstract. However, there are distinct advantages to the MC method. First, the MC method has no dependence on time. Most modern MD simulations are limited to fractions of a microsecond at most. If a physical pro-cess requires more time than this, its simulation is out of the reach of the timescale accessible with MD. Second, MC methods allow for simulations to be carried out in open ensembles where the number of particles is allowed to fluctuate. This allows one to carefully control the chemical potentials of the species involved in the simu-lation. Third, MC simulations allow one to carry out unphysical moves that greatly enhance the sampling of phase space. These last two advantages will be expanded upon in the following sections.

1.4.2.3 gibbs ensemble methodThe previous section briefly explained how an MC simulation was carried out in the canonical ensemble. Here, we extend this technique to another ensemble (the one we use in the simulation of RPLC), namely the constant pressure-constant tempera-ture, or NpT, Gibbs ensemble [149]. In this ensemble multiple subsystems (simulation

84534.indb 36 11/5/09 12:24:39 PM


boxes) are in thermodynamic contact but share no direct physical interface. The temperature and pressure of each subsystem is held fixed and the total number of molecules is constant. However, the molecules may move between the subsystems and the volume of each subsystem is allowed to fluctuate.

In the NpT Gibbs ensemble, there are three principle types of moves, as shown in Figure 1.13. In describing these moves, we will again limit ourselves to the atomic system for simplicity. The extension to molecular systems will be made in the next section. The first type of move involves particle displacement. In this type of move the particle remains in the same subsystem. The move is carried out and accepted in the exact manner as particle displacement in the canonical ensemble described above. Thus, the probability of accepting the move Paccept can be expressed as

P Eaccept = , −min[ exp( )]1 β∆ (1.16)

i.e., the move is accepted if the energy is lowered and accepted with a probability of exp(−βΔE) if the energy goes up. These particle displacement moves ensure that the system reaches thermal equilibrium, i.e., that the system is at the specified temperature.

The second type of move involves a volume change for one of the subsystems. In this move, one of the subsystems is chosen at random and given some random volume change ΔV chosen uniformly from an interval with lower and upper bounds of equal magnitude. The energy is computed at the initial volume V and the new volume V′. The move is then accepted with the following probability

P E p V NVVaccept = , − + +

′

−min exp ln1 1β β∆ ∆

(1.17)

(1) Particle displacementin either subsystem

(2) Volumechangein either subsystem

(3) Particle exchangebetweensubsystem

fIgure 1.13 Diagram of the three principal move types in the NpT Gibbs ensemble.

84534.indb 37 11/5/09 12:24:41 PM


where p is the external pressure chosen for the simulation and N is the number of particles in that subsystem. These volume moves ensure that the system reaches mechanical equilibrium and is at the specified external pressure.

The third type of move involves particle transfer between the subsystems. In this move, one particle in the entire system is chosen at random. The particle is then moved from its current subsystem (A) to a random location in subsystem (B). Again, the energy change ΔE for the move is computed and it appears in the acceptance probability.

P EV N

V NA B

B Aaccept = , − + +

−min exp ln( )

111β β∆

(1.18)

Here, VA and VB are the volume of subsystem A and B, and NA and NB are the original number of particles of the type chosen in subsystems A and B. These particle exchange moves ensure that the chemical potential for each species in the simula-tion is the same in all subsystems. This is absolutely critical for simulating processes involving phase equilibria because when a species is distributed between two phases, it is only an equilibrium distribution when its chemical potential is the same in both phases.

1.4.2.4 Configurational-bias monte CarloIn the atomic system, simple translational moves are often sufficient to adequately sample the important regions of phase space. For molecular systems, we can envision a similar type of move. Suppose we have a system composed of C18 chains. To sample the conformational degrees of freedom in the chains, we could randomly choose a chain, then randomly choose a dihedral angle. This angle could be displaced by some random amount and the initial and final energies of the system could be computed. This energy change could then be used to decide if the move should be accepted or not, in exactly the same manner as a translational displacement. The problem with this strategy is that even for a small change of a dihedral angle in the center of the chain, there could be a large displacement of the chain ends. This large displacement would lead to a very high probability of overlap with a neighboring chain molecule, especially in a system with a typical liquid density. Thus, the vast majority of these types of moves would be rejected and very little phase space would be sampled. A similar problem arises when carrying particle transfer moves in the Gibbs ensemble. It is extremely unlikely to find a favorable position by simply inserting an entire molecule in a single step.

To overcome this problem, the configurational-bias Monte Carlo (CBMC) tech-nique was developed [150]. In the CBMC technique, the chain molecule is regrown one segment at a time, which greatly enhances the acceptance probability of a confor-mational change. There are various descriptions of the CBMC algorithm, but in our work simulating RPLC we follow the procedure given in reference [151], which we explain in the following paragraphs.

It is often useful, when using CBMC, to split the potential into bonded (uint) and nonbonded (uext) parts. The bonded part of the potential, which may include torsional, bending, and stretching potentials, is used to generate trial sites for the

84534.indb 38 11/5/09 12:24:42 PM


segments of the chain. The nonbonded potential is then used to bias the selection of a trial site from the rest of the trial sites. The separation of the potential into these two parts is completely arbitrary and may be adjusted to increase efficiency for specific applications.

Consider the regrowth of a whole chain of s segments (see Figure 1.14). For the first segment of the chain, k trial sites are placed at random positions in the simulation box and one of them, call it i, is selected with a probability

Pu

w ni ii

11

1

selectingext

( )exp( )

( )b = −β

(1.19)

where

w n uj

k

j1

1

1( ) exp( )= −=

∑ β ext (1.20)

and is termed the Rosenbluth weight of the first segment. Consecutive trial segments l of the chain are then grown until the chain is complete, by first generating k trial orientations bi according to the Boltzmann weight of the internal potential of the segment

P

uuli iligeneratingint

dd

( )exp( )exp(

b bb= −

∫ −ββ ll

int d) b (1.21)

fIgure 1.14 Diagram of a CBMC regrowth or insertion. In the each step, four random locations for the next segment are generated (circles with dashed lines). One of these sites is then selected according to its Boltzmann weight (shaded circles). Trial sites resulting in unfavorable interactions with neighboring molecules or intramolecular strain are unlikely to be selected.

84534.indb 39 11/5/09 12:24:44 PM


One of the k trials is then selected with a probability, like the first segment, according to the Boltzmann weight of its external potential

Pu

w nli ili

l

selectingext

( )exp( )

( )b = −β

(1.22)

where

w n ul

j

k

lj( ) exp( )ext= −=

∑1

β (1.23)

Once complete, the probability P(n) of growing the new chain may be computed from the products of the probabilities of generating and selecting each segment

P n P Pl

s

li li( ) selecting==

∏1

generating (1.24)

where the index l denotes the trial segment that was selected. Additionally, the Rosenbluth weight W(n) for the whole chain may be computed by

W n w nl

s

l( ) ( )==

∏1

(1.25)

In order to compute the acceptance probability for the newly grown chain, the Rosenbluth weight W(o) for the old configuration of the chain must also be com-puted. To do so, k−1 random positions for the first segment are generated, to compute the old Rosenbluth weight for the first segment

w o u uj

k

j k1

1

1

1 1( ) exp( ) exp( )ext ext= − + −=

−

∑ β β (1.26)

where exp( )−βu k1ext is the actual external potential for the first segment in the old

configuration. The probability that this segment would have been selected is then

Pu

w ok kk

11

1

selectingext

( )exp( )

( )b = −β

(1.27)

Similarly, k−1 trial orientations are generated for each of the subsequent segments by the probability given in Equation 1.21. The Rosenbluth weight for each of these segments is given by

w o u ul

j

k

lj lk( ) exp( ) exp( )ext ext= − + −=

−

∑1

1

β β (1.28)

84534.indb 40 11/5/09 12:24:46 PM


and, again, exp( )ext−βulk is the actual external potential for the lth segment in the old configuration. The probability that each of the kth segments would have been gener-ated and selected is, respectively

P

uulk klkgeneratingint

dd

( )exp( )exp(

b bb= −

∫ −ββ ll

int d) b

(1.29)

and

Pu

wlk klk

l

selectingext

( )exp( )

( )b = −β

0 (1.30)

and the overall probability P(o) of growing the old chain is

P o P Pl

s

lk lk( ) ==

∏1

selecting generating (1.31)

From the Rosenbluth weights of each of the old segments, the Rosenbluth weight for the old configuration may be computed by

W o w ol

s

l( ) ( )==

∏1

(1.32)

One can then express the ratio of probability densities of the new and old con-figurations in terms of the probabilities of growing the chains and their Rosenbluth weights

ρρ

new

old

= W nW o

P nP o

( )( )

( )( )

(1.33)

From this ratio it can be shown that, in order to satisfy the proper statistical mechanical probabilities, the move should be accepted with a probability of

PW nW oacc = ,

min( )( )

1 (1.34)

In a similar manner, CBMC moves may be applied not only to the regrowth of a molecule but also to the particle transfer between subsystems in the Gibbs ensemble. It should also be noted that we make use of the SAFE-CBMC algorithm [152] to regrow the interior portions of longer chains. However, we will not go into detail of its application here.

84534.indb 41 11/5/09 12:24:48 PM


1.4.2.5 application of the CbmC method in the gibbs ensemble to simulating reversed-phase liquid Chromatography (rplC)

Both MD and MC methods have been applied to a wide variety of simulation scenar-ios and each can have its own advantages for a given application. For the simulation of RPLC we have chosen the MC method, in particular the CBMC method applied in the Gibbs ensemble, for a variety of reasons. To fully explain these reasons we need to give more details on the simulation setup.

Our simulations make use of three separate simulation boxes, each in thermo-dynamic contact, but not sharing an explicit physical interface (see Figure 1.15). The first box contains the stationary phase of our model RPLC system in contact with the mobile phase solvent. This box is of fixed volume and is elongated in the z-direction with Lx = 20 Å, Ly = 26 Å, Lx = 90 Å. In the center is a five layer slab of the β-cristobalite polymorph of silica with its (1 1 1) surfaces exposed. The positions of the silica atoms are fixed with the exception of the surface silanol groups. On this surface, the dimethyl octadecyl siloxanes (or other ligands) are bonded onto the silica by randomly replacing some of the surface silanols, but avoiding chain overlap [17,68,69]. This process has been applied to bonding densities ranging from 1.6 to 4.2 μmol/m2 [71,72]. Note, the (1 1 1) surface was chosen because this surface, unlike other crystal and random faces, permits the bonding densities relevant to RPLC to be achieved [76] and the silanol density appears to be reasonable. The remainder of this box is filled with the solvent molecules of interest. To mimic the size of actual systems, all of our boxes are surrounded by periodic replicas of themselves in all directions, thus the box described in this paragraph corresponds to a slit pore.

Box 1Stationary phase in contact with solvent

Box 2Bulk solvent

Box 3Vapor phase

90 Å

~30 Å ~100 Å

fIgure 1.15 The three-box GEMC setup used for our simulations of RPLC.

84534.indb 42 11/5/09 12:24:50 PM


The second box in our simulation setup contains a solvent phase (acting as a solvent reservoir) and the third box contains an ideal gas vapor phase (acting as a thermodynamic reference state). The volume of these latter two boxes is allowed to fluctuate in response to the external pressure. In general, we use enough solvent molecules to fill the box containing the stationary phase and maintain a cubic solvent box with length of ≈ 30 Å. The vapor box contains 10 helium atoms and (on aver-age) ≈ 10 solvent and ≈ 6 solute molecules. This cubic vapor box averages ≈ 100 Å in length.

Since the solvent box is held at constant temperature and pressure, the solvent molecules contained in this box will have a chemical potential equal to that of a bulk solvent at the temperature and pressure specified for the simulation. During the simulation, solvent molecules are allowed to exchange between all three boxes. This type of move is unique to the Gibbs ensemble and ensures that the chemical potential of the solvent is the same in all three boxes. Therefore, the chemical poten-tial of the solvent in contact with the stationary phase is the same as that of a bulk solvent. This is exactly what occurs in a real RPLC system, but this feature has not been replicated in any MD simulations to date. When carrying out an MD simula-tion, the number of solvent molecules has to be chosen, somewhat arbitrarily, at the beginning of the simulation. There is no way to tell how the solvent will interact with the chains ahead of time. The solvent may penetrate into the chains and there may be enrichment/depletion of particular solvent components at the interface. With a single box of fixed size and number of particles, MD simulations have no control over the chemical potential of the solvent. However, in our Gibbs ensemble simula-tions, the system can respond to the interactions between the mobile and stationary phases. For example, if many solvent molecules penetrate into the stationary phase at the start of the simulation, more solvent molecules will leave the solvent reservoir to replace them. Not replacing these solvent molecules can lead to an overall solvent density that is too low and/or the appearance of voids in the solvent structure during MD simulations [100,101].

Another advantage of our simulation method also relates to these particle trans-fer moves, but in this case for the solutes being examined. Like the solvent, solute molecules in our simulations are also allowed to transfer between the three boxes. In the Gibbs ensemble one can directly compute partition coefficients and Gibbs free energies of transfer (free energies of retention) from the average number densities of the solute molecules in each box or given subregions of the box via the following equation [25,153]

Kα ββ

α

ρρ→ = (1.35)

∆G RT Kα β→ = − ln (1.36)

This direct method is analogous to what is actually measured in experiment and is inherently more precise than the umbrella sampling and thermodynamic integra-tion methods that must be used in MD. Perhaps this is why few have attempted to compute these quantities in an MD simulation of RPLC.

84534.indb 43 11/5/09 12:24:50 PM


In the context of particle transfers, the purpose of the vapor box in the simula-tion should also be discussed at this point. First, the vapor box acts as a thermo-dynamic reference state, so that we may decompose the retention process into stationary and mobile phase components (see Figure 1.1) and, second, it also serves to facilitate the particle exchange moves, particularly for hydrogen- bonding species. For example, when a molecule is removed from the solvent phase hydro-gen bonds may be broken. This contributes unfavorably to the acceptance rule in Equation 1.18. Then, if the molecule is transferred to the stationary phase, there is a chance that it will initially have an unfavorable interaction. On the other hand, if the molecule is transferred from the solvent phase to the vapor phase and then, sometime later in the simulation, transferred from the vapor phase to the station-ary phase, these two energetic penalties are separated. This greatly increases the chance of accepting the (net) MC move of bringing the solute from the mobile to the stationary phase.

In addition to allowing for the precise calculation of free energies of retention, these particle interchange moves greatly enhance spatial sampling of the solvent and solute molecules. For example, when a solute is transferred from the solvent box to the box containing the stationary phase, it can be inserted in one of many possible regions. During a simulation, solutes are moved in and out of the box literally tens of thousands of times. Therefore, they are able to visit (sample) the different regions of the box numerous times. Each time they visit a region it may have a different local arrangement and the solute will have a different probability of residing there. In an MD simulation, one must wait for the solute to diffuse to the different regions of the box, which is an inherently long process. Spatial sampling is very important for simulating RPLC. To determine the retention mechanism (for example, adsorption versus partition) one needs to know exactly where the solutes prefer to reside within the stationary phase with great precision.

The preceding paragraphs demonstrated the importance of the particle transfer moves for the precise sampling of the distribution of solvent and solute molecules in the RPLC system. Another important aspect of the simulation is that the structure of the stationary phase chains is adequately sampled. The CBMC moves applied to the bonded stationary phase chains are absolutely critical for this. We have demonstrated multiple times that structural properties of the chains are able to converge to the same values (within statistical uncertainties) regardless of the starting configuration of the system [68,69,71,72]. In one set of simulations, the chains are placed in an all-trans conformation directed away from the surface. The solvent is added to this system with solvent penetration into the chains. In another set of simulations the chains are pre-equilibrated in vacuum. The C18 chains in this case tend to interact with each other and form a somewhat compressed layer. The solvent is then added to this starting structure. Thereafter, the simulations are allowed to reach equilibrium with bulk mobile phase through various types of Monte Carlo moves. The excellent agreement of the simulation data for systems started with these contrasting initial configurations verifies that our simulation protocol is capable of yielding results that are independent of the starting structure after an initial equilibration period. This ability has not been demonstrated by workers carrying out MD simulations and could be the reason for some of the conflicting results. For example, MD simulations

84534.indb 44 11/5/09 12:24:50 PM


starting with the chains in the all-trans conformation suggest that the chains are ori-ented perpendicular to the substrate surface [87,91] while MD simulations starting the chains in collapsed states suggest that the chains have many gauche defects and large tilt angles [97,154].

A final point to be made, and one that was mentioned earlier, is that MD simulations have an explicit dependence on time. In RPLC, it has been shown that it can take tens of minutes to re-equilibrate a column after switching solvents [83,155]. This is a severe problem because, as stated earlier, the timescale accessible for an MD simulation is less than a microsecond at best. Thus, processes occurring in RPLC may be completely out of reach for an MD simulation. However, our MC simula-tions, which do not depend on time, will work even for processes occurring on long physical timescales.

1.4.3 analySiS and preSentation of data

The MC simulation of RPLC produces millions of configurations for each of the systems studied. Each of these configurations is generated according to their statisti-cal mechanical probabilities. At specified intervals during the simulation, the exact coordinates of each of the atoms in these configurations are written to a file. Once a simulation is complete, this file contains a highly detailed record of the system’s trajectory through phase space. One can then analyze this trajectory to compute vari-ous properties related to the structure of the system at the molecular level. In addi-tion, this molecular-level data can be translated into bulk thermodynamic properties which may be compared directly to those properties measured in experiment. In the following sections we describe the various properties used in this review to examine structure and retention in RPLC. The first three of these sections relate to chain conformation. The fourth section deals with system composition and the last with solute distribution.

1.4.3.1 gauche defect statisticsOne of the easier metrics to study experimentally (i.e., through Raman spectroscopy) is the fraction of gauche defects within the retentive phase chains. This metric can be computed unambiguously in a simulation. We define a gauche defect ( fgauche) as a dihedral angle deviating by more than 60° from the angle of the trans conformer. From the trajectory file described above, we can compute all of the dihedral angles for each chain and determine if gauche defects are present. The number of gauche defects can then be averaged for a particular location in the chains or for the chain as a whole.

1.4.3.2 order parameterA property which gives an indication of the chain alignment with respect to the silica surface is the order parameter S defined as

Si i= ⟨ − ⟩12

3 12cos θ (1.37)

where θi is the angle between the ith 1–3 backbone vector in the alkyl chain (between carbons separated by two bonds) and the normal to the silica substrate.

84534.indb 45 11/5/09 12:24:51 PM


The brackets indicate that an average through the entire simulation has been taken. This order parameter approaches unity for vectors preferentially aligned perpendicular to the surface, −0.5 for parallel vectors, and vanishes if there is no preferential orientation (or for a very narrow distribution around the magic angle). One can examine this order parameter as a function of position within the chain, i.e., S1 is for the first 1–3 vector in a C18 chain (between carbons 1 and 3) and S16 is for the last (between carbons 16 and 18), or one can average the order parameter over all 1–3 vectors in the chain. The experimental equivalent to this order parameter is the NMR order parameter for deuterated alkyl chains [156,157].

1.4.3.3 heterogeneity in system CompositionThe RPLC system is a very heterogeneous one. This means that the various com-ponents of the system are not distributed equally and one needs a way to quantify this. The main tool used in this respect is the (specific) density profile, p(z), which allows one to the describe the composition of the system relative to the silica sub-strate. These profiles are computed by dividing the simulation box into slices of width 0.45 Å along the z-coordinate. The number of solvent molecules and retentive phase CHx segments in each of these slices is then averaged over the course of the simulation. Thus, the magnitude of p(z) allows one to discern how much of a particu-lar component resides on average at a particular location.

To compare different systems, it is useful to define a boundary between the reten-tive and solvent phases. The density profiles described above allow us to locate a GDS, a plane that defines this boundary [84,158]. To fit the GDS we use the total solvent density and a hyperbolic tangent fitting method [159]. This fitting method also allows for a determination of the interfacial width, which reflects the 10–90% range of the total solvent density.

Another quantity related to the heterogeneity of the RPLC system that we report here is the molfraction enhancement profile for the organic component of the mobile phase, x(z)/xbulk. With the density profiles for water and the organic co-solvent, the molfraction of the organic component can be computed as a function of z

x zz

z z( )

( )

( ) ( )=

+ρ

ρ ρorganic

organic water

(1.38)

This quantity is then divided by the bulk molfraction (the molfraction in the sol-vent box). Thus, values of x(z)/xbulk larger than unity at a given value of z indicate an enrichment of the concentration of the organic component at that location, and values below unity indicate a depletion.

1.4.3.4 solute distribution Coefficients and transfer free energiesAs indicated in Section 1.4.2.5, partition coefficients and free energies of transfer can be computed directly from the number densities of a particular species in each phase (i.e., in each simulation box). This information can be further localized. The partition coefficient or free energy of transfer can be computed in the same way for

84534.indb 46 11/5/09 12:24:51 PM


a given sub-region of a simulation box. This allows us to compute the z-dependent partition coefficient profiles, K(z) and incremental free energy profiles, ΔG(z). The exact procedure for this is outlined below.

Just as is done for the solvent molecules, the density profiles for the solute molecules can be computed. Dividing this density profile by the density of the sol-ute in the bulk solvent box gives K(z), the partition coefficient for transfer of the sol-ute from the solvent phase to a specific z-location in the box containing the stationary phase. This partition coefficient profile can then be converted to a free energy profile by the standard relationship ΔG(z) = −RT ln K(z). The overall free energy of transfer for a given solute (the free energy of retention) can also be computed by using the GDS described above as a border between the two phases. The excess concentration of the solute in the interfacial region is also taken into account in this process.

In our simulations we use two sets of solutes. The first set is a homologous series of n-alkanes, from methane to butane. The second set is a series of 1-alkanols, from methanol to butanol. Once ΔG(z) is computed for each member in the homologous series of alkanes, the incremental free energy profile for the methylene group ΔGCH2

(z) can also be computed. For each value of z, the slope of a linear fit to the number of carbons versus free energy is computed. This slope then corresponds to ΔGCH2

(z). The incremental free energy profile for the hydroxyl group is computed by taking ΔG(z) for a 1-alkanol and subtracting ΔG(z) for an alkane with the same number of carbons.

1.5 refleCtIons

It has taken more than ten years to develop the capabilities necessary to simu-late RPLC systems with sufficient precision and quantitative accuracy to provide insights on the retention mechanism and to compare directly to experimental reten-tion measurements. This includes the development of accurate and transferable force fields and the combination of various advanced Monte Carlo algorithms to dramatically enhance sampling efficiency. Once the simulation approach is vali-dated against experimental retention measurements, structural information and atomic-level insight on the contributions to retention can be obtained in situ, i.e., for the same model system that is also used for the prediction of retention times. Thus, the virtual computer experiment provides a level of detail that is most difficult to achieve through spectroscopic and experimental chromatographic (i.e., retention times) investigation.

Many other simulations must be done to obtain a more complete picture of reten-tion in various RPLC systems. These include investigations of more complex retentive phases (e.g., polymeric phases) and more complex solutes (e.g., polycyclic aromatic hydrocarbons or drug molecules). A particular challenge will be the cases where the interactions involve partial charge transfer between the solute and parts of the reten-tive phase. While these future studies will certainly bring further understanding, we believe that molecular simulation of RPLC systems has now reached a state of matu-rity where microscopic-level information can be backed by agreement with experi-mental retention measurements.

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aCknowledgments

Financial support from the National Science Foundation (CHE-0213387 and CHE-0718383), The Dow Chemical Company, and Frieda Martha Kunze and Graduate School Dissertation Fellowships (J. L. R.) is gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute.

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135. L. Sun, C. D. Wick, J. I. Siepmann, M. R. Schure, Temperature dependence of hydrogen bonding: An investigation of the retention of primary and secondary alcohols in gas-liquid chromatography, J. Phys. Chem. 109(31) (2005) 15118–15125.

136. L. Zhang, J. I. Siepmann, Direct calculation of Henry’s law constants from Gibbs ensemble Monte Carlo simulations: Nitrogen, oxygen, carbon dioxide, and methane in ethanol, Theor. Chem. Acc. 115 (2006) 391–397.

137. K. E. Anderson, J. I. Siepmann, Solubility in supercritical carbon dioxide: Importance of the Poynting correction and entrainer effects, J. Phys. Chem. B 112 (2008) 11374–11380.

138. J. M. Stubbs, J. I. Siepmann, Binary phase behavior and aggregation of dilute methanol in supercritical carbon dioxide: A Monte Carlo simulation study, J. Chem. Phys 121 (2004) 1525–1534.

139. L. Zhang, J. I. Siepmann, Pressure dependence of the vapor-liquid-liquid phase behavior of ternary mixtures consisting of n-alkanes, n-perfluoroalkanes and carbon dioxide, J. Phys. Chem. B 109 (2005) 2911–2919.

140. N. Rai, J. L. Rafferty, A. Maiti, J. I. Siepmann, Prediction of the bubble point pressure for the binary mixture of ethanol and 1,1,1,2,3,3,3-heptafluoropropane from Gibbs ensemble Monte Carlo simulations using the TraPPE force field, Fluid Phase Equil. 260 (2007) 199–211.

141. J. J. Potoff, J. I. Siepmann, Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide and nitrogen, AIChE J. 47 (2001) 1676–1682.

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57

2 Thermodynamic Modeling of Chromatographic Separation

Jørgen M. Mollerup, Thomas Budde Hansen, Søren S. Frederiksen, and Arne Staby

Contents

2.1 Introduction .................................................................................................... 582.2 Thermodynamic Modeling of Chromatographic Separation ......................... 582.3 The Differential Material Balance.................................................................. 592.4 Adsorption Isotherms ..................................................................................... 61

2.4.1 Estimation of the Parameters .............................................................. 622.4.2 Estimation of the Partition Coefficients ............................................. 622.4.3 Ion-Exchange ...................................................................................... 63

2.4.3.1 β-Lactoglobulins A and B ...................................................642.4.3.2 Ion-Exchange in Mixed Solvents .........................................68

2.4.4 Hydrophobic Interactions.................................................................... 702.4.4.1 Reversed-Phase Chromatography ........................................ 722.4.4.2 Salt-Induced Hydrophobic Chromatography ....................... 732.4.4.3 Linking HIC and Solubility Data......................................... 74

2.5 Mass-Transfer .................................................................................................772.6 Industrial Applications ................................................................................... 792.7 Conclusion ...................................................................................................... 81List of Symbols ........................................................................................................ 81References ................................................................................................................ 83Appendices ...............................................................................................................86

Appendix 1 Ideal Mixtures .............................................................................86Appendix 2 Real Mixtures ..............................................................................86Appendix 3 The Asymmetric Activity Coefficient .........................................87Appendix 4 Association Equilibria .................................................................88

Appendix 4.1 Ion-Exchange ...............................................................90Appendix 4.2 Hydrophobic Associations ........................................... 91

Appendix 5 Self-Association Equilibria ......................................................... 91

84534.indb 57 11/5/09 12:24:54 PM


2.1 IntroduCtIon

Process simulation has been successfully used in the chemical and oil indus-tries since the early 1960s to expedite development and optimize the design and operation of integrated processes. Similar benefits can be expected from the application of computer-aided process design and simulation in the biopharma-ceutical industries. At present, the utility of computer-aided process design and process simulation in drug product manufacturing operations is limited. The use of computer-aided process design and process simulation should result in more robust processes developed faster and at a lower cost, resulting in higher quality products [1].

To simulate a single chemical unit operation or an integrated chemical process is in principle straightforward. It requires a model of the unit operation or the integrated process, knowledge of the physical and chemical properties of the chemicals and the solutions involved, and knowledge of the process efficiencies such as mass-transfer rates, reaction rates, heat-transfer coefficients, pressure drops, heat losses, etc. In the classical chemical industries this information is available and many processes can be scaled-up from bench scale to production scale by use of process simulators. This is at present not the case in the biopharmaceutical industries. A bottleneck is the lack of knowledge of the physical and chemical properties of the pharmaceutical and biological products and adequate models to characterize the solution properties and the phase and adsorption equilibria involved.

2.2 thermodynamIC modelIng of ChromatographIC separatIon

To model a chromatographic separation is straightforward. The material balance of a chromatographic column is easy to derive, and in addition one needs mod-els of the adsorption equilibria and the mass-transfer rates. Although the subject is scrutinized in bulky textbooks (for example [2,3]) it is not commonplace to apply modeling in the development, design, optimization, and operation of biopharma-ceutical processes. The principal cause is that most models of the adsorption equi-libria are derived from kinetic and statistical considerations [2,3] rather than from thermodynamic principles. The adsorption equilibria discussed in this paper are not adsorption equilibria in the traditional sense, because in the models presented, the protein molecules do not adsorb to a surface, they associate with the immobilized ligands that are considered to be homogeneously distributed in the pore volume, thus the equilibria are treated as chemical association equilibria. Furthermore, the model

Appendix 6 Simplifying Assumptions ............................................................93Appendix 6.1 Practical Equilibrium Constants ..................................93

Appendix 7 The Convex Isotherm ..................................................................95Appendix 8 The SAS (Self-Association) Isotherm.........................................95Appendix 9 Activity Coefficient Models ........................................................96

Appendix 9.1 Wilson’s Local Composition Activity Coefficient Model ................................................................97

84534.indb 58 11/5/09 12:24:54 PM

Thermodynamic Modeling of Chromatographic Separation 59

applied for the unit volume of the column is not identical with the model applied in many textbooks [2–7], as discussed in [8]. The subject will be addressed when we analyze the differential material balance. The advantage of using a thermodynamic approach rather than a kinetic approach is also discussed in [8]. The non-ideal solu-tion properties, an integral part of the thermodynamic models, cannot be included in models derived from statistical or kinetic considerations.

Intuitively, one would expect that an accurate modeling of the adsorption equi-libria is more important than an accurate determination of the mass-transfer rates, and that is confirmed by experimental investigations. McCue et al. [9] examined the separation of a monomer and an aggregate protein mixture and a chromatographic model was formulated and used to predict the separation of the monomer and aggre-gate species. A model parameter sensitivity analysis was performed to determine the sensitivity of the model predictions to small changes in the model parameters and determine which parameters had the greatest impact on the model predictions. The results of the parameter sensitivity studies showed that small changes to the adsorption isotherm could result in a significant change to the separation perfor-mance, whereas the model predictions were insensitive to changes in the mass-transfer rates.

The current paper will go over the elements of the thermodynamic modeling of chromatographic separation with an emphasis on the modeling of the adsorption iso-therms. In Section 2.3 a discussion of the differential material balance is presented, and Section 2.4 provides an analysis and a discussion of adsorption isotherms mod-eled as chemical associations between the adsorbates and the ligands. Some examples are given. Section 2.5 deals with the modeling of the mass-transfer in the adsorbent. The model of the mass-transfer is closely related to the choice of adsorption isotherm model. Section 2.6 presents some industrial applications of adsorption models, and finally Section 2.7 provides a conclusion. The Appendix gives some basic thermo-dynamic definitions and the isotherm models are analyzed in great detail to state the prerequisites and the simplifying assumptions that are made in order to reduce the number of parameters.

2.3 the dIfferentIal materIal balanCe

In order to set up the material balance we must draw a model of the unit volume of the column. The column is cylindrical and flow only takes place in the axial direction. There are two fluid phases in the column, a mobile fluid phase and a stationary fluid phase in the adsorbent. The adsorbent is a particle composed of a solid backbone and a porous phase. The ligands are bonded to the surface of the solid phase or to a soft gel in the macro pores of the adsorbent; however, in the model it is assumed that the immobilized ligands are homogeneously distributed in the pore volume. The symbols and descriptions used are shown in Figure 2.1. The solute concentrations in the pores, ci, and the adsorbate concentrations, qi, are equilibrium concentrations. The solute concentrations, ci

m, in the mobile phase and in the pores, ci, are in general not identical due to the mass-transfer resistance at the particle surface and in the particle as indicated by the dashed line in Figure 2.1. kd,i is defined as the fraction of

84534.indb 59 11/5/09 12:24:54 PM


the column pore volume into which a solute i can penetrate. The column is assumed to be homogeneous in all radial directions and the column properties are constant in a given cross section and so are the concentrations, temperature, and the flow rate. Thus the material balance has two independent variables, time, t, and axial position in the column, z; we shall consider two functions of these variables, the concentra-tions in the mobile phase, ci

m, and in the stationary phase, ci + qi(c). The residence time or the hold-up time of the fluid in the mobile phase, t0, is a key parameter. The residence time is by definition t V Q L vc0 / /= =ε where Vc is the bed volume in the col-umn, ε is the bed porosity, Q is the volumetric flow rate, L is the bed height, and v is the average linear velocity in the interstice between the particles. Three dimension-less parameters are defined; a dimensionless axial position, z z L= / , a dimensionless time, θ = t t/ 0, and a Péclet number, Pe. The Péclet number is the ratio of the times-

cale of the axial dispersion, t L E DD mdisp = +2 /( ), to the timescale of flow through the column, t0:

Petimescale of axial dispersion

timescale=

of flowdisp /( )

/.= = + ≈

t

tL E D

L vLd

D m

p0

2

0 2ε

(2.1)

Here Dm is the ordinary diffusion coefficient, and ED is the eddy diffusion coefficient which is an empirical parameter that accounts for disturbances in the plug flow. The ordinary diffusion coefficients of proteins are small, i.e., of the order of magnitude of 10−6–10−7 cm2/sec. The approximation to the right-hand side is adapted from a cor-relation by Chung and Wen [10]. This correlation states that E D d vD m p+ = 5ε . At a bed porosity of 0.4, a particle diameter of 30µm, and a low linear interstitial velocity of 1cm/hr, E DD m+ is 1.6 × 10−6 cm2/sec which is of the order of magnitude of the diffusion coefficients of proteins.

The differential material balance of a cylindrical chromatographic column with plug flow in the axial direction is [2, Chapter 2]

Mobile phase Adsorbent

Volume fraction ε

Solute concentrations cmi

Solid backbone

Solid fraction (1–ε)(1–εp)

Pore volume fraction (1–ε)εp

Available pore volume fractions kd,i

Ligand concentration Λ

Solute concentrations ci

Adsorbate concentrations qi

fIgure 2.1 Symbols and descriptions used for the three phases in the column.

84534.indb 60 11/5/09 12:24:57 PM


∂∂

+− ∂ +

∂+ ∂

∂c k c q ci

mp d i i i i

m

θε εε θ

(1 ) ( ( ))z

, c

−− ∂∂

=10

2

Pecz

im

2 (2.2)

The first and the second terms in the material balance account for the accumula-tion of the solutes in the mobile and the stationary phase, respectively. In the second term ci and qi are the solute and the adsorbate concentrations averaged over a particle. The third term is the convective transport due to the fluid flow in the axial direction, and the last term is the axial dispersion term which accounts for the ordi-nary diffusion and the eddy diffusion. The phase ratio

φε εε

=−(1 ) ,p d ik

(2.3)

is the ratio of the accessible pore volume, V kc p d i(1 ) ,− ε ε , to the interstitial volume,Vcε. The phase ratio defined in Equation 2.3 is not identical with the definition in [2] as discussed in [8].

2.4 adsorptIon Isotherms

For the sake of brevity in the exposition, a detailed discussion of the models is deferred to the Appendix. Here we summarize the results. The general expression for the convex ion-exchange or hydrophobic isotherms is given in Equation 2.4. When m protein species adsorb, i.e., associate with the ligands, the equilibrium is calculable by solving the equations:

qc

Aq

qi ii

ii

j

jj

m i

= −

=

=∑1 1 2

1max

, ,....., ,

ν

......,m (2.4)

At low concentrations Ai are the initial slopes of the isotherms, νi are the stoichio-metric coefficients of the association scheme, and qj

max are the maximum saturation capacities. The only difference between ion-exchange and hydrophobic chromatog-raphy is the model for Ai. The models are

Ion-exchange chromatography, IEC

Ac z

K Ais s

E i i E i i

i

=

=Λ ν

γ γˆ, , 0 (2.5)

Hydrophobic interactions, HIC and RPC

Ac

K Ai H i i H i i

i

=

=Λ ν

γ γˆ, , 0 (2.6)

84534.indb 61 11/5/09 12:25:00 PM


Here Λ is the ligand concentration in the pore volume, cs is the counterion concen-tration in the pore volume, zs is the charge number of the counterion, and c is the molar density of the solution, i.e., the sum of the molar concentrations. ˆ

,KE i and ˆ,KH i

are the practical thermodynamic equilibrium constants and γ i are the asymmetric activity coefficients of the proteins in the solution. The asymmetric activity coef-ficients depend on the nature and the composition of the solvent, the modulator, and the protein concentrations.

Proteins in solution can self-associate to form dimerous solutes and in the adsorbed state a protein molecule can act as a ligand and associate with a solute protein mol-ecule to form a double layer of proteins on the adsorbent. This gives rise to a sigmoid isotherm that at low protein concentration is concave, and as the protein concentra-tion is increased, the shape changes from concave to convex. A model which can fit this sigmoid behavior is the SAS isotherm, the self-association isotherm. The SAS model, which is an extension of the classical isotherm model, is

qc

Aq

q

K

cci

ii

j

jj

mD i

i i

i

= −

+

=∑1 1 2

1max

,ˆ

ν

γ

(2.7)

Here ˆ,KD i is the practical thermodynamic equilibrium constant of the self-as-

sociation in the adsorbed state, and c is the molar density of the solution. Cross-association between unlike proteins is also possible but we have not accounted for this possibility. When ˆ

,KD i is zero, the SAS model reduces to the classical convex isotherm given in Equation 2.4.

2.4.1 eStimation of the parameterS

The principal parameter in the convex adsorption isotherm Ai is estimated from iso-cratic retention data as outlined in the subsequent section. This parameter depends on temperature, concentrations, the stoichiometric coefficient, and the asymmetric activity coefficient, γ i, of the solute. The models are given in Equations 2.5 and 2.6, respectively. What remain to be estimated are the maximum available adsorption capacities, qj

max, of all species involved. These parameters and the stoichiometric coefficients determine the curvatures of the convex isotherms. The qj

max parameters can be estimated from capacity measurements or by adjusting the simulated results to fit elution chromatograms at preparative load. The SAS isotherm has one more adjustable parameter that can be estimated in like manner.

2.4.2 eStimation of the partition CoefficientS

The partition coefficients, Ai, at low protein concentrations are determined form isocratic retention volume measurements. These experiments are easy to perform, require little material, and provide useful information about the adsorptive behavior. The model for the retention volumes is [8]

84534.indb 62 11/5/09 12:25:02 PM


V V k AR i c p d i i, ,( ) ( )= + − +( )ε ε ε1 1 (2.8)

The exclusion factors, kd i, , are estimated from the difference between the salt retention volume and the retention volumes of the solutes when they do not associate with the ligands, i.e., when Ai = 0. In ion-exchange chromatography this can be real-ized using an eluant with high salt concentration. In HIC and RPC one has to esti-mate the retention in dependence of the salt and the organic solvent concentrations in order to estimate the point of lowest retention and compare it to the salt retention volume. When no association takes place the retention volumes are

V V ki c p d iNA, ,( )= + −( )ε ε ε1 (2.9)

and since kd i, by definition is zero for common salts, the difference between the salt retention volume and the retention volume determined at conditions where no asso-ciation takes place provides an equation for calculating kd i, :

V V V kR s i c p d i, , ,( ) ( )− = − −NA 1 1ε ε (2.10)

The interstitial porosity is difficult to estimate. From the salt retention volume one can estimate ε ε ε+ −( )1 p and if the vendor cannot supply a number for the particle porosity, which they normally cannot do, a reasonable number of the particle poros-ity, εp, can be estimated by assuming that the interstitial porosity, ε, is 0.37–0.4 [8].

2.4.3 ion-exchanGe

In classical ion-exchange chromatography the modulator is an electrolyte, and the effect of the counterions is to displace the proteins. If the counterion concentration is low, the proteins will associate with the ligands, and when the counterion concentra-tion is increased the adsorbed proteins will be displaced. This exchange process is easy to model because the non-ideal solution behavior turns out to be less important. By combining Equations 2.5, 2.8, 2.9, A2.30, and A2.31 the eventual result of the retention model in the linear range of the isotherm is

ln( ) / ln ˆ ln ln( ), , ,V V V K zR i i c E i is

P− = + + −NA ν ε εΛ1 kk cd i i i s, ln ln+ −∞γ ν (2.11a)

ln /ˆ

lnˆ

, ,V V VG

zG

R i i ci

is

s−( ) = − + +NA RT RT

∆ Λ ∆ν

+ − + −∞ln( ) ln ln,1 ε ε γ νP d i i i sk c

(2.11b)

where γ i∞ is the asymmetric activity coefficient of the solute infinitely diluted in a

mixture of solvent and modulator. When the protein concentrations are very low, as they usually are in these types of experiments, the activity coefficients of the proteins will be independent of the protein concentration and can be considered to

84534.indb 63 11/5/09 12:25:05 PM


be equal to the asymmetric activity coefficients at infinite dilution, γ i∞, as indicated.

Two activity coefficient models are analyzed in the Appendix. If 1 denotes the sol-vent and 2 the modulator, the asymmetric infinite dilution activity coefficients of the solutes can be modeled by an empirical expression, such as Equation A2.49

ln ( )γ i i ix A A A x A∞ = − + − +2 12 2 22

12l (2.12)

A12 is a constant that accounts for the molecular interactions between the solvent and the modulator, A1i accounts for the molecular interactions between the solvent and the solute, and finally, A2i accounts for the molecular interactions between the modu-lator and the solute. A12 can be estimated from the symmetric activity coefficient of the modulator at infinite dilution in the solvent.

The asymmetric activity coefficient at infinite dilution depends on the type of salt, the salt concentration, and the solvent composition. Due to the normalization it is unity in pure water. It is especially the nature of the anions that has an effect on the mag-nitude of the activity coefficients of the solutes. If modulator in the aqueous eluant is sodium chloride, the contribution from the asymmetric activity coefficient, γ i

∞, is most likely modest. However, if one replaces sodium chloride by sodium sulfate, the activ-ity coefficients will increase and the contribution will no longer be negligible because sulfates have a much stronger salting-out effect on proteins than chlorides, that is, the activity coefficients of proteins in an aqueous sulfate solution are orders of magnitude larger that the corresponding activity coefficients in an aqueous chloride solution at similar concentrations. The activity coefficients of proteins in aqueous salt solutions usually parallel the Hofmeister series [11].

When we prepare a double-logarithmic plot of ln( ) /, ,V V VR i i c− NA versus the loga-rithm of the counterion concentration, ln( )cs we will in many cases observe that the resulting figure displays a straight-line plot. This indicates that γ i

∞ is almost independent of the salt concentration. If one can disregard the contribution from the asymmetric activity coefficient, γ i

∞, the only unknowns are ˆ,KE i and νi. The slope of the straight

line is −νi and ˆ,KE i can be determined from the line of intersection with the ordinate at

ln( )cs = 0. Examples of straight-line plots are shown in Figures 2.2, 2.3, and 2.8. One should not put too much emphasis on data where ln( ) /, ,V V VR i i c− NA < 0.

2.4.3.1 β-lactoglobulins a and bFigures 2.2 and 2.3 show double-logarithmic plots of isocratic retention volumes of β-lactoglobulins A and B, respectively. The adsorbent is a Source 30Q in an 8 mL column, and the modulator is sodium chloride. The pH ranges from 6 to 9. Figures 2.2 and 2.3 show that the plotted data can be modeled using the model in Equation 2.11a and that on the basis of the data it is reasonable to assume that the asymmetric activ-ity coefficients at infinite dilution do not vary with the salt concentration. The slopes of the straight lines determine the stoichiometric coefficients, νi, and the lines of intersection with the ordinate at ln( )cs = 0 determine the equilibrium constants. The experimental conditions, the data, and the parameters are from Pedersen et al. [12]. The parameters at pH 7 are given in Table 2.1. The other parameters are Λ = 0.308 M, ε = 0.40, and εp = 0.57. When the data cover a reasonable range of pH, as they

84534.indb 64 11/5/09 12:25:08 PM


do in Figures 2.2 and 2.3, it is possible to determine the standard Gibbs energy change of association of the salt and the proteins by making a simultaneous correla-tion of the data using the model given in Equation 2.11b. The estimated numbers are ∆ =ˆ / .Gs RT 0 320, ∆ =ˆ / .GA RT 3 444, and ∆ =ˆ / .GB RT 3 718 [12], where subscript s denotes salt, A denotes β-lactoglobulin A, and B denotes β-lactoglobulin B. The stoichiometric coefficients depend on pH and the pH dependence is easy to correlate [8]. This means that it is possible to model an elution that applies a pH gradient.

Jen and Pinto [13] observed the non-Langmuirian behavior of β-lactoglobulins A and B. β-lactoglobulin A forms heavy aggregates whereas β-lactoglobulin B does

–1.0

–0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

4.5 4.7 4.9 5.1 5.3 5.5 5.7Incs

In(V

R – V

NA

)/V

c

fIgure 2.2 A double-logarithmic plot of the isocratic retention volumes of β-lactoglobulin A measured on a Source 30Q adsorbent at pH 6, 7, 8, and 9 (left to right). The modulator in the eluant is sodium chloride. The salt is in mM concentrations.

–1.0

–0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6Incs

In(V

R – V

NA

)/V

c

fIgure 2.3 A double-logarithmic plot of the isocratic retention volumes of β-lactoglobulin B measured on a Source 30Q adsorbent at pH 6, 7, 8, and 9 (left to right). The modulator in the eluant is sodium chloride. The salt is in mM concentrations.

84534.indb 65 11/5/09 12:25:10 PM


not, and that is the reason why the elution chromatograms of β-lactoglobulin A dis-play strong non-Langmuirian behavior. Al-Jibbouri [14] investigated the shape of the isocratic elution chromatograms of β-lactoglobulins A and B on several anion-exchange adsorbents. The shape of the elution chromatograms depends strongly on the adsorbent and the modulator concentration. An overlay of several elution chro-matograms in a 157mM sodium chloride solution at pH 7 on a Source 30Q adsorbent is shown in [11]. To demonstrate the capabilities of the SAS isotherm, an attempt to model the elution behavior is shown in Figures 2.4 and 2.5. The parameters are given in Table 2.1. The column volume is 7.8 mL, the protein concentration is 10g/L, and the extinction coefficient 0.962 L/g/cm. The very weak non-Langmuirian behav-ior of β-lactoglobulin B has been disregarded. The steric hindrance factors, σi, of β-lactoglobulins A and B, and the association constant of β-lactoglobulin A, ˆ

,KD i

in Equation 2.7, have been fitted by the eye. The molar density of the solvent, c, in Equation 2.7 is 55.5M. The simulations demonstrate the influence of the self-association on the shape of the elution chromatograms. The simulations depicted in Figure 2.4 show that the elution chromatograms of β-lactoglobulin A display fronting and that the peak maximum moves to the right when the load is increased. The simu-lations depicted in Figure 2.5 show that this continues until a load of approximately 1000µL is injected and when the load is increased further, the peak maximum starts moving to the left and the peaks display tailing in agreement with the experimental observations. The adsorption isotherms of β-lactoglobulins A and B, correspond-ing to the parameters given in Table 2.1, are shown in Figure 2.6. The slope of the β-lactoglobulin A isotherm and the partition coefficient q/c, i.e., the slope of the cord, are shown in Figure 2.7. It has been assumed that the asymmetric activity coefficients are unity.

table 2.1the parameters for the Isotherms of β-lactoglobulins a and b on a source 30q adsorbent at ph 7

β-lactoglobulin a β-lactoglobulin b

Molecular weight 18300 18300

Composition 45% 55%

kd,i 0.7 0.7

KE,i 0.2330 0.1411

KD,i2⋅107 0

ν 6.21 5.50

σ 100 100

qmax /( )= +Λ σ ν 0.00290 M 0.00292 M

Note: The modifier in the eluant is sodium chloride.

84534.indb 66 11/5/09 12:25:12 PM


0.0E + 00

1.0E – 02

2.0E – 02

3.0E – 02

4.0E – 02

5.0E – 02

6.0E – 02

7.0E – 02

8.0E – 02

0 2 4 6 8 10 12 14 16 18 20Volume (CV)

UV

280

nm

fIgure 2.4 (See color insert following page 248.) Modeled isocratic elutions of β-lactoglobulins A (right) and B (left) on a Source 30Q adsorbent at pH 7. The salt concentra-tion is 157mM sodium chloride, and the loads are 5, 10, 20, 50, 100, 200, 350, and 500 µL, respectively, at a concentration of 10g/L. The column volume (CV) is 7.8 mL.

0.0E + 00

1.0E – 01

2.0E – 01

3.0E – 01

4.0E – 01

5.0E – 01

6.0E – 01

7.0E – 01

8.0E – 01

UV

280

nm

0 2 4 6 8 10 12 14 16 18 20Volume (CV)

fIgure 2.5 (See color insert following page 248.) Modeled isocratic elutions of β-lactoglobulins A (right) and B (left) on a Source 30Q adsorbent at pH 7. The salt concen-tration is 157mM sodium chloride, and the loads are 350, 500, 1000, 2000, 3000, 4000, and 5000 µL, respectively, at a concentration of 10g/L. The column volume (CV) is 7.8 mL. The scale of the ordinate is 10 times the scale of Figure 2.4.

84534.indb 67 11/5/09 12:25:24 PM


2.4.3.2 Ion-exchange in mixed solventsThe isocratic experiments shown in Figures 2.2 and 2.3 were measured in an aque-ous solvent. What will happen if we perform isocratic experiments by addition of an organic solvent? That depends on the effect the organic solvent has on the activity coefficients. Inspection of Equation 2.11a reveals that an increase in the asymmetric activity coefficient, γ i

∞, will increase the retention and vice versa, if the retention decreases, it indicates that the asymmetric activity coefficient has decreased by

0.E + 00

2.E – 04

4.E – 04

6.E – 04

8.E – 04

0.0E + 00 5.0E – 06 1.0E – 05 1.5E – 05 2.0E – 05Protein concentration (M)

Ads

orba

te c

once

ntra

tion

(M)

fIgure 2.6 The adsorption isotherms of β-lactoglobulins A and B on a Source 30Q adsor-bent at pH 7. The modulator is 157mM sodium chloride. The full line is the β-lactoglobulin A isotherm which is comprised of dimerous β-lactoglobulin A, , and monomer β-lactoglobulin A, ∆. The dashed line is the β-lactoglobulin B isotherm.

–1

9

19

29

39

49

59

0.0E + 00 5.0E – 06 1.0E – 05 1.5E – 05 2.0E – 05Protein concentration (M)

q/c

or sl

ope

fIgure 2.7 The slope and the partition coefficient q/c of the β-lactoglobulin A isotherm on a Source 30Q adsorbent at pH 7. The modulator is 157mM sodium chloride. The full line is the slope, and the dashed line is the partition coefficient q/c.

84534.indb 68 11/5/09 12:25:26 PM


addition of an organic solvent. For some proteins, the addition of an organic sol-vent to an aqueous protein solution will decrease the solubility because organic sol-vents act like salting-out agents, but the reverse is also observed. Figure 2.8 shows a double–logarithmic plot of the isocratic retention volumes of a biopharmaceutical measured on a Source 30Q adsorbent at pH 7.7. The retention volumes are depicted as ln( ) /, ,V V VR i i c− NA versus the logarithm of the salt concentration. The modula-tor in the eluant is sodium acetate and the solvent is a water–ethanol mixture. The ethanol concentrations are from the top downwards 15, 25, and 42.5% by weight, respectively. The slope of the lines is −3.15 which means that the stoichiometric coefficient is independent of the ethanol concentration. Since the data are well repre-sented by straight lines, a change in the salt concentration must have a modest influ-ence on the asymmetric activity coefficient at infinite dilution, γ i

∞. The asymmetric activity coefficient at infinite dilution, γ i

∞, depends on the ethanol concentration, and the data show that the activity coefficient decreases with increasing ethanol con-centration because the retention decreases; this will also indicate that the solubility will increase with increasing ethanol concentration. But the analysis is not straight-forward, due to the fact that the addition of ethanol may also change the value of the practical equilibrium constant because ˆ

,KE i is a composite parameter and the analysis in the Appendix shows that it includes several non-ideal contributions that, to simplify matters, were considered to be independent of the concentration of the modulator and the solvent composition. This may be a reasonable approximation in an aqueous solution, but may fail in mixed solvents. According to Equation A2.29

ˆˆ

ˆ, ,K KE i E i

i

i

s

s

i

=

∞γγ

γγ

ν

(2.13)

In Equation 2.13 γ i∞ is the activity coefficient of the solute at infinite dilution in

pure water, and consequently constant. γ s is the activity coefficient of the counterion

–1.5

–0.5

0.5

1.5

2.5

3.5

–3.5 –3.0 –2.5 –2.0 –1.5 –1.0lncs

ln(V

R – V

NA

)/V

c

fIgure 2.8 A double-logarithmic plot of the isocratic retention volumes of a biopharma-ceutical measured on a Source 30Q adsorbent at pH 7.7. The modulator in the eluant is sodium acetate and the solvent is a water–ethanol mixture. The ethanol concentrations are from the top 15, 25, and 42.5% by weight, respectively. The slope of the lines is −3.15.

84534.indb 69 11/5/09 12:25:28 PM


in the adsorbed state and γ s is the activity coefficient of the counterion in the solu-tion. γ i is the activity coefficient of the adsorbate, i.e., species i in the adsorbed state. In order to simplify the model and reduce the number of parameters, it has been assumed that the ratio of the counterion activity coefficients, ˆ /γ γs s, is independent of the salt concentration, as discussed in the Appendix. This assumption may hold in an aqueous solution, but we know that the electric potential of the counterion in solu-tion, µs

el, depends strongly on the permittivity of the solvent, [15, Chapter 6, Sections 3–4], and accordingly, the activity coefficient of the counterion, γ s, will depend strongly on the ethanol concentration. How the ratio of the counterion activity coef-ficients ˆ /γ γs s depends on the permittivity must be investigated experimentally. The addition of an organic solvent will also change the apparent pKa values of weak acids and bases because the definition of pKa is based on a concentration scale and not on an activity scale. Figure 2.9 shows the relative permittivity of water–ethanol mixtures at the temperatures 20, 40, and 60°C [16]. An investigation of the influence of the solute activity coefficients on the retention can be studied using hydrophobic techniques.

2.4.4 hydrophobic InteractionS

In theory, reversed-phase and HIC adsorbents are closely related. Both techniques are based upon interactions between non–polar groups on the protein and the hydropho-bic ligands. In practice, however, they are different. The reversed-phase adsorbents are much more highly substituted with hydrophobic ligands than HIC adsorbents. The degree of substitution of reversed-phase adsorbents is in the range of several hundred µmoles per mL of C4–C18 alkyl ligands, compared with 10–50 µmoles/mL

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100Weight percent ethanol

Rela

tive

perm

ittiv

ity

fIgure 2.9 The relative permittivity of water–ethanol mixtures, ◊ 20°C, 40°C, and ∆ 60°C.

84534.indb 70 11/5/09 12:25:31 PM


of C2–C8 alkyl or phenyl ligands for HIC adsorbents [17]. Consequently, protein binding to reversed-phase adsorbents is usually very strong, which requires the use of non–polar solvents for their elution, which limits their application to low molecu-lar weight polypeptides that are stable in aqueous–organic solvents.

The dependence of the activity coefficients of the solute proteins on the modu-lator concentration are often of minor importance in ion-exchange chromatogra-phy, because the salts commonly used as modulators have a low salting-out effect. In ion-exchange the effect of the modulator is due to a change in the concentration of the counterion necessary to displace the exchange process and the influence of the ions on the activity coefficients of the solutes is often modest. The addition of ethanol has an effect on γ i

∞, as discussed in the previous section, but the data show that the change in the equilibrium is moderate, when ethanol is added, compared to the influence of minor chances in the counterion concentration. However, this is not the case in hydrophobic interaction chromatography because no exchange is taking place. The effect of the modulator is to increase or decrease the activity coefficients of the solutes. In salt-induced hydrophobic retention, HIC, a salt is added to increase the activity coefficients of the solutes. In reversed-phase chro-matography, an organic solvent is added to increase the hydrophobicity of the eluant because that will often decrease the activity coefficients of the solutes at least at low modulator concentrations. That is, in hydrophobic chromatography, it is the non-ideal solution behavior that drives the retention. A model of the protein retention will then, accordingly, involve an activity coefficient model. By combin-ing Equations 2.6, 2.8, and 2.9 the model for the retention in the linear range of the isotherm is

ln( ) / ln ˆ ln ln( ), , ,V V V K

ckR i i c H i i P− = + + −NA ν ε εΛ

1 dd i i

H i P d i iA k

,

, ,

ln

ln ln( ) ln

+

= + − +

∞

∞

γ

ε ε γ0 1

(2.14)

The asymmetric activity coefficient, γ i, has been replaced by the asymmetric activity coefficient at infinite dilution, γ i

∞, because the injected amount is so low that γ i is independent of the solute concentration. The model in Equation 2.14 indicates that the retention is governed by the change of the asymmetric activity coefficient at infinite dilution, γ i

∞, with the modulator concentration. A very simple activity coefficient model is given in Equation 2.12. Note that the molar density of the solu-tion, c, in Equation 2.14, depends on the modulator concentration. The molar density of water–ethanol mixtures [18] at 20°C is shown in Figure 2.10. The figure also shows the molarity of ethanol in mixtures from 0 to 100% by weight of ethanol. The abscissa is in percent by weight because solutions are often prepared gravimetrically. The logarithm of the molar density of the solution ranges from 4 (pure water) to 2.8 (pure ethanol). In a small interval of modifier concentration the molar density of the solution can be considered constant, but over a wide range of concentrations this variation must be taken into account.

84534.indb 71 11/5/09 12:25:32 PM


2.4.4.1 reversed-phase ChromatographyFigure 2.11 shows a semi-logarithmic plot of the isocratic retention data of a biop-harmaceutical component measured on C4 and C18 reversed-phase adsorbents at pH 7.7 with sodium acetate in the eluant. It is the same component as in Figure 2.8. The asymmetric activity coefficient at infinite dilution is correlated using Equation 2.12. The constant A12 is identical with the logarithm of the activity coefficient of ethanol at infinite dilution in water at 20°C. The infinite dilution activity coefficient of etha-nol in water at 303.25K is 5.03 [19], that is A12 = ln(5.03), and thus the term x A2

212

is without importance. The constant ( )A A A12 13 23+ − determines the slope of the line. The slopes of the lines in Figure 2.11 are identical and the value is −90. When the lines have identical slopes it indicates that the relative change in the retention is independent of the bonded phase and thus only depends on the activity coefficient of the solute in the mobile phase. When the data were fitted to the model, Equation 2.14, it was assumed that AH

0 is independent of the mobile phase composition, that is, we have not taken into account that the molar density of the solution, c, depends on the ethanol concentration. In the range of ethanol concentration applied, the data in Figure 2.10 show that the change in the molar density of the solution is less than 10%, corresponding to a change in ln(c) of less than 0.1. However, if the stoichiometric coefficient is large and the data cover a wide range of ethanol concentrations, a cor-rection to the lnγ i

∞ term in Equation 2.14 should be taken into account. The change in the retention is not expected to be linear over a wide range of ethanol concentrations. Data for polypeptides measured by Hearn and Ansbach [20] on a µ-Bondapak C18 using acetonitrile as the moderator display a minimum in the retention in the range 30–50% by volume of acetonitrile. This could indicate that the chemical potentials of the ligands and the adsorbates may depend on the mobile phase composition, or that the proteins undergo conformational changes at high concentrations of organic solvent.

0

10

20

30

40

50

60

0 20 40 60 80 100Weight percent ethanol

Mol

arity

, ci ,

or m

olar

den

sity,

c

fIgure 2.10 The molar density of water–ethanol mixtures, , and molar concentration of ethanol, ∆, at 20°C. The straight lines are drawn to indicate the deviation from linearity.

84534.indb 72 11/5/09 12:25:34 PM


2.4.4.2 salt-Induced hydrophobic ChromatographyHIC adsorbents are much less hydrophobic than reversed-phase adsorbents. This means that HIC may be used for proteins that would be hard to elute from a reversed-phase adsorbent without denaturing then. In order to bind a protein to the adsorbent a salt is added to the solution to increase the chemical potential of the solute. As mentioned previously, the activity coefficients of proteins in aqueous salt solutions usually parallel the Hofmeister series [11] and that is the reason why sulfates and not chlorides are used in HIC. The concentration dependence of the molar density of salt solutions is often modest. In saturated sodium chloride and sodium sulfate solutions it is of the order of magnitude of a few percent, whereas it is 10% in a saturated ammonium chloride solution and 18% in a saturated ammonium sulfate solution. The decrease of the molar density of an aqueous ammonium sulfate solu-tion relative to the molar density of pure water at 20°C is shown in Figure 2.12 [21]. Figure 2.13 shows a semi-logarithmic plot of the experimental and calculated parti-tion coefficients of hen egg white lysozyme on two hydrophobic adsorbents against the molar ionic strength of ammonium sulfate in the eluant at pH 6, 7, and 8 from right to left, respectively [22]. The molar ionic strength I is a measure of the density of ions:

I z ci i= ∑12

2

ions

(2.15)

zi are the charge numbers of the ions and ci are the molarities of the ions. The ionic strength of ammonium sulfate is three times the molar concentration. The partition coefficients data Ai are fitted to the equation:

ln ln ln,A Ai H i i= + ∞0 γ (2.16)

–1.5

–0.5

0.5

1.5

2.5

3.5

0.13 0.14 0.15 0.16 0.17XEtOH

In(V

R – V

NA

)/V

c

fIgure 2.11 A semi-logarithmic plot of the isocratic retention data of a biopharmaceutical measured on C4, ∆, and C18, , reversed-phase adsorbents at pH 7.7 with sodium acetate in the eluant.

84534.indb 73 11/5/09 12:25:36 PM


derived from Equations 2.8, 2.9, and 2.14. The slopes of the straight lines depend on pH. The slopes of the lines are 2.29, 2.31, and 2.34 at pH 6, 7, and 8, respectively. The window of operation is one unit of ionic strength and the data in Figure 2.12 show that the corresponding change in the molar density of the solution is less than 2% and can thus be disregarded, that is, it is reasonable to assume that ln ,AH i

0 is constant. The straight-line plot shows that the activity coefficient at infinite dilution in ammonium sulfate can be correlated by a simple model such as Equation 2.12, where we can leave the second term, x A2

212, out of account.

The straight-line relationship is often observed in HIC but it is not common to utilize a thermodynamic approach in the interpretation of the data. Chen et al. [23] determined retention parameters of 20 proteins on Butyl Sepharose 4 FF at pH 7 with 0.2–1.4 M ammonium sulfate in the eluant and fitted the data to an equation that looks similar to Equation 2.14. The regressed R2 values for each linear fit were consistently greater than 0.95. The determined slopes range from 2.5 to 13.84, which correspond to activity coefficients of the proteins ranging from 10 to 106 in 1 M ammonium sulfate.

2.4.4.3 linking hIC and solubility dataThe data shown in Figure 2.13 can be used to determine the activity coefficient of lysozyme at infinite dilution in the salt solution, and what is left to be done is to determine how the activity coefficient of lysozyme in an aqueous ammonium sulfate solution depends on the lysozyme concentration. This will be difficult to do from capacity measurements because a fit of the isotherm to capacity measurements also involves determination of the maximum available capacity qmax and the stoichiometric coefficient ν, but it is straightforward to use solubility data and a model to correlate the protein concentration dependence of the activity coefficient. Here we use a sim-plified version of the activity coefficient model in Equation A2.48 taking advantage

0.80

0.85

0.90

0.95

1.00

0 2 4 6 8Ionic strength (M)

Rela

tive

mol

ar d

ensit

y

10

fIgure 2.12 The decrease of the molar density of an aqueous ammonium sulfate solution relative to the molar density of pure water at 20°C.

84534.indb 74 11/5/09 12:25:37 PM


of the fact that the mole fraction of lysozyme x3 << 1, and since the retention data shown in Figure 2.13 are linear functions of the ionic strength we can leave the term x A2

212 out of account because the solubility data are measured at ionic strengths less

that 3 and the retention data cover the range 4 to 6. That is,

ln ( )( ) ( )γ 3 2 3 12 13 23 3 3 13 21 2= − − + − − − +x x A A A x x A x22

12

2 12 13 23 3 132

A

x A A A x A − + − −( ) (2.17)

When a crystalline phase, either pure or of constant composition, is in equilib-rium with a solution, the equilibrium condition is that the chemical potential of the solute is identical with the chemical potential in the crystalline phase. Moretti et al. [24] have measured the solubility of lysozyme in ammonium sulfate. The lysozyme crystals contain 15% by weight of water. When the solid phase is of constant composition the chemical potential of the protein in the crystal, µ3

crystal, is constant, then, consequently, the solubility at equilibrium can be calculated from the equation:

µ µ γ µ γ µ3 30

3 3 3 3 3solute crystalRT= + = ⇒ = ln lnx x 33 3

0crystal RT constant−( ) =µ / (2.18)

3

2

10

Part

ition

coe

ffici

ent A 9

87654

3

2

13 4 5

Ionic strength (M)6 7

fIgure 2.13 A semi-logarithmic plot of the experimental and calculated partition coef-ficients of hen egg white lysozyme on hydrophobic Poros PH/M, phenyl, (left) and ET/M ethyl ether (right) adsorbents against the molar ionic strength of ammonium sulfate in the eluant at pH 6,7, and 8 (right to left).

84534.indb 75 11/5/09 12:25:39 PM


µ30 is the reference potential of the protein is solution. The activity coefficient of

the protein, γ 3, is calculable from Equation 2.17. The constant ( )A A A12 13 23+ − is determined from the slope of the retention data and the constant A23 is determined by fitting Equation 2.18 to the solubility data. The right-hand side of Equation 2.18 is a constant common to all the solubility data of lysozyme in ammonium sulfate at pH 8. The parameters and other details are given in [25]. The result of the correlation is shown in Figure 2.14. The solubility measurements were reported in g/kg of water and the salt concentration was in units of molar ionic strength (mol/kg water). The unit of ionic strength used in this paper is M (mol/liter of solu-tion). The calculated asymmetric activity coefficients are shown in Figure 2.15. The solid straight line shows the asymmetric activity coefficient at infinite dilu-tion, γ 3

∞, determined from the chromatographic retention data and the dashed line shows the activity coefficient at saturation, γ 3, determined from the correlation of the solubility data.

Comparing Figures 2.13 and 2.14 shows that the solubility of lysozyme is very low in the window of operation of a HIC process, that is, solubility and retention work in opposite directions in HIC. High solubility gives low retention and vice versa. A similar conclusion applies to IEC and RPC when ethanol is added. In a clas-sical IEC process, high retention corresponds to low salt concentration, and at low salt concentration the solubility is higher than it is at high salt concentration, apart from a region where salting-in may take place.

056789

2

3

4

56789

100

10

Solu

bilit

y (g

/kg

wat

er)

1 2Ionic strength (M)

3 4

fIgure 2.14 Experimental and correlated solubility of hen egg white lysozyme in ammo-nium sulfate at pH 8. The solid phase is crystalline.

84534.indb 76 11/5/09 12:25:43 PM


2.5 mass-transfer

The relationship between the concentration of a solute in the mobile phase, cim, and

the concentration in the stationary phase in the adsorbent, ci, in Equation 2.2 is determined by the rate of mass-transfer. If the rate of mass-transfer is very fast they become nearly identical. The mass-transfer from the interstitial mobile phase to the surface of the spherical particle is by diffusion, but it is convenient to apply a lin-ear driving force approximation where the resistance to mass-transfer in the mobile phase is assumed to take place in a fluid boundary layer at the external particle surface. The thickness of this boundary layer is determined by the hydrodynamic conditions in the mobile phase and depends on the flow velocity and the viscosity. The linear driving force of mass-transfer is the concentration difference ( )c ci

mi− 0

across the boundary layer where cim is the concentration in the mobile phase at the

surface of the boundary layer, and ci0 is the concentration of species i at the external

surface of the particle. The resistance to mass-transfer is 1 / ,k af i p where kf,i is the film mass-transfer coefficient and ap is the external surface area of the particle per unit volume which is 6/dp if the particle is a sphere. Most adsorbents are neither spherical particles nor monodisperse, where an equivalent mean particle diameter is used. ap is independent of the particle porosity because the area of the pore openings on the external particle surface as well as the pore volume in the particle is assumed to be proportional to the particle porosity. The rate of mass-transfer is the driving force divided by the resistance. That is,

1

10

100

1,000

10,000

100,000

1,000,000

0 1 2 3 4 5 6Ionic strength (M)

Asy

mm

etric

act

ivity

coe

ffici

ent

fIgure 2.15 Calculated activity coefficients of hen egg white lysozyme in ammonium sulfate at pH 8. The solid line is the infinite dilution activity coefficient and the dashed line is the activity coefficient at saturation calculated from the solubility data shown in Figure 2.14.

84534.indb 77 11/5/09 12:25:45 PM


∂ +

∂= − = −( ( ))

/(

,,

c qt

c ck a

k a ci i im

i

f i pf i p i

mc 0

1cci

0) (2.19)

Several correlations of film mass-transfer coefficients are available [26].The intraparticle transport is by hindered diffusion in the pores and the concen-

tration ci in the pore volume depends on the radial position. As a first approximation it can be assumed that the association kinetics is infinitely fast compared to the rate of mass-transfer in the pores and in consequence there is local equilibrium in the particle pore volume, then, accordingly q F c c c ci i m( ) ( , .... ,... )c = 1 2 and

∂

∂= ∂

∂∂∂

=∑q

tqc

ct

i i

kk

m

k( )c

1

(2.20)

Taking advantage of this assumption, a differential material balance for a sphere at the radial position r is

12

2

r rr D

cr

c q

tctp i

i i i i∂∂

∂∂

=∂ +( )

∂= ∂

∂,

( )c++ ∂

∂∂∂

=∑ q

cct

i

kk

m

k

1

(2.21)

If the isotherm is a simple convex isotherm and the solute activity coefficients are unity, the partial derivative of qi with respect to ck is

∂∂

= − −

=

−

∑qc

qc

c Aq

qi

k

i

iik i i

j

jj

m i

δν

11

1

max

11

1q

q

cjj

mj

kmax

=∑ ∂

∂ (2.22)

δik = 1 when i = k, and if i ≠ k then δik = 0. Insertion of the derivative Equation 2.22 into Equation 2.21 gives the final form of the differential material balance in the particle

11

22

r rr D

cr

qc

ct

cp ii i

i

i∂∂

∂∂

= +

∂∂

−, ii ij

jj

m

jj

mjA

q

q q

qi

11

1

1

1

−

∂∂

=

−

=∑ ∑max max

ν

ccctkk

m

k

=∑ ∂

∂1

(2.23)

Note that the terms

q

qj

jj

m

max=

∑1

and 1

11q

q

cctjj

mj

kk

m

kmax

==∑∑ ∂

∂∂∂

are common to all material balances of the associating species present. The bound-ary condition at the centre of the particle is due to the spherical symmetry. The flux of any component at the centre has to be zero

84534.indb 78 11/5/09 12:25:47 PM


∂∂

==

cri

r 0

0 (2.24)

The boundary condition at the surface is determined by the fact that the flux through the boundary layer at the external surface of the particle is equal to the flux into the particle. The external porous surface area of the particle through which a solute can diffuse into the particle is a fraction ε p d ik , of the total surface area but that applies to both fluxes and the boundary condition is then independent of ε p d ik , . The first boundary condition states that there is equilibrium at the interface, that is,

c c r Ri i0 = =( ) (2.25)

The second condition states that the fluxes through the fluid film must be identical to the fluxes into or out of the particle

k c c Dcrf i i

mi p i

i

r R, ,( )− = ∂

∂

=

0 (2.26)

There are of course other approaches for the mathematical modeling of the rate of mass-transfer than the one outlined in this paper. A general discussion of the model-ing of mass-transfer is given in Chapter V in [2].

2.6 IndustrIal applICatIons

The mathematical model of a chromatographic process comprises the material bal-ance, an appropriate model for the isotherm, and the rate of mass-transfer. In order to solve the partial differential equations one has to specify the initial and the boundary conditions. A discussion of solution methods for the partial differential equations is given in Chapters III and IX in [27].

Industrial applications of thermodynamic modeling of ion-exchange chro-matographic separations are shown by Mollerup et al. [28–30]. A major issue is to determine the parameters for the isotherm. In ion-exchange chromatography, the key-plot is the double-logarithmic plot of ln ( ) /, ,V V VR i i c− NA versus ln( )cs . Examples are shown in Figures 2.2, 2.3, and 2.8. The lines in Figures 2.2 and 2.3 show the change in the retention of β-lactoglobulins A and B, respectively, in dependence of the salt concentration and pH, and in Figure 2.8 the lines show the change in the retention of a protein in dependence of the salt and the ethanol concentration. The parameters determined from Figures 2.2 and 2.3 are shown in Table 2.1. Separations involve several components and it may be advantageous to select some as key com-ponents. The reason for doing this can be to simplify matters because it is time consuming to estimate the parameters of all components involved. A plot similar to Figures 2.2 and 2.3 for four key components of a mixture of several components is shown in Figure 3 in [28]. These data were used to determine the stoichiometric coefficients, νi, and the practical equilibrium constants, ˆ

,KE i, of the key components. Whenever the lines in a double-logarithmic plot are straight lines, it is reasonable

84534.indb 79 11/5/09 12:25:49 PM


to assume that the asymmetric activity coefficients at infinite dilution are constant. In the examples shown this assumption seems to be justified. When the parameters for the initial slope of the isotherm have been determined, one has to determine the curvature of the isotherm. When the isotherm is a simple convex isotherm the cur-vature is determined by the stoichiometric coefficient and the maximum available capacity, qi

max. The stoichiometric coefficient is determined from the slope of the double-logarithmic plot, that is, in order to complete the isotherm one only needs to determine the maximum available capacity. In principle this can be done from a single capacity measurement. In the example shown in Figure 2.16 three data points were used to determine qi

max. The parameters are reported in Table 1 [28]. Examples of comparison of simulated and experimental chromatograms to validate the quality of the simulations are shown in Figures 5 and 6 in [28], as well as an example of application of simulations for analyzing an aberration in Figures 8 and 9 in [28]. The use of a computer simulation to tune a separation of a target compo-nent in order to increase the throughput is shown in [29]. This simulation indicated that it should be feasible to increase the productivity five times. To tune a process to get an increased productivity is easily done by means of a simulator, whereas it is much more laborious to do it experimentally by trial and error in the laboratory. The simulator can also be used to identify and analyze critical process parameters and define a suitable window of operation that can ensure the development of a robust process to handle variability. An application of the SAS isotherm is shown in [30]. The experimental chromatograms display fronting which indicates that a conventional convex isotherm cannot be applied. The stoichiometric coefficients, νi, and the practical equilibrium constants, ˆ

,KE i, were determined from the usual double-logarithmic plot but the qi

max parameter and the association constant ˆ,KD i

of the associating component were determined by matching the simulated and the experimental chromatograms.

A robustness analysis is traditionally made using statistical methods including factorial design of experiments. In order for the method to be valid a linearization

0102030405060708090

100

0 1 2 3 4 5Mobile phase concentration (g/L)

Solid

pha

se c

once

ntra

tion

(g/L

pore

)

fIgure 2.16 When the initial slope of the isotherm and the stoichiometric coefficient ν have been determined from the isocratic experiments, the curvature is determined by the qmax parameter which can be determined from a few capacity measurements as demonstrated in the figure. The parameters are shown in Table 1 in [28].

84534.indb 80 11/5/09 12:25:51 PM


is applied and to limit the number of experiments, the design space is often chosen within a narrow margin. This limitation, reflecting the applied method, can be cir-cumvented by using simulations in the robustness analysis. Recently Hansen et al. [31] demonstrated how simulations can assist in the robustness analysis of a process step providing a much broader design space.

2.7 ConClusIon

Process simulation has for many years been successfully used in the chemical and oil industries, but it is not commonly used in the biopharmaceutical industry. However, this chapter shows that the theoretical knowledge is at hand and the examples dem-onstrate some industrial applications. One may anticipate it to be only a matter of time before widespread use of simulations in the biopharmaceutical industry will result in expedited development and optimized design and operation of the pro-cesses. This will reduce the time and cost of process development, ensure develop-ment of robust processes that can handle variability and deliver a predefined quality within the defined design space, and thus, process simulations will also prove to be an important tool to solve regulatory issues.

lIst of symbols

Ai parameter in the isothermAij parameter in activity coefficient model, Equation A2.43Ai

0 Ai i/γai activityai activity of an associated componentap external surface area of the particle per unit volumec molar density of the solution in the pore volumeci molar concentration of a solute in the pore volumeci average molar concentration of a solute in the pore volumeci

m molar concentration of a solute in the mobile phaseci

0 concentration of a solute at the external surface of the particleDm ordinary diffusion coefficientDp i, hindered diffusion coefficient in the particledp particle diameterED axial dispersion coefficientF Faraday’s number, 96485.34 C/mol G Gibbs energyGE excess Gibbs energyGi partial molar Gibbs energyGi

E partial molar excess Gibbs energy∆G0 standard Gibbs energy change of association (adsorption)∆G0 practical Gibbs energy change of association (adsorption)ΔH 0 standard enthalpy change of association (adsorption), Equation A2.15I molar ionic strength, defined in Equation 2.15

84534.indb 81 11/5/09 12:25:56 PM


K thermodynamic equilibrium constant defined in Equation A2.14K practical equilibrium constant defined in Appendix 6.1kd,i the fraction of the column pore volume into which a solute can penetratekf,i film mass-transfer coefficientL bed heightm number of associating componentsN number of componentsNA Avogadro’s number, 6.0221415·1023 mol−1

ni mole numbern vector of mole numbers ( , ,....., ,.... )n n n ni N1 2

P pressurePe Péclet number defined in Equation 2.1Q volumetric flow rateq vector of molar charges ( , ,....., ,.... )q q q qi N1 2 (Appendices 2 and 3)qi molar concentration of an associated componentqi average molar concentration of an associated componentqj

max maximum available capacityR gas constant, 8.31451 J/(mol K)r radial position in a spherical particleSAS Self-ASsociationT temperature t timet0 liquid residence time = timescale of flowtdisp timescale of axial dispersionuij energy parameter, Appendix 9.1Vc bed volumeV iNA, retention volume when no association takes placeVR i, retention volumevi molar volume of a pure substance, Appendix 9.1v linear fluid velocityxi mole fractionyi mole fraction of an associated componentz axial position in the bedz dimensionless axial position z/Lzi charge number of an ion

Greek Letters

γ i activity coefficient, γ i i ia x= /γ i activity coefficient of an associated component, ˆ ˆ /γ i i ia y=γ i,1

∞ activity coefficient at infinite dilution in a reference solvent 1γ i asymmetric activity coefficient, defined in Equation A2.8ε permittivity (Appendices 2 and 3)ε bed porosityε p porosity of the adsorbentζ j steric and electric exclusion factor or surface coverage factor

84534.indb 82 11/5/09 12:26:02 PM


θ dimensionless time t t/ 0Λ molar concentration of ligands in the pore volumeλij parameter in Wilson’s excess Gibbs energy model, Equation A2.50µ i chemical potentialµ i chemical potential of an associated componentµL chemical potential of a hydrophobic ligandµ i

0 reference chemical potentialµ i

0 reference chemical potential defined in Equation A2.9µ i

id ideal mixture chemical potential defined in Equation A2.1µ i

self self-potential of an ion, defined in Appendix 2µ i

el electric potential of an ion, defined in Appendix 2µ i

E excess potential defined in Equation A2.6νi stoichiometric coefficient σj steric hindrance factorψ electrical field potentialφ phase ratio, defined in Equation 2.3

Subscripts

D self-associationE ion-exchangeH hydrophobicL ligand i, j, k index of component i, j, or k, respectively s counterion 0 standard state

referenCes

1. L.X. Yu, Pharmaceutical quality by design: Product and process development, under-standing, and control, Pharmac. Res. 25 (2008) 781–791.

2. G. Guiochon, S.G. Shirazi, A.M. Katti, Fundamentals of Preparative and Nonlinear Chromatography, Academic Press 1994, ISBN 0-12-305530-X.

3. G. Guiochon, A. Felinger, D.G. Shirazi, A.M. Katti, Fundamentals of Preparative and Nonlinear Chromatography, 2nd Edition, Academic Press, 2006, ISBN 0-12-370537.

4. S. Yamamoto, K. Nakanishi, R. Matsuno, Ion-Exchange Chromatography of Proteins, Chromatographic Science Series, volume 43, Marcel Dekker, 1988, ISBN 0-8247-7903-7.

5. P. Wankat, Rate-Controlled Separations, Elsevier, 1990, Chapters 6–10, ISBN 1-85166-521-8.

6. P. Wankat, Separation Process Engineering, 2nd Edition, Prentice Hall, 2007, Chapter 17, ISBN 0-13-084789-5.

7. Preparative Chromatography of Fine Chemicals and Pharmaceutical, Editor H. Schmidt-Traub, Wiley-VCH Verlag, 2005, ISBN 3-527-30643-9.

8. J.M. Mollerup, A review of the thermodynamics of protein association to ligands, pro-tein adsorption, and adsorption isotherms, Chem. Eng. Technol. 31 (2008) 864–874.

9. J.T. McCue, P. Engel, A. Ng, R. Macniven, J. Thömmes, Modeling of protein monomer/aggregate purification and separation using hydrophobic interaction chromatography, Bioprocess Biosys. Eng., 3 (2008) 261–275.

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10. S.F. Chung, C.Y. Wen, Longitudinal dispersion of liquid flowing through fixed and fluid-ized beds, AIChE J. 14 (1968) 857–866.

11. J.M. Mollerup, The thermodynamic principles of ligand binding in chromatography and biology, J. Biotechnology 132 (2007) 187–195.

12. L. Pedersen, J.M. Mollerup, E. Hansen, A. Jungbauer, Whey proteins as a model system for chromatographic separation of proteins, J. Chromatography B 790 (2003) 161–173.

13. S.-C D. Jen, N.G. Pinto, Nonlinear chromatography of β-Lactoglobulins A and B: Non-langmuirian behaviour, Ind. Eng. Chem. Res 34 (1995) 2685–2691.

14. S. Al-Jibbouri, Annual Report to the IVCSEP 2004, Department of Chemical Engineering, Technical University of Denmark.

15. M.L. Michelsen, J.M. Mollerup, Thermodynamic Modeling: Fundamentals and Computational Aspects, 2nd Edition, Tie-Line Publications, 2007, ISBN 87-989961-3-4.

16. G. Åkerlöf, Dielectric constants of some organic solvent-water mixtures at various tem-peratures, J. Am. Chem. Soc. 54 (1932) 4125–4138.

17. Kjell-Ove Eriksson, Hydrophobic interaction chromatography, in Protein Purification, Principles, High Resolution Methods, and Applications, Edited by Jan-Christer Janson and Lars Rydén, 2nd Edition, Wiley-VCH, 1998, ISBN 0-471-18626-0.

18. N.A. Lange, Handbook of Chemistry, 10th Edition, McGraw Hill, New York 1961. 19. Z. Atik, D. Gruber, M. Krummen, J. Gmehling, Measurement of activity coefficients

at infinite dilution of benzene, toluene, ethanol, esters, ketones, and ethers at vari-ous temperatures in water using the dilutor technique. J. Chem. Eng. Data. 49 (2004) 1429–1432.

20. M.T.W. Hearn, B. Ansbach, Chemical, Physical, and Biochemical Concepts in Isolation and Purification of Proteins, in Separation Processes in Biotechnology, Editor J.A. Asenjo, Marcel Dekker Inc., New York 1990, ISBN 0-8247-8270-4.

21. O. Soehnel, P. Novotny, Densities of Aqueous Solutions of Inorganic Substances, Elsevier, Amsterdam 1985.

22. A. Staby, J.M. Mollerup, Solute retention of lysozyme in hydrophobic interaction perfu-sion chromatography, J. Chromatography A 734 (1996) 205–212.

23. J. Chen, T. Yang, S.M. Cramer, Prediction of protein retention times in gradient hydro-phobic interaction chromatographic systems, J. Chromatography A 1177 (2008) 207–214.

24. J.J. Moretti, S.I Sandler, A.M. Lenhoff, Phase equilibria in the lysozyme-ammonium sulfate-water system, Biotechnology Bioeng. 70 (2000) 1498–1506.

25. J.M. Mollerup, Applied thermodynamics: A new frontier for biotechnology, Fluid Phase Equilib. 241 (2006) 205–215.

26. M.D. LeVan, G.C. Carta, C.M. Yon, Adsorption and ion-exchange, in Perry’s Chemical Engineers’ Handbook, 7th Edition, McGraw-Hill, 1997, ISBN 0-07-049841-5.

27. G. Guiochon, B. Lin, Modelling for Preparative Chromatography, Academic Press, 2003, ISBN 0-12-044983-8.

28. J.M. Mollerup, T.B. Hansen, S. Kidal, A. Staby, Quality by design—Thermodynamic modelling of chromatographic separation of proteins, J. Chromatography A 1177 (2008), 200–206.

29. J.M. Mollerup, T.B. Hansen, S. Kidal, L. Sejergaard, A. Staby, Development, model-ling, optimisation and scale-up of chromatographic purification of a therapeutic protein, Fluid Phase Equilib. 261, 133–139.

30. J.M. Mollerup, T.B. Hansen, S. Kidal, L. Sejergaard, E. Hansen, A. Staby, Use of Quality by the Design for the Modelling of Chromatographic Separations, Journal of Liquid Chromatography & Related Technologies 32 (2009) 1577–1597.

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31. T.B. Hansen, L. Sejergaard, E. Hansen, S. Kidal, Use of simulation for robustness analysis of an industrial ion-exchange step. Poster presented at Recovery of Biological Products XIII, Quebec, Canada, 22–27 June 2008.

32. C.A. Brooks, S.M. Cramer, Steric mass-action ion exchange: Displacement profiles and induced salt gradients, AIChE Journal 38 (1992) 1969–1978.

33. C. Tanford, Chapter 2 in, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd Edition, Krieger Publishing Company, Florida, USA, 1991, ISBN 0-89464-621-4.

34. J.M. Prausnitz, R.N. Lichtentaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, 3rd Edition, Prentice-Hall 1999, ISBN 0-13-977745-8.

35. C. Tanford, The Physical Chemistry of Macromolecules, John Wiley & Sons, 1961, ISBN 0-471-84447-0.

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appendICes

appendix 1: ideal mixtureS

The ideal mixture is a hypothetical state, which no real solution strictly follows, but it is a convenient reference of normal fluid behavior. There is no unique definition of an ideal mixture, but it is most convenient that the definition of the chemical poten-tials of an ideal mixture conforms to the chemical potentials of a perfect gas mixture [15, Chapter 1, Section 10]. That is, an ideal mixture is a mixture whose chemical potentials at any composition xi are given by

µ µi i iT P T P xid RT( , , ) ( , ) lnn = +0 (A2.1)

Here µ i T P0( , ) is the reference chemical potential taken as a state of pure species i at the temperature, T, and the pressure, P, of the solution. xi is the mole fraction of spe-cies i, that by definition is x n ni i j

Nj= / Σ , where ni is the number of moles of species

i in a solution of N components, and n is the corresponding vector of mole numbers( , ,....., ,.... )n n n ni N1 2 .

appendix 2: real mixtureS

The chemical potentials of the constituents of real mixtures are calculable as partial molar Gibbs energies Gi. The chemical potentials consist of several contributions [15, Chapter 6, Section 2]. The most important contributions are given in

GGn

T P zii T,P

i i i i=∂

µ µ ε µ∂

= + +( , , ) ( , )n self eel ( , , , )T P ziε + ψq F (A2.2)

The first contribution µi(T, P, n), the so-called classical contribution, is due to the short-range attractive and repulsive intermolecular forces. The second, third, and fourth terms are contributions of species that carry electric charges. ε is the permit-tivity of the solvent, zi is the charge number of the ion, qi is the charge of ni moles of species i, and q is the corresponding charge vector. The self-potentials, µ i

self , are the potentials due to the self-energy of charging each ion in the solution in the effective absence of the other ions and these potentials are independent of the configuration of the charged molecules, that is, they do not depend on the concentration of ions. The self-potentials are also called the Born potentials. The electric potentials, µ i

el, origi-nate from the energy due to the mutual electric interactions of the various ions. The Debye–Hückel potential from 1923 is a well-known model of the electric potentials. It is analyzed in [15, Chapter 6, Section 4]. The last term in Equation A2.2 is due to the work done when moving one mole of ions of charge ziF in an electrical field of potential ψ. F = eNA, is Faraday’s number, 96485.34 C/mol, e is the unit charge and NA is Avogadro’s number. The last term contributes to the chemical potential of a sin-gle ion by an amount zieψ and this explains why the second and the third terms are insufficient to characterize ion–ion equilibrium across a membrane or in an aqueous

84534.indb 86 11/5/09 12:26:08 PM


two-phase system where the electrical field potentials of the various phases are not identical due to different electrolyte concentrations in the phases. To simplify mat-ters, in this analysis, we assume that the electrical field potentials are identical in all phases, but that may not be absolutely correct in an ion-exchange adsorbent at low ionic strength due to the presence of the immobilized charges in the adsorbent. A worked example is given in [15, p. 167–169]. Furthermore, in chromatographic sys-tems, it is convenient to assume that the permittivities of the mobile phase and of the fluid phase in the pore volume are identical because there is the same solvent in both phases. When the permittivities of the two phases are identical we can disregard the self-potentials, µ εi izself ( , ), because they do not depend on the charge concentration but only on the permittivity and the charge number. That makes it possible to simplify Equation A2.2 to include the classical contribution and the electric contribution only, (but we should always be cautious not to forget the prerequisites)

µ µ µ εi i iT P T P T P( , , , ) ( , , ) ( , , , )n q = +n qel (A2.3)

It is convenient to introduce the activity ai. Equation A2.4 defines the activities, ai, of the constituents in the mixture:

µ µi i iT P T P a T P( , , , ) ( , ) ln ( , , , )n q n q= +0 RT (A2.4)

and comparing Equations A2.1 and A2.4 shows that the activities of an ideal mixture are equal to the mole fractions. To account for the deviation from ideal mixture behavior, we introduce the activity coefficient γi. It is convenient to define the activity coefficient of species i as the ratio of the activity of species i, ai, to the corresponding mole fraction, xi, i.e., γi = ai/xi. That is, the equivalent of Equation A2.4 is

µ µ γi i i iT P T P x T P( , , , ) ( , ) ln ( , , , )n q n q= +0 RT (A2.5)

The activity coefficients are quantities that account for the deviation from the ideal mixture behavior, that is, an ideal mixture is a mixture where the activity coef-ficients are unity at all concentrations. The excess potential of species i, µ i

E, is the difference between the real chemical potential and the corresponding ideal chemical potential, whereby activity coefficients are calculable from models of excess poten-tials. Subtraction of Equation A2.1 from Equation A2.5 gives the excess potentials

µ µ µ γiE

i i i= − =id RTln (A2.6)

The excess potentials are identical to the partial molar excess Gibbs energies GiE.

appendix 3: the aSymmetric activity Coefficient

The activity coefficient defined in Equation A2.5 is unity for any substance in the pure state because the reference chemical potential is taken as a state of pure

84534.indb 87 11/5/09 12:26:10 PM


species i. However, it may in some cases be convenient to use an activity coefficient that is unity at infinite dilution in a pure solvent. An activity coefficient that is nor-malized in such a way that it is unity in a pure solvent is denoted an asymmetric activity coefficient. It is in biotechnology traditionally used for solutes in dilute solu-tions. Conversion of a normal activity coefficient to an asymmetric activity coef-ficient is straightforward. We divide the activity coefficient in Equation A2.5 by the activity coefficient at infinite dilution in a picked reference solvent. It is convenient to pick component 1 as the reference solvent. The activity coefficient of species i at infinite dilution in the pure reference solvent 1 is γ i T P n, ( , , )1 1

∞ . When we divide the activity coefficient by the activity coefficient at infinite dilution we have essentially subtracted the term RTln ( , , ),γ i T P n1 1

∞ from the potential in Equation A2.5 and in order not to redefine the potential we add the same term to the reference potential, µ i T P0( , ) , that is,

µ µ γi i iT P T P T P n( , , , ) ( , ) ln ( , , ) ln,n q = + +∞01 1RT RT

γγγ

i

ii

T PT P n

x( , , , )

( , , ),

n q

1 1∞

(A2.7)

The asymmetric activity coefficient, γ i, is defined as the ratio of the activity coefficient γ i to the infinite dilution activity coefficient, γ i,1

∞ , in the picked reference solvent 1. That is,

γ γγi

i

i

T PT P

T P n( , , , )

( , , , )( , , ),

n qn q≡

∞1 1

(A2.8)

Since the potentials on the left-hand sides of Equations A2.5 and A2.7 must be identical, the asymmetric reference state must include the excess chemical potential of species i at infinite dilution. In consequence, the reference state potential is

µ µ γi i iT P n T P T P n01

01 1( , , ) ( , ) ln ( , , ),= + ∞RT (A2.9)

Different symbols are employed for the two reference states to designate the dif-ference, because it is important to note that the asymmetric reference state chemical potentials depend on the nature of the picked reference solvent. A neater form of Equation A2.7 is

µ µ γi i i iT P T P n T P x( , , , ) ( , , ) ln ( , , , )n q n q= + 01 RT (A2.10)

The asymmetric activity coefficients at infinite dilution are not unity in a mixed solvent. They are only unity at infinite dilution in the picked reference solvent.

appendix 4: aSSociation equilibria

The adsorption equilibria in protein chromatography are modeled as chemical asso-ciation equilibria where the proteins associate with the ligands that are covalently bonded to the porous chromatographic adsorbent. If the interactions are electrostatic,

84534.indb 88 11/5/09 12:26:13 PM


as in ion-exchange chromatography, the protein displaces the counterions associated with the charged ligands. We assume that the charge number of the ligand is unity. The exchange scheme is

P L S S P Liz

i zz

iz

iz

zi

ss s i

i+ +ν ν (A2.11)

where zi is the binding charge number of the protein Pi, zs is the charge number of the counterion S, and νi i sz z= / is the corresponding stoichiometric coefficient.

In hydrophobic chromatography the interactions entail a reversible association of the protein with the ligands to form a complex by nonpolar interactions. When a pro-tein Pi associates with νi ligands by nonpolar interactions, the association scheme is

P L PLi i i i+ ν ν (A2.12)

When the association equilibrium has been established it must hold that

∆G i i

i

= =∑ν µ 0 (A2.13)

where νi are the stoichiometric coefficients in the association scheme. A sign conven-tion is adopted that makes the value of νi negative for a constituent (reactant) on the left-hand side of the association scheme and positive for a constituent (product) on the right-hand side of the association scheme. The chemical potentials are calculable from either Equations A2.5 or A2.10. When inserting Equation A2.5 in Equation A2.13 the result is

RT K RTln ln≡ = − ≡ −∑ ∑ν ν µi i i ia G0 0∆ (A2.14)

This equation defines the thermodynamic equilibrium constant K. Note that K is always dimensionless. ∆G0 is the standard Gibbs energy change of association. When the potentials in Equation A2.5 are applied the standard Gibbs energy change of association is independent of the composition of the mixture because the refer-ence chemical potentials µ i

0 are taken as the states of the pure species; consequently, the thermodynamic equilibrium constant K is independent of the composition of the mixture. The temperature dependence of the thermodynamic equilibrium constant K at constant pressure P is

∂

∂= ∆ = − ∂

∂( / )

( / )(ln )( / )

∆GT

HR T

P0 0

1 1RT K

(A2.15)

This equation gives the effect of the temperature upon the equilibrium constant, and hence on the adsorbate equilibrium. This equation does not imply that ΔH0 is independent of the temperature. It is apparent that if ΔH0 is negative, i.e., if the association is exothermic, the equilibrium constant will decrease as the temperature increases. Analogously, K will increase with T for an endothermic association.

84534.indb 89 11/5/09 12:26:15 PM


appendix 4.1: Ion-exchangeThe ion-exchange scheme is given in Equation A2.11 and the equilibrium con-stants are

Ka aa a

y xx yE i

i s

i s

i s

i s

i s

i

i

i

i

i

i

,

ˆˆ

ˆˆ

= =ν

ν

ν

ν

νγ γγ γ ss

i s

i s

i s

i si

i

i

i

i

q cc qν

ν

ν

ν

ν

γ γγ γ

=ˆ

ˆ (A2.16)

Here ai is the activity of species i associated with νi ligands, yi and γ i are the cor-responding mole fraction and activity coefficient, respectively. The molar concen-tration of the adsorbate, qi, is equal to the mole fraction times the molar density c in the pore volume, i.e., qi = yi c. ai is the activity of species i in the solution in the pore volume, xi and γi are the corresponding mole fraction and activity coefficient, respectively, and the molar concentration of the solute is ci = xic. as is the activity of the associated counterion, ys and γ s are the corresponding mole fraction and activity coefficient, respectively, and the molar concentration of counterions associated with the ligands is qs = ysc. Finally, as is the activity of the counterion in the solution, xs and γs are the corresponding mole fraction and activity coefficient, respectively, and cs = xs c.

The molar density in the pore volume is the sum of all molar concentrations in the pore volume including solvents, salts, solutes, adsorbates, and free ligands. The molarity of the solvents is in general much greater than the molarities of the solutes and the adsorbates. The molarity of pure water at room temperature is 55.5.

When m species adsorb, electroneutrality requires that

Λ ΛΛ

= + ⇔ = −

=∑ ∑z q z q q

z

q

zs s j j

m

j ss

j

j j

m

ζζ

1 1

1/

ΛΛz

q

qs

j

j

m

11

−

∑ max

(A2.17)

Here Λ is the ligand concentration in the pore volume, and ζ j is a factor accounting for steric and electric exclusion of other molecules because the associated macromol-ecule j makes a number of counterions in its vicinity unavailable for exchange with other molecules. Finally, qj

max is the maximum adsorption capacity of adsorbate j. According to Brookes and Cramer [32] ζ σj j jz= +1 / where σj is denoted a steric hindrance factor of component j. The standard Gibbs energy change of the ion-ex-change equilibrium of component i, ∆GE i,

0 , can be analyzed into

− = = − + − = −RTln ˆ ˆ, ,K G GE i E i i i s i s i∆ ∆0 0 0 0 0 0µ µ νµ ν µ ννi sG∆ 0 (A2.18)

Here µ i0 is the standard state chemical potential of the associated species i, µ i

0 is the standard state chemical potential of the solute component i, µs

0 is the stan-dard state chemical potential of the solute counterion, and finally µs

0 is the standard state chemical potential of the associated counterion. Thus ∆Gi

0 is the Gibbs energy change of association of component i, i.e., µ µi i

0 0− and ∆Gs0 is the Gibbs energy

change of association of the counterion, i.e., µ µs s0 0− .

84534.indb 90 11/5/09 12:26:21 PM


appendix 4.2: hydrophobic associationsThe association scheme of hydrophobic associations are given in Equation A2.12 and the equilibrium constants are

Ka

a a

y

x y

q c

c qH i

i

i L

i

i L

i

i L

i

ii i i

i

,

ˆ

ˆ

ˆ

ˆ= = =ν ν ν

νγγ γ LL

i

i Li iν ν

γγ γ

ˆ

ˆ (A2.19)

Here ai is the activity of species i associated with νi ligands, yi and γ i are the corre-sponding mole fraction and activity coefficient, respectively, and qi is the correspond-ing molar concentration of the adsorbate where qi = yic. c is the molar density of the solution in the pore volume. ai is the activity of the species i in the solution in the pore volume, xi and γi are the corresponding mole fraction and activity coefficient, respectively, and ci = xi c. Finally, aL is the activity of the immobilized free ligands, yL and γ L are the corresponding mole fraction and activity coefficient, respectively, and the molar concentration of free ligands is qL = yLc.

When m species adsorb, the material balance requires that

Λ ΛΛ

Λ= + ⇔ = −

= −∑ ∑q q q

q qL j

m

j j Lj

j j

m

ζ νζ ν

1 1

1 1/

jj

j

m

qmax1

∑

(A2.20)

Here Λ is the ligand concentration in the pore volume, and ζ j is a factor account-ing for steric exclusion of other molecules because the associated macromolecule j makes a number of ligands in its vicinity unavailable for association with other mol-ecules. Finally, qj

max is the maximum available capacity of adsorbate j.The standard Gibbs energy change is

− = = − −RTln ˆ ˆ, ,K GH i H i i i i L∆ 0 0 0 0µ µ ν µ (A2.21)

appendix 5: Self-aSSociation equilibria

Proteins in solution can self-associate to form dimerous solutes and in the adsorbed state a protein molecule can act as a ligand and associate with a solute protein mol-ecule to form a double layer of protein on the adsorbent. If the association entails a reversible association of a solute protein molecule Pi with a protein that has formed an association complex with νi ligands, the association scheme is

P PL P Li i ii i+ ν ν 2, (A2.22)

P2,i is the dimerous protein in the adsorbed state. The equilibrium constant KD,i is by definition

KD ii

i i

i

i i

i

i i

a

a a

y

x y

q,

,

,

,

,

,

,

ˆ

ˆ

ˆ

ˆ= = =2

1

2

1

2

1

2γγ γ

,,

,

,

,

ˆ

ˆi

i i

i

i i

c

c q1

2

1

γγ γ

(A2.23)

84534.indb 91 11/5/09 12:26:24 PM


and

− =RT Kln , ,D i D iG∆ 0 (A2.24)

Here ˆ ,a i2 is the activity of the associated dimerous protein, y i2, and ˆ,γ 2 i are the cor-

responding mole fraction and activity coefficient, respectively, and q2,i = y2,i c is the corresponding molar concentration of the adsorbate. c is the molar density of the solution in the pore volume. ai is the activity of the monomer protein in solution, xi and γi are the corresponding mole fraction and activity coefficient, respectively, and the molar concentration is ci = xi c. Finally, ˆ ,a i1 is the activity of the associated mono-mer protein, y1,i and ˆ

,γ1 i are the corresponding mole fraction and activity coefficient, respectively, and molar adsorbate concentration of the monomer is q1,i = y1,i c.

If the monomer is the only protein in the solution, the adsorbate consists of mono-mer and dimmer species and the electroneutrality balance is

Λ = + +q z z q z qs s i i i i i iζ ζ1 1 1 2 2 2, , , , , , (A2.25)

ζ,i and ζ2,i are the exclusion factors of the monomer and dimer species respectively, and z1,i and z2,i are the corresponding binding charges. However, since it is assumed, Equation A2.22, that the associated dimerous protein is formed by a hydrophobic interaction between an associated and a free protein, the binding charge is unchanged. To apply Equation A2.25 would require that one can determine the concentrations of the associated monomer and the dimer species, q1,i and q2,i, respectively, which unfortunately is not so easy to do. It will thus be an advantage to simplify the model in order to replace the concentrations of the monomer and the dimer species by the total concentration of adsorbate which is qi = q1,i + 2q2,i. If we make the simplifying assumption that z z zi i i2 1, ,= = and ζ ζ ζ2 12 2, ,i i i= = then

Λ = + + = +q z z q z q q z z qs s i i i i i i s s i iζ ζ ζ1 1 1 2 2 2, , , , , , ii (A2.26)

Similarly, if the dimerization takes place on a hydrophobic adsorbent, the mate-rial balance is

Λ = +q qL i i iζ ν (A2.27)

The total adsorbate concentration qi is calculable as

q q q qc

ci i i iD i i i

ii= + = +

1 2 1

1

2

2 1 2, , ,, ,

,

ˆ

ˆK γ γ

γ

(A2.28)

The monomer adsorbate concentration q1,i is calculable from either Equation A2.15 or Equation A2.19.

84534.indb 92 11/5/09 12:26:27 PM


Before deriving the final expressions for the isotherms, it is in place to make a number of simplifying assumptions to make the models more user-friendly, i.e., to reduce the number of parameters by introducing some simplifications.

appendix 6: SimplifyinG aSSumptionS

Three simplifications will be made and it is important to be aware of all simplifica-tions made, because although one can argue that the simplifications are reasonable, experiments may occasionally contradict what was considered to be a most obvious assumption:

a) Little is known about the excess properties of adsorbates. An associated molecule is less flexible than a molecule in solution. Therefore it is assumed that the activity coefficients of adsorbates are not influenced by moderate changes in the composition of the eluant. This is the reason to consider the activity coefficients of the proteins in the adsorbed state, γ i, to be indepen-dent of the adsorbate concentration, but one should bear in mind that these activity coefficients may depend on the solvent composition if mixed sol-vents are applied.

b) It is reasonable to suppose that the activity coefficient of the hydrophobic ligand, γ L , in contact with an aqueous electrolyte solution is independent of the salt concentration [33] because the interaction energy between a hydrophobic molecule and water varies little with the salt concentration. But the hydrophobic effect may decrease if the hydrophobicity of the solvent is decreased by adding an organic solvent, but as long as these changes are moderate, we consider the activity coefficient of the ligand to be constant.

c) It is assumed that the ratio of counterion activity coefficients in Equation A2.16, γ γs s/ ˆ , is independent of the ion concentration but careful attention should be paid to this assumption because the activity coefficient ratio may to some extent depend on the solvent composition. The activity coef-ficients of ions will increase when the permittivity of the solvent decreases. The permittivity of ethanol is one fourth of the permittivity of pure water. Models for activity coefficients of simple electrolytes in solution are avail-able but it will make the isotherm models much more elaborate to include such models, and besides, none of these models do apply to the activity coefficients of counterions in the adsorbed state.

appendix 6.1: practical equilibrium ConstantsWe will replace the remaining normal activity coefficients by asymmetric activ-ity coefficients because it is convenient to use activity coefficient models where activity coefficients are unity at infinite dilution in a pure reference solvent. It is most convenient to choose water as the reference solvent. The practical equilibrium constants are

84534.indb 93 11/5/09 12:26:28 PM


Appendix 6.1.1: Ion-Exchange Adsorbents

ˆˆ

ˆ, ,K K

q cc qE i E i

i

i

s

s

i s

i s

ii

i=

=∞γ

γγγ

ν ν

ν

1γ i

(A2.29)

where γ i are the asymmetric activity coefficients of the proteins in the eluant and

RTln ˆ ˆ, ,K GE i E i= −∆ 0 (A2.30)

and

∆ ∆ ∆ˆ ln( /ˆ ) ln(,G G GE i i i i i s s0 0 0= −( ) − −∞RT RTγ γ ν γ // ˆ ) ˆ ˆγ νs i i sG G( ) = −∆ ∆0 0 (A2.31)

Appendix 6.1.2: Hydrophobic Adsorbents

ˆ ˆˆ, ,K K

q c

c qH i H i

L i

i

i

i L i

i i

i= =

∞γ γγ γ

ν ν

ν1

(A2.32)


RTln ˆ ˆ, ,K GH i H i= −∆ 0 (A2.33)

and

∆ ∆ˆ ln ˆ ln ( /ˆ ), ,G GH i H i i L i i= − − ∞ν γ γ γRT RT (A2.34)

Appendix 6.1.3: Self-Association

ˆ ˆ

ˆ, ,,

,

,

,

K Kq c

c qD i D ii i

i

i

i i i

= =∞γ γ

γ γ1

2

2

1

1

(A2.35)


RTln ˆ ˆ, ,K GD i D i= −∆ 0 (A2.36)

and

∆ ∆ˆ ln ˆ ˆ, , , ,G GD i D i i i i= − ( )∞RT γ γ γ1 2 (A2.37)

84534.indb 94 11/5/09 12:26:31 PM


appendix 7: the convex iSotherm

The general expression for the convex ion-exchange isotherm is derived by combin-ing Equations A2.17 and A2.29, and hydrophobic isotherms are derived by combin-ing Equations A2.20 and A2.32, in order to eliminate qs and qL, respectively. The results are given in Equations A2.38 to A2.40. When m species adsorb the general expression for the convex isotherms are calculable by solving the equations

qc

Aq

qi ii

ii

j

jj

m i

= −

=

=∑1 1 2

1max

, ,...., ,.

ν

...,m (A2.38)

At low protein concentrations Ai are the initial slopes of the isotherms. The term 1 1− ∑ =j

mj jq q( )max/ is the fraction of free ligands. The model for Ai depends on the

technique. The models areIon-exchange chromatography, IEC

Ac z

K Ais s

E i i E i i

i

=

=Λ ν

γ γˆ, , 0 (A2.39)

Hydrophobic interactions, HIC and PRC

Ac

K Ai H i i H i i

i

=

=Λ ν

γ γˆ, , 0 (A2.40)

appendix 8: the SaS (Self-aSSociation) iSotherm

The adsorption isotherm of the associated monomer of species i is a convex iso-therm, that is, the adsorption isotherm of q1,i is a convex isotherm. The SAS isotherm is thus derived by combining Equations A2.28, A2.35, and A2.38, remembering that q1,i is equal to qi in Equation A2.38. The eventual result is

qc

q

c

K

cc A

q

qi

i

i

i

D ii i i

j

j

= +

= −1 1 2 1, ,

max

ˆγ

jj

mD i

i i

i

K

cc

=∑

+

1

1 2

ν

γˆ

, (A2.41)

Here q q qi i i= +1 22, , is the total concentration of molecules of species i counted as monomers, and according to the assumptions made in Appendix: 5 it follows that q qi i

max,

max= 1 because the assumptions made in Equation A2.26 implies that

q

q

q

q

q

q

q

qi

i

i

i

i

i

i

imax

,

,max

,

,max

,

,max

= + =1

1

2

2

1

1

++ =2 2

1 1

q

qq

qi

i

i

i

,

,max

,max

(A2.42)

84534.indb 95 11/5/09 12:26:33 PM


appendix 9: activity coefficient modelS

Activity coefficients are calculable as partial derivatives of excess Gibbs energy models [15, Chapter 5, Sections 1–4]. The independent variables are temperature and mole fractions. Activity coefficient models are extensively used for correlation of the non-ideal solution behavior of mixtures of fine chemicals and polymer solutions. Electrolytes need special treatment due to the long-range nature of the Coulomb potential [15, Chapter 6, Section 4]. Activity coefficient models can also be derived from equations of state as explained in [15, Chapter 1, Section 11 and Chapter 5, Section 1]. Models for electrolyte solutions as well as models derived from equa-tions of state have temperature, volume, and mole numbers as independent variables, whereby these models require that the molarities of the solutions are known. A ref-erence that covers a variety of classical models is [34]. A standard reference for the physical chemistry of macromolecules is [35]. Two models will be analyzed. The first is a simple quadratic model and the second is Wilson’s local composition model.

A very simple empirical excess Gibbs energy model for a mixture of N compo-nents is

nG n n AEi

i

N

j

j

N

ij== =

∑ ∑12

1 1

RT (A2.43)

where A Aij ji= and Aii = Ajj = 0 because GE of a pure component is zero. The cor-responding symmetric activity coefficient model of species k is

ln γ k i ik

i

N

i

i

N

j

j i

N

ijx A x x A= −= = >

∑ ∑ ∑1 1

(A2.44)

In a ternary mixture where species 1 denotes water, species 2 a modulator, and species 3 a solute, the result is

ln γ 3 1 13 2 23 1 2 12 1 3 13 2 3 23= + − − −x A x A x x A x x A x x A (A2.45)

It is convenient to eliminate the mole fraction of component 1 in order to make the activity coefficient a function of the modulator and the solute concentrations only. For that purpose we use the identity x x x1 2 31= − − . The eventual result is

ln ( )( ) ( )γ 3 13 2 3 12 13 23 3 3 131 2= − − + − − − +A x x A A A x x A xx A22

12 (A2.46)

The activity coefficient of species 3 infinitely diluted in a mixture of species 1 and 2 is

ln ( )γ 3 13 2 12 13 23 22

12∞ = − + − +A x A A A x A (A2.47)

84534.indb 96 11/5/09 12:26:35 PM


The infinite dilution activity coefficient of species 3 in a pure solvent 1 is ln ,γ 3 1 13

∞ = A and the asymmetric activity coefficient is thus

ln ( )( ) ( )γ 3 2 3 12 13 23 3 3 13 21 2= − − + − − − +x x A A A x x A x2212A (A2.48)

The infinite dilution asymmetric activity coefficient of 3 in pure 1 is unity because it has been normalized that way, but the asymmetric activity coefficient of species 3 infinitely diluted in a mixture of species 1 and 2 is

ln ( )γ 3 2 12 13 23 22

12∞ = − + − +x A A A x A (A2.49)

appendix 9.1: wilson’s local Composition activity Coefficient modelThe local composition models are more powerful models than a simple empirical model such as (A2.43). Wilson’s local composition model is analyzed in [15, Chapter 5, Section 3]. The model is

G

n v n n n n vE

i

i

N

j j ij

j

N

i i

i

N

RT= − + +

= = =∑ ∑

1 1 1

ln ln lnλ ∑∑ (A2.50)

where vj are the molar volumes of the pure components, and λij ij iiu u= − −exp( ( )/RT) are adjustable parameters where, λ λij ji≠ and λ λii jj= = 1.

The corresponding symmetric activity coefficient is

ln ln lnγ λ λk k j j kj

j

N

k i

i

N

ik

j j

v v x v x

v x

= + − −= =

∑ ∑11 1 λλ

λ

ij

j

N

k j j kj

j

N

k i

i

v c v c v c

=

= =

∑

∑= + + − −

1

1 1

1 ln ln lnNN

ik

j j ij

j

N

v c∑

∑=

λ

λ1

(A2.51)

There are two adjustable parameters λij and λji per binary pair, and for solutes vk can be treated as an adjustable parameter in cases where the molar volume is unknown. None of the models apply to electrolytes without the addition of a term that accounts for µ i

el.

84534.indb 97 11/5/09 12:26:38 PM

84534.indb 98 11/5/09 12:26:38 PM

99

3 Ultra-Performance Liquid Chromatography Technology and Applications

Uwe D. Neue, Marianna Kele, Bernard Bunner, Antonios Kromidas, Tad Dourdeville, Jeffrey R. Mazzeo, Eric S. Grumbach, Susan Serpa, Thomas E. Wheat, Paula Hong, and Martin Gilar

Contents

3.1 Introduction: A Brief History from the Beginnings of HPLC to the Development of UPLC® Instruments ........................................................... 100

3.2 The Promise of Small Particles .................................................................... 1003.3 The Principle of the Thermal Effect ............................................................. 1063.4 Pressure and Thermal Effects on Retention ................................................. 1113.5 Effect of Pressure and Temperature on Column Performance ..................... 1173.6 Applications .................................................................................................. 122

3.6.1 Higher Speed .................................................................................... 1223.6.2 Higher Performance ..........................................................................1243.6.3 A Complex Separation in a Short Analysis Time:

Physiological Amino Acids .............................................................. 1253.6.4 Bioseparations ................................................................................... 127

3.6.4.1 Peptides .............................................................................. 1273.6.4.2 Proteins .............................................................................. 1283.6.4.3 Oligonucleotides ................................................................ 131

3.7 Conclusions ................................................................................................... 137List of Symbols ...................................................................................................... 137Acknowledgment ................................................................................................... 138References .............................................................................................................. 139

84534.indb 99 11/5/09 12:26:38 PM


3.1 IntroduCtIon: a brIef hIstory from the begInnIngs of hplC to the development of uplC® Instruments

High-performance liquid chromatography (HPLC) emerged as an important analytical technique around 1972, when it became possible to pack columns with particles of diameter less than 30 µm [1–3]. Commercial 10 µm columns became available in 1973 [4]. Now, for the first time, column performance was suitable for the wide range of applications that HPLC enjoys today. Very quickly, researchers explored smaller and smaller particle sizes [5] and encountered what appeared to be the frontier of the new technology [6,7]: the pressure-induced heat of friction inside a chromatographic column results in a significant increase in the tempera-ture of the mobile phase. This effect is tolerable at pressures below 400 bar, and the technology of HPLC evolved happily and successfully below this apparent limit. Particle sizes decreased slowly, and the speed of analysis improved as the analytical demands increased. However, the thermal effects appeared to impose a permanent limit on the technology.

During the development of capillary electrophoresis, Jorgenson [8] learned that the heat generated from the electrical current could be transported readily out of the device if the diameter of the separation capillary was sufficiently small. This approach reduced an important limitation of electrophoretic separations and enabled the devel-opment of high-powered fast separations. The same principle can be applied to solve the problem caused by the pressure-induced heat in HPLC [9], allowing the operation of capillary HPLC columns at significantly higher pressures than anticipated in the early work [6,7]. The availability of higher pressures is accompanied by the ability to make good use of columns packed with sub-2-micron particles, which generate high-powered separations in a shorter time than classical HPLC particles [10]. The first commercial implementation of this idea was introduced in 2004 under the name of Ultra Performance Liquid Chromatography® or UPLC instrumentation [11].

3.2 the promIse of small partICles

During the roughly three decades of HPLC evolution before the introduction of pressures beyond 400 bar, the commonly used particle size migrated slowly, initially from 10 µm to 5 µm, and later to 3 µm. Today, the majority of the HPLC separations are still using 5 µm particles, but the proportion of the use of 3 µm columns is increasing every year. Together with the use of smaller particles, the typical column length decreased over time, from the “holy foot” (=30 cm) of the early 1970s to 5 and 10 cm length for faster separations. Together with mass spectrometry as the detection tool and very short 2 to 3 cm columns, the analysis time moved into the range of one minute, or even less [12–14], albeit often with compromises in the quality of the separation, if classical particle sizes are used.

The use of columns packed with smaller particles is paralleled by an increase in pressure, if the quality of the separation is to be maintained. This is illustrated in Figure 3.1, which compares the same separation carried out with columns packed with decreasing particle sizes, while reducing the column length in direct propor-tion with the particle size. As one can see without difficulty, the quality of the separation

84534.indb 100 11/5/09 12:26:39 PM

Ultra-Performance Liquid Chromatography Technology and Applications 101

is the same for all four columns, i.e., a 15 cm 5 µm, a 10 cm 3.5 µm, a 7.5 cm 2.5 µm, and a 5 cm 1.7 µm column. While the columns become shorter with the reduction in particle size, the linear velocity increases in the same proportion. As a consequence of the combination of the shorter column length with the increased velocity, the analysis

AU

0.00

0.10

0.20

0.00 2.00 4.00 6.00 8.00

15 cm 5 µm

10 cm 3.5 µm

7.5 cm 2.5 µm

5 cm 1.7 µm

AU

0.10

0.20

Minutes10.00

0.00

Minutes0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

0.20

AU

0.00

0.10

Minutes0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

AU

0.00

0.10

0.20

Minutes0.00 0.20 0.40 0.60 0.80 1.00 1.10

fIgure 3.1 Comparison of the same separation on columns with decreasing particle sizes. Columns from top to bottom: XBridge™ C18 2.1 × 150 mm, 5 µm at 0.2 mL/min, XBridge C18 2.1 × 100 mm, 3.5 µm at 0.3 mL/min, XBridge C18 2.1 × 75 mm, 2.5 µm at 0.5 mL/min, ACQUITY UPLC C18 2.1 × 50 mm, 1.7 µm at 0.6 mL/min. Instrument: Waters ACQUITY UPLC with tunable UV detector. Analytes and mobile phase: 1-methylxanthene, 1,3- dimethyluric acid, theobromine, 1,7-dimethylxanthene; 0.1% (v/v) formic acid in 95/5 water/acetonitrile. (Chromatograms from UPLC Seminar 2005. Courtesy of Waters Corporation.)

84534.indb 101 11/5/09 12:26:39 PM


time decreased from 10 minutes to 1.1 minutes, in full agreement with the theoretical expectation, which is a 9-fold reduction in analysis time for the same resolution.

Let us briefly recapitulate all events that enable the comparison in Figure 3.1: Both the particle size and the column length changed 3-fold. As a consequence of the reduced particle size, one is able to maintain the same separation performance with the shorter column, but one has to increase the linear velocity in proportion to the reduction in particle size. Both factors—3-fold shorter column and 3-fold higher velocity—combine to the observed decrease in the analysis time by a factor of 9. The column backpressure also increases 9-fold: the column permeability decreases 9-fold (in proportion to the square of the particle size), the column length is reduced 3-fold, but the linear velocity also increases 3-fold (to obtain the same reduced veloc-ity), and the last two influences cancel each other.

The underlying theory is very straightforward: at a fixed column length, the Kozeny–Carman equation tells us that the column backpressure increases in inverse proportion to the square of the particle size. The scaling linear velocity, i.e. the velocity at which the same column performance is reached, increases with decreasing particle size. The latter is a reflection of the definition of the reduced velocity. These two factors combine to result in a pressure increase that is proportional to the inverse of the second power of the particle size for a column of scaled length.

In the comparison in Figure 3.1, the quality of the separation, i.e., the resolu-tion, remained constant. If the column length had remained constant, which would provide increased resolution as a result of the higher efficiency of the smaller par-ticle columns, the pressure would have increased 27-fold in total: 9-fold due to the decreased column permeability, and 3-fold due to the required increase in the linear velocity to remain at the minimum in the van Deemter curve. One can see readily how one will very quickly move away from the pressure range of classical HPLC as one is exploring columns packed with sub-2-µm particles.

Another aspect of the use of very small particles is the ability to generate a large number of theoretical plates in a reasonable time. It must be stressed once again that the performance advantage of the small particles lies in the reduction in analysis time, not in the achievement of a large number of theoretical plates. With the expanded pressure of UPLC, it is possible to generate one million plates in the timeframe of one day with 10 µm particles, but to achieve 100,000 plates within a very short analysis time, columns packed with sub-2-micron particles are needed, together with higher pressures than classical HPLC.

An isocratic chromatogram with over 100,000 plates is shown in Figure 3.2. Phenone standards were injected onto three 1.7 µm UPLC columns connected in series for a total column length of 45 cm. At a flow rate of 0.32 mL/min and a temperature of 90°C, 108,848 plates were generated for heptanophenone, while octanophenone delivered 104,645 theoretical plates. The pressure needed for this separation was 960 bar and the analysis time was less than 15 minutes.

It should be noted that the elevated temperature is only needed to reduce the analysis time, not the operating pressure. As a matter of fact, it has been shown that the use of elevated temperature increases the pressure that is required to reach the minimum of the van Deemter curve [15]. We would like to repeat the essence of this important argument here.

84534.indb 102 11/5/09 12:26:40 PM


The velocity at the minimum of the plate-height versus velocity curve umin is obtained by taking the first derivative of the van Deemter equation:

uDd

BC

m

pmin = (3.1)

Dm is the molecular diffusion coefficient of the analyte, dp the particle size of the packing material, and B and C are the coefficient for the diffusion term and the mass transfer term of the van Deemter equation. The latter two terms depend on the retention factor, but may be considered to be independent of temperature at constant retention factor for a constant analyte.

The pressure drop ΔP needed to reach this velocity can be estimated using the Kozeny–Carman equation:

∆P fu L

dit

p

= ⋅ ⋅ ⋅( ) minε ε η

2 (3.2)

L is the column length, dp the particle size, η is the viscosity of the mobile phase, and εi and εt are the interstitial and the total porosity of the column.

Combining both equations while eliminating the linear velocity results in the following:

∆P fLd

BC

Di tp

m= ⋅ ⋅ ⋅ ⋅ ⋅( )ε ε η3

(3.3)

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00Minutes

fIgure 3.2 Over 100,000 plates in less than 15 minutes. Conditions: ACQUITY UPLC BEH C18 2.1 × 450 mm, 1.7 µm; flow rate: 0.32 mL/min; mobile phase: 70/30 (v/v) acetonitrile/water; temperature: 90°C, pressure: 960 bar. Analytes: thiourea (N = 61,789), toluene N = 94,203), heptanophenone (N = 108,848), octanophenone (N = 104,645), amylben-zene (N = 94,419). (Chromatogram courtesy of Waters Corporation.)

84534.indb 103 11/5/09 12:26:41 PM


Note the product of the diffusion coefficient and the viscosity at the end of Equation 3.3. As the temperature increases, the diffusion coefficient of a particular analyte increases, while the viscosity decreases. The product of diffusion coef-ficient and viscosity can be derived from any one of several equations published in the literature, such as the Wilke–Chang equation [16] or the Scheibel equation [17]. In both cases, the product of the diffusion coefficient and the viscosity increases with temperature T :

D Tm ⋅ = ⋅η const (3.4)

And as a consequence, the pressure needed to reach the minimum of the van Deemter curve increases with temperature:

∆P T∝ (3.5)

It is vital to keep this important argument in mind when considering the benefits of elevated temperature and elevated pressure in HPLC or UPLC. One can see that elevated temperature is not a substitute for elevated pressure, but of course, the combination of both parameters will result in a further increase in the speed of analysis.

Let us now switch our attention to details of the performance comparison of columns packed with different particle sizes. This is best done by a comparison of plots of measured theoretical plate heights versus linear velocity. When such comparisons are done, care must be given to experimental details. Experimental difficulties such as extra-column bandspreading, a slow response time from the detector, or an insufficiently fast sampling rate from detector or data system must be strictly avoided to obtain true performance data for the tested columns. In other words, the instrument performance must be in harmony with the increased column performance.

We compared the performance of columns packed with three different particle sizes, 1.7 μm, 3.5 μm, and 5 μm. Two columns were used for each particle size, and two different batches were used for the 1.7 μm and the 5 μm packings, while a duplicate column from the same batch was used for the 3.5 μm packing. Plots of the theoretical plate height versus the linear velocity, obtained with 2.1 mm × 50 mm columns on a UPLC instrument, are shown in Figure 3.3. One can see without diffi-culty the significantly lower plate height that is achieved with the sub-2-μm particles compared to the classical HPLC particle sizes. The patterns are the same for both analytes shown here, which were also representative of the other analytes used in these measurements.

The data shown in Figure 3.3 are also consistent with a larger data set on the same subject presented at HPLC 2006 [18]. This data set contained a wide range of differ-ent sub-2-μm particles from different manufacturers.

It is interesting to note the large difference between the performance of sub-2-μm particles and that of classical particles. Another way to objectively and directly compare the performance of columns packed with different particle sizes is to look at plots of reduced plate height versus reduced velocity. This is shown

84534.indb 104 11/5/09 12:26:42 PM


in Figure 3.4 for the same analytes and columns as in Figure 3.3. In agreement with previous findings [19], the volume-averaged particle size, measured by the electrozone sensing technique, was used for the calculation of the reduced param-eters. We see overall a good agreement between the different particle sizes. The minimum plate height of the curves is between 2 and 2.5 dp (dp is the particle size). This is expected for well-packed columns, and demonstrates that the packed bed quality of sub-2-μm columns is as good as that of columns packed with larger particles. An examination of the slopes of the plots shows that the slopes become slightly worse with decreasing particle size, although the impact is barely visible in the operation range of sub-2-micron particles. For larger particles, it is known that there is a linear relationship between the slope of the van Deemter equation and the volume-averaged particle size [19,20]. Also, it is known that this relation-ship has a positive intercept, i.e., that this slope increases slightly with declining particle size. A possible origin for this observation could be the thermal effects that occur with decreasing particle size and are already significant with 3 µm particles [20].

Amylbenzene(a)

(b)

35

40

30

20

25H

ETP

(µm

)H

ETP

(µm

)

10

15

0

5

0 2 4 6 8 10 12 14Linear velocity (mm/sec)

0 2 4 6 8 10 12 14Linear velocity (mm/sec)

Decanophenone

35

40

25

30

15

20

10

0

5

fIgure 3.3 Plate height versus velocity curves for amylbenzene (a) and decanophenone (b) on 1.7 μm (dark diamonds), 3.5 μm (light triangles), and 5 μm (light squares) particles.

84534.indb 105 11/5/09 12:26:43 PM


Clearly, the absolute separation performance of UPLC columns exceeds that of HPLC columns. However, the influence of the thermal effects that concerned Halász is still visible when the data are examined carefully. We will explore these issues in the next paragraph.

3.3 the prInCIple of the thermal effeCt

If one touches a column operated under a pressure of close to 1000 bar near the column outlet, one can clearly feel the increase in temperature due to the heating by friction that is occurring inside the column. This rise in temperature is one of the issues described by Martin and Guiochon in a recent paper on the effects of high pressure in liquid chromatography (LC) [21]. Measurements carried out on a column exposed to ambient air were reported by Gritti and Guiochon in [22]. Let us discuss this phenomenon in more detail.

As we take a volume of liquid and bring it up to pressure in the pump, several things are changing at the same time. For one thing, the liquid is now at an elevated

Amylbenzene(a)

(b)

1820

1416

81012

46

Redu

ced

plat

e he

ight

02

0 10 20 30 40 50 60 70 80Reduced velocity

0 10 20 30 40 50 60 70 80Reduced velocity

Decanophenone

1820

121416

810

46

Redu

ced

plat

e he

ight

02

fIgure 3.4 Reduced plate height versus reduced velocity curves for amylbenzene (a) and decanophenone (b) on 1.7 μm (diamond), 3.5 μm (triangles), and 5 μm (squares) particles (symbols as in Figure 3.3).

84534.indb 106 11/5/09 12:26:44 PM


pressure. In order to get to this elevated pressure, most liquids compress, which in turn is accompanied by an increase in temperature. As we will see in the following discussion, the temperature reverts to the ambient temperature as the solvent travels through the pump to the injector. Next, as the liquid percolates through the column, the pressure of the solvent slowly decreases, and two thermal effects appear: Heating due to viscous friction of the solvent in the packed bed, and cooling associated with the volumetric expansion of the solvent.

the three steps that Cover the thermal effects in uplC

1. The mobile phase is compressed in the pump, which is accompanied by an increase in temperature.

2. The heat generated by the compression in the pump is lost in the tubing, and the solvent returns to the ambient temperature.

3. As the solvent moves through the column, the remaining energy is converted to heat by friction between the solvent and the packed bed inside the column, accompanied by cooling due to solvent expansion.

We will now discuss these three events in more detail. From the first principle of thermodynamics, assuming a quasi-static transformation, a small heat change δQ can be written as

δQ C dT hdPp= + (3.6a)

where Cp is the molar heat capacity at constant pressure and the parameter h is according to the second principle of thermodynamics

h TVT P

= − ∂∂

(3.6b)

By definition, the thermal expansion coefficient αT of the solvent is

αTPV

VT

= ⋅ ∂∂

1 (3.7)

so that

δ αQ C dT TVdPp T= − (3.8)

The total change in the liquid volume is

dVV

ddT dPT= − = −ρ

ρα χ (3.9a)

84534.indb 107 11/5/09 12:26:45 PM


where χ is the isothermal compressibility coefficient

χ = ⋅

1V

dVdP T

(3.9b)

Let us now consider the changes in the energies, and the consequential changes in temperature and density of the solvent that are associated with the three steps discussed at the beginning of this section. The results are listed in Table 3.1.

In the first step, the solvent is compressed in the pump, i.e., the change in pressure dP is positive. Under these circumstances, the exchange in thermal energy with the environment is δQ = 0, and the change in mechanical energy is δW = dH = V ⋅ dP. For this case, we can derive the temperature change in the pump from Equation 3.8, and we obtain:

dTT

cdPT

p

= ⋅αρ

(3.10)

ρ is the density, and cp is the specific heat capacity, i.e., per gram of solvent. The result shown in Equation 3.10 is also listed in column 1 of Table 3.1. The change in density for this pressure change, which includes the temperature change, is shown in the last row of column 1.

Next, as shown in column 2, the temperature change from the compression is negated by transfer of the heat to the local surroundings in the instrument, i.e., the pump heads, the connection tubing, and the injector, which again affects the density. However, the pressure remains constant (dP = 0), and dH = δQ = Cp ⋅ dT.

Finally, in column 3, the changes in the column itself are shown (under adiabatic conditions). Please note first that the pressure change dP in row 1 is negative. Also, the enthalpy change in the column is dH = 0, and as a consequence, the change in thermal energy must be equal to the change in mechanical energy, i.e.,

δ δQ W V dP= − = − ⋅ (3.11)

table 3.1Changes in pressure, temperature, and density in the three steps that the solvent experiences in the Chromatography Instrument

(1) pressurization (2) loss of heat (3) heat generation

Where: Pump Pump and tubing Column

dP: > 0 0 < 0

dT =αρ

T

p

Tc

dP⋅ –dTα

ρT

p

Tc

dP− ⋅1

dρ = ρχ α−

⋅T

p

Tc

dP2

− ⋅ραT dT ρχ α α− −

⋅T T

p

Tc

dP2

84534.indb 108 11/5/09 12:26:47 PM


Consequently we obtain from Equations 3.8 and 3.11:

dTTc

dPT

p

= − ⋅αρ

1 (3.12)

This is the true temperature change observed for an adiabatic column at the column outlet. Note that the temperature change over the column is reduced by the exact same factor as the temperature increase in the pump from solvent compression, which is lost in the system. The same results have been reported by Martin and Guiochon [21]. A hypothetical completely adiabatic system from pump to column outlet would yield the temperature increase originally postulated by Halász [7], i.e., a complete conversion of the mechanical energy created at the pump into thermal energy at the column outlet. Finally, the last column and last row of Table 3.1 shows the associated change in solvent density over the column.

It is now worth examining the magnitude of the changes in temperature that might be observed at the column outlet. One needs to realize that several of the parameters that require integration are themselves a weak function of the temperature and the pressure. The following estimates are based on the simplifying assumption that the coefficients αT and χ as well as the specific heat capacity cp do not vary much over the temperature and pressure ranges of interest. However, for water, we made two estimates, for room temperature and 40°C.

The temperature change at compression to 1000 bar is 22°C for acetonitrile, 15°C for methanol, and only about 2°C for water. The differences are due to the differ-ence in αT shown in Figure 3.5 and Table 3.3. The thermal expansion coefficient of water is about 10 times lower than that for the other solvents at room temperature. This temperature change created from the pressurization of the solvent is lost in the pump, the injector, and the associated tubing. The temperature change from fric-tional heating in the column is 34°C for acetonitrile, 30°C for methanol, and 21°C for water. The two values for water at 20°C and at 40°C are nearly identical. For

Thermal expansion coefficient of water

0.00070.0008

0.00050.0006

0.00030.0004

0.00010.0002

–0.00010

0 10 20 30 40 50 60 70 80 90 100Temperature (°C)

α

fIgure 3.5 Thermal expansion coefficient αT of water as a function of the temperature (at atmospheric pressure).

84534.indb 109 11/5/09 12:26:48 PM


mixtures of water and the organic solvents, intermediate values can be expected for the temperature increases.

The figures reported in Table 3.2 are in rough agreement with the estimations made by Gritti and Guiochon in reference [22]. The same authors have also reported a mea-sured temperature change of 17.7 degrees for a non-adiabatic column exposed to ambient air together with a complete analysis of this more complex scenario [23]. Thus, the values shown in Table 3.2 for a completely adiabatic column are in line with the reported data.

Finally, it is worthwhile exploring the estimates on thermal effects given by Halász in 1975 [7]. Halász calculated the thermal effects for the case of incom-pressible fluids, i.e., for the case where αT = 0 in Equation 3.12. However, the true temperature increase for compressible fluids is lower by the factor αTT, and the mag-nitude of α is very important for all fluids. Table 3.3 contains a listing for solvents commonly used in HPLC, and Figure 3.3 shows the value of αT for water as a func-tion of temperature. As can be seen, the thermal expansion coefficient αT changes significantly with temperature for water, while it is reported to be rather constant for most solvents. Additional information is available in the literature. Changes in density with temperature and pressure have been reported for the methanol–water system in reference [25] up to 400 bar. In reference [26], the changes in the partial molar volume, the expansion coefficient, and the isothermal compressibility have been reported for methanol–water mixtures for pressures up to 2800 bar. Recently, tables for the thermal expansion coefficient αT as well as the isothermal compress-ibility coefficient χ for water–acetonitrile and water–methanol mixtures have been published for temperatures between 20 to 100°C and for pressures to 1000 bar [27],

table 3.2Changes in temperature and pressure for Compression and decompression for several solvents in the Case of an adiabatic Column

start CompressionCompression and Cooling

decompression and friction

p [bar] 1 1000 1000 1

acetonitrileT [°K] 296 318 296 330

ρ [g/mL] 0.777 0.832 0.855 0.734

methanolT [°K] 296 311 296 326

ρ [g/mL] 0.785 0.856 0.869 0.750

water 20°C

T [°K] 296 298 296 317

ρ [g/mL] 0.998 1.037 1.038 0.987

water 40°CT [°K] 313 315 313 334

ρ [g/mL] 0.990 1.031 1.032 0.981

84534.indb 110 11/5/09 12:26:48 PM


i.e., in the range of interest of current UPLC applications. Due to the current efforts in many laboratories around the world, further refinements of the estimates made above, as well as temperature measurements for the entire range of solvent composi-tions used in reversed-phase liquid chromatography are expected in the future.

The thermal effects discussed in this section affect column performance and selectivity. In addition, pressure itself also affects both parameters. We will first discuss the influence of pressure and temperature on retention, and then proceed to the more complex issue of column performance.

3.4 pressure and thermal effeCts on retentIon

Frictional heating of the mobile phase—caused by the pressure drop over the column—results in an increase in temperature from the column inlet to the outlet. This temperature change is not completely linear, since the viscosity of the mobile phase decreases with decreasing pressure and increasing temperature. Another, albeit smaller, effect is the change in density, as the temperature increases and the mobile phase expands due to the reduction in pressure. However, the change in viscosity over the length of the column also leads to a non-linear decrease in pressure over the length of the column at constant mass flux—and mass flux must remain constant. Figure 3.6 illustrates these effects for the three pure solvents acetonitrile, methanol, and water at column inlet pressures close to 1000 bar for a completely adiabatic bed, i.e., without transfer of thermal energy through the wall of the column. The data were obtained with a computer model using the COMSOL software (COMSOL Multiphysics®, COMSOL Group) that permits a complete modeling of the entire column, including the wall region and the external thermal environment [29]. Such a model needs to incorporate the pressure-induced changes in temperature, den-sity, heat capacity, compressibility; and also, ultimately—for deriving performance

table 3.3thermal expansion Coefficients of several solvents that are used in reversed-phase Chromatography (at atmospheric pressure and room temperature)

solvent αT

Acetonitrile 0.00137

Methanol 0.0012

Ethanol 0.0011

Propanol 0.00096

i-Propanol 0.00107

THF 0.00113

Source: Riddick, J. A. and Bunger, W. B., Organic Solvents, Physical Properties and Methods of Purification, Wiley-Interscience, New York, 1970.

84534.indb 111 11/5/09 12:26:49 PM


data—the changes in the diffusion coefficients of the analytes over the length and the radius of the column.

We see that neither the temperature profiles nor the pressure profiles are linear, and that their details depend on the solvent properties. First, the overall changes in tem-perature are in agreement with the estimations shown in Table 3.2. The details of the temperature profile depend on the exact thermal environment of the column. We have shown here a case where the column itself is in an adiabatic environment. Second, the pressure profiles also depart from linearity. The reason for this is the higher viscosity of the solvent at the column inlet, due to the combined effect of the high pressure and the lower temperature at the column inlet. As the solvent moves through the column, the viscosity decreases, and this is the cause for the curved relationship of pressure over

335(a)

(b)

330

320

325

315

305

310

Tem

pera

ture

(°K

)

300

295–2 0 2 4 6 8 10 12

z-Position (cm)

1000

800

600

400Pres

sure

(bar

)

200

0–2 0 2 4 6 8 10 12

z-Position (cm)

AcetonitrileMethanolWater

AcetonitrileMethanolWater

fIgure 3.6 Temperature (a) and pressure (b) profiles for a completely adiabatic column at a pressure of 1000 bar. The column extends from z = 0 to z = 10 cm. The values at z < 0 and at z > 10 cm correspond to the frits and the connection tubing. The dashed-dotted line in 3.6b is a straight line as an aid to visualizing the departure from linearity.

84534.indb 112 11/5/09 12:26:49 PM


the column length (Figure 3.6b). Similar simulated plots, without the consideration of the influence of the endfittings, can be found in reference [30].

Radial differences in temperature do not exist in a completely adiabatic bed. Also, in a real column made out of steel with large endfittings, the models show that radial differences in temperature and thus viscosity and velocity are rather small if the column is in an adiabatic environment. Actual measurements are difficult to implement, but data obtained for the column wall temperature and the temperature of the solvent exiting the column are in reasonable, but as yet imperfect, agreement with the simpler models used by Gritti and Guiochon [30]. However, such radial temperature differences would have an impact on column performance and they will be discussed below for the case of an isothermal column.

Both these changes in temperature and pressure lead to changes in retention from the column inlet to the column outlet. In most chromatographic techniques, an increase in temperature leads to a decrease in retention, via the van’t Hoff equation:

ln ( ) ln ( )kH

RTSR

= − + +∆ ∆0 0

β (3.13)

where k is the retention factor, ΔH0 and ΔS0 are the enthalpy and the entropy of adsorption, R is the universal gas constant, and β is the phase ratio of the column. While this decrease in retention is the most common event, more complex scenarios can arise, if multiple equilibria play a role. For example, if the pKa of the analyte and of the mobile phase buffer are not too different from each other, a change in tem-perature can result in a change in the ionization of the analyte, which complicates the dependence of retention on temperature [31].

Changes in retention with temperature have also been used to optimize the selec-tivity of a separation [32–40]. Thus there is the concern that, due to the variable mobile phase temperature, separations developed in HPLC would not translate well into UPLC separations and vice versa. However, due to the averaging of the retention from column inlet to outlet, changes in selectivity remain moderate when compar-ing separations obtained on columns with different particle sizes. Furthermore, if changes were to occur, they certainly could be accommodated with a small adjust-ment in the overall operating temperature. The good transfer of many methods from UPLC to HPLC demonstrates that the pressure induced temperature gradients are not a significant issue in practice [41,42]. However, we need to keep in mind that such effects do exist, in order to be able to take action, if needed.

In the same context, we can ask ourselves the question: could these changes in retention be avoided by actively thermostating the column? Unfortunately, the answer is not positive. Heat is generated everywhere in the packed bed, while the stainless steel wall is an excellent medium for heat transfer. As we put the column into a water bath or related means of active temperature control, we cre-ate a strong radial temperature gradient between the center of the UPLC column and the region close to the wall that is rather consistent over most of the column length (Figure 3.7.a). The consequence is a difference of the migration velocity between the column center and the column wall (Figure 3.7b), which results in a significant loss in column performance, especially for retained analytes. On

84534.indb 113 11/5/09 12:26:50 PM


Temperature (K)(a)

(b)

298

297.8

297.6

297.4

297.2

297

296.8

296.6

296.4

296.2

2960 0.5 1 1.5 2 2.5 3.53 4.54 5×10–3

×10–3

×10–3

Radial position

Radial position

Velocity (m/s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

3.65

3.6

3.55

3.5

3.45

3.35

3.4

Inlet_of_bedCenter_of_bedOutlet_of_bed

Inlet_of_bedCenter_of_bedOutlet_of_bed

fIgure 3.7 Radial profiles of temperature (a) and superficial velocity (b) in a UPLC col-umn operated isothermally at 1000 bar in water, with three different curves corresponding to different axial locations. The radial temperature profile covers the particulate bed and the stainless steel column wall. The velocity profile extends through the bed only.

84534.indb 114 11/5/09 12:26:51 PM


one hand, the viscosity is lower in the center, resulting in a faster mobile phase velocity in the center. On the other, the retention factor is lower in the center of the bed, which further aggravates the difference in migration speed between wall and center. The deterioration in column performance has been verified experimen-tally also by Pat Sandra [43]. Unless the column diameter becomes very small, a control of the column temperature via a uniform wall temperature is not a good idea. However, the ratio of surface to volume increases with decreasing diameter, enabling an increased amount of the heat generated to be transferred out of the system, while the decreasing path length also increases the heat transfer. Both events combine, and the thermal problem decreases therefore with the square of the column radius for isothermal conditions. For very small diameter columns, the radial temperature difference is therefore also very small, and this was the key enabling technology for the initial studies by Jorgenson on ultra-high pressure chromatography [9].

Pressure itself also affects retention [21,44–52]; however, many studies reported the combination of pressure effects with thermal effects. For reversed-phase sepa-rations, there is an increase in retention with pressure [21]. The effect is larger for larger molecules [21,52]. For small, purely hydrophobic molecules, the increase in retention is almost negligible to 1000 bar [44]. While the combination of pressure effects and thermal effects are readily observable, it is necessary to take special precautions to observe the influence of pressure alone [45,46]. For example, in the study by McCalley and coworkers [44], the pressure was increased by putting a 30 µm capillary with negligible volume behind a short column packed with large 5 µm particles. This permitted the study of pure pressure effects on retention in the absence of thermal effects.

The observed changes in retention ∂ln(k) due to pressure P are commonly associ-ated with a change in the molar volume of the analyte between the stationary phase and the mobile phase ΔV:

∂

∂

= − + ∂∂

ln ( ) ln ( )kP

VRT PT T

∆ β (3.14)

where β is the phase ratio. In cases of sufficiently large changes, and negligible changes in the stationary phase volume itself, indeed linear changes were observed [44,47,48,51]. At higher pressures, one can directly measure the changes in the sta-tionary phase volume [44] and apply corrections.

Since retention increases roughly with the molar volume of the analyte, resolution between analytes of different molecular weight changes with pressure. If the analyte with the larger volume already has the higher retention at low pressure, the rela-tive retention α will increase with pressure. For example, the retention of toluene changes more than the retention of benzene, and the retention of phenylpropanol changes more than either one. Thus the resolution between benzene and toluene increases with pressure. Since phenylpropanol is retained less than benzene, its larger change in retention with increasing pressure compared to benzene leads to a loss in resolution between benzene and phenylpropanol at higher pressure.

84534.indb 115 11/5/09 12:26:52 PM


Table 3.4 gives the changes in volume ΔΔV = ΔV2 – ΔV1 for several substituted benzenes and pyridine (ΔV2) relative to the change for benzene, ΔV1. These data were derived following Equation 3.14 for two different analytes:

ln ( ) ln ln (,

,

α ≡

=

− ∆kk

k

k2

1

2

1

ref

ref

VV VP

2 1− ∆ ⋅) RT

(3.15)

The volume change is—as expected—larger for toluene than for benzene, result-ing in a ΔΔV value of 1.5 [mL/mol]. The difference is about the same for nitroben-zene, and just a bit smaller for acetophenone, 1.3 [mL/mol]. The relative change for pyridine compared to benzene was expected to be around 0, based purely on the molecular weights of benzene and pyridine. Also, the change for phenylpropanol is larger than expected from the molecular weight difference. Both observations can be explained by the fact that the observed volume changes reflect the transition from the mobile phase into the stationary phase, for which one needs to include the hydra-tion of polar functions such as the nitrogen in pyridine and the alcohol function in phenylpropanol.

Ionized analytes were observed to change retention much more than neutral mol-ecules [44]. This is seen in Table 3.5, where the retention changes (normalized to a pressure change of 500 bar) are compared for neutral, basic, and acidic analytes. Of course, the changes are expected to increase with molecular weight. However, they are much larger for the analytes in the ionized form compared to the neutral analytes. The degree of retention change also depends strongly on structural characteristics of the analytes, as can be seen from the behavior of the tricyclic antidepressants com-pared to propranolol and diphenhydramine: the molecular weight of all basic ana-lytes differs very little. It is believed that all these effects are due to the characteristic solvation of the analyte, especially to the hydration of the ionizable group.

table 3.4differences in the volume Changes for substituted benzenes relative to benzene for the transition from the mobile phase into the stationary phase

analyte pair ΔΔV [ml/mol]

Aniline/Benzene – 0.7

Toluene/Benzene – 1.5

Acetophenone/Benzene – 1.3

Nitrobenzene/Benzene – 1.5

Pyridine/Benzene – 1.5

Phenylpropanol/Benzene – 4.4

Source: Fallas, M. M., Neue, U. D., Hadley, M. R., and McCalley, D. V., J. Chromatogr. A, 1209, 195, 2008.

84534.indb 116 11/5/09 12:26:52 PM


Both thermal and pressure effects on retention have been known for a long time [45,48]. The phenomena exist already in normal HPLC, which operates up to pres-sures of 400 bar. In UPLC, which operates to 1000 bar, the effects are roughly 2.5 times larger, and may become more obvious. On the other hand, pressure increases the retention, while the pressure-induced temperature increase decreases retention [46]. Both effects appear to cancel each other in most applications, and thus the influence of very high pressures on peak spacing has not caused any problems in practice. In the next paragraph, we are examining the influence of pressure and temperature on column performance.

3.5 effeCt of pressure and temperature on Column performanCe

Inside the column, the pressure decreases from the column inlet to the column out-let. Due to frictional heating, the temperature increases from the inlet to the outlet. As a consequence of both, the viscosity of the solvent is high at the column inlet, and lower at the column outlet. The change in viscosity with pressure has recently

table 3.5Changes in retention with pressure for Ionizable analytes in their Ionic form Compared to neutral hydrophobic analytes

analyte % Change in k per 500 bar

Neutrals (in MeCN/H2O 40:60 for Toluene and MeCN/H2O 70:30 for the others)

Benzene 2.4%

Toluene 5.3%

Anthracene 12.2%

Pyrene 15.6%

Bases (MeCN/Phosphate Buffer wwpH 2.7 30:70)Propranolol 35.3%

Diphenhydramine 34.7%

Protriptyline 50.0%

Nortriptyline 50.8%

Amitriptyline 50.6%

Acids (MeCN/Phosphate Buffer wwpH 2.7 20:80)Benzene Sulfonic Acid 23.5%

p-Xylene-2-Sulfonic Acid 29.2%

2-Naphthalene Sulfonic Acid 33.7%

Source: Fallas, M. M., Neue, U. D., Hadley, M. R., and McCalley, D. V., J. Chromatogr. A, 1209, 195, 2008.

84534.indb 117 11/5/09 12:26:52 PM


been studied by Jorgenson and coworkers [54]. In turn, as the viscosity increases, the diffusion coefficient decreases. Since the diffusion coefficient of the analyte is important for the performance of the column, we end up with a change in the incre-mental contributions to the height equivalent to the theoretical plate from column inlet to column outlet [24].

The effect of both pressure and temperature on the viscosity η can be described by the following equation:

η η θ= ⋅ + ⋅ ⋅ − ⋅ −0 1 0( ) ( )b P e T T (3.16)

where η0 is the viscosity under reference conditions (room temperature and atmospheric pressure), and b and θ are constants. The diffusion coefficient can be estimated from the viscosity dependence using the Wilke–Chang equation [16] or the Scheibel equation [17] (see above), which results in:

DD

TT

eb P

m

m

T T

,

( )

( )0 0

0

1= ⋅

+ ⋅

⋅ −θ (3.17)

In order to estimate this influence on the HETP, we need to define the local HETP inside the column:

HddL

A d B Dk

uC

d

Dup m

p

m

= = ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅σ δ2 21 (3.18)

A, B, and C are the coefficients of the van Deemter equation, and u is the linear velocity. δ is the ratio of the diffusion coefficient in the stationary phase to that in the mobile phase. We can integrate over the length of the column to obtain the total variance at the column outlet:

σ δ2

0 0

21= ⋅ ⋅ + ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅∫ ∫d A dLBu

k D dL d u C kp

L

m

L

p( ) ( )) ⋅ ⋅∫ 1

0D

dLm

L

(3.19)

While we have discussed the changes in the retention factor with pressure and tem-perature in the previous section, we will focus here on the changes in efficiency caused by pressure-induced and temperature-dependent changes of the diffusion coefficient only. After appropriate substitution and simplification, the integration of Equation 3.19 results in the following expression for the reduced theoretical plate height h as a function of both pressure and temperature [24]:

h AB

k C ke= + ⋅ + ⋅ + ⋅ ⋅ + ⋅ −

⋅νδ ν τ

τ π

π( ) ( )

ln( ) ( )1

1 1 (3.20)

84534.indb 118 11/5/09 12:26:54 PM


where ν is the reduced velocity, and the temperature-dependent variable τ and the pressure-dependent variable π are defined as

τ θα

ρ= ⋅ ⋅

− ⋅( )⋅

⋅mT

cPT

v

1 0 (3.21a)

π = ⋅b P (3.21b)

where m is a constant with a value of 1.325. Of course, the temperature increase is caused by the pressure drop P, which in turn is proportional to the linear velocity via the Kozeny–Carman equation, here expressed with the nominal viscosity η0 at room temperature and atmospheric pressure:

Pd

u Li

i

T

p

= ⋅ − ⋅ ⋅ ⋅ ⋅1801 2

3 2 0( )ε

εε η (3.22)

εi and εt are the interstitial and the total porosity, respectively.The influence of this variation of pressure and temperature are shown in

Figure 3.8. Figure 3.8a shows the effect of pressure alone and Figure 3.8b the effect of temperature alone. The solid line in both plots is for the van Deemter curve with-out either influence.

It is interesting to observe that the influence of pressure alone would deteriorate the column performance. On the other hand, the increase in temperature increases the column performance, especially at higher velocity. The combination of both effects is shown for three solvents in Figure 3.9, as a function of pressure. The effect is small for acetonitrile and methanol, but does result in a curvature of the van Deemter curve at elevated pressure. For water, the effect of pressure on the C-term is beneficial at all pressures, due to the small compressibility of water compared to the organic solvents.

One complication, though, arises from the change in retention over the length of the column. The retention factor also changes from the column inlet to the column outlet. As pointed out above, the increase in pressure increases the retention. At the column outlet however, the retention is reduced due to the increase in temperature. This double gradient may result in only small overall changes in retention, which is good for the practice of chromatography. However, it makes it practically impossible to properly measure the column performance: the gradients inside the column do not permit the estimation of the true migration velocity at the column outlet from the recorded chromatogram, which is a prerequisite for the calculation of the band width in length units inside the column and thus the theoretical plate height. This is similar to the situation in gradient chromatography.

However, the assessment of true column performance under these complicating conditions does not escape attempts toward quantitative modeling. The advantage of a model is that true plate counts can be determined, whereas actual measurements are problematic (see above). An example of such a modeling is shown in Figure 3.10.

84534.indb 119 11/5/09 12:26:55 PM


The graph compares the performance of stainless steel columns of different lengths with a realistic design (i.e., including bulky endfittings) packed with 1.7 μm particles up to a pressure of 2000 bar under adiabatic conditions for a molecule with a diffusion coefficient of 2.10−5 cm2/sec and acetonitrile as the mobile phase (which translates roughly to an analyte molecular weight around 500). At the same limiting pres-sure, the overall temperature increase of the mobile phase is approximately the same under adiabatic conditions, independent of the column length. However, the overall impact of this temperature profile is a slight improvement in column performance with increasing column length. Considering that currently existing instruments only reach 1000 bar, one can see that the impact of pressure on the column performance remains small for a completely adiabatic column. Note that the conditions were chosen specifically to demonstrate the expected effects.

12(a)

(b)

10

8

4

6

2

Redu

ced

plat

e he

ight

hRe

duce

d pl

ate

heig

ht h

00 5 10 15 20 25 30 35 40 45 50

Reduced velocity v

0 5 10 15 20 25 30 35 40 45 50Reduced velocity v

8

7

5

6

3

4

1

2

0

fIgure 3.8 Pressure-induced influences on van Deemter curves, (a) Pure pressure effects and (b) Effects caused by frictional heating. The solid line is the van Deemter curve without pressure effects and thermal effects. The dashed and dotted lines show the increasing depar-tures from the original van Deemter curve with increasing pressure effects (a) and increasing thermal effects (b). The arrows show the directions of the increase in the pressure effect (a) and the thermal effect (b). (From Neue, U. D. and Kele, M., J. Chromatogr. A, 1149, 236, 2007. With permission from Elsevier.)

84534.indb 120 11/5/09 12:26:56 PM


Our more recent modeling studies demonstrate that column efficiency is barely affected at pressures below 1000 bar on columns packed with 1.7 μm particles under adiabatic conditions or with a mild heat transfer to the surrounding environment, equivalent to the immersion of a column into still air in a closed compartment. We also modeled various other thermal environments, such as a moderate air flow. In all these cases, the departure from the adiabatic temperature profile had only a small influence on the true column performance.

Other authors have made similar attempts. We need to keep in mind that most stud-ies currently available put the column into a fixed environment, such as immersion

1.200

1.400

0.800

1.000

0.600

0.200

0.400

C-t

erm

pre

ssur

e fu

nctio

n

0.0000 200 400 600 800 1000 1200 1400 1600 1800 2000

Pressure (bar)

fIgure 3.9 Combined effect of pressure and frictional heating on the mass transfer term of the van Deemter equation. Solid line: water; dashed line: methanol; dashed-dotted line: acetonitrile. The solid line in the center represents the pressure limit of 1000 bar of current UPLC instrumentation. (From Neue, U. D. and Kele, M., J. Chromatogr. A, 1149, 236, 2007. With permission from Elsevier.)

18

16

12

145 cm

8

10

H (µ

m)

15 cm

10 cm

4

6

0

2

0 1 2 3 4 5u (cm/sec)

fIgure 3.10 Modeled data of theoretical plate height versus linear velocity for 1.7 μm particles packed into three column lengths: 5 cm, 10 cm, and 15 cm. Pressures to 2000 bar.

84534.indb 121 11/5/09 12:26:57 PM


into the laboratory air [23,53], or a water bath [43]. Neither are the recommended environment, and this impacts relevance and generality of the reported results.

3.6 applICatIons

Despite the principal complications from the thermal effects caused by high pressure and the pure pressure effects, practical UPLC applications are largely unaffected. The reason for this is that the detrimental and beneficial effects of pressure and temperature cancel each other for the most part, at least for the pressure range of cur-rent UPLC instrumentation. Increased pressure increases retention, but the pressure-induced increase in temperature reduces retention. A similar effect is active with respect to column performance: the slower diffusion at the column inlet due to the increase in viscosity is compensated by the faster diffusion at the column outlet due to the increase in temperature. The consequence of the mutual cancellations of the different effects is that method development and method execution in UPLC appli-cations proceed in the same way as in HPLC, but much faster due to the improved performance per unit time achievable with UPLC columns (see Section 3.2 “The Promise of Small Particles”).

In the following, this will be demonstrated for a few different application areas. The first is the achievement of very fast separations, with run times under one min-ute. The second example proves that a very high separation performance is possible in a reasonable analysis time. Then we examine an important application example, the analysis of physiological amino acids. This is followed by a few application examples out of the biotechnology world: the separations of peptides, proteins, and oligonucleotides; these all benefit from the reduced diffusion path due the smaller particle size, which is important for all molecules of a larger molecular weight.

3.6.1 hiGher Speed

The scaling of a chromatographic separation has been demonstrated in Section 3.2. If we are interested exclusively in very fast gradient separations, short columns should be used at high flow rates [12,13]. For a constant ratio of column length to particle size, the speed of a separation increases at equal performance with a reduction in particle size. Examples of such transitions are separations scaled from a 5 cm 3 μm column to a 3 cm 1.7 μm column or from a 3 cm 2.5 μm column to a 2 cm 1.7 μm column. True high-speed separations can be accomplished, both with isocratic separations and with gradient separations [55]. Application problems that use such high-speed separations are, for example, generic cleaning validation methods, which require good resolution of multiple potential contaminants in a short period of time [56]. A rapid gradient separation in less than one minute is shown in Figure 3.11. The gradient run time was 0.5 minutes. The good resolution between all peaks was obtained by running this separation at a high flow rate, 1.5 mL/min. We have previously shown the benefits of operating at a high linear velocity for maximizing resolution in a fixed analysis time [12,57], and this example demonstrates this effect again.

The key principle features that enable such rapid separations are a small particle size combined with a short column [58,59]. These rapid separations are carried out

84534.indb 122 11/5/09 12:26:57 PM


0.60

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fIgure 3.11 Fast gradient separation of standards on an ACQUITY UPLC BEH C18 2.1 × 20 mm, 1.7 µm column. Conditions: mobile phase (a) 10 mM CH3COO- NH4

+, pH 5; mobile phase (b) 90:10 acetonitrile:H2O with 10 mM CH3COO- NH4

+, pH 5; linear gradient from 95:5 to 5:95 over 0.5 minutes; flow rate: 1.5 mL/min; temperature: 30°C. Analytes: 1. lidocaine, 2. prednisolone, 3. naproxen, 4. amitriptyline, 5. ibuprofen. (Reprinted from Neue, U. D., Grumbach, E. S., Kele, M., and Mazzeo, J. R., Ultra-Performance Liquid Chromatography, in HPLC Made to Measure: A Practical Handbook for Optimization, Wiley-VCH, Weinheim, 2006, p. 417; Neue, U. D., Grumbach, E. S., Kele, M., Mazzeo, J. R., and Sievers, D., Ultra-Performance Liquid Chromatography, in HPLC richtig optimiert, Wiley-VCH, Weinheim, 2006, p. 492. With permission.)

84534.indb 123 11/5/09 12:26:58 PM


under conditions where the rapid mass transfer of the packing is the key contributor to the separation performance, and the resistance to mass transfer decreases with the square of the particle size. High velocities are needed, and the required backpres-sure is reduced by using a short column length. In order to cover a broad range of analytes, the gradient covers a wide solvent composition. The high velocity at these short gradient times maintains a flat gradient. The theory of this has been outlined earlier [12,57] and the practice has been demonstrated in reference [13].

3.6.2 hiGher performance

An important goal at the other end of the interest of chromatographers is to achieve high-powered separations in a reasonable run time. Once again, the use of very small particles is beneficial, especially when combined with high temperature. Both parameters increase the speed of analysis, and their combination results in outstand-ing separations in a reasonable run time. An example is shown in Figure 3.12 [60].

This separation was carried out at 90°C on a 15 cm column packed with 1.7 μm particles. The peak capacity was calculated by dividing the gradient time tg by the aver-age peak width w measured for multiple peaks over the chromatographic space [61]:

Pt

wcg= +1 (3.23)

Inte

nsity

Time (minutes)

05.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00

100

%

fIgure 3.12 Total ion chromatogram of rat urine obtained with a 2.1 × 150 mm, 1.7 μm Acquity BEH C18 column and a gradient over 60 minutes at 90°C at 0.8 mL/min. Gradient: 0-95% B; A = 0.1% formic acid in water, B = acetonitrile with 0.1% formic acid. (Reprinted from Plumb, R. S., Rainville, P., Smith, B. W., Johnson, K. A., Castro-Perez, J., Wilson, I. D., and Nicholson, J. K., Anal. Chem., 78, 7278, 2006. With permission from American Chemical Society.)

84534.indb 124 11/5/09 12:27:00 PM


The peak capacity estimated by the authors of [60] for the chromatogram in Figure 3.12 was 1024—a quite impressive value. Computer estimations of peak capacity for the same column and gradient at room temperature give values between 600 and 700, with the higher values obtained at a reduced flow rate, around 0.4 mL/min. A larger influence on the value of the peak capacity comes from a reduction of the particle size. An estimation of the peak capacity under the same conditions using a column packed with 3.5 micron particles results in roughly half the peak capac-ity, even if the flow rate is reduced. One can see that the impact of the choice of the smaller particle size is larger than the choice of the elevated temperature, at least for this case. Nevertheless, both parameters complement each other to achieve the result obtained.

It should be pointed out that the use of small particles serves to achieve a high peak capacity in a reasonable run time. Combined with the use of the smaller particles is the need for higher pressures, as pointed out in other parts of this paper. However, at a given pressure, very high and even higher plate counts are also achievable with larger parti-cles. The disadvantage of the use of large particles is an increase in the analysis time for equal performance, as shown for an isocratic separation in Figure 3.1. One can estimate that it is possible to obtain about one million theoretical plates in an isocratic separation with columns packed with 5 μm particles and a total length of about 12 m at 90°C with a run time of one day and a reasonable retention factor under UPLC conditions, but such an achievement is of little consequence for the practice of chromatography.

3.6.3 a complex Separation in a Short analySiS time: phySioloGical amino acidS

The high separation power per unit time provided by the use of sub-2-μm particles enables the development of complex separations that are carried out in a surprisingly short analysis time. An example is the analysis of physiological amino acids, which requires the separation of 46 peaks, including analytes derived from the derivatiza-tion reagent. An estimate of the sample peak capacity Pc

** required to accomplish such a separation can be made [57]:

Pc** ≈ n1.5 (3.24)

which translates to a peak capacity of about 310 needed for achieving the separation of 46 peaks.

A method (for research use only) was developed for this analysis. A standard mixture of physiological amino acids was derivatized off-line with 6-aminoquinolyl N-hydroxysuccinimidyl carbamate (AQC reagent). The separation of the derivatives is shown in Figure 3.13. The analysis is completed in 33 minutes with a 150 mm × 2.1 mm UPLC column packed with 1.7 μm particles. In addition, the method is very sensitive: the detection limit is 50 femtomoles using a standard UPLC TUV detector at 260 nm. The measured peak capacity for this analysis determined from the chro-matogram of the segmented gradient is 250, slightly better than the rule-of-thumb prediction of Equation 3.24.

84534.indb 125 11/5/09 12:27:00 PM


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84534.indb 126 11/5/09 12:27:01 PM


3.6.4 bioSeparationS

Biomolecules and their fragments—from proteins to peptides, from nucleotides to glycans—have one common feature: a high molecular weight. High molecular weight is associated with slow diffusion. In order to get the same separation power for these slowly diffusing analytes as we are used to for small molecules, we need to reduce the diffusion distance, and the best and compromise-free way to achieve this goal is to use a column with a small particle size.

3.6.4.1 peptidesThe analysis of complex peptide mixtures, such as protein digests, improves with the use of smaller particles. This improvement, reflecting reduced band-broadening, can be exploited in different ways depending on the application. The principle is shown in Figure 3.14, where the options for a scaling of a separation from a 25 cm 3 µm HPLC column to a 15 cm 1.7 μm UPLC column are shown (it should be pointed out that in this analysis the ratio of gradient run time to column void time remains constant; thus the retention pattern is not affected).

One strategy, demonstrated already in the example separation in Figure 3.1, is to gain analysis time while maintaining resolution. The same principle can be applied to peptide or protein separations. This is demonstrated in the horizontal line, which shows a 3-fold improvement in analysis time for the switch from the 25 cm 3 µm column to a 15 cm 1.7 μm column. An alternative strategy is to simply use the higher performance possible, at the same analysis time, as shown in the vertical line. The exact gain in separation power depends on the details of the operating conditions, but in the case shown in Figure 3.14 the benefit is substantial. Of course, one can

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84534.indb 127 11/5/09 12:27:02 PM


always choose an intermediate case, where one gains some speed together with some resolution, as the diagonal arrow demonstrates.

An example of the latter case, gain in analysis time and resolution, is shown in Figure 3.15 for a protein digest. The objective of this experiment is to reduce the run time with similar or better resolution while maintaining the relative elution posi-tion of the peptides. One can readily see the reduction in analysis time. Furthermore, in the windows a small section of the chromatogram is enlarged, demonstrating the gain in resolution. (The patterns of peaks are similar on the two columns, but they are not perfectly identical. To ensure transfer of peak identification between the two columns, the separation was monitored with ToF – MS.)

The UV chromatogram obtained at 214 nm, the total ion chromatogram, and the extracted mass chromatograms of these sections are shown in Figure 3.16. One can clearly see the improved resolution obtained in UPLC together with the fact that the peaks obtained in UPLC are narrower than those obtained with the HPLC column. Equally important, with the scaled gradient, the order of elution of the specific peptides and their relative positions are the same in HPLC and UPLC.

The resolution of peptide maps is important not only for identification of sample constituents but also for the quantitation of each component. Sensitivity and linear-ity are most often treated as properties of the detector. However, chromatographic resolution is essential for real samples where the analysis most often requires measurement of small amounts of one material in the presence of a much more abundant component. With improved resolution, the small and large peaks will be more reliably integrated. This improved resolution must not compromise the chro-matographic dynamic range. That is, there must not be a change in peak shape or retention over the intended mass loading range of the assay. This is demonstrated for a UPLC peptide map in Figure 3.17: the inset shows the detection of decreasing amounts of the peptide marked with a star, down to 0.2% of the entire mass. With the use of UPLC, this wide range of quantitation is observed with constant peak shape and retention, even where the smaller peak elutes after the major peak.

3.6.4.2 proteinsFor the separation of proteins, a larger pore size and a shorter chain length of the ligand is required. A pore size of about 300 Å does not inhibit the penetration of a typical protein into the pores of the packing. Short ligand chain lengths improve the recovery of proteins. If these criteria are met, the smaller particle size contrib-utes significantly to the resolution of protein analytes. As an example, Figure 3.18 shows the separation of IgG heavy and light chains after reduction and alkylation. One can clearly see the improvement in resolution, especially for the heavy chain protein group on the right, when using the 1.7 μm packing compared to the 3.5 μm packing. The lengths of both columns as well as the operating conditions were identical.

The improvement in separation power delivered by UPLC is not limited to small molecules, but translates to large molecules such as peptides and proteins as well. Let us next explore the subject of oligonucleotides.

84534.indb 128 11/5/09 12:27:02 PM


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84534.indb 130 11/5/09 12:27:06 PM


3.6.4.3 oligonucleotidesNucleic acids such as silencing RNA and antisense oligonucleotides are currently under investigation as a promising form of biopharmaceuticals. Typical therapeutic probes are 21 to 25 nucleotides long (molecular weight 6000–8000 Da).

Liquid chromatography has been used for the separation of oligonucleotides from their truncated sequences (termed n−1, n−2, …) for decades [62,63,64]. Because the target oligonucleotide and its shorter n−x fragments are structurally related, the chromatographic separation selectivity is rather low, regardless of the LC mode (anion exchange, size exclusion, or ion-pair reversed-phase liquid chromatography (IP RP LC).

We have explored the method of IP RP LC for advanced separation and LC MS analysis of oligonucleotides [65–67]. It has been shown that relatively short

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fIgure 3.17 A tryptic digest of bovine hemoglobin was spiked with a standard peptide mixture to represent surrogate modified peptides. The chromatogram shows the full pep-tide map of bovine hemoglobin with peptide standards spiked at 0.2-2% on a molar basis. Each injection represents 200 pmol of hemoglobin digest on-column. Panel b zooms into under 1 minute of the chromatogram. Conditions: column: Waters ACQUITY UPLC BEH C18, 2.1 × 100 mm, 1.7 μm. Mobile phase: A: 0.1% TFA in Milli-Q water B: 0.08% TFA in acetonitrile. Gradient: 0–50% B in 58 minutes at 0.2 mL/min. The inset shows that the sensitivity is adequate with decreasing amounts of the peak marked with a star down to 0.2%.

84534.indb 131 11/5/09 12:27:08 PM


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m; b

otto

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dge

BE

H30

0 C

4, 3

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m. C

ondi

tion

s: s

ampl

e co

ncen

trat

ion

0.5

mg/

mL

pre

pare

d in

0.1

% T

FA in

wat

er. M

obil

e ph

ase

A: 0

.1%

TFA

in w

ater

; mob

ile

phas

e B

: 0.1

% T

FA in

ace

toni

tril

e; g

radi

ent:

20–

55%

B o

ver

60 m

in a

t 0.2

mL

/min

; tem

pera

ture

: 80°

C.

84534.indb 132 11/5/09 12:27:08 PM


columns packed with a small particle size sorbent are best suited for fast and effi-cient separations. Naturally, the separation selectivity does not change by scaling down the sorbent particle size; the enhanced oligonucleotide separation is achieved solely due to the greater column peak capacity [67,68] which is in turn due to the higher column performance.

More recently we have proposed a theoretical model suitable for the prediction of peak capacity (or resolution) of oligonucleotides, and potentially other oligomers exhibiting a regular retention pattern (longer oligonucleotides are more retained, separation selectivity gradually decreases with the length of the chain) [69]. UPLC columns packed with 1.7 µm sorbent were shown to bring significant benefits to oligonucleotide separations in terms of resolution and speed. Baseline separation of oligonucleotide species with a chain length from 10 to 35 units has been accom-plished in under five minutes [69].

Figure 3.19 compares the performance of columns packed with 1.7 µm versus 3.5 µm for the separation of a 25–30 nt oligonucleotide ladder. The peak capacity was calculated using Equation 11 in reference [69]. The absolute peak capacity values are higher for the 1.7 µm particle size packed columns, as expected. An interesting phenomenon can be deduced from Figure 3.19. The peak capacity appears to be relatively insensitive to the column length for short gradients. A similar resolution is achieved for 10 to 150 mm columns when they are oper-ated under constant gradient time. This will be discussed in the later part of this section.

Figure 3.20 shows the separation of oligonucleotides using 2.1 × 50 mm BEH columns packed with 1.7 µm particles with a ten minute gradient. The chosen 15–35 nt oligonucleotides are representative of a typical length for a therapeutic oli-gonucleotide. Figure 3.20b shows a simulated chromatogram using a model with experimentally derived retention constants for the reversed-phase retention (the retention factor at the beginning of the gradient k0 and slope of the relationship of the retention factor with solvent composition B have been determined experimentally [69]). The moderate difference in retention of earlier peaks is caused by the gradient delay of the instrumentation, not considered in this simplified model. However, the prediction of the retention pattern matches with reasonable accuracy the experimen-tal chromatogram, and correctly represents the selectivity and resolution trends for later eluting peaks.

In the remaining discussion, we employ this model to investigate the intercon-nected effects of column length and gradient slope on peak capacity. Figure 3.21a illustrates the separation of 25–30 nt oligonucleotides using different column length and a constant gradient duration. As discussed above (Figure 3.19), the resolution appears to be similar regardless of the column length. This somewhat counterintui-tive phenomenon was described earlier for proteins [70]. The explanation is that the gains in efficiency for longer columns are undermined by the impact of the gradient slope G = ∆c t0/tg, which becomes progressively steeper for longer columns (∆c and tg are constant, t0 increases with column length).

Gains in resolution are realized when the gradient time is scaled proportionally to the column volume, as shown in Figure 3.21b. In such case the peak capacity improves with the square root of the column length, i.e., with the square root of

84534.indb 133 11/5/09 12:27:09 PM


60

(a)

(b)

40

20

14

Peak

cap

acity

Peak

cap

acity

0

68

1012

5060

24

1020

3040

Colum

n len

gth (c

m)

Gradient time (minutes)


60

40

20

14

0

68

1012

5060

24

1020

3040

Colum

n len

gth (c

m)

fIgure 3.19 (See color insert following page 248.) Representation of peak capacity for 25–30 nt oligodeoxythymidines varying gradient and column length. Peak capacity calculated from Equation 11 in reference [69] for columns packed with (a) 1.7 µm or (b) 3.5 µm sorbent. Flow rate: 0.2 mL/min, separation temperature: 60°C, gradient start: 17.5% MeOH, difference in solvent composition ∆c: 0.05. Calculated for a 15 mM TEA – 400 mM HFIP aqueous ion-pairing system. Experimental constants for the model were obtained using XBridge and ACQUITY BEH C18 packed columns.

84534.indb 134 11/5/09 12:27:10 PM


the column plate count [69]. Both Figures 3.19 and 3.21 suggest that the maximum peak capacity is achieved with the longest columns and gradients at the expense of analysis time and operational pressure. Nevertheless, due to the high efficiency of short UPLC column, a useful separation of oligonucleotides can be achieved

0 2 4 6Minutes

20 nt

(a) (b)25 nt

30 nt

35 nt 20 nt25 nt 30 nt

35 nt

8 10 0 2 4 6Minutes

8 10

fIgure 3.20 Separation of 25–30 nt oligonucleotides. (a) Experimental data. Conditions were similar to Figure 3.19; 50 × 2.1 mm, 1.7 µm BEH C18 OST column. (b) Predicted chro-matogram from theoretical model.

Minutes0 2 4 6 8 10 12 140 1 2 3 4 5 6 7

Minutes

t0

25 nt 30 nt

L=20 mmtg = 5 min

(a) (b)

L=50 mmtg = 5 min

L=100 mmtg = 5 min

L=150 mmtg = 5 min

L=20 mmtg = 2 min

L=50 mmtg = 5 min

L=100 mmtg = 10 min

L=150 mmtg = 15 min

fIgure 3.21 Simulated chromatograms of 25–30 nt. Resolution was predicted from the model. For conditions see Figure 3.19 captions. (a) Separation achieved with different col-umns (1.7 µm sorbent) at a constant gradient time. (b) Separation for constant gradient slope. Gradient time was adjusted proportionally to column volume (length).

84534.indb 135 11/5/09 12:27:12 PM


within minutes (Figure 3.20a). UPLC with mass spectrometry detection will cer-tainly find its application in the analysis of therapeutic nucleic acids and other biopolymers.

At the time of this writing close to 400 papers have been published that cover aspects of UPLC applications. It is therefore not possible to give a complete over-view. However, what we will present here is a short review of key attributes of the technique. In addition, we will focus on applications and techniques that are benefit-ing from these special features of the UPLC technique.

Peak capacity measurements as a function of flow rate gradient duration were demonstrated early on by Wren [71]. The measured curves were in agreement with the patterns predicted by Neue [72–74]. As demonstrated in Figures 3.1 and 3.12 and in many publications by UPLC users [75–86], small particles maximize the peak capacity per unit time. This results in a reduction in the analysis time compared to classical methods [75,76,86]. Veuthey and coworkers occupied themselves with the principles of the transfer of HPLC methods to UPLC, for both isocratic methods [79] and the more complicated case of gradient methods [80]. The advantage of the com-bination of UPLC with a multimode ionization source was demonstrated by Yu [81]. Fast UPLC methods are of special interests to QC departments in the pharmaceutical industry [82]. The validation of an ultra-fast UPLC-UV method for the content of antituberculosis tablets was demonstrated by Nguyen [83]. High-throughput screen-ing of active pharmaceutical ingredients by UPLC was recently investigated by Al-Sayah [84]. A high-speed solubility screening assay was reported by Yamashita [85].

Another important aspect for UPLC applications is the improved resolution for complex samples, which in turn enables or at least facilitates new analytical tech-niques. An example is the study of metabolomic profiles, now often called meta-bonomics [87–98]. Reviews of the subject were published in 2005 [87,88]. Many application examples of metabonomic analyses using UPLC techniques have been demonstrated by Wilson or Plumb and coworkers [89–100]. Reference [91] includes a clear description of the advantages of the combination of the small particle size with the increased pressure capability of the UPLC instrumentation: the sharper UPLC peaks in the complex chromatograms made them more distinct, which in turn resulted in the fact that a more information-rich data set could be extracted from the chromatograms. The sharper resolution gave a reduction in mutual ion suppres-sion in MS detection which in turn yielded a roughly 5-fold increase in the number of metabolites detectable in mouse urine. The combination of data obtained from UPLC reversed-phase separations, HPLC Hydrophilic Interaction Chromatography (HILIC) separations, and gas chromatography has been applied to the search for markers for kidney cancer in urine samples [99]. Yin et al. [100] carried out a meta-bonomics study of intestinal fistulas using UPLC-MS techniques. Both are examples of the potential impact of UPLC on metabonomic analyses.

Higher resolution is also a key benefit for the study of the metabolism of phar-maceuticals. In any complex matrix, the improvement in MS sensitivity due to the improved chromatographic resolution is a benefit [101–103]. These findings have been confirmed by many users [e.g., 104–110]. Common sample matrices are plasma

84534.indb 136 11/5/09 12:27:12 PM


or urine, but applications to other biological matrices such as hair [111] or dried blood spots [112] can be found as well.

UPLC is also used in the analysis of drugs of abuse [113,114]. The reported advan-tages are faster analysis time, and good peak shapes for basic analytes. Other appli-cation areas are food analysis and environmental analysis [115–120]. The subjects range from pesticides in baby foods [116] to aflatoxins in beer [117]. A more pleasant subject is the analysis of cocoa polyphenols in chocolate [120].

A special area of complex matrices is the analysis of Chinese medicines and related natural products [121–137]. The mechanism of action of traditional Chinese medicines is often not very well known. With the help of the combination of UPLC and mass spectrometry, it is possible to identify potential or known active ingredients even in such a difficult sample. For example, Li and coworkers [122] reported on a rapid UPLC electrospray ionization mass spectrometry (UPLC-ESI-MS) method for the qualitative and quantitative analysis of the constituents of the flower of Trollius ledibouri Reichb. They identified and quantified 15 active compounds in the etha-nol extract. Zhou and coworkers [121] identified six flavanone O-diglycosides with a UPLC-ESI-MS method in the traditional Chinese medicine Fructus aurantii (Zhi qiao). On the other hand, when the active ingredients are known, UPLC-UV is a useful tool for the quality control of Chinese medicines [e.g., 124,125,130]. One can expect that many more applications in the complex field of traditional Chinese medicine will emerge in the future.

3.7 ConClusIons

In this article we have outlined the advantages and the difficulties associated with the use of UPLC pressures (i.e., pressures up to 1000 bar) and columns packed with sub-2-μm particles. Either a very high speed with very good perfor-mance, or superb performance in a reasonable time, is achievable with this tech-nique. The technical difficulties associated with pressure-induced temperature increases inside the column have been discussed in detail, as have been the changes in selectivity caused by pressure and temperature. Furthermore, the benefits of the use of UPLC columns have been shown in many application examples, with special focus on separations involving analytes with a large molecular weight. Application areas with very complex samples such as meta-bonomics or traditional Chinese medicines benefit especially from the use of UPLC techniques.

While the difficulties first investigated in the early days of HPLC have been found and are better understood now, further improvements in speed and perfor-mance are still possible. The future of HPLC and UPLC technology continues to be bright.

lIst of symbols

A, B, C coefficients of the van Deemter equation; A = eddy dispersion term, B = diffusion term, C = mass transfer term

84534.indb 137 11/5/09 12:27:12 PM


Cp molar heat capacity at constant pressurecp specific heat capacity (per gram) at constant pressureDm molecular diffusion coefficientdp particle size∆c difference in concentration (between the beginning and the end of a

gradientΔP pressure dropΔH0 enthalpy of adsorptionΔS0 entropy of adsorptionG gradient slopeH enthalpyk retention factorL column lengthn number of analytesQ thermal energyPc peak capacityPc

** sample peak capacityR universal gas constantS entropyT temperaturet0 column dead timetg gradient durationu linear velocityumin linear velocity at the minimum of the plate-height versus velocity curveV molar volumeW mechanical energyw average peak width (4 standard deviations)α relative retentionαT thermal expansion coefficientβ phase ratio of the columnεi interstitial porosityεt total porosityδ ratio of the diffusion coefficient in the stationary phase to that in the

mobile phaseη viscosityπ normalized pressure parameterρ densityυ reduced velocityχ isothermal compressibility

aCknowledgment

This paper is dedicated to the memory of Marianna Kele, a warm-hearted and dedicated coworker, who contributed substantially to the development of UPLC technology and to our understanding of its theoretical underpinnings.

84534.indb 138 11/5/09 12:27:13 PM


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M. M. Al-Sayed, Z. Al-Hassnan, M. Al-Owain, H. Al-Zeidan, Biomed. Chromatogr. 22: 1181 (2008).

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(2006). 117. M. Ventura, D. Guillen, I. Anaya, F. Broto-Puig, J. L. Lliberia, M. Agut, L. Comellas,

Rapid Commun. Mass Spectrom. 20: 3199 (2006). 118. X. Cui, B. Shao, R. Zhao, J. Meng, X. Tu, Se Pu 24: 213 (2006). 119. X. Cui, B. Shao, R. Zhao, Y. Yang, J. Hu, X. Tu, Rapid Commun. Mass Spectrom. 20:

2355 (2007). 120. K. A. Cooper, E. Campos-Gimenez, D. Jiménez Alvarez, K. Nagy, J. L. Donovan,

G. Williamson, J. Agric. Food. Chem. 55: 2842 (2007). 121. D. Y. Zhou, Q. Xu, X. Y. Xue, F. F. Zhang, X. M. Liang, J. Pharm. Biomed. Anal. 42: 441

(2006). 122. X. Li, Z. Xiong, X. Ying, L. Cui, W. Zhu, F. Li, Anal. Chim. Acta 580: 170 (2006). 123. B. Lu, Y. Xhang, X. Wu, J. Shi, Anal. Chim. Acta 588: 50 (2007). 124. J. Guan, C. M. Lai, S. P. Li, J. Pharm. Biomed. Anal. 44: 996 (2007). 125. X. J. Chen, H. Ji, Q. W. Zhang, P. F. Tu, Y. T. Wang, B. L. Guo, S. P. Li, J. Pharm.

Biomed. Anal. 46: 226 (2007). 126. M. Liu, Y. Li, G. Chou, X. Cheng, M. Zhang, Z. Wang, J. Chromatogr. A 1157: 51

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2214 (2008). 129. G. B. Ge, H. W. Laun, Y. Y. Zhang, Y. Q. He, X. B. Liu, L. Wang, Z. T. Wang, L. Yang,

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145

4 Biointeraction Affinity Chromatography: General Principles and Recent Developments

John E. Schiel, K. S. Joseph, and David S. Hage

Contents

4.1 Introduction .................................................................................................. 1464.1.1 What Is Biointeraction Affinity Chromatography? .......................... 1464.1.2 Advantages of Biointeraction Affinity Chromatography ................. 146

4.2 Equilibrium and Thermodynamic Measurements ........................................ 1474.2.1 Zonal Elution .................................................................................... 148

4.2.1.1 General Principles .............................................................. 1494.2.1.2 Binding and Competition Studies ...................................... 1514.2.1.3 Temperature and Solvent Studies ....................................... 1534.2.1.4 Characterization of Binding Sites ...................................... 1554.2.1.5 Practical Considerations .................................................... 156

4.2.2 Frontal Analysis ................................................................................ 1584.2.2.1 General Principles .............................................................. 1584.2.2.2 Binding Studies .................................................................. 1594.2.2.3 Competition Studies ........................................................... 1614.2.2.4 Temperature and Solvent Studies ....................................... 1634.2.2.5 Practical Considerations .................................................... 164

4.3 Kinetic Measurements .................................................................................. 1644.3.1 General Principles ............................................................................ 1664.3.2 Linear Elution Methods .................................................................... 168

4.3.2.1 Plate Height Measurements ............................................... 1684.3.2.2 Peak Profiling .................................................................... 1714.3.2.3 Practical Considerations .................................................... 173

4.3.3 Non-Linear Elution Methods ............................................................ 1744.3.3.1 Non-Linear Peak Fitting .................................................... 1744.3.3.2 Frontal Analysis ................................................................. 1764.3.3.3 Split-Peak Method .............................................................. 1784.3.3.4 Peak Decay Method ........................................................... 1814.3.3.5 Combined Assay Methods ................................................. 1834.3.3.6 Practical Considerations .................................................... 183

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4.1 IntroduCtIon

4.1.1 what IS biointeraction affinity chromatoGraphy?

Affinity chromatography has been used for decades as a selective means for the purification and analysis of chemicals in biological systems (Hage and Ruhn 2006; Hage 2006; Turkova 1978; Scouten 1981; Parikh and Cuatrecasas 1985; Walters 1985). The method can be defined as a type of liquid chromatography in which a biologically-related agent is used as the stationary phase (Ettre 1993; Hage and Ruhn 2006). This biologically-related agent, referred to as the affinity ligand, can consist of an immobilized sequence of DNA or RNA, a protein or enzyme, a biomimetic dye, an enzyme substrate or inhibitor, or a small target molecule, among others (Hage 2006). Many affinity separations have been conducted using low-performance sup-ports such as agarose or polyacrylamide (Gustavsson and Larsson 2006). However, HPLC media such as silica or monolithic supports can also be used as the support material in affinity separations, resulting in a technique that is known as high perfor-mance affinity chromatography (HPAC) (Hage 2002; Schiel et al. 2006; Gustavsson and Larsson 2006; Mallik 2006; Hage 2006).

Affinity chromatography is commonly used for the separation, purification, and analysis of agents that can bind to the given immobilized ligand, making this method an important tool in modern biochemistry and chemical analysis (Hage and Ruhn 2006; Turkova 1978; Scouten 1981; Parikh and Cuatrecasas 1985; Walters 1985). However, affinity chromatography and HPAC can also be employed as tools to study biological interactions. The use of affinity chromatography for this purpose has been called quantitative affinity chromatography, analytical affinity chromatography, or biointeraction affinity chromatography (Chaiken 1987; Hage 1998; Hage and Tweed 1997; Winzor 2006; Hage and Chen 2006). This review will describe the general principles of this technique and will examine recent developments and applications in this field. The focus of this review will be on work that has been conducted using HPAC, but many of the principles that will be discussed also apply to past studies that have used more traditional low-performance supports.

4.1.2 advantaGeS of biointeraction affinity chromatoGraphy

There are a number of advantages to utilizing affinity chromatography for studying biological interactions. For instance, the immobilized ligand in an affinity column can often be used for a large number of sample injections. This feature helps to pro-vide optimum run-to-run precision and minimizes batch-to-batch variations in the experiments because the same preparation of ligand is used for multiple studies. The same feature reduces the total amount of ligand that is needed for the experiments and lowers the cost when expensive ligands such as monoclonal antibodies or cell

4.4 Conclusions ................................................................................................... 184Acknowledgments .................................................................................................. 185Abbreviations ......................................................................................................... 185References .............................................................................................................. 187

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Biointeraction Affinity Chromatography 147

receptors are used. In addition, biointeraction studies that are conducted by using HPAC can be easily automated and used as the basis for relatively high-throughput measurements (Hage and Chen 2006).

The proper use of affinity chromatography does require that careful attention be given to the nature of the affinity ligand and the way in which this ligand is used to study a biological interaction. There are two general formats for the ligand by which the interaction between this ligand and a target can be examined. The first approach uses a soluble ligand and an immobilized analog of the desired target, which can be used indirectly to examine binding by the ligand to a soluble form of the target. Although this technique is appealing from a theoretical point of view for use with soluble ligands, it does require that care be taken in choosing the proper immobiliza-tion method and linker size to attach the target analog, in order to get a stationary phase that has good binding to the desired soluble ligand. In addition, possible exclu-sion effects and restriction to diffusion must be considered when a large ligand such as a protein is being used as the injected analyte.

A more common approach used in biointeraction chromatography is to immobi-lize a large ligand and to examine its binding to a small applied solute. This tech-nique is typically utilized with ligands that are proteins and is particularly useful if the ligand occurs in a non-soluble form (e.g., as part of a membrane). It is necessary in this format to immobilize the ligand in a manner that does not significantly alter its ability to interact with the injected analyte. Fortunately, it is often possible to address this issue through the correct selection of immobilization conditions. As an example, it is known that affinity columns that contain highly cross-linked albu-min or α1-acid glycoprotein columns (AGP) can show significant deviations from the behavior expected for these ligands in solution (Allenmark 1991; Jewell et al. 1989; Schill et al. 1986). However, a number of milder immobilization methods have been used with both human serum albumin (HSA) and bovine serum albumin (BSA) to provide good agreement with the drug binding behavior seen for soluble HSA or BSA (Domenici, Bertucci, Salvadori, Felix et al. 1990; Domenici, Bertucci, Salvadori, Motellier et al. 1990; Domenici et al. 1991; Loun and Hage 1992, 1994; Loun and Hage 1996; Miller and Smail 1977; Noctor, Pham et al. 1992; Noctor, Wainer et al. 1992; Sengupta and Hage 1999; Yang and Hage 1997; Yang and Hage 1996); this result has been explained through recent proteomic studies of immobi-lized HSA (Wa et al. 2006). AGP can similarly be immobilized in a form that mim-ics the activity of soluble AGP through the use of mild oxidation of this glycoprotein and its coupling with a hydrazide-activated support (Xuan and Hage 2005). Another alternative to covalent immobilization is to physically entrap the ligand in the sup-port material, as has been used with sol gels and agarose in recent work conducted with proteins, enzymes, liposomes, and cells (Kim and Hage 2006).

4.2 equIlIbrIum and thermodynamIC measurements

The most common application of affinity chromatography and HPAC in the study of biological interactions is the use of this tool to examine the binding equilibrium and thermodynamics of a solute–ligand interaction. This is generally performed in one of two formats: zonal elution or frontal analysis (see Figures 4.1 and 4.2).

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Zonal elution involves the injection of a small band of solute on the affinity column, while frontal analysis involves the continuous application of a solution that con-tains the analyte. More details on each of these approaches are provided in the following sections.

4.2.1 Zonal elution

Zonal elution is currently the most common way in which binding studies are conducted through the use of affinity chromatography (Hage 2002). Zonal chromatog-raphy is typically used in affinity chromatography and in HPLC to separate compounds by injecting a small plug of sample onto a column. However, this method can also be used to obtain information on the binding equilibria and thermodynamic properties of the analyte as it interacts with the stationary phase (i.e., the immobilized ligand in the case of an affinity column). This type of experiment is usually performed under linear elution conditions (i.e., concentration independent conditions) to simplify the analysis (Hage and Chen 2006); although it has been suggested that work under non-linear con-ditions can also be employed (Vidal-Madjar et al. 1988; Arnold et al. 1986).

The first reported use of zonal elution for thermodynamic studies in affinity chromatography was in 1974 when a low-performance Sepharose column contain-ing thymidine-5′-phosphate-3′-aminophenylphosphate was used to characterize binding by the enzyme staphylococcal nuclease to soluble thymidine biphosphate (Dunn and Chaiken 1974). Over the last few decades, this method has been used to examine interactions in numerous systems and has been used in both low- and high- performance systems with affinity columns. Examples of these applications

tR

σR2

Sampleinjector

Pump

Detector

Affinity column

Mobile phasereservoir

Pump

Detector

Affinity column

Mobile phasereservoir withsolute

Pump

Mobile phasereservoir withno solute

ExcessExcess

tbrkthruσ2brkthru

(a) (b)

fIgure 4.1 Typical experimental systems and corresponding chromatograms for performing (a) zonal elution or (b) frontal analysis.

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can be found in Table 4.1 and in previous reviews that have appeared on this topic (Sebille and Thuaud 1978; Loun and Hage 1992; Dalgaard et al. 1989; Fitos et al. 1992; Winzor 2004).

4.2.1.1 general principlesIn zonal elution, a small plug of analyte is injected onto a column in the presence of a mobile phase with a known composition and that is being applied at a constant flow-rate. The mobile phase is often a buffer with a physiological pH but may also contain a known concentration of a salt, organic modifier, or a competing agent that is known to bind at a specific site on the immobilized ligand. As the analyte interacts with the immobilized ligand, it is retained by the column. The retention time or volume of

86 10 12 14Time (min)

(a)

(b)

Abs

orba

nce

(327

nm

)

10 12 14 16Time (min)

Abs

orba

nce

(327

nm

)

fIgure 4.2 Examples of (a) zonal elution experiments and (b) frontal analysis experi-ments examining the binding of 7-hydroxycoumarin to immobilized HSA. The results in (a) were obtained through competition studies performed by injecting samples of 5.0 µM 7-hydroxycoumarin in the presence of mobile phases that contained (from top-to-bottom) 20, 15, 10, 5.0, 1.0, or 0 µM racemic warfarin as a competing agent. The frontal analysis curves in (b) were obtained for the application of solutions that contained (from left-to-right) 10, 7.5, 5.0, 2.5, or 1.0 µM 7-hydroxycoumarin.

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the analyte can be measured either online or offline by using an appropriate detector. Information on analyte retention can be obtained by looking at changes in mobile phase composition. This technique can also be used to explore changes in the system due to alterations in temperature, pH, or mobile phase conditions.

An example of a typical zonal elution study is shown in Figure 4.2a. In this example, racemic warfarin was used as a competing agent in the mobile phase while 7-hydroxycoumarin was injected as the analyte of interest (Joseph et al. 2008). The column contained immobilized HSA as the ligand. These studies were per-formed to examine the binding of 7-hydroxycoumarin with respect to warfarin. The 7- hydroxycoumarin peaks shifted to the left as the concentration of warfarin increased, indicating that some type of direct or allosteric competition was occur-ring between these two compounds and HSA. The advantages that have been noted for this type of experiment include its high precision, small sample requirements, and the ability to perform this method on a standard HPLC system with the addition of a device for temperature control (Hage 2002).

Zonal elution has been used in a large assortment of studies to gain information on analyte–ligand systems (Winzor 2004; Hage 2002). A majority of these studies focus on binding in order to determine the strength and location of the bound analyte to the ligand. Other studies look at how those interactions change as conditions are altered. These studies often look at temperature, pH, or mobile phase variations. Yet

table 4.1applications of biointeraction affinity Chromatography in equilibrium and thermodynamic studies

method type of ligand analyte (references)

Zonal elution

Serum proteinsa Warfarin (Loun and Hage 1994); coumarins (Joseph et al. 2009; Noctor et al. 1993); benzodiazepines, triazole derivatives (Noctor et al. 1993); carbamazepine (Kim and Hage 2005); phenytoin, ibuprofen (Chen and Hage 2004)

Frontal analysis

Serum proteinsa Carbamazepine (Kim and Hage 2005); propranolol (Mallik et al. 2008); berberine chloride (Lei et al. 2007); salicylic acid (Nakano et al. 1982); thyroxine (Kimura et al. 2005), warfarin (Loun and Hage 1994); tryptophan (Yang and Hage 1996)

Enzymes/receptorsb Nicotine, β-estradiol (Schriemer 2004); enzyme inhibitors (Kovarik et al. 2005; Ng et al. 2005)

Lectins Glycopeptides (Tachibana et al. 2006); oligosaccharides (Arata et al. 2007; Nakamura-Tsuruta et al. 2006); glycosaminoglycans (Iwaki et al. 2008)

Aptamers Adenosine (Ruta et al. 2008)

Quinidine carbamate Naproxen (Asnin et al. 2008)

a See (Hage 2002) for a more complete list of applications that involve this type of ligand and analysis method.

b See (Schriemer 2004) for a more complete list of applications that involve this type of ligand and analysis method.

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other studies look at altering the ligand by mutations or structural changes. More details on these applications follow.

All of these applications rely on the same foundation: namely, that the analyte will have some reversible interaction with the immobilized ligand within the column. The extent of this interaction can be examined by measuring the retention factor (k) of the analyte as it passes through the column, as defined below.

kt t

tV V

VR M

M

R M

M

= − = − (4.1)

In this equation, tR is the retention time of the analyte of interest while tM is the elu-tion time of a non-retained compound (i.e., the void time); VR is the corresponding retention volume and VM is the void volume. The retention factor that is calculated according to Equation 4.1 for an affinity column can also be related by Equation 4.2 to the number of binding sites within the column as well as the binding affinity of the analyte to each site (Hage and Tweed 1997).

kK n K n m

VA A n L

M

= + +( ... )1 1 n (4.2)

The terms KA1 through KAn in this equation represent the association equilibrium constants at binding sites 1 through n within the column, and n1 through nn represent the fraction of each type of individual site in the column. The term mL represents the total moles of binding sites within the column. It can be seen from this equation that a change in the binding strength, location of binding, or number of binding sites within the column could significantly alter the retention factor for the analyte.

4.2.1.2 binding and Competition studiesOne of the primary applications for zonal elution in biointeraction studies is to examine the extent of binding between an analyte and the immobilized ligand. One way this can be done is to relate the retention factor of an injected analyte to the fraction of analyte that is bound to the ligand (b) and the free fraction of analyte in solution (f) at the center of the analyte peak. This relationship can be made under linear elution con-ditions for a system with fast association/dissociation kinetics by using Equation 4.3.

kbf

= (4.3)

The sum of bound and free analyte fractions must equal 1 (i.e., b + f = 1), which means Equation 4.3 can be rearranged so that either the bound or free fraction of the analyte at equilibrium can be calculated from the measured retention factor (Noctor et al. 1993).

bk

k=

+1 (4.4)

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Binding studies in this area have been used to explore a variety of analyte–ligand systems. Examples of such work include the binding of groups of benzodiazepines, coumarins, and triazole derivatives to HSA (Noctor et al. 1993). The retention fac-tors of two solutes can also be compared if they bind to the same site on a ligand. If the binding site is identical for the two solutes and they each interact at only a single specific region on the ligand, the ratio of their two retention factors should also be equal to the ratio of the association equilibrium constants. These values cannot be directly compared, however, if the analytes bind to the ligand at multiple sites or if their binding sites are slightly different from one another. This latter situation occurs because binding regions on an immobilized ligand may lose activity to slightly different extents when covalent immobilization methods are employed (Loun and Hage 1992; Yang and Hage 1993).

The most prevalent application for zonal elution is in competition studies. This application can be used to see if the binding site for one solute is also a binding site for a second solute. This type of experiment is performed by continuously passing through the affinity column a mobile phase with a known amount of competing agent I, which represents one of the two solutes being compared, while injecting a small plug of the second solute or analyte A onto the column. If A and I compete for the same sites on the ligand and have fast association/dissociation kinetics, the following equation can be used to describe the observed change in the retention fac-tor for A as it competes with I for binding sites in the column (Hage 2002; Nakano et al. 1982).

1k

K V IK m

VK m

I M

A L

M

A L

= +[ ] (4.5)

The terms KI and KA in this equation represent the association equilibrium constants for the ligand with the competing agent and analyte, respectively, at their site of competition in the column. Similar equations can also be derived for more complex models, such as those that involve more than one binding site, non-specific interac-tions, or allosteric effects (Hage 2002).

Relationships such as the one in Equation 4.5 can be valuable tools in deter-mining the nature of the competition that occurs between the analyte and mobile phase additive (Chen and Hage 2004; Kim and Hage 2005; Joseph et al. 2009). For example, if a plot of 1/k versus [I] that is made according to Equation 4.5 gives a linear relationship, then A and I are following a model in which they have competi-tion at a single class of binding sites on the immobilized ligand. If this plot shows only random variations in the value of 1/k (or k) as [I] is increased, this behavior indicates that the analyte and competing agent are not binding at a common site nor do they have any allosteric interactions with one another. If the response of the plot is non-linear with a positive slope, the analyte is either binding to multiple sites or there are negative allosteric effects occurring between the analyte and the compet-ing agent. If a non-linear plot is obtained with a negative slope, this is an indication that positive allosteric effects are present between A and I as they interact with the ligand (Hage 2002).

84534.indb 152 11/5/09 12:27:20 PM


Advantages of this method are the speed with which the experiments can be carried out, the good run-to-run precision, and the need for only a small amount of analyte per run. Once an appropriate model has been found to describe the reten-tion data (e.g., the use of Equation 4.5 for a system with single-site binding), it is possible to also determine the association equilibrium constants for the competing agent and/or analyte with the ligand from these experiments. The precision of these measurements is typically in the range of 5 to 10% using a standard HPLC system, with a long-term change in ligand activity resulting in only a small variation in the association equilibrium constants that are determined by this approach (Loun and Hage 1992).

Zonal elution has been used in many past studies in a quantitative fashion to examine direct competition between solutes and to estimate the association equi-librium constants for these interactions. It has also been shown more recently how quantitative information can be obtained from zonal elution and competition studies to look at allosteric effects between two compounds. Allosteric effects occur when the binding of an analyte to a ligand at one binding site interferes with the binding of a second analyte to the ligand at a different binding site. This interference can either hinder or promote the binding of the analytes to the ligand. The effect of these interactions during a zonal elution study can be described by the following equation (Chen and Hage 2004), where k0 is the retention factor for the ligand in the absence of any competing agent in the mobile phase.

k

k k K II A

0

0

11

11

−=

−⋅ +

→β IL[ ]

(4.6)

In this equation, the ligand is viewed as having at least two binding sites, one for the injected analyte (A) and one for the competing agent in the mobile phase (I). The binding of A with the ligand is altered as I also binds to the ligand, which causes the association equilibrium constant for A with the ligand to change from KAL to K′AL. This change is represented in the above equation by the coupling constant βI→A, which is equal to the ratio K′AL/KAL. Equation 4.6 predicts that a plot of k0/(k − k0) versus 1/[I] will give a linear relationship for a simple allos-teric interaction and that, through this relationship, the values of βI→A and KIL can be obtained (Chen and Hage 2004). An example of such a plot is shown in Figure 4.3. Studies on drug–protein systems have been performed to examine the allosteric effects occurring between several agents, such as the interactions between R- or S-ibuprofen with S-lorazepam or the enantiomers of oxazepam on HSA, as well as the interactions between L-tryptophan and phenytoin on HSA (Chen and Hage 2004).

4.2.1.3 temperature and solvent studiesZonal elution can also be used to see how a biological interaction will change as one varies the conditions under which this interaction takes place. For instance, alter-ing the temperature of a system has been shown to have an effect on the association equilibrium constants for a variety of compounds with HSA (Kim and Hage 2005; Loun and Hage 1994; Yang and Hage 1996). This relationship can be described for

84534.indb 153 11/5/09 12:27:20 PM


a system with single site binding and over a reasonably narrow temperature range by using the following equation,

lnRT

KH S

RA = − +∆ ∆ (4.7)

in which ∆H is the change in enthalpy of the reaction, ∆S in the change in entropy, T is the absolute temperature, and R is the gas law constant. Preparing a plot of ln KA versus 1/T in this situation would be expected to result in a graph where the slope is equal to –∆H/R and the intercept is equal to ∆S/R. Using this information it is pos-sible to calculate the overall change in enthalpy and entropy of the reaction. The total change in free energy (∆G) can also be calculated using Equation 4.8.

∆G K A= −RTln (4.8)

This information can be used to determine what force has the greatest contribution to the free energy on the binding of an analyte to a ligand (Loun and Hage 1994).

Three other factors that can be altered during zonal elution experiments are the pH, ionic strength, and content of organic modifier in the mobile phase. Figure 4.4 shows examples of experiments in which these parameters were varied during a zonal elution study. Increasing the ionic strength of a buffer solution, for instance, tends to decrease coulombic interactions in this particular example by creating a shield-ing effect that occurs due to the increase in ion concentration. However, increasing the ionic strength also tends to increase the adsorption of nonpolar solutes onto the column. A change in pH can alter the conformation of the ligand and the overall net charge of the ligand, which will also change coulombic interactions. Adding organic modifier can disrupt the analyte–ligand binding. For example, if the ligand is a pro-tein, the nonpolar bonds could be affected as well as the protein conformation by adding only a small amount of organic modifier.

2

1.5

k 0/(k

– k 0)

(S-lo

raze

pam

ace

tate

)

0.5

R

S

0 0.03 0.06 0.091/(Ibuprofen) (µM–1)

0.120

1

fIgure 4.3 Allosteric effect of R- and S-ibuprofen on the binding of S-lorazepam acetate to immobilized HSA, as analyzed according to Equation 4.6. (From Chen, J. and Hage, D. S., Nat. Biotechnol., 22, 1445–1448, 2004. With permission.)

84534.indb 154 11/5/09 12:27:24 PM


4.2.1.4 Characterization of binding sitesZonal elution-based competition studies are often used as a way to characterize and determine the location of the analyte binding site on a ligand. In these studies, compet-ing agents with known binding sites on the ligand are used to determine whether these agents compete with an analyte for interactions with the ligand. This type of competition experiment can not only allow the binding site to be identified for the analyte, but can also provide the association equilibrium constant for the analyte at this specific binding site, such as is obtained through the use of Equation 4.5 or related expressions.

6(a)

(b)

(c)

4

22 3 4 5

pH6 7 8

0 0.1Phosphate conc. (M)

0.2 0.3

0 2% Propanol (v/v)

4 6

6

k (C

arba

maz

epin

e)

8

4

2

6

4

2

0

fIgure 4.4 Shift in the retention factor of carbamazepine on an immobilized HSA column with changes in pH (a), ionic strength (b), or organic modifier content of the mobile phase (c). (From Kim, H. S. and Hage, D. S., J. Chromatogr. B, 816, 57–66, 2005. With permission.)

84534.indb 155 11/5/09 12:27:25 PM


Another way to map out the binding sites for a particular analyte is by chemically altering these binding regions and then using zonal elution to determine if there are any resulting changes in the retention of the analyte. This approach has been used along with the modification of specific residues on HSA that are thought to lie within one of its major binding sites. One such study examined the binding of drugs to the Sudlow site II of HSA by altering Tyr-411 on this protein; the resulting affinity column was shown to have altered binding for a number of compounds when compared to normal HSA in zonal elution studies (Noctor and Wainer 1992). Similar results were obtained for analytes that could bind to Sudlow site I when Trp-214 on HSA was modified and the resulting ligand was compared to normal HSA in zonal elution and frontal analysis studies (Chattopadhyay et al. 1998).

4.2.1.5 practical ConsiderationsWhile zonal elution is an easy method with which to work, it does have a number of factors that must be considered to ensure that the approach is properly performed. For example, the choice of affinity column must be considered and reported. Items that should be noted include the column dimensions, the support within the col-umn, and the immobilized ligand. The support within the column should be chosen based upon factors such as the mobile phase pH that will be used, the desired flow rate range for the experiments, the allowed column backpressure, and the degree of non-specific binding that can be tolerated (Gustavsson and Larsson 2006). If the experiments will be using high flow rates, for example, the backpressure that would be created with a porous silica column might be too high and a more suitable approach might involve the use of a monolithic column (Gustavsson and Larsson 2006; Mallik and Hage 2006). Some supports such as silica have a limited range of pH stability, which must also be considered. For example, silica will start to dis-solve above a pH of approximately 8.0 or below 2.0. This pH range of stability can be increased by several means, such as incorporating zirconium or aluminum on to the silica surface which might improve the support’s stability under alkaline condi-tions (Schiel et al. 2006).

When a new column has been created with unknown binding properties, it should be tested using an analyte with known binding properties to ensure that the column, support, and immobilized ligand have all been chosen properly for the upcoming studies. Also, when measuring analyte retention, it is crucial that the true center of the peak be determined. This is typically not the tallest point of the peak due to peak tailing, but rather the point at which the two areas of the peak would be equal if the peak were to be split in half vertically. It is recommended that this be done with computer software to obtain the most accurate results.

If the analyte has high retention, a low-capacity column might be desirable to pro-duce shorter retention times. The easiest way to solve this problem is to simply use a smaller column. This could mean shortening the column length, decreasing the inner diameter of the column, or both. Whenever a column containing an immobilized ligand is created, a control column that was made following the same procedure (minus the addition of the ligand) should be used to account for any non-specific binding that might occur. One precaution that must be followed when reducing col-umn size during binding studies is that it must be ensured that conditions are still

84534.indb 156 11/5/09 12:27:25 PM


present that allow a local equilibrium to be established at the true center of the analyte peak. This is true if consistent results are still being obtained in the retention factor as the column size is altered.

Another point to consider when performing zonal elution studies is the concen-tration range that should be used for the competing agent or additive in the mobile phase. It is important to be able to observe a shift in analyte retention, and in order to do so an appropriate concentration range must be chosen for the competing agent. This can be done by looking at the shift in k as it moves between its maximum value (kmax) and its minimum value (kmin), as shown in Figure 4.5. The following equation can be used to describe this relationship for an analyte and a competing agent that engage in direct competition for a single binding site (Hage 2002).

k k

k k K II

−−

=+

min

max min [ ]1

1 (4.9)

It is important to note in this particular case that the shift in retention is due only to change in the concentration and association equilibrium constant of the compet-ing agent ([I] and KI, respectively). The ideal range for this experiment is when the mobile phase concentration of the competing agent gives the greatest change in (k − kmin)/(kmax − kmin), as occurs between values of 0.1 and 0.9 for this term in Figure 4.5. However, other concentrations above or below this optimum range should also be used to ensure that the correct model is being used to describe the biological interaction (Hage 2002).

Although it is possible to work under non-linear elution conditions (Arnold et al. 1986) zonal elution studies are usually performed under linear elution conditions. This is the region where the concentration of analyte is small compared to the amount of immobilized active ligand within the column. Columns containing larger ligands, such as proteins, often have a smaller capacity than traditional small molecule

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00KI(I)

(k –

km

in)/

(km

ax –

k min

)

fIgure 4.5 Relative shift in analyte retention as a function of competing agent concentra-tion for a zonal elution experiment in which there is direct competition between A and I at a single site on an immobilized ligand, as predicted by Equation 4.9.

84534.indb 157 11/5/09 12:27:26 PM


columns, thus making it more difficult to stay within this region. Fortunately, testing for linear elution conditions simply involves injecting a range of analyte concentra-tions and seeing whether there is any shift in retention. Sample concentrations are then selected over which no significant change in retention occurs. These concentra-tion conditions often vary from one compound to the next, so it is important to test this feature with each new compound that is to be examined by zonal elution meth-ods (Yang and Hage 1996).

Other factors to consider are the solubility and response or detectability of the analyte. Solubility will place an upper limit on the concentration range that can be used for the analyte, while the detector response and analyte detectability will place a lower limit on this range. Solubilizing agents such as cyclodextrins can often be used to increase the solubility of an analyte but require the use of more complex models to describe how the retention of an analyte will vary with the concentra-tions of both the competing agent and solubilizing agent (Hage and Sengupta 1998). Absorbance detectors are often used for zonal elution studies, but if there are issues with the detectability of the analyte then a more sensitive detection mode can be employed.

4.2.2 frontal analySiS

While zonal elution works with a small pulse of injected analyte to obtain informa-tion on the interaction of the analyte with a stationary phase, frontal analysis uses the continuous application of the analyte to gain more information by fully saturating the column. Although frontal analysis was originally used as a purification technique, it has grown into a popular method for gathering equilibrium data on the affinities and binding sites of various analyte–ligand systems. Kasai and Ishii were the first to explore the use of frontal analysis and affinity columns for this purpose when in 1975 they used a low-performance affinity column to study the affinity of trypsin to a mixture of oligopeptides obtained from a tryptic digest of protamine (Kasai and Ishii 1975). The use of silica columns for biointeraction studies began about a decade later, with other HPLC media such as monoliths and capillary systems also now being employed for such work (Schiel et al. 2006; Mallik 2006; Schriemer 2004).

4.2.2.1 general principlesFrontal analysis is performed when an analyte is continuously applied to a column containing an immobilized ligand. As the analyte interacts with the ligand, the binding sites slowly become saturated (see Figure 4.2b). Upon saturation, excess analyte leaves the column and forms a characteristic breakthrough curve. If fast association and dissociation kinetics are present for this system, the center of this breakthrough curve can be related to the concentration of applied analyte, the num-ber of binding sites within the column, and the affinity to which the analyte binds to the ligand.

The advantages of using frontal analysis and affinity chromatography for bioin-teraction studies are similar to those already described for zonal elution. Although frontal analysis requires a larger volume of sample than zonal elution, this method also provides more information per analysis. The main advantage of frontal analysis

84534.indb 158 11/5/09 12:27:26 PM


is that equilibrium constants and binding capacities can be obtained separately, making it possible to characterize both binding affinities and column properties. These experiments can also be carried out using a standard HPLC system with the addition of a temperature controller. Applications of frontal analysis are similar to those already described for zonal elution and include binding studies, competition studies, and temperature and solvent studies. Frontal analysis has also been used in recent years to screen the binding of a ligand against mixtures of compounds. The following sections provide more details on each of these applications.

4.2.2.2 binding studiesOne of the most common uses of frontal analysis is in the determination of the affinity and binding capacity of an analyte with an immobilized ligand. This can be accomplished by measuring the breakthrough time or breakthrough volume of an analyte that has been continuously applied to a column containing an immo-bilized ligand. Once obtained, the breakthrough time or volume can be related to the apparent number of moles of analyte needed to saturate the column, mLapp. For instance, if an analyte binds reversibly to the immobilized ligand at only one type of site, Equations 4.9 and 4.10 can be used to relate the measured value of mLapp to the parameters that describe the affinity of this interaction (as represented by KA) and the moles of binding sites in the column (as represented by mL) (Loun and Hage 1992).

mm K A

K AL A

ALapp

[ ][ ]

=+1

(4.10)

or

1 1 1

m K m A mA L LLapp [ ]= + (4.11)

Equivalent expressions can be written in terms of the breakthrough volume, as will be discussed later. For a system with 1:1 binding, Equation 4.11 can be used to find the values of both KA and mL if a plot is made of mLapp versus 1/[A]. An example of such a plot is shown in Figure 4.6a. Alternatively, Equation 4.10 and a non-linear fit can also be used to analyze such data.

If more than one binding site is involved in the interaction of the applied analyte with the immobilized ligand, a negative deviation will occur from Equation 4.11 at high analyte concentrations (or lower 1/[A] values), as shown in Figure 4.6b. These deviations indicate that multisite binding is present, which requires the use of expanded forms of Equations 4.10 or 4.11. As an example, the following equations would be used to model a system that has two-site binding (Tweed et al. 1997),

mm K

K A

m K

K AL A

A

L A

ALapp [ ] [ ]

=+

++

1 1

1

2 2

21 1

(4.12)

84534.indb 159 11/5/09 12:27:27 PM


or

1 1

1 1 12 22 2

1 2m

K A K A K A

mA A A

LLapp

[ ] [ ] [ ]

(=

+ + ++

β βα β −− +{ }α β β1 2 2

2 21 1

) [ ] [ ]K A K AA A

(4.13)

where β2 = KA2/KA1

and α1 = mL1/mL2

, and all other terms are as defined previously.

0

20

40

60

80

0 250 500 750 10001/[Coumarin] (× 10–3 M–1)

1/m

Lapp

(× 1

0–6 m

ol–1

)

0

5

10

15

20

0 40 80 120 160 200

(a)

0

20

40

60

80

0 250 500 750 1000

1/[4-Hydroxycoumarin] (× 10–3 M–1)

1/m

Lapp

(× 1

0–6 m

ol–1

)

0

5

10

15

20

0 40 80 120 160 200

(b)

fIgure 4.6 (a) Single-site binding of coumarin and (b) multisite binding of 4-hydroxcoumarin to an immobilized HSA column, as examined by frontal analysis and Equations 4.11 and 4.13.

84534.indb 160 11/5/09 12:27:28 PM


Since frontal analysis can provide information on both the number of binding sites and association equilibrium constants for an interaction, this is a valuable method for bioint-eraction studies. A number of studies have been done in this area, as has been discussed in previous reviews (Hage 2002; Winzor 2004). More recent examples have included work examining the binding of HSA with carbamazepine (Kim and Hage 2005), α1-acid glycoprotein (AGP) with oxybutynin (Kimura et al. 2006) and R- and S-propranolol (Mallik et al. 2008), naproxen with a chiral stationary phase containing quinidine car-bamate (Asnin et al. 2008), and BSA with berberine chloride (Lei et al. 2007).

4.2.2.3 Competition studiesCompetition studies can also be performed by frontal analysis through the use of a competing agent that is added to the mobile phase. An example of this is the com-petition of sulphamethizole with salicylic acid for HSA, as by Nakano et al. (1982). Typically, a shift to shorter breakthrough times is seen in these studies as the amount of competing analyte is increased. The degree of competition, including positive or negative allosteric effects, can also be observed using this method.

Over the last decade there has been a large amount of work in the use of frontal analysis and affinity chromatography in screening mixtures of compounds for any targets that might bind to a given immobilized ligand. The combination of these tools with mass spectrometry, a method commonly known as frontal affinity chro-matography-mass spectrometry (FAC-MS) has been of particular interest (Schriemer et al. 1998). This approach has been shown to be able to screen mixtures of com-pounds in a relatively short amount of time. As a mixture of analytes flows through the column, the individual analytes bind to the ligand based on their affinity for this agent. Using mass spectrometry as the detection method allows for a multitude of analytes to be evaluated simultaneously, as shown by the example in Figure 4.7 for a mixture of eight solutes that were injected onto a column containing immobilized sorbitol dehydrogenase. Selective detection at the characteristic mass-to-charge (m/z) value for each compound makes it possible to generate separate breakthrough curves for each of these analytes. This information is then used to evaluate and rank

0

2.5 Void123,4,5678

Kd,1 = 2 µM

Kd,8 = 8 nM

2.0

1.5

1.0C/C

0

0.5

0.05 10

Time (min)15 20 25

fIgure 4.7 Use of FAC/MS to examine the binding by eight compounds in a library to an immobilized sorbitol dehydrogenase column. (From Chan, N. C., et al. Anal. Biochem., 319, 1–12, 2003. With permission.)

84534.indb 161 11/5/09 12:27:29 PM


the relative affinity of each compound in the mixture for the ligand in the affinity column (Schriemer 2004).

An expression that is often used with breakthrough volume measurements in these competition studies to evaluate binding affinity is given in Equation 4.14 (Schriemer 2004), which is equivalent to the mass relationship that was given earlier in Equation 4.10.

V VB

A KA Mt

D

− =+[ ]

(4.14)

In this alternative expression, VA is the measured breakthrough volume, VM is the column void volume, [A] again represents the concentration of applied analyte, Bt is the total amount of immobilized active ligand, and KD is the dissociation equilibrium constant for the interaction (where KD = 1/KA).

One variation on this approach is to make sequential injections of the analytes starting with the lowest concentrations and finishing at the highest concentrations. These injections are performed without washing steps in between infusions. The breakthrough volumes that are measured are then related to the applied concentra-tions of the analyte by using the following equation (Schriemer 2004),

[ ]A y BV V

Kj j tAj M

D+ =−

−1

(4.15)

where

yA A V V

V Vji

j

i i Aj M

Aj M

=− −

−−

−

−∑ 1

1

1([ ] [ ] )( ) (4.16)

for the jth injection in a series. A plot of the analyte concentration versus the cor-rected breakthrough volume is then used to give a graph where the slope is equal to the column capacity and the negative of the intercept is equal to the dissociation equilibrium constant.

Examples of systems that have recently been studied using this approach include galactosaminoglycans as a ligand for galectins (Iwaki et al. 2008), jacalin as a ligand for various glycopeptides (Tachibana et al. 2006), HSA with thyroxine (Kimura et al. 2005a), and high-throughput lectin-oligosaccharide systems (Nakamura-Tsuruta et al. 2006). A number of articles have been published using this method in the past few years and more detailed information can be found in the literature (Schriemer 2004; Kovarik et al. 2005; Iwaki et al. 2008; Tachibana et al. 2006; Chan et al. 2007; Slon-Usakiewicz et al. 2005; Nakamura-Tsuruta et al. 2006; Ng et al. 2005; Arata et al. 2007; Kimura et al. 2005b; Itakura et al. 2007).

84534.indb 162 11/5/09 12:27:30 PM


4.2.2.4 temperature and solvent studiesThe ability to measure both the amount of binding sites and affinity is a useful feature of frontal analysis in examining how changes in temperature or other conditions alter biological interactions. Temperature studies have been performed with this technique on systems such as HSA with R- and S-warfarin (Loun and Hage 1994), carbamazepine (Kim and Hage 2005), and D- and L-tryptophan (Yang and Hage 1996); aptamers with adenosine (Ruta et al. 2008); and BSA with berberine chloride (Lei et al. 2007). In these studies it has been shown that shifts in retention with temperature can cor-respond to a change in the number of available binding sites (Loun and Hage 1994; Kim and Hage 2005; Yang and Hage 1996; Lei et al. 2007) as well as the binding affinity of the compound (Loun and Hage 1994; Yang and Hage 1996; Ruta et al. 2008; Lei et al. 2007). Figure 4.8 gives an example of such a study, showing how the retention, activity, and affinity constant for berberine chloride change under various conditions when using an immobilized BSA column. Frontal analysis has also been

10(a)

(b)

(c)

864

k´m

L (1

0–7 m

ol)

K (1

04 L m

ol–1

)

20

0

5.25

4.84.64.44.2

123456

0 10 20 30T (°C)

40 50

0 10 20 30T (°C)

40 50

0 10 20 30T (°C)

40 50

fIgure 4.8 Observed changes as a function of temperature in (a) the retention factor, (b) moles of active binding sites, and (c) and association equilibrium constant for berberine chlo-ride on an immobilized BSA column. (From Lei, G., Yang, R., Zeng, X., Shen, Y., Zheng, X., and Wei, Y. Chromatographia, 66, 847–852, 2007. With permission.)

84534.indb 163 11/5/09 12:27:31 PM


used to examine how changes in solvent composition affect solute–ligand binding, as has been used for systems such as naproxen with a chiral stationary phase containing quinidine carbamate (Asnin et al. 2008), and HSA with D- and L-tryptophan (Yang and Hage 1996) or carbamazepine (Kim and Hage 2005).

4.2.2.5 practical ConsiderationsMany of the practical factors that should be considered in the use of frontal analysis are the same as those that have already been described in Section 4.2.1.5 for zonal elution. The key differences in these methods are the approaches they use for sample application and data analysis. In the case of binding studies that are performed by frontal analysis, it is necessary to have an observable shift in the breakthrough curve as the concentration of analyte is varied. It is possible to determine the optimum analyte concentrations to employ for this experiment by using an expression such as Equation 4.17, which has been previously derived for systems with 1:1 interactions between the analyte and ligand (Hage and Chen 2006).

m

mK A

K AL

A

A

Lapp [ ][ ]

=+1

(4.17)

According to this expression, as the analyte concentration [A] ranges from zero to infinity, the fraction of binding sites that are occupied by the analyte at equilibrium (as given by the ratio mLapp/mL) will be between zero and one, respectively. It is at some intermediate analyte concentration that this ratio will have its greatest change with analyte concentration. For a 1:1 binding system, this occurs when [A] = 1/KA, with concentrations both above and below this optimum then being used for binding studies. Somewhere within these values the analyte will have a concentration range that will show its greatest shift in retention. Analyte solubility and detectability must also be considered in choosing the range of analyte concentrations to be used in these studies, as discussed previously for zonal elution.

It is relatively easy to analyze and determine the breakthrough time of a sim-ple, symmetrical frontal analysis curve. In this situation, the point that is halfway between the baseline and plateau would be the breakthrough time. Unfortunately, many breakthrough curves are not perfectly symmetrical in shape and, therefore, the analysis approach has to be slightly altered. One approach is to find the point at which the areas below the front portion of the curve and above the latter half of the curve are equal. An equivalent approach for analyzing a breakthrough curve is to take the first derivative of the curve and then determine the central moment of this derivative (Hage 2002).

4.3 kInetIC measurements

Affinity chromatography can not only provide information on binding equilibria and thermodynamics but it can also be used to examine the kinetics of a biological interaction.

84534.indb 164 11/5/09 12:27:32 PM


This can be accomplished by considering the rates of the various processes that are occurring as an analyte passes through the column and interacts with the immobilized ligand. This information has been used in the past to help study antibody–antigen interactions, lectin binding to sugars, and drug–protein interac-tions, among other systems of biological interest, as is illustrated by the examples given in Table 4.2.

It has been known for decades that the behavior of an analyte as it passes through a chromatographic system is related not only to the thermodynamics of the interac-tions that are occurring in the column but also the various kinetic processes that are taking place. The role of kinetics in processes such as chromatographic band broadening was suggested by Giddings and Eyring in 1955 (Giddings 1965; Giddings and Eyring 1955) and has since been included in numerous theoretical treatments of chromatography (Felinger 2008; Giddings 1965; Golshan-Shirazi and Guichon 1992; Grushka et al. 1975). This section of this review will examine how chromatographic theory has been used to develop various approaches that can be used in biointerac-tion affinity chromatography to measure rate constants for analyte–ligand interac-tions. Tools that will be discussed in this section will include approaches based on band broadening measurements, peak profiling, frontal analysis, split-peak analysis, and peak decay analysis.

table 4.2applications of biointeraction affinity Chromatography in kinetic studies

ligand analyte (references)

Human serum albumin Tryptophan (Schiel, Ohnmacht et al. 2009; Talbert et al. 2002; Yang and Hage 1997); warfarin (Chen and Hage 2003; Loun and Hage 1996); propranolol, imipramine (Schiel, Papastavros et al. 2009)

Antibodies β-Lactoglobulin (Puerta et al. 2002; Puerta et al. 2006); human serum albumin (Jaulmes et al. 2001; Renard, Vidal-Madiar, and Lapresle 1995; Renard, Vidal-Madiar, Sebille et al. 1995; Renard and Vidal-Madjar 1994; Vidal-Madjar et al. 1997); 2,4-dichlorophenoxyacetic acid (2,4-D) and related herbicides (Moser 2005)

Concanavalin A Various sugars and related derivatives (Anderson and Walters 1986; Moore and Walters 1987; Muller and Carr 1984; Munro et al. 1994, 1993; Wade et al. 1987)

Nicotinic acetylcholine receptors

Various inhibitors (Jozwiak et al. 2002; Jozwiak et al. 2003; Jozwiak et al. 2007; Jozwiak et al. 2004; Moaddel et al. 2005; Moaddel and Wainer 2007)

Heat shock protein 90 Novobiocin (Marszall et al. 2008)

Bovine neurophysin II Vasopressin (Swaisgood and Chaiken 1986)

Protein A and protein G Antibodies (Hage and Walters 1988; Hage et al. 1986; Lee and Chuang 1996; Rollag and Hage 1998)

Cibacron Blue 3G-A Lysozyme (Lee and Chen 2001; Mao et al. 1991)

Peptides Fibrinogen (de Lucena et al. 1999)

84534.indb 165 11/5/09 12:27:32 PM


4.3.1 General principleS

To understand the methods that are used in biointeraction affinity chromatography to obtain kinetic information, it is first necessary to examine the various transport processes and reactions that an analyte can undergo as it passes through an affin-ity column. The reactions in Equation 4.18 show a common model that is used to describe the retention of an analyte A with an immobilized ligand on a porous sup-port. In this model, as the analyte travels through the column in the mobile phase, the analyte can undergo mass transfer from the flowing region of the mobile phase to a stagnant layer of mobile phase that surrounds, and is contained within, the inte-rior of each support particle. This mass transfer is represented by the process to the left of Equation 4.18 and is described by the forward and reverse mass transfer rate constants k1 and k−1, respectively. In this process, AE represents analyte in the flowing mobile phase (i.e., in the excluded volume of the column) and A is the analyte when it is present in the stagnant mobile phase layer.

Ak

kAE

1

1−

A Lk

kALa

d

+ KkkA

a

d

= (4.18)

Once the analyte is inside of the support pores, it can then react with the immo-bilized ligand that is in contact with the stagnant mobile phase. This interaction of A with L is represented in Equation 4.18 by a simple 1:1 reversible interaction with association and dissociation rate constants given by the terms ka and kd. In this model, the ratio of these rate constants also gives the association equilibrium constant for the formation of the analyte–ligand complex. The kinetic effects due to the stagnant mobile phase mass process on the left of Equation 4.18 is also sometimes referred to as the diffusional kinetic contribution, while the stationary phase interactions in the center of Equation 4.18 are called the chemical contribu-tion to the kinetics. In this review, the symbol ki,app will be used to describe any apparent rate constant that is a function of both these processes. The individual rate constants k1 and k−1 will be used to specifically represent the diffusional/mass transfer process and ka and kd will be used to represent the chemical interac-tion between the analyte and ligand.

The affinity and rate of the analyte–ligand interaction will determine the par-ticular methods that can be used to characterize this process by biointeraction affin-ity chromatography. However, each of these methods is again based on either the injection of a small plug of the analyte (zonal elution) or the continuous applica-tion of an analyte (frontal analysis). It is also possible to characterize these methods according to whether they use a trace amount of applied analyte (i.e., linear elution conditions, giving a result that is independent of the amount of injected analyte) or a significant amount of analyte versus immobilized ligand (i.e., non-linear elution con-ditions, where the response is affected by the amount of applied analyte) (Golshan-Shirazi and Guichon 1992). A summary of the methods that have been described for such work is given in Table 4.3. Further details on each of these methods and their applications are provided in the following sections.

84534.indb 166 11/5/09 12:27:33 PM


tab

le 4

.3C

ompa

riso

n of

met

hods

for

kin

etic

mea

sure

men

ts b

y b

ioin

tera

ctio

n a

ffini

ty C

hrom

atog

raph

y

met

hod

app

licat

ion

Con

diti

ons

usa

ble

ran

ge o

f a

ffini

ties

a

Info

rmat

ion

obt

aine

db

app

roac

hes

use

d to

Cor

rect

for

stag

nant

mob

ile p

hase

m

ass t

rans

ferc

Plat

e he

ight

m

easu

rem

ents

Lin

ear

zona

l elu

tion

Wea

k to

mod

erat

e af

finity

k dE

xper

imen

tal a

nd th

eore

tical

met

hods

(va

ry fl

ow r

ate

for

non-

reta

ined

spe

cies

)

Peak

pro

filin

gL

inea

r zo

nal e

lutio

nW

eak

to m

oder

ate

affin

ityk d

,app

or

k d

Exp

erim

enta

l (va

ry p

artic

le d

iam

eter

of

supp

ort)

Zon

al e

lutio

n pe

ak fi

tting

Non

-lin

ear

zona

l elu

tion

Wea

k to

str

ong

affin

ityk d

,app

or

k dT

heor

etic

al e

stim

atio

n

Fron

tal a

naly

sis

curv

e fit

ting

Non

-lin

ear

fron

tal

anal

ysis

Mod

erat

e to

str

ong

affin

ityk a

,app

or

k aE

xper

imen

tal (

vary

bin

ding

cap

acity

of

colu

mn,

mL

)

Fron

tal a

naly

sis

mom

ent

anal

ysis

Non

-lin

ear

fron

tal

anal

ysis

d

Mod

erat

e to

str

ong

affin

ityk a

,app

, ka,

conc

or

k aE

xper

imen

tal (

vary

flow

rat

e fo

r no

n-re

tain

ed s

peci

es)

Peak

dec

ay m

etho

dN

on-l

inea

r zo

nal e

lutio

nW

eak

to m

oder

ate

affin

ityk d

or

k −1

(whi

chev

er

is r

ate

limiti

ng)

Exp

erim

enta

l (va

ry fl

ow r

ate,

col

umn

leng

th, o

r co

mpe

ting

agen

t con

cent

ratio

n un

til li

miti

ng v

alue

is o

btai

ned)

Split

–pea

k m

etho

dN

on-l

inea

r or

line

ar

zona

l elu

tiond

Stro

ng a

ffini

tyk 1

,con

c and

k1

or k

a,co

nc

and

k a

Exp

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enta

l (va

ry fl

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ate

for

non-

reta

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spe

cies

)

a T

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asso

ciat

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equi

libri

um c

onst

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(K

a):

wea

k af

finity

, K

a <

104

M-1

; m

oder

ate

affin

ity,

Ka

= 1

04 –

106

M-1

; St

rong

affi

nity

, K

a >

106

M-1

.b

Sym

bols

and

abb

revi

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ns:

k d,

diss

ocia

tion

rate

con

stan

t; k d

,app

, ap

pare

nt d

isso

ciat

ion

rate

con

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ith p

ossi

ble

cont

ribu

tions

fro

m b

oth

mas

s tr

ansf

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hem

ical

in

tera

ctio

ns; k

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ssoc

iatio

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te c

onst

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ent a

ssoc

iatio

n ra

te c

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ant w

ith p

ossi

ble

cont

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m b

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mas

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hem

ical

inte

ract

ions

; ka,

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trat

ion-

depe

nden

t app

aren

t ass

ocia

tion

rate

con

stan

t; k −

1, re

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e m

ass

tran

sfer

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con

stan

t for

mov

emen

t of a

sol

ute

from

the

stag

nant

mob

ile p

hase

to th

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g m

obile

pha

se i

n a

colu

mn;

k1,

for

war

d m

ass

tran

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nsta

nt f

or m

ovem

ent

of a

sol

ute

from

the

flow

ing

mob

ile p

hase

to

the

stag

nant

mob

ile p

hase

; k 1

,con

c, co

ncen

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aren

t for

war

d m

ass

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e co

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cor

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plat

e he

ight

con

trib

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n to

sta

gnan

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mas

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ansf

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Hsm

) co

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tion

can

be m

ade

by m

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of

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alcu

latio

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r ex

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men

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estim

ates

. The

pro

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are

list

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bove

are

thos

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at h

ave

been

util

ized

in th

e lit

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d T

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esul

ts in

this

met

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can

be e

xtra

pola

ted

to in

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dilu

tion

to c

orre

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ny c

once

ntra

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depe

nden

ce in

the

resu

lts.

84534.indb 167 11/5/09 12:27:33 PM


4.3.2 linear elution methodS

4.3.2.1 plate height measurementsThe measurement of plate heights and chromatographic band broadening was the earliest approach developed for using affinity chromatography in the study of reac-tion rates for biological systems. The concept of a theoretical plate in chromato-graphic theory was first developed by Martin and Synge (Martin and Synge 1941) and has since been the subject of many theoretical approaches for describing band broadening (Chen 1988; Felinger 2008; Giddings 1965; Grushka et al. 1975; Horvath 1978; Horvath and Lin 1976). This technique views a chromatographic column as being divided into a number of equally sized regions (i.e., theoretical plates) that each represent a single interaction between the analyte and stationary phase. The height of a theoretical plate (i.e., the plate height, H) is the corresponding aver-age distance that a given analyte travels through the column between each of these interactions. The number of theoretical plates (N) and total plate height (H or Htotal) that are observed for an analyte in a chromatographic system can, in turn, be related to the measured variance (σR

2) and retention time (tR) of the analyte, as shown in Equation 4.19,

NtR

R

=2

2σ H

LN

= (4.19)

where L is the length of the column.A number of different processes contribute to the broadening of a chromato-

graphic profile as an analyte travels through a column, each of which can be described by its own plate height term. For instance, the plate height contribution due to mobile phase mass transfer and eddy diffusion (Hm) describes the broadening that occurs due to differential migration paths and interparticle flow profiles. The plate height contribution due to the longitudinal diffusion (HL) describes broad-ening due to axial diffusion of solutes. Two other important contributions to the measured band broadening are the plate height contributions due to stagnant mobile phase mass transfer (Hsm) and stationary phase mass transfer (Hk), which are related to the mass transfer and interaction processes, respectively, that were given earlier in Equation 4.18. The result of each of these processes is that one subset of the analyte population moves faster than another, resulting in broadening of the peak profile of the analyte (Giddings 1991). Equation 4.20 shows how the total observed plate height (Htotal) for an analyte on a column is equal to the sum of the individual contributions of these processes to the broadening of the profile for the analyte.

HL

tH H H HR

Rm L ktotal = ⋅ = + + +σ2

2 sm (4.20)

As its name implies, the plate height method (or band broadening method) makes use of plate height and band broadening measurements to obtain information on the

84534.indb 168 11/5/09 12:27:34 PM


rate of an analyte–ligand interaction. In this method, it is typically assumed that the contribution of HL to the total plate height is negligible and that Hm is constant, as is often true at the flow rates that are commonly used in affinity chromatography. The following equations are then used to provide estimates of Hsm and Hk or to measure these terms from independent band broadening studies with retained and non-retained solutes, respectively (Walters 1987).

Hu V

VV

k

k V k

PM

P

Msm =

⋅ ⋅ + ⋅

⋅ +−

2 1

1

2

12( )

(4.21)

Hu k

k kkd

= ⋅ ⋅⋅ +2

1 2( ) (4.22)

In these equations, u is the linear velocity of the flowing mobile phase, VP is the pore volume of the support, VM is the column void volume, k is the retention factor of the analyte, and all other terms are as described previously.

In the first step of the plate height method, Equations 4.20 to 4.22 combine to give the following expression for a non-retained solute (k = 0); this makes it possible to estimate k−1 and the plate height terms Hm and Hsm (as represented by the terms on the right) for the analyte.

H Hu V

k VmP

MTotal = + ⋅ ⋅

−

2

1

(4.23)

To use this relationship, the analyte of interest is injected onto an inert control column or a non-retained species is injected onto a column containing the desired ligand. These injections are made at various flow rates to obtain plate height measurements at k = 0. A plot of Htotal versus u is then made and examined by linear regression to give k−1 from the best-fit slope and Hm from the best-fit intercept.

In the second step of the plate height method, injections of the analyte of inter-est are made on the column containing immobilized ligand over the same flow rate range. The k−1 value determined from Equation 4.23 is then used along with the analyte retention data to obtain an estimate of the value for Hsm at each flow rate by using Equation 4.21. These resulting values of Hsm and previously determined estimate of Hm are then subtracted in Equation 4.20 from the total measured plate height for the analyte to give the plate height contribution due to stationary phase mass transfer (Hk) at each flow rate. A plot of Hk versus the term [u k/(1 + k)2] is then prepared according to Equation 4.22 (see Figure 4.9). The slope of this plot should have an intercept of zero, and the inverse of the slope can be used to provide the dis-sociation rate constant for the analyte/ligand system. The association rate constant (ka) can then be calculated using an independent measure of KA (e.g., from the frontal analysis or zonal elution equilibrium methods described earlier). In this approach

84534.indb 169 11/5/09 12:27:35 PM


the values of kd and ka that are obtained are true chemical interaction rate constants because the mass transfer contribution has been eliminated in the correction for Hsm. The conditions that are required to allow for accurate measurements of rate con-stants by this approach have been described previously (Walters 1987).

An early application of the plate height method involved its use to examine the rates at which various sugars bind to concanavalin A (Anderson and Walters 1986). More recently, this technique has been used to measure rate constants for drug and solute interactions with the protein HSA (Loun and Hage 1996; Yang and Hage 1997). The information obtained from this latter type of study has been shown to be important in optimizing chiral separations based on HSA, including the effects of

0.06(a)

(b)

0.04

0.02

Hto

t (cm

)

0

0.04

0.02

0.03

0.01

Hs (

cm)

0

0 4 8 12u (cm/min)

16 20

0 2 4u k´/(1 + k )2 (cm/min)

6 8

fIgure 4.9 Typical results obtained in the plate height method for (a) plots of the total plate height (Htot) versus linear velocity (u) using the injection of D-tryptophan onto an immo-bilized HSA column, and (b) the corresponding plot of the plate height contribution due to stationary phase mass transfer (Hk ) versus u k/(1 + k)2 after correcting the data for other band broadening contributions. (From Yang, J. and Hage, D. S., J. Chromatogr. A, 766, 15–25, 1997. With permission.)

84534.indb 170 11/5/09 12:27:36 PM


varying the temperature, pH, and solvent polarity on drug–protein interactions (Loun and Hage 1996; Yang and Hage 1997). This kinetic data has also been shown to be useful in describing the pharmacokinetics of drugs that bind to HSA (Berezhovskiy 2006; Smith et al. 2000) and in developing new assays for measurement of free drug or hormone fractions in serum (Clarke et al. 2005; Ohnmacht et al. 2006).

4.3.2.2 peak profilingAn approach that is closely related to the plate height method is the technique of peak profiling. The theory for this approach in affinity chromatography was first reported in 1975 by Denizot and Delaage, who based their work on the molecular dynamic theory of chromatography that was previously developed by Giddings and Eyring (Denizot and Delaage 1975; Giddings and Eyring 1955). In this method, the retention time of an analyte from a column and the distribution of this analyte (i.e., as given by its peak variance and second statistical moment) are seen as being depen-dent on the number of interactions that occur as the analyte passes through the col-umn and on the corresponding rates of analyte–ligand association and dissociation. Both measurements of the retention time for an analyte (tR) and the elution time of a non-retained solute (tM) are made on the same system by this approach. These elution times are then used with variances observed for the peaks of the analyte (σR

2 ) and non-retained species (σM

2 ) in Equation 4.24 to calculate the dissociation rate constant (kd,app) for this interaction (Denizot and Delaage 1975),

kt t tt tdM R M

R M M R,

( )app = ⋅ ⋅ −

⋅ − ⋅2 2

2 2 2 2σ σ (4.24)

where kd,app values calculated using Equation 4.24 are for data measured at a single linear velocity and will be referred to as such in this review.

An early application of the peak profiling method involved its use in studying the kinetics of bovine neurophysin II (BNP II) self association and the binding of this agent with the neuropeptide Arg8-vasopressin (AVP). In these experiments, BNP II was immobilized on either non-porous or porous glass beads. However, it was found that rate constants determined by this initial approach were underestimated by orders of magnitude compared to solution phase studies, especially when using porous sup-ports (Swaisgood and Chaiken 1987, 1986). One likely reason for these deviations include the presence of differences in the stagnant mobile phase mass transfer con-tributions for the retained and non-retained species, and the use of relatively low flow rates and fraction collection for these studies. Later, this same method was utilized as part of an HPLC system to examine the dissociation kinetics of sugars injected onto an immobilized concanavalin A column (Muller and Carr 1984). Further analysis of this system indicated these results were also underestimated due, in part, to working under non-linear conditions (Muller and Carr 1984; Wade et al. 1987). Later work examined the binding of L-tryptophan with immobilized HSA by this approach in a system that used smaller columns, a monodisperse HPLC support material, and high injection flow rates, giving good agreement with literature values (Talbert et al. 2002). However, this method still assumed that the value of Hsm was either negligible or similar for the retained and non-retained species.

84534.indb 171 11/5/09 12:27:37 PM


A hybrid version of this approach that combines features of both peak profiling and band broadening measurements was recently developed to better understand the chromatographic variables that might affect rate constant measurements using Equation 4.24 (see Figure 4.10). In this method, Equation 4.24 was rearranged into a form that is expressed in terms of the plate heights for the retained and non-retained species (HR and HM), the retention factor for the retained species, and the linear velocity of the mobile phase (Schiel, Ohnmacht et al. 2009).

H Hu k

k kHR M

dk− = ⋅ ⋅

⋅ +=2

1 2,app ( )

(4.25)

Equation 4.25 predicts that a plot of HR−HM versus [u k/(1 + k)2] should be linear with a best-fit slope from which the dissociation rate constant for the analyte-ligand interaction can be estimated. The results of this approach were compared to those obtained by the traditional peak profiling measurements at a single linear velocity by using the L-tryptophan/HSA system as a model. It was found that the single point method resulted in a kd,app value that varied with linear velocity, while the use of Equation 4.25 and data obtained at multiple linear velocities allowed for more precise and accurate estimates of dissociation rate constants (Schiel, Ohnmacht et al. 2009).

SampleinjectorPump

Detector

Affinity column

Inject analyteand void markerat multiple flowrates

Calculate HR, HM, k,and u from peakmoments

Repeat with columnscontaining supportswith different particlediametersCombine multi-

column data

tR (or M)

00.010.020.030.040.050.06

0 0.01 0.02 0.03 0.04 0.05 0.06

HR-H

M

u k/(1 + k)2

2slope =k

d,l

00.10.20.30.40.50.60.70.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6d

P2 (cm2 × 106)

Mea

sure

d slo

pe

2k

d intercept=

0 100

Abs

orba

nce

200 300Time (s)

400 500 600 0 10

Abs

orba

nce

20 30Time (s)

40 50 60

σ2R(orM)

fIgure 4.10 Scheme for a multi-column peak profiling method.

84534.indb 172 11/5/09 12:27:38 PM


It is possible to expand Equation 4.25 to differentiate between binding of an analyte with an immobilized ligand or non-specific interactions with the chromato-graphic support, as is shown in Equation 4.26 for a two-site binding model (Schiel, Papastavros et al. 2009).

H Hkk k kR M

L

dL

n

dn

− = ⋅+

⋅ ⋅ + ⋅

u( ) ,app ,app1

2 22

α α

= +H Hk L k n, , (4.26)

In this equation, the subscript L refers to the immobilized ligand, the subscript n refers to non-specific interaction with the support, and α is the fraction of total retention due to interaction at site i. This expanded equation has been successfully used to examine the kinetics of binding between immobilized HSA and the drugs impramine and propranolol, which both had significant non-specific binding to the chromatographic support employed in these experiments (Schiel, Papastavros et al. 2009).

Equation 4.25 can also be expanded and modified to correct for the contribution of stagnant mobile phase mass transfer in peak profiling studies, as illustrated in Equation 4.27 (Schiel, Ohnmacht et al. 2009).

H Hkk k

d k

DR Md

p− = ⋅+

⋅ ++ ⋅⋅ ⋅

u( )

( )

12 2 3

602

2

γ (4.27)

In this relationship, dp is the particle diameter of the support packing material, γ is the tortuosity factor, and D is the diffusion coefficient of the analyte. This expanded form of Equation 4.25 has been compared with Equation 4.25 in the rate constant measurements for the L-tryptophan/HSA system by using a series of columns that contained supports with different particle diameters. The overall process used in this work is illustrated by the example in Figure 4.10. In this method, a graph was made by using the slopes for plots of HR − HM versus [u k/(1 + k)2] and the known values of dp for each column. This graph made it possible to correct for stagnant mobile phase mass transfer (as represented by the term in parenthesis to the far right of Equation 4.27) and provided an intercept that gave the true dissociation rate constant for the analyte–ligand interaction (Schiel, Ohnmacht et al. 2009).

4.3.2.3 practical ConsiderationsMany of the practical considerations that were described for zonal elution in equilibrium and thermodynamic measurements also apply to the plate height and peak profiling methods. The conditions needed to obtain linear elution behavior can be determined in these methods by first injecting increasing sample concen-trations and finding the range that provides consistent analyte retention and peak shape. The appropriate column size can then be selected to give retention times that are in a usable range for such studies, with higher affinity analytes requir-ing smaller columns to provide reasonable elution times. In addition, the use

84534.indb 173 11/5/09 12:27:39 PM


of small diameter packing materials can be used to reduce any contributions to rate constant estimates due to stagnant mobile phase mass transfer. Corrections for errors that are due to stagnant mobile phase mass transfer are most accu-rately made by using the multi-column approach in peak profiling; however, this approach does increase the analysis time because experiments must be performed on multiple columns.

It is important in both the plate height and peak profiling methods to use the true retentions and variances of the experimental peaks. This is typically achieved by measuring the first statistical moment (giving the retention time) and second statistical moment (giving the variance) for each peak. It is also neces-sary to correct for any extra-column elution time or band broadening that may be present, which can be measured by injecting the analyte onto the chromato-graphic system when all components except the column are present (Hage and Chen 2006).

The plate height and the traditional peak profiling methods both require that the analyte–ligand interaction (as represented by the plate height term Hk) is the domi-nant factor contributing to the overall measured plate height and variance for the analyte. Theoretical studies have shown that the relative contribution of Hk to the total plate height is highest when k = 1 for an analyte (Walters 1987). This condition can be reached by varying the amount of ligand in the column or by adding a com-peting agent to adjust retention for the analyte (Hage and Chen 2006). The multi- column approach in peak profiling is capable of correcting for these Hsm-related errors by allowing kinetic values to be measured in cases even where the contribu-tion of stationary phase mass transfer is relatively small.

The peak profiling method can increase the throughput of kinetic measurements compared to the plate height method. In addition, there is no need to individually estimate each plate height contribution in the peak profiling methods, thus simpli-fying the data analysis and minimizing the possibility of propagated errors. One possible limitation of the peak profiling method versus the plate height method is that higher linear velocities are often used in the former method. These higher linear velocities mean that relatively sharp peaks must be produced in the technique, which requires a fast sampling rate to minimize the effect of any electronic dampening on the measured peak variance.

4.3.3 non-linear elution methodS

4.3.3.1 non-linear peak fittingThe plate height and peak profiling methods described in the last section both use dilute amounts of analyte and linear elution conditions to examine the kinet-ics of analyte–ligand interactions. Similar methods have also been developed that allow the use of much higher analyte concentrations in such work (i.e., non-linear elution conditions), thus affording easier analyte detection. The first group of these non-linear methods uses theoretical descriptions of eluting peak profiles and fitted peak parameters to obtain information from experimental peaks on analyte/ligand kinetics.

84534.indb 174 11/5/09 12:27:39 PM


Equation 4.28 shows one common equation that is used to fit peaks obtained under non-linear conditions in zonal elution studies (Thomas 1944; Wade et al. 1987).

yaa

e

ax

Ia x

ae

a a

x a

= −[ ]⋅⋅

−( )

− −

0

3

11

1

21

2

3 2/

11 2

3 21 11

2 2

/

/,

a

a aTaa

xa

e−

−[ ]

−

(4.28)

In this equation, y is the intensity of the measured signal, x is the reduced retention time, T is a switching function, and I1 is a modified Bessel function. The terms a0 through a3 are the best-fit parameters used in fitting this equation to an experimental peak. These parameters are then used to estimate the value of the rate constants and equilibrium constant for the analyte–ligand interaction. For instance, the values of k, kd,app, and KA are determined directly from the fit parameters by using the relation-ships k = a1, kd,app = 1/a2tM, and KA = a3/Co, where tM is the column void time and Co is the concentration of injected solute multiplied by the sample width (Moaddel and Wainer 2007). The apparent value of the association rate constant can then also be determined by using the expression ka,app = kd,appKA.

Equation 4.28 was developed by extending the theory of non-linear frontal application to an infinitely narrow zonal injection (i.e., impulse input) (Thomas 1944; Wade et al. 1987). The model used to obtain this equation assumes that the axial dispersion contribution to band broadening (i.e., HL ) is negligible and that stagnant mobile phase mass transfer (i.e., Hsm) can be included as part of apparent values for ka,app and kd,app. This method was initially used by Wade et al. to study the binding of pNp-mannoside to an immobilized concanavalin A column (Wade et al. 1987).

More recently this approach has been used by Wainer and co-workers to char-acterize the binding of various inhibitors to immobilized nicotinic acetylcholine receptor (nAChR) membrane affinity HPLC columns (Jozwiak et al. 2002; Jozwiak et al. 2003; Jozwiak et al. 2007; Jozwiak et al. 2004; Moaddel et al. 2005; Moaddel and Wainer 2007). An example of this type of experiment is given in Figure 4.11 for two enantiomeric inhibitors, levomethorphan and dextromethorphan. The rela-tive retention and broadening of these two peaks is a function of the affinity and kinetic parameters that characterize the α3β4 nAChR-inhibitor interaction. The best-fit parameters for these peaks yielded a slower dissociation rate constant for dextromethorphan than levomethorphan, which was in agreement with other methods and highlights the influence of kinetics on this inhibitory effect. Similar experiments on other inhibitors were used to develop quantitative-structure activity relationships (QSARs) for these inhibitor/nAChR interactions. This approach has also been used to perform studies on immobilized heat shock protein 90, a molecu-lar chaperone protein that has been noted to have increased activity in some types of cancer (Marszall et al. 2008).

A relationship similar to Equation 4.28 was derived by Lee and Chuang to describe peak shapes for the non-specific elution of an otherwise irreversibly retained solute

84534.indb 175 11/5/09 12:27:40 PM


(Lee and Chuang 1996). The derivation of this expression was similar to that used in obtaining Equation 4.28 (Wade et al. 1987); however, it was now assumed in the initial boundary conditions that the amount of injected sample was small compared to the column binding capacity and it was assumed that analyte movement from the column began only after the mobile phase was changed to an elution buffer. Data obtained for the use of a pH step to elute human IgG from immobilized protein A on non-porous silica were fit to the equation. A good fit to the peaks for IgG were obtained, giving an estimated dissociation rate constant of 1.5 s−1 for IgG from pro-tein in the presence of pH 3.0, 0.1 M phosphate buffer (Lee and Chuang 1996). The same technique and equation have been used to examine the elution of lysozyme from a Cibacron Blue 3GA affinity column in the presence of various concentrations of sodium chloride in the mobile phase (Lee and Chen 2001).

4.3.3.2 frontal analysisThe kinetics of solute–ligand interactions have also been measured by fitting pro-files that have been generated when using frontal analysis and affinity chromatography. These experiments involve the continuous application of a mobile phase containing the analyte of interest, as opposed to a finite injection band as is used in zonal elution (see Figures 4.1 and 4.2). Many of the models and expressions that are used for this purpose are based on the initial work of Thomas (1944). This model gives an appar-ent rate constant for analyte binding to the column (ki,app), in which it is assumed that mass transfer is infinitely fast and analyte adsorption is described by second-order Langmuir kinetics based on interaction at a single type of homogeneous ligand bind-ing site (Golshan-Shirazi and Guichon 1992; Mao et al. 1991; Thomas 1944).

This general model has been used to examine the adsorption of lysozyme to a Cibacron Blue F3GA column containing non-porous support particles (NPPAM) (Mao et al. 1991). Although a Langmuir adsorption mechanism was assumed to be

1200

1000

800Si

gnal

inte

nsity

(TIC

)

600

400

200

00 20 40

Retention time (min)

DM

LM

60 80 100

fIgure 4.11 Representative chromatograms obtained under non-linear conditions and analyzed by peak fitting for levomethorphan (LM) and dextromethorphan (DM) on an immobilized α3β4 nAChR membrane affinity column. (From Jozwiak, K., Hernandex, S. C., Kellar, K. J., and Wainer, I., J. Chromatogr. B, 797, 373–379, 2003. With permission.)

84534.indb 176 11/5/09 12:27:41 PM


present, no assumption was made as to whether mass transfer or adsorption was the rate limiting step in analyte retention. Instead, mass transfer was treated as a film resistance mechanism. Simulations with this model were used to help understand the effects of particle diameter, concentration, flow rate, and the association rate constant on frontal analysis profiles. Such simulations were then used to examine the binding of lysozyme to Cibacron Blue 3GA. As is commonly seen for simple Langmuir models, the resulting fit was good at the beginning of the breakthrough curve, but ligand heterogeneity was thought to result in deviations from the fitted model at the end of the breakthrough curve (Mao et al. 1991).

The binding of HSA to affinity columns containing immobilized antibodies was examined by using frontal analysis along with a Langmuir adsorption model and a rectangular isotherm, in which dissociation of the analyte was assumed to be negli-gible on the timescale of the experiment (i.e., kd was essentially zero) (Renard et al. 1995). A flow rate dependence of the measured apparent association rate constant was observed due to the contribution of mass transfer. Columns of various loading capac-ity were used along with the following equation to correct for such contributions,

1 1

k kq VFna a

x M

mt,app

= + (4.29)

in which nmt is an overall mass transfer coefficient dependent on the packing and column dimensions, F is the flow rate, VM is the void volume, and qx is the load-ing capacity of the column. A plot of 1/ka,app versus qx was then prepared, and the intercept used to calculate the true association rate constant ka for the HSA-antibody interaction, giving results in good agreement with those reported in the literature (Renard et al. 1995). A similar approach for correcting for mass transfer contribu-tions has been utilized to study the interaction of fibrinogen with immobilized pep-tides (de Lucena et al. 1999).

Langmuir models based on two independent binding sites have been employed in some studies to examine the rates of analyte–ligand interactions by frontal analy-sis. This bi-Langmuir model was found to be useful in comparing the adsorption of HSA to various chromatographic stationary phases (Jaulmes et al. 2001) and in describing the adsorption of ß-lactoglobulin to immobilized polyclonal antibodies (Puerta et al. 2002). However, repeated injections indicated that the interaction of ß-lactoglobulin with the polyclonal antibodies was not irreversible over the timescale of the experiment, making it impossible to determine equilibrium binding constants under such conditions. This lead to the development of a sequential frontal analysis system which made use of two sequential frontal applications of the analyte that were separated by a rinsing step of a predefined duration (Puerta et al. 2006). During this rinsing step some, but not all, of the adsorbed analyte was able to desorb as a function of the dissociation rate constant. This effect alters the results of the second frontal application due to incomplete washing of the binding sites, and allowed the use of the simultaneous fitting of both frontal curves by a bi-Langmuir adsorption model to provide the apparent association and dissociation rate constants for this system (Puerta et al. 2006).

84534.indb 177 11/5/09 12:27:41 PM


Another interesting treatment of non-linear frontal analysis data has involved the use of linear chromatographic theory to determine concentration-dependent rate constants, and then to extrapolate these values to infinite dilution. According to chro-matographic theory, the following equation is true under linear elution conditions (Hethcote and Delisi 1982a, 1982b; Munro et al. 1993; Winzor et al. 1991; Winzor 2006).

kV V

d dFdA A

A

=−( )2

2

*

/σ (4.30)

In this equation, VA is the breakthrough volume of the analyte, and VA* is the break-

through volume of a non-retained solute, F is the flow rate, and σ A2 is the variance

of the breakthrough curve. A plot of σ A2 versus F is prepared for data obtained

by frontal analysis at a range of flow rates and gives a slope which yields (dσ A2 /

dF)app. The effects of slow mass transfer can be corrected for empirically in this approach by making analyte injections on a column with no immobilized ligand (Munro et al. 1993) or by using an analytical solution (Munro et al. 1994) to obtain the corrected value for dσ A

2 /dF. This process is done for a range of concentrations, each of which will result in a different value for dσ A

2 /dF. Each dσ A2 /dF result is

then used to calculate a kd,conc, which is corrected for mass transfer contributions but is still concentration-dependent due to the concentration range that is used in frontal analysis. The resulting values of kd,conc at various concentrations are then extrapolated to infinite dilution to give the true value of kd. This general approach has been used to examine the binding of sugars with immobilized concanavalin A (Munro et al. 1994, 1993).

4.3.3.3 split-peak methodThe split-peak method is based on the idea that there is a given probability during any separation process that a small fraction of analyte will elute non-retained from the column without interacting with the stationary phase. This phenomenon, which is illustrated in Figure 4.12a, is known as the split-peak effect. The following equa-tion derived under linear elution conditions shows how the presence of either slow mass transfer (as represented by 1/k1 Ve) or slow adsorption (represented by 1/ka mL ) will affect the fraction of solute that elutes non-retained from the column ( f) when the split-peak effect occurs.

− = +

1 1 1

1ln fF

k V k me a L

(4.31)

In this equation, F is the flow rate, mL is the active moles of immobilized ligand, and Ve is the excluded volume, k1 is the forward mass transfer rate constant and ka is the association rate constant for analyte–ligand binding (Hage et al. 1986). The advan-tage of using such an equation for rate constant determinations is that it is simple to perform and only requires area measurements. The main limitation of this approach is that it is typically limited to analytes with slow dissociation kinetics (generally

84534.indb 178 11/5/09 12:27:43 PM


indicating the presence of high affinity interactions), as is assumed in the derivation of Equation 4.31.

Although Equation 4.31 was originally derived for work under linear elution conditions, it has been used under non-linear elution conditions by extrapolating its results to infinite dilution. This extrapolation is done by measuring the peak areas of the retained and non-retained analyte fractions over a range of flow rates. The ratio of the peak areas at each flow rate is then analyzed according to Equation 4.31 by making a plot of −1/ln f versus F for a series of analyte concentrations (see Figure 4.12b). The measured slope at each analyte concentration is then extrapolated to an infinitely dilute sample by using linear regression (Hage et al. 1986; Walters 1987). As can be seen from Equation 4.31, the slope of such a plot is expected to be a function of both mass transfer and adsorption rate constants. The process which is making the dominant contribution to this slope can be determined by compar-ing the measured slope of this plot with independent estimates of the mass transfer

Diol-bonded silica column, 2.0 ml/min

Protein G column, 2.0 ml/min

1.5 ml/min

1.0 ml/min

0.5 ml/min

0 6 12Time after injection (sec)

(a)

(b)0.6

0.4

–1/ln

f

0.2

0.0

Abs

orba

nce,

280

nm

18 24

0.0 1.0Flow-rate (ml/min)

2.0 3.0

fIgure 4.12 (a) Representative split-peak data for the injection of immunoglobulin G (IgG) onto a diol-bonded control column or a protein G column and (b) analysis of such data by using a plot of −1/ln f versus F, as prepared according to Equation 4.31. (From Rollag, J. G. and Hage, D. S., J. Chromatogr. A., 795, 185–198, 1998. With permission.)

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contribution made by injecting the same analyte on an inert control column or on a column with rapid association kinetics (Hage et al. 1986; Walters 1987).

The split-peak method was used by Hage et al. to study the binding kinetics of rabbit IgG on various affinity columns containing immobilized protein A. The results suggested that the rate limiting process for analyte retention (i.e., mass trans-fer or adsorption) was dependent on the support characteristics and immobilization method (Hage et al. 1986). This information made it possible to determine the appar-ent rate constant for IgG binding to protein A and to optimize the performance of protein A affinity supports for the analysis of clinical samples (Hage et al. 1986; Walters 1987).

The presence of non-linear elution conditions is known to increase the size of the split-peak effect compared to the response that is predicted by Equation 4.31 under linear conditions (Hage et al. 1986). Computer simulations have been used to determine the extent of these deviations for a homogeneous ligand under both mass transfer- and adsorption-limited conditions (Hage and Walters 1988). Equation 4.31 and the simulations for an adsorption-limited case have also been expanded to consider the effect of a heterogeneous ligand on the split-peak method (Rollag and Hage 1998). The binding of IgG on columns that contained recombinant single domain protein A and/or protein G were used as experimental models in these studies, as illustrated in Figure 4.12. These studies have confirmed the use of linear extrapolation to infinitely dilute samples as a means that can accurately determine association rate constants for either homogeneous (Hage and Walters 1988) or heterogeneous ligand systems (Rollag and Hage 1998) displaying adsorption limited-kinetics. For example, independent estimates of apparent association rate constants measured on columns containing only protein A or protein G were used to calculate the values that were expected for a column containing a known mixture of these two ligands. This approach gave good agreement with the extrapolated value of 2.5 (± 0.1) x 106 M−1s−1 that was found when using the results in Figure 4.12 (Rollag and Hage 1998).

It is possible in some cases to obtain an exact solution for the split-peak effect under non-linear elution conditions. The most common example is given in Equation 4.32, which has been derived in various forms to describe the split-peak effect for a homogeneous ligand with an adsorption-limited rate for analyte retention and essen-tially irreversible adsorption of the analyte under the sample application conditions (Hage et al. 1993; Jaulmes and Vidal-Madjar 1991; Renard et al. 1995; Renard and Vidal-Madjar 1994; Rollag and Hage 1998; Vidal-Madjar et al. 1997).

fS

Ae eo A S So o= + −( )[ ]−

Loadln Load / /1 1 1 (4.32)

In this expression, Load A is the relative moles of analyte applied versus the total moles of active ligand in the column, and So is a combination of system parameters (referred to as the split-peak constant), where So = F/(ka,app mL ). This equation elimi-nates the need to extrapolate to infinite dilution for homogeneous ligands by incor-porating the degree of sample overload directly into the mathematical description of the split-peak effect. This method has been employed to study the binding kinetics

84534.indb 180 11/5/09 12:27:45 PM


of HSA to various antibody systems (Renard et al. 1995; Renard and Vidal-Madjar 1994; Vidal-Madjar et al. 1997) and to describe chromatographic-based competitive binding immunoassays that are based on the split-peak effect (Hage et al. 1993).

4.3.3.4 peak decay methodThe peak decay method is a technique for rate constant measurements where all or most of the ligand sites in a column are first saturated with analyte. In one form of this method, a high concentration of an agent that competes with the analyte for ligand binding sites is later applied to the column. This creates a situation in which once an analyte dissociates from the ligand it is unlikely to rebind. High flow rates are also typically utilized to ensure that once a dissociated analyte molecule enters the flowing mobile phase it will tend to elute from the column rather than reenter the stagnant mobile phase layer. Under these conditions, the observed rate of elu-tion for the analyte should follow a curve that is related to its rate of dissociation from the immobilized ligand if mass transfer is fast versus this dissociation rate (Walters 1987).

The theoretical description of the peak decay method was first reported in 1987 (Moore and Walters 1987). This was done with a model in which band broadening due to longitudinal diffusion and mobile phase mass transfer was considered to be negligible compared to stagnant mobile phase mass transfer and stationary phase mass transfer (i.e., Hsm and Hk are large compared to HL and Hm). The dissociation of the analyte from the ligand and diffusion of the analyte out of the stagnant phase were also treated as irreversible processes on the time scale of the experiment. If dis-sociation is the slower of these latter two processes, it is possible to use Equation 4.33 to find the apparent dissociation rate constant for the analyte during its release from the column by using slope of a plot of the natural logarithm of the peak response versus time (Moore and Walters 1987).

ln lndm

dtmE

E d de

ok k t

= ( ) − (4.33)

In this equation, Ee represents the analyte in the flowing mobile phase that is elut-ing from the column and Eo represents the initial quantity of analyte that was bound to the column. A similar expression can be derived for the case in which the mass transfer of the analyte from the stagnant mobile phase to flow mobile phase is the rate limiting case in analyte release, in which the term kd is replaced with k−1 in Equation 4.33. Computer simulations have been used to find the chromatographic conditions that are needed to obtain accurate estimates of kd by this approach. This method has also been tested by using it to examine the dissociation of sugars from immobilized concanavalin A. It was found in this work that the peak decay method did allow for accurate and precise dissociation rate constants to be obtained for this system as long as sufficiently high flow rates were used for the measurements (Moore and Walters 1987).

This early work with concanavalin A represented a system with moderate-to-high affinity that required the use of a competing agent for analyte elution. In this

84534.indb 181 11/5/09 12:27:45 PM


approach it is necessary for the competing agent to not produce any signal that might interfere with the detection of the decay response for the analyte (Walters 1987). It has recently been shown that the peak decay method can also be used with weak to moderate affinity systems without requiring any competing agent (Chen 2003). This was accomplished by using short affinity columns (e.g., 2.5 mm in length) and high flow rates to reduce the probability of analyte re-association to the point where no competing agent was necessary. This non-competitive peak decay method was used to measure the dissociation rates of R- and S-warfarin from immobilized HSA. Figure 4.13 shows representative chromatograms for this system and logarithmic peak decay profiles that were analyzed according to Equation 4.33. This method was found to be relatively fast to perform and gave dissociation rate constants for R- and S-warfarin with HSA (0.56 and 0.66 (± 0.01) s−1, respectively) that were in good agreement with previous measurements for this system (Chen 2003; Chen et al. 2009).

(a)

10 15 20 25Time (s)

Resp

onse

(b)

0 5

0 5 10 15 20 25Time (s)

ln (r

espo

nse)

fIgure 4.13 Results for a peak decay analysis as represented by (a) the original chromato-grams and (b) logarithmic response for 100 µL injections of racemic warfarin onto an inert control column (dashed lines) or immobilized HSA column (solid lines) at 4 mL/min and 25°C at pH 7.0. (Adapted from Chen, J., Chromatographic studies of drug–protein interac-tions, PhD dissertation, University of Nebraska, 2003.)

84534.indb 182 11/5/09 12:27:46 PM


4.3.3.5 Combined assay methodsA few studies have combined several methods for kinetics measurements to study biological interactions by affinity chromatography. One example is work that has been conducted using frontal analysis, the split-peak method, and peak decay anal-ysis to examine analyte retention and elution on immobilized antibody columns (Hage et al. 2006; Nelson 2003). The method was first used to measure the apparent association rate constants for the binding of 2,4-dichlorophenoxyacetic acid (2,4-D) and related herbicides to immobilized monoclonal anti−2,4-D antibodies. A fit of the split-peak expression in Equation 4.32 made it possible to estimate the association rate constants for this system under the same application conditions, while analysis of the breakthrough point of the frontal analysis curve according to Equation 4.11 provided an estimate of the association equilibrium measurements for the same interaction. The mobile phase was then changed to a pH 2.5 buffer for elution of the retained analytes. It was found that this elution could be modeled as a first order decay process, thus allowing the peak decay method to be used to find the appar-ent dissociation rate constant for the analyte under these solution conditions (Hage et al. 2006; Nelson 2003). A similar approach has recently been utilized to examine the binding and elution of an anti-thyroxine aptamer to an immobilized thyroxine column to study the effects of mobile phase ionic strengths on the association kinet-ics of the aptamer-thyroxine complex (Moser 2005).

4.3.3.6 practical ConsiderationsNon-linear methods for kinetic studies in affinity chromatography are well suited to analytes that are highly soluble and/or produce only a limited signal when passed through a detector. In addition, these non-linear methods can be particularly useful when only a small amount of ligand is present in an affinity column, thus making column overloading likely to occur. As was noted for the linear elution methods, it is desirable to use small particle diameter packing materials (or even non-porous mate-rials) in these studies if the goal is to obtain accurate estimates of analyte–ligand dissociation rates. The use of such materials will help to minimize contributions due to stagnant mobile phase mass transfer and make it easier to examine the kinetics of the analyte–ligand interaction.

The approach that should be used for a given system will depend on such factors as the affinity of this system and the degree of accuracy that is desired. Non-linear peak fitting is a relatively fast method and can be used to quickly measure rate constants for a large number of compounds. However, this method is based on an iterative fit to a limited data set and does include stagnant mobile phase contributions as part of the apparent rate constants that it measures. Frontal analysis methods are also easy to perform but are limited by analyte availability and cost. The split-peak method requires only peak area measurements and works well for high affinity analytes, but this approach requires conditions where a portion of the analyte elutes non-retained (e.g., the use of small columns and high injection flow rates). The peak decay method can be used with either weak or moderate affinity analytes but relies on the assump-tion that a molecule is not able to re-adsorb during elution, as is achieved by working at high flow rates and with small columns.

84534.indb 183 11/5/09 12:27:46 PM


Regardless of the method that is chosen for such studies, care must be taken in experimental design to ensure that all assumptions made in the particular theory are valid under the experimental conditions used. Care must also be taken to ensure that the reported values reflect the desired rate constant for the system, whether it is an apparent rate constant or one that specifically describes the rate of mass transfer, dissociation, or adsorption. Apparent rate constants can be useful for comparing different columns or in optimizing separations, but appropriate corrections must be made if the goal is to instead obtain a rate constant that reflects the true interaction rate for the analyte–ligand pair.

4.4 ConClusIons

It has been shown in this review how affinity chromatography can be a valuable tool in the study of biological interactions. Reactions that can be examined by this method vary from simple one-site binding to competitive interactions, multi-site binding, and allosteric processes. Some important advantages of using affinity chromatography to study these processes include the ability of this method to reuse a biological ligand for a large number of experiments, the good precision and accu-racy of this approach, and the capability of modern affinity columns to be used in HPLC systems for high-throughput measurements. All of these features have lead to a growing interest in affinity chromatography as a tool in characterizing biologi-cal interactions.

Many techniques have been described for the investigation of biological inter-actions by affinity chromatography. For instance, equilibrium and thermody-namic studies can be conducted by using either zonal elution or frontal analysis methods. These techniques have been used to obtain information on the binding and competition of solutes for ligands; to examine the effect of changing pH, temperature, or solution conditions on these interactions; and to identify and char-acterize binding sites on ligands. In addition, frontal analysis methods have been shown to be useful tools in combination with mass spectrometry for screening mixtures of compounds (e.g., drug candidates) in their ability to bind to a given immobilized ligand.

A variety of approaches for studying the kinetics of biological interactions have also been reported for use in affinity chromatography. These kinetic tools include plate height measurements, peak profiling, peak fitting in zonal elution or frontal analysis, the split-peak method, and the peak decay method. These methods make it possible to perform kinetic studies for systems that range from weak-to-moderate affinities to those with high affinities. Some of these methods are performed under linear elution conditions (e.g., plate height measurements), while others can be used under non-linear conditions (e.g., frontal analysis with peak fitting or peak decay analysis).

A variety of applications for biointeraction affinity chromatography were discussed in this review. Some examples included the use of this method to examine the inter-actions of drugs with serum proteins, sugars with lectins, receptors with their inhibi-tors, antibodies with antigens, and drug candidates with target proteins. The range of uses for biointeraction affinity chromatography and the continued development of

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new techniques in this field indicate that this area will continue to be a valuable tool in the characterization of biological interactions.

aCknowledgments

This work was supported, in part, by the National Institutes of Health under grants R01 GM044931 and R01 DK069629.

abbrevIatIons

A AnalyteAE Analyte in the flowing mobile phaseA-L Analyte-protein complex (or analyte complex with a binding agent L)a0…a3 Non-linear peak fitting parametersb Fraction of ligand-bound analyteBt Amount of immobilized active ligand (frontal affinity application)D Diffusion coefficientdp Support particle diameterEe Represents analyte in the flowing mobile phase that is elutingEo Represents the initial quantity of analyte that was boundf Fraction of solute eluting non-retained (split-peak fraction); free- fraction

of analyteF Flow rateI1 Modified Bessel functionH or Htotal Total plate heightHk Plate height contribution due to stationary phase mass transferHL Plate height contribution due to longitudinal diffusionHm Plate height contribution due to mobile phase mass transfer and eddy

diffusionHM Total plate height for a non-retained speciesHR Total plate height for a retained speciesHsm Plate height contribution due to stagnant mobile phase mass transferk Retention factork1 Rate constant describing movement of a solute from the flowing mobile

phase to the stagnant mobile phasek−1 Rate constant describing movement of a solute from the stagnant mobile

phase to the flowing mobile phase in a columnKA Association equilibrium constantka Association rate constantka,app Apparent association rate constant which lumps mass transfer and

chemical interaction rate informationKd Dissociation equilibrium constantkd Dissociation rate constantkd,app Apparent dissociation rate constant which lumps mass transfer and

chemical interaction rate information

84534.indb 185 11/5/09 12:27:47 PM


kd,conc Apparent dissociation rate constant due to concentration dependence of non-linear analyte application and use of linear theory

kdL,app Apparent dissociation rate constant for interaction with the immobilized ligand (in situations where the analyte displays non-specific binding with the support)

kdn,app Apparent dissociation rate constant for interaction with the support (in situations where the analyte displays non-specific binding with the support)

kmax Retention factor at maximumkmin Retention factor at minimumL Column length (or ligand in the case of an analyte–ligand interaction)Load A Relative moles of solute applied to the column versus the total moles of

active ligandm Slope of a linear plot to examine peak profiling datamL Mole of active immobilized ligandsn Number of theoretical platesn1…nn Fraction of each type of site in the columnnmt Global mass transfer coefficientqx Column loading capacityR Ideal gas law constantSo Split-peak constant, where So = F/ka,app mL for a homogeneous ligandT Absolute temperaturetM Column void time (corrected for extra column time)tR Retention time for an analyte on a column (corrected for extra column

time)u Linear velocity of the mobile phaseVA Analyte breakthrough volume (frontal application)VA* Non-retained species breakthrough volume (frontal application)VM Column void volumeV0 Breakthrough volume of void marker (frontal affinity application)VP Pore volumeVR Retention volume of analyte (zonal application)Ve Excluded volumex Reduced retention timey Signal intensityκ Kinetic factor for peak profilingγ Tortuosity factorα Ratio of binding capacities for two binding sites (mL1/mL2)αL Fraction of k due to interaction with an immobilized ligandαn Fraction of k due to non-specific interactions with the supportβ Ratio of association equilibrium constants for two binding sites

(Ka2/Ka1)∆G Change in free energy∆H Change in enthalpy∆S Change in entropyσ A

2 Variance of analyte breakthrough curve (frontal application)

84534.indb 186 11/5/09 12:27:47 PM


σM2 Peak variance for a non-retained species (corrected for extra-column

variance)σR

2 Peak variance for a retained species (corrected for extra-column variance)

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195

5 Characterization of Stationary Phases in Supercritical Fluid Chromatography with the Solvation Parameter Model

Caroline West and Eric Lesellier

5.1 IntroduCtIon

Supercritical fluid chromatography (SFC) has long held an uncertain place among other separation techniques. However, recently, packed column SFC (pSFC) has become more attractive again to drug discovery [1–4] because it offers aqueous-free purification capabilities with a reputed green solvent (carbon dioxide), together with

Contents

5.1 Introduction .................................................................................................. 1955.2 Experimental Conditions .............................................................................. 201

5.2.1 Chromatographic System ................................................................. 2015.2.2 Choice of Chromatographic Conditions ...........................................2025.2.3 Selection of Columns ........................................................................2035.2.4. Selection of a Set of Test Compounds ..............................................2065.2.5 Data Analysis .................................................................................... 218

5.3 Choice of Solvation Descriptors for Supercritical Fluids .............................2255.4 A General Database for Packed Column SFC ..............................................228

5.4.1 Variation of the System Constants among the Stationary Phases ....2285.4.2 A Visual Representation of the Database ......................................... 2325.4.3 ODS Phases ......................................................................................2405.4.4 Method Development with the Solvation Parameter Model .............2445.4.5 Predictive Capability of the Models ................................................. 247

5.5 Conclusion ....................................................................................................248References ..............................................................................................................249

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high speed. As a matter of fact, the lower eluent viscosities and higher solute diffu-sivities in SFC often translate into increased efficiency and shorter separation times when compared with high-performance liquid chromatography (HPLC). Shorter analysis time is also the result of the use of larger flow rates (typically 3 to 5 ml min−1) in comparison to HPLC, as the low viscosity of the fluid induces only small pressure drops along the chromatographic column.

Nearly all current research in pSFC is performed with column packings prepared for HPLC, as those work equally in SFC. Only a few manufacturers produce col-umns dedicated to pSFC. Thus, just as for HPLC, most stationary phases are silica-based, chemically bonded or encapsulated, or polymeric; and all available in a wide range of chemistries. The most widely used are bare silica and silica-based sorbents of the monomeric type, bonded with 3-aminopropyl-, 3-cyanopropyl-, or a spacer bonded propanediol-siloxane, thus mostly normal phase HPLC (NP-HPLC) station-ary phases. The 2-ethylpyridine phase introduced by Princeton Chromatography is one of the only original packing designed specifically for SFC, which has faced a certain success. Besides, numerous applications (see for example references [5–13]) have shown in the past that nonpolar phases as octadecylsiloxane-bonded silica (ODS) phases can also be very useful in SFC as they provide improved separations compared to reversed-phase HPLC (RP-HPLC). All stationary phase chemistries are indeed useful in developing an SFC method.

As a matter of fact, due to the variety of possibilities, the initial choice of a chromatographic system (mobile phase and stationary phase) in SFC is a complex problem. Actually, all stationary phases available for HPLC, and any solvent that is miscible to carbon dioxide (and compatible with the stationary phase) can be com-bined. Unfortunately, this wide diversity is generally associated to a global lack of knowledge of the interactions established between the analytes and the chromato-graphic system. Knowledge of the behavior in liquid phase is often of no help as the absence of water in the mobile phase causes drastic differences between reversed-phase HPLC (RPLC) and SFC behaviors. Thus only SFC studies are helpful when developing an SFC method.

As there are few clear guidelines for the choice of a stationary phase for a particu-lar analyte, often more than one phase needs to be examined in order to obtain a suit-able resolution. Luckily, rapid column equilibration makes it easy to use fast gradient analysis or to change the chromatographic parameters as well as the stationary phase for rapid method development. The approach of changing separation selectivity with the stationary phase is especially useful and made easy by modern systems of col-umn selection provided by most SFC systems. With such systems, columns with dif-ferent stationary phases are rapidly scouted using automatic column switching with a single or different mobile phase. However, in too many cases, column selection is based on which column worked best previously. Besides, changing the column for another one that would provide the same selectivity is of no use. Therefore, a tool was needed to determine which stationary phases are most orthogonal and would thus provide complementary selectivities in order to obtain the required separations.

Despite some studies describing the relationship between the chromatographic behaviors and the compound chemical structure, or the eluotropic strength of varied CO2-modifier mobile phases in regards to the one measured in HPLC, performed

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Characterization of Stationary Phases 197

either with ODS [14–18] or polar stationary phases [19–21], there has been surpris-ingly little work done to understand and compare the interactions involved in SFC separations when the stationary phase is varied. Indeed, the primary goal of most pSFC studies was to provide an understanding of the role of solvent modifiers and additives on retention properties. Whenever one separation was investigated on dif-ferent stationary phases, they were only compared under a limited set of conditions. While this information is useful for that particular type of separation, it does not pro-vide information as to which stationary phase is most appropriate for a different sep-aration problem. Furthermore, a direct comparison of literature data from different publications cannot be made easily because most published studies are application studies intended for different solutes, so different operating conditions were used to optimize the separations. As chromatographic effects are compound-dependent, a column superior in one application can appear worse in another.

The retention and selectivity properties of different phases were compared by Schoenmakers et al. [22]. However, this work was carried out with the intent to evaluate stationary phases for use with pure CO2 as a mobile phase, to retain compat-ibility with flame ionization detection. As a matter of fact, the partial conclusions on the elution and on the peak deformation are only valid for these operating conditions, as some stationary phases that were found inappropriate can be very useful if a polar modifier is used in the mobile phase. For instance, the amino phase did not perform well in pure CO2, while it is generally found appropriate when used with a mixed mobile phase. However, the use of a modifier is common practice in pSFC today, thus studies carried out in pure CO2 have no reason for living anymore.

Heaton et al. [23] proposed a retention model for pSFC based on solubility param-eters dissociated into components such as dispersive, dipole–dipole, dipole-induced dipole, and hydrogen bonding. This approach was promising but the authors did not furnish any interpretation of the results, their intention was simply to evaluate the capability of the method for retention prediction.

Judging from this confused situation, a standardized method for the characteriza-tion and comparison of pSFC systems was required. Consequently, we investigated a number of columns containing various bonding chemistries and obtained from a variety of manufacturers. Our objective was to acquire semi-quantitative knowl-edge of the physico-chemical interactions governing retention and separations in a given chromatographic system. We wished to be able to compare different stationary phases, but also different mobile phases. Indeed, as the stationary phase is solvated and, as this solvation can be selective when the mobile phase is binary or ternary, the three-dimensional structure and the solvation state of the stationary phase depend on the composition of the mobile phase. As a matter of fact, the chromatographic behav-ior of a stationary phase depends on the mobile phase used. Thus the chosen testing procedure had to allow knowing the chromatographic properties of the stationary phase equilibrated with a given mobile phase. Besides, the interest in comparing mobile phase effects with one stationary phase was also related to our will to com-pare HPLC and SFC on a reasonable basis.

Among the possible criteria used to evaluate the stationary phase properties, the physical parameters of the column (carbon load, particle size, specific surface area…) generally show no simple and direct correlation with their performances,

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and thus are not very informative on the final separation quality. The spectromet-ric analyses (NMR, infrared, or x-ray fluorescence spectroscopic techniques) are employed to study the surface of the stationary phase but the relationship with chro-matographic performance is variable. Only the observation of the chromatographic behavior of varied compounds can inform on the selectivity of a chromatographic system. However, a method was required to extract microscopic information (the nature of the molecular interactions established between the solutes and station-ary and mobile phases) based on macroscopic data (chromatographic retention factors).

No standard test has been accepted and prevails for the characterization of chro-matographic systems but some of them are more popular than others. In order to com-pare SFC observations with HPLC, we chose to focus on existing testing procedures, which relevance had already been established, rather than trying to conceive a new test for the chromatographic systems we wished to characterize. Besides, an accept-able testing procedure had to be relatively rapid, reproducible, and cheap. A variety of such tests established for HPLC or GC can be found in the literature.

The key-solute method has been widely used, particularly for the characteriza-tion of ODS phases in HPLC. It is based on the use of a small set of solutes, which behavior (retention factor or separation factors between two solutes) is supposed to be representative of the retention of any possible solute, or characterizes a particular property of the stationary phase as bonding density, or the accessibility to resid-ual silanol groups. However, depending on the chosen solutes, the results are not always consistent between two tests. The choice of compounds itself can be dubious. Methods exist that can help selecting the best solute set, as principal component analysis (PCA), but chromatographic common sense is often the most efficient tool for this selection.

PCA is a powerful tool for the comparison of a great amount of data. However the interpretation of the results is generally not simple because each principal com-ponent may contain information from several different parameters, thus its signifi-cance often remains abstract. The reduction of the number of parameters can help in simplifying the problem and improving the understanding, but this operation can be a delicate one.

Quantitative structure-retention relationships (QSRRs) are another alternative to the above methods. They consist of extracting precise data for the characterization of chromatographic systems from a great number of key-solutes. Judging from the abundant literature on QSRRs, it is clear that they allow comparisons of chromato-graphic systems in an efficient manner. Two types of data are necessary to construct a QSRR: chromatographic retention data for a sufficiently large group of compounds, and a group of data supposedly reflecting the physico-chemical properties of the said solutes. This last point, the representation of molecular structures, is the very heart of QSRRs. Indeed, it is necessary to convert the molecular structure into mathemati-cal data; that is to say to calculate solute descriptors.

Among QSRRs, the solvation parameter model using Abraham descriptors has gained acceptance as a general tool to explore the factors affecting retention in chromatographic systems [24–26]. The retention of selected probes can be related

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through this relationship, also known as linear solvation energy relationship (LSER), to specific interactions by the following equation, with the notation that is now com-monly adopted:

log k = c + eE + sS + aA + bB + vV (5.1)

In this equation, capital letters represent Abraham solute descriptors, related to particular interaction properties, while lower case letters represent the system con-stants, related to the complementary effect of the phases on these interactions. c is the model intercept term, which when the retention factor is used as the dependent variable is dominated by the phase ratio, i.e., the ratio of stationary and mobile phase volumes. The following terms are represented on Figure 5.1. E is the excess molar refraction (calculated from the refractive index of the molecule) and models polariz-ability contributions from n and π electrons; S is the solute dipolarity / polarizability; A and B are the solute overall hydrogen-bond acidity and basicity; V is McGowan characteristic volume in units of cm3 mol–1/100. The system constants (e, s, a, b, v), obtained through a multilinear regression of the retention data for a certain num-ber of solutes with known descriptors, reflect the magnitude of difference for that particular property between the mobile and stationary phases. Thus, if a particular coefficient is numerically large, then any solute having the complementary property will interact very strongly with either the mobile phase (if the coefficient is negative) or the stationary phase (if the coefficient is positive). Moreover, Equation 5.2 can be deduced from Equation 5.1:

log α = eΔE + sΔS + aΔA + bΔB + vΔV (5.2)

Where α is the separation factor between two solutes and ΔX represents the differ-ence in the X descriptor between these two solutes. Consequently, the coefficients (e, s, a, b, v) do not reflect only the retention properties of the chromatographic system but also its selectivity toward any particular molecular interaction.

The possible use of the above equations naturally depends on the availability of Abraham descriptors in the scientific literature. Those are now accessible for a wide range of solutes (about 4000) but for the model to have practical utility it will always be necessary to determine them for new solutes. This can be achieved through exper-iments (for all descriptors) [24], simple calculation (for E and V) [27–28], or with a fragment method of calculation (for E, S, A, B, and L) [29–30], which is the base of a software program (Absolv, Pharma Algorithms) [31].

Furthermore, the solvation parameter model uses parameters issued from chro-matographic retention data obtained in GC and HPLC, as well as solvent–solvent equilibrium constants. As a matter of fact, it is principally based on data issued from partition processes. However, no assumption is made on the processes involved in the investigated system and it has been successfully used to describe phenom-ena relevant to adsorption processes. Although the statistical quality of models for adsorption processes are not as good as for partition systems, the results are chemi-cally sound [32]. A consequence of this is the wide applicability of the model to

84534.indb 199 11/5/09 12:27:50 PM


B:O

H

OO

OO

OO

OO

OO

XHO

OO

H

Eπ–

π in

tera

ctio

nsdi

pole

-indu

ced

dipo

ledi

sper

sive

SD

ipol

e–di

pole

dipo

le-in

duce

d di

pole

AH

ydro

gen-

bond

ing

with

a H

-don

or s

olut

e

BH

ydro

gen-

bond

ing

with

a H

-acc

epto

r sol

ute

VD

ispe

rsiv

e in

tera

ctio

nsca

vity

effe

cts

(in c

onde

nsed

pha

ses)

fIg

ur

e 5.

1 P

rinc

iple

of

the

solv

atio

n pa

ram

eter

mod

el: i

nter

acti

ons

rela

ted

to e

ach

solu

te d

escr

ipto

r.

84534.indb 200 11/5/09 12:27:51 PM


diverse and complex processes, as evidenced by the abundant literature. This was perfectly suited to our needs, as we expected to be able to compare very different stationary phase chemistries, ranging from bare silica to ODS phases.

At the time we started our studies, there were only a few reported SFC applica-tions of the use of the solvation parameter model: retention has been studied on ODS phases [33], cyanopropylsiloxane-bonded silica [34–35], divinylbenzene-ODS [36–37], polydimethylsiloxane [38–39], and porous graphitic carbon (PGC) [40–42] stationary phases. These models were all established with different mobile phases, temperatures, and pressure conditions, again rendering all comparisons quite diffi-cult. Indeed, since the system constants represent the difference in sorption interac-tions for the solute in the mobile and stationary phase, any meaningful comparison of stationary phases must be made for the same mobile phase composition. Besides, these studies were mostly concerned with understanding the role of solvent modifiers and/or additives on retention properties, not much in understanding the stationary phase contribution. Moreover, different model types (as will be discussed below) further complicate the comparisons.

In the following, we will discuss some particular aspects of the use of the solva-tion parameter model in pSFC. First of all, we will focus on the experimental condi-tions selected for this study then on the choice of solvation descriptors. Then we will present a database of stationary phases characterized with the solvation parameter model, all under the same supercritical conditions, and the way to exploit it for par-ticular applications.

5.2 experImental CondItIons

5.2.1 chromatoGraphic SyStem

Chromatographic separations were carried out using equipment manufactured by Jasco (Tokyo, Japan, supplied by Prolabo, Fontenay-sous-Bois, France). Two model 980-PU pumps were used, one for carbon dioxide (N45 quality, contained in gas-eous tank) and a second for the modifier (methanol). The modifier pump performed control of the mobile phase composition. The pump head used for pumping carbon dioxide was cooled to −5°C by a cryostat (Julabo F10c, Seelbach, Germany, sup-plied by Touzart et Matignon, les Ulis, France). When the two mobile phase solvents (methanol and CO2) were mixed, the fluid was introduced into a dynamic mixing chamber PU 4046 (Pye Unicam, Cambridge, UK) connected to a pulsation damper (Sedere, supplied by Touzart et Matignon). The injector valve was supplied with a 20 µL loop (model 7125 Rheodyne, Cotati, CA, USA). Injection volumes ranged from 1 to 5 µL.

The columns were thermostated by an oven (Jetstream 2 Plus, Hewlett-Packard, Palo Alto, USA), regulated by a cryostat (Haake D8 GH, Karlsruhe, Germany). The detector was a UV-visible HP 1050 (Hewlett-Packard), with a high-pressure resis-tant cell. The detection wavelength was 254 nm. After the detector, a Jasco 880-81 pressure regulator (supplied by Prolabo, Fontenay-sous-Bois, France) controlled the outlet column pressure. The outlet regulator tube (internal diameter 0.25 mm) was heated to 60°C to avoid ice formation during the CO2 depressurization.

84534.indb 201 11/5/09 12:27:51 PM


Chromatograms were recorded using Azur software version 4.6 (Datalys, France). Methanol (MeOH) was HPLC grade and provided by Carlo Erba (Milan, Italy).

5.2.2 choice of ChromatoGraphic ConditionS

As our aim was to investigate the differences in stationary phase properties, it was important to choose some operating conditions that would be suitable to the wide variety of stationary phase chemistries that needed to be investigated. The operating conditions also needed to be consistent with common practice of pSFC today. On another hand, subcritical conditions were preferred to supercritical conditions for a variety of reasons.

A supercritical fluid is defined as a fluid above its critical pressure and tempera-ture. The name of SFC is thus very unfortunate as it lets those who are not familiar with the technique think that the fluid must be in its supercritical state. Actually, the fulfilment of both conditions (pressure and temperature) is not absolutely necessary as one can also work in the subcritical state, when only one of the two conditions is respected. Indeed, particularly in enantioselective pSFC, column temperatures of 25–30°C are frequently selected as providing the optimum resolution. Under these conditions, a carbon dioxide-based mobile phase will be below its critical tempera-ture and will thus be subcritical. Besides, the addition of a modifier to the carbon dioxide mobile phase causes an increase in the critical parameters. For instance, if the critical temperature for pure CO2 is 31°C, for a MeOH-CO2 18:82 (v/v) mobile phase the critical temperature is increased to 75°C [43]. Thus studies carried out with a composition gradient varying the percentage of modifier from 5 to 40% while maintaining the pressure and temperature constant may well start with a supercritical fluid and end with a subcritical fluid. Fortunately, there are no sig-nificant changes in properties on going from super- to subcritical temperatures at moderate or high pressure [44–45], and there would be no reason for a change, as the so-called transition does not exist: there is a continuum of the state of matter when going from subcritical to supercritical region. Consequently, in this paper, the term SFC will be applied to chromatography carried out with both subcritical and supercritical fluids. Another good reason for working in subcritical conditions is that temperatures are very mild and, as a result, thermolabile solutes can be ana-lyzed and the columns are very stable and have prolonged lifetimes. Consequently, we set the temperature at 25°C.

The outlet pressure was maintained constant (15 MPa). This means that the inter-nal pressure is not strictly constant for all columns, depending on column length, particle size, or porosity. However, modified subcritical fluids are less compressible than supercritical fluids, thus less susceptible to pressure variations, and most of our studies were performed with columns having the same geometrical dimensions, filled with 5 µm particles.

The choice of mobile phase is highly significant because, as explained above, the solvation parameter model characterizes a whole chromatographic system, compris-ing the mobile phase and the stationary phase equilibrated with the said mobile phase. It was important to choose a mobile phase with a composition comparable to the mobile phases currently in use by pSFC chromatographers. According to

84534.indb 202 11/5/09 12:27:52 PM


common practice observed, and to the solubility of studied compounds, methanol was chosen as reference modifier.

Studies carried out in SFC showed that the few percents of modifier (typically from 0 to 5%) induce significant retention decrease [16,23,33,36,39,46]. This reten-tion decrease is less and less significant when the percentage of modifier is fur-ther increased. Different causes have been attributed to these observations. First of all, the first percents of modifier strongly adsorb onto the stationary phase, thereby reducing the interactions between the solutes and the stationary phase. Secondly, the addition of modifier is responsible for increased eluting strength of the mobile phase, due to two different processes: the great increase in the possible interactions between the solute and the mobile phase components and the slight variation in the density of the mobile phase. All in all, these factors together contribute to decreased retention. It is clear that the modification induced by the addition of co-solvent is therefore largely dependent on the nature of this solvent and on its ability to interact with the stationary phase or with the analyzed solutes.

Besides, in the aim of characterizing stationary phases, it is not advisable to use large proportions of modifier in the mobile phase because, in this case, the influ-ence of the stationary phase itself in the separation process is lessened, while the influence of the mobile phase is increased. Thus stationary phases become more alike at high modifier percentage. In order to be able to see significant differences in the stationary phase behaviors, it was found reasonable to use no more than 10% modifier in the mobile phase.

Another important point is that the chosen mobile phase should allow measuring appropriate retention factors for all columns: the elution strength must be sufficient, so that the analysis time remains reasonable, but not too important otherwise the precision on the measurement of retention factors is poor. The 10% methanol content of the mobile phase rendered it possible. For the same reason, total flow rate was kept constant at 3 ml min−1.

In addition to the modifier, it is common practice in pSFC to use small proportions of acids or bases, then called additives. Although they generally appear to provide improved peak shapes, the mechanisms of their action is still not well understood and seems to depend on the stationary phase and solutes used.

We were concerned by the fact that different additives would adsorb onto the sta-tionary phase to different extents, further complicating the understanding of already complex phenomena. Consequently, we chose not to use any additive in the mobile phase.

5.2.3 Selection of columnS

All stationary phases presented in this work are commercially available. They are presented in Table 5.1. We were interested in scanning a large diversity of stationary phases, bonded or polymeric coated, based on silica, carbon, or polymers, and with different types of bonding chemistries, as can be seen on Figure 5.2. Sometimes, more than one column of each type is used. For example, three columns from dif-ferent manufacturers were used to evaluate phenyl-hexyl-siloxane bonded silica phases.

84534.indb 203 11/5/09 12:27:52 PM


tab

le 5

.1v

arie

d st

atio

nary

pha

ses

Cha

ract

eriz

ed in

thi

s st

udy

abb

revi

atio

nn

atur

e of

the

sta

tion

ary

phas

etr

ade

nam

em

anuf

actu

rer

C4

But

ylsi

loxa

ne-b

onde

d si

lica

Upt

isph

ere

C4

Inte

rchi

m

C8

Oct

ylsi

loxa

ne-b

onde

d si

lica

Upt

isph

ere

C8

Inte

rchi

m

C12

Dod

ecyl

silo

xane

-bon

ded

silic

aSy

nerg

i Max

RP

Phen

omen

ex

C18

Oct

adec

ylsi

loxa

ne-b

onde

d si

lica

Kro

mas

il C

18 1

00E

ka N

obel

C18

-CO

ctad

ecyl

silo

xane

-bon

ded

type

-C s

ilica

Cog

ent B

iden

tate

C18

Mic

roSo

lv T

echn

olog

ies

RPH

Oct

adec

yl-

and

phen

ylsi

loxa

ne-b

onde

d si

lica

Upt

isph

ere

RPH

Inte

rchi

m

MIX

Oct

adec

yl-

and

phen

ylpr

opyl

-bon

ded

silic

aN

ucle

odur

Sph

inx

RP

Mac

here

y-N

agel

PE1

Am

ide-

embe

dded

hex

adec

ylsi

loxa

ne-b

onde

d si

lica

Supe

lcos

il A

BZ

+ P

lus

Supe

lco

PE2

Eth

er-s

ulfo

nam

ide-

embe

dded

hex

adec

ylsi

loxa

ne-b

onde

d si

lica

Acc

laim

Pol

ar A

dvan

tage

Dio

nex

PE3

Car

bam

ate-

embe

dded

hex

adec

ylsi

loxa

ne-b

onde

d hy

brid

sili

caX

Bri

dge

Shie

ldW

ater

s

CH

LC

hole

ster

yl-b

onde

d si

lica

Cos

mos

il C

hole

ster

Nac

alai

Tes

que

FDFl

uoro

decy

lsilo

xane

-bon

ded

silic

aC

hrom

egab

ond

Fluo

rode

cyl

ES

Indu

stry

SISi

lica

gel

Kro

mas

il SI

L 1

00K

rom

asil

PEG

Poly

(eth

ylen

e gl

ycol

) bo

nded

on

silic

aD

isco

very

HS

PEG

Supe

lco

PVA

Poly

(vin

yl a

lcoh

ol)

bond

ed o

n si

lica

YM

C-P

ack

PVA

-Sil

YM

C

AM

DPo

lyam

ide

gel b

onde

d on

sili

caT

SK-g

el A

mid

eTo

soh

DIO

LPr

opan

edio

l-bo

nded

sili

caD

iol

Prin

ceto

n C

hrom

atog

raph

y

NH

2A

min

opro

pyl-

bond

ed s

ilica

Am

ino

Prin

ceto

n C

hrom

atog

raph

y

84534.indb 204 11/5/09 12:27:52 PM


CN

Cya

nopr

opyl

-bon

ded

silic

aC

yano

Prin

ceto

n C

hrom

atog

raph

y

EP

2-E

thyl

pyri

dine

-bon

ded

silic

aE

thyl

pyri

dine

Prin

ceto

n C

hrom

atog

raph

y

PGC

Poro

us g

raph

itic

carb

onH

yper

carb

The

rmo-

Hyp

ersi

l Key

ston

e

PSPo

lyst

yren

e-di

viny

lben

zene

PLR

P-S

Poly

mer

Lab

OPH

EPh

enyl

-oxy

prop

yl-b

onde

d si

lica

Syne

rgi P

olar

RP

Phen

omen

ex

DP

Dip

heny

l-pr

opyl

-bon

ded

silic

aPu

rsui

t Dip

heny

lV

aria

n

DP-

XD

iphe

nyl-

prop

yl-b

onde

d si

lica

Purs

uit X

Rs

Dip

heny

lV

aria

n

C3P

Phen

yl-p

ropy

l-bo

nded

sili

caU

ptis

pher

e PH

Inte

rchi

m

C6P

-LPh

enyl

-hex

yl-b

onde

d si

lica

Lun

a Ph

enyl

hexy

lPh

enom

enex

C6P

-GPh

enyl

-hex

yl-b

onde

d hy

brid

sili

caG

emin

i Phe

nylh

exyl

Phen

omen

ex

C6P

-ZPh

enyl

-hex

yl-b

onde

d si

lica

Zor

bax

Ecl

ipse

+ P

heny

lhex

ylA

gile

nt

NA

PN

apht

yl-e

thyl

-bon

ded

silic

aC

osm

osil

π-N

AP

Nac

alai

Tes

que

PYE

2-Py

reny

l-et

hyl-

bond

ed s

ilica

Cos

mos

il 5P

YE

Nac

alai

Tes

que

DN

AP

Din

itroa

nilid

o-pr

opyl

-bon

ded

silic

aU

ptis

pher

e D

NA

PIn

terc

him

PNP

p-N

itrop

heny

l-bo

nded

sili

caN

ucle

osil

NO

2M

ache

rey-

Nag

el

PFP

Pent

afluo

roph

enyl

-pro

pyl-

bond

ed s

ilica

Dis

cove

ry H

S F5

Supe

lco

PBB

Pent

abro

mob

enzy

l-ox

ypro

pyl-

bond

ed s

ilica

Cos

mos

il 5P

BB

Nac

alai

Tes

que

84534.indb 205 11/5/09 12:27:52 PM


All columns were 250*4.6 mm, apart from PGC (100*4.6 mm) and PS (150*4.6 mm). All columns were 5 µm, apart from C12, OPHE (4 µm), DIOL, NH2, CN and EP (6 µm).

We put a special emphasis on ODS-bonded stationary phases, as they are the most widely used type in HPLC and a great diversity of bonding chemistries exist. The ODS phases selected, together with the known properties, can be found in Table 5.2. The columns were chosen for their representativeness of the possible treatments and bonding modes present in modern ODS phases. We were particularly interested in phases possessing a polar function in the endcapping group, or embedded in the alkyl chain. Unfortunately, not all manufacturers are willing to divulge the functionality, bonding technology and composition of their commercially available stationary phase column chemistries. As a matter of fact, some of the ODS phases selected have proprietary structure. By comparison of their system constants with those in the database, we hoped to shed some light on their chemistry.

5.2.4 Selection of a Set of teSt compoundS

The number of solutes used in our testing protocol has increased with time. Indeed, introducing new columns, with different retention behaviors, rendered it necessary

C18

Si

Si

Si

Si

O

FF

FF

FF

FF

FF

FSi

FF

FF

FF

FF

FF

Si NO2

NO2

NO2

HN

SiSiSiSi

C12 C8 C4

PS AMD

H2NO

nn

n n

O

H

OH

OHOH

SiSi

N CN NH2

Si Si Si

Si

SiO

OOO

O

OH

R

RSi RR

H

OH PEG PVA

SI

PGC

CHL

C18-C

HO

O

O

OOOO

Si Si Si

PE1 PE2

Si Si Si Si

NHNH

S

S

Si Si Si Si Si Si

F

F

FF

F O

Br

BrBr

Br

Br

SiO

O

NO

OO

O O

PE3 RPH MIX OPHE

C3PC6P-LC6P-GC6P-Z

PNP DNAP

NAP PYE PFP PBB

FD DPDP-X

Si

EP CN NH2

DIOL

fIgure 5.2 Chemical structures of the stationary phases compared in this study. (See Table 5.1 for identification of the columns.)

84534.indb 206 11/5/09 12:27:53 PM


tab

le 5

.2o

ds

phas

es C

hara

cter

ized

in t

his

stud

y

n°st

atio

nary

pha

se n

ame

man

ufac

ture

r

spec

ific

surf

ace

are

a (m

2 g−1

)

Car

bon

Con

tent

(%

)

pore

d

iam

eter

(Å

)b

ondi

ng t

ype

endc

appi

ng

1Z

orba

x St

able

Bon

d C

18A

gile

nt18

010

80m

onof

unct

iona

l Dib

uC18

N

2Z

orba

x R

x C

18A

gile

nt18

012

80m

onof

unct

iona

l sila

neN

3Z

orba

x E

xten

dA

gile

nt18

512

.180

prop

ylen

e bi

dent

ate

Y

4Z

orba

x E

clip

se X

DB

Agi

lent

180

10.3

80m

onof

unct

iona

l sila

neY

5K

rom

asil

C18

EK

A N

obel

350

21.4

100

mon

omer

ic la

yer

Y

6G

amm

abon

d C

18E

S In

dust

ries

nana

naco

ated

pol

ymer

7U

ptis

pher

e O

DB

Inte

rchi

m32

017

120

mon

ofun

ctio

nal s

ilane

Y

8U

ptis

pher

e H

DO

Inte

rchi

m32

018

120

mon

ofun

ctio

nal s

ilane

Y

9U

ptis

pher

e T

FIn

terc

him

310

14na

poly

mer

ic la

yer

10U

ptis

pher

e N

EC

Inte

rchi

m32

016

120

mon

ofun

ctio

nal s

ilane

N

11N

ucle

osil

50 C

18M

ache

rey-

Nag

el45

014

50m

onom

eric

laye

rN

12N

ucle

osil

100

C18

Mac

here

y-N

agel

350

1410

0m

onom

eric

laye

rN

13N

ucle

osil

5 C

18 A

BM

ache

rey-

Nag

el35

025

100

cros

slin

ked

poly

mer

ic la

yer

Y

14C

hrom

olith

C18

Mer

ck30

017

130

Y

15X

Terr

a M

S C

18W

ater

s17

515

.512

5hy

brid

sili

ca, t

rifu

nctio

nal s

ilane

Y

16A

tlant

is d

C18

Wat

ers

330

1210

0di

func

tiona

l sila

neY

17C

apce

ll Pa

k C

18Sh

isei

do30

015

120

coat

ed p

olym

er

P1U

ptis

pher

e R

PHM

ache

rey-

Nag

el33

015

120

OD

S an

d ph

enyl

silo

xane

Y

(Con

tinu

ed)

84534.indb 207 11/5/09 12:27:54 PM


tab

le 5

.2

(Con

tinu

ed)

n°st

atio

nary

pha

se n

ame

man

ufac

ture

r

spec

ific

surf

ace

are

a (m

2 g−1

)

Car

bon

Con

tent

(%

)

pore

d

iam

eter

(Å

)b

ondi

ng t

ype

endc

appi

ng

P2N

ucle

odur

Sph

inx

RP

Mac

here

y-N

agel

340

1511

0m

ixed

OD

S an

d pr

opyl

phen

ylY

P3C

ogen

t C18

Bid

enta

teM

icro

Solv

Tec

hnol

ogy

350

1610

0bi

dent

ate

CH

2Si2

P4Pl

atin

um C

18 E

PSG

race

Vyd

ac10

05

300

low

bon

ding

den

sity

N

P5A

quas

il C

18T

herm

o-E

lect

ron

310

1210

0po

lar

endc

appe

d

P6Pr

evai

l C18

Gra

ce V

ydac

350

1511

0m

onom

eric

laye

rY

P7A

lltim

a H

P C

18 A

QG

race

Vyd

ac45

020

100

pola

r en

dcap

ped

Y

P8Sy

nerg

i Hyd

ro R

PPh

enom

enex

474

1980

pola

r en

dcap

ped

P9H

yPur

ity A

quas

tar

The

rmo-

Ele

ctro

n20

010

190

pola

r en

dcap

ped

P10

Hyp

ersi

l Gol

d A

QT

herm

o-E

lect

ron

220

na17

5po

lar

endc

appe

d

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84534.indb 208 11/5/09 12:27:54 PM


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84534.indb 209 11/5/09 12:27:54 PM


to introduce new solutes. For instance, our initial set had been established for charac-terization of PGC [40], which is a highly retentive stationary phase. Then, when less retentive phases were characterized, it was necessary to inject different solutes that would be sufficiently retained to allow for precise measurement of their retention factors. Such compounds are different for different stationary phases: for instance, when a nonpolar phase needs to be characterized, nonpolar compounds are more retained, whereas polar compounds are more retained on polar phases. Thus, for most stationary phases in Table 5.1, only a subset of the solutes in Table 5.3 was used. In the end, we believe to have achieved a set of test solutes that is sufficiently wide and diverse for the characterization of phases of all available polarities. The solutes in the final set are presented in Table 5.3, along with their Abraham descrip-tors. The latter were extracted from an in-house database, based on a great variety of published works.

Besides, there are some essential rules to follow in order to obtain meaningful results from multiple linear regression analysis. One is that the set of probe solutes must be sufficiently large to ensure the statistical significance of the calculated sys-tem constants. A rule of thumb indicates that a minimum of four solutes per variable should be used, although it is clearly better to over-determine the system by using more input retention factors. In our case, we have chosen to work with a much larger solute set. The system constants, particularly in small data sets, are strongly influ-enced by statistical outliers. This is another reason for increasing the initial data set so experimental errors have less weight on the final equation. Actually, in SFC, the time required to generate data is favorable for the collection of larger data sets with minimal additional effort.

Size of the solute set is not the only requirement: an equilibrated set of solutes should have a wide variety of chemical functions, so much so that the introduction of additional solutes would not significantly modify the results. This means that the chosen solutes must differ in physico-chemical properties and have different three-dimensional structures. While building our solute set, we have been careful to intro-duce a great variety of functional groups, sizes, and shapes. Figure 5.3, showing the repartition of the solutes of Table 5.3 in each descriptor space, evidences this point. It is clear from this figure that the solutes are distributed in such a manner that each descriptor covers a wide range. Clustering should be avoided as much as possible. The only exception to this rule is the A descriptor, because, due to the very definition of this parameter, a large proportion of solutes have A values equal to zero.

Besides, an essential rule of QSRRs is that the variables employed in the regres-sion be independent, that is to say the descriptors used in one equation should be as orthogonal as possible. Cross-correlation must be avoided because it results in difficulties in the interpretation of the coefficients, as the multiple linear regression analysis is unable to distinguish between correlated descriptors. Thus it is necessary that the probe solutes be chosen so as to minimize correlation between the variables. This point is demonstrated in Table 5.4, representing the correlation matrix for the solutes in Table 5.3. The largest correlation coefficient observed is 0.727, calculated between the E and S descriptors. It is well known to the chromatographers using the solvation parameter model that a certain correlation exists between the E and S descriptors, particularly when only aromatic solutes are used, which is the case here

84534.indb 210 11/5/09 12:27:54 PM


table 5.3Chromatographic solutes and lser descriptors e, s, a, b, v, and l

no. Compound e s a b v l

1 Benzene 0.610 0.52 0.00 0.14 0.7164 2.786

2 Toluene 0.601 0.52 0.00 0.14 0.8573 3.325

3 Ethylbenzene 0.613 0.51 0.00 0.15 0.9982 3.778

4 Propylbenzene 0.604 0.50 0.00 0.15 1.1391 4.230

5 Butylbenzene* 0.600 0.51 0.00 0.15 1.2800 4.730

6 Pentylbenzene 0.594 0.51 0.00 0.15 1.4209 5.230

7 Hexylbenzene 0.591 0.50 0.00 0.15 1.5620 5.720

8 Heptylbenzene 0.577 0.48 0.00 0.15 1.7029 6.219

9 Octylbenzene 0.579 0.48 0.00 0.15 1.8438 6.714

10 Nonylbenzene 0.578 0.48 0.00 0.15 1.9847 7.212

11 Decylbenzene 0.579 0.47 0.00 0.15 2.1256 7.708

12 Undecylbenzene* 0.579 0.47 0.00 0.15 2.2665 8.159

13 Dodecylbenzene 0.571 0.47 0.00 0.15 2.4074 8.600

14 Tridecylbenzene 0.570 0.47 0.00 0.15 2.5483 9.132

15 Tetradecylbenzene 0.570 0.47 0.00 0.15 2.6892 9.619

16 Allylbenzene 0.717 0.60 0.00 0.22 1.0961 4.136

17 Cumene 0.602 0.49 0.00 0.16 1.1391 4.084

18 t-Butylbenzene 0.614 0.49 0.00 0.16 1.2800 4.730

19 o-Xylene* 0.663 0.56 0.00 0.16 0.9980 3.939

20 m-Xylene 0.623 0.52 0.00 0.16 0.9980 3.839

21 p-Xylene 0.613 0.52 0.00 0.16 0.9980 3.839

22 Naphthalene 1.340 0.92 0.00 0.20 1.0854 5.161

23 1-Methylnaphthalene 1.344 0.90 0.00 0.20 1.2260 5.802

24 2-Methylnaphthalene* 1.304 0.92 0.00 0.20 1.2260 5.617

25 1-Ethylnaphthalene 1.371 0.87 0.00 0.20 1.3670 6.226

26 2-Ethylnaphthalene 1.331 0.87 0.00 0.20 1.3670 6.203

27 Aniline 0.955 0.96 0.26 0.50 0.8162 3.934

28 N, N-dimethylaniline* 0.957 0.84 0.00 0.47 1.0980 4.701

29 Phenylurea* 1.110 1.40 0.77 0.77 1.0730

30 Pyridine* 0.631 0.84 0.00 0.52 0.6753 3.022

31 2-ethylpyridine 0.613 0.70 0.00 0.49 0.9570 3.844

32 Indazole 1.180 1.25 0.54 0.34 0.9050

33 Carbazole 1.787 1.42 0.47 0.26 1.3150 7.638

34 Acridine* 2.356 1.32 0.00 0.58 1.4130

35 Nicotinamide 1.010 1.09 0.63 1.00 0.9317

36 Caffeine 1.500 1.60 0.00 1.35 1.3630 7.352

37 o-Toluidine 0.966 0.92 0.23 0.45 0.9570 4.442

(Continued)

84534.indb 211 11/5/09 12:27:55 PM


table 5.3 (Continued)


38 m-Toluidine* 0.946 0.95 0.23 0.55 0.9570 4.463

39 p-Toluidine 0.923 0.95 0.23 0.52 0.9570 4.452

40 1-Naphtylamine 1.670 1.26 0.20 0.57 1.1850 6.490

41 Benzoic acid 0.730 0.90 0.59 0.40 0.9317 4.395

42 Isophthalic acid 0.940 1.46 1.14 0.77 1.1470 6.108

43 Trimesic acid 1.140 1.84 1.71 1.10 1.3623

44 1-Naphtoic acid* 1.200 1.27 0.52 0.48 1.3007 6.794

45 1-Naphtylacetic acid 1.300 1.35 0.54 0.40 1.4416

46 Anisole 0.708 0.75 0.00 0.29 0.9160 3.890

47 Benzaldehyde 0.820 1.00 0.00 0.39 0.8730 4.008

48 Naphthylaldehyde 1.470 1.19 0.00 0.47 1.2420

49 Acetophenone* 0.818 1.01 0.00 0.48 1.0139 4.501

50 Propiophenone 0.804 0.85 0.00 0.51 1.1548 4.971

51 Valerophenone 0.795 0.95 0.00 0.50 1.4366 5.902

52 o-Methylacetophenone 0.780 1.00 0.00 0.51 1.1550

53 m-Methylacetophenone 0.806 1.00 0.00 0.51 1.1550 5.167

54 p-Methylacetophenone* 0.842 1.00 0.00 0.52 1.1550 5.081

55 Methylbenzoate 0.733 0.85 0.00 0.48 1.0726 4.704

56 Ethylbenzoate 0.689 0.85 0.00 0.46 1.2140 5.075

57 Propylbenzoate 0.675 0.80 0.00 0.46 1.3540 5.718

58 Butylbenzoate* 0.668 0.80 0.00 0.46 1.4953 6.210

59 Dimethylphthalate 0.780 1.41 0.00 0.88 1.4290 6.051

60 Diethylphthalate 0.729 1.40 0.00 0.88 1.7110

61 Dipropylphthalate* 0.713 1.40 0.00 0.86 1.9924

62 Dibutylphthalate 0.700 1.40 0.00 0.86 2.2700

63 Naphthylacetate 1.130 1.25 0.00 0.62 1.4416

64 Coumarine 1.060 1.79 0.00 0.46 1.0620 6.023

65 Benzonitrile 0.742 1.11 0.00 0.33 0.8711 4.039

66 Cyanonaphthalene* 1.190 1.25 0.00 0.41 1.2401

67 Naphtylacetonitrile 1.430 1.44 0.00 0.53 1.3810

68 Nitrobenzene 0.871 1.11 0.00 0.28 0.8906 4.557

69 Nitronaphthalene* 1.600 1.51 0.00 0.29 1.2596 6.816

70 o-Nitrotoluene 0.866 1.11 0.00 0.28 1.0320 4.878

71 m-Nitrotoluene 0.874 1.10 0.00 0.25 1.0320 5.097

72 p-Nitrotoluene* 0.870 1.11 0.00 0.28 1.0320 5.154

73 o-Nitrobenzylalcohol 1.059 1.11 0.45 0.65 1.0900

74 m-Nitrobenzylalcohol 1.064 1.35 0.44 0.64 1.0900

75 p-Nitrobenzylalcohol* 1.064 1.39 0.44 0.62 1.0900

84534.indb 212 11/5/09 12:27:55 PM




76 o-Nitrophenol 1.045 1.05 0.05 0.37 0.9490 4.760

77 m-Nitrophenol 1.050 1.57 0.79 0.23 0.9490 4.692

78 p-Nitrophenol 1.070 1.72 0.82 0.26 0.9490 5.876

79 Chlorobenzene 0.718 0.65 0.00 0.07 0.8288 3.657

80 Bromobenzene 0.882 0.73 0.00 0.09 0.8910 4.041

81 Iodobenzene* 1.188 0.82 0.00 0.12 0.9750 4.502

82 1-Fluoronaphthalene 1.320 0.82 0.00 0.18 1.1030

83 1-Chloronaphthalene 1.540 0.92 0.00 0.15 1.2078 6.154

84 1-Bromonaphthalene 1.670 0.97 0.00 0.17 1.2604 6.567

85 1-Iodonaphthalène 1.840 1.04 0.00 0.20 1.3436

86 1-Phenylethanol 0.784 0.83 0.30 0.66 1.0570 4.431

87 Benzyl alcohol* 0.803 0.87 0.39 0.56 0.9160 4.221

88 Naphthalene methanol 1.640 1.19 0.27 0.64 1.2850

89 Naphthalene ethanol* 1.670 1.21 0.23 0.72 1.4259 7.046

90 Phenol 0.805 0.89 0.60 0.30 0.7751 3.766

91 Eugenol 0.946 0.99 0.22 0.51 1.3540

92 Vanillin* 1.040 1.33 0.32 0.67 1.1313 5.730

93 Pyrocatechol 0.970 1.10 0.88 0.47 0.8338 4.450

94 Resorcinol 0.980 1.00 1.10 0.58 0.8340 4.618

95 Hydroquinone* 1.000 1.00 1.16 0.60 0.8337 4.827

96 Phloroglucinol 1.355 1.12 1.40 0.82 0.8925

97 α-Naphtol 1.520 1.05 0.61 0.37 1.1441 6.140

98 β-Naphtol* 1.520 1.08 0.61 0.40 1.1440 6.124

99 o-Chlorophenol 0.853 0.88 0.32 0.31 0.8975 4.178

100 m-Chlorophenol 0.909 1.06 0.69 0.15 0.8975 4.773

101 p-Chlorophenol* 0.915 1.08 0.67 0.20 0.8975 4.775

102 o-Cresol 0.840 0.86 0.52 0.30 0.9160 4.218

103 m-Cresol 0.822 0.88 0.57 0.34 0.9160 4.310

104 p-Cresol* 0.820 0.87 0.57 0.31 0.9160 4.312

105 2,3-Dimethylphenol 0.850 0.85 0.52 0.36 1.0569 4.866

106 2,4-Dimethylphenol* 0.840 0.80 0.53 0.39 1.0570 4.770

107 2,5-Dimethylphenol 0.840 0.79 0.54 0.37 1.0570 4.774

108 2,6-Dimethylphenol 0.860 0.79 0.39 0.39 1.0570 4.680

109 3,4-Dimethylphenol 0.830 0.86 0.56 0.39 1.0570 4.980

110 3,5-Dimethylphenol 0.820 0.84 0.57 0.36 1.0570 4.856

111 o-Isopropylphenol 0.822 0.79 0.52 0.44 1.1978

112 m-Isopropylphenol 0.811 0.92 0.55 0.46 1.1978

(Continued)

84534.indb 213 11/5/09 12:27:55 PM


to allow for UV detection [26]. For this reason, a number of positional aromatic iso-mers were introduced as they allow limiting the correlation between E and S.

However, it should be pointed out that covariance estimated through the correla-tion coefficient is somewhat overestimated because this coefficient can be strongly influenced by a few points acting as levers, while the rest of the points would be scattered. Indeed, the correlation between the E and S coefficients among the group of solutes we have selected can be observed on Figure 5.4. It is clear from this fig-ure that the largest PAH solutes (solutes 121 to 134 in Table 5.3) largely contribute to the correlation observed. When they are removed, the correlation coefficient between E and S falls down to 0.561. Thus the correlation observed is not really as important as Table 5.4 would suggest. A better correlation coefficient, expressing a total covariance that would be more representative of the whole distribution and



113 p-Isopropylphenol 0.791 0.89 0.55 0.38 1.1978

114 Biphenyl 1.360 0.99 0.00 0.26 1.3242 6.014

115 1-Phenylnaphthalene 1.910 1.08 0.00 0.30 1.6932

116 Diphenylméthane 1.220 1.04 0.00 0.33 1.4651 6.313

117 Benzophenone 1.447 1.50 0.00 0.50 1.4810 6.852

118 Acenaphthene 1.604 1.05 0.00 0.22 1.1726 6.469

119 Acenaphtylene 1.750 1.14 0.00 0.26 1.2156 6.415

120 Fluorene 1.588 1.03 0.00 0.20 1.3570 6.928

121 Phenanthrene* 2.055 1.29 0.00 0.26 1.4540 7.632

122 Anthracene 2.290 1.34 0.00 0.26 1.4540 7.568

123 9-Methylanthracene 2.290 1.30 0.00 0.26 1.5950

124 Fluoranthene 2.377 1.53 0.00 0.20 1.5850 8.702

125 Pyrene 2.808 1.71 0.00 0.29 1.5850 8.833

126 Chrysene* 3.027 1.73 0.00 0.36 1.8230

127 Benz[a]anthracene 2.992 1.70 0.00 0.33 1.8230

128 Tetracene 2.847 1.70 0.00 0.32 1.8230

129 Benzo[a]pyrene* 3.625 1.98 0.00 0.44 1.9536 11.736

130 Perylene 3.256 1.76 0.00 0.42 1.9536

131 Binaphthyl 2.820 1.81 0.00 0.31 2.0622

132 Triphenylene 3.000 1.71 0.00 0.42 1.8234

133 o-Terphenyl 2.194 1.61 0.00 0.38 1.9320

134 p-Terphenyl 2.194 1.61 0.00 0.38 1.9320

Note: E: Excess molar refraction; S: Dipolarity/polarizability; A: Hydrogen bond acidity; B: Hydrogen bond basicity; V: McGowan’s characteristic volume; L: logarithm of the gas-hexadecane partition coefficient.

Compounds marked with an asterisk are the test solutes used to assess the predictive capability of the models.

84534.indb 214 11/5/09 12:27:56 PM


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84534.indb 215 11/5/09 12:27:57 PM


less influenced by levers would be useful but we have not found anything satisfying so far.

For the ODS phases in Table 5.2, only the 29 solutes in Table 5.5 were analyzed. In this case, we chose to work with a smaller set of compounds, knowing that the precision of the results is lesser than when larger sets of solutes are used. However, the compounds were chosen so as to retain diversity and absence of cross- correlation as described above. Besides, comparison of the models obtained with the larger (Table 5.3) and smaller (Table 5.5) sets of solutes on several ODS phases showed no significant difference, at the 95% confidence level. Therefore, we consider this small set as perfectly valid and representative of the possible interactions occurring between the solutes and the chromatographic systems.

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

E

S

fIgure 5.4 Plot of the S descriptor vs. the E descriptor for the solutes in Table 5.3. Open diamonds are solutes 1 to 120; black diamonds are solutes 121 to 134.

table 5.4Covariance matrix for the solute set in table 5.3

r e s a b v l

e 0.727 −0.131 0.027 0.352 0.611

s 0.727 0.168 0.473 0.169 0.367

a −0.131 0.168 0.374 −0.363 −0.178

b 0.027 0.473 0.374 −0.048 0.007

v 0.352 0.169 −0.363 −0.048 0.842

l 0.611 0.367 −0.178 0.007 0.842

84534.indb 216 11/5/09 12:27:57 PM


To possibly reduce the testing procedure, we have devised an extremely reduced set of nine test solutes [47]. This set allows estimating the solvation parameter coef-ficient, when rapid information is required. However, the precision of the results is naturally less satisfying than with larger sets.

The solutes were obtained from a range of suppliers. Solutions were prepared in methanol, or methanol-tetrahydrofurane for the least soluble polynuclear aro-matic hydrocarbons and long-chain alkylbenzenes. Solutions were prepared in such

table 5.5reduced test set for ods phases e, s, a, b and v

no. Compound e s a b v

1 Benzene 0.610 0.52 0.00 0.14 0.7164

2 Toluene 0.601 0.52 0.00 0.14 0.8573

3 Ethylbenzene 0.613 0.51 0.00 0.15 0.9982

4 Propylbenzene 0.604 0.50 0.00 0.15 1.1391

5 Butylbenzene 0.600 0.51 0.00 0.15 1.2800

6 Pentylbenzene 0.594 0.51 0.00 0.15 1.4209

7 Allylbenzene 0.717 0.60 0.00 0.22 1.0961

8 Anisole 0.708 0.75 0.00 0.29 0.9160

9 Methyl benzoate 0.733 0.85 0.00 0.48 1.0726

10 Benzaldehyde 0.820 1.00 0.00 0.39 0.8730

11 Acetophenone 0.818 1.01 0.00 0.48 1.0139

12 Benzonitrile 0.742 1.11 0.00 0.33 0.8711

13 Nitrobenzene 0.871 1.11 0.00 0.28 0.8906

14 Chlorobenzene 0.718 0.65 0.00 0.07 0.8288

15 Bromobenzene 0.882 0.73 0.00 0.09 0.8910

16 Naphtalene 1.340 0.92 0.00 0.20 1.0854

17 Biphenyl 1.360 0.99 0.00 0.26 1.3242

18 1-Phenylethanol 0.784 0.83 0.30 0.66 1.0570

19 Benzyl alcohol 0.803 0.87 0.39 0.56 0.9160

20 o-Cresol 0.840 0.86 0.52 0.46 0.9160

21 m-Cresol 0.822 0.88 0.57 0.34 0.9160

22 p-Cresol 0.820 0.87 0.57 0.31 0.9160

23 Phenol 0.805 0.89 0.60 0.30 0.7751

24 Resorcinol 0.980 1.00 1.10 0.58 0.8340

25 Phloroglucinol 1.355 1.12 1.40 0.82 0.8925

26 Benzoic acid 0.730 0.90 0.59 0.40 0.9317

27 Isophthalic acid 0.940 1.46 1.14 0.77 1.1470

28 Aniline 0.955 0.94 0.26 0.50 0.8162

29 N,N-Dimethylaniline 0.957 0.84 0.00 0.47 1.0980

Note: E: Excess molar refraction; S: Dipolarity/polarizability; A: Hydrogen bond acidity; B: Hydrogen bond basicity; V: McGowan’s characteristic volume.

84534.indb 217 11/5/09 12:27:58 PM


a concentration that no variation of retention factor is observed on the PGC phase when further diluted solutions are injected. As PGC has the smallest specific sur-face area of all phases investigated, no saturation occurred on the other stationary phases. The sunscreen molecules were kindly provided by L’Oreal (Chevilly Larue, France).

5.2.5 data analySiS

Retention factors (k) were calculated based on the retention time tr, determined using the peak maximum (even when tailing did occur, on some columns, for some of the most acidic and basic solutes) and on the hold-up time t0 measured on the first nega-tive peak due to the unretained dilution solvent.

The system constants for each chromatographic system, presented in Table 5.6, were obtained by multiple linear regression analysis on the logarithm of the measured retention factors (log k). Compared to our previously published works, some addi-tional compounds were injected to improve the predictive capability (as explained above) thus the results may be slightly different. However, none of our previous con-clusions regarding chromatographic behaviors is called into question by the new models established.

Multiple linear regression analysis and statistical tests were performed using the XL Stat software (Addinsoft, New York, NY, USA). The quality of the fits was estimated using the overall correlation coefficient (R), adjusted determina-tion coefficient (R2

adj), standard error in the estimate (SE) and Fischer F statistic. The statistical significance of individual coefficients was evaluated using the t-ratio, which is defined as the ratio of the regression coefficient to its standard error.

In each case, a few outliers were eliminated from the set, as their residuals were too high. These solutes were different for each stationary phase and most of the time showed no common property, apart for some basic solutes, as will be detailed later. On another hand, solutes that were not retained enough were also eliminated, and these are different depending on the nature of the stationary phase. For instance, the large alkylbenzenes are not retained enough on the polar phases while the very polar solutes such as phloroglucinol are not retained enough on nonpolar phases. Independent variables E, S, A, B, and V, which were not statistically significant, with a confidence interval of 99.9%, were eliminated from the model.

The fits were all of reasonable quality, R ranging from 0.930 to 0.995, SE vary-ing from 0.029 to 0.229. These results are reasonably good and confirm that the solvation parameter model adequately describes retention even when applied to a wide variety of columns. The somewhat poor fit obtained on PGC will be explained below.

Deviations from the experimental values for the predicted values are generally within the uncertainty indicated by the model fits but, for some solutes, there is a systematic trend in the data. Indeed the residuals of the fit are consistent from col-umn to column: most often, those compounds that are actually less retained than predicted by the model, or those that are more retained than predicted by the model, or those that are well predicted, are the same on all stationary phases. This fact can

84534.indb 218 11/5/09 12:27:58 PM


(Con

tinu

ed)

tab

le 5

.6sy

stem

Con

stan

ts a

nd s

tati

stic

s fo

r th

e 35

Col

umns

in t

able

5.1

stat

iona

ry

phas

ec

es

ab

vn

RR

2 adj

seF

u

C4

−1.1

930.

220

−0.1

70−

−0.

111

0.23

011

40.

985

0.96

80.

030

860

0.38

0.

013

0.00

80.

017

0.02

00.

008

C8

−0.9

980.

322

−0.2

68−0

.278

−0.

219

0.27

212

10.

986

0.97

10.

045

801

0.61

0.

019

0.01

20.

025

0.01

80.

027

0.01

2

C12

−0.7

710.

379

−0.2

42−

0.37

2−

0.44

40.

313

115

0.99

00.

980

0.04

411

200.

80

0.

020

0.01

20.

023

0.01

80.

029

0.01

2

C18

−0.7

790.

587

−0.4

59−

0.45

7−

0.47

90.

439

110

0.99

50.

989

0.04

319

681.

09

0.

019

0.01

40.

025

0.02

00.

028

0.01

2

C18

-C−0

.829

0.65

8−0

.447

0.19

9−

0.27

611

50.

982

0.96

30.

066

748

0.87

0.

028

0.01

60.

028

0.02

20.

018

RP

H−0

.809

0.47

0−0

.261

−0.

407

−0.

411

0.37

376

0.99

20.

983

0.05

486

30.

87

0.

039

0.02

20.

032

0.02

40.

040

0.03

9

MIX

−0.9

500.

309

−0.1

06−

0.15

6−

0.25

40.

328

118

0.99

40.

988

0.02

918

600.

55

0.

013

0.00

80.

016

0.01

00.

017

0.00

8

PE

1−1

.190

0.66

1−0

.317

1.26

3−

0.42

70.

345

113

0.99

10.

981

0.05

811

511.

56

0.

026

0.01

70.

032

0.02

20.

033

0.01

6

PE

2−0

.822

0.52

7−0

.091

0.49

9−

0.42

80.

305

116

0.98

90.

987

0.05

310

170.

90

0.

022

0.01

50.

028

0.01

70.

030

0.01

4

PE

3−1

.171

0.57

7−0

.214

0.79

5−

0.46

20.

308

108

0.99

50.

991

0.03

722

441.

15

84534.indb 219 11/5/09 12:27:58 PM


tab

le 5

.6

(Con

tinu

ed)

stat

iona

ry

phas

ec

es

ab

vn

RR

2 adj

seF

u

0.

017

0.01

00.

021

0.01

30.

021

0.01

0

CH

L−1

.135

0.59

5−0

.172

0.32

8−

0.62

50.

469

116

0.98

20.

962

0.06

459

01.

05

0.

030

0.02

00.

031

0.02

30.

035

0.01

8

FD

−1.0

690.

282

−0.

457

0.96

1−

0.50

198

0.93

00.

859

0.10

014

91.

21

0.

053

0.02

40.

039

0.05

60.

060

SI−1

.354

0.35

20.

336

1.19

61.

011

−0.

571

100

0.96

70.

931

0.11

726

91.

74

0.

064

0.03

60.

081

0.05

50.

075

0.06

0

PE

G−1

.113

0.34

10.

256

1.23

6−

0.22

3−

840.

981

0.96

00.

083

496

1.33

0.

029

0.02

60.

054

0.03

60.

056

PV

A−1

.080

0.53

5−

1.18

90.

878

−0.

477

110

0.98

50.

969

0.08

883

91.

64

0.

038

0.01

50.

038

0.04

40.

030

AM

D−1

.118

0.49

90.

290

1.36

81.

184

−0.

618

125

0.97

40.

946

0.15

443

52.

00

0.

068

0.04

00.

074

0.05

60.

094

0.05

9

DIO

L−0

.715

0.46

0−

0.92

80.

945

−0.

561

111

0.93

30.

865

0.15

617

71.

51

0.

072

0.03

30.

057

0.08

10.

077

NH

2−1

.033

0.47

50.

301

1.34

90.

901

−0.

678

109

0.96

20.

922

0.16

025

51.

85

0.

078

0.04

40.

083

0.06

30.

106

0.07

4

84534.indb 220 11/5/09 12:27:59 PM


(Con

tinu

ed)

CN

−0.9

930.

339

0.37

20.

696

0.44

9−

0.34

611

80.

965

0.92

90.

110

305

1.03

0.

052

0.02

80.

053

0.03

90.

064

0.04

0

EP

−1.0

570.

588

0.56

41.

053

0.79

0−

0.69

212

00.

964

0.92

60.

191

297

1.70

0.

086

0.05

00.

094

0.06

90.

120

0.07

1

PG

C−2

.175

1.55

20.

391

0.59

3−

0.30

71.

145

910.

936

0.86

80.

229

119

2.08

0.

140

0.10

60.

121

0.09

10.

151

0.09

0

PS

−0.6

690.

762

−0.

132

−0.

279

0.26

868

0.98

70.

973

0.07

759

50.

86

0.

052

0.02

40.

033

0.04

70.

055

OP

HE

−1.0

920.

346

0.09

90.

185

0.10

10.

192

132

0.97

20.

943

0.06

543

50.

46

0.

028

0.01

60.

032

0.02

20.

038

0.01

7

DP

−1.4

890.

297

−0.

311

0.21

30.

209

119

0.96

70.

933

0.06

441

10.

52

0.

028

0.01

00.

022

0.03

00.

024

DP

-X−1

.067

0.31

1−

0.21

80.

076

0.26

111

30.

987

0.97

40.

040

1042

0.47

0.

019

0.00

70.

014

0.01

80.

015

C3P

−1.2

170.

280

−0.

218

0.12

10.

279

135

0.97

50.

949

0.05

362

90.

47

0.

020

0.00

80.

017

0.02

10.

014

C6P

-L−1

.068

0.32

6−

−−

0.12

50.

285

119

0.99

00.

980

0.03

619

260.

45

0.

013

0.00

60.

014

0.00

9

C6P

-G−1

.120

0.31

9−

0.08

4−

0.24

90.

312

125

0.98

80.

975

0.04

012

320.

52

0.

016

0.00

60.

013

0.01

70.

011

C6P

-Z−1

.142

0.33

8−

−−

0.16

30.

306

125

0.98

90.

979

0.03

818

840.

48

0.

013

0.00

60.

015

0.00

9

84534.indb 221 11/5/09 12:27:59 PM


tab

le 5

.6

(Con

tinu

ed)

stat

iona

ry

phas

ec

es

ab

vn

RR

2 adj

seF

u

NA

P−1

.243

0.33

30.

132

0.12

6−

0.30

712

40.

977

0.95

30.

066

621

0.49

0.

028

0.01

50.

027

0.02

10.

017

PY

E−1

.362

0.33

30.

398

0.14

50.

277

0.36

473

0.97

80.

953

0.08

629

10.

71

0.

083

0.04

70.

069

0.04

80.

077

0.08

3

DN

AP

−1.5

770.

737

0.51

00.

750

0.50

1−

0.08

610

70.

983

0.96

50.

117

588

1.27

0.

060

0.03

10.

060

0.04

30.

071

0.03

3

PN

P−1

.357

0.47

00.

267

1.01

00.

622

−0.

226

114

0.97

30.

943

0.12

137

71.

32

0.

058

0.03

10.

060

0.04

50.

073

0.04

5

PF

P−1

.101

0.16

90.

482

−0.

054

−−

0.31

311

50.

956

0.91

20.

076

296

0.60

0.

021

0.02

00.

038

0.02

30.

045

PB

B−1

.245

0.72

8−

0.21

4−

0.47

982

0.98

50.

970

0.10

287

20.

90

0.

050

0.02

00.

037

0.04

5

n is

the

num

ber

of s

olut

es c

onsi

dere

d in

the

regr

essi

on

R is

the

mul

tiple

cor

rela

tion

coef

ficie

ntR

2 adj i

s th

e ad

just

ed c

orre

latio

n co

effic

ient

SE in

the

stan

dard

err

or in

the

estim

ate,

F is

Fis

cher

’s s

tatis

tic

u is

the

solv

atio

n ve

ctor

leng

th a

ccor

ding

to E

quat

ion

5.7

and

the

num

bers

in s

econ

d lin

es r

epre

sent

99.

9% c

onfid

ence

lim

itsD

ashe

s in

dica

te c

oeffi

cien

ts th

at w

ere

not i

nclu

ded

in th

e m

odel

due

to s

tatis

tical

insi

gnifi

canc

e

84534.indb 222 11/5/09 12:27:59 PM


be observed on Figure 5.5, where the normalized residuals for 16 compounds have been plotted for 5 columns displaying very different chemistries and polarities. More columns and compounds could have been used, which would have shown exactly the same tendencies but we have chosen to simplify the figures for the purpose of clarity. Thus the observed deviations are obviously not related to experimental errors but might originate from limited adequacy and/or precision of the used descriptors or from some molecular interactions that are not accounted for by the solvation param-eter models.

As far as limited adequacy of the descriptor is concerned, we have to point out that descriptors available in the literature are not always very accurate, which seems normal judging by the variety of partition and chromatographic processes used to calculate them.

Concerning the molecular interactions that are not accounted for by the solva-tion parameter model, electrostatic interactions may sometimes occur. Indeed, in most cases, the compounds needing to be excluded were of varied nature and no systematic trend was observed. However, for some columns (as PFP, C18-C or C4), some basic solutes (among solutes 27 to 40) had to be removed, as they were extreme outliers and were largely more retained than what would be expected, based on the model calculations. These are the only N-containing bases in the solute set. Since oxygen-containing compounds of similar capacity for H-bond and dipole-type inter-actions (as 1-phenylethanol and benzyl alcohol, for instance) are not influenced to the same extent, we presume that this additional retention results from a contribution to retention that is not considered by the model, such as electrostatic interactions with residual silanol groups (in the non-endcapped phases) or other possibly ionized groups. Indeed, the solvation parameter model—in the form employed here—uses descriptors characteristic of the neutral form of the molecule. It is not expected to provide accurate predictions of chromatographic properties of solutes in a fully or partially ionized form. Different authors have suggested additional terms for ioniz-able solutes [48–53] but these descriptors require knowledge of the pH and pKa of

Tol

uene

Ethy

lben

zene

Prop

ylbe

nzen

eBu

tylb

enze

nePe

ntyl

benz

ene

o-xy

lene

m-x

ylen

ep-

xyle

neo-

tolu

idin

eA

niso

leo-

nitr

oben

zyla

lcoh

olm

-nitr

oben

zyla

lcoh

olp-

nitr

oben

zyla

lcoh

olPh

enan

thre

neA

nthr

acen

eFl

uora

nthe

ne

–2.0–1.5–1.0–0.5

0.00.51.01.52.0

Nor

mal

ized

resid

ual

PFPOPHEC4PE2AMD

fIgure 5.5 Plot of the normalized residuals calculated for PFP, OPHE, C4, PE2, and AMD for 16 representative solutes.

84534.indb 223 11/5/09 12:28:00 PM


the species, while the pH of the carbon dioxide-methanol mobile phase is unknown. However, some studies carried out with pH indicators tend suggest that it could be acidic [54–56], possibly below 5. Even if the pKa of the silanol groups might be larger in the subcritical mobile phase than in aqueous environment, it is reasonable to think that it should remain lower than 5. Therefore, silanol groups are expected to be partly dissociated in the CO2-MeOH subcritical mobile phase. On the other hand, a number of N-containing basic solutes would be present in their cationic form, thus would establish electrostatic interactions with the anionic silanol groups. As no more pre-cise information is available, we have to admit that electrostatic interactions occur but that we can so far not evaluate them. In the same manner, some acidic solutes (as benzoic acids) may be present in their anionic form, which would explain why they may be badly predicted on some stationary phases, where attractive or repulsive electrostatic interactions would occur.

Besides, the adsorption phenomenon on the surface could also partly explain the worse correlations obtained for SI and PGC. Selective adsorption and steric require-ments for sorption at sites of different sorption energy may not be perfectly modeled. In those cases, when it is reasonable to think that adsorption is the principal reten-tion mechanism, the molecular volume may not perfectly model the contact surface area for non-planar molecules [57]. For these solutes, the trends in the residual graph is generally different from the one observed on other stationary phases. This can be seen on Figure 5.6, where the normalized residuals for 17 solutes are plotted for PGC, SI, and C18. For those solutes which show generally small normalized residual on C18, thus cannot be suspected for having wrong descriptors, the deviation on PGC and SI is larger. Thus, when working with adsorbents, replacing the molecular volume by a contact surface area may improve the fit and reduce the residuals for angular molecules. We already had the opportunity to discuss this point for PGC [40]. However, as we wish to compare the results between all stationary phases, we chose to use the molecular volume in all cases.

Benz

ene

Tol

uene

Ethy

lben

zene

Prop

ylbe

nzen

eC

umen

eD

ieth

ylph

thal

ate

Dip

ropy

lpht

hala

teD

ibut

ylph

thal

ate

Chl

orob

enze

neBr

omob

enze

neIo

dobe

nzen

e2,

3-D

imet

hylp

heno

l

2,4-

Dim

ethy

lphe

nol

2,5-

Dim

ethy

lphe

nol

2,6-

Dim

ethy

lphe

nol

3,4-

Dim

ethy

lphe

nol

3,5-

Dim

ethy

lphe

nol

–3.0–2.5–2.0–1.5–1.0–0.5

0.00.51.01.5

Nor

mal

ized

resid

ual

SIPGCC18

fIgure 5.6 Plot of the normalized residuals calculated for SI, PGC, and C18 for 17 representative solutes.

84534.indb 224 11/5/09 12:28:01 PM


Nevertheless, the results are reasonably good and, it is worth noting that the sign and magnitude of each regression coefficient obtained are always in accordance with the chemical nature of the stationary–mobile phases system.

5.3 ChoICe of solvatIon desCrIptors for superCrItICal fluIds

The solvation parameter model can also be used with a second equation, represented below:

log k = c + eE + sS + aA + bB + lL (5.3)

Equation 5.1 is applied to processes involving condensed phases while Equation 5.3 is applied to processes in gaseous phases. As a consequence, the solvation parameter model can be used either with Equation 5.1 or with 5.3, depending on the density of the mobile phase used. The case of supercritical fluids is critical regarding the choice of the most appropriate equation because the density of these fluids varies with a number of operating parameters. The choice of one or the other of the equations is thus not trivial. Some supercritical fluid studies were carried out with the L descrip-tor [33–39,58], others with the V descriptor [59–61]. Some authors [60] suggest that this choice is of no importance because the two descriptors would be supposedly correlated. However, this is not the case, as evidenced by Figure 5.7, where the L descriptor is plotted against the V descriptor for 600 solutes. The covariance essen-tially exists when a single family of solutes is considered, as homologous series, for instance, but not when a variety of solutes are considered, as must be the case for the calculation of QSRRs. Consequently, V and L are not interchangeable.

Since the properties of supercritical fluids are intermediate between gases and liquids, both V and L could be appropriate descriptors. To choose between the two, it is important to understand the nature of each of these descriptors.

R2 = 0.7485

–2

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5 2.0 2.5 3.0

V

L

fIgure 5.7 Plot of the gas-hexadecane partition coefficient (L) vs. McGowan’s volume (V) for 600 solutes.

84534.indb 225 11/5/09 12:28:02 PM


V is McGowan’s molecular volume. Expressed in cm3 mol–1/100, it represents the volume of one mole of the solute, when the molecules are immobile. It can be calcu-lated very simply, using the equation below [62]:

VV V= −Σ Σatoms bonds

100 (5.4)

where ΣVatoms represents the sum of the volumes of all atoms in the molecule and ΣVbonds the sum of the volumes of all bonds. As the volume of one bond is considered to be always the same, whatever the atoms it links and whatever the multiplicity of the bond (single, double, or triple), we only need to know the number of bonds (B). The latter can be determined with the following equation:

B = N – 1 + R (5.5)

where N is the number of atoms and R the number of rings.L represents the logarithm of partition coefficient between gas and hexadecane at

25°C. It is thus reasonable to think that L is related to the boiling point of the solute. This is evidenced by Figure 5.8a, where L values for 300 solutes have been plotted versus their boiling points. In this case, the correlation coefficient is large (0.921). When V values for the same 300 solutes are plotted against the same boiling point values the correlation is significantly lower (Figure 5.8b).

However, in the subcritical conditions we have chosen, retention is not related to volatility, contrary to what occurs in the supercritical state at elevated temperatures [63]. This is a first argument for preferring the V descriptor.

Besides, one problem encountered when working with the L descriptor is that L has a different dimension than the other Abraham descriptors. The other descriptors roughly range from 0 to 5, while L ranges from 0 to 30 [27]. As a consequence, the interpretation of the coefficients issued from the multiple linear regression analysis is not as immediate because the largest coefficient is not necessarily associated to the strongest interactions.

Replacing V by L generally induces an increase in the associated system con-stant, with a concomitant decrease in all other system constants. This can be partly explained by the lack of independence of L with the other Abraham descriptors. Indeed, we have shown that L is strongly correlated to the boiling point. However, volatility of a solute is not only associated to its molecular weight but also to the interactions existing between the solutes, depending on their physico-chemical prop-erties. As a result, it can be seen in the covariance matrix in Table 5.4 that the corre-lation coefficients relating L to E and S are larger than those relating V to E and S.

Consequently, the information contained in L is partly redundant with the infor-mation contained in E and S. In other words, L would be less pure than V. Thus when V is replaced by L, the associated system constant is increased, not because the dispersion interactions really are stronger than estimated with V, but because the l coefficient is associated to a blend of interactions: dispersive, charge-transfer, dipole–dipole. The use of L instead of V might induce erroneous and/or confuse interpretation of the chromatographic system.

84534.indb 226 11/5/09 12:28:03 PM


In short, there are, in our case, different important reasons to choose V rather than L:

L is correlated to volatility, a factor that is not relevant to explain retention •in subcritical conditions.L is not on the same scale as the other Abraham descriptors, thus the •amplitudes of the system constants are not directly comparable to estimate the relative importance of each type of interaction toward the retention behavior.L is itself a composite descriptor, associating information related to molec-•ular volume, polar, and polarizable characters, further complicating the interpretation of the results.

For all these reasons, we chose to work with V instead of L.Besides, Lagalante and Bruno [59] have found it important to introduce an addi-

tional descriptor to achieve an exact description of processes occurring in supercritical

R2 = 0.9209

0

2

4

6

8

10(a)

(b)–200 –100 0 100 200 300 400 500

–200 –100 0 100 200 300 400 500

bp(°C)

L

R2 = 0.5745

0.0

0.5

1.0

1.5

2.0

2.5

3.0

bp(°C)

V

fIgure 5.8 Plots of (a) the gas-hexadecane partition coefficient (L); (b) McGowan’s vol-ume (V) vs. boiling point (bp) for 300 solutes.

84534.indb 227 11/5/09 12:28:04 PM


fluids. The authors base their reasoning on the fact that, if solvents remain at a constant temperature and pressure when used in the liquid state, it is not the case when they are in the supercritical state because the eluting strength is modulated through changes in pressure and temperature. When the density of the fluid changes, variations in the polarity parameter π* of the mobile phase are observed: the polar or polarizable character of the fluid varies with its density. The other descriptors supposedly remain constant. The authors considered that this should be taken into account in the solvation parameter model when applied to supercritical fluids.

Indeed, the polar character of supercritical fluids varies linearly with density, and faces a sudden change of slope when the density is changed from gas-like to liquid-like. But the fact that other characters would remain constant with density changes is questionable. This was verified for pure carbon dioxide fluids but not for carbon dioxide-modifier mixtures, which are commonly used in pSFC today. If density varies, be it through a change in temperature, pressure, flow rate, or mobile phase composition, and if the modifier presents an acidic or basic character (as is the case of most modifiers commonly used), it seems logical that the acidic and basic character of the mobile phase should change with density, and not only polarity. In this case, other additional descriptors would be required to account for these phenomena.

In our case, the fluid density variations are strongly limited by the subcritical conditions and by the fact that the chromatographic mobile phase and operating conditions are kept constant to compare the stationary phases. Thus we chose to use the classical Abraham equation, without any additional descriptor.

5.4 a general database for paCked Column sfC

The original database described in our previous works [64–65] has since been expanded and upgraded. In the current database, 35 columns of varying chemistries and 49 ODS phases are included.

5.4.1 variation of the syStem ConStantS amonG the stationary phaSeS

Since the descriptors represent the solute effect on various solute-phase interac-tions, the coefficients obtained from the multiple linear regression analysis corre-spond to the complementary effect of the stationary and mobile phases on these interactions. The regression coefficients are thus very important, because they will encode chromatographic system properties. As the chromatographic conditions and mobile phase are kept constant, it is reasonable to think that the regression coef-ficients encode stationary phase properties. The coefficients can then be regarded as constants characterizing the stationary phase. The intercept, c, is not assigned any chemical significance. It represents a part of the retention factors that is not accounted for by the solvation parameters. Therefore, the c coefficients are not easily compared or interpreted, and they will always be omitted in this section.

The various stationary phases may be compared relative to their regression coef-ficients to establish a relative order of selectivities toward specific types of molecu-lar interactions. Indeed, as discussed in the introduction, the system constants are

84534.indb 228 11/5/09 12:28:04 PM


also related to the system’s selectivity through Equation 5.2. Therefore, to enhance the separation of compounds differing in their X property, one should choose the chromatographic system where the x coefficient is the largest. For instance, to sepa-rate compounds differing primarily in their molecular volume, as is the case in homologous series, it is advisable to choose a chromatographic system with a large v coefficient. Indeed, along a series of homologues, the E, S, A, and B descriptors will be almost the same, and the only descriptor to vary will be V. Then the v coef-ficient will be the only system constant of importance. Thus, a first possibility is to observe the system constants one by one through histogram plots (Figure 5.9). We have shown in previous works how small differences in the bonding chem-istry of the stationary phase can result in large differences in individual system constants [66–68].

At the same time, it is interesting to evaluate the part taken by each type of interaction in the dispersion of the studied chromatographic systems. Indeed, each coefficient represents a certain proportion of the initial information which can be estimated through the calculation of the percentage of variance explained. The five types of interactions (e, s, a, b, and v) can be associated to five axes, in the same manner as five principal components in a PCA. On each axis, the percentage of variance explained can be calculated very simply with a formula similar to the one used in PCA. First of all, the barycenter G of all points must be determined (using equal weights for all chromatographic systems), then the percentage of variance is expressed by:

%var( )

( )=

′−

−

∑∑

ii

ii

M G

M G

2

2

(5.6)

where Mi-G is the distance between a chromatographic system Mi and G and Mi′-G is the distance between the projection of the Mi system on the axis considered and G.

The e coefficient shows the tendency of the phase to interact with solutes through π and n electron pairs. The e axis carries only about 6% of the variance observed among the 35 columns. One reason for the small variance is the fact that all columns display positive e coefficients (Figure 5.9a). This indicates that the respective inter-actions are always stronger in the stationary than in the mobile phase. No general tendency can be found to explain the variations of the e coefficient.

This, and the fact that the e coefficient is always positive, is possibly related to its composite nature. Indeed the E descriptor represents the capability of the solute to interact through π and n electrons thus can be associated to dispersive, dipole-induced dipole, and π–π interactions. Another reason for the poor variance could be the fact that the solute set is only constituted of aromatic molecules, thus provid-ing little opportunity to observe a variance in the e interactions: each type of phase (polar, nonpolar, or aromatic) can present high or low e coefficient.

PGC is the only stationary phase to exhibit significantly different e-type interac-tions from the other stationary phases with an e value being twice as large as the largest e value calculated for all other phases. The extended planar aromatic surface

84534.indb 229 11/5/09 12:28:04 PM


of PGC, covered with π electrons, is responsible for this, as we discussed in previous works [68].

The s coefficient gives the tendency of the phase to interact with dipolar and/or polarizable solutes. The s coefficient is the second least important coefficient in terms of variance between the columns. Indeed, the s axis carries about 14% of the variance. As can be seen on the histogram plot (Figure 5.9b), the s coefficient varies from small negative values (for alkyl-type phases) to moderate positive values (for polar and aromatic phases). Negative values indicate that dipole–dipole interactions

PFP C4

C3P FD D

PM

IXD

P-X

C6P

-G C8

C6P

-LPY

EN

AP

C6P

-Z CN

PEG

OPH

E SIC

12D

IOL

RPH

PNP

NH

2A

MD

PE2

PVA

PE3

C18 EP

CH

LC

18-C PE

1PB

BD

NA

P PSPG

C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8(a)

(b)

(c)

Column

e

C18

C18

-C PE1

C8

RPH

C12 PE

3C

HL C4

MIX PE

2FD

PVA

DIO

L PS DP

DP-

XC

3PC

6P-L

C6P

-GC

6P-Z

PBB

OPH

EN

AP

PEG

PNP

AM

DN

H2 SI C

NPG

CPY

EPF

PD

NA

P EP

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

0.8

Column

s

C18

RPH

C12 C

8M

IX PFP C4

C6P

-LC

6P-Z

C6P

-GN

AP PS

PYE

OPH

EC

18-C

PBB

DP-

XC

3P DP

CH

LFD PE

2PG

CC

ND

NA

PPE

3D

IOL

PNP EP

PVA SI

PEG

PE1

NH

2A

MD

–1.0

–0.5

0.0

0.5

1.0

1.5

Column

a

fIgure 5.9 Histogram plots of the system constants in Table 5.6, in order of increasing value, of a) the e coefficient; b) the s coefficient; c) the a coefficient; d) the b coefficient; e) the v coefficient.

84534.indb 230 11/5/09 12:28:05 PM


are more favorable in the mobile phase when the stationary phase is nonpolar, which is in accordance with chemical sense. The stationary phases are equally parted between negative, positive, and zero values of the s coefficient. A negative coefficient does not mean that no s-type interactions (dipole–dipole and dipole-induced dipole interactions) occur, but that they are equally strong between the solute and stationary phase and between the solute and mobile phase.

The limited variations of the s coefficient can possibly be explained by the fact that the E and S descriptors are partly correlated, thus some information contained in the s coefficient is already described in the e coefficient.

The a, b, and v axes carry 26, 29, and 25% of the variance, respectively, thus they are nearly equivalent.

The a coefficient denotes the hydrogen-bond basicity of the phase, because acidic solutes will interact with a basic phase. Only a few columns display a negative a coefficient (Figure 5.9c). Most of them are alkyl-bonded silica phases possessing no polar group to provide a hydrogen-bonding acceptor site. The largest a values are generally found among polar phases but it is worth noting that polar-embedded ODS phases as PE1 (amide-embedded) and PE3 (carbamate) can also display a strong basic character, whereas PE2 (ether-sulfonamide) displays a smaller a value.

The b coefficient is a measure of the hydrogen-bond acidity of the phase, because basic solutes will interact with an acidic phase. The situation for the b coefficient is a little different (Figure 5.9d) as about a half of the phases investigated possess

CH

LC

18 PE3

C12 PE

2PE

1RP

HPG

C PSM

IXC

6P-G

PEG C8

C6P

-ZC

6P-L C4

C18

-C PFP

PBB

NA

PD

P-X

OPH

EC

3P DP

PYE

CN

DN

AP

PNP EP

PVA

NH

2D

IOL

FD SIA

MD

–1.0

–0.5

0.0

0.5

1.0

1.5(d)

(e)Column

bEP

NH

2A

MD SI

DIO

LFD

PVA

CN

PFP

PNP

DN

AP

PEG

OPH

ED

P C4

DP-

X PS C8

C18

-CC

3PC

6P-L

PE2

C6P

-ZN

AP

PE3

C6P

-G C12

MIX PE

1PY

ERP

HC

18C

HL

PBB

PGC

–1.0

–0.5

0.0

0.5

1.0

1.5

Column

v

fIgure 5.9 (Continued)

84534.indb 231 11/5/09 12:28:06 PM


a negative b coefficient (mostly alkyl-bonded phases and some aromatic phases as phenyl-hexyl bonded phases), with the other half possessing a positive b coefficient (mostly polar phases). Variance among the positive values is twice as large as among the negative values. Comparing the three polar embedded ODS columns, one can remark they display close values, whatever the polar embedded group nature.

In our column set, there are three stationary phases grafted with the same bonded group (phenyl-hexyl) but three different silica gels. In particular, C6P-G is bonded on hybrid organic/inorganic silica in which silane bridges are replaced by ethane bridges. Consequently, there should be less residual silanol groups on the silica sur-face. Indeed C6P-G displays lower acidity than the two other phenyl-hexyl phases (C6P-L and C6P-Z), probably due to this special silica.

The v coefficient is a combination of exoergic dispersion forces that make a posi-tive contribution and an endoergic cavity term that make a negative contribution. Cavity effects in the mobile phase should be negligible in our case because the cohe-siveness of the supercritical mixture used here is low. Therefore, dispersive inter-actions and cavity effects mainly occur with the stationary phase. Only a third of the columns tested display a negative v coefficient and all of them are polar phases (Figure 5.9e). Indeed, it generally requires more energy to create a cavity in a polar stationary phase than in a nonpolar stationary phase as the latter is less cohesive. The other stationary phases, moderately polar (aromatic) and nonpolar (alkyl) phases have a positive v coefficient. In this case, the dispersion interactions dominate. Thus the v coefficient seems to be a useful measure of the hydrophobicity of a stationary phase. This is also clearly visible on Figure 5.10, which represents the separation of some alkylbenzenes on five stationary phases with increasing v values. On the PEG phase, where the v coefficient is zero, the five homologues coelute. On the four other phases, which are all alkylsiloxane-bonded silica phases with increasing alkyl chain length, the v values are increasing with the chain length and it is clear that the separa-tion of the homologues is improving when the v value is increasing.

Again, by far the largest value is the one calculated for PGC, with its highly dis-persive surface.

While all these observations match intuition, the solvation parameter model pro-vides a quantitative estimate of the relative importance of these effects.

5.4.2 a viSual repreSentation of the databaSe

As described above, using the solvation parameter model, the different chromato-graphic systems can be compared based on raw values of the regression coefficients. However, to compare the 35 columns based on numerical values or using five histo-gram plots is a complicated task. Thus we have devised a way to plot the results so as to represent the five-dimensional repartition of the chromatographic systems in the five-dimensional space of selectivities defined by the solvation descriptors [69]. We have also looked for numerical tools, which would help measuring similarities between stationary phases in an objective manner.

The spider diagram (Figure 5.11) is very simply plotted: each chromatographic system is placed at the extremity of the normalized solvation vector positioned from the origin defined as the center of the five-branched-star. This means that the

84534.indb 232 11/5/09 12:28:06 PM


PEG

C4

C8

C12

C18

12

Min

utes

12

Min

utes

12

Min

utes

12

3M

inut

es1

23

Min

utes

fIg

ur

e 5.

10

Chr

omat

ogra

ms

of a

lkyl

benz

ene

com

poun

ds, w

ith

carb

on n

umbe

r in

the

alk

yl c

hain

ran

ging

fro

m 1

1 to

15

on fi

ve s

elec

ted

colu

mns

w

ith

incr

easi

ng v

val

ue. M

obil

e ph

ase:

CO

2-M

eOH

90:

10 (v

/v).

Tem

pera

ture

: 25°

C. O

utle

t pre

ssur

e: 1

5 M

Pa. F

low

rat

e: 3

ml m

in−1

84534.indb 233 11/5/09 12:28:08 PM


chromatographic systems are plotted according to the normalized values of their system constants. Indeed, plots of data of very different absolute magnitudes can exhibit skewed data classification. Consequently, a range-scaling transformation of some sort is required.

One way to do this is to divide e, s, a, and b by the v coefficient, as has been sug-gested by other authors [25,70]. This would allow assessment of the relative part of interactions—other than dispersive—to retention. However, in our case, contrary to what occurs in RPLC, the v coefficient is not always positive but it can be negative or zero. Thus, this operation does not really make sense.

On another hand, the contribution of one type of interaction relative to all inter-actions established in a system can be evaluated if each coefficient is divided by u, defined by the following equation:

u e s a b vi i i i i i= + + + +2 2 2 2 2 (5.7)

u is the length of the solvation vector associated to the chromatographic system. We have shown in previous works [69] that the vector length is a valuable tool to compare the amplitude of the interactions developed in a chromatographic system. It was calculated for each column tested and the values appear in the last column in Table 5.6. It must be noted that u is not correlated to the total retentive power of a chromatographic system as it takes both positive and negative coefficients into account in the same manner: interactions established with the stationary or mobile

PGC

PS

OPHE

DP

DP-XC3P

C6P-LC6P-G

PYE

FD

PFP

PBB

EP

CN

SI

PEG

PVADIOL

NH2AMD

C4

C8

C12C18

RPH

MIX

PE1

PE2

PE3

C18-C

CHL

PNP

DNAP

NAP

C6P-Z

e

s

ab

v

fIgure 5.11 Spider diagram for a five-dimensional representation of the solvation param-eter models in Table 5.6. The stationary phases are identified according to the abbreviations in Table 5.1. Bubble size is related to the vector length (u), calculated with Equation 5.7. Ellipses circle the columns, which were found similar through the calculation of J (Equations 5.9 to 5.11) Chromatographic conditions as in Figure 5.10.

84534.indb 234 11/5/09 12:28:09 PM


phase are both considered. Furthermore, it does not take into account the value of the c system constant, thus the phase ratio is not included in the comparison, only the interaction terms.

Thus each x coefficient is divided by the vector length (u) to normalize the data before plotting the spider diagram. This way, the experimental behaviors are consis-tent with the observations based on the figure: when two columns are close on the spider diagram, they provide nearly identical elution order of the analytes. The size of the bubbles is related to u, thus the intensity of the interactions is also apparent on the figure. Thus, when two columns are close but have different bubble sizes, it indicates that the analytes are eluted in the same order on the two columns, but with larger retention factors are larger separation factors on the column with the larger u value.

The way of reading this figure is not obvious at first sight as anyone familiar with PCA plots would be tempted to interpret the proximity of a point and an axis as an indication of the dominant factor contributing to retention on this stationary phase. However, it is absolutely not the case. The centered star composed of the five solvation axes is only represented to indicate the origin of the referential space and the directions that allowed placing the points in the figure, but only the distances between the points are significant, not their positions regarding the centre or the axes. Moreover, the position of the points is not indicative of the amplitude of each type of interaction and cannot distinguish the difference in the sign of the coeffi-cients, as would be the case with a radar plot.

This plot is more advantageous than the plots produced by a PCA, as only one figure represents all the information, while PCA generally results in more than two principal components, therefore requires two or more figures to exhibit all the infor-mation. Besides, any new chromatographic system can be added in a very simple manner, without the need of calculating the position of every other point, as is the case with PCA. Moreover, this plot can be used to compare numerous phases together, without the need for a reference phase.

However, it must be mentioned that the five axes are not independent on the two-dimensional paper and that the view of the five-dimensional space offered by this two-dimensional figure can be somewhat distorted. In any case, the figure cannot stand for itself and it is always preferable to use it in conjunction with Table 5.6, before drawing any conclusions. Nevertheless, we must point out that, so far, this figure has never contradicted the observations based on the values of the solvation coefficients.

Furthermore, the angle between two solvation vectors (ω) associated to two chro-matographic systems can be calculated according to the following equation, based on the solvation parameter model coefficients of the two systems noted i and j:

cos*

*θ

ω ωω ωij

i j

i j

i j i j i j i je e s s a a b b v= =

+ + + + ii j

i i i i i j j j j j

v

e s a b v e s a b v2 2 2 2 2 2 2 2 2 2+ + + + + + + + (5.8)

This method was first introduced by Ishihama and Asakawa to evaluate the similar-ity between liquid–liquid partition systems [71].

84534.indb 235 11/5/09 12:28:10 PM


The angle between two columns provides a mean to measure the informational equivalence of different chromatographic systems: the wider the θ angle, the more different the systems are. Conversely, when the angle is close to zero, it indicates that the vectors have the same direction (although not necessarily the same length) and this would mean that the interactions established in these two systems are proportionally identical; therefore the two chromatographic systems would provide identical elution order of the solutes. We have shown in previous works that the proximities and distances between the columns on the spider diagram are perfectly consistent with calculated values of the θ angles [68,70,72]. Moreover, the similarity between two chromatographic systems is evaluated through the calculation of the J similarity factor, determined through Equations 5.9–5.11:

J = cos θij – cos (θdi + θdj) (5.9)

cos( )θ θω ω

di dji

i

j

j

D D+ = −

−

1 1

2

2

2

2 −−D Di j

i j

ω ω

(5.10)

D = TINV(1−0.99, N) · SEav (5.11)

where TINV is the inverse of the Student’s t-distribution for the specified degrees of freedom N, and SEav is the average of the standard errors of the solvation parameter model coefficients.

In Equation 5.9, when J is positive, the systems compared are found to be similar; in the opposite case, they are considered to be different.

It is worth noting that the angle alone is not sufficient to judge the similarity between two chromatographic systems, as it does not take into account the confi-dence limits associated to the system constants. There is no absolute limit angle that would provide a decision for similarity, because the calculation of J takes into account a sphere of uncertainty depending on the standard error associated to each coefficient and the degrees of freedom related to the number of solutes that were used to calculate the solvation coefficients (Equation 5.11). Thus, there is a further interest in injecting more solutes to achieve a higher precision in the comparisons: when the number of solutes injected is increased, the degrees of freedom increase, thus the D factor decreases. As a matter of fact, the uncertainty spheres are smaller, and thus the limit angle for dissimilarity is smaller. Under-determining the system could lead to considering two columns similar when they are not, just because their positions are not determined with enough precision. For instance, we will show later in this paper that the discrimination obtained on ODS phases is not as good as the one obtained here, because the solvation parameter models for ODS phases were only determined with 29 solutes.

The θij angles existing between the solvation vectors associated to all the station-ary phases characterized above through the use of the solvation parameter model and the J similarity factors between them were calculated. At the 99% confidence limit, some columns were found to be similar. Thus, the groups of stationary phases that were judged to be similar are circled in Figure 5.11.

84534.indb 236 11/5/09 12:28:10 PM


As an example of how the spider diagram representation can be related to practi-cal solute retention, let us compare three aromatic columns: C3P, DP-X, and OPHE. The three of them are placed in close positions in the diagram, but only C3P and DP-X are circled, indicating that they were found to be similar through the cal-culation of J. Indeed, as appears on Figure 5.12, the vectors representing C3P and DP-X point in directions separated by a 7° angle and the uncertainty spheres cover a common angle, revealing that the two columns cannot be discriminated. Looking at Figure 5.12, it is clear that the two columns provide highly correlated retention factors (R2 = 0.985). Moreover, because the vector lengths are identical for the two columns (u = 0.467), indicating identical interaction strengths, the slope of the cor-relation curve is close to 1. All in all, C3P and DP-X are interchangeable.

On another hand, Figure 5.12 shows that the vector for OPHE points toward a slightly different direction, establishing a 19° angle with the C3P solvation vector. Moreover, the uncertainty spheres do not cover any common angle thus the phases were found to be dissimilar through the calculation of J. This is in accordance with Figure 5.12, as some more dispersion is found among the retention factors between C3P and OPHE (R2 = 0.900). However, as the vector length for OPHE (u = 0.459) is close to that of C3P (u = 0.467), the slope of the regression line is still close to 1. As a result, C3P and DP-X cannot be exchanged for OPHE as the latter would provide slight differences in the separation of complex mixtures.

First of all, the spider diagram allows us to evaluate the extent of the separation space that can be employed for separations in pSFC and to observe what part of the selectivity space is occupied by existing phases. A first observation is that the super-critical chromatographic systems are scattered in a wide selectivity space, mostly along a diagonal line. The regions of empty space on the plot provide a clear indica-tion that the characterized columns do not occupy the selectivity space uniformly: they only fill a fraction of the selectivity space and allow targets for new stationary phases with complementary separation properties to be identified. For example, the PFP phase is the only one to occupy the top right of the figure, and no stationary phase is present at the bottom left. To fill this latter space, a stationary phase provid-ing a high b value together with a low a value would be required. This means produc-ing a stationary phase, which would be highly acidic but not basic.

A closest examination of Figure 5.11 allows synthesizing the behaviors of the numerous tested columns. The nonpolar alkyl bonded phases of varying chain length (from C8 to C18) are located in the same area, indicating that they develop

DP-Xθ=7°

θ=19°OPHE

C3P C3P

fIgure 5.12 Two-dimensional representation of the solvation vectors associated to C3P, DP-X and OPHE. The circles indicate the uncertainty spheres (D) calculated with Equation 5.11. The θ angle values were calculated with Equation 5.8.

84534.indb 237 11/5/09 12:28:11 PM


identical interactions. As expected, the alkyl chain length does not modify the phase properties, but induces changes in the intensity of these interactions (see the differ-ences in bubbles size or in u values in Table 5.6). The most polar phases are located in the opposite area of the spider diagram, underlying that these phases develop totally different interactions from the ones developed by the alkyl bonded phases. Between these two groups, there are numerous phases with different characters. Most of them are aromatic phases, but the polar embedded ODS phases (PE1, PE2, PE3) are also in the middle part of the figure.

Secondly, the spider diagram can serve as a tool for stationary phase selection during method development. Indeed, the observation of individual system constants with histogram plots is helpful when simple separation problems are encountered: as discussed above, homologous series are best separated using a chromatographic system providing high v value; compounds differing in the aromatic character or number of double bonds are best separated using a chromatographic system provid-ing a high e value, etc. However, most of the time, more than one chemical function is varied among the analytes, thus several terms must be taken into account and the combination of interactions is most important.

On the spider diagram, when two columns are close, it means that their five nor-malized system constants (e/u, s/u, a/u, b/u, v/u) are close. Indeed, as the distances between the different columns in Figure 5.11 are consistent with the calculated values of the θ angle, two close columns have their solvation vectors pointing in the same direction thus proportionally identical system constants. When normalized system constants are identical, the two columns are judged similar by the calculation of the J similarity factor indicating that there is no difference in the effective selectivity of the two systems: the analytes will be eluted in highly similar order. However, in the course of method development, it is advisable to screen chromatographic systems providing different effective selectivities, thus being distant on the spider diagram. After identifying the most suitable stationary phase for a separation, near neighbors can be investigated for optimization.

For instance, all polar phases are very close on the diagram and display quite small angles between them, because they globally show an identical pattern of inter-actions (an increase in polarity causes an increase in retention while an increase in the molecular volume causes a decrease in retention) with a slightly different blend of polar interactions, but they are not all found to be similar, thus small differences in the elution order can occur. More precisely, when largely different compounds need to be separated, the differences between the polar phases will not be obvious but, for the separation of closely spaced compounds, EP will not always retain the same order as those observed on SI and one column cannot be substituted for the other when the separation of complex mixtures are of interest. Thus, in the course of method development, initial screening of all polar phases is of no use: it is more valu-able to screen stationary phases that are scattered in the whole spider diagram then, if a polar phase seems to be the most appropriate, screening of phases providing slightly different effective selectivities can be useful. Besides, it can be an advantage to possi-bly exchange a column for another one that would provide identical elution order with higher selectivity, as is the case when CN is exchanged for EP. As a matter of fact, the high selectivity of a column can be an advantage for the separation: high selectivity

84534.indb 238 11/5/09 12:28:11 PM


is important in that more selective columns do not need as many plates to achieve a specified resolution and thus shorter columns or higher flow rates can be used.

A detailed example is provided (Figure 5.13) with the separation of nitrophe-nols. This choice is significant because, apart from the molecular volume, all other descriptors vary among the three isomers (see descriptor values in Table 5.3). The solvation vectors of CN and EP are only separated by a 6° angle, indicating that the two columns provide proportionally identical interactions thus will elute the ana-lytes in the same order. However, the length of the solvation vectors is not identical (uEP = 1.696 while uCN = 1.029) indicating that EP establishes stronger interactions than CN. Judging from Equations 5.1 and 5.2, EP should provide both larger reten-tion factors and larger separation factors (α) than CN. Indeed, the retention factors for o−, m−, and p-nitrophenols are, respectively, −0.279, 0.404, and 0.507 on EP; −0.485, 0.090, 0.170 on CN and the logarithms of separation factors between o/m and m/p are, respectively, 0.683 and 0.103 on EP; 0.575 and 0.080 on CN. Thus changing CN for EP is a means to retain identical elution order while increasing separation factors, where need be SI, on the contrary, is not judged to be similar to the other two columns, although it displays a small angle with each of them (15°). This is indica-tive of a slightly different blend of interactions, which can result in different separa-tions. Figure 5.13 indeed shows that the separation of m− and p-nitrophenols is not complete with this column, while they were baseline resolved with EP and CN. Thus when a separation is not perfect with CN or EP, it can be worth testing SI.

Regarding the screening of orthogonal columns, we have shown how this dia-gram can be used to build a panel of complementary stationary phases to achieve

CN

1 2Minutes

1 2Minutes

3 1 2Minutes

3 4 5

oo

o

m

m

m

p

p

p

EP SI

fIgure 5.13 Chromatograms of ortho-, meta, and para-nitrophenols on three polar col-umns. Chromatographic conditions as in Figure 5.10.

84534.indb 239 11/5/09 12:28:13 PM


separations in a screening method [72]. It is recognized today that SFC is especially well suited for these screening methods, as elution gradients (and subsequent equili-bration) can be performed in a few minutes, due to the high fluid diffusivity.

In practice, any approach to method development in pSFC would have to include mobile phase optimization. Therefore, some care is needed in comparisons of sta-tionary phases at a single reference mobile phase composition. The few studies avail-able [73] and our own experience indicate that selectivity changes with mobile phase composition are dependent on the identity of the stationary phase. The phase con-stants generally (but not always) decline with increasing percentage of modifier in the mobile phase, often in a non-linear manner and with different slopes. For this reason, it cannot be assumed that the selectivity comparison of stationary phases in the chromatographic conditions used here would be exactly the same in other chro-matographic conditions. This point is currently under investigation.

5.4.3 odS phaSeS

In this part, we will put a special emphasis on ODS phases, as the large diversity of chemistries existing are the object of many characterization tests [74]. Indeed, the structures of the ODS phases are very varied and can lead to very diverse selectivities:

Types of silica base: A, B (high purity), or C (surface covered with Si-H •groups), organic/inorganic hybrid silica, silica covered with a polymethyl-silicone polymer layer pore diameter (from 60 to 300 Å).Surface area (from 180 to 450 m• 2/g).Functionality of the bonding (mono- or polymeric phases).•Bonding density (from 1.5 to 3.6 • µmol/m2).Endcapping treatment: nature of the endcapping reactant, hydrophilic end-•capping, bonded chains with steric protection and bidentate bonding.Horizontal polymerization of the bonded chains.•Embedded polar groups (amide, urea, carbamate, quaternary ammonium, •ether, or sulfonamide).

The majority of these processes are intended to produce base-deactivated pack-ings, that is to say to reduce the accessibility to residual silanol groups to basic com-pounds, and to favor the stability of the silica at the high pH often required to avoid the ionic form of these basic compounds. The columns and their potentially very dif-ferent selectivity require a classification in order to facilitate the selection of appro-priate stationary phases for a given application. We have shown in previous works [65,75] how the solvation parameter model can help in this task, in the same manner as for the other types of phases described above. The database presented here has since been updated.

The ODS phases in Table 5.2 were characterized with the solvation parameter model, using the 29 solutes in Table 5.5. In the same manner as for the varied phases above, angles and similarities were calculated between the solvation vectors, using Equations 5.8 to 5.11. The results are presented on the spider diagram (Figure 5.14).

84534.indb 240 11/5/09 12:28:13 PM


Again, the phases that were judged to be similar are circled. As mentioned above, the discrimination obtained in this case is inferior due to the smaller number of solutes analyzed resulting in larger uncertainty spheres.

However, the solvation parameter model allows a fine evaluation of dipole– dipole and hydrogen-bonding interactions occurring on these phases, either due to the residual silanol groups on non-endcapped phases, or to the polar embedded (amide, carbamate, sulfonamide, ether…) and hydrophilic endcapping groups. As a matter of fact, the non-endcapped phases (10 to 12 in Table 5.2) are well discriminated from the endcapped or “protected” phases. The case of phases possessing a hydrophilic endcapping group (P5 to P12 in Table 5.2) is more confuse as the phases identified as such are scattered. The variety of possible treatments and the absence of clear indica-tions from the manufacturers do not help in understanding the differences observed.

The polar-embedded phases (P13 to P33 in Table 5.2), on the contrary, are gener-ally clearly distinguished from all others. In some cases, different polar groups can be discriminated. For instance, the ether-sulfonamide group from P16 and the ether group from P27 are clearly distinguished from the amide-embedded group, which is most commonly found. However, the carbamate groups are not discriminated from the amide groups. It is also worth noting that P28 and P29 (Polaris A and Polaris B), which both have undisclosed structures, are also clearly discriminated from the amide-em-bedded phases. Thus it can be concluded that they must not possess any amide group.

As an example of the different selectivities, which can be expected when vary-ing the nature of the ODS bonding chemistry, we analyzed three non-steroidal

1

10

1112

17P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

P13

P14

P15

P16

P17

P18P19

P20

P21

P22

P23P24

P25P26

P27

P28P29

P30

P31P32

6

2 to 913 to 16

e

s

ab

v

fIgure 5.14 Spider diagram for a five-dimensional representation of the solvation param-eter models of the ODS columns. The stationary phases are identified according to the num-bers in Table 5.2. White bubbles are the classical ODS phases (1 to 17), black bubbles are the polar-type ODS phases (P1 to P32). Bubble size is related to the vector length (u), calculated with Equation 5.7. Ellipses circle the columns, which were found similar through the calcula-tion of J (Equations 5.9 to 5.11). Chromatographic conditions as in Figure 5.10.

84534.indb 241 11/5/09 12:28:14 PM


anti-inflammatory drugs (NSAID) (aspirin, phenylbutazone, and sulindac) having very different structures (Figure 5.15). Figure 5.16 shows how the elution order changes when a well-protected column (Uptisphere ODB No.7, Atlantis dC18 No.16) is changed for a non-endcapped phase (Uptisphere NEC No.10), for a phase with a hydrophilic endcapping group (Aquasil C18 No.P5, Alltima HP C18 AQ No.P7), then for a polar-embedded phase. The effect of the nature of the embedded group is seen with the reversal of elution order between a sulfonamide-embedded phase (Acclaim Polar Advantage No.P16) and amide-embedded phases (Alltima HP C18 Amide No. P15, Acclaim Polar Advantage II No.P17, Uptisphere PLP No.P19, Discovery RP Amide No.P22, Ascentis RP Amide No.P23, and Supelcosil ABZ + Plus No.P26). Moreover, the chromatograms provided in Figure 5.17 show how the retention and selectivities vary among the different ODS phases.

This all shows that even when comparing structurally related stationary phases, differences in their intermolecular interaction abilities can easily be detected, pro-viding a better semi-quantitative understanding of their behavior. [26]

O

F

O OH

O

O

N

N

O

OHO

SO

Aspirin (A) Phenylbutazone (P) Sulindac (S)

fIgure 5.15 Structures of the non-steroidal anti-inflammatory drugs analyzed as an example of different selectivities of ODS phases.

1

2

3

4

7 16 10 P5 P7 P16 P15 P17 P19 P22 P23 P26Column no.

Elut

ion

orde

r

AspirinSulindacPhenylbutazone

fIgure 5.16 Elution orders of the NSAID in Figure 5.15 on twelve selected ODS columns with varying selectivities. The stationary phases are identified according to the abbreviations in Table 5.2. Chromatographic conditions as in Figure 5.10.

84534.indb 242 11/5/09 12:28:16 PM


78

10P5

16

P16

A11.

5M

inut

es1

2M

inut

es1

1.5

2M

inut

es1

23

45

Min

utes

11.

52

Min

utes

12 Min

utes

12

1.5 M

inut

es2.

51.

52.

253

Min

utes

18

1216

Min

utes

3

P

PP

AA

SS

S

P

A

S

PAS

P

A

SP

A

S

PA

SP

A

S

P19

P23

P22

fIg

ur

e 5.

17

Chr

omat

ogra

ms

of t

hree

non

-ste

roid

al a

nti-

infla

mm

ator

y dr

ugs

on n

ine

sele

cted

OD

S co

lum

ns w

ith

vari

ed b

ondi

ng c

hem

istr

ies

(see

Fi

gure

5.1

5 fo

r id

enti

ficat

ion

of t

he c

ompo

unds

). T

he s

tati

onar

y ph

ases

are

ide

ntifi

ed a

ccor

ding

to

the

abbr

evia

tion

s in

Tab

le 5

.2.

Chr

omat

ogra

phic

co

ndit

ions

as

in F

igur

e 5.

10.

84534.indb 243 11/5/09 12:28:17 PM


However, it must be pointed out that only little discrimination is possible between the classical, endcapped or protected ODS phases (1 to 9, 13 to 17 in Table 5.2) with the solvation parameter model, although these phases are known to have different chromatographic behaviors, and particularly different steric selectivities. It is a well-known defect of the solvation parameter model that steric impedance to insertion into the bonded phases is totally absent from Abraham descriptors: there is no term related to molecular shape as, in the calculation of the molecular volume (V), no account is taken for three-dimensional shape, only the number of atoms and bonds is taken into account.

Regarding ODS phases, we have solved this problem by combining the solvation parameter model with another characterization test, which can provide an evaluation of steric selectivity, based on the analysis of carotenoid pigments in SFC [76]. The two tests are complementary as the carotenoid test has no ability to distinguish between different sources of polar interactions [77], while the solvation parameter model can.

For other types of phases, different solutions are needed. A new descriptor in the solvation parameter model, which could account for shape selectivity without being redundant with the already existing descriptors, could be introduced. This is a difficult task as, among the varied descriptors having been introduced to estimate shape, no one offers a universal description. In general, the parameters describing molecular shape cannot be shortened to a unique term, unless the solutes are limited to a single structural family. We will address this point in future works.

5.4.4 method development with the solvation parameter model

At this time, the use of the solvation parameter model for systematic selectivity opti-mization is only poorly developed. With the following examples, we wish to demon-strate how a clever selection of columns based on utilization of the above results can help in achieving a separation of a real complex mixture.

A set of seven sunscreen molecules was selected as test mixture (Figure 5.18). These compounds are classically encountered in cosmetic products in which they are combined at different concentrations, following maximum concentration authorized by regulatory authorities around the world. Five of the chosen molecules (OCR, BDM, BZ3, ES, and EMC) have related chemical structures, while the last two (ET and EMT) also have common features. This choice of molecules is an interesting one because it allows estimating the orthogonality or similarity of the stationary phases toward similar structures, a situation that is representative for impurity profiling of drugs. Besides, we were interested in the role of multifunctional and high molecular mass compounds as ET and EMT, because the great majority of real sample solutes have higher molecular mass and more functional groups than the test compounds that served to establish the solvation coefficients.

It must be noted that ET and EMT are possibly ionized basic compounds, thus the phases which were suspected to establish ionic interactions were not tested on this sample. First of all, the elution orders of the seven sunscreen molecules on eight stationary phases covering a wide range of selectivities are presented in Figure 5.19. The varied elution orders obtained are a clear indication of the variety of separations that can be achieved when stationary phases are chosen in distant places of the spider

84534.indb 244 11/5/09 12:28:18 PM


diagram. Besides, the close elution orders obtained on columns issued from close regions of the diagram (as EP and NH2; MIX and C6P-L; C3P and OPHE) are also consistent with all above comments. On the other hand, one can remark that reten-tion of BZ3 strongly depends on the phase polarity, due to its hydroxyl function, in

1

0

2

3

4

5

6

7

8

MIX C6P-L PE1 C4 C3P OPHE EP NH2

Elut

ion

orde

r

Column

BDM BZ3 EMC EMT ES ET OCR

fIgure 5.19 Elution orders of the sunscreen molecules (see Figure 5.18 for identification of the compounds) on eight selected columns with varying selectivities. The stationary phases are identified according to the abbreviations in Table 5.1. Chromatographic conditions as in Figure 5.10.

OCROH O

MeO

BZ3

OO O

OO

CN

O

O

ES

O

MeO EMCOMe

BDM

OO

OO

OO

O

OH

N N

N

NH

NH

O

O

N N

N

OHOH

EMT

O

O

OMeET

HN

fIgure 5.18 Structures of the sunscreen molecules analyzed as an example of complex mixture for method development.

84534.indb 245 11/5/09 12:28:19 PM


accordance to the stationary phase chemical structure. However, chromatographic behaviors are difficult to estimate, because EMT which has two hydroxyl groups is the less retained compound on PE1, whereas BZ3 was one of the most retained on this phase. One can suppose that the great size of EMT hinders it to deeply penetrate into the stationary phase, avoiding the interactions between the hydroxyl groups and the polar embedded group of the bonded chain, which is located close to the silica surface.

Secondly, the observation of the chromatograms obtained on these eight columns (Figure 5.20) show the varied qualities of peak shapes that can be observed. In the course of a method development, the stationary phase providing the best start for

C6P-LMIX

PE1OPHEC3P

NH2EP

C4 OCR+BDM

EMC + BZ3

OCR + BDM

ESEMT

EMT-BZ3 + OCR

EMC

ES

BDM

ET

ES

EMC

EMT

BDMBZ3 + OCR

ET

ET

C3EMC

BZ3

OCR

BDM

EMTET

BDM

BZ3

OCR + ES + EMC

ET

EMT

EMCES + BZ3

0.75 1.5Minutes

2.25 2 4Minutes

6 8 2 4Minutes

6 8 10

2 4Minutes

6 8 10 12 14

2 4Minutes6 8 10 12 1 2

Minutes3 4 5

2 4Minutes

6 8 10 12 14 2 4Minutes

6 8

ET + EMT

OCR

BDM

ET

EMT

EMCBZ3

ES

EMC + BZ3

OCR

BDM

ET–EMTES

fIgure 5.20 Chromatograms of the seven sunscreen molecules (identified in Figure 5.18) on eight columns with varying selectivities. The stationary phases are identified according to the abbreviations in Table 5.1. Chromatographic conditions as in Figure 5.10.

84534.indb 246 11/5/09 12:28:21 PM


optimization, based on resolution and peak shapes, would be selected. In the case presented here, several columns appear to be possible starters: MIX, OPHE, or NH2 would all be potential candidates. It is worth pointing out that these phases are situ-ated in three totally different regions of the spider diagram. This is a clear indication that all stationary phase polarities can be helpful in developing a separation method in pSFC.

5.4.5 predictive Capability of the modelS

A tool to predict the behavior of compounds on column would facilitate the selec-tion of the stationary phase before compounds are analyzed. However, the solvation parameter model is not expected to provide predictions of retention to an accuracy that would be chromatographically useful for method development (± 0.03 in ln k) [26].

Indeed, prediction of retention requires that a suitable model be generated. Then the retention for any solute with known solute descriptors, or solutes for which rea-sonable estimates of the descriptors are possible, could be estimated by simple arith-metic. The accuracy of the prediction depends both on the uncertainty in the solute descriptors and the model system constants. The average uncertainty of the model system constants can be estimated through the standard error in the estimate of the multiple linear regression analysis. In our pSFC database, they range from 0.029 to 0.229.

In order to assess the predictive capability of the solvation parameter models established, a second set of models was established, based on a reduced set of ana-lytes. For this purpose, 30 compounds were removed from the initial set (compounds marked with an asterisk in Table 5.3). These compounds were selected so as to cover a wide range of properties (acidic and basic character, size, polarity, and polarizabil-ity) and in such a manner that the homogeneous repartition of the descriptor values in the remaining set would not be disturbed.

Then, based on this second series of models, the predictive retention factors of the 30 test-compounds were calculated and compared to the measured experimental retention factors. Figure 5.21 is given as an example of these comparisons.

The correlation coefficients among all models tested ranged from 0.879 (for the worst PGC phase) to 0.990. The predictive capability is quite good for most columns (see Figure 5.21) and, apart from solutes which elute very close, it would be possible to predict the elution order for most simple compound mixtures. Only the adsorbent-type stationary phases (PGC and SI) show poor correlations, indicating that tentative prediction of elution orders would be more uncertain.

One limitation of this demonstration is that the solutes in the validation set are much simpler structurally than the broad, complex array of pharmacologi-cally active compounds that are targets for quantitative prediction of retention and selectivity. Such compounds set two problems regarding retention prediction: the first one is that improved methods for estimating solute descriptors from structure for complex molecules are required; the second is that stereo-induced interactions might occur on certain stationary phases. We will address this question in future works.

84534.indb 247 11/5/09 12:28:21 PM


5.5 ConClusIon

Modern pSFC mostly relies on a more restricted range of stationary phases than those depicted in this study. In practice polar stationary phases (SI, NH2, DIOL, CN, and EP) virtually monopolize the market. However, we have shown that these phases occupy only a fraction of the selectivity space and provide limited possibili-ties for selectivity optimization. The point we want to make here is that the nonpolar and moderately polar phases provide an opportunity to extend the selectivity space significantly beyond that which can be explored using polar phases.

The solvation parameter model has had a considerable impact on our understand-ing of the retention mechanism of non-ionic compounds in pSFC. The spider dia-gram provides a convenient visual classification of packed columns for SFC. It can be used for the rational choice of columns. It is easy to identify those stationary phases with separation properties that are most similar to each other, and phases with less similarity. It is a valuable technical aid to the chromatographer faced with the need to make rapid decisions in SFC.

The columns characterized encompass the full range of polarity of commercial packed columns currently available. They span a wide selectivity space, although

R2 = 0.9893

R2 = 0.98

R2 = 0.9307

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5(a) (b)

(c)–1.5 –1.0 –0.5 0.0 0.5 1.0 1.5

Log kexpPE3 Log kexpSI

Log kexpPVA

Log ktheo Log ktheo

Log ktheo

–1.5

–1.0

–0.5

0.0

0.5

1.0

–1.5 –1.0 –0.5 0.0 0.5 1.0

–2.0

–1.5

–1.0

–0.5

0.0

0.5

1.0

–2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0

fIgure 5.21 Comparison of the calculated and measured retention factors obtained on (a) PE3 (b) SI and (c) PVA for the compounds marked with an asterisk in Table 5.3, when the models are calculated omitting these solutes.

84534.indb 248 11/5/09 12:28:22 PM


there remain empty areas of the selectivity space which would benefit by the intro-duction of new stationary phase chemistries.

Moreover, these studies underline that pSFC with modifier allows us to cover both the normal and the reversed-phase domains. Whereas these two domains are strictly separated when using liquid mobile phases (HPLC), the use of an identical super-critical mobile phase whatever the stationary phases allows the unification of these domains in SFC [64]. It also opens a new field of research for orthogonal separation on line.

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46. Smith R.M., Sanagi M.M. 1990. Retention and selectivity in supercritical fluid chroma-tography on octadecylsilyl-silica column. J. Chromatogr. 505:147–159.

47. West C., Lesellier E. 2007. Characterization of stationary phases in supercritical fluid chromatography with the solvation parameter model: V. Elaboration of a reduced set of test solutes for rapid evaluation. J. Chromatogr. A 1169:205–219.

48. Li J. 2002. Prediction of internal standards in reversed-phase liquid chromatography: III. Evaluation of an alternative solvation parameter model to correlate and predict the retention of ionizable compounds. J. Chromatogr. A 982:209–223.

49. Li J. 2004. Prediction of internal standards in reversed-phase liquid chromatography: IV. Correlation and prediction of retention in reversed-phase ion-pair chromatography based on linear solvation energy relationships. Anal. Chim. Acta 522:113–126.

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50. Rosés M., Bolliet D., Poole C.F. 1998. Comparison of solute descriptors for predicting retention of ionic compounds (phenols) in reversed-phase liquid chromatography using the solvation parameter model. J. Chromatogr. A 829:29–40.

51. Abraham M.H., Zhao Y.H. 2004. Determination of solvation descriptors for ionic spe-cies: hydrogen bond acidity and basicity. J. Org. Chem. 69:4677–4685.

52. Zhao Y.H., Abraham M.H., Zissimos A.M. 2003. Determination of McGowan vol-umes for ions and correlations with van der Waals volumes. J. Chem. Inf. Comput. Sci. 43:1848–1854.

53. Li J., Sun J., Cui S., He Z. 2006. Quantitative structure-retention relationship studies using immobilized artificial membrane chromatography I. Amended linear solvation energy relationships with the introduction of a molecular electronic factor. J. Chromatogr. A 1132:174–182.

54. Wen D., Olesik S.V. 2000. Characterization of pH in liquid mmixtures of methanol/H2O/CO2. Anal. Chem. 72:475–480.

55. Toews K.L., Shroll R.M., Wai C.M., Smart N.G. 1995. pH-defining equilibrium between water and supercritical CO2. Influence on SFE of organics and metal chelates. Anal. Chem. 67:4040–4043.

56. Zheng J. 2005. Supercritical fluid chromatography of ionic compounds. PhD diss., Virginia Polytechnic Institute, Blacksburg, VA

57. Reta M., Carr P.W., Sadek P.C., Rutan S.C. 1999. Comparative study of hydrocarbon, fluorocarbon and aromatic bonded RP-HPLC stationary phases by linear solvation energy relationships. Anal. Chem. 71:3484–3496.

58. Wang T., Wang X., Smith R.L. Jr. 2005. Modeling of diffusivities in supercritical carbon dioxide using a linear solvation energy relationship. J. Supercrit. Fluids 35:18–25.

59. Lagalante A.F., Bruno T.J. 1998. Modelling the water-supercritical CO2 partition coef-ficients of organic solutes using a linear solvation energy relationship. J. Phys. Chem. B 102:907–909.

60. Bush D., Eckert C.A. 1998. Prediction of solid-fluid equilibria in supercritical car-bon dioxide using linear solvation energy relationships. Fluid Phase Equilib. 150–151:479–492.

61. Timko M.T., Nicholson B.F., Steinfeld J.I., Smith K.A., Tester J.W. 2004. Partition coef-ficients of organic solutes between supercritical carbon dioxide and water: experimental measurements and empirical correlations. J. Chem. Eng. Data 49:768–778.

62. Poole S.K., Poole C.F. 2003. Separation methods for estimating octanol-water partition coefficients. J. Chromatogr. B 797:3–19.

63. Smith R.M., Cocks S., Marsin Sanagi M., Briggs D.A., Evans V.G. 1991. Retention in supercritical fuid chromatography on cyano-bonded silica columns, Analyst 116:1281–1285.

64. West C., Lesellier E. 2008. A unified classification of stationary phases for packed-column supercritical fluid chromatography. J. Chromatogr. A 1191:21–39.

65. West C., Fougère L., Lesellier E. 2008. Combined supercritical fluid chromatographic tests to improve the classification of numerous stationary phases used in reversed phase liquid chromatography, J. Chromatogr. A 1189:227–244.

66. West C., Lesellier E. 2006. Characterisation of stationary phases in subcritical fluid chromatography by the solvation parameter model: I. Alkylsiloxane-bonded stationary phases. J. Chromatogr. A 1110:181–190.

67. West C., Lesellier E. 2006. Characterisation of stationary phases in subcritical fluid chromatography by the solvation parameter model: III. Polar stationary phases. J. Chromatogr. A 1110:200–213.

68. West C., Lesellier E. 2006. Characterisation of stationary phases in subcritical fluid chromatography by the solvation parameter model: IV. Aromatic stationary phases. J. Chromatogr. A 1115:233–245.

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69. West C., Lesellier E. 2006. Characterisation of stationary phases in subcritical fluid chro-matography with the solvation parameter model II: Comparison tools. J. Chromatogr. A 1110:191–199.

70. Abraham M.H., Rosés M., Poole C.F., Poole S.K. 1997. Hydrogen bonding. 42. Characterisation of reversed-phase liquid chromatographic C18 stationary phases. J. Phys. Org. Chem. 10:358–368.

71. Ishihama Y., Asakawa N. 1999. Characterization of lipophilicity scales using vectors from solvation energy descriptors. J. Pharm. Sci. 88:1305–1312.

72. West C., Lesellier E. 2008. Orthogonal screening system of columns for supercritical fluid chromatography. J. Chromatogr. A 1203:105–113.

73. Bui H., Masquelin T., Perun T., Castle T., Dage J., Kuo M.-S. 2008. Investigation of retention behaviour of drug molecules in supercritical fluid chromatography using linear solvation energy relationships. J. Chromatogr. A 1206:186–195.

74. Lesellier E., West C. 2007. Description and comparison of chromatographic tests and chemometric methods for packed column classification. J. Chromatogr. A 1158:329–360.

75. Lesellier E., West C. 2007. Combined supercritical fluid chromatographic methods for the characterization of octadecylsiloxane-bonded stationary phases, J. Chromatogr. A 1149:345–357.

76. Lesellier E., Tchapla A. 2005. A simple subcritical chromatographic test for an extended ODS high-performance liquid chromatography column classification. J. Chromatogr. A 1100:45–59.

77. Lesellier E., West C., Tchapla A. 2006. Classification of special octadecyl-bonded sta-tionary phases by the carotenoid test. J. Chromatogr. A 1111:62–70.

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255

6 Silica Hydride—Chemistry and Applications

Joseph J. Pesek and Maria T. Matyska

6.1 IntroduCtIon

6.1.1 backGround

While some facets of silica hydride have been know for many years, its use as a sepa-ration medium did not begin until around 1990 [1,2]. However, significant advances in the technology and the development of the material did not begin until after 2000.

Contents

6.1 Introduction .................................................................................................. 2556.1.1 Background ....................................................................................... 2556.1.2 Synthesis of Silica Hydride ...............................................................256

6.2 Hydride-Based Stationary Phases for HPLC ................................................ 2576.2.1 Synthesis and Characterization ........................................................ 2576.2.2 Stability of Silica Hydride Materials ................................................ 2586.2.3 Chromatographic Properties of Silica Hydride Phases .................... 259

6.3 Applications of Hydride-Based Phases in HPLC .........................................2646.3.1 Overview ...........................................................................................2646.3.2 Reversed-Phase .................................................................................2646.3.3 Aqueous Normal Phase .................................................................... 2676.3.4 Dual Mode Retention ........................................................................ 2726.3.5 Organic Normal Phase ...................................................................... 2756.3.6 Microcolumn HPLC ......................................................................... 277

6.4 Hydride-Based Etched Capillaries ............................................................... 2786.4.1 Fabrication ........................................................................................ 2786.4.2 Characterization of Capillary Properties .......................................... 2796.4.3 Dual Separation Modes ....................................................................2806.4.4 Other Capillary Formats ................................................................... 2826.4.5 Applications of Etched Chemically Modified Capillaries ................ 283

6.5 Conclusions ...................................................................................................286Acknowledgments ..................................................................................................287References ..............................................................................................................287

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The chemical difference between ordinary silica and silica hydride is illustrated in Figure 6.1. The essential feature is that the silanol groups (Si-OH) on ordinary silica have been replaced by Si-H moieties on the hydride silica, which leads to profound differences in the surface properties of the two materials. Silica hydride has unique properties that can be exploited as part of the solid support of stationary phases for HPLC and on the inner walls of capillaries for electrophoretic separation media.

6.1.2 SyntheSiS of Silica hydride

There are two general approaches for the fabrication of silica hydride surfaces. The first involves the conversion of silanol groups on particulate silica with thionyl chlo-ride to the Si-Cl function and then reducing this with lithium aluminum hydride, as shown in the following sequence [1]:

≡ Si-OH + SOCl2 → ≡ Si-Cl + SO2 + HCl

≡ Si-Cl + LiAlH4 → ≡ Si-H + LiAlH3Cl

This process must be done under relatively inert conditions, since the Si-Cl bond is hydrolytically unstable and easily reverts back to a silanol in the presence of any moisture.

Another approach for creating a silica hydride surface utilizes the condensation reaction between silica and triethoxysilane. This method is illustrated by the follow-ing reaction [2]:

H Η + nΕtΟΗSi SiOH+

OY

OY

OH + (OEt)3SiSi

Y = H or Si depending on the extent of cross-linkingThis is a single step process that is not sensitive to the presence of water, and in

fact a small amount of acid is needed as a catalyst.

OH

O

O

OHSiO

O

O

OHSiO

O Si O Si O

O

O

OSiO

O

O

OSiO

Si H

O

O

HSi

O

O

HSi

Ordinary silica Silica hydride

fIgure 6.1 Chemical surface structures of ordinary silica and silica hydride.

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Silica Hydride—Chemistry and Applications 257

In both processes there is a number of reaction variables that control the exact nature of the hydride surface produced, i.e., relative number of Si-H groups vs. residual silanols. With the onset of commercialization of silica hydride materials for separation, the exact process used to fabricate each product is a proprietary piece of information as is the precise formulation of ordinary HPLC stationary phases by each individual manufacturer, even though most use some form of organosilanization.

6.2 hydrIde-based statIonary phases for hplC

6.2.1 SyntheSiS and characteriZation

Silica hydride HPLC stationary phases are based on the use of high purity/low metal content manufacturing technology of commercial silica. As depicted in Figure 6.1, the surface of the hydride material is predominantly populated (> 95% as determined in a study by 29Si CP-MAS NMR [2]) with nonpolar, silicon-hydride (Si-H) groups instead of the polar silanol groups (Si-OH) that dominate the surface of ordinary silica. Further modification of the hydride surface can be made using hydrosilation [3] that produces a bonded stationary phase with specific properties as a separation medium (hydrophobic, hydrophilic, ion-exchange, chiral, etc.):

HYDROSILATION

RCH2CH2Sicat.CH RSi H + CH2

cat = catalyst, typically hexachloroplatinic acid or free radical initiatorAs shown above, one of the advantages to this process is the attachment of the

bonded organic moiety to the surface by a stable Si-C bond. This feature leads to the high stability reported in chromatographic experiments [4–6]. While the most common approach for attaching an organic species to the silica hydride involves a terminal olefin, it is also possible to bond molecules with the olefin in a nontermi-nal position [7], alkynes [8], and other functional groups such as cyano [9]. This versatility in the attachment of organic moieties to the surface hydride leads to the possibility of producing stationary phases not feasible by other bonding methods. One interesting example is the double attachment of the bonded group that has been

Si

O

O

Si

O

Structure I

CH CH2 R

Si

O

C

H

Si

O

Structure II

C

R

O

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shown to occur when an alkyne is used in the hydrosilation reaction [8]. The two structures postulated on the basis of NMR studies are shown above.

6.2.2 Stability of Silica hydride materialS

The long-term viability of the hydride surface is a crucial aspect of this material. This is a reasonable concern because of the limited stability of small organosilanes in aqueous solutions. However, the Si-H moiety on a silica surface is in a completely different chemical environment and does not have the same properties as free silane molecules in solution since it is stabilized by the larger polymer matrix of the silica. A nonchromatographic example of the viability of Si-H has been demonstrated on silicon wafers where silicon hydride groups have been created chemically and then exposed to a variety of aqueous conditions including acid and basic environments [10].

The stability of the Si-H group on a silica surface has been demonstrated both spectroscopically and chromatographically. One test was a series of diffuse reflec-tance infrared Fourier transform (DRIFT) analyses of several archived silica hydride samples prepared on various commercial silica over a period of more than 10 years. No special precautions were taken since the samples were kept in laboratory drawers in screw-top containers. Therefore, the samples were essentially under atmospheric conditions with no temperature or humidity control. DRIFT spectra of several of these samples that had been prepared between six and eight years previously were obtained and compared to the original spectrum taken right after synthesis. The key feature in each spectrum is the Si-H stretching band at 2250 cm−1 [11,12]. In each case the intensity of this band in the archived sample was identical to the intensity obtained at the time of synthesis, proving that these materials have excellent stability when stored as an unprotected solid. Another test of the hydride stability was obtained by packing this material in a chromatographic column and pumping degassed DI water through it for several hours. The column was then unpacked and the DRIFT spectra before and after the water test were compared. The results of this experiment were that the inten-sities of the Si-H stretching peaks at 2250 cm−1 before and after the water test were essentially the same, indicating little or no decomposition of the hydride layer under these conditions. Further evidence for the stability of the hydride moiety on the silica surface involved a silica hydride material stored in columns for eight months in 0.05% phosphoric acid. Chromatograms run on one of these columns over an eight-month period showed no noticeable change in retention of the three test solutes, indicating good hydrolytic stability of the hydride under these mobile phase conditions.

These results are reinforced by more extensive chromatographic studies on hydride-based stationary phases where columns have been used for thousands of column volumes at low pH (∼2) and high pH (9–10) with little evidence of deterioration [5,6]. In one test a bidentate C18 column (fabricated by hydrosilation of silica hydride with 1-octadecyne) was used for more than one thousand column volumes with a vari-ety of samples and several organo/aqueous mobile phases. Subsequently the column was subjected to a 90:10 ammonium formate-ammonia (pH 10)/acetonitrile mobile phase for more than 1000 additional column volumes. The mixture uracil/pyridine/phenol was periodically injected during the elution of this mobile phase. The k′ of pyridine was determined to be 0.3 + 0.05 while the k′ of phenol was 8.9 + 0.1 over

84534.indb 258 11/5/09 12:28:27 PM


the 1000 column volume test. The DRIFT spectrum of the material from this column after the chromatographic testing was compared to the spectrum obtained immedi-ately after synthesis. Both the carbon-hydrogen stretching bands between 2800 and 3000 cm−1 and the Si-H band at 2250 cm−1 are nearly identical in both spectra, con-firming the results of the chromatographic tests that no significant decomposition of the bonded phase and the underlying surface occurred as a result of exposure to the various mobile phases.

6.2.3 chromatoGraphic propertieS of Silica hydride phaSeS

An example of the fundamental difference between silica hydride and typical bare silica (where silanols are the predominant functional group on the surface) is dem-onstrated by the measurement of the retention of, pyridine, and phenol under reverse phase conditions. The polarity of ordinary silica results in no retention of uracil and phenol while pyridine is retained because of its basic properties. However, the much less polar silica hydride surface shows only marginal retention of pyridine (slightly separated from uracil) and more significant retention of phenol. The elution order is typical reversed-phase with the most polar compound eluting first and the least polar species being the last eluted. This silica hydride retention behavior can also be compared to a commercial C18 phase that is not endcapped. The presence of a significant number of silanols on the stationary phase results in elution of pyridine after phenol. It has been postulated that the nonpolar nature of the silica hydride surface results in less adsorption of polar solvents (particularly water) on the surface of the separation media. The consequence of this property is that aggressive compo-nents in the mobile phase (such as trifluoroacetic acid, phosphate, or bases) are less likely to attack the surface and the bonded moiety providing enhanced stability, and changes in the mobile phase composition can be accomplished efficiently so that the separation system rapidly reaches equilibrium. The latter property is of particular advantage when doing gradient separations because repeated analyses can be done with a minimum of time between runs. For aromatic and polyaromatic hydrocarbons on both C8 and C18 hydride-based columns made from the respective alkynes, it was possible to get reproducible retention for equilibration times after the end of the gradient of less than 5 minutes for all the solutes tested.

In HPLC, retention properties are determined by the relative degree of interac-tion of the solute with the stationary phase and the mobile phase. Adsorption occurs at the silica surface and the bonded phase surface. Partitioning can take place in the solvent layer that forms at the surface of the stationary phase. Depending on the nature of the bonded phase and liquid phase surrounding it, the amount of par-titioning will vary. With ordinary silica, water is strongly adsorbed onto the silica surface due to the active silanol groups. This water forms a stable hydration shell which often leads to chromatographic difficulties such as long equilibration times when the mobile phase composition is changed, lack of reproducibility in normal phase, and pH hysteresis. The Si-H groups found on the surface of silica hydride are not prone to such strong water retention as ordinary silica, making them more suitable for organic-normal phase (ONP) separations. The weaker water adsorption also accounts for the negligible or no hysteresis observed when changing pH. This

84534.indb 259 11/5/09 12:28:27 PM


effect is in contrast to some bonded phases that often exhibit long-term memory effects. Silica hydride materials operate in the normal phase mode with solvent sys-tems ranging from hexane/ethyl acetate all the way to water/acetonitrile. An example of the difference between ordinary silica and silica hydride using a water/acetonitrile mobile phase (aqueous normal phase) is shown in Figure 6.2 for the retention of phe-nylalanine and phenylglycine. In this example, retention increases on both columns as the amount of acetonitrile in the mobile phase is increased. However, resolution of the components is only observed on the silica hydride column. Since the only difference between the columns is the hydride surface, the improved normal phase behavior must be the result of the Si-H moieties.

Silica hydride-based columns have the unique capability to be used in any of the following three chromatographic modes: aqueous reverse phase (ARP); aque-ous normal phase (ANP), defined below; and organic normal phase (ONP). When utilizing mobile phases with an aqueous component, methods having solvent com-positions of water/acetonitrile or water/acetone that varies in the concentration of the organic constituent from 0% to between 50 and 70% will result in decreasing retention of hydrophobic analytes as the less polar solvent is increased. With a 100% aqueous mobile phase, retention is at a maximum for neutral compounds. Under these conditions the hydride columns display typical reversed-phase behavior. What is unique is that when analyzing ionizable or other polar compounds and the ace-tonitrile or acetone concentration is above 50 to 70%, a second retention maximum occurs at 100% organic. Thus the solute behavior in this region is that the reten-tion time decreases as the more polar solvent (water) increases, indicative of a nor-mal phase mechanism. This section of the solute retention map (tR vs. % organic in the mobile phase) is given the designation aqueous normal phase. An example of such a retention map is shown in Figure 6.3. Therefore, for polar compounds the elution order and/or the retention times can be changed either by varying the pH

1

0.8

(a) (b)

0.6

mA

U

0.4

0.2

0

2

1.5

1

Nor

m.

0.5

0

–0.5

2 4Min

2 4Min

1 2

1+2

fIgure 6.2 Separation of phenylglycine (1) and phenylalanine (2) on (a) silica hydride and (b) ordinary silica.

84534.indb 260 11/5/09 12:28:28 PM


(removing the charged state for ionizable compounds) or the organic concentration of the mobile phase. With the hydride columns in both the aqueous (using water) and organic (using nonpolar solvents) normal phase modes, the retention time of the ana-lyte decreases as the more polar solvent is increased. The elution order is primarily based on the functionality or ionic state of the solutes. Since the maximum retention of the analytes is at 100% concentration of the least polar solvent, the behavior fits the definition of normal phase. For some basic compounds retention reaches a mini-mum at both high and low pH. This minimum is shifted to higher percent organic as the pH increases. At lower organic mobile phase compositions the column displays reverse phase behavior, while at higher organic percentages the column functions in the ANP mode. This behavior is in contrast to a typical commercial phase such as C18 or C8 that only displays reversed-phase characteristics and has no ANP reten-tion at all. For acids at high pH, retention is at a minimum for low amounts of organic in the mobile phase, and then increases at about 70% and higher. In a few cases ANP behavior has been observed on hydride-based stationary phases with methanol as the organic solvent if the solute has multiple amine groups.

The fundamental reversed-phase properties of silica hydride-based columns are similar to typical commercial stationary phases. The solutes are eluted in the usual reversed-phase order, i.e., from the most polar to the least polar at all pH values. The efficiency (typically around 100,000 plates/m) and peak symmetry (0.98 to 1.15) of these solutes on silica hydride stationary phases is also excellent. Therefore, when necessary, a silica hydride material bonded with an alkyl moiety such as C8 or C18 can be used for reversed-phase applications with separation capabilities similar to those of monomeric stationary phases. Some differences are found since the base material (silica hydride) is not the same as typical commercial phases (ordinary silica). These variations in selectivity have been documented in column equivalency tests [13].

The ability of a silica hydride bonded material to function in the normal phase is illustrated by the separation of a group of closely related phenols (Figure 6.4). Two examples of the separation of these four compounds are shown illustrating the

0 10 20 30 40 50 60 70 80 90 100% Organic in mobile phase

02468

101214161820

Rete

ntio

n tim

e (m

in)

fIgure 6.3 Retention map (tR vs. % organic in the mobile phase) for a compound displaying both reversed-phase and aqueous normal phase retention on a silica hydride-based column.

84534.indb 261 11/5/09 12:28:29 PM


versatility of the hydride-based stationary phases. In the first example (Figure 6.4a) the separation is accomplished on silica hydride material. The second case (Figure 6.4b) shows the same analysis on an ordinary bare silica column. As dem-onstrated, the silica hydride-based stationary phase provides adequate separation of the four phenols while the ordinary bare silica column does not. In contrast to what is common practice for many normal phase separations, the mobile phase solvents were not rigorously dried before use and were not placed in an air-tight or purged reservoir system to prevent adsorption of water. It is interesting that both bare silica hydride as well as a C18 modified phase (essentially a reversed-phase column) can provide good normal phase capabilities.

A feature of the reversed-phase silica hydride materials is their ability to function in a 100% aqueous environment without any detrimental effects such as phase col-lapse. This problem has been encountered with many C18 phases and is evident by drastically reduced retention in comparison to mobile phases with a small amount of organic component (5–10%) Figure 6.5 shows an example of a separation for some carbohydrate structural isomers on an octadecyl modified silica hydride col-umn using a 100% aqueous mobile phase containing 0.5% formic acid with MS detection. This analysis was repeated with 10 consecutive injections with no change (%RSD < 1) in the retention times of the four components. The first (A) and tenth (B) injections are shown. This result not only indicates the stability of the bonded

100 1.22(a)

0

%(b)100

00.00 1.00 2.00

Time (min)3.00 4.000.00 1.00 2.00

Time (min)3.00 4.00

%

1.57 1.87

2.27

2.47

3.08

3.35

fIgure 6.4 Normal phase separation of phenols on (a) a silica hydride column and (b) a bare silica column. Mobile phase: 10% diethyl ether in hexane. (Adapted from Pesek, J. J., Matyska, M. T., and Sharma, A., J. Liq. Chromatogr. & Rel. Technologies, 31, 134, 2008).

0

100(a) (b)1

23

4

%

05.00 10.00

Time (min)15.00 20.005.00 10.00

Time (min)15.00 20.00

100 1

2 34

%

fIgure 6.5 Separation of carbohydrate structural isomer using a 100% aqueous mobile phase containing 0.5% formic acid. (a) first injection and (b) tenth injection.

84534.indb 262 11/5/09 12:28:30 PM


phase under these mobile phase conditions but also confirms that no phase collapse occurred as a consequence of operation in a purely aqueous mobile phase. If the mobile phase composition is changed to typical reversed-phase conditions by the inclusion of an organic modifier, the column equilibrates rapidly so that another analysis can be undertaken within a few minutes.

An example illustrating the dual retention capabilities of silica hydride phases is demonstrated by the chromatographic behavior of two compounds with vastly different properties. The elution characteristics of the highly polar pharmaceutical molecule metformin (Log P −2.64) and the relatively nonpolar drug molecule gly-buride (Log P 4.79) are compared on a C18 bonded hydride stationary phase. With such a large disparity in polarities most stationary phases, particularly those designed for reversed-phase retention would not be able to separate the two compounds iso-cratically unless elution of the polar component in the void volume was acceptable. Figure 6.6 shows two chromatographic options for the separation of metformin and glyburide on the hydride-based stationary phase with both compounds having reten-tion beyond the void volume. In the first case (Figure 6.6a) the least polar compound elutes first, and in the second chromatogram (Figure 6.6b) the most polar compound (metformin) has the lowest retention. By utilizing the ANP elution characteristics of metformin and the reversed-phase behavior of glyburide, it is possible to put either the highly polar or the more hydrophobic component first, and have the second close by or infinitely retained. In one set of mobile phase conditions these compounds of vastly different polarities (polarity differences of greater than 6 orders of magnitude) will actually co-elute.

A number of hydride-based bonded phases have been synthesized and charac-terized since the concept was first introduced [12]. Many have distinctly different properties and each has been characterized both chromatographically and spectro-scopically. Some specific applications are presented below which illustrate both the variety of potential uses as well as some of their unique properties. These examples

8

(a) (b)

1

26

mA

U

4

2

0

0 2Time (min)

8

101

2

6

mA

U

4

2

0

0 2Time (min)

fIgure 6.6 Separation of metformin (1) and glyburide (2) on a hydride-based C18 column length, 2.1 × 20 mm. (a) 50:50 acetonitrile/water, reversed-phase conditions and (b) 85:15 acetonitrile/water, aqueous normal phase conditions.

84534.indb 263 11/5/09 12:28:31 PM


are only representative of the many applications developed to date on hydride-based separation materials. New uses for these materials are continuously being developed.

6.3 applICatIons of hydrIde-based phases In hplC

6.3.1 overview

As outlined above, silica hydride-based stationary phase can be used in any of the three following modes: reversed-phase, ONP and ANP. While to some extent every hydride stationary phase synthesized to date can operate in all of these formats, some function optimally in one mode. The general trend is that as the hydropho-bicity of the bonded organic group increases the retention in the reversed-phase mode increases. Smaller bonded groups or lower surface coverages tend to favor the ANP and ONP modes (techniques used for the analysis of more polar com-pounds). However, each of the stationary phases based on a hydride surface has been shown to have some retention capabilities in all of the three basic modes of operation. Even the bare silica hydride surface has some reversed-phase retention characteristics.

6.3.2 reverSed-phaSe

Since several of the stationary phases synthesized on hydride surfaces have hydro-phobic organic moieties (octadecyl, octyl and cholesterol) bonded, they possess fea-tures which are typical of reversed-phase materials. A verification of this property is seen in the chromatograms for a simple hydrophobic test sample shown in Figure 6.7. In Figure 6.7a the mixture is run on a C8 hydride-based phase and in Figure 6.7b the same mixture is tested on a C18 hydride-based column in both cases using a simple methanol/water isocratic mobile phase. As expected the elution order occurs with increasing hydrophobicity of the analyte and retention on the C18 column is consid-erably longer than on the C8 bonded phase. Thus for samples that require the use of reversed-phase methods, the hydride-based materials have similar capabilities to other commercial RP columns, but with in some cases different selectivity [13].

Another example of the RP behavior of the hydride phases is demonstrated in Figure 6.8 where a mixture of steroids is separated on a cholesterol column. The mobile phase is 50:50 methanol water and retention of the solutes increases as the amount of the aqueous component is increased. The elution order on the cholesterol column is based on two factors: hydrophobicity as well as shape [14]. The size and shape capabilities of the cholesterol bonded phase are a result of the liquid crystal nature of the unbonded compound. Some of these properties are preserved in the bonded material thus creating a more ordered structure on the surface. In general, molecules with a large length:breadth ratio are retained preferentially over more bulky compounds. [15,16]. Variable temperature chromatographic and NMR experi-ments [17, 18] have shown that phase transitions in the bonded material take place confirming the more ordered structure of stationary phase on the silica hydride sur-face. Thus the cholesterol bonded phase can provide different selectivity in the reversed-phase mode beyond hydrophobic effects.

84534.indb 264 11/5/09 12:28:32 PM


00

255075

100

mA

U

125150175

(a)

(b)

0

40

20

60

80

mA

U1

2

3

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5 6

1 2

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fIgure 6.7 Separation of reversed-phase text mixture on (a) C8 hydride-based column and (b) C18 hydride-based column.

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fIgure 6.8 Separation of a mixture of steroids on a C18 hydride-based stationary phase. Mobile phase: 50:50 methanol/water. Mobile phase 70:30 methanol/DI water. Detection MS in the APCI mode. Solutes: 1 = Andrenosterone; 2 = Corticosterone; 3 = 4-androstene-3,17-dione; 4 = 11-alpha-acetoxyprogesterone; 5 = Estrone; 6 = Estradiol. (Adapted from Pesek, J. J., Matyska, M. T., and Dalal, L., Chromatographia, 62, 595, 2005.)

84534.indb 265 11/5/09 12:28:34 PM


As described for Figure 6.5 above the C18 bonded material functions well on hydride surfaces in a 100% aqueous mobile phase. A similar test was run using a series of organic acids. A mixture of oxalic, formic, fumaric, and propionic acid can be separated using a 100% aqueous mobile phase containing 0.05% phosphoric acid. The separation is reproducible with very good efficiency indicating that the bonded material maintains a constant morphology on the surface, i.e., no phase collapse.

A number of applications have been developed since the introduction of silica hydride phases that cover a broad range of samples. It has been shown that cat-echolamines in very high aqueous content mobile phases (5:95 acetonitrile/water) can be separated on a hydride C18 column [19]. For MS compatibility and pH control 25 mM ammonium formate was added to the mobile phase. As demonstrated above it is possible to use the C18 and C8 hydride-based stationary phases for typical RP applications. Another example is shown in Figure 6.9 for the separation of polycyclic

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eak

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fIgure 6.9 Separation of a mixture of polycyclic aromatic hydrocarbons on a silica-hydride-based C18 stationary phase. Mobile Phase: 70:30 acetonitrile/water.

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aromatic hydrocarbons on a C18 column. The very hydrophobic PAH compounds generally required relatively high amounts of organic in the mobile to elute them in a reasonable time isocratically (70% in this case). Among the many other compounds where methods have been developed in reversed-phase on the silica hydride C18 stationary phase, two pharmaceutical compounds, acetaminophen and sulfonamide, can be analyzed rapidly and reproducibly with gradient elution. For sulfonamide, the mobile phase consists of acetonitrile/water + 0.1% formic acid and the gradient goes from 30% to 100% acetonitrile over 5 minutes. Under these conditions the elution time on a 4.6 × 75 mm column with a flow rate of 1 mL/min is about 7 minutes. For acetaminophen, the mobile phase consists of acetonitrile + 0.1% acetic acid + 0.005% TFA/water + 0.1% acetic acid + 0.005% TFA. This particular mobile phase illus-trates another interesting property of hydride columns. When TFA is added to the mobile phase to improve peak shape or control other solute properties, only between 0.001 and 0.005% is generally needed. This feature is especially important when using MS for detection since higher levels of TFA can suppress the ionization of the sample. The gradient for this analysis goes from 100 to 70% aqueous over 3 minutes after a one minute hold at 100%. Under these conditions with a 1 mL/min flow rate on a 4.6 × 75 mm column the retention time is about 5 minutes.

One more significant property of the hydride-based stationary phases that can have a substantial impact on method development is their ability to equilibrate rapidly after gradient elution. Figure 6.10 provides an example for a typical reversed-phased gradient separation on a C18 hydride column. The mixture analyzed consists of five aromatic hydrocarbons and the gradient runs from 50 to 100% acetonitrile. To illus-trate equilibration capability an unusually fast recycle time of one minute between runs is tested. The reproducibility between the initial run (Figure 6.10a) and the following separation (Figure 6.10b) demonstrates that this column has equilibrated over this short time span. While such a short equilibration period is not normally practical on most HPLC systems due to longer dwell times, a more reasonable time such as five minutes can be routinely used for a variety of applications.

6.3.3 aqueouS normal phaSe

If the silica hydride-based columns only provided slightly different selectivity in the reversed-phase then they would not represent a significant advance in HPLC bonded phase technology. However, in addition to the properties described above, these materials provide other capabilities, some not available in other phases, that make them unique in their range of chromatographic applications. Among the features that make the silica hydride phases useful, the ability to operate in the ANP mode is one where significant advancements in applications can be made. Retention of hydrophilic compounds is not as simple and straightforward as hydrophobic reten-tion, especially when the method needs to be coupled to MS for detection. The des-ignation of ANP for the retention of polar compounds such as those discussed below is used in this review to distinguish silica hydride materials from HILIC stationary phases.

The ANP properties of the silica hydride-based materials were initially identified on the stationary phases that were designed for RP applications: the bidentate C18

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and the cholesterol materials. These applications involved compounds that would not normally be done by RP because of their hydrophilicity, unless ion-pairing reagents, derivatization, or some other approach to create a more hydrophobic species was used. Therefore, it was surprising to discover that such analytes could be retained by a stationary phase at high organic content in spite of the bonded hydrophobic moiety. For example, applications have been developed for several pharmaceutical com-pounds in the ANP mode on the silica hydride C18 column. These include analyses for methotrexate, metanephrine, normetanephrine, and amino-caproic acid. These are all basic pharmaceutical compounds and they all exhibit increasing retention on the C18 column as the amount of organic solvent in the mobile phase is increased. The mobile phases in all cases were acetonitrile/water with formic acid added in the range of 0.1 to 0.5%. The hydride-based cholesterol phase, also with excellent RP properties as described above, can be used in the ANP mode. The physiologically significant compounds choline and acetylcholine have been successfully separated using a mobile phase of 91:9 acetonitrile/water containing 0.5% formic acid. With MS detection the lower limit of quantitation was determined to be less than 5 pmol. The highly polar drug tobramycin can also be retained on the cholesterol column at relatively low concentrations of acetonitrile in the mobile phase. Depending on the length and diameter of the column, as little as 60% acetonitrile with a mobile phase containing 0.5% formic acid will provide sufficient retention as shown in

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fIgure 6.10 Gradient separation of a mixture of aromatic hydrocarbons. (a) initial chro-matogram and (b) chromatogram obtained following a one minute equilibration time after completion of initial run. Gradient: 0–3 min ACN/water (50:50); 3–18 min to 100% ACN; 18–23 min 100% ACN. Equilibration to 50:50 ACN/water. Solutes in order of elution: ben-zene; naphthalene; phenanthrene; anthracene; and pyrene.

84534.indb 268 11/5/09 12:28:37 PM


Figure 6.11. This result is typical for a range of very hydrophilic species on the hydride stationary phases where typical RP applications can also be developed.

It was concluded from the above examples that it was likely that the silica hydride surface was responsible for the ANP behavior observed on the stationary phases with organic groups attached to the surface. The test of that theory was described in Figure 6.2, showing the chromatogram for the separation of phenylalanine and phenylglycine in a mobile phase containing 80:20 acetonitrile/ DI water with 0.1% formic acid. As can be seen, the two closely related compounds are separated on a relative short column (75 mm) in under 5 minutes. If these same two compounds are run on an ordinary silica column under these conditions, there is some retention but no separation of the pair of solutes as shown in Figure 6.2. Thus it was verified that the silica hydride surface is an essential feature of the ANP retention in all the applications discussed in the review.

A number of other hydrophilic compounds were tested on unmodified silica hydride columns with retention being observed for most of them, but in some instances peak shape was not always symmetric (both fronting and tailing were observed). In order to preserve the high ANP retention capabilities of the silica hydride-based stationary phases as seen for the unmodified surface, but to generally improve peak shape, it was determined that a minimally modified material was the most desirable.

The analysis of amino acids, an area where substantial efforts have been made over many decades due to their importance in biological and physiological processes, still requires further development in order to increase sample throughput, be applicable to increasingly complex samples, and be compatible with detection by mass spectrometry. It has been shown that through the combination of HPLC-MS all amino acids can be analyzed in approximately 15 minutes on a Diamond Hydride column (DH, a minimally modified silica hydride material) by resolving all compounds that are isobaric or with

2.00 4.00Time (min)

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Uracilm/z 113

Tobramycinm/z 468

0

%

fIgure 6.11 Analysis of tobramycin on a hydride-based cholesterol stationary phase in the ANP mode. Mobile phase: 60:40 /water in 0.5% formic acid. Detection by APCI MS.

84534.indb 269 11/5/09 12:28:39 PM


a difference of one amu [20]. Either acetonitrile or acetone can be used as the organic component in the mobile phase and formic acid and acetic acid are the MS-compatible additives for amino acids. It was also demonstrated that when using gradient methods, the DH column can equilibrate within 5 minutes, thus further reducing the analysis time when compared to other methods such as ion-exchange and HILIC.

Other hydrophilic metabolites and compounds of physiological significance can also be analyzed on the DH column. For example, organic acids can be retained and separated using a mobile phase containing ammonium formate or ammonium acetate, such that the pH is above the pKa of the acid. A good example is shown is Figure 6.12 where two isobaric acids are separated by a gradient elution method. This particular application illustrates why mass spectroscopy alone cannot be used for the analysis of complex samples. Whenever isobaric compounds are present, then separation is essential for positive identification. While amino acids are detected as position ions by MS, acids are done in the negative ion mode. Repeatability is generally less than 0.5% RSD and equilibration is less than five minutes after gradient methods. Good retention and separation can also be obtained for carbohydrates on this stationary phase as well. Unlike amino acids and the organic acids, the ANP retention of sugars is not as sensitive to changes in pH. Thus methods can be developed for these ana-lytes that utilize formic or acetic acid for low pH conditions, or ammonium acetate or ammonium formate where pH values closer to 7 are obtained. For MS detection the positive ion mode is used. In all cases repeatability and gradient equilibration are comparable to that obtained for amino acids and organic acids.

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- EIC(115.00000-115.20000) Scan Maleic_acid_GrJneg_01_18.d

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fIgure 6.12 Separation of maleic (1) and fumaric (2) acids on the DH column in an ANP gradient from 80 to 60% ACN with 0.1% ammonium formate in 7 minutes. m/z = 115 for both compounds. (Adapted from Pesek, J. J., Matyska, M. T., Fischer, S. M., and Sana, T. R., J. Chromatogr. A, 1204, 48, 2008.)

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Other polar compounds have been tested on the DH column to determine the range of retention capabilities in the ANP mode. For example, simple mobile phases with acetonitrile/water and 0.1% formic acid can be used to separate serotonin and its metabolites and analogs. Usually a gradient is necessary because compounds such as 5-hydroxy-3-indole acetic acid and 3,4-dihydroxyphenylacetic acid require high amounts of acetonitrile for good retention, while serotonin and epinephrine require more water for elution in a reasonable time. The toxilogically significant compound melamine requires relative low amounts of acetonitrile in this same type of mobile phase (usually only 60 to 70%) due to its high basicity. With MS detection a rapid screening method was developed for a wide variety of food products. The nucleosides adenosine and guanine can be separated using a mobile phase consisting of acetonitrile/water containing 0.1% formic acid and 0.001% TFA. At high amounts of acetonitrile, good retention and peak shape are obtained. A similar mobile phase is used for the retention of biogenic amines such as tryptamine. But it has also been demonstrated that a mixture of tryptamine, serotonin, and dopamine can be sepa-rated under gradient conditions using an acetonitrile/water mobile phase with 0.1% ammonium formate. Thus the DH material is versatile enough to often provide more than one set of conditions for particular sample types. This capability is useful when complex mixtures containing a variety of hydrophilic compounds need to be ana-lyzed so that a single method could be developed for such a sample. A number of nucleotides and sugar nucleotides were also well-retained on the DH column using an acetonitrile/water mobile phase containing 0.1% ammonium formate. Peak shape was improved by adding a small amount of ammonia to the sample solution.

The most challenging samples are those that come from physiological fluids. Although some sample preparation is done, usually to remove proteins, the matrix is complex with hundreds of compounds often being present. Such samples are best ana-lyzed with MS detection since mass differences along with chromatographic retention can be used to identify the components. However, even MS is not always straightfor-ward since the presence of various compounds in differing amounts from sample to sample can often lead to variations in retention as well as ionization efficiency. Small variations in retention are generally not crucial since the m/z will provide the identifi-cation needed, but variations in ionization efficiency are a serious problem when quan-titative data is needed. This situation is partially alleviated by having a broad range of retention, thus minimizing co-elution and variable ionization properties.

The compounds creatine and creatinine, along with the isobaric compound 4- hydroxyproline in urine, are well-separated from each by a gradient method. The chromatogram using MS detection is shown in Figure 6.13. The top portion shows the total ion chromatogram and establishes the complex nature of the sample with many compounds being eluted during the analysis time of 20 minutes. The bottom portion of the figure shows the extracted ion chromatogram (EIC) for m/z 114 (crea-tinine) and m/z 132 (creatine and 4-hydroxyproline). Good peak shape and efficiency are obtained with a mobile phase of acetonitrile/water and 0.1% formic acid using a linear gradient from 95 to 50% ACN over 30 minutes. Using a similar gradient, other metabolites such as hypoxanthine, chenodeoxycholic acid, betaine, and choline are analyzed as shown in Figure 6.14 using their EICs. The antioxidant, trans-3-hydroxycinnamic acid, was also identified in the same sample using its EIC. These

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examples illustrate a powerful medium for the separation of hydrophilic compounds that can be done in a simple and reproducible manner, comparable to reversed-phase methods, which has been sought for many years.

6.3.4 dual mode retention

Each of the sections above has detailed the reversed-phase and ANP properties of hydride-based stationary phases separately. But from these descriptions it can be seen that since one material is providing both capabilities, it should be able to

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fIgure 6.13 Separation of creatinine (1) and creatine (2) with 4-hydroxyproline (3) in human urine on a DH column using an ANP gradient from 90 to 50% ACN with 0.1% formic acid in 30 minutes. (A) TIC = total ion chromatogram of urine sample, and (B) extracted ion chromatogram of selected compounds. (Adapted from Pesek, J. J., Matyska, M. T., Fischer, S. M., and Sana, T. R., J. Chromatogr. A, 1204, 48, 2008.)

84534.indb 272 11/5/09 12:28:42 PM


function simultaneously depending on the compounds and the mobile phase condi-tions selected [21]. This property can be illustrated by the retention map (tR vs. % organic in the mobile phase) as shown in Figure 6.15a. It clearly highlights the dual mechanisms that are present in most silica hydride-based stationary phases. At high % of water in the mobile phase the reversed-phase properties dominate leading to strong hydrophobic retention while at high amounts of organic in the mobile phase the ANP mode takes over leading to the retention of hydrophilic compounds. In addition to being able to operate over the entire range of mobile phase compositions where one mechanism prevails at the two extremes, in the middle region where both organic and water are present in substantial amounts both RP and ANP can oper-ate simultaneously. This leads to an interesting prospect for compounds with both hydrophobic and hydrophilic groups. These compounds can be retained under both ANP and RP conditions. The chromatographic behavior for these types of com-pounds on a silica hydride-based column is shown in Figure 6.15b. As the mobile phase composition is varied, retention goes through a minimum, but increases as either the percentage of water or organic solvent is increased. This allows method development for such compounds to be done in either the reversed-phase or ANP modes. Thus, there are two domains in which to obtain the best experimental condi-tions leading to greater versatility and flexibility in method development. Another area where this capability can be utilized is for mixtures containing both polar and nonpolar compounds. The region of intermediate mobile phase compositions where both RP and ANP retention are possible can be used for the separation of such mix-tures. Figure 6.15c illustrates this point. There are three compounds of high polarity and four hydrophobic species. At the mobile phase composition selected, the three

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fIgure 6.14 Separation and identification of various metabolites on a Diamond Hydride column with mass spectroscopy detection. Same gradient as Figure 6.13. Solutes: 1 = xan-thine; 2 = uric acid; 3 = unknown with m/z = 153.0608; 4 = hypoxanthine; 5 = unknown with m/z = 153.0660; 6 = chenodeoxycholic acid; 7 = unknown m/z with 118.0872; 8 = unknown with m/z = 118.0875; 9 = betaine; 10 = choline.

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fIgure 6.15 (a) Retention map for hydrophobic and hydrophilic compounds on a silica hydride-based stationary phase. (b) Chromatograms for retention of a compound with hydro-philic and hydrophobic components at various mobile phase compositions. (c) Chromatogram of a mixture containing both hydrophilic and hydrophobic compounds on a silica-hydride-based cholesterol column. Mobile phase 60:40 acetonitrile/water. Compounds 1–3 are hydrophilic and 4–7 are hydrophobic. (Adapted from Pesek, J. J., Matyska, M. T., and Larrabee, S., J. Sep. Sci. 30, 637, 2007.)

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hydrophilic compounds are eluted first but separated, and the four hydrophobic com-pounds are more strongly retained but also separated. Switching to a higher organic content mobile phase reverses the elution order with the polar compounds being more strongly retained, but the resolution is not as good. However, with the hydride-based columns method development can be tested in both the domain where RP is dominant as well as at mobile phase compositions favoring ANP. These features can all be achieved using mobile phases that are compatible with mass spectrometry as opposed to many stationary phases that have either limited applications or utilize additives that cannot be used with MS detection.

6.3.5 orGanic normal phaSe

One of the other more interesting features of the hydride-based separation materials is their ability to operate in the ONP mode. The retention properties are somewhat analogous to the usual ONP stationary phases such as bare silica, as well as amino, diol, and cyano phases. This capability has been found for every hydride-based stationary phase tested. Thus, bare silica-hydride, as well as Diamond Hydride, function well under typical ONP conditions for the separation of low to moderate polarity solutes. In addition, stationary phases with C8 or C18 can also provide organic normal retention capabilities [22]. This is in contrast to typical reversed-phased materials based on ordinary silica that have little or no retention in the ONP mode. Thus it appears as is the case for the ANP mode, that the silica hydride surface plays an important role in the normal phase properties of these materials. Another property of the hydride materials that has a significant impact on their utility in the ONP mode is a low affinity for water in comparison to ordinary silica. This prop-erty is responsible for the rapid equilibration after gradients in the reversed-phase mode. In ONP, silica hydride-based phases do not require the mobile phase solvents to be scrupulously dry as is the case for ordinary silica phases. The organic solvents can contain small amounts of water with no noticeable effect on reproducibility or efficiency. The solvents can also be exposed to air and the columns can still func-tion well for many analyses without the need for drying of the mobile phase.

A good example of an ONP application involves the retention and separation of various structurally related phenols. Using the unmodified hydride material, a mobile phase of 95:5 hexane/ethyl acetate will separate phenols with other structural groups as aldehydes, ketones, and acids. Under these conditions using ordinary silica, all compounds are retained but elute as a single broad peak. If a C18 hydride-based stationary phase is used under the same conditions, approximately the same reten-tion is obtained, although slightly better efficiency is achieved as shown in Figure 6.16. It has also been demonstrated that the unmodified hydride surface provides a good separation medium for heterocyclic aryl compounds [22]. Depending on the type of heterocycle and the substitution on the aryl portion of the compound, good retention was obtained using mobile phases containing 95:5 hexane/ethyl acetate or 90:10 hexane/methylene chloride or 90:10 hexane/THF. Thus, it appears that the hydride surface is primarily responsible for retention in the ONP mode. If a typical commercial C18 column is used, no retention of these compounds is obtained under these experimental conditions confirming the need for the hydride surface. Two

84534.indb 275 11/5/09 12:28:45 PM


other examples of ONP retention on hydride-based columns are carvone and lora-tidine. Both compounds can be retained on a C18 hydride-based column using a hexane/THF mobile phase. Reasonable retention is obtained for carvone with a 95:5 hexane/THF solvent but under these conditions loratidine does not elute in any prac-tical time frame. If the mobile phase is change to 75:25 then loratidine has a k of ~3.0 but carvone elutes at the solvent front. Thus to do an analysis of both compounds in the same sample requires a gradient going from 95 to 75% hexane over a 7 minute time frame. The data are very reproducible (< 0.5% RSD) with equilibration times of about 5 minutes between runs.

OH OHO Br

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fIgure 6.16 Separation of 4 phenols on the silica hydride-based C18 column in the organic normal phase mode. Mobile phase 90:10 hexane/ethyl acetate. (Adapted From Pesek, J. J., Matyska, M. T., and Sharma, A., J. Liq. Chromatogr. & Rel. Technologies, 31, 134, 2008.)

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6.3.6 microcolumn hplc

The use of hydride-based materials for microcolumn liquid chromatography and capillary electrochromatography is another promising application for this technol-ogy. The full potential of these techniques have not been realized but their future depends on both the development of reliable instrumentation and improved column technology to provide a broad range of selectivity to match current HPLC options. Some examples of applications using silica hydride stationary phases with these two formats are presented below.

For microcolumn HPLC, it was shown that good separations of steroids could be obtained using a capillary packed with a hydride-based C18 stationary phase [23]. Good retention and separation were achieved using a 100 µm × 30 cm (20 cm packed length) capillary with an 80:20 acetonitrile/DI water (0.1% formic acid) mobile phase at a flow rate of 70 µL/min. The elution order and the same high amount of organic required in the mobile phase were identical to the results obtained on a standard (4.6 × 75 mm) column packed with the same material. Solvent composition studies verified the reversed-phase behavior of these solutes. The identical mixture on the same column was tested in the pressurized capillary electrochromatography (p-CEC) mode. Figure 6.17 shows the electrochromatogram obtained using an applied field

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fIgure 6.17 Separation of steroid mixture by pCEC on column packed with 4.0 µm hydride-based C18. Applied votage: 20 kV. Mobile phase 80:20 acetonitrile/DI water (0.1% formic acid). Detection at 254 nm. Solutes: 1 = Prednisolone; 2 = Corticosterone; 3 = Norgestrel; 4 = Progesterone. (Adapted from Pesek, J. J., Matyska, M. T., and Sukul, D., J. Chromatogr. A, 1191, 136, 2008.)

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of 20 kV. The presence of electroosmotic flow (EOF) results in a shortened analysis time and in addition the EOF component produces higher efficiency than obtained with the pressure only flow used in the capillary LC method. A plot of migration time vs. applied voltage demonstrates that as the field is increased the analysis time for all solutes is decreased due to increased EOF.

The p-CEC technique has more dramatic effects when the elution of charged com-pounds is investigated. For a compound such as cytidine the elution time is reduced by more than 50% with the application of 10 kV when compared to the analysis done under only pressure-driven flow. The use of an electric field also affects selectivity since for charged analytes the elution time is a combination of the chromatographic effects present in the HPLC experiment plus the electrophoretic mobility that results from the applied voltage. Thus, for difficult separations, improvements in resolution can be obtained through the standard variation in mobile phase composition used in HPLC as well as varying the strength of the electric field.

As described above, one of the unique features of the hydride-based stationary phases is their ability to operate in both the reversed-phase and ANP modes. This capability has also been tested in both the µ-HPLC and p-CEC formats with a C18 bonded material. For two hydrophilic pharmaceutical compounds, metformin and amphotericin, ANP retention was obtained under µ-HPLC conditions. When a volt-age was applied for p-CEC operation, the same increase in retention with an increase in organic composition of the mobile phase was observed. Thus the dual retention properties of the hydride-based stationary phases are present under µ-HPLC opera-tion as expected and in p-CEC since chromatographic retention has a substantial effect on the overall elution of polar analytes.

The use of small particles (sub-2 micron) as a support for a hydride-based C18 phase has also been investigated for both µ-HPLC and p-CEC. In the chromato-graphic format, modest increases (∼30%) are observed for the analysis of steroids. However, with the application of 20 kV in the p-CEC mode the efficiencies more than double, to over 200,000 plates/m. For charged solutes the improvement in efficiency is not as great since the combined effects of EOF and electrophoretic mobility have a more substantial effect on peak width than the decrease in particle size. Certainly the use of hydride-based separation materials in µ-HPLC and p-CEC are viable options and can be used to expand the application of these techniques to a broader range of practical analyses.

6.4 hydrIde-based etChed CapIllarIes

6.4.1 fabrication

A column configuration has been developed to improve the performance of open tubular capillary electrochromatography (OTCEC) that includes a silica hydride sur-face. The fabrication of this separation medium involves etching the inner wall of a fused silica capillary by heating it at a temperature of 300 to 400°C in the presence of ammonium hydrogen difluoride (NH4HF2) for three to four hours. The surface area of the inner wall can be increased by a factor of 1000 or more and radial exten-sions of up to 5 µm in length can also be created by this treatment [24,25]. This

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process is used to overcome the low capacity of the bare capillary and shorten the distance solutes must travel to interact with a stationary phase attached to the etched surface. In addition, nitrogen and fluoride from the etching reagent are also incorpo-rated into the new surface matrix [26]. Their presence diminishes some of the strong adsorptive properties of the silanols thus making the new surface more biocompat-ible. Further improvements in capillary performance are obtained from the bonding procedure used to modify the etched surface. The effects of residual silanols are substantially reduced by the silanization reaction used to create a new surface com-posed primarily of hydride moieties as described above for particulate silica. The selectivity of the capillary is controlled by attaching various organic moieties to the etched hydride surface via a hydrosilation reaction in a manner similar to that used for HPLC stationary phases.

6.4.2 characteriZation of capillary propertieS

The etching process produces an altered surface matrix composed of silicon, oxygen, fluoride, and nitrogen. The presence of these species near the etched surface has been confirmed by ESCA and EXAFS spectroscopy [26]. In particular nitro-gen at the solution/surface interface has a significant effect on the electrophoretic behavior of the capillary. At low pH these nitrogens close to the surface become protonated giving an overall positive charge to the inner wall of the capillary and producing a reverse EOF. As the pH is increased, the EOF passes through zero and then becomes cathodic due to the deprotonation of the nitrogens, ionization of the remaining silanols, and the negatively charged fluoride species [26,27]. The presence of these additional elements in the surface matrix does not interfere with the subsequent chemical modification (silanization/hydrosilation). The typical EOF behavior of an etched chemically modified capillary is shown in Figure 6.18. The ability to have either cathodic or anodic EOF adds another dimension to improving and optimizing selectivity. The biocompatibility of the etched surface can be illus-trated by monitoring the electrophoretic behavior of a sample containing basic

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fIgure 6.18 Plot of EOF vs. pH in an etched chemically modified capillary.

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proteins or peptides. One such example is a tryptic digest of a protein containing many peptides having basic amino acids that could readily interact with silanols on the surface. The electropherogram of the tryptic digest of transferrin obtained on an etched capillary with no further chemical treatment contains at least fifty peaks, all of which have high efficiency and good symmetry [28]. A large number of constituents are well-resolved with excellent peak symmetry thus indicating a minimum of surface adsorption effects. Similar electropherograms with good peak shapes have been obtained for samples of various peptides as well as small basic compounds [25,29–35].

6.4.3 dual Separation modeS

The migration behavior of solutes in the etched chemically modified capillaries is a function of both chromatographic and electrophoretic effects thus falling into the category of OTCEC. OTCEC is a versatile technique where a number of experimen-tal variables can be used to optimize the separation capabilities of the capillaries. The primary variables in OTCEC include the bonded phase moiety, pH, buffer com-ponents, amount and type of organic modifier in the buffer, and temperature. The effects of some of the above experimental parameters on retention and resolution can be used to illustrate how separations can be controlled with these columns. In many instances, the choice of stationary phase (in this case the organic moiety bonded to the etched capillary wall), such as in HPLC, has a substantial effect on elution behav-ior and resolution. An example is the separation shown in Figure 6.19 of a synthetic peptide sample containing some minor components in addition to the main product. Using an etched C18 modified capillary (Figure 6.19a), four components in addi-tion to the main product are well resolved under the experimental conditions used. In contrast, a cholesterol column (Figure 6.19b) and a butylphenyl column (Figure 6.19c) result in the complete resolution of only one minor component and partial res-olution of the others under the same experimental conditions. Another variable that

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fIgure 6.19 Electrochromatogram of synthetic peptide sample (sequence: Gln His Asn His Phe His Arg) on three etched capillaries with different types of chemical modification: (a) octa-decyl; (b) cholesterol; and (c) butylphenyl. Mobile phase: 90:10 pH 2.14 buffer/methanol.

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can have a substantial impact on either chromatographic or electrophoretic behavior is the choice of an organic modifier in the mobile phase. In another synthetic peptide sample with methanol in the mobile phase only one minor constituent is observed, while if ethanol is used as the organic modifier at least five well-resolved minor com-ponents can be detected. A crucial variable in OTCEC as in other electrophoretic methods is the pH of the running buffer which can be used to control the migration of various components in the sample. In Figure 6.20, the elution order of the two components in the sample is reversed by changing the pH from 2.14 (Figure 6.20a) to 3.00 (Figure 6.20b). Such large effects in retention properties can make pH one of the most effective variables for optimizing OTCEC separations. Another variable that can have a substantial effect on solute migration is temperature. The migration behavior as a function of temperature on two different capillaries is often completely different. If the van’t Hoff plots under the same experimental conditions for the migration of two peptides on cholesterol and C18 modified capillaries are compared, it is observed that the elution order of the two peptides are reversed at two different points on the cholesterol capillary, while only minor changes in the migration are observed on the octadecyl capillary [36]. The substantial effect of temperature on the etched cholesterol capillary has been documented in a number of studies and has been attributed to the liquid crystal properties of this particular compound [37].

4

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6Time (min)

8 4 65Time (min)

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fIgure 6.20 Effect of pH on the migration of synthetic peptide sample (sequence: Gln Asp Gln His Asn His Phe His Arg) using an etched butylphenyl modified capillary: (a) pH = 2.14 and (b) pH = 3.00. Mobile phase 90:10 buffer/methanol. (Adapted from Pesek, J. J., Matyska, M. T., Dawson, G. B., Chen-Chen, J., Boysen, R. I., and Hearn, M.T.W., Anal. Chem., 76, 23, 2004.)

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Liquid crystals are materials which have properties intermediate between a true liq-uid (with unrestricted movement of molecules) and a solid that has a fixed structure and is highly ordered. Movement of the molecules is possible in a liquid crystal but with certain restrictions due to the fact that some degree of ordering of the moieties is present. For a liquid crystal stationary phase that is bonded to the wall of a capil-lary, movement is further restricted by the attachment of one end of the molecule to the support surface. The degree of ordering and the exact structure of the liquid crystal moiety on the surface of the inner wall can be affected by temperature and the solvent composition around it.

The above examples can be used to demonstrate that both electrophoretic and chromatographic mechanisms are present in the open tubular etched chemically mod-ified capillaries. The choice of stationary phase as shown in Figure 6.19 illustrates the chromatographic effect. While there may be some variations in EOF between different bonded moieties, this change would not cause an alteration of the elution order and relative migration among the peptide species. This result and other similar measurements made on etched capillaries with different modifications clearly show that this electrophoretic format has a chromatographic contribution to solute migra-tion. Changes in migration as the type of organic solvent in the buffer is varied can be explained by either chromatographic or electrophoretic effects, or a combination of both. Significantly lower EOF could result in improved resolution of analytes as well as a difference in the degree of interaction between the solutes and the bonded moiety. The predominant effect may well vary depending on the organic solvent selected, the analytes in the sample, and the bonded group on the surface, but the type of organic modifier in the running buffer has been shown to have a substantial impact on separa-tion capabilities. Changes in pH (and likely the charge state of the analyte) can have a major influence on the migration behavior in these capillaries. For proteins and peptides a difference of one pH unit can result in a substantial change in the overall charge of multicomponent samples leading to shifts in elution order. Another possible influence can be a difference in interaction with the stationary phase based on the polarity of the solutes as they become more positively charged as the pH is reduced. Since it is likely that the charge characteristics of any two peptides or proteins are not the same, then either a substantial difference in electrophoretic behavior and/or interaction with the hydrophobic bonded material can occur as a result of polar-ity changes in the solutes. The temperature behavior described above is the result of solute interaction with the stationary phase. If the migration of the solutes were con-trolled mainly by electrophoretic effects and/or changes in EOF then the two solutes would have a very similar van’t Hoff plot. Since appreciable differences are observed, it can be concluded that chromatographic effects have a substantial influence on solute migration as the temperature is varied.

6.4.4 other capillary formatS

Some basic variations in producing the etched chemically modified capillaries have also been undertaken. Alternate etching formulas have been investigated where different inorganic salts are included with the etching agent, ammonium dihydrogen fluoride [38]. These changes result in different EOF characteristics for the capillary

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after it is chemically modified. Selectivities, peak shape, and symmetry can also be affected by the presence of other ions in the surface matrix and hence can provide another means for optimizing separations. The other major process in the fabrication of these separation media involves the surface modification after the etching pro-cess. In a comparison between organosilanization and silanization/hydrosilation (the method used for producing hydride surfaces), it was determined that with respect to efficiency and peak symmetry the latter approach was superior [39]. It was concluded that the silanization/hydrosilation was most likely better because it resulted in fewer residual silanols on the surface of the etched capillary. Another variation in fabrica-tion involves the use of a rectangular channel instead of a circular one. [40] All of the separation efficiencies and selectivity are similar to the circular format but detection can be improved by rotating the capillary so that the light path passes through the long axis of the channel. The features of the etched chemically modified capillaries outlined above have been exploited in a number of applications that demonstrate the potential of this separation medium to solve challenging analytical separation prob-lems. Some examples are described in the following sections that represent a range of analytes from small molecules to proteins and peptides.

6.4.5 applicationS of etched chemically modified capillarieS

A number of small molecules, including many basic compounds such as tricyclic antidepressants and tetracyclines, have been analyzed using etched chemically modi-fied capillaries [29]. One interesting example of both the resolving ability of these capillaries and the effect of the stationary phase for small molecule analysis is demon-strated by a mixture containing purine/pyrimidine bases and a nucleoside separated on two etched capillaries with different bonded moieties but under the same buffer, pH, and applied voltage conditions [26]. The mixture is separated successfully by both columns with high efficiency and good peak shape. However, the elution order is different on the two capillaries illustrating the influence of the bonded group attached to the etched surface. The importance of the stationary phase has also been demon-strated for the separation of heterocyclic aromatic amines. A diol bonded phase at low pH provided the best separation for a mixture of genotoxic compounds produced when proteinaceous food is grilled or fried [35]. Another application for small mol-ecules is the analysis of antibiotics in milk [41]. Using a liquid crystal stationary phase bonded to the etched surface, a method was developed through optimization of pH and an appropriate organic modifier in the mobile phase.

The usefulness of these capillaries for peptide analysis has been described to some extent above and shown in Figures 6.19 and 6.20. High efficiencies, excellent resolving power, and good peak shape have been documented in a number of studies on synthetic peptide species [36,42–46]. In addition, when analyzing the same sam-ples by gradient HPLC, the separations are almost uniformly better when using the OTCEC method. Partially resolved or unresolved minor components are more read-ily identified by the OTCEC method. Peptide analysis has also been done for tryptic digests thus suggesting the technique might be useful for proteomics [47]. In order to test the performance of this OTCEC format for such applications, a bovine cyto-chrome c sample was digested with trypsin, and separated with a cholesterol-bonded

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capillary under pH 7.0 conditions. As shown in Figure 6.21a, good separation was achieved, with all the major peptide fragments easily identified by mass spectrometry. The separation of the two isobaric peptides, T6 (GGK) and T11 (NK), as illustrated in Figure 6.21b, shows the advantage of coupling OTCEC to MS. These two peptides are not well resolved by high performance reversed-phase liquid chromatography, due to the similarity in their hydrophobicities. However, an excellent separation of these two peptides in terms of their selectivity and peak shapes was achieved with the OTCEC capillary. Although these two peptides have identical mass-charge ratios and were not distinguishable from their mass spectra, the difference in their tandem mass spectra resulted in a positive identification.

Another area where a broad range of applications for the etched chemically modi-fied capillaries has been demonstrated is in the analysis of proteins. CE has already proven to be a valuable tool for such analyses but often suffers from poor reproduc-ibility of migration times and quantitation, usually the result of irreversible adsorption of proteins to the capillary wall. Physically coating or chemically bonding various organic compounds or polymers to the inner wall of the capillary can usually elimi-nate or diminish the problem, but the more biocompatible surface produced during the etching process usually provides superior results. A number of applications of protein separations have been reported using etched chemically modified capillaries [25,27,28,30,32]. Among these is the analysis of basic proteins, the compounds that

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fIgure 6.21 Separation of a cytochrome c tryptic digest with an etched cholesterol- modified OT-CEC capillary. (a) BPC of the tryptic peptides; (b) EIC of ions with a m/z of 261.2 that correspond to the tryptic peptide T6 and T11. Separation buffer: 20 mM NH4Ac in 20% ACN. Voltage: 20.0 kV. Injection: 50 mbar × 5 s. (Adapted from Yang, Y., Boysen, R. I., Matyska, M. T., Pesek, J. J., and Hearn, M. T. W., Anal. Chem., 79, 4942, 2007.)

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are usually the most difficult to elute with good recovery and symmetrical peaks. The experimental conditions span a variety of buffers, pH values between 2.1 and 8.5, and in some cases utilize an organic modifier in the mobile phase.

Another example of a protein application involves the analysis of PEGylated com-pounds. Analysis of PEG proteins and peptides for clinical and quality assurance measurements is complicated by the heterogeneity that results from the distribution of the PEG among a number of different sites on the biopolymer [48]. Attaching polyethylene glycol to a peptide or protein involves activating PEG in order to bond it to a specific functional group [49,50]. The most common sites for bonding of PEG are lysine and N-terminal amino groups. The number of potential species created by attachment of PEG, and hence the maximum number that might need to be identified in any analysis, is given by the following formula [51]:

P = N

N k k!

( – )! ( !) (6.1)

where N = is the number of possible sites and k is the number of sites actually modi-fied. HPLC analysis often fails to determine the actual number of PEGylated species present in a particular sample because of insufficient resolving power. The OTCEC analysis of three PEGylated proteins using etched chemically modified capillaries provided the high resolution and give an elution profile that could be used for iden-tification or quality control tests [52]. In each case there were a substantial num-ber of components in these samples indicating extensive PEGylation of two of the proteins, catalase and protease. The resolution, time of analysis, peak shape (AS is 1.1 or less), and efficiencies (N/m generally in the range of 100,000 to 200,000) found in these columns is excellent compared to the other separation methods such as HPLC. In comparison to the most reliable analytical method developed for PEG proteins, MALDI-TOF, the analysis is simpler and less costly.

Recently it has been demonstrated that metalloproteins can also be separated using etched chemically modified capillaries [53]. Electrochromatograms for car-bonic anhydrase under acidic conditions, obtained on the C5 capillary, show excel-lent peak shape (AS ≅ 1) and high efficiency (N > 1,000,000 plates/m). These results can be contrasted to the electrochromatogram for carbonic anhydrase using a C18 modified etched capillary where lower efficiency and poorer peak shape indicate that the solute has significant hydrophobic interactions with the octadecyl bonded moiety. Similar peak shapes and symmetries are obtained on the two capillaries over the pH range of 2.14 to 6.0. Comparable results are also obtained for human serum albumin and human IgG, i.e., better peak shape and higher efficiencies are achieved on the etched C5 capillary than on the etched C18 column. The separation of these two proteins on the C5 column is shown in Figure 6.22. The migration time for the two proteins on both the C5 and C18 columns decreases from pH 2.1 to 4.38 and then increases as the pH is raised up to 8.10. A similar trend was observed for both transferrin and carbonic anhydrase. The initial decrease in migration time at low pH is due to the decrease in anodic EOF as the pH is increased and the increase in migration time above pH 4.38 is due to the decrease in protein charge and greater interaction with the bonded moiety.

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Another feature of the etched chemically modified capillaries is their durabil-ity and reproducibility. Several studies have shown that the column lifetime is at least several hundred injections with many capillaries performing well after 300 to 400 analyses [32,44,51]. Reproducibility studies involving consecutive runs of a particular analyte give %RSD values less than one; and less than two when an initial injection is compared to a result taken after one hundred or more subsequent analy-ses. Capillary to capillary reproducibility is also good with variations in the rela-tive migration of two analytes (α values) on the order of one percent. These results demonstrate that all of the factors involved in the fabrication of the capillaries are reproducible and that the hydride surface and the organic moiety bonded to it are stable as well.

6.5 ConClusIons

Silica hydride-based materials represent an evolutionary chromatographic technology that can provide unique stationary phases for HPLC. The properties of hydride silica and its bonded phases produce a broad range of chromatographic capabilities that are not normally available from the ordinary silica widely used for current commercial products. These stationary phases have been investigated and characterized since the early 1990s and more recently have become a viable commercial product. As the number of users increase, the range of applications that take advantage of the unique properties of these materials (such as operation in three retention modes, dual reten-tion mechanisms under a single mobile phase condition, rapid equilibration, operation in 100% aqueous conditions) will expand accordingly. The ANP capabilities of these phases provide a long sought answer to the retention of many polar compounds using conditions that are compatible with mass spectrometry detection for use in challeng-ing pharmaceutical, biological, clinical, and food product applications. A better theo-retical understanding of how silica hydride phases operate is still needed.

Etched chemically modified capillaries based on silica hydride technology have been shown to possess unique properties that make them suitable for a variety of electrophoretic analyses. The EOF characteristics and biocompatible surface are

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fIgure 6.22 Separation of human IgG and human serum albumin on etched C5 capil-lary at pH 3.0. Detection at 210 nm. V = 25 kV. Injection hydrodynamic at 50 mbar for 8 s. (Adapted from Pesek, J. J., Matyska, M. T., and Salgotra, V. J., Electrophoresis, 29, 1, 2008.)

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especially suited for the analysis of small basic compounds, peptides, and proteins. Coupling to mass spectrometry should provide a useful tool for proteomic applica-tions. Numerous examples of analyses of these types of compounds have already been demonstrated. In addition, both the durability and reproducibility of this elec-trophoretic separation format are excellent.

aCknowledgments

The financial support of the National Institutes of Health (GM079741-01) and the National Science Foundation (CHE 0724218) is gratefully acknowledged. One of the authors (JJP) would like to acknowledge the support of the Camille and Henry Dreyfus Foundation through a Scholar Award. The advancement and commercial-ization of silica hydride materials would not have been possible without the support and dedication of Microsolv Technology Corporation.

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Related Technologies, 1996, 19: 2843. 5. Matyska, M.T., Pesek, J.J., Pan, X. J. Chromatogr. A, 2003, 99: 57. 6. Pesek, J.J., Matyska, M.T., Yu, R.J. J. Chromatogr. A, 2002, 907: 195. 7. Akapo, S.O., Dimandja, J.M., Pesek, J.J., Matyska, M.T., Chromatographia, 1996, 42: 141. 8. Pesek, J.J., Matyska, M.T., Oliva, M., Evanchic, M. J. Chromatogr. A, 1998, 818: 145. 9. Pesek, J.J., Matyska, M.T., Muley, S. Chromatographia 2000, 52: 439. 10. Cicero, R.L., Chidsay, C.E., Lopinski, G.P., Wayner, D.D.M., Wolkow, R.A., Langmuir,

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13. Gilroy, J.J., Dolan, J.W., Snyder, L.R. J. Chromatogr. A, 2003, 1000: 757. 14. Pesek, J.J., Matyska, M.T., Dawson, G.B.,Wilsdorf, A., Marc, P., Padki, M. J. Chromatogr.

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289

7 Multidimensional Gas Chromatography

Peter Quinto Tranchida, Danilo Sciarrone, and Luigi Mondello

7.1 IntroduCtIon

The invention of the open-tubular capillary (OTC) column [1] can certainly be considered one of the fundamental events in the history of gas chromatography (GC), since its introduction in 1952 [2]. Through Golay’s intuition, the unsuspected high complexity of many real-world samples has been revealed in the last five decades. Today, single-column GC is the most commonly applied method for the analysis of volatiles and semi-volatiles.

If an OTC column is operated under ideal analytical conditions, for a given sepa-ration, then the two aspects which govern a GC analysis are (1) peak capacity (nc), and (2) stationary-phase selectivity. Obviously, the former parameter is related to the column characteristics (length, internal diameter, stationary phase thickness, intensity of analyte-stationary phase interaction), while the latter feature is related to the chemi-cal composition of the stationary phase. Ideally, a chromatographic analysis will be

Contents

7.1 Introduction .................................................................................................. 2897.2 Heart-Cutting Two-Dimensional Gas Chromatography: Historical

Details and Fundamental Principles ............................................................. 2937.2.1 Modern MDGC Systems and Applications ...................................... 295

7.3 Comprehensive Two-Dimensional Gas Chromatography: Fundamental Principles ................................................................................3027.3.1 Modulators ........................................................................................3057.3.2 Operational Parameters: Method Development................................ 310

7.3.2.1 Column Selectivities .......................................................... 3107.3.2.2 Temperature Program(s) .................................................... 3107.3.2.3 Gas Flows ........................................................................... 3117.3.2.4 Detection ............................................................................ 312

7.3.3 Applications ...................................................................................... 3147.3.3.1 Comprehensive 2D GC Combined with Mass

Spectrometry ...................................................................... 3157.3.3.2 Spatial Order and Enhanced Sensitivity ............................ 319

References .............................................................................................................. 326

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achieved in the minimum time, for a given sample, if a capillary is characterized by the most appropriate stationary phase and generates the minimum required peak capacity.

The number of peaks that can be stacked side by side (with a specific resolu-tion value) in the one-dimensional space generated by a capillary column is usually in the 200–600 range. However, it has been emphasized, particularly during the last 20 years, that such peak capacities fall far from the separation-power require-ments for many applications. Giddings demonstrated, from a theoretical standpoint, that “no more than 37% of the peak capacity can be used to generate peak resolu-tion” and that “many of the peaks observed under these circumstances represent the grouping of two or more close-lying component,” to conclude that “s (the number of single component peaks) can never exceed 18% of nc” [3]. Although the latter value is a generic one, not considering stationary-phase selectivity, it provides an excellent indication of the resolving power of a monodimensional chromatography system.

From Equation 7.1, which measures resolution for a pair of compounds with capacity factors equal to

RN k

kSB

B

= −

+

4

11

αα

(7.1)

kA and kB, it can be easily derived that RS can be doubled if the peak capacity is increased by a factor of four. It follows that an evident improvement in peak resolu-tion can only be achieved by extending column length considerably. Such a modifi-cation is commonly undesirable and often not a practical solution: a 400 m column, generating a 1.3 million plate number, did not succeed in the total separation of a fuel sample [4]. With regards to column selectivity, from Equation 7.1 it can be derived that at lower values an increase in the separation factor will determine a substantial increase in resolution, namely, up until an α value of ~ 3 (α −1/α = 0.66). At higher separation factor values, the function tends to unity and levels off. It can be con-cluded that selectivity has a big effect on resolution and, hence, it is of the upmost importance to choose the most appropriate stationary phase for a given separation. However, in GC, it can be affirmed that irrespective of the liquid stationary phase, analyte vapor pressures play a major role in all GC separations. No two liquid sta-tionary phases present entirely independent separation mechanisms and, therefore, partial correlation between different stationary phases exist, whatever type of col-umn combination is employed. Studies concerning a wide variety of GC phases have highlighted the lack of entirely different selectivities and the need for novelty in this research field [5]. Finally, an increase in the capacity factor has a substantial effect on resolution only for components with low k values (≤ 3). The different degrees of influence, of N, α, and k on resolution, can be observed in Figure 7.1.

As aforementioned, the complete separation of the compounds of interest, with the least time-expenditure, must always be the primary aim in any GC analysis. Now, tak-ing for granted that the most appropriate sample preparation process has been carried out, the reasons behind insufficient GC resolution can be related essentially to five factors, namely: (1) the lack of column selectivity, (2) the lack of column peak capac-ity, (3) the combination of factors (1) and (2), (4) suboptimum GC parameters, and (5) excessively high sample complexity. Such events occur commonly in GC and can

84534.indb 290 11/5/09 12:28:55 PM

Multidimensional Gas Chromatography 291

lead to difficulties or possible mistakes in the qualitative/quantitative analysis of target analytes. However, in several instances co-elution is acceptable if the detector can selectively reveal specific substances; or if it consists, in its own right, in an additional separation dimension (mass spectrometry). Consequently, a detector can contribute significantly to the separation power and/or selectivity of a chromatography system.

In the field of separation science, it is very common to distinguish analysts in two well-defined groups:

(1) GC experts who tend to dedicate a great deal of time toward the chroma-tography optimization and are inclined to under-exploit the power of mass spectrometry; as long as the ion source receives entirely isolated analytes (then identified by using MS libraries) no problems occur. However, prob-lems can arise when peak overlapping occurs, and a thorough exploitation of the MS step is required;

(2) MS specialists who do not worry if the ion source receives multi-compound effluent bands, because the mass analyzer can resolve a group of ions on a mass basis. As will be seen, mass spectrometry can be very useful for the unraveling and, hence, reliable identification of overlapping GC peaks. However, the reliability of peak assignment is inversely proportional to the extent of compound co-elution.

In truth, chromatography and MS processes are equally important, should be consid-ered as complementary, and should be pushed to their full potential.

The most effective way of enhancing the resolving power and selectivity of a GC system, considering equivalent detection conditions, is by using a multidimen-sional gas chromatographic (MDGC) system; nowadays, the latter consists basically of the combination of two capillary columns of differing selectivity, with a dedicated

0

1

0

1

2

Column :10 m × 0.50 mm id

R ~( )

R ~ √N

αα – 1

n = 20.000α = 1.05k2 = 5.00

3

4

R

5 10 15 20

1.01 1.02 1.05 1.10 1.15

20 40 60 80 ×103n

k

α

R ~( )k + 1k

fIgure 7.1 Resolution: influence of N, α, and k. (From Cortes, H. J., Multidimensional Chromatography: Techniques and Applications. Marcel Dekker, New York, 1990. With permission.)

84534.indb 291 11/5/09 12:28:56 PM


interface located between them. MDGC approaches can be divided in two large groups, namely, heart-cutting and comprehensive methodologies. Classical heart-cutting MDGC enables the transfer of selected bands of overlapping compounds from a primary to a secondary column of generally the same or similar efficiency, connected by means of a transfer device (either a switching valve or a Deans switch). Preliminary monodimensional applications are necessary to select the first-dimen-sion (defined as pre-column) effluent bands, that require analysis on the secondary column (defined as analytical column) [6,7]. The great advantage of heart-cutting MDGC is that the transferred fractions are subjected to separation on a full-length and relatively high-efficiency conventional column. The higher instrumental com-plexity and the moderate operational expertise required can represent a drawback; moreover, the number of samples that can be re-injected on the analytical capillary is restricted because excessive (or continuous) heart-cutting would cause the loss of a substantial part of the primary column resolution. In terms of peak capacity, the latter equals the sum of that of the first and second dimension, the latter multiplied by the number (x) of heart-cuts [nc1 + (nc2 × x)]. However, if the entire sample requires analysis in two different dimensions, then a different analytical route must be taken.

The complete separation of a sample in two dimensions of a chromatography setup was first achieved more than sixty years ago [8]: a mixture of wool amino acids were placed in the corner of a sheet of cellulose; the latter was developed in one direction with one solvent, and then in an orthogonal direction by rotating the paper by 90°, using a different solvent. The experiment described can be considered as the first comprehensive two-dimensional chromatography application.

The introduction of comprehensive two-dimensional GC (GC × GC) in 1991 marked a turning point in the history of GC [9]. The separation power leap, observed passing from monodimensional GC to GC × GC, is probably greater than that between the packed and OTC column. A multitude of samples have been rediscovered, from a chromatographic standpoint, after the introduction of comprehensive 2D GC, and a great deal of information relative to many samples remains to be unraveled. It is still the enjoyment of many GC × GC analysts (and of the authors of the present chapter) to discover the unsuspected complexity of what are considered as well-known matrices.

A typical comprehensive 2D GC application is achieved on two columns with a different selectivity, connected by using a transfer device (usually situated at the head of the secondary column), defined as modulator. The latter is the heart of a GC × GC instrument and functions in a continuous mode throughout the analysis. Any modula-tor must enable the collection of narrow analyte bands from a primary conventional column and inject them onto a short microbore capillary segment. The time period required to achieve each heart-cutting process is defined as the modulation period (typically in the 4–8 second range), and it corresponds to the analysis time of each second dimension separation. The time required to ultimate the heart-cutting process is defined as the modulation period, and corresponds to the time-window of each analysis in the second dimension. Ideally, a GC x GC system should generate a peak capacity equivalent to the product of the peak capacities (nc1 × nc2) relative to each dimension. Although it will be shown that such a value certainly exceeds the realistic peak capacity, comprehensive 2D GC is certainly the most powerful tool available today for the analysis of complex volatile samples.

84534.indb 292 11/5/09 12:28:56 PM


Before a more in-depth discussion on heart-cutting and comprehensive MDGC procedures, it must be emphasized that the objective of the present chapter is to describe the fundamental characteristics of MDGC technology, to show a series of demonstrative applications (in various research fields) and to discuss current-day limitations and recent developments, as well as future prospects. More attention will be devoted to the more recent, and probably more exciting, of the two approaches; that is, comprehensive two-dimensional GC. With regards to heart-cutting MDGC, considerable attention will be directed to ultimate-generation instrumentation, which appears to satisfy all the requisites for user-friendly, effective analyses. In truth, in the field of classical MDGC research there appears to be little room for further instrumental improvement. Perhaps the development of a combined MDGC system, enabling both heart-cutting and comprehensive experiments, could be the next, most important, evolutional step. A comprehensive description of both MDGC method-ologies, from their introduction up until today, is outside the scope of the present contribution.

7.2 heart-CuttIng two-dImensIonal gas Chromatography: hIstorICal detaIls and fundamental prInCIples

In terms of peak capacity, comprehensive two-dimensional GC is certainly the most powerful method available today for volatile analysis. However, considering the obliged short length of the second column, the peak capacity generated in a single GC × GC cut is always much lower than that produced by a classical MDGC system. Consequently, the latter technique can be considered as an ideal choice whenever the 2D analysis of a limited number of 1D fractions is required. During the last five decades, heart-cutting MDGC has been extensively used for the analysis of petroleum products [10], environmental pollutants [11], and flavors and fragrances [12–14].

The most challenging task in the construction of an MDGC instrument has always been the development of the transfer device. Heart-cutting MDGC was first introduced in 1958 by Simmons and Synder [15], who described a boiling-point first- dimension separation of C5–C8 hydrocarbons, and a polarity-based separation of each of the four hydrocarbon groups in the second dimension, in four separate appli-cations. The results attained by using a valve-based instrument were quite remark-able and the two scientists stated that “separations can be obtained with this column arrangement which are not normally possible with previously described arrange-ments of single columns and multiple columns connected in series.” Although col-umn technology has evolved considerably during the last 50 years, this statement is still fully valid today.

Heart-cutting 2D GC is generally employed for the analysis of a part of the ini-tial sample, while the remaining fraction is of no interest in analytical terms. The methodology is rarely used whenever all sample constituents need to be analyzed, although in principle it is possible to carry out multiple-cut, multiple-analysis MDGC experiments, such as that described in 1958. It is obvious that the main disadvantage of a multi-analysis application is the high time cost; however other alternatives have

84534.indb 293 11/5/09 12:28:56 PM


been developed: for example, parallel traps located between the two dimensions can be used to store single heart-cuts, and then analyzed in a sequential mode on the sec-ondary column. A further solution consists of the use of a series of second dimension columns, one for each 1D heart-cut [6]. Although such systems can fulfill the initial analytical objectives, they result of elaborate construction and unpractical use.

The first use of capillary columns in heart-cutting MDGC was reported in 1964 [16]: a pneumatically operated diaphragm 6-port valve was positioned between two 150 ft capillaries; when the valve was in the cutting mode columns 1 and 2 were connected in series, while when the valve was in the standby mode (an ordinary single-column analysis) column 2 was bypassed by using a flow restriction tube (Figure 7.2). The effectiveness of the primordial MDGC instrument was demon-strated in the separation of a series of benzene derivatives.

The concept of pressure switching was introduced by Deans at the end of the 1960s [17]; the approach introduced a series of undoubtable advantages, such as the lack of contact between sample constituents and valve mechanical parts; no temperature restrictions, memory effects, or artefact formation; as well as a neglectable contribu-tion to band enlargement. Apart from heart-cutting, the methodology also enabled basic operations such as venting and backflushing, processes readily achieved by using mechanical valves.

Substantial technological advances in valve design were accomplished in the 1980s, with the introduction of micro-volume connections, use of thermally sta-ble elastomeric material, and elimination of unswept volumes. Satisfactory results were attained on a test solution and real-world samples, with no apparent problems related to valve activity observed [18].

Traditional MDGC applications can be carried out using a single or a twin-oven configuration, the latter being the most preferable option. The employment of a twin-oven instrument was reported, presumably for the first time, about 35 years ago

Injectionport

Flowswitching

valve

Flowrestriction

FID

Capillarycolumn 1

Capillarycolumn 2

fIgure 7.2 Scheme of a primordial valve-based MDGC system. (From McEwen, D. J., Anal. Chem., 36, 279, 1964. With permission.)

84534.indb 294 11/5/09 12:28:57 PM


[19]: the analysis of tetrahydrocannabinol in blood was achieved by using a packed column in the first oven and a capillary one in the second one, while the transfer device consisted of an 8-port switching valve. The pre- and analytical columns were operated under temperature-programed and isothermal conditions, respectively. The authors reported that the main reason for using such a configuration was related to the high sensitivity of the second-dimension detector, an ECD, toward column bleed. In present-day MDGC applications, the major disadvantages that a twin-oven system overcomes are essentially two, namely: 1) if two columns are housed in a single oven, then the maximum operational temperature is related to the less thermally stable capillary (if a polydimethylsiloxane phase is used in combination with a polyethylene glycol one, then the maximum GC temperature becomes 250–260°C); and (2) first- dimension fractions are directed onto the secondary column at a specific temperature, which may, or may not be the most appropriate to fully exploit the 2D selectivity. For example, highly retained 1D compounds are introduced onto a second dimension at high temperatures, under-utilizing the potential separation power. It is obvious that the economical expenditure related to use of dual ovens is considerably higher.

The MDGC instrument described in [19] was also characterized by the presence of what the authors defined as a “cold trap.” The latter was cooled down with water and was employed to entrap a specific first dimension analyte fraction. Cold-trapping is currently achieved in the MDGC field by using cryogenic gases (liquid N2 or CO2), is usually applied between the two dimensions, and is commonly used for three objec-tives: (1) Enhancing peak capacity by reducing the width of a column outlet analyte band to that of an inlet one. It is well-known that the peak capacity generated by a GC system is inversely proportional to the width of the injected sample band. For example, if a 25 cm/s 1D outlet gas linear velocity is considered, and a peak with a 10 s base width is transferred onto a second column, this essentially means that a plug measuring at least 2.5 m has been injected! Leaving aside band broadening, and con-sidering that all of the band components start moving simultaneously, then not more than 12 equally spaced peaks could be located at the same time on a 30 m capillary! On the contrary, if the same band was focused down to a length of 1 cm, then 3000 peaks could be theoretically stacked side by side along the 30 m column. It must be added that the values given provide very approximate indications; (2) enhancing sensitivity through solute re-concentration. It is obvious that the effects of Gaussian analyte distribution are nullified through an effective trapping process; (3) the detec-tion of extremely low-amount compounds, overlapping (or not) with other sample constituents, applying multiple-trapping processes; the latter are carried out on the same fraction, in sequential MDGC applications. It must be added that focusing can be attained if, during heart-cutting, the second oven is kept at a low temperature (e.g., ambient temperature).

7.2.1 modern mdGc SyStemS and applicationS

Following the introduction of benchtop GC-MS systems and then later of compre-hensive 2D GC, heart-cutting MDGC has suffered a gradual decrease in popularity over the last decades. However, this powerful methodology has been recently gain-ing a firmer foothold in both academia and industrial areas, due to the introduction

84534.indb 295 11/5/09 12:28:57 PM


of highly effective and user-friendly instrumentation. In fact, modern-day MDGC systems equipped with accurate electronic pressure control units are of much less elaborate construction than they were in the past, do not require high expertise levels, and produce highly reliable and reproducible results.

Schemes of an MDGC transfer system (in the standby and cut positions), based on the Deans switching principle and used in an ultimate generation, twin-oven MDGC-MS instrument, are shown in Figure 7.3 [20].

In both configurations (the application was carried out on gasoline constituents), an advanced pressure control unit (AUX) supplies a gas flow at constant pressure (in this case 130 kPa) to an external (with respect to the GC oven) fused-silica restriction (R3) and to a three-way electrovalve (EV). The latter is connected to two metallic branches, one with another fused-silica restriction (R2) and one without: R2 produces a pressure drop (ΔP2 = 1.2 kPa) slightly higher than that generated by R3 (ΔP3 = 0.5 kPa). In the standby configuration (Figure 7.3a), the AUX pressure is reduced on the side of the first dimension (129.5 kPa), while it reaches the second dimension branch, passing through the electrovalve, unaltered. It is clear that using such a configuration, analytes eluting from column 1 are directed to Det1. The instru-ment is switched to the cutting mode (Figure 7.3b), by activation of the electrovalve: the 1D branch pressure remains unaltered, while the 2D branch pressure becomes 128.8 kPa. In this case, the primary column flow is directed onto the secondary col-umn, the FID 1 flame is maintained by a gas flow that derives from the APC unit. The first and second dimension columns are linked by using a low dead-volume, chemically inert, and thermally stable stainless steel interface; the latter, housed in the first GC oven, is also connected to the 1D and 2D metallic branches, and to Det1 (in this case a flame ionization detector). The second column is located in an additional GC oven, which is connected to the first by means of a heated transfer

R3(∆P3= 0.5 kPa)

2DR1

Aux

1D

Det1

R2

129.5 kPa

(a) (b)

130.0 kPa

130.0 kPa

ū1D 25.0 cm/s ū1D 25.0 cm/s

EV

GC1

1D2DR1

Aux

Det1

R2 (∆P2 = 1.2 kPa)R3

129.5 kPa128.8 kPa

Recovery 100%

EV

130.0 kPa

ū2D 54.0 cm/sGC1

fIgure 7.3 Schemes of the Deans switch MDGC interface in the standby (a) and cutting (b) modes.

84534.indb 296 11/5/09 12:28:58 PM


line. The latter can be subjected to cryogenic cooling (using liquid N2), followed by rapid electrical heating if desired. The instrument is automatically controlled by using dedicated software, which also enables the calculation of fundamental opera-tional parameters, such as gas flows, linear velocities, and analyte recovery. Method optimization becomes a rather simple task if correct gas linear velocities are known; for example, it can be seen in Figure 7.3 that the linear velocities applied were ideal and suboptimum in the first and second dimension, respectively (two 30 m × 0.25 mm ID columns were employed).

The instrument described in [20] has been employed for the qualitative/quantita-tive analysis of perfume allergens [21]: a 14-cut experiment was carried out on a commercial perfume, with the heart-cut time windows defined on the basis of aller-gen linear retention index values. The following apolar/polar column combination was employed: 1D 30 m × 0.25 mm ID × 0.25 µm 5%diphenyl/95%polydimethylsiloxane + 2D 30 m × 0.25 mm ID × 0.25 µm 100% polyethylene glycol. A chromatogram relative to the first-dimension analysis (the position of each cut is numbered), after heart-cutting, is illustrated in Figure 7.4.

Comparing a chromatogram derived from an analysis with the transfer device maintained in the standby position (a conventional GC run), and the chromatogram shown in Figure 7.4, it was observed that the degree of retention time shift was neglectable. This undesirable effect occurs when the first-dimension gas flow differs in the standby and cut modes. In this case the 1D pressure drop was always constant, namely, Pinlet − (PAUX − ΔP3). The 2D TIC chromatogram is shown in Figure 7.5.

Twelve target analytes are nicely separated from other matrix interferences; many of the allergens overlapped severely with other perfume analyst in single-column applications. Finally, the general spectral purity was satisfactory, with MS library % matches always higher than 90%.

00.000.250.500.751.001.251.501.752.002.252.502.753.003.253.503.754.00

uV(×

10,0

00)

10 20 30 40I II III IV V VI

VII VIIIIX

XXIIXI

XIII

XIV

50 60Min

70 80 90 100 110 120

fIgure 7.4 First-dimension FID chromatogram of a commercial perfume, after 14 cuts. (From Mondello, L., Casilli, A., Tranchida, P. Q., Sciarrone, D., Dugo, P., and Dugo, G., LC GC Eur., 21, 130, 2008. With permission.)

84534.indb 297 11/5/09 12:28:59 PM


A further highly effective MDGC instrument, characterized by a microfluidic transfer system, has been recently reported [22]. The interface consisted of a leak free, thermally stable, inert, minute dead volume, Deans switch device; devel-oped by using capillary flow technology: flow channels and through holes are etched into stainless steel plates halves, which are folded, heated to over 1000°C, and using high pressure to produce a diffusion-bonded metallic sandwich. The internal channels, created in a similar manner to the manufacture of integrated cir-cuits, are coated with a deactivation layer. Metal ferrules are employed to provide leak-free connections. Electronic pressure controllers are used to create the opti-mum conditions for standby, cutting, and backflushing processes. Such instrumen-tation makes heart- cutting MDGC accessible to anyone with basic, conventional GC knowledge.

A highly flexible classical MDGC, in which capillary flow technology was com-bined with low thermal mass (LTM) GC, has been recently described [23]. The microfluidic interface was used successfully in multiple-cut and backflushing opera-tions, while LTM methodology was exploited independently in both dimensions, for rapid column heating and cooling. The benefits of LTM GC, in terms of sample throughput enhancement, have been described [24]. A nice example of the high potential of the above described instrument, exploited for the determination of light oxygenated compounds in a fuel sample, is illustrated in Figure 7.6.

The target compounds were separated in the second dimension (10 m × 0.25 mm ID × 1.2 µm 100% polyethylene glycol) using the following temperature pro-gram: 45°C (3 min) to 150°C (3 min) at 30°C/min (Figure 7.6a). For character-ization of the hydrocarbons in the first dimension (30 m × 0.25 mm ID × 1.0 µm 100% dimethylpolysiloxane), a different temperature program was applied: 150°C

01.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Min80.0 90.0 100.0 110.0 120.0 130.0

TIC*1.05,00,0001,000,0001,500,0002,000,0002,500,0003,000,0003,500,0004,000,0004,500,0005,000,0005,500,0006,000,0006,500,0007,000,0007,500,0008,000,0008,500,0009,000,0009,500,000

10,000,00010,000,000

1 3

6

816

I.S.5

711

13

12

22

14

fIgure 7.5 Second-dimension MDGC-MS TIC chromatogram of perfume allergens. Peak identification: 1) limonene; 3) linalool; 5) citronellol; 6) neral; 7) geraniol; 8) geranial; 11) hydroxy-citronellal; 12) cinnamic alcohol; 13) eugenol; 14) coumarin; 16) α-isomethylionone; 22) hexyl cinnamaldehyde. I.S.: 1,4-dibromobenzene. (From Mondello, L., Casilli, A., Tranchida, P. Q., Sciarrone, D., Dugo, P., and Dugo, G., LC GC Eur., 21, 130, 2008. With permission.)

84534.indb 298 11/5/09 12:29:01 PM


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84534.indb 299 11/5/09 12:29:02 PM


(4 min)–300°C (3 min) at 30°C/min (Figure 7.6b). To shorten the analytical time, a demonstrative backflush operation on the hydrocarbon fraction was also carried out (Figure 7.6c).

Let it be hypothesized that 2 compounds (A and B) are analyzed in a single GC oven, on two directly coupled columns with different selectivities (e.g., an apolar– polar set), under ideal conditions of temperature and gas flow. In such an application all sample constituents are subjected to two separations, on two capillaries connected in series. However, the approach is not a multidimensional one because the separa-tion achieved in the first dimension can be degraded in the second; the possible outcomes are four, namely, (1) A and B remain separated on both columns; (2) A and B overlap on both columns; (3) A and B are resolved on column 1, but then co-elute on column 2; and (4) A and B overlap on column 1, and are separated on column 2. Considering factors 1 and 2, the use of a second column is superfluous; in the case of factor 3, the secondary column has a disastrous effect, while the contrary is true in the case of factor 4. If this simple example is extended to a complex sample, then the number of possible compound combinations becomes extremely high. However, the final number of compounds that we could expect to separate on such a twin-phase setup, would probably not be much different from that attained using a single-phase column of the same dimensions. The final separation result is controlled mainly by the total plate number, selectivity differences have been hardly or not at all exploited, and hence, the entire separation potential of the system is not expressed. One way to improve the chromatography of the system would be to use twin ovens and, hence, develop a temperature program for each stationary phase. A further way of improv-ing selectivity can be achieved by manipulation of the gas flows in each column. In 1985, Kaiser et al. reported that great selectivity changes occurred in series-coupled capillaries of different polarities, when the gas flows through each column were manipulated [25]. Several interesting experiments, focused on the application of columns junction-point pressure pulses, have been described by R. Sacks and col-laborators [26–28]. A scheme representing a “series-coupled column ensemble with stop-flow operation” is shown in Figure 7.7.

Midpoint gas flow regulation is carried out by using pressure pulses, produced by a pneumatically activating valve (V). The valve is connected on one side to the columns junction point by using a deactivated fused-silica capillary segment and a glass splitter, and on the other to an aluminium ballast chamber. The pressure in the chamber is controlled by an electronic pressure controller. An FID is also connected to the junction point, by using another fused-silica column segment. If a pressure pulse, equal to that of the column-set head pressure, is applied to the capillary junction point, then the flow in the first dimension is stopped, while elution continues in the second dimension. The dual-column stop-flow instrument was employed in combination with a third separative dimension, namely, a time-of-flight (ToF) mass spectrometer, in the high-speed analysis of essential oil com-pounds [28]. Such MS systems possess the unique capacity to unravel overlapping GC peaks through spectral deconvolution (the topic will be discussed more in depth in the comprehensive 2D GC section). Figure 7.8 illustrates three chromato-grams relative to the analysis of nine compounds, using the tandem-column ToF MS system.

84534.indb 300 11/5/09 12:29:02 PM


Approximately 10% of the primary polar column (7 m × 0.18 mm ID × 0.2 µm tri-fluoropropylmethyl polysiloxane) effluent was directed to an FID; the chromatogram relative to the 1D analysis (Figure 7.8a) shows that peaks 3 and 4 undergo a com-plete co-elution, while compounds 5 and 6 are partially overlapped. Observing the middle TIC chromatogram, representing an application carried out without the use of mid-pressure manipulation, it can be concluded that the first-dimension separation has been degraded: peaks 1 and 2, which were resolved on the primary column, co-elute completely; peaks 3 and 5 are now entirely separated from components 4 and 6, respectively; however, peak 4 now overlaps completely with peak 6; compounds 7, 8, and 9, previously resolved, show no degree of resolution. At this point a four-point stop-flow experiment was achieved, at times indicated by arrows in Figure 7.8a: considering the first stop-flow point (left-hand arrow), compound 1 elutes onto the secondary column, while compound 2 is stopped for 5s in the first dimension. The chromatography result, illustrated in Figure 7.8c, indicates that peaks 1 and 2 are fully resolved using the stop-flow approach. The 1D gas flow was interrupted an additional three times, once to separate peaks 4–6 and twice to resolve components 7, 8, and 9. In terms of MS operation, spectral deconvolution was necessary for the chromatogram illustrated in Figure 7.8b, but was not required in the stop-flow application. A limit of the approach, reported by the authors, is that to use the stop-flow approach, target peaks must be base-line resolved. For example, if peaks 5 and 6, illustrated in Figure 7.8a, co-eluted in the second dimension, then the stop-flow approach could not have been used to separate them. For this reason, the stop-flow method cannot be defined as a truly multidimensional one, because in some cases it is not possible to avoid the degradation of the first-dimension separation. Although the stop-flow methodology is probably not suitable for highly complex samples, because these produce chromatograms with a severe degree of overlapping, it appears of high interest for samples of low or medium complexity.

CG

CG

C1 C2

MS

FID

PCBC

V

I

fIgure 7.7 Scheme of the series-coupled column system with stop-flow operation. Abbreviations: C1: first dimension; C2: second dimension; V: pneumatic valve; BC: ballast chamber; PC: pressure controller; I: injector; CG: carrier gas source.

84534.indb 301 11/5/09 12:29:03 PM


7.3 ComprehensIve two-dImensIonal gas Chromatography: fundamental prInCIples

In the field of comprehensive 2D-GC applications, it is of common use to employ a nonpolar or weakly polar column as primary column and, thus, separation is achieved essentially (although not entirely) on a boiling-point basis. Each isolated 1D fraction is subjected to a fast 2D analysis, generally on a moderately or highly polar capillary: isovolatile solutes are isolated in relation to the degree of functional group polarity-

10

1 2

1,2

2

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20 30 40 50Time (s)

60 70

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9

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5

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(b)

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15 20 25 30 35 40 45 50 55

fIgure 7.8 Test-mixture chromatograms relative to the FID primary-column analysis (a), to the TIC MS result without stop-flow operation (b), and to the TIC MS analysis with stop-flow operation (c). Peak identification: (1) camphene; (2) furfural; (3) eucalyptol; (4) ter-pinolene; (5) benzaldehyde; (6) octanal; (7) β-caryophyllene; (8) geranyl acetate; (9) eugenol. (From Veriotti, T. and Sacks, R., Anal. Chem., 73, 3045, 2001. With permission.)

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based interactions; such a column combination, defined as orthogonal, guarantees slow and rapid peak generation in the first and second dimension, respectively. It is obvious that a GC × GC separation will be all the more effective in relation to the degree of difference between the two displacement mechanisms.

An example of how the (dual-stage) thermal modulation process initially worked is shown in Figure 7.9.

Initially, a narrow band of first-dimension effluent, in this case containing three hypothetical co-eluting compounds, is generated at the modulator head (primary band compression); the latter is maintained at a sufficiently low temperature (phase I); ana-lyte mobilization is achieved through a heating shot, of millisecond duration (Δ1), and directed to the first segment of the modulator (phase II); the isolated fraction, trans-ported by the carrier gas, impacts a second cold modulator spot ( secondary band com-pression); meanwhile, volatiles begin to accumulate at the modulator head, which has rapidly cooled down (phase III); the narrow band inside the modulator is injected onto the second dimension, through another heating shot (Δ2), directed this time to the sec-ond segment of the modulator tube (phase IV); ideally, the different secondary dimen-sion selectivity will enable the delivery of three separated analytes to the detector (phase V); it must be emphasized that during each 2D analysis, modulation is carried out on the subsequent fraction. It is worthy of note that even if GC × GC experiments are currently achieved through a variety of modulation systems, the principles of the afore-described twin-stage process remain essentially unaltered. Thermal modulation has a beneficial outcome on sensitivity: the band compression effect produces a signal-to-noise increase in the 10–50 factor range, depending on the modulator type and the specific GC × GC operational conditions. Second dimension analyte bands are typi-cally very narrow, both in time and space, and require fast detection systems (a sam-pling frequency of minimum 50 Hz is necessary) for proper peak construction.

The analytes resolved in each rapid 2D analysis are characterized by the same first-dimension retention time (expressed in minutes) and different second dimension

Dual-stage modulator

Δ2

Δ1

Detector

I

II

III

IV

V

fIgure 7.9 Schematic of a dual-stage modulation process carried out on three co-eluting compounds (represented by symbols , , ).

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elution times (expressed in seconds). A fundamental requisite is that all compounds must reach the detector before the next 2D analysis and, thus, within the modulation time-window; wraparound is a phenomenon that occurs if a second-dimension reten-tion time exceeds the modulation period. If a 4000 sec GC × GC application with a 5-sec modulation period is considered, then eight hundred 5-sec 2D chromatograms, stacked side by side, will form a (monodimensional) comprehensive 2D-GC chro-matogram (only a single detector is used). In an ideal GC × GC application, each peak eluting from the first column is subjected to several modulations (at least three), in order to maintain the degree of 1D resolution already achieved. It is obvious that it is entirely impractical to evaluate a raw GC × GC chromatogram as such; in fact, dedicated software is necessary to generate a bidimensional separation space: the single rapid chromatograms, positioned orthogonally to an x-axis, are characterized by first-dimension retention times that are usually expressed in minutes. The com-pounds resolved in the second dimension, aligned along a y-axis, are characterized by an oval form and with elution times that are expressed in seconds. The color and dimension of each spot is directly related the detector response. The occurrence of peak overlapping is greatly reduced, because this undesirable event would require equal capacity factors on two different stationary phases. In fact, in GC it is rather rare to encounter two compounds with equal linear retention indices on both an apo-lar and a polar stationary phase. Comprehensive GC peak quantitation is achieved as follows: the pulsed peak areas relative to the same compound in each fast 2D chro-matogram are summed; again, the use of dedicated software for GC × GC quantita-tion is mandatory. No differences should be observed comparing unmodulated and modulated quantitative results for a single component.

It is widely accepted throughout the GC × GC community that any 2D analysis must abide the following rules [29]:

a. Any two peaks that are resolved in the first dimension must remain isolated in the second dimension; as aforementioned this objective can be achieved with at least three modulations per peak.

b. All sample constituents are analyzed on two stationary phases with distinct separation mechanisms.

c. The elution profiles in both dimensions are maintained.

It must be added that in several published GC × GC separations point a) is not always met: modulation sampling frequencies are nearly always in the 0.25–0.125 Hz range and require 1D peak widths in the 15–25 second range. Such a condition is rarely observed for all peaks across a GC chromatogram, unless the analysis is slowed down considerably. If a peak is under-modulated in GC × GC (e.g., 1 or 2 samplings), there is a good possibility that it will be partially remixed with a vicinal peak. If the overall analytical objectives have been reached, then such an event is acceptable.

In general, there are five main advantages of comprehensive over conventional GC methods:

1. Speed—comparable to very fast GC considering the number of peaks resolved/unit of time.

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2. Selectivity—two stationary phase of different selectivity are employed. 3. Sensitivity—thermal modulation is normally achieved using cooling gases,

generating a beneficial effect on S/N ratios. 4. Separation—enhanced resolving power. 5. Spatial order—the 2D chromatogram formation of chemically similar com-

pound patterns.

As will be illustrated, point (5) is of great help in the identification of unknown compounds, when: no pure standard components are available; an experimental MS spectrum is very similar to others (i.e., fatty acid methyl esters) or there is no match with an MS library spectrum.

7.3.1 modulatorS

Almost all modern GCs can be fitted with a modulator, and carry out GC × GC experiments, provided that the instrument is provided with a rapid detection system. Virtually any comprehensive 2D GC analyst has stated at one time or another that the modulator is the heart of the system. The primordial modulators did achieve their analytical objectives, but were characterized by lack of robustness [9,30]. More effi-cient dual-stage modulators, such as the longitudinally modulated cryogenic system (LMCS) [31] and the thermal sweeper [32,33], were developed right at the end of the 1990s, stimulating an upsurge in the diffusion of the methodology. The former system, a cryo-trap of approximately 3 cm length (Figure 7.10), is located at the head of the secondary column and entraps/focuses effluent fractions through an internal CO2 flow that generates intense cooling (typically 100°C below the GC oven tem-perature). Following the entrapment step, the cold region is exposed to the GC oven heat through the longitudinal movement of the trap along the column, and, thus, the entrapped volatiles are launched onto the secondary column.

The thermal sweeper, illustrated in Figure 7.11, consists essentially of a slotted heater (S), rotated by means of a shaft. Band entrapment/focusing is achieved at the GC oven temperature, on a capillary segment (A) with a thick stationary phase coat-ing (phase-ratio focusing), located between the two dimensions. The heart-cutting-zone compression-band injection sequence is achieved through the anticlockwise rotation of the heater over the aforementioned column. The entrapped solutes are expelled onto an uncoated column (P).

Since the introduction of the LMCS system, several CO2 and liquid N2 jet-based modulators have been developed and have gradually conquered the GC × GC scene. However, it must be added that cryogenic modulation is usually a rather costly issue, due to the high requests of cooling gases per analysis. Consequently, the concept and development of cryogenic-free modulation is of high interest.

Pneumatic-modulated GC × GC was first described by J. Seeley et al. in 2000 [34]: a six-port diaphragm valve was located between the first and second dimension; two stages characterized the modulation process, namely, a collection stage, during which a primary column band was accumulated in a valve sample loop, followed by a reinjection stage, during which the first dimension fraction was launched onto the secondary column, using a very high flow rate. The valve was held in the

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Injector M

S

C1A P

C2

C3

1D 2D

Detector

fIgure 7.11 The thermal sweeper. Details are reported in the text. (From Mondello, L., Lewis, A. C., and Bartle, K. D., Multidimensional Chromatography. © John Wiley & Sons Limited, West Sussex, 2002. With permission.)

Injector

Detector

T

1D

2D

Column join

MN2 inletCO2 inlet

fIgure 7.10 The longitudinally modulated cryogenic system. Details are reported in the text. (From Mondello, L., Lewis, A. C., and Bartle, K. D., Multidimensional Chromatography. © John Wiley & Sons Limited, West Sussex, 2002. With permission.)

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accumulation position for 80% of each modulation period, and in the reinjection mode for the remaining 20% of time; during the latter period the primary column effluent was directed to waste. Using this type of GC × GC configuration the first-dimension bands were compressed in time rather than space; the second-dimension analysis of rather long, rapidly moving effluent fractions would not appear to be the best condition for a very fast GC experiment. Furthermore, a major disadvantage of using a diaphragm valve inside a GC oven is a rather low operational tempera-ture limit, which greatly restricts its application range. Many other flow modulation experiments followed the primary application and were characterized by substantial progress, related particularly to the temperature limitations and to the partial loss of the initial sample [35,36].

Capillary flow technology has been used to construct a pneumatic modulator, exploiting an approach developed by Seeley and collaborators [37,38]; the modulator, illustrated in Figure 7.12 (in the 2D injection state), contains a storage chamber and is connected via two metal branches to a three-way solenoid valve, which receives a controlled gas supply from an auxiliary electronic pressure control module.

The collection chamber is filled periodically with primary column effluent when the solenoid valve is in the collection mode; the time required to fill the cham-ber, typically less than 2 seconds, depends on the 1D gas flow. At the end of the col-lection period, the chamber is flushed by using a very high gas flow (typically 20 mL/min), generated by switching the valve to the flush mode, the duration of which is usually 0.1 second.

Low-cost pneumatic GC × GC is a certainly a highly interesting and desirable approach, however up until today it has not gathered many followers. It appears that further technological improvement is necessary in order to decrease the wide gap that separates flow and cryogenic modulation, in terms of the comprehensive end result. In fact most of the applications described up until now are focused on the analysis

Modulationvalve

H2

Flus

h flo

wdi

rect

ion

Flow modulator

Split/splitless inlet

Column 1 (25–30 m)

Column 2 (5 m)

FID

Collectionchannel

Collection channelis flushed in about100 ms

fIgure 7.12 Deans switch-type flow modulator in the injection state.

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of pure standard compounds and/or on petrochemical samples, rather than complex matrices formed of compounds characterized by a wide range of polarities.

A reportedly robust thermal modulator with electric heating and air cooling, requiring no cryogenic materials, has been described recently [39]: the single-stage device, illustrated in Figure 7.13, uses an 8 cm segment of stationary phase-lined stainless steel tubing (180 µm ID), with the center portion cooled for sample entrap-ment. The steel tube is located in an aluminum block containing a ceramic tube. The cold air, derived from a refrigeration unit, reaches the internal part of the steel tubing, through holes drilled in the ceramic tube, and generates temperatures as low as −30°C. The modulator tube is heated by current pulses from a DC power supply. The overall performance provided by the modulator was indeed promising. It is the authors’ opinion that such directions, related to the origins of GC × GC methodology, appear to be worth taking.

A modulation feature of the highest importance is that related to the width of the analyte band launched onto the second dimension. Under very fast GC condi-tions, using a short microbore column segment, it is obvious that the peak capacity

Pump Exchanger

Injector

GC ovenPower supply

FID

Retainingring

Air

O-ring

Septum Housing

Insulator

Column

Modulator

C-1 C-2

Cryo-cooler

fIgure 7.13 GC × GC instrument with a single-stage air-cooled and electrically heated thermal modulator. Details are reported in the text. (From Libardoni, M., Waite, J. H., and Sacks, R., Anal. Chem., 77, 2786, 2005. With permission.)

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is intimately related to the width of the injected plug. This aspect has been recently defined as a GC × GC bottleneck, because peak capacities are reduced to only a frac-tion of the theoretical values [40].

As aforementioned, the development of a user-friendly, unified heart-cutting and comprehensive MDGC system would be an interesting evolution step. It must be added that some experiments in this research field have already been carried out. Figure 7.14 shows a unified MDGC instrument constructed by Marriott et al. using an LMCS device and a 10-port microswitching valve [41].

When the valve is in the standby state, 1D analytes are directed to FID1 through a 1 m uncoated capillary segment, while a gas flow from a second injector reaches the second dimension (which is passed through the LMCS device), and then FID2.

Inj 1

(a)

(b)

Inj 2

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FID 1 FID 2

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fIgure 7.14 (a) Scheme of the integrated MDGC instrument; (b) Details of the valve connections during standby and cutting modes. Abbreviations: CT: cryotrap; V: 10-port valve; 1D and 2D are the first and second dimension columns; UT: uncoated transfer line. (From Marriott, P., Dunn, M., Shellie, R., and Morrison, P., Anal. Chem., 75, 5532, 2003. With permission.)

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During the cutting stage, 1D analytes are directed to the second dimension, while the FID1 flame is maintained by injector 1. Four operational modes are possible using this highly flexible instrument, namely, monodimensional GC, cryogenically modulated comprehensive 2D GC, classical MDGC, and cryogenically modulated heart-cutting MDGC.

7.3.2 operational parameterS: method development

Comprehensive two-dimensional GC method optimization is undoubtedly one of the most challenging aspects related to the technique: apart from the modulation conditions (modulation period, entrapment, and reinjection temperatures), the most important parameters that must be considered are stationary-phase selectivities, tem-perature gradient(s), column dimensions, gas linear velocities, outlet pressure, and detection settings. It is clear that the scenario is much more complex if compared with a single-column system, while acquired experience in the field of conventional, classical MD, and very fast GC is of great help.

7.3.2.1 Column selectivitiesAs aforementioned, in all liquid stationary-phase GC separations, the analyte boiling point has always a considerable influence on the elution order. Extending the concept to comprehensive GC, it can be affirmed that it is not possible (at the moment) to com-bine two capillaries with entirely orthogonal selectivities. Consequently, it is rather rare that a component is characterized by a high and low retention factor (or vice versa) on the primary and secondary column, respectively. The degree of correlation between the two dimensions, an ever-present factor, has a great influence on the real GC × GC peak capacity value, which is always somewhat far from the ideal value. Many chromatograms reported in the literature present a fan-type analyte distribution, extending from the bottom left-hand side to the upper right-hand one (some will be shown in the present contribution). There is normally a lot of empty space surround-ing these compound locations, because specific 2D regions remain inaccessible.

Although the orthogonal column configuration is usually the first to be tested on any type of new sample, it is often found that other combinations can provide a better result. As for any GC analysis, the most important objectives to be considered are: (1) the separation of the highest number of solutes; and/or (2) the isolation of target analytes. However, in comprehensive GC other issues must not be neglected, namely, the formation of 2D group-type patterns and the avoidance of wraparound. The for-mer phenomenon provides unquestionable advantages in terms of peak assignment, and, whenever possible, must be sought for; the latter phenomenon easily occurs whenever compounds with highly polar functional groups are analyzed on a polar secondary column. However, wraparound can be tolerated as long as the overall analytical objectives have been achieved.

7.3.2.2 temperature program(s)The temperature gradient is another aspect of high importance in GC × GC, requir-ing careful optimization. Comprehensive 2D GC experiments are carried out using either a single or twin-oven configuration, with the latter option being certainly the

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best solution, as it guarantees a high degree of flexibility. Two main disadvantages derive from using a single GC oven, namely: the maximum column-set operational temperature is that of the less thermally stable capillary (e.g., 280°C if a polyeth-ylene glycol phase is employed) and the second-dimension analyses temperatures are entirely dependent on the first-dimension elution temperatures. Primary capil-lary temperature ramps are rather slow, usually in the 1 to 3°C/min range, generat-ing broadened peaks prior to modulation. Using such conditions in a single-oven instrument, modulated fractions reach the secondary column at relatively low tem-peratures, overlapping components interact more intensely with the 2D stationary phase, resolution improves (up until a specific k value), and a greater amount of the bidimensional space is occupied. However, an excessively slow temperature rate can generate wraparound and a sensitivity reduction; if required, both of these negative effects can be avoided by using a second oven. Second-dimension separations are run under near-to-isothermal conditions: for example, if a 2°C/min temperature gra-dient is used, with an 8 s modulation time, then a 0.27°C increase will be observed during each modulation. As a consequence, secondary-column retention times, rela-tive to the same solute, will undergo a slight reduction from one modulation to the next. The main effect, relative to the latter phenomenon, is that 2D spots can present a downwardly incline.

7.3.2.3 gas flowsIn general, a favorable aspect relative to flow modulation is that an independent pressure source is employed for each column, and, thus, distinct gas flows can be used in each dimension. On the contrary, a single flow control unit is normally employed in thermal modulation instruments to generate a gas flow in a column setup, usually of the following dimensions: 30 m × 0.25 mm ID × 0.25 µm df + 1 m × 0.10 mm ID × 0.01 µm df. What can be defined as the traditional combination apparently satisfies the prerequisites of an effective GC × GC analysis, namely, rather slow first dimension, and very fast GC secondary separations. However, as in any GC experiment, one of the most important questions that an analyst must ask himself is “how far is the performance of my developed method from an ideal one?” Now, considering the analytical potential of the traditional GC × GC setup, the answer to this question is “quite far.” In terms of column efficiency, most comprehensive GC analyses are carried out at gas linear velocities that are ideal (or slightly suboptimum) in the first dimension and far too high in the second dimension [42,43]. Very high gas 2D linear velocities are an additional cause of the reduced exploitation of the bidimensional space. A series of first and second dimension average hydrogen linear velocities, using a 30 m + 1 m column setup, are reported in Table 7.1.

As can be observed, if an ideal linear velocity is used in the first dimension, then a great part of the second dimension efficiency is lost. However, if higher secondary capillary efficiency is desired, then a substantial part of the first-column separation power must be sacrificed. It is clear that, with the traditional column combination, ideal gas linear velocities cannot be generated in both dimensions.

In recent research, a GC × GC experiment was carried out under much improved gas flow conditions [44]: a first-dimension capillary was connected, by using a

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T union, to a second-dimension analytical column (which passed through the modu-lator) and a short segment of retention gap; the latter was linked to a split valve, which was manually adjusted to regulate the 2D linear velocity. The approach, which was defined by the authors as split-flow GC × GC, provided a much improved separa-tion when compared to a conventional GC × GC method, in applications carried out on a fish oil and fuel sample. Gas flow optimization is a further GC × GC aspect, where there is room for additional development.

Another interesting approach, defined as stop-flow GC × GC, has been reported [45]; in this methodology, the first-dimension gas flow is stopped for a predefined period, following the reinjection of the modulator-entrapped fraction, onto the sec-ondary capillary. Analyses in the second dimension are achieved by using a gas flow generated by an additional pressure source. At the end of each 2D analysis, the first-dimension gas flow is restored, and the modulator starts to accumulate another effluent band. The main advantage of stop-flow GC × GC is that longer modula-tion periods can be applied, thus generating greater separation space, while first- dimension peaks can still be sampled a sufficient number of times.

7.3.2.4 detectionThe combination of zone compression and high 2D linear velocities generates nar-row and rapid solute bands at the column outlet. Comprehensive GC peak base-widths are usually comprised in the 50–500 msec range, and can vary in relation to the 2D column ID, stationary phase chemistry and thickness, gas flow, and oven temperature. Such effluent bands, altogether comparable to those attained in micro-bore capillary very fast GC, necessitate detectors with high-speed responses to con-centration variations, minimized internal volumes, and high acquisition frequencies (at least 50 Hz) to avoid incorrect peak construction (minimum 10 data points/peak are required) and excessive extra-column band broadening. The most commonly used detection system has been the flame ionization detector, followed by the mass spectrometer. However, a variety of selective detectors have been studied and used in GC × GC (NPD, µ-ECD, SCD, NCD), proving to be very useful in situations where an element-selective is convenient or even necessary. In fact, it is common that the

table 7.1average hydrogen linear velocities Calculated in both dimensions of a Conventional gC × gC system, and respective Column efficiency percentage losses (∆N%)

1d μ (cm/s) ∆N% 2d μ (cm/s) ∆N%

35 −2.9 330 −82.0

30 −5.3 277 −76.3

25 −12.5 215 −62.5

20 −19.2 158 −40.4

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increased peak capacity of a GC × GC system can fail in the total separation of a complex matrix. Consequently, if target analytes contain a halogen, or sulfur, nitro-gen, or phosphorous atoms, then selective detection can become a prime option. A detailed description of the detectors used in GC × GC (apart from the mass spec-trometer) has been recently published [46].

Although it is not to be discussed that a GC × GC-FID contour plot can contain a greater amount of information than a GC-FID counterpart, it is unquestionable that MS detection is still extremely desirable. As will be illustrated, the formation of highly structured GC × GC chromatograms can be of great help in the structural elucidation of unknown compounds. However, it is unthinkable to rely only upon this valuable feature for general, reliable peak assignment.

It is noteworthy that J. Phillips highlighted a series of similarities between GC × GC and GC-MS; that is bidimensional methodologies [47]: in both approaches, sub-samples of the first dimension effluent are delivered to a secondary analytical system. The latter, in GC × GC, is a microbore column segment on which each subsample is subjected to rapid analysis; the separated subsample constituents are positioned along a secondary retention-time axis. In GC-MS experiments, each subsample is com-monly subjected to electron-ionization, with the generated fragments separated and located along a secondary m/z axis. Obviously, both techniques are capable of over-coming first-dimension compound overlapping. The main differences are that a) the second-dimension sampling frequency is much lower in GC × GC, and b) a single retention time is generated by a single compound in GC × GC, whereas several m/z signals are produced by a single constituent in GC-MS. The introduction of a third mass spectrometric dimension in a GC × GC system generates the most powerful analytical tool today for volatile and semi-volatile analytes. Three-dimensional com-prehensive 2D GC-MS has been on the scene for about 10 years, with the first experi-ments appearing at the end of the 1990s [48]: in a well-known fuel application, the column-set effluent was directed to a quadrupole mass spectrometer (qMS), operated in the full scan mode (45–350 amu). The MS system employed was characterized by a far too low spectral acquisition frequency (2.43 Hz), if GC × GC requirements are considered. The analytical problem was circumvented by the authors through the use of a very slow temperature program (30–250°C at 0.5°C/min), which led to a runtime of over seven hours and, more importantly, to broadened 2D peak widths. The inten-tional generation of excessive band broadening greatly reduced the second-dimension peak capacity, but enabled acquisition of around 3 spectra/peak—sufficient for iden-tification purposes. Although the outcome of the experiment was certainly positive, it also highlighted the shortcomings of quadrupole MS for such a GC methodology, in that time period. In fact, the authors stated that a “solution would be to use a time-of-flight MS that can produce hundreds of full-scans per second.”

The suitability of time-of-flight mass spectrometry (ToF MS) for the analysis of rapidly eluting analyte bands has been demonstrated in several high-speed GC appli-cations. In particular, van Deursen et al. demonstrated the effectiveness of ToF MS under extreme GC conditions [49]. The authors carried out an ultra-fast GC-ToF MS analysis in 500 msec, using a microbore capillary segment; the highest instrumental

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acquisition frequency, namely 500 spectra, and a 40–200 amu mass range were employed. Although the analyte band widths were very narrow (approximately 12 msec), peak construction was very good, while the similarities observed between library and experimental spectra were generally satisfactory. An additional aspect of high interest was the capability of the ToF MS to deconvolute co-eluting compounds on the basis of mass spectral dissimilarities: a retention time difference of 10 msec between two overlapping analytes (corresponding to 5 spectra) was enough for the deconvolution algorithm to unravel them. It is noteworthy that the high-speed GC analysis time and the band widths encountered were both considerably lower than those observed in second-dimension GC × GC experiments.

Van Deursen et al., passing from ultra-fast GC to comprehensive 2D GC, employed a ToF MS system for the analysis of kerosene [50]. The authors avoided excessively high 2D linear velocities by connecting a 1 m deactivated capillary to the 0.7 m (0.1 mm ID) analytical column. This column configuration generated a rather low second-dimension He linear velocity (a value of 100 cm/s was estimated) and, hence, relatively wide 2D solute bands (around 200 msec at half height). The latter were constructed in a correct manner by using a 50 Hz acquisition frequency. Although the spectral acquisition rate was much lower than observed in many current-day experiments (100 spectra/s or higher), each experiment produced 210,000 spectra, requiring a powerful PC with a large disk space. The generation of huge data files is a constant characteristic in any GC × GC-MS application. If deeper information on comprehensive 2D GC, in general, and on GC × GC-MS is desired, recent reviews devoted to these specific topic have been published [51–55].

7.3.3 applicationS

The published literature in the past 10 years is scattered with many examples illus-trating the “outstanding” or “overwhelming” separation power of comprehensive 2D GC. It is the habit of many authors to incorrectly compare unmodulated and modulated GC experiments, defining the former as the conventional result and the latter as the modulated one. Now, neglecting the contribution of the short secondary column on the overall separation, an unmodulated chromatogram is nearly always the result of a primary column separation carried out under suboptimum gas-flow conditions. With regards to the GC × GC result, as aforementioned, non-ideal flow conditions are present in both dimensions. It is clearly not possible to compare two methodologies, each with a different, undefined level of optimization. Although, it would be more preferable to compare single-column and comprehensive 2D GC methods, both under optimized conditions, the best option is to make no comparison at all. The potential of GC × GC has been widely demonstrated, although not fully expressed, and can be appropriately used if a 100-compound plus sample needs to be analyzed using a universal detector (not a mass spectrometer). Optimized monodi-mensional GC can provide satisfactory results on samples characterized by low-to-medium complexity.

A series of GC × GC applications will be described, each highlighting a specific advantage or characteristic of the methodology. The first part of the present section will be devoted mainly to GC × GC-MS applications on highly complex samples,

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while the shorter second part is directed to experiments demonstrating the benefits of 2D spatial order and enhanced sensitivity.

7.3.3.1 Comprehensive 2d gC Combined with mass spectrometryIn the immediate years following the first GC × GC-MS experiments (1999–2002), relatively few applications were described. In particular, the GC × GC-ToF MS analysis of mainstream cigarette smoke was reported by Dallüge et al. [56]. Smoke volatiles, collected by using a sample tube packed with three sorbent plugs, were thermally desorbed before analysis on an apolar–polar column setup. Cryogenic modulation was carried out every 6 s, while the ToF MS instrument generated 100 spectra/s. The high complexity of the smoke extract is immediately evident, observ-ing the baseline-corrected TIC GC × GC-MS chromatogram in Figure 7.15.

Now, considering that only the most volatile smoke constituents are present in the 2D chromatogram (C7 – C12 retention time range), an easy evaluation can be made on the sample complexity. Some conclusions can be made observing Figure 7.15: first, the 2D space is rather fully occupied, a consequence of the extensive wraparound suffered by many polar compounds. Second, many compounds remain unresolved, especially in the 0–2 s (nonpolar) zone of the 2D plane; it is clear that even compre-hensive 2D GC, let alone 1D GC, can fall far short of the peak-capacity requirements for such an application. As aforementioned, ToF MS can be used to overcome insuf-ficient chromatography resolution: deconvolution software was used generating good quality spectra for many overlapping components (mainly alkanes and alkenes), as can be observed in Figure 7.16: an expansion of the 2D chromatogram shown in the previous figure, with a vertical line locating a single cut, is illustrated in A; the raw fast chromatogram, relative to the single cut, is shown in B. In the 2-second

65

43210

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4

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2nd

dim

ensio

n (s

)

2

1

0750 1000

1000 1500 2000 2500 35003000

1250 225017501st dimension (s)

1500 25002000

fIgure 7.15 (See color insert following page 248.) TIC GC × GC–ToF MS contour plot of cigarette smoke showing the first-dimension range between 500 and 2600 seconds. (From Dallüge, J., van Stee, L. L. P., Xu, X., Williams, J., Beens, J., Vreuls, R. J. J., and Brinkman, UATh, J. Chromatogr. A, 974, 169–184, 2002. With permission.)

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(c) Peak

true

-sam

ple

“dru

m c

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84534.indb 316 11/5/09 12:29:24 PM


elution range, the deconvolution software unraveled 18 compounds, indicated by the horizontal lines. Nine out of 18 solutes were positively assigned, considering a mini-mum MS match factor value. Evidence of the good-quality spectra attained can be observed comparing the experimental spectrum of 2-methyl-1,5-hexadiene I and the best MS library match (D).

The enormous amount of data generated in each GC × GC-MS experiment and, hence, the difficulties encountered during data-handling were issues emphasized by the authors. Moreover, in relation to the comprehensive GC operational condi-tions, the GC-MS software used obviously did not foresee the employment of two columns with differing diameters and, thus, did not enable the calculation of the correct gas flow. Generation of 2D chromatograms was carried out by using exter-nal programs, while further data processing was achieved using the instrumental GC-MS software. The latter considered all peaks with a signal-to-noise ratio of more than 30, in the untransformed chromatogram; for all peaks found, mass spec-tra were attained by means of deconvolution. This process, which could only be applied to 500 s chromatogram portions due to peak table limitations (maximum 9999 peaks could be contained), was followed by MS library matching. The whole procedure required seven hours for the untransformed chromatogram relative to the 2D space plane reported in Figure 7.15. Although the final peak list contained 30,000 peaks, the number of different compound names was much less, namely 7,500. Obviously, modulation generates a series of sequential peak pulses relative to the same compound. Such a number of separated components is unheard of in 1D experiments: considering the 2600 s elution-time range, nearly 3 peaks/s were gener-ated. However, the chromatography was not matched by the mass spectral results; after filtering out library hits with low match factors, and using literature-derived retention indices for confirmation purposes (only 238 reference values were found), the authors reported that only 152 compounds were positively identified.

A GC × GC-qMS experiment worthy of note was reported in 2002 by Shellie and Marriott [57]. The main interest of the authors was devoted to the proper selection of column dimensions, to exploit the vacuum-outlet conditions: a first- dimension 10 m × 0.1 mm ID × 0.1 µm apolar column was combined with a 1 m × 0.25 mm ID × 0.25 µm chiral capillary. The use of a wider bore column, which favored low- pressure conditions across the entire second dimension, caused an increase in solute-gas diffusion coefficients. It is well known that higher optimum gas linear velocities can be attained under such GC conditions: for example, if a short 0.53 mm ID column is hyphenated to a mass spectrometer, the optimum gas velocity nears the 100 cm/s mark. On the contrary, if a microbore capillary is used, then subatmospheric conditions are exploited only in a short end segment. Furthermore, wide-bore columns can accommodate large sample quantities with no efficiency loss and generate greater peak widths (very high mass-spectral acqui-sition rates are not necessary). A restriction is usually applied at the head of the mega-bore capillary to avoid an extension of the low-pressure conditions to the injector. The column setup described in [57] met the conditions of low-pressure high-speed chromatography, namely, the 1D microbore capillary was used for both separation and restriction properties, while the 2D mega-bore column was suited for fast GC analysis.

84534.indb 317 11/5/09 12:29:24 PM


Quadrupole mass spectrometry is widely used as a GC detector and is character-ized by lower economical costs with respect to ToF systems. Consequently, the use of such instrumentation is quite attractive for many groups operating in the GC × GC field. The introduction of rapid-scanning qMS systems acted as a stimulant for their employment in comprehensive GC applications and, hence, quite a lot of work has been devoted to feasibility studies. In particular, Shellie et al. used a rapid-scanning system for the analysis of ginseng volatiles [58]. Mass spectra were acquired at a 20 Hz frequency in a reduced mass range (41–228.5 m/z), that enabled the detection of molecular ions up until the oxygenated sesquiterpenes. The authors reported that the number of data points attained per peak, namely 3–4, were enough for identification means, but were insufficient for correct peak reconstruction. Even if not observed in the experiment, an excessively low acquisition rate can also cause inconsistent 2D elution times for pulsed bands relative to the same component. The extent of MS skewing, which was investigated observing spectral variations across single peaks, was found to be negligible.

The analysis of major and minor perfume constituents (comprehending sus-pected allergens) is commonly achieved by using monodimensional GC with FID detection and/or GC–MS. However, extensive co-elutions commonly occur both on apolar and polar stationary phases, generating highly overcrowded chromato-grams. Mondello et al. proposed, as an alternative, the use of comprehensive 2D GC in combination with a rapid-scanning qMS for the analysis of commercial perfume [59]: apolar 30 m × 0.25 mm ID × 0.25 µm and polar 1 m × 0.25 mm ID × 0.25 µm columns were used in the first and second dimension, respectively. The authors exploited the aforementioned advantages of using a relatively wide-bore secondary column, under low-pressure conditions. An LMCS system was employed with an 8 s modulation period, while the qMS was operated using a 40–400 m/z mass range and a 20 Hz spectra acquisition rate. The TIC GC × GC–qMS perfume chromatogram is illustrated in Figure 7.17. The total number of entirely or partially resolved peaks in the space plane is 866; peak identification was carried out with the support of monodimensional linear retention indices (LRI). The mass spectrometer generated 3–4 high quality MS spectra for the narrower 2D peaks—a number suf-ficient for peak assignment. Moreover, mass spectral variations relative to different points across a given peak were negligible demonstrating low skewing effects. The number of peaks identified with a match quality of at least 90% was 169 (reference LRI were not available in 38 cases), with 14 of these consisting of skin sensitiz-ers. A good example of the enhanced resolving power of comprehensive GC was provided by the authors: Figure 7.18 illustrates the descending part of a peak in an 8 s chromatogram expansion relative to a conventional GC–MS experiment, as well as the background corrected averaged spectrum, the best MS library match and the subtraction result.

An unsatisfactory spectral similarity result of 72%, for estragole, was the highest value attained. The presence of interfering compounds is immediately evident, if the subtraction result is observed. The greatly increased separation power of GC × GC-qMS is well-demonstrated in Figure 7.19, which illustrates the modulated result relative to the 1D peak reported in the previous figure.

84534.indb 318 11/5/09 12:29:25 PM


Eight entirely resolved compounds are present in the chromatogram expansion, four of which were identified (numbered peaks). The most abundant of the 4 com-pounds was identified as estragole, with a 98% spectral similarity.

Ryan et al. employed a ToF MS and rapid-scanning qMS systems in LMCS GC × GC experiments for the analysis of roasted coffee volatiles [60]; the latter, extracted by using headspace solid-phase microextraction, were separated on an inverted col-umn set, which provided a better chromatographic profile than the orthogonal com-bination. The samples analyzed revealed a very high complexity, as can be observed in the qMS result for Arabica coffee (Figure 7.20).

The qMS instrument enabled the application of a normal mass range (40–400 m/z) at a scanning rate of 20 spectra/s, again sufficient for reliable peak assignment. The ToF mass spectrometer, on the other hand, generated 100 spectra/s, over a 41–415 m/z mass range. TIC chromatograms were automatically processed using the instrumen-tal (Chroma-TOF) software. The number of processed peaks was limited to 1000 (S/N > 100), an obliged choice related to the extensive time requirements (8 h) for data processing.

7.3.3.2 spatial order and enhanced sensitivityIn recent research, Tranchida et al. exploited orderly structured 2D chromatograms and the high sensitivity of GC × GC for the elucidation of a sample-type of great scientific importance, namely methyl ester-derivatized plasma fatty acids (FAMEs) [61]. The analysis of FAMEs in human plasma is a well-known GC procedure: both apolar and polar stationary phases have been used in the conventional GC separation of plasma FAMEs, with a preference for the more polar capillaries (e.g., polyethylene glycol). In recent years, a series of studies related to human blood or plasma FAMEs

7.00

6.00

5.00

4.00

Sec

3.00

2.00

1.00

0.004 14 24 34 44 54

Min64 74 84

fIgure 7.17 (See color insert following page 248.) TIC GC × GC-MS result for perfume. (From Mondello, L., Casilli, A., Tranchida, P. Q., Dugo, G., and Dugo, P., J. Chromatogr. A, 1067, 235, 2005. With permission.)

84534.indb 319 11/5/09 12:29:27 PM


Spectrum comparisonSpectrum1 #Data# data451.QGD R.Time:26.002(Scan#:26403)MassPeaks:82 BasePeak:147.80(1000)RawMode:Averaged 25.999-26.141(26400-26570) BG Mode:Averaged 26.173-26.178(26608-26614)

3.5TIC

(×100,000)

3.0

2.5

2.0

1.5

0.5

26.025

41

30 40 50 60 70 80 90 100 110 120 130 140

30Spectrum3 #Calcuration Result#MassPeaks:86 BasePeak:82.00(803)

40

39

Spectrum2 #Library# wiley229.lib Entry:26477 Formula:C10 H12 O CAS:140-67-0MolWeight:148 RetIndex:0MassPeaks:50 BasePeak:148.00(1000)Compname:Benzene, 1-Methoxy-4-(2-propenyl)-(CAS) p-Allylanisole $$ Anisole, p-allyl-$$ Methylchavicol $$ 1-Allyl-4-methoxybenzene $$ 4-A

41

1000

1000

1000

0

43 67 8293 107

121147136

5165

7791 105

117133

148

50 60 70 80 90 100 110 120 130 140

30 40 50 60 70 80 90 100 110 120 130 140

4367

82

91105

121

133

148

26.050 26.075 26.100 26.125

1.0

fIgure 7.18 GC-qMS result for a single perfume peak. (From Mondello, L., Casilli, A., Tranchida, P.Q., Dugo, G., and Dugo, P. J. Chromatogr. A, 1067, 235, 2005. With permission.)

84534.indb 320 11/5/09 12:29:29 PM


26.0000.00.51.01.52.02.53.03.54.04.55.0

6.0 TIC(×100,000)

1000

1000

1000

Spectrum comparisonSpectrum1 #Data# data450.QGD R.Time:26.088(Scan#:26507)MassPeaks:84 BasePeak:147.80(1000)RawMode:Averaged 26.085–26.091(26503–26510) BG Mode:Averaged 26.074-26.080(26490-26497)

Spectrum3 #Calcuration Result#MassMeaks:79 BasePeak:77.00(124)

Spectrum2 #Library# wiley229.lib Entry:26477 Formula:C10 H12 O CAS:140-67-0MolWeight:148 RetIndex:0MassPeaks:50 BasePeak:148.00(1000)CompName:Benzene. 1-methoxy-4-(2-propenyl)-(CAS) p-Allylanisole $$ Anisole, p-allyl-$$Methl chavicol $$ 1-allyl-4-methoxybenzene $$ 4-A

30 40

4151 65

77 91 105121

133

148

4151 63

77 91 105 117 133

148

40 51 65 77 91 105 121 133 146

50 60 70 80 90 100 110 120 130 140 150

30 40 50 60 70 80 90 100 110 120 130 140 150

30

0

40 50 60 70 80 90 100 110 120 130 140 150

5.5

26.025 26.050 26.075

53 52 54

55

26.100 26.125

fIgure 7.19 GC × GC-qMS result for the peak illustrated in Figure 7.18. Peak identifica-tion: 52) estragole; 53) cis-dihydrocarvone; 54) γ-terpineol; 55) neo-dihydrocarveol. (From Mondello, L., Casilli, A., Tranchida, P. Q., Dugo, G., and Dugo, P., J. Chromatogr. A, 1067, 235, 2005. With permission.)

84534.indb 321 11/5/09 12:29:32 PM


have been described, reporting the presence of not more than 30 well known and widely reported FAs [62–66].

In general, the main drawbacks that can be encountered in the GC-FID and/or GC-MS analysis of fatty acid matrices are: (1) the difficulties related to the identi-fication of double-bond positional isomers; for example, the mass spectra of C18:3ω3

and C18:3ω6 are very similar; (2) an additional less-known drawback, related to the separation process, is that the number of fatty acids contained in these sample-types often exceed the separation potential of a 30 m capillary column; and (3) a final prob-lem is related to the limits of detection, because many FAMEs reach the detector at excessively low concentrations to be revealed. In [61] the authors demonstrated that these three disadvantages can be almost completely eliminated by using GC × GC. The 2D chromatogram relative to the GC × GC separation a plasma sample is shown in Figure 7.21.

The fatty acids are located within a typical GC × GC band, generated by using an orthogonal column set. The FAMEs are grouped on the basis of their:

Carbon number (the CN• 14–24 zones are indicated by arrows)Double-bond number (DB): seven distinct bands, grouping FAMEs in the •DB0-6 range.ω• number: FAMEs with the same location of the last double bond are aligned along descending diagonal bands.

Of the 65 identified compounds, 36 were identified by using pure standard com-pounds, while the remaining 29 FAMEs were identified through the highly ordered

8.3 12.6 34.216.7 21.2 25.6 29.9 38.5 42.8 47.1 51.5 55.8 60.1 64.4 68.7 73.0 77.3 81.7 86.0 90.3Min

0.7

1.4

2.1

2.7

3.4

4.1

4.7

5.4

Sec

fIgure 7.20 (See color insert following page 248.) Headspace SPME-GC × GC-qMS result for Arabica coffee volatiles. (From Mondello, L., Tranchida, P. Q., Dugo, P., and Dugo, G., Mass Spectrom. Rev., 27, 101, 2008. With permission.)

84534.indb 322 11/5/09 12:29:36 PM


structure of the 2D chromatogram (Table 7.2). A series of fatty acids were identified by considering the intersection points of the DB bands with the ω-number diagonals; an example of this simple procedure is shown in the C20 group 2D chromatogram, reported in Figure 7.22: peak 45 corresponds to C20:3ω6, because it is situated within the C20 group 2D space and is located at the intersection point of the DB3 band and the ω6 diagonal.

With regards to the benefits of sensitivity enhancement, a series of rather unex-pected odd-CN fatty acids (i.e., C11:0, C19:0, C21:0, C19:3, C21:4, C21:5, etc.) were determined at very low relative-% amounts. Furthermore, a (probable) homologous series of unassigned compounds (defined with the letters a, b, c, d, e, f, and g in Figure 7.21) appeared in the nonpolar zone of the space plane. The authors affirmed that these analytes appeared to be n-hydrocarbons with a 2CN difference. Finally, the advantages of the isolation of chemical bleed, especially in trace-amount analysis, were also highlighted: a series of descending streaks, corre-sponding to modulated 1D stationary-phase release, and separated from the plasma FAMEs, is evident in Figure 7.21.

Without a doubt, the most typical and common GC × GC application is that related to fuel samples; apart from the possibility to increase the number of sepa-rated analytes, the 2D methodology generates highly structured chromatograms in this type of experiment. As an example, Figure 7.23 illustrates both an orthogonal

DB1

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DB2

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6.01Sec

5.34

4.68

4.01

3.34

2.68

1.35

2.01

0.68

0.0210.67 23.2220.084.4 7.54 13.81 16.95 26.36 29.49 32.63

Min

fIgure 7.21 (See color insert following page 248.) GC × GC-FID result for plasma FAMEs. Refer to Table 7.2 for peak identification. (From Tranchida, P. Q., Costa, R., Donato, P., Sciarrone, D., Ragonese, C., Dugo, P., Dugo, G., and Mondello, L., J. Sep. Sci., 31, 3347, 2008. With permission.)

84534.indb 323 11/5/09 12:29:38 PM


table 7.2Identification of gC × gC plasma fames. st = standard Compound peak assignment

peak fame2-d gC rel.% peak fame

2-d gC rel.%

1 C8:0 0.015 34 C17:2 0.013

2 C9:0 0.015 35 C18:2ω6 (st) 30.386

3 C10:0 (st) 0.009 36 C20:2 0.023

4 C11:0 (st) 0.019 37 C20:2ω6 (st) 0.267

5 C12:0 (st) 0.097 38 C22:2ω6 (st) 0.005

6 i-C14:0 0.003 39 C24:2ω6 0.015

7 C14:0 (st) 1.124 40 C18:3ω6 (st) 0.451

8 i-C15:0 (st) 0.019 41 C18:3ω3 (st) 0.789

9 a-C15:0 (st) 0.021 42 C18:3 0.027

10 C15:0 (st) 0.169 43 C19:3 0.013

11 i-C16:0 (st) 0.035 44 C19:3ω6 0.078

12 C16:0 (st) 20.785 45 C20:3ω6 (st) 1.814

13 i-C17:0 (st) 0.059 46 C20:3ω3 (st) 0.033

14 a-C17:0 0.085 47 C22:3ω6 0.006

15 C17:0 (st) 0.194 48 C18:4ω3 0.041

16 i-C18:0 0.019 49 C20:4ω6 (st) 5.091

17 C18:0 (st) 5.326 50 C20:4ω3 (st) 0.136

18 a-C19:0 0.007 51 C21:4 0.003

19 C19:0 0.011 52 C22:4ω6 0.178

20 C20:0 (st) 0.036 53 C22:4ω3 0.011

21 C21:0 (st) 0.002 54 C24:4ω6 0.007

22 C22:0 (st) 0.058 55 C20:5ω3 (st) 0.428

23 C23:0 (st) 0.021 56 C20:5ω1 0.020

24 C24:0 (st) 0.046 57 C21:5 0.004

25 C14:1ω5 (st) 0.092 58 C22:5ω6 0.089

26 C16:1ω7 (st) 2.511 59 C22:5ω3 (st) 0.427

27 C17:1ω7 (st) 0.134 60 C24:5ω3 0.008

28 C18:1ω9 (st) 18.349 61 C24:5 0.004

29 C19:1 0.036 62 C20:6ω1 0.013

30 C20:1ω9 (st) 0.116 63 C22:6ω3 (st) 1.539

31 C22:1ω9 (st) 0.017 64 C23:6 0.021

32 C24:1ω9 (st) 0.058 65 C24:6ω3 0.012

33 C16:2ω6 0.025

Source: Tranchida, P. Q., Costa, R., Donato, P., Sciarrone, D., Ragonese, C., Dugo, P., Dugo, G., and Mondello, L., J. Sep. Sci., 31, 3347, 2008. With permission.

84534.indb 324 11/5/09 12:29:38 PM


( apolar– polar) and inversed (polar-medium polarity) GC × GC-FID analysis on diesel oil [67]. Using the orthogonal combination, the analytes are: (a) subjected to a boiling-point 1D separation with little inter-class distinction (e.g., there is no group separation between monoaromatics and alkanes); (b) subjected to a polarity-based 2D analysis, with satisfactory inter-group separation between diaromatics and monoaromatics, and partial border overlapping between the monoaromatics and the alkanes. The quality of intra-class separation is good for diaromatics and monoaro-matics, while, as expected, the secondary polar column showed a low selectivity for the alkanes. Employing the inversed combination, the solutes are: (a) subjected to a polarity-based 1D separation, showing some degree of inter-group separation (e.g., there is partial group isolation between monoaromatics and alkanes); (b) sub-jected to a medium polarity-based 2D analysis, with good inter-group separation between all chemical classes. However, the quality of intra-class separation cannot be defined as satisfactory for any of the three chemical groups. Considering both applications, it can be concluded that both column combinations generate structured chromatograms; however, the orthogonal approach provided better inter-class sepa-ration, while the inversed set was to be preferred for inter-group resolution.

DB5ω3

ω6

3020

36 374549

ω1 DB66256

4650

55

C20

6.01

DB4DB3DB2DB1DB0

5.34

4.67

4.01

3.34

2.67

2.01

1.34

0.67

0.01

Sec

20.2 20.72 21.23 21.75 22.26 22.78 23.29 23.81 24.8424.33Min

fIgure 7.22 (See color insert following page 248.) Expansion relative to the 2D chro-matogram shown in Figure 7.21, illustrating the C20 FAMEs group (see Table 7.2 for peak assignment). (From Tranchida, P. Q., Costa, R., Donato, P., Sciarrone, D., Ragonese, C., Dugo, P., Dugo, G., and Mondello, L., J. Sep. Sci., 31, 3347, 2008. With permission.)

84534.indb 325 11/5/09 12:29:43 PM


referenCes

1. Golay MJE. Gas Chromatography. Academic Press, New York, 1958. 2. James AT, Martin AJP, Biochem. J. 50, 679, 1952. 3. Giddings JC in: Multidimensional Chromatography: Techniques and Applications,

H.J. Cortes (Ed.), Marcel Dekker, New York, 1990. 4. Berger TA, Cromatographia 42, 63, 1996. 5. Poole CF, Poole SK, J. Chromatogr. A 1184, 254, 2008. 6. Bertsch W, J. High Resol. Chromatogr. 22, 647, 1999. 7. Schomberg G, J. Chromatogr. A 703, 309, 1995. 8. Consden R, Gordon AH, Martin AJP, Biochem. J. 38, 224, 1944. 9. Liu Z, Phillips JB, J. Chromatogr. Sci. 29, 227, 1991. 10. Boer H, van Arkel P, Chromatographia 4, 300, 1971. 11. Kinghorn RM, Marriott P, Cumbers M, J. High Resol. Chromatogr. 19, 622, 1996. 12. Mondello L, Catalfamo M, Proteggente AR, Bonaccorsi I, Dugo G, J. Agric. Food Chem.

46, 54, 1998. 13. Mondello L, Catalfamo M, Cotroneo A, Dugo G, J. High Resol. Chromatogr. 22,

350, 1999.

Di-aromatics

Mono-aromatics

7.5

5.0

2.5BP20

,2 t R (s)

BPX

-35,

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0.013 25 38 50

DB-1, 1tR (min)63 75 88

0 10 20 30BP21, 1tR (min)

40 50 60 70

5

4

3

2

1

0

Alkanes

Di-aromaticsMono-aromatics

Alkanes

fIgure 7.23 (See color insert following page 248.) GC × GC–FID chromatograms of die-sel oil obtained on two different column sets, namely, apolar–polar (top) and polar– medium polarity. (From Adahchour, M., Beens, J., Vreuls, R. J. J., Batenburg, A. M., and Brinkman UATh, J. Chromatogr. A, 1054, 47, 2004. With permission.)

84534.indb 326 11/5/09 12:29:46 PM


14. Mosandl A, Bruche G, Askari C, Schmarr H-G, J. High Resol. Chromatogr. 13, 660, 1990.

15. Simmons MC, Synder LR, Anal. Chem. 30, 32, 1958. 16. McEwen DJ, Anal. Chem. 36, 279, 1964. 17. Deans RR, Chromatographia 1, 18, 1968. 18. Jennings W, J. Chromatogr. Sci., 22, 129, 1984. 19. Fenimore DC, Freeman RR, Loy PR, Anal. Chem. 45, 2331, 1973. 20. Sciarrone D, Tranchida PQ, Ragonese C, Schipilliti L, Mondello L. Submitted to J. Sep.

Sci. 21. Mondello L, Casilli A, Tranchida PQ, Sciarrone D, Dugo P, Dugo G, LC GC Eur. 21,

130, 2008. 22. Quimby B, McCurry J, Norman W, LC GC Eur. 25, 174, 2007. 23. Luong J, Gras R, Yang G, Cortes H, Mustacich R, J. Sep. Sci. 31, 3385, 2008. 24. Luong J, Gras R, Yang G, Cortes H, Mustacich R, J. Chromatogr. Sci. 44, 253, 2006. 25. Kaiser RE, Leming L, Blomberg L, Reider RI, HRC & CC. 8, 92, 1985. 26. Veriotti T, McGuigan M, Sacks R, Anal. Chem. 73, 279, 2001. 27. Veriotti T, Sacks R, Anal. Chem. 73, 3045, 2001. 28. Veriotti T, Sacks R, Anal. Chem. 75, 4211, 2003. 29. Schoenmakers P, Marriott P, Beens J, LC-GC Eur., 16, 335, 2003. 30. Liu Z, Sirimanne SR, Patterson Jr DG, Needham LL, Phillips JB, Anal. Chem. 66,

3086, 1994. 31. Kinghorn RM, Marriott PJ, J. High Resol. Chromatogr. 22, 235, 1999. 32. Phillips JB, Gaines RB, Blomberg J, van der Wielen FWM, Dimandja J-M, Green V,

Granger J, Patterson D, Racovalis L, de Geus H-J, de Boer J, Haglund P, Lipsky J, Sinha V, Ledford Jr EB, J. High Resol. Chromatogr. 22, 3, 1999.

33. Mondello L, Lewis AC, Bartle KD in: Multidimensional Chromatography, John Wiley & Sons Limited, West Sussex, 2002.

34. Seeley JV, Kramp F, Hicks CJ, Anal. Chem. 72, 4346, 2000. 35. Bueno Jr. PA, Seeley JV, J. Chromatogr. A 1027, 3, 2004. 36. Seeley JV, Seeley KS, Libby EK, Breitbach ZS, Armstrong DW, Anal. Bioanal. Chem.

390, 323, 2008. 37. Seeley JV, Micyus NJ, McCurry JD, Seeley SK, Am. Lab. 38, 24, 2006. 38. Quimby B, McCurry J, Norman W, LC-GC 25, 174, 2007. 39. Libardoni M, Waite JH, Sacks R, Anal. Chem. 77, 2786, 2005. 40. Sandra P, David F, Klee MS, Blumberg LM, Proceedings of the Dalian International

Symposia and Exhibition on Chromatography, June 4–7, 2007, Dalian, China. 41. Marriott P, Dunn M, Shellie R, Morrison P, Anal. Chem. 75, 5532, 2003. 42. Shellie R, Marriott P, Morrison P, Mondello L, J. Sep. Sci. 27, 504, 2004. 43. Beens J, Janssen H-G, Adahchour M, Brinkman UATh, J. Chromatogr. A 1086,

141, 2005. 44. Tranchida PQ, Casilli A, Dugo P, Dugo G, Mondello L, Anal. Chem. 79, 2266, 2007. 45. Oldridge N, Panic O, Górecki L, J. Sep. Sci. 31, 3375, 2008. 46. von Mühlen C, Khummueng W, Alcarez Zini C, Bastos Caramão E, Marriott PJ, J. Sep.

Sci. 29, 1909, 2006. 47. Phillips JB, Xu J, J. Chromatogr. A 703, 327, 1995. 48. Frysinger GS, Gaines RB, J. High Resol. Chromatogr. 22, 251, 1999. 49. van Deursen M, Beens J, Janssen H-G, Leclercq PA, Cramers CA, J. Chromatogr. A 878,

205, 2000. 50. van Deursen M, Beens J, Reijenga J, Lipman P, Cramers C, Blomberg J, J. High Resol.

Chromatogr. 23, 507, 2000. 51. Mondello L, Tranchida PQ, Dugo P, Dugo G, Mass Spectrom. Rev. 27, 101, 2008.

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52. Adahchour M, Beens J, Vreuls RJJ, Brinkman UATh, Trends Anal. Chem. 25, 438, 2006.




56. Dallüge J, van Stee LLP, Xu X, Williams J, Beens J, Vreuls RJJ, Brinkman UATh, J Chromatogr A 974, 169, 2002.

57. Shellie R, Marriott PJ, Anal. Chem. 74, 5426, 2002. 58. Shellie RA, Marriott PJ, Huie CW, J Sep. Sci. 26, 1185, 2003. 59. Mondello L, Casilli A, Tranchida PQ, Dugo G, Dugo P, J. Chromatogr. A 1067,

235, 2005. 60. Ryan D, Shellie R, Tranchida P, Casilli A, Mondello L, Marriott P, J. Chromatogr. A

1054, 57, 2004. 61. Tranchida PQ, Costa R, Donato P, Sciarrone D, Ragonese C, Dugo P, Dugo G, Mondello

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MC, Rivero-Urgell M, J. Chromatogr. A 778, 435, 1997. 65. Akoto L, Vreuls RJJ, Irth H, Pel R, Stellaard F, J. Chromatogr. A 1186, 365, 2008. 66. Tvrzická E, Vecka M, Stanková B, Žák A, Anal. Chim. Acta 465, 337, 2002. 67. Adahchour M, Beens J, Vreuls RJJ, Batenburg AM, Brinkman UATh, J. Chromatogr. A

1054, 47, 2004.

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329

8 Sample Preparation for Chromatographic Analysis of Environmental Samples

Tuulia Hyötyläinen

8.1 IntroduCtIon

Determination of the chemical composition of complex environmental samples is a challenging task, owing to myriad species of compounds, many of them present in only trace amounts. Typically, chromatographic techniques are utilized in the analy-sis of complex environmental samples. However, most samples cannot be injected directly into the chromatographic system without sample preparation. It is worth stressing that the sample preparation step required before the chromatographic sepa-ration largely determines the quality of obtained results. The sample preparation procedure also significantly impacts assay throughput, data quality, and analysis

Contents

8.1 Introduction .................................................................................................. 3298.2 Sample Preparation Techniques.................................................................... 331

8.2.1 Drying and Homogenization of Solid Samples ................................ 3338.2.2 Extraction .......................................................................................... 333

8.2.2.1 Vapor-Phase Extraction ...................................................... 3348.2.2.2 Liquid Samples .................................................................. 3358.2.2.3 Solid and Semisolid Samples .............................................344

8.3 Cleanup of Extracts ...................................................................................... 3508.3.1 Lipid Removal from Biological Extracts .......................................... 3508.3.2 Sulfur Removal from Sediment Extracts .......................................... 3518.3.3 Fractionation ..................................................................................... 3518.3.4 Derivatization ................................................................................... 3538.3.5 Online Techniques ............................................................................ 3558.3.6 Selection of Sample Preparation Method Methods .......................... 356

8.4 Conclusions and Future Perspectives............................................................366Abbreviations ......................................................................................................... 367References .............................................................................................................. 367

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cost. It should also be noted that sampling and sample preparation steps typically account for over 80% of the total analysis time. Therefore, selecting and optimiz-ing an appropriate sample preparation method is essential for successful method development.

One of the major problems with environmental samples is that the conventional sample preparation techniques are seldom sufficient in terms of speed, sensitiv-ity, selectivity, and reliability. Several interlaboratory studies have shown that even established laboratories applying well validated methods frequently produce incon-sistent data, for example for brominated flame retardants (BFRs), polyfluorinated chemicals (PFCs), and other organic compounds.1 In some cases, interlaboratory results will reveal a relation between the use of nonoptimal techniques or methods and poor results. In many other cases, however, laboratories suffer from multiple difficulties which hinder clear identification of the error source. Issues needing to be addressed are often related to poor sample preparation methods, such as inef-ficient extraction methods, matrix effects, and the cleanup steps needed to remove them.1 In short, obtaining reliable data depends upon systematic development of techniques and methods, particularly for the sample preparation part. Moreover, sample preparation methods with lower consumption of toxic organic solvents to minimize the generation of hazardous residues and health risks for operators are needed.2,3,4

Sample processing and pretreatment can take a number forms depending on the nature of the sample.5 Typical processes may include sample filtration, centrifuga-tion, distillation, dilution, target amplification, and extraction. Successful execution of these processes is required to ensure that the analyte is present in a form compati-ble with the analytical system. The most classical sample preparation techniques rely on extraction with solvents, including traditional techniques such as liquid–liquid extraction (LLE) and Soxhlet extraction. The broad polarity range of solvents and general applicability made these techniques popular. However, from an environmen-tal point of view, the use of large amounts of organic and often chlorinated solvents is unfavorable. Furthermore, they often require complex time-consuming multistep procedures which can lead to low accuracy, contamination, and losses of analytes. Various other techniques, such as solid-phase extraction (SPE) and pressurized liquid extraction (PLE), have been developed to replace these traditional sample pretreat-ment techniques. In addition, solid-phase microextraction (SPME), membrane-based techniques (dialysis, ultrafiltration, supported liquid membrane extraction (SLM)), and other miniaturized extraction techniques have been developed to overcome the problems of traditional methods. At present, the sample pretreatment is often the weakest and most time-consuming part in the analytical procedure. Thus, much effort has been put into exploring the possibilities of miniaturization and automation of the extraction procedures to minimize or eliminate the limitations of the sample preparation.

No universal sample preparation technique suitable for all types of sample exists. The sample preparation required is dependent on the nature of analytes, matrix, and final separation method. Naturally, the sample preparation must be tailored to the final analysis. The sample matrix and the type and amount of analytes in the sample are of primary importance. Moreover, a method good for target-compound analysis

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Sample Preparation for Chromatographic Analysis of Environmental Samples 331

may not be good for comprehensive chemical profiling of samples. Selectivity of the sample preparation is often a key factor for target-compound analysis while an exhaustive extraction is the better choice for profiling. In the selection of a sample preparation technique, not only the effectiveness needs to be considered but many other factors that affect the analytical scheme.6 The major factors are cost of the equipment, operating costs, complexity of method development, amount of organic solvent required, and level of automation. In addition, the number of samples to be analyzed is also of importance—the question is whether the planned procedure will be unique or whether it will be used in carrying out routine analysis. In the latter case, the techniques facilitating automation and low cost per analysis are preferred.

Sample preparation methods are required for large number of different analytes and matrices. Levels of persistent organic pollutants (POPs), radionuclides, and toxic metals are extensively measured in various compartments of the environment, such as water, soil, sediment, air, and biota. POPs include industrial compounds and flame retardants such as polychlorinated biphenyls (PCBs); polychlorinated naphtha-lenes (PCNs); polybrominated diphenyl ethers (PBDEs); polybrominated biphenyls (PBBs); industrial by-products such as polychlorinated dibenzo-p- dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs); and organochlorine (OC) pesticides such as dichlorodiphenyltrichloroethane (DDT), hexachlorobenzene (HCB), and hexachlorocyclohexane (HCH). More recently, emphasis has been put on the deter-mination of levels of emerging contaminants, such as surfactants, human and vet-erinary drugs, fragrances, antiseptics, new brominated/chlorinated flame retardants (beyond PBDEs), sunscreens/UV filters, contaminant dibutylphthalates (DBPs), benzotriazoles, naphthenic acids, perfluorinated surfactants (including perfluorooc-tanoic sulfates (PFOS) and perfluorooctanoic acid (PFOA)), algal toxins, perchlo-rate, pesticide degradation products, chiral contaminants, and microorganisms.7,8 Due to the large number of different compounds and matrices, the development of sample preparation schemes is challenging. Recently, much effort has gone into the development of more efficient extractions that could replace the conventional methods, which typically are laborious and time-consuming multistep procedures, requiring much manual handling of the extracts.

8.2 sample preparatIon teChnIques

Sample preparation includes several steps, of which the most time- and labor- consuming part is the extraction and further cleanup of the extracts. Different meth-ods are required for different types of samples, as shown in Figure 8.1. Liquid samples are generally easier to handle than solid samples which require exhaustive methods.

The first step of sample preparation for solid and semisolid samples is drying and homogenization. For liquid sample, simple filtration is often sufficient. Then, the tar-get analytes are extracted from the sample (solid or liquid), and the extract is usually purified, fractionated, and concentrated before the final analysis, which is typically performed with gas or liquid chromatography. The extraction procedure is dependent on the sample matrix; different methods are used for sediment, soil, plant, tissue, and liquid samples. After extraction, it will usually be necessary to purify and fraction-ate the extract, because most extraction methods are insufficiently selective and the

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separation power of the analytical technique not good enough. Extracts typically contain several analytes similar to the flame retardants, which may be present in much higher quantities. The fractionation procedures are similar for the different types of extracts.

Sample

Solid Liquid

YES

NO

NO

NO

NO

NO

NO

NO

NO

YES

YESSelective

extraction byLLESPE

SPMESBSELPMEMASE

YES

YES

Sample dissolution bydigestion

organic solventaqueus solvent

Column chromatographySPE filtration

dialysis

Are analytesthermally/chemically

unstable

Derivatize

Analyse

Doessample/

extract needpurification

Is sample/extractsuitable for direct

analysis?

HeadspaceSPMESBSEMESIPLE

SLESoxhletSAEMAESFE

YES

YES

YES

Particle sizereductionrequired?

Is thewhole sample

of interest?Hard sample

Mill, grind, crushor pulverize

Chop, macerate,cut or mince

Is the samplehomogeneous?

Homogenizesample

Take a samplealiquot

Is thewhole sample

of interest?

Are analytesvolatile?

Semi-soft, soft sample

fIgure 8.1 Typical sample preparation schemes used in environmental analysis.

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During recent years, many modified, innovated sample preparation methods have been developed. This review focuses on the advanced and promising methods and highlights the new trends in developing the methods for sample preparation.

8.2.1 dryinG and homoGeniZation of Solid SampleS

Drying of solid samples, such as soil, sediment, and sewage sludge, is usually the first step in the analysis. Dry samples are more effectively homogenized, allowing accurate subsampling for parallel analyses for other determinants. In addition, the absence of water in the samples makes the sample matrix more accessible to organic solvents. Because some of the POPs are relatively volatile, both losses and uptake of compounds from air can occur if the drying is done at room temperature or in a heated oven (<40°C). Freeze-drying (water evaporation below 0°C under vacuum conditions) is a more gentle option. Also chemical drying of samples can be per-formed by grinding with anhydrous Na2SO4. Intensive grinding and the addition of sufficient quantity of drying salt to obtain a free-flowing powder are of vital impor-tance for a complete extraction. Drying with water-adsorbing materials (alumina, silica, etc.) may also be an alternative, but in this case water is not bound irreversibly and can only easily be released when polar solvents are used for extraction. The use of a mixture of less polar solvents (e.g., hexane, dichloromethane) may help to avoid these problems.

8.2.2 extraction

The extracting phase can be vapor or liquid, and the extraction can be performed in static or dynamic mode, using equilibrium mode or an exhaustive extraction. The extraction techniques may be divided into three main types, according to the kind of extractant phase: vapor-phase extraction, liquid-phase extraction, and extraction in which solid adsorbents are applied.

A large number of different methods and techniques have been developed for different types of analytes and sample matrices. Extraction procedures vary in degree of selectivity, speed, and convenience depending on the approach and con-ditions used as well as on geometric configurations of the extraction phase and conditions. The selection of the best method or optimization of the parameters is often not an easy task. The choice of the extraction method is largely dependent on the matrix: different methods are required for liquid and solid (or semi-solid) samples. In addition, different methods are often needed for target-compound analysis than for comprehensive chemical profiling for the samples. For target-compound analysis, selectivity of the sample preparation is often one of the key features in the selection while for profiling an exhaustive extraction method is a better choice.

In each extraction technique, the operating principle is the same: the partitioning of analytes between the sample matrix and an extracting phase. The selective extraction of analytes is based on differences in their chemical and physical properties. These typically include molecular weight, charge, solubility, polarity (hydrophobicity), or

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differences in volatility. Some extraction methods, such as solid-phase extraction with immunoaffinity materials and imprinted polymers, utilize selectivity for spe-cific structural groupings or mimic a biological selectivity.

In the selection and optimization of the extraction conditions, theoretical models developed for various techniques can be utilized. For homogeneous sample matrices (e.g., clean water or air) the kinetics of the partitioning process can be described mathematically, by the equations for the diffusive and convective transport of ana-lytes in the sample matrix and the extracting phase. In a solid or semisolid matrix the situation is more complex and two processes need to occur to successfully extract components: release of analytes from the matrix followed by partitioning of analytes into the extracting phase. The release of analytes from the matrix can involve swell-ing of the matrix or dissociation of an analyte-matrix complex. Either the processes of release or the partitioning rate of released analytes can control the overall extrac-tion rate. In the practical optimization, by optimizing the extraction procedures using experimental design and combining them with formal optimization strategies it has been possible to obtain optimum operating conditions with a minimal amount of labor, time, and cost. In most cases, parameters affecting the extraction process are interdependent and thus, optimization of each parameter in time is not the best option.

The extraction can be an equilibrium method or an exhaustive extraction. Both types have their own advantages and disadvantages. Equilibrium methods are typically much simpler and less expensive than exhaustive methods. They are also often more selective because they take full advantage of differences in extracting phase-matrix distribution constants to separate target analytes from interferences. However, the sensitivity is lower in equilibrium methods. In exhaustive extraction approaches selectivity is frequently sacrificed to obtain quantitative transfer of target analytes into the extracting phase. Therefore equilibrium methods typically do not require a cleanup step while exhaustive methods frequently do. The clear advantage of exhaustive methods is the sensitivity, and also the quantitative analysis is more reliable than in equilibrium methods.

8.2.2.1 vapor-phase extractionIf the analytes of interest are volatile, solvent extraction is not always necessary, and headspace (HS) techniques can be applied for the analysis, typically utilizing gas chromatography (GC) as the final analytical step. HS analysis can be defined as a vapor-phase extraction, involving the partitioning of analytes between a non volatile liquid or solid phase and the vapor phase above the liquid or solid. Typically the vapor-phase mixture contains fewer components than the usually complex liquid or solid sample and thus, the online coupling with GC is simple. There are a number of techniques for sampling HS vapors and introducing them to a GC. The main chal-lenge is the reconcentration of the vapor extract before the GC analysis, and as the analytes are volatile, this is usually done by an adsorbent or a cold trap or a combi-nation of these two. In case of liquid samples, particularly containing water, water is partially evaporated during analyte removal, and trapping of it in an appropriate device is mandatory in order to avoid problems on its passage through the chromato-graphic system.

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Traditionally HS sampling operates either in static (S-HS) or in dynamic mode (D-HS) but other modes are available as well, such as high concentration capacity headspace techniques (HCC-HS). HCC-HS techniques are based on either the static or the dynamic accumulation of volatile(s) on (ad)sorbent. Several successful tech-niques based on the HCC-HS approach are widely used in addition to conventional S-HS and D-HS samplings: HS-solid-phase microextraction (HS-SPME)9, in-tube sorptive extraction (INCAT, HS-SPDE)10,11 headspace sorptive extraction (HSSE)12, HS-liquid-phase microextraction (HS-LPME)13 and large surface area HCC-HS sampling (MESI, MME, HS-STE).14,15,16,17

Dynamic headspace (DHS), or purge-and-trap technique, is easily coupled online with GC. Because of the constant depletion of the analytes from the sample or from the adjacent atmosphere, the general approach on dynamic system potentially pro-vides improved analytical sensitivity when compared to static methods and other equilibrium extraction procedures. In an online system, desorption of trapped ana-lytes for subsequent analysis is usually performed using online automated thermal desorption (ATD) devices.

Also two types of membrane-assisted methods for vapor-phase extraction have been developed for online coupling with GC, namely membrane extraction with sorbent interface (MESI) and analytical pervaporation.18,19,20 In pervaporation, the permeate is extracted into a gas, and this method is mainly used for the analysis of VOCs, and for sample preconcentration.

The vapor-phase extraction techniques have several key advantages, the most important of which in comparison with the well-established solvent extraction method is a faster analysis. No chemical sample pretreatment is necessary and a smaller sample amount is required for the analysis, while reducing costs and elimi-nating the need for hazardous solvents. Interfering peaks caused by solvent impurities enriched during concentration steps are minimized and there is a lower amenability to laboratory contamination. Additionally, the method is fully automated (usually it is readily available commercially) and can be used for quantitative determination. Thermal extraction has, however, some limitations. Not all types of substrates are suitable for high temperature desorption. The use of thermal extraction is therefore complicated by the potential for carryover, transfer loss, molecular rearrangement, fragmentation, or breakdown of more thermally labile analytes at higher extraction temperatures, and matrix effects, leading to quantification inaccuracies.

8.2.2.2 liquid samplesLiquid environmental samples include water, wastewater, plasma, urine, and milk. For liquid samples, conventional methods, such as LLE, are being replaced by SPE, and more recently by SPME and stir-bar sorptive extraction (SBSE). Miniaturization of the extraction in terms of sample amount, amount of solvents, and extraction materials is a clear trend. The SPME and SBSE techniques are (nearly) solventless sample preparation methods for liquid samples. Several other miniaturized sample preparation systems have been developed in order to minimize the required volumes of solvent and sample in techniques based on SPE and LLE. The miniaturized format of SPE can be performed with SPE disks or with SPE pipette tip (SPEPT). LPME21 and membrane extraction techniques22 have also been developed as miniaturized

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versions of LLE. All share a common principle—analytes are extracted into an acceptor medium (sorbent or solution) by equilibrium processes. Although only a fraction of the analytes contained in the sample is typically recovered in SPME, SBSE, and LPME, in contrast with SPE and LLE which are exhaustive processes, the practically solvent-free techniques have the advantage of being more sustain-able and easily implemented, and they reduce exposure of the analyst to solvents. They also enable more selectivity in sample preparation than do the exhaustive extraction approaches. Generally, a disadvantage of miniaturization is that smaller sample volumes have to be used, hereby possibly decreasing the sensitivity if a suf-ficient amount of sample is available. On the other hand, the miniaturization of SPE enhances the potential for automation and online coupling with various separation systems. The mechanisms of the techniques for liquid samples are summarized in Table 8.1.

Recently, ionic liquids (IL) have also been tested in sample preparation mainly for liquid samples. The application of ILs in solid matrix samples has been limited, partly due to their high viscosities. The ILs have been used, for example, as solvents for LPME.23,24

8.2.2.2.1 Solid Phase ExtractionTraditional SPE is a widely used technique because it is suitable both for nonpolar and polar analytes, with varying volatility. A large range of adsorbents are available, from nonpolar adsorbents such as C18 to ion-exchange materials and to selective immunosorbents. In recent years, a lot of effort has been put into the development of novel SPE materials25 such as selective molecularly imprinted materials (MIP),26,27,28, and restrictive access materials (RAM).29

Reversed-phase, normal-phase, ion-exchange, and immunoaffinity adsorbents, and molecularly imprinted polymers (MIPs), exploit mainly one retention interactions only, whereas mixed-mode adsorbents combine several interaction mechanisms. RAM adsorbents combine hydrophobic, ionic, or affinity interactions and large matrix com-ponents (e.g., proteins) are excluded by appropriate selection of pore size or by use of chemical repulsion (by applying an appropriate hydrophilic coating to the adsorbent surface). The mode of interaction selected depends on the demands of the method, for

table 8.1basics of the Considered microextraction techniques

technique sample extracting phase equilibrium phenomena

SPME/SBSE Liquid Absorbent Liquid–solidSorption and partition

HS-SPME Gas Absorbent Liquid–gas–solidSorption and partition

LPME/MASE Liquid Liquid Liquid–liquid Partition

HS-LPME Gas Liquid Liquid–gas–liquid Partition

LLLME Liquid Liquid Liquid–liquid–liquid Partition

MEPS Liquid Solid Adsorption

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example screening or target analysis, the sensitivity required, and the final composi-tion (for example organic extract for GC or aqueous extract for HPLC). In the selec-tion of suitable adsorbent, the base material should also be considered. Silica-based columns have secondary hydrophilic or ionic interactions when reversed-phase and ion-exchange columns are used due to underivatized silanol groups. The silica-based adsorbents are stable within a pH range of approximately 2 to 7.5. Polymeric adsorbents (e.g., styrene–divinylbenzene) are more hydrophobic, more retentive, stable within the pH range 0 to 14, and no secondary interactions are observed. Newer polymers, for example Oasis HLB, combine hydrophilic and hydrophobic interactions.

Conventional SPE has been adopted for microextraction through three approaches. Microextraction can be performed off-line in well-plates or with minicolumns, or in a syringe or pipette tip packed with suitable solid-phase material. A wide range of sorbents are available in all of the methods, including C8 and C18 bonded phases on silica, poly-meric resins (polystyrene/divinyl benzene copolymer), polar sorbents such as alumina and silica, and ion-exchange sorbents. Mixed-mode sorbents, utilizing both the primary and secondary mechanisms for selective retention of analytes and some very specific selective sorbents are also available. These different phases enable interactions based on adsorption, H-bonding, polar and nonpolar interactions, cation, anion exchange, or size exclusion to be utilized in extraction. However, even though the miniaturization enhances the sample handling speed, the various steps in the SPE procedure, that is activation, conditioning, sampling, washing, drying, and elution, are still necessary.

Generally, SPE disks contain a smaller bed with a more homogeneous particle size distribution than conventional cartridges. The disk is typically a membrane-like bed with a thickness of about 0.5 mm and a diameter of down to 4 mm, which can be easily adapted to an at-line 96-well approach, thus decreasing the handling time per sample. Microextraction in a packed pipette tip30,31 or in a packed syringe (MEPS) is a relatively new technique.32–35 A small amount (ca. 1–4 mg) of the SPE material is inserted to a syringe (100–250 µl) or pipette tip as a plug, which is secured by frits at either end (Figure 8.2).36 Several pipettes can be used automatically, as shown in

fIgure 8.2 Microextraction in: (a) a packed syringe, or (b) packed pipette tip. (From Blomberg, L. G., Anal. Bioanal. Chem., 393 (2009) 797. With permission.)

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Figure 8.2. The sample is withdrawn through the solid-phase plug, and the analytes adsorb on the SPE material. The SPE material can then be washed before being eluted with a suitable organic solvent. The parameters to be optimized are the same as in any SPE procedure (Table 8.2). The procedure can be performed automatically by an autosampler, and even connected online with HPLC or even GC, if large vol-ume injection techniques are used.

Online connection with LC or GC is possible with MEPS. Most current MEPS applications involve online connection with LC, although some applications with online connection with GC have been reported. The reason for this is that with the automated procedure it is not easy to dry the SPE material before elution, and small amounts of water get injected into the GC instrument. In addition, the elution is typically performed with relatively polar solvents, such as methanol, which in GC can cause problems.

8.2.2.2.2 Solid-Phase Microextraction and Stir-Bar Sorptive ExtractionSPME and SBSE are both based on sorptive extraction, i.e., the analytes are extracted either from headspace or from liquid sample into a polymeric coating material.37 The main differences in the two techniques are the design of the extraction sys-tem and the amount of the sorbent material. Similar materials, such as polydim-ethylsiloxane, polyacrylate, Carbowax and, divinylbenzene, are used as sorbents. One significant advantage of both SPME and SBSE is that extractions can be done on-site.38,39

Sorptive extraction is an equilibrium technique, and for water samples the extraction of solutes from the aqueous phase into the extraction medium is con-trolled by the partitioning coefficient of the solutes between the sorbent phase and the aqueous phase. Although not fully correct, the octanol-water distribution coef-ficient (Ko/w) gives a good indication if and how well a given solute can be extracted with SPME or SBSE. Figure 8.3 shows the influence of Ko/w and phase ratio on extraction efficiency. For SPME, the volume of polydimethylsiloxane is approxi-mately 0.5 μL. For a sample of 10 mL, the phase ratio is thus 20,000. This results in poor recoveries for solutes with low Ko/w values. A solute with log Ko/w = 3 (e.g., naphthalene, Ko/w = 3.17), is only recovered for 4.8% with SPME while in SBSE the

table 8.2Critical parameters in meps

parameter Comments

Type of sorbent Selection as in conventional SPE, typically silica, C2, C8, C18, benzenesulfonic acid cation exchanger; polystyrene particles; MIP material and organic monolithic sorbent. Amount ca. 1 mg, particle size 40–60 μm.

Sample volume 25 to 250 µl. The sample may be pumped up and down several times, if necessary.

Conditioning and washing Same as in conventional SPE.

Elution solvent and volume Same as in conventional SPE. Volumes 20–100 µl.

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recovery is ca. 71%.37 In SBSE quantitative extraction (100%) is reached at much lower Ko/w values than in SPME.

SPME is very easy to use, and direct injection into a gas chromatograph is possible since the extraction system can be used in a similar manner to the GC injector syringe. Most applications involve SPME with GC and analytes are ther-mally desorbed in the heated GC injector. The main limitation of SPME is the small amount of sorbent and thus the low sample capacity. In-tube SPME and membrane SPME modes are also available. In SBSE, the amount of sorbent is considerably greater than in SPME; up to ca. 125 µl of sorbent can be coated onto a stir-bar. The liquid sample is simply stirred with this bar, and after extraction the stir-bar is removed and dried with a soft tissue. The analytes are desorbed either thermally (for GC analysis) or with liquid (mainly for LC analysis). In contrast to SPME, a special interface is required for thermal desorption.

SPME and SBSE devices are easily stored and transported so that the alteration of the extracted analytes is minimized. Field sampling is effective because only the fiber or stir-bar with the adsorbed analytes need to be brought back to the laboratory. Transportation of large sample volumes is avoided, and no sampling accessories such as pumps or filters (as required in on-site SPE, for example) are required. These techniques are also very useful for samples where the sample volume is limited.

For both SPME and SBSE, the main parameters to be optimized are the type and thickness of coating, extraction time, sample properties (pH, ion strength), agita-tion, temperature, and analyte desorption as shown in Table 8.3. In both cases, the extraction is based on an equilibrium process. In SPME, the extraction is usually non-exhaustive and the absolute recoveries are low. With SBSE, quantitative recoveries are possible due to the clearly higher sample capacity. For both methods, the extrac-tion times are typically quite long (15–90 minutes for SPME and up to 12 hours for SBSE). The applicability of both SPME and SBSE can be evaluated by using octanol-water distribution coefficient ( Ko/w ) as an indicator of how well, if at all, a given solute can be extracted with SPME (or SBSE).2,40 The sorption equilibrium is also dependent on the phase ratio, and thus on the thickness of the coating. Typically,

100

80

60Re

cove

ry (%

)

40

20

00 2

Log Ko/w

4 6

SBSESPME

fIgure 8.3 (See color insert following page 248.) Maximum extraction yield of SPME and SBSE with different logKo/w values.

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solutes should have relatively high log Ko/w values for SPME (< ca. 3). Quantitative extraction is only possible for solutes with log Ko/w values above ca. 5.

The main disadvantage of SPME and SBSE is that the extraction efficiency for highly polar analytes is poor. The extraction is diffusion-driven and non-exhaustive, which can result in low yields, especially in comparison with SPE. The diffusion also limits the throughput due to the long times required to reach equilibrium. For the extraction of polar analytes either direct derivatization in the sample matrix, or derivatization in GC injection port or the coating, can be applied to improve the extraction and analysis.41 The first approach is also the simplest as the derivatization occurs in the aqueous sample before or simultaneously with the extraction step. Both the affinity of the parent analytes for the sorbent and the efficiency of the subsequent GC separation are improved. For obvious reasons this strategy is not suitable for moisture-sensitive reagents. With in-port derivatiza-tion, polar analytes, with acid-base properties, are extracted into the SPME/SBSE sorbent as ion pairs, which are further decomposed at the high temperatures of the GC injection port to produce volatile by-products and alkyl derivatives of the target compounds. On-coating derivatization is performed either by preload-ing the sorbent with the derivatization agent so that the reaction occurs as soon as analytes are incorporated in the sorbent material (for water-sensitive reagents only the HS mode can be employed) or, alternatively, by first concentrating the analytes in the sorbent and then exposing the sorbent to the vapor of the deriva-tization reagent. The most suitable approach depends on the properties of the analytes and the derivatization reaction to be performed. It should also be noted that the extraction in SPME particularly is rarely quantitative, and thus, careful calibration is needed.42–44

SPME had been widely used for analysis of environmental pollutants in air, water, soil, and sediment samples, in on-site or off-site analysis. Hundreds of papers reporting environmental analysis with SPME have been published in recent

table 8.3Critical parameters in spme and sbse

parameter Comments

Type of sorbent Type and amount (thickness) of the sorbent are critical: larger amount leads to higher yield but slower desorption.

Sample volume To increase extraction efficiency, the volume of the headspace in the vial should be minimized. Usually, the vial is filled to half of its capacity.

Temperature Optimal temperature depends on the matrix composition and the sorbent used.

Extraction time Critical. Depends also on the extraction temperature.

Salt addition Addition of salting-out agents usually improves extraction efficiency. The effect depends on the particular analyte and salt concentration in the sample.

Stirring Usually improves the extraction.

Desorption Desorption should be as short as possible at a temperature somewhat higher than the boiling point of the component with the highest boiling point. Limited by the thermal stability of the sorbent.

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years and these applications have been reviewed recently.45 Table 8.4 presents the choice of fiber material for environmental applications of SPME.45 Several different coatings are commercially available. The most widely used coating is poly(dimethylsiloxane) (PDMS). Other materials include poly(acrylate) (PA), car-boxen/poly(dimethylsiloxane) (CAR/PDMS), carbowax/templated resin (CW/TPR), divinylbenzene/carboxen/poly(dimethylsiloxane) (DVB/CAR/PDMS) and carbowax-polyethylene glycol (PEG).46 CAR/PDMS is ideal for gaseous/volatile analytes; CW/DVB is suitable for the extraction of polar analytes, especially for alcohols. Sol-gel coatings have been introduced to overcome some problems of commercial fibers, such as solvent instability and swelling, low operating tempera-ture, and stripping of coating.

SBSE has also been widely applied in the environmental analysis. Most applica-tions deal with semi-volatile compounds such as polyaromatic hydrocarbons (PAHs), PCBs, pesticides, endocrine disrupting compounds (EDCs), phenols, organotin, and estrogens.47 In most applications, PDMS is used as the coating.

8.2.2.2.3 Liquid-Phase MicroextractionMiniaturized format of LLE, called LPME, single-drop microextraction (SDME), solvent microextraction, or liquid–liquid microextraction is a relatively new tech-nique. In LPME, a microdrop of solvent is suspended from the tip of a conventional microsyringe and then is either exposed to the headspace of the sample or immersed in a sample solution in which it is immiscible. The operation of LPME has been described in several literature reviews.48–51

Two-phase and three-phase systems are possible in LPME. The three-phase sys-tem can be regarded as a micro liquid–liquid extraction-back-extraction system which exploits the acid-base character of the analytes to achieve simultaneous enrichment and cleanup.52,53,54,55 The simplest mode of LPME is the SDME mode in which analytes are extracted from a stirred aqueous sample into a drop of organic solvent (ca 1–3 μL)

table 8.4Choice of spme fiber material in environmental analysis

Coating analytes

PDMS PAHs, pesticides, PBDEs, PBBs, PCDDs.

PEG BTEX, phenols, diesters, and pesticides.

Carbowax BTEX.

PDMS–PVA Pesticides, PCB.

PTMOS–MTMOS Benzene, toluene, ethylbenzene, 2-octanone, benzaldehyde, acetophenone, dimethylphenol, and tridecane.

LTGC BTEX, monohalogenated benzene.

Calix[4]arene Organochlorine pesticides, chlorophenols, phenolic compounds.

Crown ether Phenols, organochlorine pesticides, aromatic amines, BTEX, chlorobenzenes, arylamines.

Source: Modified from G. Ouyang, J. Pawliszyn, Anal. Bioanal. Chem. 386 (2006), 1059.

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suspended from the needle of a microsyringe. Once extraction is complete, the drop is retracted into the syringe and injected into the chromatographic system for analysis. The main limitation of LPME is the drop stability.

Another development of LPME is dispersive liquid–liquid microextraction (DLLME) in which a dispersive solvent, miscible with both the extracting solvent (microlitres) and the aqueous sample matrix, is used. In this method, the appropriate mixture of extraction solvent and disperser solvent is injected rapidly into an aqueous sample resulting in a cloudy solution. The cloudy solution consists of minute droplets of disperser solvent and extraction solvent in aqueous solution. In fact, the technique can be regarded as multiple-drop microextraction. In DLLME, the instantaneous mixing of the three components ensures equilibration within a few seconds due to the infinitely large interface between the fine extractor droplets and aqueous solution. Thus, transfer of analytes from the aqueous phase to the organic phase is very short compared with typical equilibrium extraction times for SPME and LPME. To sepa-rate the phases, centrifugation is required. Miscibility of disperser solvent in organic phase (extraction solvent) and aqueous phase is the main point for selection of dis-perser solvent. Typical disperser solvents are acetone, acetonitrile, and methanol.56,57,58 Also ultrasounds can be utilized for more efficient extraction in DLLME.59

The extraction in LPME is based on diffusion and the extraction is promoted by high partition coefficients. The most important parameters are the volume ratio of the solvent (drop volume) and sample phases, pH and ionic concentration of the sample, extraction time, properties of the organic solvent, and agitation of the sample (Table 8.5). Extraction of very hydrophilic compounds can be improved by ion-pair reagents, complexation reactions, or chemical derivatization. The enrichment factor (EF) and extraction efficiency (EE) are the two major parameters used to evaluate the effectiveness of a particular extraction. The EF is defined as the ratio of analyte concentration in the extract to that in the initial donor.

Environmental applications of LPME have been recently reviewed.55,60 Various types of environmental contaminants identified in different matrices include, among others, pesticides, PAHs, and PCBs.

table 8.5Critical parameters in the optimization of lpme

parameter Comments

Solvent type Volatility of the solvent is critical for GC. Usually, n-octyl alcohol, isoamyl alcohol, undecane, octane, nonane, and ethylene glycol are used.

Solvent drop volume Usually 1–2 μl

Drop exposure temperature

Usually ambient, although increasment of the temperature results in increased the extraction efficiency. High temperature can cause drop instability and partial evaporation

Extraction time Critical. Equilibrium should be reached between the extracting liquid and the headspace and water.

pH, salt addition Salt addition usually decreases the yield.

Stirring At low speed; stirring increases the yield but causes drop instability.

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8.2.2.2.4 Membrane-Assisted ExtractionOne way of minimizing the problem with drop stability which is a common problem in LPME is to add a polymeric membrane, which serves as a support for the extract-ing solvent, enabling the use of larger volumes, but also as a physical barrier between the phases. In this membrane assisted solvent extraction (MASE), the membrane is usually made of a porous or nonporous hydrophobic material (normally polypropyl-ene). A further benefit of the use of membrane is that, owing to its pore structure, the concentration of high-molecular-weight compounds in the sample extract is reduced. This membrane-assisted liquid extraction, which can be considered as a subtech-nique of LPME, can be performed either in a hollow fiber, membrane bag, or in a flat-sheet membrane module and either in static or dynamic mode.61–64 As in LMPE, two-phase and three-phase systems are possible in these techniques. Membrane extraction systems based on closed hollow-fibers are also available, and can be used for on-site sampling.

Many types of extractions utilizing membranes have been carried out as shown in Table 8.6. The two most common approaches in analytical separations are SLM and microporous membrane liquid– liquid extraction (MMLLE). The MMLLE is usually done from aqueous to organic solvent and thus, used mainly in combina-tion with GC. The final SLM extract is aqueous and thus the technique is typically combined with LC and electro-driven separations.

Static membrane-assisted extraction typically employs hollow fibers or membrane bags, both typically disposable. In dynamic MMLLE, the membrane unit is either a planar membrane or a hollow-fiber membrane. In the planar configuration the mem-brane is clamped between two blocks and separates two flow channels; the donor and acceptor channels. In the hollow-fiber membrane module, the acceptor phase flows inside and the donor phase outside of the membrane.65,66 Different forms of MASE are shown in Figure 8.4.

The extraction in MASE is based on diffusion and, as in LPME, the extraction is promoted by high partition coefficients. The most important parameters are the

table 8.6different types of membrane extraction

name of technique acronymtype of

membraneCombination of phases used for

donor/membrane/acceptor

Supported liquid membrane extraction

SLM Nonporous Aqueous/organic/aqueous

Microporous membrane liquid–liquid extraction

MMLLE Nonporous (microporous)

Aqueous/organic/organic Organic/organic/aqueous

Polymeric membrane extraction

PME Nonporous Aqueous/polymer/aqueous Organic/polymer/aqueous Aqueous/polymer/organic

Membrane extraction with a sorbent interface

MESI Nonporous Gaseous/polymer/gaseous Liquid/polymer/gaseous

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volume ratio of the acceptor (extractant) and donor (sample) phases, pH of the phases, ionic concentration of the donor phase, extraction time, properties of the organic solvent (sole or binary), and agitation of the sample. As in LPME, the extraction of very polar compounds can be improved by addition of ion-pair reagents, using com-plexation or derivatization or even an external driving force such as electrical field. The latter technique, in which electrical field is applied either side of the organic phase, is suitable for extraction of polar charged analytes.

Environmental applications of MASE are similar to those of LPME and include organic pollutants such as pesticides, PAHs, PCBs, aromatic amines.67 Both two- and three-phase modes have been utilized for extraction of environmental pollutants and contaminants.

8.2.2.3 solid and semisolid samplesEnvironmental solid samples include different types of matrices, including soil, sedi-ment and sewage sludge, plant and tissue samples and aerosol particles. Extraction techniques for solid and semi solid samples should be essentially exhaustive to guaran-tee efficient recoveries in different types of samples and also because the low levels at which microcontaminants are generally present in the environment. This requirement for quantitative extraction explains the general preference for Soxhlet or Soxtec rather than more selective techniques, such as supercritical fluid extraction (SFE), which

Needle forinjection ofacceptorsolvent

(a) (b)

(c)

Needle forcollection ofacceptorsolvent

Screw top

Vial

Sample solution

Sample solution in Sample solution out

Acceptor solution in Acceptor solution out

Steel blockPeek blockMembraneGrooveTeflon blockSteel block

Porous hollow fiber+ acceptor solvent

Magnetic crimp cap

Steel funnel

VialTeflon ring

Sample solution

Porous membrane bag+ acceptor solvent

fIgure 8.4 Different forms of MASE: (a) hollow fiber membrane extraction, (b) mem-brane bag, and (c) flat-sheet membrane extraction unit.

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are highly analyte- and/or matrix-dependent. In general, the alternative techniques allow a more efficient extraction of the analytes from the matrix by improving the contact of the target compound(s) with the extraction solvent. Extraction time and organic solvent consumption are both reduced, and sample throughput is increased. Enhanced extraction efficiency can be achieved by using microwave energy, as in microwave-assisted solvent extraction, also known as microwave assisted solvent extraction (MAE), ultrasound, as in sonication-assisted extraction (SAE), or solvents at high pressure and temperature, as in PLE. Also fluidized-bed extraction technique can be utilized.68 However, this technique has not been widely applied for the analysis of environmental samples. The selectivity of an extraction method for target analytes in preference to bulk matrix organic compounds (e.g., humic matter from sediment) is also a crucial parameter, since the presence of co-extracted matrix organics fre-quently requires post-extraction cleanup before chromatographic analysis. It should also be noted that soil, sediment and sewage sludge samples require more exhaustive methods of extraction, because the analytes tend to be very tightly bound to the sam-ple matrix. For the extraction of, for example, air particles, less exhaustive methods, such as SAE is often sufficient.

8.2.2.3.1 Conventional Techniques: Solid–Liquid Extraction and Soxhlet Extraction

Solid–liquid extraction (SLE) is a simple technique which is based on extraction of target analytes with a suitable solvent by stirring the solid sample in the extraction solvent. Soxhlet extraction is another well-established technique which is based on exhaustive extraction by an organic solvent, which is continuously refluxed through the sample contained in a porous thimble. SLE and Soxhlet extraction are the oldest technique used for the isolation of nonpolar and semi-polar organic pollutants from different types of solid matrices, including biota samples.

In both techniques, the main parameters affecting the extraction are the type of solvent and extraction time. It is essential to match the solvent polarity to the solute solubility and to thoroughly wet the sample matrix with the solvent for the extrac-tion. Typical solvents to extract POPs are n-hexane, dichloromethane, and mixtures of toluene–methanol, n–hexane–acetone, and dichloromethane–acetone.

Soxhlet extraction is still an attractive option for routine analysis for its general robustness and relatively low cost. The system is also simple and easy to use, and it allows the use of large amount of sample (e.g., 1–100 g) and the technique is not matrix dependent. There are a few commercial systems are available in which sev-eral samples can be extracted in parallel with much shorter extraction times and less organic solvent than using conventional Soxhlet. The parameters to be optimized are the type of solvent and the extraction time, so optimization is simple, although it can take quite a lot of time because the extraction time is long and the cleanup is also time-consuming. The main drawback still is the long extraction times, high amount of solvents required in the extraction which also means that the solvent must be evaporated to concentrate analytes before determination. Moreover, Soxhlet extracts are typically dirty and require extensive and time-consuming cleanup. In a similar manner to SLE, Soxhlet is still a good technique, if the sample amount is not very large, and if the results are not needed during the same day.

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8.2.2.3.2 Pressurized Liquid ExtractionIn PLE extractions are fast because of the higher diffusivity, improved solubilization capability and more efficient analyte interactions in a liquid solvent at temperatures above its boiling point. PLE is also known as pressurized fluid extraction (PFE), pres-surized solvent extraction (PSE), accelerated solvent extraction (ASE) and enhanced solvent extraction. PLE provides quantitative extractions with reduced consumption of solvents and substantially shorter extraction times than Soxhlet. For a number of organic trace pollutants, in various solid and semi solid matrices, the recoveries in PLE are comparable or even better than those with Soxhlet.69 The basic set-up for PLE has been described in detail.70–72 Miniaturized versions of the PLE system have been developed.73

The most important variables affecting the efficiency of the PLE process are the nature of the solvent, the temperature of the extraction and the extraction time (Table 8.7). Typically, similar solvents to those used for Soxhlet extraction give good results. Thus, it is relatively straightforward to replace old methods by PLE. Mixtures of low- and high-polar solvents generally provide more efficient extrac-tions of analytes than do single solvents. The temperatures usually range from ca. 60 to 200°C. With the exception of labile analytes or samples, higher extraction temperatures will increase the efficiency of PLE as a result of enhanced sample wetting and better penetration of the extraction solvent and also because of higher diffusion and desorption of the analytes from the matrix to the solvent. Typical extraction times vary between 10 and 30 minutes. PLE can be carried out in static or dynamic mode, and majority of PLE applications are performed in the static mode followed by a brief post-extraction dynamic flush with the organic solvent. In most cases, pressure does not have significant effect on the recoveries, and a relatively high pressure (from 4 to 20 MPa) is usually applied. Similarly, the flow-rate at which the extraction solvent is eluted in dynamic PLE has been found to have little effect on the recoveries.

It is possible to utilize purely aqueous solvents in PLE, i.e., to use pressurized hot water extraction (PHWE), also called subcritical water extraction (SWE), hot water extraction, high-temperature water extraction, superheated water extraction,

table 8.7Critical parameters in optimization of ple

parameter Comments

Nature of the solvent Similar solvents that are used in Soxhlet or SLE can be used; solvent mixtures typically used.

Temperature Elevated values enhance the extraction, due to increased diffusivity of the solvent into the matrix. Typically 60–200°C.

Pressure Often the effect of pressure is minimal.

Extraction time Extraction time has a large effect. Typically 5–30 min. For thermolabile compounds, long extraction times may result in degradation.

Number of cycles Depends on the type of the sample.

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and hot liquid water extraction. This technique utilizes water as extraction sol-vent at temperatures between 100 and ca. 350°C and at a pressure high enough to keep it in liquid state. Quantitative recoveries for polar compounds such as phe-nols can be obtained at temperatures below 100°C74 while less polar species (e.g., pesticides) require temperatures of about 200°C75,76 Temperatures of 250 to 300°C are required for the extraction of PCBs77 and PAHs66,78,79 and BFR.80,81 n-Alkanes are only extracted at temperatures higher than 300°C.82 PLE instruments can sel-dom be used for PHWE because the sealing materials do not withstand the high temperatures.

8.2.2.3.3 Sonication-Assisted and Microwave-Assisted ExtractionSAE utilizes acoustic vibrations causing cavitations in the liquid while microwave-assisted extraction (MAE) is based on the heating of an organic solvent by applying microwaves to the sample and extraction solvent.

In MAE, two techniques can be used. In traditional MAE multiple samples are placed in an oven where the microwave energy is dispersed throughout the oven cavity, while in focused microwave (FME) system, all of the microwave energy is applied to an individual sample in a smaller oven cavity, resulting in higher overall energy transfer to the sample relative to MAE. In a similar manner, SAE can be performed by placing the sample vessels into an ultrasound bath, or by using focused acoustic vibrations by placing the probe to each individual sample.

The most important variables affecting the efficiency of both SAE and MAE are the nature of the solvent, the temperature of the extraction and the extraction time (Table 8.8). In SAE, the solvents used in Soxhlet extraction typically make suitable solvents. In MAE, polar solvents that are capable of absorbing microwaves are used as the extraction solvents. Usually, methanol, isopropanol, and mixtures of hexane and acetone are used in MAE.83,84 The typical extraction times are 5–20 minutes. Both SAE and MAE are usually done statically in a discontinuous, batch mode. However, dynamic mode is possible in both of the techniques. Dynamic mode has several advantages over the conventional batch mode, one being that the sample is continuously exposed to fresh solvent, so that the extraction kinetics is improved. Furthermore, the filtration and rinsing steps after extraction are avoided and solvent consumption and the danger of loss and/or contamination of the extracted species during manipulation are minimized. A considerable reduction of extraction time, solvent consumption, and sample handling in Dynamic sonication-assisted extrac-tion (DSAE), with respect to the extraction in static way, has been reported.85,86 An increase in polarity of the extraction conditions (including solvents, analytes, and matrix) increases the efficiency, which may be either better or similar to that obtained by Soxhlet.

Several applications of SAE in environmental analysis have been reported.87–90 SAE has also been approved by EPA as method 3550B.91

8.2.2.3.4 Supercritical Fluid ExtractionSFE relies on supercritical fluids for the extraction, the most common fluid being carbon dioxide. SFE is an attractive technique because of its high diffusivity com-bined with high and easily tunable solvent strength. Another attractive feature is the

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ease of collection and concentration of the extract. Both static and dynamic modes can be used, and often the two modes are combined for efficient extraction. Typical extraction times vary from 5 to 60 minutes. A significant advantage of SFE is that various cleanup steps are easily added with it.92 For example, the sulfur and lipid cleanup steps can easily be combined with the extraction step. Before the extrac-tion, the sediment sample can be mixed with copper powder and sodium sulfate for the removal of moisture and sulfur. The main limitation of SFE is that it is unable to extract polar compounds, although it is possible to change the polarity of the supercritical fluid, thereby increasing its solvating power toward the target analytes, through the use of polar modifiers.

There are several parameters that affect the extraction recovery, including temperature and pressure, extraction time, flow rate, choice of modifier, and the col-lection mode (Table 8.9). The optimal conditions are strongly matrix dependent, i.e., fresh optimization may be required for different types of sample matrices.

An interesting application of SFE is the utilization of selective extraction as a tool for POP bioavailability studies93 in the extraction of POPs from various envi-ronmental samples. This is important, as recent data suggest that only a fraction of the total POP concentration in sediment is available for equilibrium partitioning, the rest being so sequestered that it is unavailable on a relevant time scale.94 SFE is also a good choice for the extraction of POPs from solid biological samples, although it has not been utilized very widely yet. Utilization of SFE in environmental analysis has been reviewed recently.95

table 8.8Critical parameters in optimization of mae and sae

parameter mae sae

Nature of the solvent

Solvents with high dielectric constant should be used. Typically, hexane–acetone dichloromethane–methanol and dichloromethane are used.

Selection based on solubility of the analytes. Typically similar solvents as used in Soxhlet or SLE.

Temperature Elevated values usually enhance the extraction, due to increased diffusivity of the solvent into the matrix. Typically 80–150°C.

Elevated values usually enhance the extraction, due to increased diffusivity of the solvent into the matrix. Typically 30–80°C.

Power/ energy of ultrasounds

Often the effect of power is not substantial.

Often the effect is not substantial.

Extraction time Extraction time has a large effect, typically 5–30 min. For thermolabile compounds, long extraction times may result in degradation.

Extraction time has a large effect, typically 5–60 min. For thermolabile compounds, long extraction times may result in degradation.

Nature of the matrix Particle size of sample affects the extraction and for reproducible results control of the matrix water content is required.

Particle size of sample affects the extraction.

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8.2.2.3.5 Matrix Solid Phase DispersionMatrix solid phase dispersion (MSPD) is based on manually blending the solid or semisolid sample in a mortar with a suitable solid phase material, such as derivatized C8- and C18-bonded silica, silica gel, sand, or Florisil. The solid support and sample are then transferred into a column and eluted with a suitable solvent, for example, hexane, dichloromethane, or acetonitrile. The most important factors affecting the MSPD extraction are the characteristics of the solid phase material (e.g., particle size), the ratio of sample to support material, use of chemical modifiers (e.g., acids, bases, chelating agents), elution solvents, and elution volume.96 The samples are usu-ally dried with anhydrous sodium sulfate or freeze-dried before blending with the MSPD sorbent. For most applications, particles with diameters of about 40 μm or in the range 40–100 μm are used.

In MSPD, sample disruption and dispersal onto the particles of the support mate-rial takes place in a single step. MSPD is usually done manually, although the elution can be accomplished also using, for example, PLE.96,97

For analyte extraction from animal tissues, C18-bonded silica is by far the most popular sorbent. For plant samples, both C8- and C18-bonded silica and Florisil are used extensively. Liquid samples are mostly dispersed on Florisil or C18-bonded silica. MSPD has successfully been employed for the extraction of PCBs, organo-chlorine pesticides (OCPs), and BFRs in fish samples,98–102 as well as for extraction of pesticides from fruit, vegetables and animal tissue.103 The benefits of this method are the ease of operation, low solvent consumption, and no investments in (expensive) equipment are required. The application is best suited for tissue and plant samples and cannot be easily applied to sediments due to the strong adsorption of the pollutants to the sediment, which may be a drawback for laboratories aiming at both matrices.

table 8.9Critical parameters in optimization of sfe

parameter Comments

Nature of the matrix Sample amount, particle size, water amount, type of matrix compounds. One of the main factors involved in the reproducibility. Particle size typically between 0.25 to 2.0 mm.

Temperature A rise in temperature will reduce the density of the CO2 (for a given pressure) thus reducing its solvating power, increasing the volatility of the compound to be extracted and the mass transfer velocity. Typically 35–150°C.

Pressure The higher the pressure, the greater the solvating power and the lower the extraction selectivity, usually described with density. Typically the density is ranging from 0.15 to 1.0 g/cm3.

Extraction time Critical, varies with each type of sample.

Modifier Required for the extraction of (semi)polar compounds. Typically methanol or acetone.

CO2 flow Has an effect on the solubility and mass transfer of the SFE process.

Collection media Typically solvent or adsorbent or empty vessel.

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8.3 Cleanup of extraCts

In most cases, particularly for solid samples, extracts require cleanup or fractionation, or both before the final analysis. The complexity of many environmental samples, such as sediment and biota matrices, often forces the use of multistep purification methods. The extremely low concentrations of POPs in environmental samples (e.g., sub-pg/g concentrations for PCDD/Fs) demand a thorough cleanup of the extracts in order to remove co-extracted substances (e.g., lipids, fatty acids, elemental sulfur, and humic acids) that are normally present at concentrations that are several orders of magnitude higher than those of the target pollutants.

The cleanup of the extract is important, even if selective detection is used with the chromatographic technique utilized. With selective detection, matrix compounds may be undetected; however, they can disturb the separation system and cause prob-lems in the following analyses. In GC, non-volatile matrix compounds can affect in several ways. Matrix compounds can cause problems in the injection, and if they enter to the column, contamination and even damage of the column stationary phase. In split and splitless injection a large amount of matrix compounds may change the evaporation process leading to changes in the amount of analytes entering the column. In splitless injection, matrix compounds can cause severe matrix effects. In on-column injection the non volatile compounds will enter to the column, caus-ing contamination of the column. PTV injection tolerates dirty samples relatively well and this technique is thus best suited to dirty samples. Also in LC analysis dirty samples cause problems. Matrix compounds usually shorten the lifetime of the column. Because the separation efficiency of the LC is not as good as in GC analy-sis, coelution of the target analytes with matrix compounds is a typical problem. In selective detection, coelution is typically not a serious problem with, for example, fluorescence detection. In MS, however, coelution causes matrix effects leading to problems in quantitation. Thus, with MS detection, careful cleanup of the samples is typically required.

Although novel methods have been developed for the extraction, the cleanup step still heavily relies on column chromatographic fractionation utilizing classical adsorbents, including silica, alumina, Florisil, and carbon. A few methods utilizing high performance liquid chromatographic separation (HPLC) have been reported.104 The benefit of HPLC is that different compound classes are clearly better separated and the separation as well as optimization of the separation can then be monitored with a HPLC detector. A gel permeation chromatography (GPC) is a good technique for removal of fat from the extracts. Both HPLC and GPC are easily automated since the same column can be used for hundreds of samples.

8.3.1 lipid removal from bioloGical extractS

The extracts of biological samples usually contain high concentration of lipids, which must be removed before the analysis. Particularly, if GC is used in the analysis, effi-cient removal of lipids is crucial. As the concentrations of many lipophilic POPs are related to the amount of lipids, the lipid content is often measured gravimetrically prior to the cleanup, or determined separately by a total lipid determination. Lipids

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can be removed by destructive or non-destructive methods. For serum or plasma samples, the lipid determination can be conveniently done on separate aliquots by enzymatic tests.

Although treatment with concentrated sulfuric acid is frequently used for the removal of lipids, it may destroy some of the compounds. Alumina columns offer less harsh treatment for lipid removal, and they are also often used for further cleanup of sediment extracts. GPC offers another approach for the removal of lipids from the biological extracts. For more selective removal of the lipids it can also be used in combination with Florisil columns.

8.3.2 Sulfur removal from Sediment extractS

Sediment extracts, and sometimes also soils and sewage sludge, often contain rela-tively large amounts of elemental sulfur, which would disturb the GC analysis and must be removed. The typical methods for sulfur removal are treatment with concen-trated sulfuric acid, copper powder, and tetrabutylammonium hydroxide /sulfite.

8.3.3 fractionation

After extraction, fractionation and further cleanup of the extracts is often needed. The goal of the fractionation is to remove interfering species and compounds that could disturb the analysis, and to concentrate the sample. In some cases, relatively simple cleanup is sufficient. In some cases, however, very careful fractionation is needed to remove compounds that have similar chemical characteristics than the target analytes. For example, in dioxin analysis, it is typically necessary to remove PCBs, which are present in much higher quantities than the dioxins. Since these compounds are structurally relatively similar, the fractionation must be done carefully.

Fractionation by column chromatography, liquid–liquid partitioning, or liquid chromatography can be used in the cleanup of extracts. In column chromatography, Florisil and silica columns are used, often in combination with alumina columns, to fractionate the extract into different classes of compound. Both pure silica and acid treated silica are used for fractionation. HPLC and GPC have also been used for cleanup and fractionation of the extract. HPLC fractionation has several ben-efits over the conventional column chromatography. Because the particle size of the HPLC columns is smaller than in column chromatography, the separation efficiency in HPLC is clearly better. Moreover, the fractionation can be monitored with detector and this feature allows not only the precise cutting of the fractions but also quicker optimization of the fractionation conditions.

Particularly in the purification of biological extracts, liquid–liquid partitioning is often used, followed often by further purification by column chromatography. In partitioning, ethanolic KOH solutions are often used together with a suitable organic solvent, such as hexane. Aqueous fractions are then neutralized, and often further purified by column chromatography.

Table 8.10 shows typical adsorbent materials used in fractionation of selected POPs. Often very complicated fractionation procedures are required. Particularly in

84534.indb 351 11/5/09 12:29:54 PM


the analysis of dioxins, which are typically present in very small quantities, careful fractionation is needed in order to separate them from the non-planar compounds (e.g., bulk of PCBs). An example of multistep cleanup procedure is the fraction-ation of polyhalogenated dibenzo-p-dioxins (PXDDs), dibenzofurans (PXDFs), and diphenylethers with five different columns.105 The Soxhlet extract of sewage sludge was purified first with a use of a multilayer silica column. The analyte fraction was eluted with hexane/dichloromethane and transferred to a macro alumina column where it was eluted with hexane/acetone, and it was further purified by GPC with use of cyclohexane/ethyl acetate for elution of the analytes. The sample was then fractionated by HPLC using NO2 column and rechromatographed with micro alu-mina column with benzene and two mixtures of hexane and dichloromethane as

table 8.10adsorbents used in the fractionation of selected pops

Compound adsorbent material

PAHs Silica cartridges after alkaline digestionAluminaAlumina after alkaline digestionFlorisil

PCBs SilicaFlorisil after sulfuric acid treatmentSilica + aluminaSulfuric acid + silica + silver nitrate coated silica + Florisil

Neutral silica + acidic silica + ENVI-Carb cartridge

PCBs, OCPs, PAHs, OPPs Silica Silica impregnated with sulfuric acid

OCPs Silica Florisil Alumina + Florisil cartridgesFlorisil + silica Alumina + silica + Florisil impregnated with KOH

PBDEs Silica after sulfuric acid treatment Alumina Alumina + silica Acidic silica + neutral silica + basic silica Acidic silica + neutral silica + basic silica followed by alumina

DDTs Florisil after sulfuric acid treatment

Trichlorobenzenes Alumina + acidic silica

PBDEs, PCDDs/Fs, PCBs, PBBs Acidic silica + neutral silica + basic silica Alumina + silica + acidic silica

Silica + carbon Silica + alumina + acidic silica + carbon

84534.indb 352 11/5/09 12:29:54 PM


eluents. The benzene and the first hexane and dichloromethane fractions were used for the determination of PCBs and chlorobenzenes, and the last hexane and dichlo-romethane fraction was used for the determination of PBDEs. After an additional cleanup step, polyhalogenated PXDDs, PXDFs, and octachlorothianthrene (OcCTA) were determined in the third fraction.

Several of the aforementioned cleanup steps may be combined in one step for simplification of the cleanup procedure. Multilayer columns loaded with, for example, alumina oxide, anhydrous sodium sulfate, acidified silica, basic silica, neutral silica, and porous graphitic carbon can be applied. In recent years, complete cleanup systems (e.g., PowerPrep, Fluid Management Systems, USA) have been developed for environmental analyses, which combine and automate several cleanup steps in a modular system using disposable columns. After sample extraction, the extract is loaded in this system and automatically processed resulting in the final extract, ready for injection. For PCDD/Fs and dl-PCBs, the used columns are a multilayer silica column, followed by alumina and finally porous graphitic carbon.106 With commercial systems, manual work is signifi-cantly reduced, however, the initial investments for such system are high and moreover, consumables are expensive compared to homemade multilayer columns.

HPLC fractionation has shown to be an effective system in fractionation of vari-ous types of environmental extracts.107–109 The fractionation can be done by using single column, on columns in series, either off-line or online. An example of multi-step HPLC fractionation utilizing several HPLC columns is shown in Figure 8.5.110 The fractionation method was based on coupled and automatically connected pre-parative HPLC columns, including cyanopropyl- and nitrophenylpropyl-bonded sil-ica and porous graphitized carbon stationary phases. Exploiting the potential of each column, compounds were separated mainly according to their polarity, number of aromatic carbons, and planarity. The fractionation procedure resulted in 18 fractions of which four were blank fractions. Excellent group-specific resolution, high repro-ducibility, and good recoveries were obtained in one HPLC-run.

8.3.4 derivatiZation

For GC analysis, polar compounds need to be derivatized prior their analysis. In HPLC, derivatization is seldom required, but can be used for enhancing the detection or retention.

Samples that contain highly polar compounds, such as organic acids, alcohols, amines, amides, polyhydroxy compounds, thiols, phenols, enols, glycols, and amino acids typically need to be derivatized before their GC analysis. The aim of the deriva-tization is to improve volatility, reduce the polarity of the substance and thus improve the peak shape, and reduce peak tailing of the GC analysis. Sometimes the derivatiza-tion also improves the stability of those compounds that are thermally labile. For GC analysis, the most typical derivatization procedures utilize silylation, alkylation, and acylation reactions. In silylation, the active hydrogens from acids, alcohols, thiols, amines, and other groups in the molecules are modified with an inert trimethylsilyl (TMS) group. Silylation also increases the molar mass and makes compounds more suitable for gas chromatography. In acylation, compounds that contain active hydro-gens (e.g., -OH, -SH, and -NH) are converted into esters, thioesters, and amides,

84534.indb 353 11/5/09 12:29:54 PM


200

Peak

1Pe

ak 2

Peak

3

Peak

4

Peak

5Pe

ak 6

Peak

8

Peak

7Peak

9

12

34

56

78

910

1112

1314

–16

1718

Frac

tiona

tion

win

dow

s and

ass

ocia

ted

subs

tanc

e cl

asse

s

ft (

min

:sec)

0–12

:00

1 212

:01–

17:0

0

Smal

l PA

Hs s

uch

as a

cena

phth

ylen

ew

ith m

ore

than

two

arom

atic

ring

sPA

Hs w

ith th

ree

arom

atic

ring

s(a

nthr

acen

e)PA

Hs w

ith fo

ur a

rom

atic

ring

s(p

yren

e)PA

Hs w

ith fo

ur a

rom

atic

ring

s(c

hrys

ene)

PAH

s with

five

aro

mat

ic ri

ngs

(ben

zo [a

]pyr

ene)

PAH

s with

six

arom

atic

ring

s(in

deno

[1,2

,3-c

d]py

rene

)PA

Hs w

ith se

ven

arom

atic

ring

s(c

oron

ene)

Mai

nly

mon

onitr

o-PA

Hs

(Hyd

roxy

-)qu

inon

es, k

eto-

, din

itro-

,hy

drox

y-PA

Hs,

and

N-H

eter

ocyc

les

with

risin

g po

larit

y

2-H

ydro

xyan

thra

quin

one

Mos

t pol

ar c

ompo

unds

Cha

ract

erisi

ng c

ompo

unds

are

giv

en in

bra

cket

s. f:

frac

tion,

CI:

chlo

rine

atom

s.

No

mod

el c

ompo

und

iden

tifie

dPC

Bs, e

lutin

g in

ord

er o

fch

lorin

atio

n in

ort

ho-p

ositi

on a

ndch

lorin

atio

n de

gree

, PC

Ns w

ith 3

Cl

317

:01–

30:0

0

430

:01–

40:0

05

40:0

1–65

:00

665

:01–

70:3

0

770

:31–

74:3

0

874

:31–

79:0

0

979

:01–

86:0

0

1086

:01–

96:0

0

1196

:01–

109:

00

1210

9:01

–121

:00

1312

1:01

–127

:00

1412

7:01

–131

:00

1513

1:01

–134

:00

1613

4:01

–138

:00

1713

8:01

–145

:00

1814

5:01

–151

:30

Co-

plan

ar P

CBs

with

out c

hlor

inat

ion

in o

rtho

-pos

ition

, PC

Ns w

ith 3

–6 C

lPC

DD

s/Fs

, PC

Ns w

ith ≥

6 C

l

Com

poun

d cl

asse

s

150

100

Intensity (mV)

50 025

5075

Tim

e (m

in)

100

125

150

fIg

ur

e 8.

5 A

ppli

cati

on o

f au

tom

ated

fra

ctio

nati

on p

roce

dure

by

HPL

C in

the

frac

tion

atio

n of

PO

Ps in

ext

ract

of

cont

amin

ated

sed

imen

t. Fr

acti

ons

1–18

are

sep

arat

ed b

y do

tted

line

s. (

From

Lüb

cke-

von

Var

el, U

., St

reck

, G.,

and

Bra

ck, W

., J.

Chr

omat

ogr.

A, 1

185,

31,

200

8. W

ith

perm

issi

on.)

84534.indb 354 11/5/09 12:29:55 PM


respectively, through the action of a carboxylic acid or a carboxylic acid derivative. In alkylation, active hydrogen is replaced by an aliphatic or aliphatic-aromatic (e.g., benzyl) group. Usually the derivatization is performed after the sample pretreatment procedure, just before the GC analysis. In some cases, the derivatization is done prior the sample preparation in order to improve the extraction efficiency, for example, before SPME or SBSE. However, then particular attention has to be paid on the selection of the derivatization procedure because most GC derivatizations cannot be done in the presence of water.

In liquid chromatography, the chemical derivatization is typically used to improve detection sensitivity by converting a compound with a poor detector response into a highly detectable product. In LC analyses, UV chromophores and fluorophores are often introduced into sample molecules to increase their sensitivity to UV absorption and fluorescence detection. Also in MS detection derivatization of the analytes can improve the selectivity and sensitivity of the detection. Benzoyl chloride, m-toluol chloride, and p-nitrobenzoyl chloride are reagents that can add a benzene ring to a solute molecule and turn it into UV absorbing compound. For example, to introduce UV chromophores into a solute containing a carbonyl group, 3,5-dinitrophenylhy-drazine and p-nitrobenzylhydroxylamine are probably the two most common and effective reagents. To prepare fluorescent derivatives of phenols, and primary and secondary amines, dansyl chloride (5-dimethyl aminonaphthalene-1-sulfonyl chlo-ride) is often used. Another fluorescent derivative is 4-chloro-7-nitrobenz-2,1,3- oxadiazole (NBD chloride) which provides highly fluorescent derivatives of primary and secondary amines but aromatic amines, phenols, and thiols only yield weakly or non-fluorescent derivatives.

8.3.5 online techniqueS

A recent trend in the development of analytical methodologies is the integration of the sample preparation step directly with the chromatographic system. In integrated online systems, extraction, cleanup, separation, and detection are connected with each other and the whole analytical procedure takes place in a closed, usually auto-mated system. Several of the problems associated with the traditional approaches are avoided in online techniques. Additional benefits are the increased sensitivity and reliability because the sample cleanup tends to be more effective.

The most common online systems are SPE-LC, and automated commercial sys-tems are available.111–115 SPE-GC is relatively easy to perform as well.116,117 Other extraction techniques utilized in online systems are LLE, SFE, PLE, MAE, SAE, and membrane-based sample pretreatment.118–128 The coupling is most commonly performed with the help of multiport valves. The SPE, LLE, and membrane-assisted techniques are best suited to liquid samples, while the other techniques are typically applied to solid samples. The various approaches for online coupling have recently been reviewed4,129 and they are summarized in Table 8.11. An example of automated MMLLE-GC system is shown in Figure 8.6. The system was applied to the analy-sis of POPs in water samples.130 In this application, aqueous sample was pumped through the MMLLE unit with toluene as the acceptor solvent. After the extraction was completed, the whole extract was transferred online to GC utilizing on-column

84534.indb 355 11/5/09 12:29:55 PM


interface. High enrichment factors and good sensitivity and selectivity were obtained with the online system.

8.3.6 Selection of Sample preparation methodS

In the following, general guidelines on the selection of the suitable extraction method depending on the type of the sample (analytes, matrix) are given and discussed. Methods used for the analysis of PAHs, PCBs, PCNs, PBDEs, PBBs, hexabromo-cyclododecane (HBCD), dioxins, synthetic musk fragrances, antimicrobials, drugs, sunscreens, UV filters, surfactants, algal toxins, pesticides, and organometallic compounds utilizing novel extraction techniques are summarized in Table 8.12 and relevant parameters of each extraction method are compared in Table 8.13.

For the analysis of volatile compounds with GC, thermal extraction techniques, such as DHS or headspace techniques combined with, for example, SPME are feasible alternatives of more conventional approaches. As solvent-free techniques, solvent peak does not disturb the following GC separation. Furthermore, during the partitioning,

table 8.11selected examples of applications utilizing online extraction Chromatography in the analysis of environmental samples

sample technique ref

Pesticides in water SPE-RPLC-MS-MS 113

Sulfonamide antibiotics and pesticides in natural water

SPE-RPLC-MS/MS 114

Estrogens in natural and treated waters SPE-LC-ESI-MS-MS 115

Endocrine disruptors in water SPE-GC-MS 116

PAHs, chlorofluorohydrocarbons, alkoxylated and alkylated phenols, and benzothiazole derivatives in sediment extracts

SPE-GC-MS 117

Nonpolar and polar ionizable compounds in water

SLM/MMLLE-RPLC-UV 118

Thiophanate-methyl, carbendazim, and 2-aminobenzimidazole in water

SLM-RPLC-UV, MMLLE-RPLC-UV

119

Pesticides in water MMLLE-GC-FID 120

Organochlorine pesticides in raw leachate water MMLLE-GC 121

Explosives in filters SFE-RPLC-UV 122

Organophosphorus esters in air particulates DMAE-SPE-GC-NPD 123

Organophosphorus esters in air particulates DSAE-SPE-GC-NPD 124

Caffeine, nitrotoluene, PCBs, chlorophenols, and anilines

PHWE-LC-UV 125

PAHs in sediment PHWE-NPLC-GC-FID 80

Brominated flame retardants in sediment PHWE-NPLC-GC-FID 81

PAHs in soil and sediment PHWE-MMLLE-GC-FID 130

Organic compounds in aerosol particles SFE-NPLC-GC-MS 126,127,128

84534.indb 356 11/5/09 12:29:56 PM


non-volatile high-molecular-mass compounds are eliminated which prevents contam-ination of the separation column and therefore makes this method very rugged. Due to its lack of concentrating effect, the static HS technique suffers from low sensitiv-ity and thus is not suitable for trace analysis. Of these methods, the instrumentation of SPME and SBSE is simpler than required in DHS, and thus, these methods have gained popularity in the extraction of volatiles in environmental matrices.

Also liquid of fluid-based extraction methods can be used for the extraction of volatile compounds. In a recent study, hydrodistillation (HD), focused microwave- assisted hydrodistillation (fMAE), and SFE were compared in the extraction of vola-tile metabolites of the brown alga Dictyopteris membranacea.131 The three techniques gave quite different composition of the extracted species, as shown in Figure 8.7. In the SFE at high pressure, the fluid showed a low selectivity leading to extraction of a large variety of relatively heavy compounds (sulfur compounds, alkanes, fatty

1. Sample

(a)

(b)

1 4 4

3 5 6 9 10

87

V1

2c2b

2. a-c pump3. Membrane unit4. Toluene5. Sample loop6. On-column interface

00.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

1.2E+06

5

1

2

3

4 11 12

56 7 8 9 10 13

1617

18

14,15

19

10 15Time (min)

20 25 30 35

7. Retention gap8. Analytical column9. Solvent vapor exit (SVE)10. DetectorV1. GC transfer valve

fIgure 8.6 (a) Online coupled MMLLE-GC-FID, and (b) analysis of POPs in water sam-ple by the MMLLE-GC-FID. (From Lüthje, K., Hyötyläinen, T., and Riekkola, M.-L., Anal. Bioanal. Chem., 378, 1991, 2004. With permission.)

84534.indb 357 11/5/09 12:29:57 PM


tab

le 8

.12

met

hods

use

d fo

r th

e a

naly

sis

of s

elec

ted

gro

ups

of p

ops

in e

nvir

onm

enta

l sam

ples

wit

h n

ovel

ext

ract

ion

tech

niqu

es

ana

lyte

sam

ple

prep

arat

ion

liqu

id s

ampl

esso

lid/s

emi s

olid

sam

ples

Poly

arom

atic

hyd

roca

rbon

s (P

AH

)SP

E (

Oas

is-H

LB

, EN

V1)

SP

ME

(PA

, PD

MS)

SBSE

(PD

MS)

LPM

E (

octa

nol)

SAE

(D

CM

:MeO

H),

PL

E (

tol,

H2O

, DC

M:E

tOH

),

MA

E (

Ace

t:Hex

), S

FE, D

MA

E (

DC

M:H

2O)

Chl

orop

heno

lsH

F-L

PME

(to

luen

e)SP

ME

(PA

NI,

CW

-TPR

, Pac

, PD

MS/

CA

R-P

DM

S, P

A)

SBSE

(PD

MS;

SDM

E (

buty

l ace

tate

SPE

(O

asis

MA

X, L

iChr

olut

EN

/3; S

DS-

alum

ina,

L

iChr

olut

; Bon

d E

lute

PPL

MA

SE (

PPy,

AcE

tO

SLE

(0.

1 M

HC

lSo

xhle

t (A

cet:

n-C

6,; M

eOH

: H2O

)M

AE

(M

eOH

:H2O

)PL

E (

tolu

ene:

acet

ic a

nhyd

ride

:pyr

idin

e, w

ater

)SA

E

Poly

chlo

rina

ted

biph

enyl

s (P

CB

s)SP

ME

(PD

MS,

PA

)L

PME

(to

luen

e)SA

E (

DC

M:M

eOH

),

PLE

(to

l, H

2O, D

CM

:EtO

H),

M

AE

(A

cet:H

ex, I

PA, h

ep),

SF

E,

DM

AE

(D

CM

:H2O

)

Poly

chlo

rina

ted

naph

thal

enes

(PC

Ns)

SPM

E (

PDM

S, P

A)

SAE

(D

CM

:MeO

H),

PL

E (

tol,

H2O

, DC

M:E

tOH

),

MA

E (

Ace

t:Hex

, IPA

, hep

), S

FE, D

MA

E (

DC

M:H

2O)

Poly

brom

inat

ed d

iphe

nyl e

ther

s (P

BD

Es)

an

d po

lybr

omin

ated

bip

heny

ls (

PBB

s)SP

ME

(PD

MS)

MM

LL

E (

unde

cane

, tol

uene

)SA

E (

DC

M:M

eOH

),

PLE

(to

l, H

2O, D

CM

:EtO

H),

M

AE

(A

cet:H

ex, I

PA, h

ep),

SFE

, DM

AE

(D

CM

:H2O

)

84534.indb 358 11/5/09 12:29:57 PM


Hex

abro

moc

yclo

dode

cane

(H

BC

D)

SPM

E (

PDM

S, P

A)

SAE

(D

CM

:MeO

H),

PL

E (

tol,

H2O

, DC

M:E

tOH

),

MA

E (

Ace

t:Hex

, IPA

, hep

), S

FE, D

MA

E (

DC

M:H

2O)

Poly

chlo

rina

ted

dibe

nzo-

p-di

oxin

s (P

CD

Ds)

pol

ychl

orin

ated

dib

enzo

fura

ns

(PC

DFs

)

SPM

E (

poly

dim

ethy

lsilo

xane

),SP

E (

C18

)PL

E (

hep,

N-H

exan

e, to

luen

e, a

ceto

ne, a

ceto

ne/n

-hex

ane

and

acet

one/

tolu

ene)

, MA

E to

luen

e-IP

A),

SF

E

Synt

hetic

mus

k fr

agra

nces

SPE

(C

18),

XA

D-2

)SP

ME

(PD

MS,

PD

MS-

DV

B, P

A, C

AR

-PD

MS)

SAE

(M

eOH

, Ace

tone

, DC

M);

PL

E (

Hex

:ace

t or

DC

M, H

2O:I

PA),

SF

E

Ant

imic

robi

als

SPE

(C

18, O

asis

HL

B, O

asis

MA

X, X

AD

-4)

SAE

(ac

eton

e, E

tAc)

, PL

E (

DC

M, H

2O, H

2O:I

PrO

H, S

FE

Hum

an a

nd v

eter

inar

y dr

ugs

SPE

(C

18, O

asis

HL

B, O

asis

MA

X, X

AD

-4)

LPM

E (

3-ph

ase;

HC

l/1-o

ctan

ol/ N

aOH

)SA

E (

acet

one,

EtA

c),

PLE

(D

CM

, H2O

, H2O

:IPr

OH

, SFE

Suns

cree

ns/U

V fi

lters

SPE

(C

18),

Oas

is H

LB

, Bio

head

s SM

-2),

SPM

E (

DV

B)

PL

E (

CH

ex/D

CM

, eth

yl a

ceta

te/H

2O)

Perfl

uori

nate

d su

rfac

tant

s (i

nclu

ding

PFO

S an

d pe

rfluo

rooc

tano

ic a

cid

(PFO

A))

SP

E (

C18

, Oas

is W

AX

, Oas

is H

LB

)PL

E (

EtA

c/D

MF,

H2O

/H3P

O4)

Alg

al to

xins

(e.

g. s

axito

xin,

ana

toxi

n-A

, do

moi

c ac

id, n

odul

arin

, mic

rocy

stin

s,

okad

aic

acid

, and

din

ophy

sist

oxin

-1)

-SA

E(M

eOH

, H20

-MeO

H),

PL

E

Pest

icid

esSP

E (

Env

i-C

arb,

C18

, Pol

ysty

rene

-.D

VB

,), M

ML

LE

(c

yclo

hexa

ne)

SPM

E (

PA, P

DM

S, P

DM

S-D

VB

)L

PME

(to

luen

e, h

exan

e, C

CL

4)

MA

E (

DC

M, h

ex, A

CN

, Hex

:ace

ton)

, SA

E (

MeO

H),

PL

E (

MeO

H:H

2O, H

2O)

Org

anom

etal

lic c

ompo

unds

( e

.g.

orga

notin

s)SB

SESP

ME

SAE

(to

luen

e),

SFE

84534.indb 359 11/5/09 12:29:57 PM


tab

le 8

.13

rel

evan

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acids). The HD and the fMAE extracts contained a large amount of compounds with higher volatility. Interestingly, sesquiterpene compounds were found in the extract obtained with fMAE, while these compounds were absent in the volatile fractions from HD and SFE. It is clear that sesquiterpenes, which have a relatively low volatil-ity, were steam distilled under the effect of microwaves energy. This study showed clearly that the choice of the extraction technique could induce dramatically the preferential obtaining of a given chemical class of compounds.

In selection of extraction method for liquid samples, the best options are SPE, SPME, SBSE, or LPME techniques.

SPE techniques, including miniaturized SPE methods such as MEPS and pipette-tip SPE, are adsorptive extraction techniques and they give quantitative recoveries, unlike the abovementioned sorptive extraction techniques, and are therefore well suited to trace analysis. A wide range of SPE materials are available, and not only nonpolar but also polar analytes can be extracted efficiently. These SPE techniques tend to be less selective, and matrix components are often extracted as well. On the other hand, the rather low selectivity is an advantage for profiling type of analysis, i.e., when all or most of the sample components are of interest. Pipette-tip SPE is simple to use but it is performed manually, and is user-dependent. The optimization is easy and flexible, only small volumes of solvents are needed, and as new pipette-tip can be used for each extraction, there are no problems with memory effects. MEPS can be employed as an automated online technique. The main advantage of the SPE methods over SPME, SBSE, and LPME is that because the extrac-tion is typically quantitative, the calibration is straightforward. This is in contrast to the other techniques, where various calibration methods are employed, includ-ing classical calibration relying on equilibrium extraction or more novel kinetic calibration.

For the extraction of volatile and semivolatile compounds, SPME and SBSE are highly useful techniques. The instrumentation of these two techniques is commer-cially available, and particularly SPME has been widely applied to the analysis of several types of volatile compounds in combination with GC analysis. SPME instrumentation is simpler, as the injection in SBSE requires a special interface for thermal desorption. However, the EE is clearly better in SBSE than in SPME, and SBSE thus more suitable for trace analysis. Both techniques are solvent-free and easy to use, and the EFs are typically high. In addition, SPME and SBSE devices are easily stored and transported, and they can be applied even in on-site sam-pling. Field sampling is effective because only the fiber or stir-bar with the absorbed analytes needs to be brought back to the laboratory. Transportation of large sam-ple volumes is avoided, and no sampling accessories such as pumps or filters (as needed in on-site SPE) are required. SBSE is the more rugged system for on-site sampling because SPME fibers are quite fragile. In addition, if trace amounts are to be extracted, SBSE gives higher recoveries and thus better sensitivities. Both techniques are very useful for samples where the sample volume is limited, as for example, in the determination of the composition of pore water in marine sedi-ments.132 Although derivatization can improve the extraction of polar analytes, both SPME and SBSE are best suited to the extraction of relatively nonpolar and reason-ably volatile analytes.

84534.indb 362 11/5/09 12:30:00 PM


The LPME techniques are not yet as widely applied as SPE, SPME, or SBSE. Of the LPME techniques, membrane assisted systems are slightly more complex sys-tems, but the ruggedness of these systems is clearly better. The membrane-assisted extraction techniques, which apply the same extraction mechanism as LPME, are best suited for semi-volatile to (relatively) nonvolatile analytes. The choice of solvent is less critical than in LPME. The repeatability is typically better than in LPME because there are no problems with drop stability as in LPME, and larger volumes can be extracted. Static membrane-assisted extraction, with either hollow fibers or mem-brane bags, is inexpensive and simple to use, and since the membranes are typically for single use, there are no problems with cross contamination. The flat-sheet modules are best suited to dynamic extraction of larger sample volumes and to online connec-tion with GC. In the flat-sheet modules the membranes are normally used for several extractions, and careful cleaning between extractions is required to minimize the risk of cross contamination. In a recent study, SMBSE and membrane assisted LLE were compared in the extraction of PAHs, PCBs, PBDEs, PBBs, PEs, NPs, and NPEOs in water samples.133 SBSE was applied with TD-GC–MS and MASE was combined with LVI-PTV-GC–MS. In general, the SBSE method provided better sensitivity, whereas MASE resulted in similar recoveries, but faster extraction. With SBSE, extraction time was 12 hours, and with MASE one hour.

Several studies have shown that similar sensitivities are obtained with SPE and SPME or SBSE.134,135 The latter two techniques are particularly suitable for the analy-sis of relatively nonpolar and volatile analytes which can be analyzed with GC. Since SPME and SBSE are more selective methods than SPE and can be performed in solvent-free mode, the enrichment is clearly higher and well compensates the lower recoveries of the less exhaustive SPME and SBSE. In some cases, higher recoveries can be obtained with SBSE than with SPE, as shown in a method developed for the extraction of PAHs in aquatic samples, where the recovery was improved with use of SBSE.135 In particular, recoveries of the more hydrophobic PAHs (log KOW>5) were noticeably higher with SBSE than with SPE. A further benefit of SBSE is that it is easy to apply as it is nearly solvent-free, and no restriction or cleanup procedures are necessary. In a study where SPME and SBSE were compared for the extraction of PAHs and organochlorine compounds in water and GC-MS was used for analysis, SBSE was found to be more robust and to enable higher recoveries (20.1–97.2%) than SPME (recoveries of 6.3–51.6%).136 Thus, lower detection limits (0.05 and 1.0 ng/L) were obtained for SBSE than for SPME (0.1 - 4.5 ng/L).

Also, MAE and PLE can be used for the extraction of liquid samples. In a recent study SPE, PLE, and MAE were compared with LLE in the extraction of organic contaminants (PCBs, OCPs, and PBDEs) from blood matrices.137 Two different MAE techniques, namely, cavity-dispersed MAE and focused microwave-assisted (FME) extractions were applied. Figure 8.8 shows the comparison of the tested methods. Of the tested methods FME method was found to be the most reliable, with highest IS recovery and low to moderate variability in the results. Also the precision of the method was generally better than other methods. All methods other than FME presented quantification problems for PBDEs. The highly reproducible concentrated microwave energy from this method is likely the cause of its optimal performance. LLE gave the poorest efficiency, precision, and accuracy of the techniques studied.

84534.indb 363 11/5/09 12:30:00 PM


For the extraction of solid, environmental samples, the solvent extraction techniques utilizing high temperatures or pressures, microwaves or sonication are typically a bet-ter option than SLE or Soxhlet. Of these techniques, PLE and MAE are more exhaus-tive in nature, and thus, suitable for samples in which the target analytes are tightly bound to the matrix, i.e., sediments and soils. SAE, on the other hand, is well suited for the extraction of less complex samples, such as aerosol particles collected on filters. In further comparison of PLE, MAE, and SAE, the latter in static mode is simple and fast, but it is labor-intensive and requires a skilled operator to obtain reproducible data. DSAE avoids many of the problems of the static mode. MAE and PLE, on the other hand, offer various advantages and disadvantages. While MAE is capable of extract-ing multiple samples simultaneously in a short time, additional cleanup is required to remove the sample matrix from the analyte-containing solvent, after cooling of the sample vessels. Like DSAE, MAE can also be done in dynamic mode. PLE allows multiple samples to be extracted sequentially in an automated system, but the instru-mentation is relatively expensive.

Several studies have compared the performance of these new extraction systems for the extraction of solid samples.131,138–141 Results have been slightly different, depend-ing on the study. However, in most cases, under optimized conditions, PLE, MAE, SAE, and SFE give similar or better recoveries than conventional Soxhlet methods. In a recent study, for example, the performances of MAE, SAE, Soxhlet, and PLE were compared for the extraction of PAHs from marine sediment and sewage sludge samples.138 The results are summarized in Table 8.14. In terms of extraction effi-ciency, extraction time, and amount of solvent required, PLE was superior over the

14000CertifiedLLEMAEFMEPFESPE

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fIgure 8.8 Comparison of extraction efficiencies of five different extraction techniques, in the extraction of PCBs in certified serum (SRM 1589a). (From Keller, J. M., Swarthout, R. F., Carlson, B. K. R., Yordy, J., Guichard, A., Schantz, M., and Kucklick, J. R., Anal. Bioanal. Chem., 393, 747, 2009. With permission.)

84534.indb 364 11/5/09 12:30:02 PM


other techniques. In the comparison it must be pointed out that, in this particular study, sonication was used without any optimization of the experimental conditions. Concentration and cleanup steps were the same for all the techniques. Similar selec-tivities have been obtained for all the techniques employed, with numerous interfer-ing compounds remaining despite the cleanup step. In another recent study, SAE, MAE, and PLE were compared in the extraction of different BFRs (TBBPA, HBCD congeners, and deca-BDE).140 Almost complete extraction of TBBPA and HBCD was achieved using MAE and PLE and particularly for deca-BDE, the pressurized condi-tions of PLE gave by far the highest extraction yields. SAE gave the lowest recover-ies, particularly for deca-BDE. It was also noticed that mixed polar/nonpolar solvent systems such as isopropanol/n-hexane allow higher extraction rates than polar mix-tures such as methanol/isopropanol alone. In another study, two validated European standard methods, based on LSE and LLE, were compared with PLE and SAE in the extraction of pesticides in soil.141 The results showed that with SAE was successful to recover all the selected substances with a good repeatability; however, the extraction efficiency was lower (57.0%) than with PLE (median recovery of 68.3.5%) and the two standard techniques (median recoveries of 72.7% and 65.7%).

SAE has been shown to enable efficient extraction of PAHs from biological marine samples. With the optimized ultrasonic extraction procedure, aromatic hydrocarbons from NIST-2977 were extracted with recoveries higher than 80% for most analytes.142 Similarly, for PCBs and organochlorine pesticides in sediments, good recoveries have been obtained with MAE, PLE, and SAE.143 Good recoveries have also been achieved with MAE for simultaneous extraction of PAHs, PCBs, phthalate esters, and nonylphenols in sediments.144 SFE has not been used on a rou-tine basis in the extraction of POPs in laboratory analysis, owing to the high cost of the instruments and the need to optimize a large number of operating parameters for each matrix. However, the greatest advantage of SFE in the analysis of complex biological and environmental samples is the possibility of obtaining highly selec-tive extractions and relatively pure and preconcentrated extracts. SFE has further been compared with Soxhlet extraction for the determination of PCBs and PCDDs in sediment.92 The study showed that concentrations of PCBs obtained by SFE were very similar to those of Soxhlet: agreement was good for 35 congeners out of 38. In another study of SFE where the extraction of PCDD/PCDFs was of interest,

table 8.14Comparison of ple, mae, and sae with soxhlet in the extraction of pahs in sludge sample

soxhlet ple fmae sae**

Efficiency 100 * 80–156% 54–79% 52–87%

Time 180 min 20 min 10 + 10 min 45 + 10 min

Solvent volume 250 ml 20 ml 30 ml 60 ml

Source: From Thordarson, E., Jönsson, J. Å., and Emnéus, J., Anal. Chem., 72, 5280, 2000.*Results compared with the value obtained with Soxhlet; ** method not optimized

84534.indb 365 11/5/09 12:30:02 PM


recoveries for lower chlorinated compounds were satisfactory in comparison with Soxhlet while the recoveries of highly chlorinated PCDD/PCDFs were lower.92 Evidently the highly chlorinated congeners are more tightly bound to sediment than the lower ones. A clear advantage of the SFE method was that the SFE method was much faster than the Soxhlet. SFE combined with an extra cleanup on alumina takes only 1.5 h, whereas Soxhlet takes 18 h plus several days of cleanup on differ-ent columns.

Compared with the other extraction methods for solid samples, MSPD is differ-ent in several respects. It is a manual technique, which combines sample disruption and dispersal of the sample onto particles of a solid phase support. Elution is also usually accomplished manually, although instrumental techniques such as PLE can be utilized for elution as well. The MSPD technique is well suited particu-larly for biological samples and plant-derived samples. The main advantage of the technique is the possibility to use a very small sample sizes and also the solvent consumption is low.

8.7 ConClusIons and future perspeCtIves

Sample preparation is still the most critical and time-consuming step within the overall analytical procedure needed to obtain accurate determination of POPs in environmen-tal biota samples. Due to the peculiarities of these samples, selection of the appropriate techniques to extract, purify, and preconcentrate the analytes, along with a careful optimization of the corresponding operational parameters, are critical. New analytical tools are continually being developed both for sample preparation and final analysis. Powerful and relatively fast extraction techniques are now available for the diverse sample matrices and analytes. Among the novel extraction techniques for solid sam-ples PLE is gradually replacing conventional Soxhlet extraction for solid and semisolid samples, both because the extraction is much faster and because of the commercial automated systems available. In addition, literature data from the Soxhlet methods can easily be utilized in selecting extraction solvent. However, the comparatively high investment cost of PLE instrument explains why conventional Soxhlet extraction, in combination with adsorption columns and/or GPC for purification and fractionation of extracts, is still widely used, being the sample preparation reference method in numerous applications. (D)SAE and (D)MAE offer efficient extraction of a variety of samples at considerably lower cost. SFE is an excellent method in many respects, but the matrix-dependent extraction mechanism, expensive instrumentation, and rather demanding optimization make the technique unsuitable for large-scale analyses. SFE has nevertheless proven to be an excellent tool for determination of bioavailable frac-tions of organic pollutants, particularly in sediment. It should also be noted that espe-cially the extracts from solid and semi solid samples require further purification and extract cleanup is usually still done by tedious conventional methods, i.e., using man-ual column chromatographic approaches. Improvement of this part of the analytical procedure requires much work, as it is becoming the bottleneck of the whole scheme.

Among the techniques for sample preparation of liquid samples, LLE methods continue to be widely used, but SPE has fast been gaining ground. The more novel extraction techniques, such as SPME, SBSE, MSPD, and LPME, can be expected

84534.indb 366 11/5/09 12:30:02 PM


to find a place in future, particularly because they can be used for on-site sampling, something that is particularly advantageous in environmental analysis.

abbrevIatIons

BFR Brominated flame retardantDHS Dynamic headspaceGC Gas chromatographyHPLC High performance liquid chromatographyHS HeadspaceLLE Liquid–liquid extractionLLLME Liquid–liquid–liquid microextractionLPME Liquid-phase microextractionMAE Microwave assisted extractionMASE Membrane assisted solvent extractionMESI Membrane extraction with sorbent interfaceMMLLE Microporous membrane liquid–liquid extractionMS Mass spectrometryPAH Polyaromatic hydrocarbonPOP Persistent organic pollutantPCB Polychlorinated biphenylPCN Polychlorinated naphthalenePBDE Polybrominated diphenyl etherPBB Polybrominated biphenylPCDD Polychlorinated dibenzo-p-dioxinPCDF Polychlorinated dibenzofuranPHWE Pressurized hot water extractionPLE Pressurized liquid extractionPME Polymeric membrane extractionPT Purge and trapOC Organochlorine pesticideSAE Sonication assisted extractionSBSE Stir-bar sorptive extractionSFE Supercritical fluid extractionSHS Static headspaceSLE Solid–liquid extractionSLM Supported liquid membraneSPE Solid-phase extractionSPME Solid-phase microextraction

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373

9 Sample Preparation for Gas Chromatography Using Solid-Phase Microextraction with Derivatization

Nicholas H. Snow

9.1 IntroduCtIon

Solid-phase microextraction (SPME) has been an important sample preparation technique in gas chromatography for almost 20 years. First developed for the analy-sis of volatile organic contaminants from water, its application has grown to numer-ous compound classes, including both volatile and non-volatile analytes. SPME may be combined with classical derivatization reactions to assist in transferring analytes from the sample to the fiber coating, from the fiber coating into and through the GC, or to aid in detection. This chapter summarizes techniques and efforts in the devel-opment and application of SPME methods for GC that include derivatization. Pre and post-extraction derivatization and simultaneous extraction and derivatization are possible and have been used for a variety of analytical problems. Using SPME for sample transfer makes derivatization readily automated and much simpler than

Contents

9.1 Introduction .................................................................................................. 3739.2 Overview ....................................................................................................... 374

9.2.1 Brief History and Timeline of SPME ............................................... 3749.2.2 Derivatization and Gas Chromatography ......................................... 3749.2.3 Modes of Derivatization with SPME ................................................ 376

9.3 Pre-Extraction Derivatization ....................................................................... 3769.4 Simultaneous Extraction and Derivatization ................................................3809.5 Post-Extraction Derivatization on the Fiber ................................................. 3819.6 Post-Extraction Derivatization in the Inlet ................................................... 3829.7 Summary and Conclusions ........................................................................... 386Acknowledgments .................................................................................................. 386References .............................................................................................................. 386

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in classical solution-based methods. The development of derivatization techniques involving SPME necessitates a further examination of classical derivatization reac-tions applied to GC.

9.2 overvIew

9.2.1 brief hiStory and timeline of Spme

It has been nearly 20 years since the initial development of SPME by Pawliszyn and colleagues.1,2 Over these two decades, the initial concept of extraction on the sur-face of fused silica fibers has evolved significantly and numerous related analytical techniques have developed. Most importantly, the dramatic rise of interest in SPME has opened a relatively new field of sample preparation: sorptive microextraction, in which many configurations of sorbents and equipment have been used to apply the original basic concept of sample preparation using a solid (or nearly solid) phase sorbent to trap analytes, followed by thermal desorption into a gas chromatograph to eliminate the use of traditional extraction solvents. The fundamental processes and techniques involved in SPME have been reviewed extensively elsewhere; the 1998 text by Pawliszyn is must reading for anyone interested in beginning SPME method development.3–6

SPME was originally conceived for the analysis of volatile organic contaminants from water. Following the initial development of direct immersion methods and discussion of the implications of the very small volume fiber phase on the kinetics and thermodynamics of liquid–liquid and liquid–solid extraction, additional extraction modes were developed.7 Headspace-SPME was introduced in 1993, followed shortly thereafter in the 1990s by interfacing with HPLC, CE, and various spectroscopic techniques.8–12 Originally, SPME was conducted on a bare fused silica fiber. When it was commercial-ized in 1993, coated fibers were used, with polydimethylsiloxane (PDMS) coating for nonpolar analytes, and polyacrylate (PA) for polar analytes. Since 1993, development of fiber coatings has been brisk, with several coatings of varying polarity and thickness now available.13 Applications development has also been brisk, with a Sci-finder search using “solid phase microextraction” as keywords producing about 3040 references from Chemical Abstracts, and an applications CD provided by the main SPME vendor pro-viding hundreds of references and application notes.14,15 Two books have also exten-sively reviewed SPME applications.16,17 In examining these references, it is interesting to note the progression of journals over 20 years, from chromatography and analytical chemistry journals (although the very first article was in a water research-specific jour-nal) to more applied journals in a wide range of disciplines. This is a strong indication of the acceptance of SPME as a routine and important analytical technique.

9.2.2 derivatiZation and GaS chromatoGraphy

Gas chromatography is generally applied to the analysis of volatile compounds, with the required level of volatility determined by the mass and chemical structure of the stationary phase. Non- or semi-volatile compounds can be analyzed by gas chromatog-raphy, but these compounds may require derivatization to form more volatile analogs prior to analysis. In classical packed column gas chromatography, derivatization is quite

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SPME with Derivatization 375

common, as the mass of stationary phase in the column is relatively high, promoting strong analyte retention, and the ability to temperature program is limited by the ther-mal mass of the column itself and by possible bleeding or decomposition of the station-ary phase material. Specific derivatization reactions for gas chromatography have been extensively treated in the literature, so except for a few reactions commonly used with SPME, they are not treated here. The classical text by Knapp and the review by Wells provide detailed information on myriad derivatization reactions for chromatography.18,19 In classical liquid–liquid or solid-phase extraction methods, derivatization may be car-ried out prior to extraction, or following extraction. If carried out following extraction, the derivatizing agent is often added directly to the dried extract.

Figure 9.1, adapted from a thorough review of techniques for extending the analyt-ical range of gas chromatography by Kaal and Janssen, illustrates the place of deriva-tization in extending the range of compounds for gas chromatographic analysis and places it into context with other techniques such as pyrolysis and high temperature GC.20 Derivatization generally allows analysis of more polar compounds by reacting them to form less polar, although often higher molecular weight, analogs. However, Kaal and Janssen also note that the need for derivatization has appeared to decrease over the past 20 years as alternative methods for chromatographic analysis of polar and/or high molecular weight compounds, such as LC-MS have become routine. They further note that the need for high peak capacity or separation efficiency for complex biological samples still makes derivatization with GC favorable for many applications, such as metabolomics.

The replacement of polar substituent groups with nonpolar substituents can improve chromatographic performance in several ways. First, the substitution of a polar alcohol with a nonpolar silyl ester improves injection performance as there are no longer polar groups present which may hydrogen bond with active glass surfaces in the inlet, causing possible tailing and discrimination during the injection process. Secondly, this substitu-tion of polar groups with nonpolar groups limits reactivity of the compound to active

GC

Pyrolysis Thermochemolysis

Derivatization

LC

MW

Polarity

HT-GC

fIgure 9.1 Diagram showing relationship between analyte molecular weight, polarity, and analysis technique. In gas chromatography, derivatization generally decreases polarity and increases molecular weight of the analyte. (From Kaal, E. and Janssen, H-G., J. Chromatogr. A, 1184, 43–60, 2008. Copyright 2008, Elsevier Science. With permission.)

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sites in the column itself, reducing peak tailing. Thirdly, replacement of a polar group with a less polar group such as trimethylsilyl, methyl, or acetyl to the molecule, while it does increase the molecular weight, generally will decrease the energy of intermolecu-lar interactions with the stationary phase, reducing retention on most polar phases while increasing retention slightly on nonpolar phases. Finally, derivatization can improve detection by adding a detector-specific moiety to the analyte or, most commonly in elec-tron impact GC-MS applications, by substituting a nonpolar functional group in place of a reactive proton, making the molecular ion more likely to be observed.

9.2.3 modeS of derivatiZation with Spme

In 1997, Pan and Pawliszyn thoroughly described the various modes of derivatizing when SPME fibers are used for the extracting phase and progress was recently reviewed by Stashenko and Martinez.21,22 They described three possibilities:

1. Derivatization of the analytes prior to extraction. 2. Doping of the fiber with the derivatizing reagent followed by simultaneous

extraction and derivatization. 3. Derivatization of the analytes in the fiber following extraction.

Flow charts for these possibilities are illustrated in Figure 9.2, with the additional post-extraction possibility of performing the derivatization directly in the gas chro-matographic inlet following desorption from the fiber.

The choice of derivatization scheme will depend on a number of factors. Pre-extraction derivatization is often used when the sample matrix is not complex or not reactive with the derivatization reagents themselves. It may also be used to enhance partitioning of the analytes into the fiber. For situations in which the sample matrix or interferences may react with the derivatizing reagents, post-extraction derivatiza-tion in the SPME fiber coating matrix or simultaneous extraction and derivatization within the fiber coating can be used. Often these methods were developed as analogs to classical methods; the choice or pre- or post-extraction derivatization was made based on the original method.

9.3 pre-extraCtIon derIvatIzatIon

Pre-extraction derivatization in the sample vial, often termed in situ derivatization involves addition of the derivatizing reagent directly to the sample prior to extraction by the SPME fiber. Shown in Figure 9.2a, the process involves addition of the deriva-tization reagent to the sample solution, followed by exposure of the fiber to the sam-ple, either by headspace or direct immersion, followed by exposure of the fiber to the GC inlet to desorb the derivatives into the GC. Pre-extraction derivatization is often used for the analysis of small, polar molecules, to make them more amenable to head-space SPME or to the more commonly used nonpolar fibers. In the forensic analysis of amphetamines, while the analytes are generally volatile enough for headspace extrac-tion, derivatives are often desired to ensure effective confirmation of the structures by mass spectrometry.23,24 For the analysis of amphetamines from hair, samples of hair are first digested with 1M sodium hydroxide and then pH adjusted with phosphate to

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pH 6.0. This solution is then mixed with a small amount of HFB-Cl (heptafluorobutyryl chloride), followed by exposure of a PDMS SPME fiber to the headspace of the solution. The fiber is then desorbed into the gas chromatographic inlet as usual. Figure 9.3 shows a key result from this work: quantitative comparison of derivatization-SPME results with a more classical solid-phase extraction approach. The results were very similar.

In situ derivatization followed by SPME has also been used for analysis of halo-acetic acids and related compounds in drinking water supplies.25 These compounds are by-products of traditional water purification methods and some are considered by the US EPA as possible or probable human carcinogens. Haloacetic acids are

b.

a.

- Analyte

- Derivatizing reagent

- Derivative

(a) (b)

1 2

(c)

3

fIgure 9.2 Flow charts showing SPME derivatization procedures. (a) Derivatization in the sample matrix. 1: Sample in the matrix; 2: Derivatization reagent added and reacts with sample; 3: Derivatives are formed in solution and extracted by SPME either headspace or direct immersion. (b) Pre-extraction on-fiber derivatization. 1: Fiber is exposed to headspace of derivatization reagent, reagent is absorbed into fiber matrix; 2: Fiber is exposed to sample; 3: Derivatives are formed in the fiber matrix. (c) Post-extraction on-fiber derivatization: 1: Fiber is exposed to ana-lyte either headspace or direct immersion; 2: Fiber containing analyte is exposed to headspace of derivatization reagent; 3: Derivatives are formed in the fiber matrix. (From Stashenko, E. and Martinez, J., Trends Anal. Chem., 23(8), 553–561, 2006. With permission.)

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derivatized with demethyl or diethyl sulfate in the original aqueous solutions to form methyl esters, which are much more amenable to analysis by GC than the parent com-pounds. In both examples, the derivatization procedure is quite simple, involving just addition of the derivatization reagent to the original sample, immediately followed by exposure of the SPME fiber to the headspace in the sample vial. Figure 9.4 shows the TIC and several extracted ion chromatograms showing separations of derivatized haloacetic acids extracted from swimming pool water. These were measured in aque-ous solution at approximately 0.2–250 µg/L with detection limits in the approximate 0.01–0.5 µg/L range, depending on the specific analyte.

Stashenko and colleagues used pre-extraction derivatization in combination with headspace SPME to determine low molecular weight aldehydes and carboxylic acids from a variety of matrices including air is a shoe factory, car exhaust, foot sweat, breath, and rainwater.26 In this work, they made pentafluorobenzyl derivatives of the carboxylic acids and pentafluorophenyl derivatives of the aldehydes in solution prior to extraction, followed by headspace extraction onto PA fibers.

Finally, in another application designed to make the analytes amenable to headspace extraction, Cancho, Ventura, and Galceran derivatized volatile aldehydes in water using PFBHA (O-(2,3,4, 5,6-pentafluorobenzyl)hydroxyamine hydrochloride) prior to headspace SPME extraction.27 They examined C2–C10 aldehydes and thoroughly described method development and validation for both the derivatization reaction step and then the ensuing headspace-SPME extraction using a divinylbenzene-PDMS fiber. They observed separation of E- and Z-isomers of several derivatives and linear ranges of about 0.1–20 µg/L. A standard chromatogram is shown in Figure 9.5. Note the sepa-ration of isomeric E- and Z-pairs shown as peaks 2 and 3 for E- and Z-acetaldehyde, 4 and 5 for E- and Z- propanal and the separation from some artifacts of the in-matrix derivatization. Additional details are provided in the reference.

45

30C

once

ntra

tion

(pm

ol/c

m)

15

00 – 1 1 – 2 2 – 3

Distance from hair root (cm - cm)

SPME

Extrelut

3 – 4 4 – 5

fIgure 9.3 Comparison of amphetamine recovery from hair using SPME with pre-extraction derivatization and solid-phase extraction on EXtrelut. Note the similar responses to both meth-ods for all samples. (From Liu, J., Hara, K., Kashimura, S., Kashiwagi, M., and Kageura, M., J. Chromatogr. B, 758, 95–101, 2001. Copyright 2001, Elsevier Science. With permission.)

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100TIC

m/z 59

m/z 83

m/z 117

m/z 129

m/z 173

m/z 163

m/z 209

m/z 165

m/z 251

%

0100

% 1

2

3

4

5

6

7

IS

8

0100

%

0100

%

0100

%

0100

%

0100

%

0100

%

0100

%

0100

%

02.50.0 5.0 7.5

Time (min)10.0 12.5 15.0

fIgure 9.4 Headspace-SPME-GC-MS total-ion chromatogram and single ion chromato-grams of methyl haloacetates from swimming-pool water. Compound identifications: 1, monochloroacetic acid; 2, dichloroacetic acid; 3, trichloroacetic acid; 4, bromochloroacetic acid 5, dibromoacetic acid; 6, bromodichloroacetic acid; 7, chlorodibromoacetic acid; and 8, tribromoacetic acid methyl esters; IS, 2,3-dibromopropionic acid methyl ester. Methyl esters were prepared in situ using demethyl or diethyl sulfate. (From Sarrion, M., Santos, F., and Galceran, M., Anal. Chem., 72, 4865–4873, 2000. Copyright, 2000, American Chemical Society. With permission.)

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9.4 sImultaneous extraCtIon and derIvatIzatIon

Simultaneous extraction and derivatization may be performed by first doping or loading the SPME fiber with a derivatizing reagent and then exposing the fiber either directly to the analytical sample or to its headspace. Shown in Figure 9.2b, the fiber is first exposed, usually to the headspace vapor of the derivatization reagent or a solution containing the reagent. The fiber containing the reagent is then exposed to the sample, usually in headspace, to avoid extraction of the derivatization reagent into the sample and analytes are extracted and derivatized in a single step. The fiber is then exposed in the inlet of the GC to desorb the derivatives.

In their 1995 article, Pan, Adams, and Pawliszyn demonstrated extraction of fatty acids with simultaneous derivatization by reagents pre-doped into the fiber.28 This was the first report anywhere in the literature, of a derivatization reaction being per-formed within the SPME fiber coating. They studied short chain fatty acids that were too polar to effectively extract into a polar PA fiber as native compounds. The fiber was pre-doped with 1-pyridinyldiazomethane by exposing it directly to a 5 mg/mL solution in hexane for 60 minutes. The fiber, now containing the derivatizing reagent, was exposed to the headspace of a solution containing the fatty acids. The practical and theoretical development of derivatization in a pre-doped fiber, presented in this paper, is important reading.

300

250

Resp

onse

(mV

)

200

150

100

50

00 2 4 6

*

d

1

3

245

6

789

101112

13

14

1516

1718

1920

21

22 2624

23+25

d dd

8 10 12 14 16 18 20 22Retention time

24 26 28 30 32 34 36 38 40 42 44

fIgure 9.5 In situ PFBHA–headspace-SPME–GC–ECD chromatogram of a water sam-ple (30 ml) spiked with aldehydes at 5 mg/ l. Extraction was performed by headspace-SPME with DVB–PDMS fiber. Identification of peaks: 2,3: E, Z-acetaldehyde; 4,5: E,Z-propanal; 7,8: E,Z-butanal. *: 1,2-dibromopropane; w: E, Z-2,4,5-trifluoroacetophenone; d: artifacts. (From Cancho, B., Ventura, F., and Galceran, M., J. Chromatogr. A, 943, 1, 2002. Copyright, 2002, Elsevier Science. With permission.)

84534.indb 380 11/5/09 12:30:12 PM


Analysis of formaldehyde is often difficult due to reactivity of the analyte under many extraction and environmental conditions. In one of the classical examples of SPME in the field, Koziel, Noah, and Pawliszyn used a PFBHA doped fiber to extract formaldehyde from indoor air.29 They showed that the pre-doping technique was espe-cially effective because slow kinetics of desorption and saturation of the derivatizing reagent in the fiber allowed complete reaction of PFBHA and formaldehyde to form a more stable oxime. The oxime product is then desorbed into a GC for analysis. Stability of the oxime allowed extraction in the field followed by later analysis in the lab.

9.5 post-extraCtIon derIvatIzatIon on the fIber

The basic procedure for post-extraction on-fiber derivatization is very straightfor-ward and demonstrated in Figure 9.2c. First, SPME is performed on a sample as usual, typically by direct immersion with consideration of the typical extraction conditions, including: choice of fiber phase and film thickness, extraction time and temperature, agitation method and speed, addition of modifiers such as salt and/or pH adjustment to the sample, and sample volume. Following extraction, the fiber, now containing the extracted analyte(s) and matrix components, is exposed to the derivatizing reagent. Since typical gas chromatographic derivatizing reagents are commonly volatile and highly reactive, exposure is often to the headspace of a small quantity of the derivatizing reagent, rather than directly to the reagent itself. Important considerations in the derivatization step include choice of the derivatizing reagent, reaction time, and temperature. Finally, the fiber, containing the derivatized analytes, is exposed in the inlet of the gas chromatograph as usual for an SPME injection, with consideration to injection liner volume, deactivation and temperature, splitless time, purge flow and initial column conditions.30

While the bulk of SPME-GC applications have involved volatile analytes, it was recognized relatively early on that the use of SPME could be significantly widened if derivatization, either before or after the extraction, could be performed, and the first reports of derivatization in combination with SPME for drug analysis were made in the 1990s, for the analysis of estrogens.31 Especially in drug analysis, applications such as in vivo sampling combined with the practical difficulties with SPME-HPLC raise interest in post-extraction derivatization of the extracted analytes on the SPME fiber. In the analysis of drugs from biological and environmental samples, post- extraction derivatization is preferred over pre-extraction fiber doping with the derivatizing reagents, or over derivatizing directly in the sample matrix, as it allows the use of water sensitive derivatizing reagents and limits reaction of the derivatizing reagents with unwanted matrix components.

Much of the work using post-extraction derivatization on the fiber has focused on the analysis of estrogens, steroids, and other endocrine disrupting compounds. We note that estrogens are excellent model compounds for testing pharmaceutical analy-sis techniques because both the derivatives and the parent compounds are detectable by gas chromatography. Several authors have described analyses of estrogens and steroids employing SPME with post-extraction on-fiber silylation using BSTFA as the derivatizing reagent.32 Most recently, Yang, Luan, and Lan demonstrated an SPME-post-extraction derivatization-GC-MS determination of several estrogens

84534.indb 381 11/5/09 12:30:13 PM


and steroid hormones that provides a useful example of the method development process and typical analytical figures of merit.33 Figure 9.6 shows typical GC-MS data for a mixture of eight analytes, spiked in water at 1–100 µg/L.

Herbicides are another family of suspected endocrine disruptors that have received continuing attention in the literature. SPME with post-extraction on- fiber derivatization has been used to determine several acidic herbicides in water.34 Following extraction with a PA fiber, extracted herbicides were derivatized using MTBSFA (N-methyl-N-(tert-butyldimethylsilyl)-trifluoroacetamide) to form silyl derivatives. This derivatization was performed by exposing the extracted fiber to the vapor of the derivatizing reagent at room temperature in a sealed vial for 10 minutes. Figure 9.7 shows typical chromatograms for several herbicides. As seen in the figure, the extracted ion chromatograms are relatively interference free, showing both the selectivity of the extraction process and the additional selectivity provided by the on-fiber derivatization, which, as observed by several authors, appears to provide more regioselective reactions than traditional solution derivatization methods. They also found that the SPME-based derivatization method compared favorably with more traditional SPE and LLE based methods.

Bisphenol A, one of the most widely used monomers in polymer synthesis and a common contaminant in finished polymers, has received much recent attention in the press due to concerns about toxicity and wide exposure to the public.35 Post-extraction derivatization on the fiber has been used to determine bisphenol A in landfill leachates in China.36 Landfill leachate samples were adjusted to pH 2 and extracted using a PA fiber. Following extraction, derivatization was performed on the fiber by exposing it to BSTFA (bis-trimethylsilyl trifluoroacetamide) vapor in a sealed vial for 5 minutes at 25°C. As observed by other authors for drug analysis, increased derivatization time and temperature led to reduced analyte signals, probably due to evaporative loss of the derivative. A linear range of 0.09–200 ng/mL was observed.

9.6 post-extraCtIon derIvatIzatIon In the Inlet

Derivatization may also be performed directly in the gas chromatographic inlet. Typically this involves performing the SPME procedure as usual and then desorbing the analytes into a gas chromatographic inlet that has been pre-saturated with deriva-tization reagent, typically by injecting an aliquot of reagent into the inlet prior to des-orption. Derivatization in the gas chromatographic inlet following SPME extraction was originally proposed by Pan and Pawliszyn in their early work on fatty acid methyl esters.21 They formed the more volatile methyl esters from the parent fatty acids by pre-doping the glass sleeve within the inlet with the derivatizing reagent. Alzaga and col-leagues used derivatization in the inlet to propose SPME as a tool for analysis of anionic surfactants in water.37 Linear alkylbenzenesulfonates were first combined with an ion pairing reagent (tetrabutylammonium) in the sample matrix. The resulting low polarity ion pairs were then extracted using PDMS fibers, followed by reaction (again with the same ion pairing reagent) upon heating in the GC inlet to form sulfonated butyl esters. Thus both ion pair extraction and derivatization were performed with the addition of a single reagent to the original samples. Figure 9.8 shows selected ion chromatograms of standard water, waste water, and sea surface waters obtained by this method.

84534.indb 382 11/5/09 12:30:13 PM


3000

000

1

2

3a3b

45

7 6

82

3a

2

3b

3a

3b

(a)

2600

000

Abundance

2200

000

1800

000

1400

000

1000

000

6000

00

2000

00

5500

000

4500

000

Abundance

3500

000

2500

000

1500

000

5000

0007.

008.

009.

0010

.00

11.0

0T

ime

12.0

013

.00

14.0

015

.00

16.0

017

.00

18.0

0

1

23a

3b4

57 6

8

(b)

7.00

8.00

9.00

10.0

011

.00

Tim

e12

.00

13.0

014

.00

15.0

016

.00

17.0

018

.00

fIg

ur

e 9.

6 SP

ME

-hea

dspa

ce s

ilyla

tion

-GC

-MS

full

-sca

n ch

rom

atog

ram

(a)

and

SIM

chr

omat

ogra

m (

b) o

f es

trog

ens

and

ster

oids

. Pea

k id

enti

fica-

tion

: 1: o

ctyl

phen

ol, 2

: non

ylph

enol

, 3a,

3b:

die

thyl

stil

best

rol,

4: d

ehyd

rois

oand

rost

eron

e, 5

: est

rone

, 6: 1

7-β-

estr

adio

l, 7:

test

oste

rone

, 8: p

regn

enol

one.

Sp

ike

leve

l: D

ES

at 1

µgL

−1, T

and

PR

EG

at 1

00 µ

gL−1

, oth

er c

ompo

unds

at 1

0 µg

L−1

. (Fr

om Y

ang,

L.,

Lua

n, T

., an

d L

an, C

., J.

Chr

omat

ogr.

A, 1

104,

23

–32,

200

6. C

opyr

ight

200

6, E

lsev

ier

Scie

nce.

Wit

h pe

rmis

sion

.)

84534.indb 383 11/5/09 12:30:14 PM


130

KCouns

25 1520 10 5 015

.0KCouns12

.5 7.5

10.0 5.0

2.5

0.0

KCouns

7.5

10.0 5.0

2.5 0

KCouns

304050 20 10 0

30

KCouns

20 10 0

KCouns

7.5

10.0 5.0

2.5

0.0

KCouns

3040506070 20 10 0

KCouns

304050 20 10 0

23

4

5

m/z

: 225

+227

m/z

: 277

+279

m/z

: 211

+213

m/z

: 245

+247

1617

1819

2021

2223

24M

inut

es16

1718

1920

2122

2324

Min

utes

6

7

8

9

m/z

: 279

+281

m/z

: 283

+285

m/z

: 199

+201

m/z

: 219

+221

fIg

ur

e 9.

7 SP

ME

-pos

t-ex

trac

tion

on-fi

ber

deri

vati

zatio

n-G

C-M

S ex

trac

ted

ion

chro

mat

ogra

ms

of h

erbi

cide

s fo

r a

spik

ed w

ater

sam

ple

(0.1

ng/

ml

per

com

poun

d).

Peak

ide

ntifi

catio

n: 1

: 2-

(4-c

hlor

o-2-

met

hylp

heno

xy)

prop

anoi

c ac

id (

Mec

opro

p),

2: 3

,6-d

ichl

oro-

2-m

etho

xybe

nzoi

c ac

id (

dica

mba

), 3:

2,

4-di

phen

oxya

cetic

aci

d (2

,4-D

), 4:

4-c

hlor

o-2-

met

hylp

heno

xy a

cetic

aci

d (M

PC

A),

5: 2

-(2,

4-di

chlo

roph

enox

y) p

ropa

noic

aci

d (2

,4-D

P), 6

: 2-

(2,4

,5-

tric

hlor

ophe

noxy

) pr

opan

oic

acid

(2,

4,5-

TP)

, 7:

2,4

,5-t

rich

loro

phen

oxya

cetic

aci

d (2

,4,5

-T),

8: 4

-(4-

chlo

ro-2

-met

hylp

heno

xy)

buta

noic

aci

d (M

CPB

), 9:

4-(

2,4-

dich

loro

phen

oxy)

but

anoi

c ac

id (

2,4-

DB

). N

ote

sele

ctiv

ity g

aine

d by

com

bini

ng d

eriv

atiz

atio

n w

ith s

elec

tive

dete

ctio

n. (

From

Rod

rigu

ez,

I.,

Rub

i, E

., G

onza

lez,

R.,

Qui

ntan

a, J

., a

nd C

ela,

R.,

Ana

l. C

him

. Act

a., 5

37, 2

59–2

66, 2

005.

Cop

yrig

ht 2

005,

Els

evie

r Sc

ienc

e. W

ith p

erm

issi

on.)

84534.indb 384 11/5/09 12:30:17 PM


100

(a)

(b)

(c)80 60 40

I.S.

I.S.φ–

5 φ–4

φ–3

φ–5+

6

φ–2 φ–

4φ–

3

φ–6 φ–

5 φ–2

φ–4

φ–3

φ–6+

7φ–

5 φ–2 φ–

4φ–

3φ–

2

I.S.

φ–5+

6φ–

3

φ–5

φ–2 φ–

4φ–

2 φ–4

φ–3

φ–6

φ–5 φ–

2φ–

4 φ–3

φ–6+

7

φ–2

C10

LA

SC

11 L

AS

C12

LA

SC

13 L

AS

20 100 80 60 40

Relative abundance

20 100 80 60 40 20 0

17.0

18.0

19.0

20.0

Tim

e (m

in)

21.0

22.0

23.0

fIg

ur

e 9.

8 SP

ME

–in-

port

der

ivat

izat

ion–

GC

–MS

reco

nstr

ucte

d se

lect

ed io

n ch

rom

atog

ram

s fr

om m

/z 1

71 +

185

+ 2

71 s

how

ing

isom

eric

sep

ara-

tion

of

(a)

LA

S st

anda

rd, (

b) u

rban

was

te w

ater

, and

(c)

sea

surf

ace

mic

rola

yer

sam

ples

. The

sur

roga

te n

-C8

-LA

S is

ind

icat

ed (

I.S.

). T

he n

otat

ion

φ-x

mea

ns th

e ca

rbon

num

ber

whe

re p

heny

l is

subs

titu

ted.

Not

e th

e gr

oup

sepa

rati

on b

y ca

rbon

num

ber.

(Fro

m A

lzag

a, R

., Pe

na, A

., O

rtiz

, L.,

and

Bay

ona,

J.

, J. C

hrom

atog

r. A

, 999

, 51–

60, 2

003.

Cop

yrig

ht 2

003,

Els

evie

r Sc

ienc

e. W

ith

perm

issi

on.)

84534.indb 385 11/5/09 12:30:19 PM


9.7 summary and ConClusIons

The development of SPME over the past 20 years, and the more recent wide avail-ability of automated SPME systems, has generated renewed interest in derivatization with gas chromatography for the analysis of highly polar or labile analytes. By using an SPME fiber as the extracting phase, the derivatization process is straightforward and readily automated. From anecdotal examination of the literature, it appears that the fiber may offer benefits over traditional liquid phase reactions in that control over the selectivity of the reaction for the desired product and fewer interfering by-products may be more readily achieved. Nearly all authors have reported that SPME-based derivatization methods provide equivalent or superior analytical performance to their traditional counterparts. While attention to derivatization in general has waned among gas chromatographers, the advent of procedures in combination with SPME makes derivatization again attractive and worthy of consideration in analyti-cal method development.

aCknowledgments

The author gratefully acknowledges Sanofi-Aventis for providing funding for the Center for Academic Industry Partnership and Supelco (Sigma-Aldrich), which has provided nearly all of the SPME fibers used by the author over the years.

referenCes

1. Belardi, R., Pawliszyn, J. The application of chemically modified fused silica fibers in the extraction of organics from water matrix samples and their rapid transfer to capillary columns. Water Pollution Res. J. Canada 24 179–91 1989.

2. Arthur, C., Pawliszyn, J. Solid phase microextraction with thermal desorption using fused silica optical fibers, Anal. Chem. 62(19) 2145–8 1990.

3. Pawliszyn, J. Solid Phase Microextraction: Theory and Practice, John Wiley and Sons, New York, 1997.

4. Lord, H., Pawliszyn, J., Evolution of solid-phase microextraction technology, J. Chromatogr. A, 885 153–193 2000.

5. Ouyang, G., Pawliszyn, J. Recent developments in SPME for on-site analysis and moni-toring Trends. Anal. Chem. 25 692–703 2006.

6. Mustaeta, F., Pawliszyn, J., Bioanalytical applications of solid-phase microextraction, Trends Anal. Chem. 26 36–45 2007.

7. Louch, D., Matlagh, S., Pawliszyn, J., Dynamics of extraction on coated fused silica Fibers, Anal. Chem. 64 1187–1192 1992.

8. Zhang, Z., Pawliszyn, J., Headspace solid-phase microextraction, Anal. Chem. 65 1843–52 1993.

9. Abdel-Rehim M., Bielenstein M., Arvidsson T., Evaluation of solid-phase microextrac-tion in combination with gas chromatography (SPME-GC) as a tool for quantitative bioanalysis, J. Microcolumn Sep. 12(5) 308–315 2000.

10. Theodoridis, G., Koster, E., de Jong, G., Solid-phase Microextraction for the Analysis of Biological Samples, J. Chromatogr. B 745 49 2000.

11. Vas G., Vekey K. Solid-phase microextraction: a powerful sample preparation tool prior to mass spectrometric analysis J. Mass Spectrom. 39 233–254 2004.

84534.indb 386 11/5/09 12:30:20 PM


12. Witkamp, B.L., Tilotta, D.3, Determination of BTEX compounds in water by solid-phase microextraction and raman spectroscopy, Anal. Chem. 67 600–605 1995.

13. http://www.sigmaaldrich.com/analytical-chromatography/sample-preparation/learning-center/spme.html, accessed in October, 2008.

14. Sci Finder ScholarTM, American Chemical Society, Accessed October, 2008. 15. SPME CD, 7th Edition, Supelco, Bellefonte, PA, 2008. 16. Pawliszyn, J. (ed), Applications of SPME, Royal Society of Chemistry Monographs,

London, 1999. 17. Wercinski, S., Solid Phase Microextraction: A Practical Guide, Marcel Dekker,

New York, 1999. 18. Knapp, D., Handbook of Analytical Derivatization Reactions, John Wiley and Sons,

New York, 1979. 19. Wells, R., Recent advances in non-silylation derivatization for gas chromatography,

J. Chromatogr. A 843 1 1999. 20. Kaal, E., Janssen, H-G., Extending the molecular application range of gas chromatogra-

phy, J. Chromatogr. A 1184 43–60 2008. 21. Pan, L., Pawliszyn, J., Derivatization/solid-phase microextraction: new approach to

polar analytes, Anal. Chem. 69 196–205 1997. 22. Stashenko, E., Martinez, J., Derivatization and solid-phase microextraction, Trends

Anal. Chem., 23(8) 553–561 2006. 23. Liu, Z, Hara, K., Kashimura, S., Liu, J., Fujii, H., Kashiwagi, M., Miyoshi, A.,Yanai, T.,

Kageura, M., Two simple methods for enantiomeric analysis of urinary amphetamines by GC/MS using deuterium-labeled L-amphetamines as internal standards, Forensic Toxicol. 24(1) 2–7 2006.

24. Liu, J., Hara, K., Kashimura, S., Kashiwagi, M., Kageura, M., New method of derivati-zation and headspace solid-phase microextraction for gas chromatographic–mass spec-trometric analysis of amphetamines in hair J. Chromatogr. B 758 95–101 2001.

25. Sarrion, M., Santos, F., Galceran, M., In situ derivatization/solid-phase microextraction for the determination of haloacetic acids in water, Anal. Chem. 72 4865–4873 2000.

26. Stashenko, E., Mora, A., Cervantes, M., Martinez, J., HS-SPME determination of volatile carbonyl and carboxylic compounds in different matrices, J. Chromatogr. Sci. 44 347–353 2006.

27. Cancho, B., Ventura, F., Galceran, M., Determination of aldehydes in drinking water using pentafluorobenzylhydroxylamine derivatization and solid-phase microextraction J. Chromatogr. A 943 1 2002.

28. Pan, L., Adams, M., Pawliszyn, J., Determination of fatty acids using solid phase micro-extraction Anal. Chem. 67(23) 4396–4403 1995.

29. Koziel, J., Noah, J., Pawliszyn, J., Field Sampling and determination of formaldehyde in indoor air with solid-phase microextraction and on-fiber derivatization, Environ. Sci. Technol. 35 1481–1486 2001.

30. Okeyo, P., Snow, N., Optimizing SPME-GC Injections, LC-GC, 15(12), 1130–1136 1997.

31. Okeyo, P., Rentz, S., Snow, N., Analysis of steroids from human serum by SPME with headspace derivatization and GC/MS, J. High Res. Chromatogr., 20, 171–173 1997.

32 Kawaguchi, M., Ito, R., Sakui, Okanouchi, N., Saito, K., Nakazawa, H., Dual deriva-tization–stir bar sorptive extraction–thermal desorption–gas chromatography–mass spectrometry for determination of 17β-estradiol in water sample, J. Chromatogr. A 1105 140–147 2006.

33. Yang, L., Luan, T., Lan, C., Solid-phase microextraction with on-fiber silylation for simultaneous determinations of endocrine disrupting chemicals and steroid hormones by gas chromatography-mass spectrometry, J. Chromatogr A. 1104 23–32 2006.

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34. Rodriguez, I., Rubi, E., Gonzalez, R., Quintana, J., Cela, R., On-fibre silylation following solid-phase microextraction for the determination of acidic herbicides in water samples by gas chromatography, Anal. Chim. Acta 537 259–266 2005.

35. Parker-Pope, T., Panel faults FDA in stance that chemical found in plastic is safe, New York Times, October 30, 2008.

36. Xiangli, L., Li, L., Shichun, A., Chongyu, L, Tiangang, L., Determination of bisphenol A in landfill leachate by solid phase microextraction with headspace derivatization and gas chromatography-mass spectrometry, Chin J. Anal. Chem. 34(3) 325–328 2006.

37. Alzaga, R., Pena, A., Ortiz, L., Bayona, J., Determination of linear alkylbenzenesulfonates in aqueous matrices by ion-pair solid-phase microextraction-in port derivatization-gas chromatography-mass spectrometry, J. Chromatogr. A 999 51–60 2003.

84534.indb 388 11/5/09 12:30:20 PM

389

Index

a

Abraham solute descriptors, 199; see also Packed column SFC (pSFC)

Absorbance detectors, 158Accelerated solvent extraction (ASE), 346Acetaminophen separation, 267Acetonitrile–water mixture studies, 12

computed incremental transfer free energy diagrams, 13

K(z) profile for, 22n-octadecane chain solvated in, 21

Acetylcholine separation, 268ACQUITY UPLC®, 101, 103

gradient separation of, 123Activity coefficient models, 96Acylation, 353, 355Adiabatic column, temperature and pressure

change in, 110Adsorbates excess properties, 93Adsorption equilibria

association equilibrium, 89in protein chromatography, 88standard Gibbs energy change of

association, 89stoichiometric coefficient, 89thermodynamic equilibrium constant, 89

Adsorption isothermsasymmetric activity coefficients of

proteins, 62estimation of

parameters, 62partition coefficients, 62–63

ion-exchange, 63–64β-lactoglobulins A and B, 64–68hydrophobic interactions, 70–72in mixed solvents, 68–70

self-association isotherm, 62thermodynamic equilibrium constants, 62

Advanced molecular simulation methods, 3Affinity chromatography, 164–165; see also

Biointeraction affinity chromatography

kinetic measurements methods, comparison of, 167

linear elution methodspeak profiling, 171–173plate height measurements, 168–171practical considerations, 174

non-linear elution methodscombined assay methods, 183frontal analysis, 176–178non-linear peak fitting, 174–176peak decay method, 181–182practical considerations, 183–184split-peak method, 178–181

principles, 166zonal elution in, 148

applications of, 150in binding and competition

studies, 151–153temperature and solvent

studies, 153–155binding sites, characterization

of, 155–1567-hydroxycoumarin binding to HSA,

149, 150practical considerations for, 156–158principles, 150–151

Affinity ligand, 146; see also Biointeraction affinity chromatography

biological interaction study by, 147AGP, see Albumin/α1-acid glycoprotein

columns (AGP)Albumin/α1-acid glycoprotein columns

(AGP), 147Alcohol incremental free energy, 13Alkane incremental free energy, 13Alkylbenzene

distribution coefficient, 9incremental transfer free energy

diagram, 10Allosteric effects, between analyte and

competing agent, 152–154studies on drug–protein systems, 153–154

Amino-caproic acid separation, 2686-Aminoquinolyl N-hydroxysuccinimidyl

carbamate (AQC reagent), 125Ammonium dihydrogen fluoride as etching

agent, 282Ammonium sulfate activity coefficients, 77Amphetamine recovery from SPME, 378Amylbenzene

plate height and velocity curves, 105reduced plate height and reduced velocity

curves, 106Analyte–ligand systems, zonal elution studies

on, 149–151

84534.indb 389 11/5/09 12:30:20 PM

390 Index

Analytical affinity chromatography, see Biointeraction affinity chromatography

ANP, see Aqueous normal phase (ANP) of silica hydride-based columns

Antituberculosis tablets and ultra-fast UPLC-UV method, 136

Apolar/polar column combination, 297AQC reagent, see 6-Aminoquinolyl

N-hydroxysuccinimidyl carbamate (AQC reagent)

Aqueous normal phase (ANP) of silica hydride-based columns, 260

properties, 267–270retention capabilities in, 271

Aromatic hydrocarbons gradient separation, 267–268

ASE, see Accelerated solvent extraction (ASE)Asymmetric activity coefficients, 87

defined, 88at infinite dilution, 88of proteins, 62reference state potential, 88

ATD, see Automated thermal desorption (ATD) devices

Automated thermal desorption (ATD) devices, 335

AUX, see Advanced pressure control unit (AUX)

Advanced pressure control unit (AUX), 296Avogadro’s number, 86

b

Band broadening method, see Plate height method

Band entrapment/focusing, 305Benzene, 352–353Betaine identification, 271BFR, see Brominated flame retardants (BFRs)Biointeraction affinity chromatography, 146

advantages of, 146–147applications, 150equilibrium and thermodynamic

measurements by, 147–148frontal analysis (see Frontal analysis

uses)zonal elution (see Zonal elution, in

affinity chromatography)and kinetic measurements (see

Kinetic studies, in affinity chromatography)

Bioseparationsoligonucleotides, 131–137peptide mixtures

chromatogram, 128, 130gain analysis time, 127–128

resolution of, 128tryptic digest of bovine hemoglobin, 131

proteins, 128Bisphenol A, 382Bis-trimethylsilyl trifluoroacetamide

(BSTFA), 382as derivatizing reagent, 381

BNP II, see Bovine neurophysin II (BNP II)Boltzmann weight, 39–40Born potentials, 86Bovine hemoglobin tryptic digest, 131Bovine neurophysin II (BNP II), 171Bovine serum albumin (BSA), 147Brominated flame retardants (BFRs), 330

in fish samples, 349Brown alga Dictyopteris membrana, volatile

metabolites determination, 361BSA, see Bovine serum albumin (BSA)BSTFA, see Bis-trimethylsilyl

trifluoroacetamide (BSTFA)Bulk molfraction, 46n-Butane distribution coefficient profiles, 23

C

Capillary electrophoresis, 100Capillary flow technology, 307Carbohydrate structural isomer separation, 262Carbonic anhydrase

electrochromatograms for, 285Carbowax

carbowax-polyethylene glycol (PEG) coating, 341

carbowax/templated resin (CW/TPR) coating, 341

Carboxen/poly(dimethylsiloxane) (CAR/PDMS) coating, 341

Catecholamines separation on hydride C18 column, 266

Chenodeoxycholic acid identification, 271Chinese medicines and natural products,

analysis by UPLC®, 1374-Chloro-7-nitrobenz-2,1,3-oxadiazole

(NBD chloride) fluorescent derivative, 355

Choline separation, 268choline identification, 271

2DChromatograms, 322–323expansion relative to, 322–323generation of, 317

Classical contribution, 86Classical isotherm model, 62Cold-trapping, 295Column choice in zonal elution

studies, 156–157Combined assay methods for kinetics

measurements, 183

84534.indb 390 11/5/09 12:30:21 PM

Index 391

Complex environmental sampleschromatographic techniques, 329interlaboratory studies, 330preparation procedure, 329–330sample

and matrices, 330–331preparation technique, 330–331processing and pretreatment, 330

Comprehensive two-dimensional chromatography application, 292

COMSOL software, 111–112Configurational-bias Monte Carlo (CBMC), 38

application of, 42Boltzmann weight, 39–40probability, 39, 41regrowth/insertion, 39Rosenbluth weight, 39–40

Contaminated sediment extract, 354Continuum solvation models, 31Convex ion-exchange, 61

convex isothermsexpression for, 95HIC and PRC, 95IEC, 95

Coulombic potentials, 31Counterion activity coefficients, 93Creatine and creatinine separation

by gradient method, 271with 4-hydroxyproline in human

urine, 272Cyclodextrins, 158Cytidine separation, 278

d

Database for pSFC, 228method development with solvation

parameter model, 244–247ODS phases, 240–244predictive capability of models,

247–248variation of system constants among

stationary phases, 228–232visual representation of, 232–240

DBP, see Dibutylphthalates (DBPs)DDT, see Dichlorodiphenyltrichloroethane

(DDT)Deans switching principle, 298

Deans switch-typeflow modulator in injection state,

307schemes, 296

Debye–Hückel potential, 86Decanophenone

plate height and velocity curves, 105reduced plate height and reduced velocity

curves, 106

Derivatizationand gas chromatography

SPME, 374–375GC-MS applications, 376modes with

sample matrix, 376Diamond hydride column with mass

spectroscopy detectionONP conditions and, 275separation and identification of

metabolites, 273Dibenzofurans (PXDFs), 352–353Dibutylphthalates (DBPs), 331Dichlorodiphenyltrichloroethane

(DDT), 331Dichloromethane fractions, 352–353Differential material balance

model of unit volume of column, 59ion-exchange chromatography, 61ordinary and eddy diffusion

coefficient, 60phase ratio, 60–61plug flow in axial direction, 60residence time, 60timescale of flow through, 60

Diffuse reflectance infrared Fourier transform (DRIFT)

silica hydride analysis, 2583,4-Dihydroxyphenylacetic acid for retention,

2715-Dimethyl aminonaphthalene-1-sulfonyl

chloride fluorescent derivatives, 355Diphenylethers, 352Dispersive liquid-liquid microextraction

(DLLME), 342Dissociation equilibrium constant, 162

rate constant, 169, 171–173, 175–177, 181, 182

Divinylbenzene/carboxen/poly(dimethylsiloxane)(DVB/CAR/PDMS) coating, 341

DLLME, see Dispersive liquid-liquid microextraction (DLLME)

Drugs of abuse analysis for UPLC, 137DSAE, see Dynamic sonication-assisted

extraction (DSAE)Dual-column stop-flow instrument, 300Dual mode retention of silica hydride phases

capabilities, 263, 272chromatographic behavior for, 273

Dual separation modes, hydride-based etched capillaries

electrophoretic format, 282liquid crystals, 282methanol in, 281synthetic peptide sample,

electrochromatogram, 280

84534.indb 391 11/5/09 12:30:21 PM

392 Index

Dynamic headspace (DHS), 335Dynamic sonication-assisted extraction

(DSAE), 347

e

Eddy diffusion, 61EE, see Extraction efficiency (EE)Electrovalve (EV), 296EF, see Enrichment factor (EF)Electroneutrality, 90Electronic pressure controllers, 298Electrozone sensing technique, 105Embedded polar groups (EPGs), 7Enrichment factor (EF), 342Environmental applications

of LPME, 342of MASE, 344samples with novel extraction techniques

methods used for, 358–359EPGs, see Embedded polar groups (EPGs)Epinephrine for retention, 271Etched chemically modified capillaries, 282;

see also Hydride-based etched capillaries

analysispeptide, 283–284proteins, 284–285

cytochrome c tryptic digest, separation of, 284EOF characteristics, changes result, 282–283PEGylated compounds, analysis, 285surface modification, 283tricyclic antidepressants and

tetracyclines, 2832-Ethylpyridine phase, 196EV, see Electrovalve (EV)Excess potentials, 87Exchange process, 63Exclusion factors, 63Extract cleanup

derivatizationGC analysis, 353, 355liquid chromatography (LC), 355

fractionationautomated fractionation procedure by

HPLC, 354cleanup systems, 353ethanolic KOH solutions, 351and GPC, 351HPLC, 351, 353liquid–liquid partitioning, 351POPs, adsorbents used in, 351–352PXDD and PXDF, 352Soxhlet extract of sewage sludge,

purification, 352–353lipid removal from biological

extracts, 350–351

online techniquesMMLLE-GC system, 355–356

sample preparation methods, selectionfor analysis of selected groups of POPS

in, 358–359HD, fMAE and SFE techniques

for, 357, 362liquid of fluid-based extraction

methods, 357–358LPME techniques, 363MAE and PLE used for, 363merit of extraction methods, relevant

figures, 360PCB extraction, comparison of, 364PCDD/PCDFs, extraction of, 365–366Soxhlet in extraction of PAHs in sludge

sample, comparison, 364–365volatile and semivolatile compounds,

extraction, 362volatile compounds, analysis

with, 356–357sulfur removal from sediment extracts, 351treatment with concentrated sulfuric

acid, 351Extracted ion chromatogram (EIC) for creatine

and creatinine, 271Extraction efficiency (EE), 342Extraction procedures

brown alga Dictyopteris membrana, volatile metabolites

comparison of extraction methods, 361cleanup of extract

fractionation, 351–353lipid removal from biological

extracts, 350–351matrix compounds, 350sulfur removal from sediment

extracts, 351treatment with concentrated

sulfuric acid, 351liquid environmental samples

ionic liquids (IL), 336liquid-phase microextraction

(LPME), 341–342LPME and membrane extraction

techniques, 335–336membrane assisted solvent extraction

(MASE), 343–344microextraction techniques, basics, 336solid phase extraction (SPE), 336–338SPME and SBSE, 338–335, 341–336

solid and semisolid samplesand ASE, 346MAE and SAE, 345matrix solid phase dispersion

(MSPD), 349pressurized liquid extraction (PLE), 346

84534.indb 392 11/5/09 12:30:21 PM

Index 393

SAE and MAE, 347–348SFE, 344–345, 347and Soxhlet extraction, 345–346supercritical fluid extraction

(SFE), 344–345vapor-phase extraction

dynamic headspace (DHS), 335HS and GC techniques, 334thermal extraction, 335

f

FAME, see Methyl ester-derivatized plasma fatty acids (FAMEs)

Faraday’s number, 86Fiber coating, 374FID primary-column analysis, test-mixture

chromatograms, 302Flavanone O-diglycosides with UPLC®-

ESI-MS method, 137Florisil, 349, 351Flory–Huggins parameters, 8Fluidized-bed extraction technique, 345fMAE, see Focused microwave assisted

hydrodistillation (fMAE)FME, see Focused microwave (FME) systemFocused microwave assisted hydrodistillation

(fMAE), 357Focused microwave (FME) system, 347

methods, 363Force field parameters, 32Formaldehyde analysis, 381Free energy terms for solvophobic theory,

5–6Frontal affinity chromatography-mass

spectrometry (FAC-MS), 161Frontal analysis uses, 148, 158

advantages of, 158–159applications of, 159

in binding studies, 159–161in competition studies, 161–162in temperature and solvent studies,

163–164general principles of, 158practical considerations for, 164

Fructus aurantii (Zhi qiao) with UPLC-ESI-MS method, 137

Fumaric acid separation, 270Fused-silica restriction, 296

g

Gas chromatography (GC), 289, 334and derivatization

reagents, 381SPME, 374–375

experts, 291preliminary monodimensional

applications, 292resolution, 290, 291

Gauche defects, 16–17average fraction of, 19statistics, 45

GC, see Gas chromatography (GC)GDS, see Gibbs dividing surface (GDS)Gel permeation chromatography (GPC),

350–351Gibbs dividing surface (GDS), 20Gibbs energy models, 96Gibbs ensemble method, 36

acceptance probability, 37–38types of, 37

Glyburide elution characteristics, 263GPC, see Gel permeation chromatography

(GPC)Gradient elution method, 270Group contribution methods, 8–9

h

Haloacetic acidsanalysis of, 377–378

Harmonic approximation, 31HCB, see Hexachlorobenzene (HCB)HCH, see Hexachlorocyclohexane (HCH)HD, see Hydrodistillation (HD)Headspace-SPME-GC-MS total-ion

chromatogramand single ion chromatograms of methyl

haloacetates, 379Headspace techniques (HCC-HS), 334–335Heart-cutting two-dimensional gas

chromatography, 293heart-cutting zone compression-band

injection, 305pressure switching and capillary columns,

use, 294Heat shock protein 90, 175Herbicides, 382Heterocyclic aryl compounds separation, 275Heterogeneity in system composition, 46Hexachlorobenzene (HCB), 331Hexachlorocyclohexane (HCH), 331n-Hexadecane

as model for retentive phase material, 10solvent distribution coefficient

measurements, 9Hexane fractions, 352–353Hexane/THF mobile phase, 276High performance affinity chromatography

(HPAC), 146High performance liquid chromatographic

separation (HPLC)

84534.indb 393 11/5/09 12:30:21 PM

394 Index

detector, 350fractionation method and derivatization, 353POPs fractionation in extract of

contaminated sediment, 354High-performance liquid chromatography

(HPLC), 100High-speed solubility screening assay, 136Hofmeister series, 64HPAC, see High-performance affinity

chromatography (HPAC)HPLC, see High-performance liquid

chromatography (HPLC)HPLC hydrophilic interaction

chromatography (HILIC) separations, 136

HSA, see Human serum albumin (HSA)Human serum albumin (HSA), 147; see also

Biointeraction affinity chromatography

and human IgG, separation on etched C5 capillary, 285–286

Hydride-based etched capillariescapillary properties, characterization

electrophoretic behavior, 279–280EOF and pH, plot of, 279tryptic digest, electropherogram of, 280

dual separation modeselectrophoretic format, 282liquid crystals, 282methanol in, 281synthetic peptide sample,

electrochromatogram, 280etched chemically modified capillaries, 282

cytochrome c tryptic digest, separation of, 284

EOF characteristics, changes result, 282–283

PEGylated compounds, analysis, 285peptide analysis, 283–284proteins analysis, 284–285surface modification, 283tricyclic antidepressants and

tetracyclines, 283fabrication

nitrogen and fluoride, 279OTCEC, 278

Hydrodistillation (HD), 357Hydrophobic and hydrophilic compounds

retention map, 274Hydrophobic isotherms, 61

hydrophobic associationsmaterial balance, 91scheme of, 91standard Gibbs energy change, 91

interactions, 70linking HIC and solubility data, 74–77modulator effect, 71

reversed-phase chromatography, 72salt-induced hydrophobic

chromatography, 73–74Hydrophobic ligand activity coefficient, 93Hydrosilation process, 257–2585-Hydroxy-3-indole acetic acid for retention, 271Hydroxyl increment, 14Hypoxanthine identification, 271

I

Ideal mixtureactivity coefficients, 87behavior, 87chemical potentials, 86

Ideal vapor reference state in RPLC, 5IL, see Ionic liquids (IL)Industrial applications of thermodynamic

modeling of chromatographic separation, 79–81

Intermolecular potential energy function, 31Interstitial porosity, 63Ion-exchange chromatography (IEC), 61

electroneutrality, 90ion-exchange scheme, 90mole fraction and activity coefficient, 90

Ionic liquids (IL), 336Ionizable analytes, 117Ion-pair reversed-phase liquid chromatography

(IP RP LC), 131IP RP LC, see Ion-pair reversed-phase liquid

chromatography (IP RP LC)Isobaric acids separation, 270Isotherm

compressibility coefficient, 108and stoichiometric coefficient, 80

k

Kidney cancer in urine samples, markers search, 136

Kinetic studies, in affinity chromatography, 164–165

kinetic measurements methods, comparison of, 167

linear elution methodspeak profiling, 171–173plate height measurements, 168–171practical considerations, 174

non-linear elution methodscombined assay methods, 183frontal analysis, 176–178non-linear peak fitting, 174–176peak decay method, 181–182practical considerations, 183–184split-peak method, 178–181

principles, 166

84534.indb 394 11/5/09 12:30:22 PM

Index 395

Kohn–Sham density functional theory, 31Kozeny–Carman equation, 102–103, 119

l

β-Lactoglobulins A and Bassociation constant of, 66double-logarithmic plots of isocratic

retention volumes of, 64–65isocratic elution chromatograms, 66

modeled, 67isotherms

adsorption, 68parameters for, 66slope and partition coefficient, 68

non-Langmuirian behavior, 65–66Landfill leachate samples, 382Langmuir adsorption models, 176–177Lattice theories

ordering of chains, 8solvent properties, 8

LC, see Liquid chromatography (LC)Lennard-Jones potentials, 31

portion of, 32Linear alkylbenzene sulfonates, 382Linear elution methods

peak profiling, 171–173plate height measurements, 168–171practical considerations, 174

Linear retention indices (LRI), 318Linear solvation energy relationship (LSER),

199Lipophilic interaction for nonpolar molecules in

RPLC, 14Liquid chromatography (LC)

UV chromophores and fluorophores, 355Liquid crystal

problems, 8stationary phase, 282

Liquid environmental samplesionic liquids (IL), 336liquid-phase microextraction (LPME),

341–342LPME and membrane extraction techniques,

335–336membrane assisted solvent extraction

(MASE), 343–344microextraction techniques, basics, 336solid phase extraction (SPE), 336–338SPME and SBSE, 335–336, 338–341techniques, 363

Liquid–liquid extraction (LLE), 330, 365Liquid-phase microextraction (LPME)

DLLME, 342hydrophilic compounds, extraction of, 342optimization, critical parameters in, 342two-phase and three-phase systems, 341–342

Lithium aluminium hydride, 256LLE, see Liquid–liquid extraction (LLE)LMCS, see Longitudinally

modulated cryogenic system (LMCS)

Local solubility model, 25Longitudinally modulated cryogenic system

(LMCS), 305GC×GC experiments

ToF MS and rapid-scanning qMS systems in, 319

system, 318Lorentz–Berthelot combining rules, 32Low thermal mass (LTM)

benefits, 298capillary flow technology, 299

LPME, see Liquid-phase microextraction (LPME)

LRI, see Linear retention indices (LRI)LSER, see Linear solvation energy relationship

(LSER)LTM, see Low thermal mass (LTM)Lumped constant thermodynamic model, 4Lysozyme binding to Cibacron Blue

3GA, 176–177

m

MAE, see Microwave-assisted extraction (MAE)

Maleic acid separation, 270Many-body systems, 5Martin equation for methylene increment, 14Mass spectrometry (MS)

mass spectrometerspectra, 318system, 313

specialists, 291Mass-transfer, 77

boundary condition, 78–79coefficients of, 78rate of, 79

Matrix solid phase dispersion (MSPD)technique, 366

C8-and C18-bonded silica and Florisil, 349

McGowan’s molecular volume, 226MDGC, see Multidimensional

gas chromatographic (MDGC) system

Membrane assisted solvent extraction (MASE)extraction in, 343–344forms, 344MMLLE membrane, 343types of, 343

Membrane extraction with sorbent interface (MESI), 335

84534.indb 395 11/5/09 12:30:22 PM

396 Index

Membrane liquid–liquid extraction (MMLLE), 343

MEPS, see Microextraction in packed pipette/syringe (MEPS) technique

Metabonomics, 136Metal ferrules, 298Metanephrine normetanephrine

separation, 268Metformin elution characteristics, 263Methanol–water mixtures

isothermal compressibility, 110studies, 12

computed incremental transfer free energy diagrams, 13

n-octadecane chain solvated in, 21Methotrexate separation, 268Methylene

incremental free energies of transfer, 24increment and Martin equation, 14lipophilic interactions in, 24

Methyl ester-derivatized plasma fatty acids (FAMEs), 319, 322

Methyl haloacetatesheadspace-SPME-GC-MS total-ion

chromatogram and single ion chromatograms of, 379

Microcolumn HPLC with hydride-based C18 stationary phase, 277

Microextraction techniques, 337basics of, 336microextraction in packed pipette/syringe

(MEPS) technique, 337online connection with LC/GC, 338parameters in, 338

Microwave-assisted extraction (MAE), 345, 347, 364

optimization, critical parameters in, 348Midpoint gas flow regulation

pneumatically activating valve, 300MIP, see Molecularly imprinted

polymers (MIPs)Mixed-mode sorbents, 337MMLLE, see Membrane liquid–liquid

extraction (MMLLE)MMLLE-GC system, 355

POPs in water sample, analysis, 357Model parameter sensitivity analysis, 59Modulation period, 292Modulators, 292

capillary flow technology, 307Deans switch-type flow modulator in

injection state, 307LMCS, 305longitudinally modulated cryogenic

system, 306low-cost pneumatic GC×GC, 307–308pneumatic-modulated GC×GC, 305, 307

short microbore column segment, 308–309single-stage air-cooled and

electrically heated thermal modulator, GC×GC instrument with, 308

thermal sweeper, 305–306tube, 308

Molecular dynamics (MD) simulation technique, 29

Molecularly imprinted polymers (MIPs), 336–337

Molecular simulations of RPLCGibbs ensemble method, 36–38heterogeneity in system composition, 46Monte Carlo methods for, 34–36order parameter, 45–46solute distribution coefficients and transfer

free energies, 46–47transferable potentials for phase equilibria

force field, 31–34Monte Carlo method

algorithms for particle-based simulations, 12for molecular simulation, 34–35

application of, 36phase equilibria, computation of, 30

MS, see Mass spectrometry (MS)MSPD, see Matrix solid phase dispersion

(MSPD)MTBSFA, see N-methyl-N-(tert-

butyldimethylsilyl)-trifluoroacetamide (MTBSFA)

Multidimensional gas chromatographic (MDGC) system, 291

and applications, 295AUX and EV, 296first-dimension FID chromatogram

of, 297instrument, 296–297LTM, capillary flow technology, 299microfluidic transfer system, 298midpoint gas flow regulation, 300second-dimension MDGC-MS TIC

chromatogram of, 298series-coupled column system

with stop-flow operation, scheme, 301

spectral purity, 297stop-flow methodology, 301target compounds, 298, 300test-mixture chromatograms, 302transfer system, schemes of, 296

classical heartcutting, 293advantage, 292

cold-trapping, 295primordial valve-based, scheme of, 294twin-oven configuration, 294–295

Murine monoclonal antibody separation, 132

84534.indb 396 11/5/09 12:30:22 PM

Index 397

n

NBD chloride, see 4-Chloro-7-nitrobenz-2,1,3-oxadiazole (NBD chloride) fluorescent derivative

Neutral hydrophobic analytes, 117Nicotinic acetylcholine receptor (nAChR), 175Nitrophenols separation, 239N-methyl-N-(tert-butyldimethylsilyl)-

trifluoroacetamide (MTBSFA), 382Non-competitive peak decay method, 182Non-crystalline systems, 16Nonequilibrium process, 30Non-Langmuirian behavior of β-lactoglobulins

A and B, 65–66Non-linear elution methods

combined assay methods, 183frontal analysis, 176–178non-linear peak fitting, 174–176peak decay method, 181–182practical considerations, 183–184split-peak method, 178–181

Non-linear peak fitting method, 174–176Non-steroidal anti-inflammatory drugs

chromatograms of, 243elution orders of, 242structures of, 242

o

OcCTA, see Octachlorothianthrene (OcCTA)Octachlorothianthrene (OcCTA), 353Octadecyl silane (ODS) phase

backbone orientation, 20EPG phases and, 25–26grafting densities for, 16hydrogen bonds in, 15K(z) profile for n-butane, 22organic modifier, chain solvation by, 21in RPLC mechanism, 12solute-ODS interaction, 14solvent penetration in, 11transfer free energy, 14

Octadecylsiloxane-bonded silica (ODS) phases, 196

Octanol-water distribution coefficient (Ko/w), 338–339

ODS, see Octadecylsiloxane-bonded silica (ODS) phases

Oligodeoxythymidines peak capacity, 134Oligonucleotides separation

BEH columns, 133and column peak capacity, 133experimental data, 135flow rate gradient duration, 136gains in resolution, 133–134liquid chromatography, 131

retention pattern, 133simulated chromatograms, 135UPLC with mass spectrometry

detection, 135–136On-coating derivatization, 340Online techniques

MMLLE-GC system, 355–356online coupled MMLLE-GC-FID, 357

online extraction chromatographyenvironmental samples, analysis of, 356

ONP, see Organic-normal phase (ONP) separations

Open tubular capillary electrochromatography (OTCEC), 278, 280–281, 283

human IgG and serum albumin separation on etched C5 capillary, 285–286

PEGylated proteins, analysis of, 285reproducibility studies, 286

Open-tubular capillary (OTC) column, 289–290Operational parameters

applicationsArabica coffee volatiles, headspace

SPME-GC×GC-qMS result, 322cigarette smoke, TIC GC×GC-ToF MS

contour plot, 315, 3172D chromatograms, 316, 317, 322–3232D GC combined with mass

spectrometry, 315diesel oil, GC×GC-FID

chromatograms, 326expansion relative to, 325fatty acid matrices, GC-MS analysis

of, 322GC experiments, 314GC×GC plasma FAMEs,

identification, 324GC×GC-qMS experiment, 317GC×GC, series, 314–315GC-MS software use, 317intra-class separation, quality, 325LMCS system and LRI, 318major and minor perfume constituents,

analysis, 318orthogonal combination, 323, 325peak identification, GC-qMS result

for, 321plasma FAMEs, GC×GC-FID result, 323quadrupole mass spectrometry, 3182-second elution range, 315, 317single perfume peak, GC-qMS

result, 320spatial order and enhanced

sensitivity, 319–325TIC GC×GC-MS result for

perfume, 318–319ToF MS and rapid-scanning qMS

systems in, 319

84534.indb 397 11/5/09 12:30:22 PM

398 Index

column selectivitiesdegree of correlation, 310

detectionbidimensional methodologies, 313GC×GC-FID contour plot, 313GC-MS experiments, 313GC peak base widths, 312–313time-of-flight mass spectrometry (ToF

MS), 313–314gas flows

GC×GC experiment, 311–312ideal linear velocity, 311–312stop-flow GC×GC, 312

temperature gradientdegree of correlation, 310–311disadvantages, 311primary capillary temperature

ramps, 311second-dimension separations, 311

Order parameter, 45–46Organic acids separation, 265Organic modifier molfraction enhancement, 21Organic-normal phase (ONP)

hydride-based separation materials and, 275phenols separation by, 275

separations, 259Organo-chlorine pesticides (OCPs)

in fish samples, 349Organosilanes in aqueous solutions stability, 258Orthogonal column configuration, 310OTCEC, see Open tubular

capillary electrochromatography (OTCEC)

Oxime, 381

p

Packed column SFC (pSFC), 195–196choice of stationary phase, 196–197chromatographic systems, 196

characterization of, 198database for, 228

method development with solvation parameter model, 244–247

ODS phases, 240–244predictive capability of models, 247–248variation of system constants among

stationary phases, 228–232visual representation of, 232–240

mobile phase effects with stationary phase, comparison of, 197

phases, stationary of, 196solvation parameter model uses in, 199–201

chemical structures, of stationary phases, 206

choice of solvation descriptors, 225–228chromatographic system, 201–202

covariance matrix for solute set, 216data analysis, 218–225descriptor values among test set,

distribution of, 210, 215normalized residuals, plot of, 223ODS phases, selected in study, 206–209operating conditions, choice of, 202–203plot of S and E descriptor for solutes, 216reduced test set for ODS phases, 217selection of columns, 203–206set of test solutes, selection of,

206, 210–218solutes in final set with Abraham

descriptors, 211–214stationary phases, characterized in

study, 204–205system constants for, 219–222

Partial molar excess Gibbs energies, 86–87Particle-based simulation methodology, 3PBB, see Polybrominated biphenyls (PBBs)PBDE, see Polybrominated diphenyl ethers

(PBDEs)PCA, see Principal component analysis (PCA)PCB, see Polychlorinated biphenyls (PCBs)PCDD, see Polychlorinated dibenzo-p-dioxins

(PCDDs)PCDF, see Polychlorinated dibenzofurans

(PCDFs)p-CEC, see Pressurized capillary

electrochromatography (p-CEC)PCN, see Polychlorinated naphthalenes (PCNs)PDMS, see Polydimethylsiloxane (PDMS)Peak decay method, 181–182Peak profiling method, 171–173

multi-column peak profiling method, 172Péclet number, 60O-(2,3,4, 5,6-Pentafluorobenzyl) hydroxyamine

hydrochloride (PFBHA), 378Peptide mixtures separation

chromatogram, 128, 130gain analysis time, 127–128resolution of, 128tryptic digest of bovine hemoglobin, 131

Perfluorooctanoic acid (PFOA), 331Perfluorooctanoic sulfates (PFOS), 331Persistent organic pollutants (POPs)

levels of, 331PFBHA, see O-(2,3,4, 5,6-Pentafluorobenzyl)

hydroxyamine hydrochloride (PFBHA)

PFC, see Polyfluorinated chemicals (PFCs)PFOA, see Perfluorooctanoic acid (PFOA)PFOS, see Perfluorooctanoic sulfates (PFOS)PGC, see Porous graphitic carbon (PGC)Phase ratio, 61Phase retention on silica hydride-based

column, 261

84534.indb 398 11/5/09 12:30:23 PM

Index 399

Phenols phase separation, 262by ONP mode, 275

on silica hydride-based C18 column, 276Phenylalanine separation, 260

chromatogram for, 269Phenylglycine separation

chromatogram for, 269Phosphorylase b MassPREP™ Digestion

Standard, 129Physiological amino acids separation by

UPLC, 125–126Plate height method, 168–171PLE, Pressurized liquid extraction (PLE)Pneumatic-modulated GC×GC, 305, 307Poly(acrylate) (PA) coating, 341Polybrominated biphenyls (PBBs), 331Polybrominated diphenyl ethers (PBDEs), 331Polychlorinated biphenyls (PCBs), 331Polychlorinated dibenzofurans (PCDFs), 331Polychlorinated dibenzo-p-dioxins

(PCDDs), 331Polychlorinated naphthalenes (PCNs), 331Polycyclic aromatic hydrocarbons separation

on silica-hydride-based C18 stationary phase, 266

Polydimethylsiloxane (PDMS) coating, 341, 374Polyfluorinated chemicals (PFCs), 330Polyhalogenated dibenzo-p-dioxins

(PXDDs), 352–353Polymeric adsorbents, 337POP, see Persistent organic pollutants (POPs)Porous graphitic carbon (PGC), 201, 206, 210,

218, 221, 228–230Positive free energy, 14Post-extraction on-fiber derivatization

estrogens and steroids, analyses of, 381–382gas chromatographic derivatizing

reagents, 381herbicides and bisphenol A, 382SPME-GC applications, 381

Practical equilibrium constants, 93hydrophobic adsorbents

asymmetric activity coefficients of proteins, 94

ion-exchange adsorbentsasymmetric activity coefficients of

proteins, 94self-association

asymmetric activity coefficients of proteins, 94

Pre-extraction derivatizationamphetamines analysis, 376–377haloacetic acids analysis, 377–378headspace-SPME-GC-MS total-ion

chromatogram and single ion chromatograms of methyl haloacetates, 378

(O-(2,3,4, 5,6-pentafluorobenzyl)hydroxyamine hydrochloride) (PFBHA), 378

PFBHA–headspace-SPME–GC–ECD chromatogram of water sample, 380

Pressure switching, 294Pressurized capillary electrochromatography

(p-CEC), 277elution of charged compounds, 278

Pressurized liquid extraction (PLE), 330, 346–347, 364–365

optimization, critical parameters in, 346quantitative recoveries for, 347SWE, 346–347

Primary capillary temperature ramps, 311Primordial modulators, 305Principal component analysis (PCA), 1981-Propanol distribution coefficient profiles, 23Protein

concentrations, estimation of, 62–63separation by UPLC

chromatogram, 128gain analysis time, 127–128resolution of, 128

solute, activity coefficients of, 71pSFC, see Packed column SFC (pSFC)Purge-and-trap technique, 335PXDD, see Polyhalogenated dibenzo-p-dioxins

(PXDDs)PXDF, see Dibenzofurans (PXDFs)

q

qMS, see Quadrupole mass spectrometer (qMS)QSARs, see Quantitative-structure activity

relationships (QSARs)QSRRs, see Quantitative structure-retention

relationships (QSRRs)Quadrupole mass spectrometry (qMS)

rapid-scanning qMS systems, 318spectrometer, 313

instrument, 319Quantitative affinity chromatography,

see Biointeraction affinity chromatography

Quantitative structure activity relationships (QSARs), 175

Quantitative structure-retention relationships (QSRRs), 198

r

RAM, see Restrictive access materials (RAM)Rapid UPLC electrospray ionization mass

spectrometry (UPLC-ESI-MS) method

flavanone O-diglycosides analysis, 137

84534.indb 399 11/5/09 12:30:23 PM

400 Index

Fructus aurantii (Zhi qiao) analysis, 137Trollius ledibouri Reichb, constituents

analysis, 137Rat urine, total ion chromatogram, 124Real mixtures

chemical potentials, 86Restrictive access materials (RAM), 336–337Retention factor, 151Retention mechanism for RPLC, 11; see also

Reversed-phase liquid chromatography (RPLC)

average stationary phase structural and interfacial properties, 19

bonded-phase–solvent–solute environment, 27–28

density profiles, 18driving forces for, 12–15embedded polar groups, effects of, 25–26partition/adsorption, 21–25phase volumes, determination of, 26–27pressure and pore curvature effects, 27simulation approach, 12simulation snapshots of, 16–17solvent penetration, 20

Reversed-phase adsorbents, 70–71Reversed-phase chromatography

of hydrophobic isotherms, 72thermal expansion coefficients, 111

Reversed-phase liquid chromatography (RPLC), 2

ideal vapor reference state in, 5molecular simulations of, 29–30

analysis and presentation of data, 45configurational-bias Monte

Carlo, 38–45gauche defect statistics, 45Gibbs ensemble method, 36–38heterogeneity in system

composition, 46Monte Carlo methods for, 34–36order parameter, 45–46solute distribution coefficients and

transfer free energies, 46–47transferable potentials for phase

equilibria force field, 31–34retention mechanism, 11

average stationary phase structural and interfacial properties, 19

bonded-phase–solvent–solute environment, 27–28

density profiles, 18driving forces for, 12–15embedded polar groups, effects of, 25–26partition/adsorption, 21–25phase volumes, determination of, 26–27pressure and pore curvature effects, 27simulation approach, 12

simulation snapshots of, 16–17solvent penetration, 20

thermodynamic-based models of, 3Reversed-phase silica hydride-based columns

C18 and C8 hydride-based stationary phases, 264–265

properties of, 261verification, 264

Robustness analysis, 80–81Robust thermal modulator

steel tube, 308Rosenbluth weight, 39–40RPLC, see Reversed-phase liquid

chromatography (RPLC)

s

SAE, see Sonication-assisted extraction (SAE)SAFE-CBMC algorithm, 41Salt

induced hydrophobic retention, 71retention volume, 63salting-out effect, 71

Sample preparation extraction (SPE)drying and homogenization of solid

samples, 333procedure, 331, 333

liquid environmental samples, 335–344solid and semisolid samples, 344–349vapor-phase extraction, 334–335

schemes, 332SBSE, see Stir-bar sorptive extraction (SBSE)SCFA, see Self consistent field theory for

adsorption (SCFA )Scheibel equation, 104, 118Self-association isotherm (SAS), 62, 95Self-association equilibria

association scheme, 91electroneutrality balance, 92equilibrium constant, 91exclusion factors, 92material balance, 92mole fraction and activity coefficient, 92monomer adsorbate concentration, 92total adsorbate concentration, 92

Self consistent field theory for adsorption (SCFA), 8

Self-potentials, see Born potentialsSequential frontal analysis system, 177Serotonin for retention, 271SFE, see Supercritical fluid extraction (SFE)Silanol, 256Silica columns for biointeraction studies,

156, 158Silica hydride

based etched capillariesapplication, 283–286

84534.indb 400 11/5/09 12:30:23 PM

Index 401

capillary properties, characterization of, 279–280

dual separation modes, 280–282fabrication, 278–279formats, 282–283

based stationary phases for HPLCapplications, 264–278chromatographic properties of, 259–264materials, stability of, 258–259synthesis and characterization, 257–258

C8-and C18-bonded silica, 349C18 column, ANP mode on, 268chemical surface structures, 256difference between ordinary silica and, 256as separation medium, 255synthesis of, 256–257

Silylation, 353Simplifying assumptions, 93Simulation methodology

and theory of liquids, 28–29Simultaneous extraction and derivatization

fiber and fatty acids, 380formaldehyde, analysis of, 381

Sinanoglu’s theory, 5Single component systems, 32Single ion chromatograms of methyl

haloacetates, 379SLE, see Solid-liquid extraction (SLE)SLM, see Supported liquid membrane

extraction (SLM)Small particles

separation, 100–101analysis time, 101–102instrument performance, 104Kozeny–Carman equation, 102linear velocity, 103molecular diffusion coefficient, 103particle size and column length, 102resolution, 102scaling linear velocity, 102Scheibel equation, 104use of, 102van Deemter curve, 102–104Wilke–Chang equation, 104

Solenoid valve, 307Sol-gel coatings, 341Solid and semisolid samples

and ASE, 346MAE and SAE, 345matrix solid phase dispersion (MSPD)

C8-and C18-bonded silica and Florisil, 349

pressurized liquid extraction (PLE)optimization, critical parameters

in, 346quantitative recoveries for, 347SWE, 346–347

SAE and MAE, 347optimization, critical parameters in, 348

SLE, 345and Soxhlet extraction, 345–346supercritical fluid extraction (SFE), 344–345,

347, 366optimization, critical parameters in, 349POP bioavailability studies, 348

Solid–liquid extraction (SLE), 345Solid-phase extraction (SPE), 330

disk, 337MIP and RAM, 336molecularly imprinted polymers (MIPs),

336–337polymeric adsorbents, 337

Solid-phase microextraction (SPME), 330, 335, 373

amphetamine recovery, comparison of, 378analyte molecular weight, polarity and

analysis technique, relationship between, 375

derivatizationin gas chromatographic inlet, 382modes of, 376procedures, 377reactions for, 375

environmental pollutants, analysis, 340–341extraction efficiency, 340fiber material in environmental analysis,

choice, 341gas chromatography, 374–375headspace silylation-GC-MS full-scan

chromatogram, 383history and timeline

sorptive microextraction, 374in-port derivatization–GC–MS

reconstructed selected ion chromatograms from, 385

instrumentation of, 362maximum extraction yield, 339parameters in, 340polar substituent groups with nonpolar

substituents, replacement, 375–376polydimethylsiloxane, volume, 338–339post-extraction on-fiber derivatization,

381–382GC-MS extracted ion chromatograms

of herbicides for spiked water sample, 384

pre-doping technique, 381pre-extraction derivatization

hair amphetamines, analysis of, 376–377simultaneous extraction and derivatization

of fiber, 380sorptive extraction, 338–340

Solute distribution coefficients and transfer free energies, 46–47

84534.indb 401 11/5/09 12:30:23 PM

402 Index

Solute retention process, 5Solvation parameter model, use in

pSFC, 199–201choice of solvation descriptors, 225–228experimental conditions

chemical structures, stationary phases of, 206

chromatographic system, 201–202covariance matrix for solute set, 216data analysis, 218–225descriptor values among test set,

distribution of, 210, 215normalized residuals, plot of, 223ODS phases, selected in study, 206–209operating conditions, choice of, 202–203plot of S and E descriptor for solutes, 216reduced test set for ODS phases, 217selection of columns, 203–206set of test solutes, selection of, 206,

210–218solutes in final set with Abraham

descriptors, 211–214stationary phases, characterized in

study, 204–205system constants for chromatographic

system, 219–222Solvation process, 6Solvent

box, 43extraction techniques, 364saturated ODS bonded phase, 15

Solvophobic theory, 3deficiencies of, 7–8distribution coefficient, 7free energy terms, 5–6molecular surface areas, 7Sinanoglu’s theory, 5solute retention process, 5solvation process, 6thermodynamic model for, 4–5

Sonication-assisted extraction (SAE), 347, 364–365

optimization, critical parameters in, 348Sorptive extraction, 338–340Sorptive microextraction

solid-phase microextraction (SPME), 374Soxhlet extraction, 330, 345–346

Soxhlet extractof sewage sludge purification, 352–353

Spatial order and enhanced sensitivityFAMEs, analysis, 319, 322

SPE, see Solid-phase extraction (SPE)SPE pipette tip (SPEPT) extraction

techniques, 335–336SPEPT, see SPE pipette tip (SPEPT)Spider diagram, plotting in SFC, 232, 234–241Split-peak method, 178–181

SPME, see Solid-phase microextraction (SPME)SPME-GC applications, 381Standard Gibbs energy change of association,

89–90Stationary phase of silica hydride-based column

hydrophobic and hydrophilic compounds, retention map for, 274

Steroids separationon cholesterol column, 264–265by pCEC on column, 277

Stir-bar sorptive extraction (SBSE), 338–341extraction efficiency, 340instrumentation of, 362maximum extraction yield, 339parameters in, 340polydimethylsiloxane, volume, 338–339sorptive extraction, 338–340

Stir-bar sorptive extraction (SBSE) techniques, 335

Subcritical water extraction (SWE), 346Sulfonamide separation, 267Sunscreen molecules set for developing

separation method, 244, 246–247chromatograms, 246elution orders of, 245structures of, 245

Supercritical fluid, 202supercritical fluid chromatography

(SFC), 195Supercritical fluid extraction (SFE), 344–345,

357, 366optimization, critical parameters in, 349POP bioavailability studies, 348

Supported liquid membrane extraction (SLM), 330

SWE, see Subcritical water extraction (SWE)Symmetric activity coefficient model, 96Synthetic peptide sample migration, pH effect

on, 281

t

Thermal effectadiabatic column at column outlet, 109changes in temperature, magnitude of, 109for incompressible fluids, 110isothermal compressibility coefficient, 108liquid volume, 107mechanical energy, change in, 108principle, 106quasi-static transformation, 107second principle of thermodynamics

and, 107small heat change, 107specific heat capacity, 108temperature change, 109thermal expansion coefficient, 107

84534.indb 402 11/5/09 12:30:23 PM

Index 403

Thermal sweeper, 305–306Thermodynamic-based models of RPLC, 3Thermodynamic cycle for solute retention, 5Thermodynamic modeling of chromatographic

separation, 58industrial applications, 79–81

Three-box GEMC setup, 42Time-of-flight mass spectrometry (ToF MS),

300, 313–314TMS, see Trimethylsilyl (TMS) groupTobramycin separation, 268–269ToF MS, see Time-of-flight mass spectrometry

(ToF MS)Transferable potentials for phase equilibria

(TraPPE-UA)force field, 31intramolecular potential, 32parameterization philosophy, 33

validation of, 34Trans-3-hydroxycinnamic acid

identification, 271TraPPE-UA, see Transferable potentials for

phase equilibria (TraPPE-UA) force field

Triethoxysilane and silica, condensation reaction between, 256

Trimethylsilyl (TMS) group, 353Trollius ledibouri Reichb, constituents analysis

by UPLC-ESI-MS method, 137Tryptic digest, 129

of bovine hemoglobin, 131Two-dimensional gas chromatography, 302

advantages of, 304–305dual-stage modulation process, schematic

of, 303GC×GC chromatogram, 304modulation time-window

wraparound, 303–304modulator

capillary flow technology, 307cutting stage, 310Deans switch-type flow modulator in

injection state, 307integrated MDGC instrument,

scheme, 309LMCS, 305longitudinally modulated cryogenic

system, 306low-cost pneumatic GC×GC, 307–308pneumatic-modulated GC×GC, 305, 307short microbore column

segment, 308–309single-stage air-cooled and electrically

heated thermal modulator, GC×GC instrument with, 308

thermal sweeper, 305–306tube, 308

operational parameterscolumn selectivities, 310detection, 312–314gas flows, 311–312GC×GC applications, series, 314–326temperature gradient, 310–311

u

Ultra-fast UPLC-UV method for antituberculosis tablets, 136

Ultra performance liquid chromatography (UPLC instrumentation), 100

applications ofbioseparations, 127–137higher performance, 124–125higher speed, 122–124physiological amino acids, 125–126

column performance, effect of pressure and temperature on

combined effect of, 121frictional heating, 117Kozeny–Carman equation, 119local HETP inside, 118modeling studies, 121pressure-induced and temperature-

dependent changes, 118–119pressure-induced influences, 120Scheibel equation, 118van Deemter equation, 118viscosity, 118Wilke–Chang equation, 118

retention, pressure and thermal effects on, 111–117

adiabatic column, temperature and pressure profiles for, 112

benzene and phenylpropanol, resolution between, 115

changes in, 117column performance, deterioration

in, 115degree of, 116ionized analytes, 116migration velocity, 113mobile phase, frictional heating of, 111radial temperature differences, 113selectivity of, 113stationary and mobile phase, 115temperature and superficial velocity,

radial profiles of, 114van’t Hoff equation, 113volume changes, 116

small particles for separationanalysis time, 101–102instrument performance, 104Kozeny–Carman equation, 102linear velocity, 103

84534.indb 403 11/5/09 12:30:23 PM

404 Index

molecular diffusion coefficient, 103particle size and column length, 102resolution, 102scaling linear velocity, 102Scheibel equation, 104use of, 102van Deemter curve, 102–104Wilke–Chang equation, 104

thermal effectadiabatic column at column outlet, 109changes in temperature, magnitude

of, 109for incompressible fluids, 110isothermal compressibility coefficient,

108liquid volume, 107mechanical energy, change in, 108principle, 106quasi-static transformation, 107second principle of thermodynamics

and, 107small heat change, 107specific heat capacity, 108temperature change, 109thermal expansion coefficient, 107

Ultrasound, as in sonication-assisted extraction (SAE), 345

UNIFAC, see Universal Functional Activity Coefficient (UNIFAC) model

Universal Functional Activity Coefficient (UNIFAC) model, 8–9

UPLC instrumentation, see Ultra Performance Liquid Chromatography (UPLC instrumentation)

v

van Deemter curve, 102–104, 118, 120van’t Hoff equation, 113Vapor–liquid coexistence curves (VLCCs), 32Vapor–liquid equilibrium (VLE) simulations of

molecule, 33

Vapor-phase extractiondynamic headspace (DHS), 335HS and GC techniques, 334thermal extraction, 335

VLCCs, see Vapor-liquid coexistence curves (VLCCs)

w

Waterthermal expansion coefficient, 109water–ethanol mixtures

molar density, 71–72relative permittivity of, 70

Waters ACQUITY UPLC with tunable UV detector, 101

Whelk-O1 stationary phase, 30Wilke–Chang equation, 104, 118Wilson’s local composition activity coefficient

modelsymmetric activity coefficient, 97

x

XBridge®, 101XL Stat software, 218

z

Zonal chromatography, 148Zonal elution, in affinity chromatography, 148

applications of, 150in binding and competition studies,

151–153temperature and solvent studies,

153–155characterization of binding sites

by, 155–1567-hydroxycoumarin binding to HSA,

149, 150practical considerations for, 156–158principles, 150–151

84534.indb 404 11/5/09 12:30:24 PM

0 012 1224 24 36z (Å) z (Å)

Figure 1.4 Simulation snapshots of stationary phase configurations taken from simula-tions of various RPLC systems. The left column, from top to bottom, shows snapshots for systems ODS-2.9/WAT, ODS-2.9/33M, ODS-2.9/67M, and ODS-2.9/33A. The right column, from top to bottom, shows snapshots for systems ODS-1.6/50M, ODS-4.2/50M, Amide-2.9/33M, and Ether-2.9/33M. The silica substrate and grafted alkyl chains are shown as tubes with oxygen in orange, silica in yellow, and CHx groups in gray. Methanol, acetonitrile, and water are shown in the ball and stick representation with oxygen in red, hydrogen in white, nitrogen in green, and methyl groups in blue. Solutes are shown as large spheres with CHx groups in cyan, oxygen in red, and hydrogen in white.

84534_CI.indd 1 11/5/09 10:59:37 AM

0

0.4

0.8

1.2

0

0.4

0.8

0

0.4

0.8

ρ (z

) (g/

mL)

z (Å) z (Å)

0

0.4

0.8

0 12 24 0 12 24 36

ODS-2.9/WAT

ODS-2.9/33M

ODS-2.9/67M

ODS-2.9/33A

ODS-1.6/50M

ODS-4.2/50M

Amide-2.9/33M

Ether-2.9/33M

Figure 1.5 The density profiles for the grafted chains (black), water (red), methanol (blue), and acetonitrile (green) in the retentive phase. The eight panels depict ensemble aver-ages for the same eight systems shown in Figure 1.4. The total system density, computed as the sum of bonded phase and solvent densities, is shown in purple. The interfacial region (all panels), defined by the range where the total solvent density falls between 10 and 90% of its bulk value, is shaded in gray while the Gibbs dividing surface fitted to the total solvent density is shown by the dashed orange vertical line. The location of z = 0 Å corresponds to the silica surface.

84534_CI.indd 2 11/5/09 10:59:39 AM

0

800

1600

2400

0

40

80

120

0

5

10

15

0

1

2

3

0

30

60

0

2

4

0

12

24

0

1

2

0

4

8

K (z

)

0

1

2

0

15

30

0

2

4

K (z

)

z (Å)

0

10

20

0

1

2

0 12 24 36 0 12 24 36z (Å)

0

6

12

0

1

2

ODS-2.9/WAT

ODS-2.9/33M

ODS-2.9/67M

ODS-2.9/33A

Amide-2.9/33M

Ether-2.9/33M

ODS-4.2/50M

ODS-1.6/50M

Figure 1.8 The distribution coefficient profiles for n-butane (blue) and 1-propanol (red). The eight panels depict ensemble averages for the same eight systems shown in Figure 1.4. The interfacial region (all panels) is shaded in gray while the Gibbs dividing surface is shown by the dashed orange vertical lines. The blue axis labels correspond to n-butane and the red to 1-propanol.

84534_CI.indd 3 11/5/09 10:59:41 AM

0.0E + 00

1.0E – 02

2.0E – 02

3.0E – 02

4.0E – 02

5.0E – 02

6.0E – 02

7.0E – 02

8.0E – 02

0 2 4 6 8 10 12 14 16 18 20Volume (CV)

UV

280

nm

Figure 2.4 Modeled isocratic elutions of β-lactoglobulins A (right) and B (left) on a Source 30Q adsorbent at pH 7. The salt concentration is 157mM sodium chloride, and the loads are 5, 10, 20, 50, 100, 200, 350, and 500 µL, respectively, at a concentration of 10g/L. The column volume (CV) is 7.8 mL.

0.0E + 00

1.0E – 01

2.0E – 01

3.0E – 01

4.0E – 01

5.0E – 01

6.0E – 01

7.0E – 01

8.0E – 01

UV

280

nm

0 2 4 6 8 10 12 14 16 18 20Volume (CV)

Figure 2.5 Modeled isocratic elutions of β-lactoglobulins A (right) and B (left) on a Source 30Q adsorbent at pH 7. The salt concentration is 157mM sodium chloride, and the loads are 350, 500, 1000, 2000, 3000, 4000, and 5000 µL, respectively, at a concentration of 10g/L. The column volume (CV) is 7.8 mL. The scale of the ordinate is 10 times the scale of Figure 2.4.

84534_CI.indd 4 11/5/09 10:59:54 AM

60

(a)

(b)

40

20

14

Peak

cap

acity

Peak

cap

acity

0

68

1012

5060

24

1020

3040

Colum

n len

gth (c

m)



60

40

20

14

0

68

1012

5060

24

1020

3040

Colum

n len

gth (c

m)

Figure 3.19 Representation of peak capacity for 25–30 nt oligodeoxythymidines vary-ing gradient and column length. Peak capacity calculated from Equation 11 in reference [69] for columns packed with (a) 1.7 µm or (b) 3.5 µm sorbent. Flow rate: 0.2 mL/min, separation temperature: 60°C, gradient start: 17.5% MeOH, difference in solvent composi-tion Δc: 0.05. Calculated for a 15 mM TEA – 400 mM HFIP aqueous ion-pairing system. Experimental constants for the model were obtained using XBridge and ACQUITY BEH C18 packed columns.

84534_CI.indd 5 11/5/09 10:59:58 AM

65

43210

5

4

3

2nd

dim

ensio

n (s

)

2

1

0750 1000

1000 1500 2000 2500 35003000

1250 225017501st dimension (s)

1500 25002000

Figure 7.15 TIC GC × GC–ToF MS contour plot of cigarette smoke showing the first-dimension range between 500 and 2600 seconds. (From Dallüge, J., van Stee, L. L. P., Xu, X., Williams, J., Beens, J., Vreuls, R. J. J., and Brinkman, UATh, J. Chromatogr. A, 974, 169–184, 2002. With permission.)

84534_CI.indd 6 11/5/09 11:00:18 AM

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84534_CI.indd 7 11/5/09 11:00:26 AM

7.00

6.00

5.00

4.00

Sec

3.00

2.00

1.00

0.004 14 24 34 44 54

Min64 74 84

Figure 7.17 TIC GC × GC-MS result for perfume. (From Mondello, L., Casilli, A., Tranchida, P. Q., Dugo, G., and Dugo, P., J. Chromatogr. A, 1067, 235, 2005. With permission.)

8.3 12.6 34.216.7 21.2 25.6 29.9 38.5 42.8 47.1 51.5 55.8 60.1 64.4 68.7 73.0 77.3 81.7 86.0 90.3Min

0.7

1.4

2.1

2.7

3.4

4.1

4.7

5.4

Sec

Figure 7.20 Headspace SPME-GC × GC-qMS result for Arabica coffee volatiles. (From Mondello, L., Tranchida, P. Q., Dugo, P., and Dugo, G., Mass Spectrom. Rev., 27, 101, 2008. With permission.)

84534_CI.indd 8 11/5/09 11:00:43 AM

DB1

DB6DB5

DB3DB4

DB2

123 4 5 IS

610

7 891112

1314

1516 17

1819 20 21 22 23 24

2526

27 2829 30

3132

3335 36

37 3839

40 4143 45

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34

48 4950

51 5253 54

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C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

55 5657 58

596061

62 63 64

DB0

ω6 ω3

ω1 65

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g

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ω6 ω3ω6 ω3

6.01

Sec

5.34

4.68

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3.34

2.68

1.35

2.01

0.68

0.0210.67 23.2220.084.4 7.54 13.81 16.95 26.36 29.49 32.63

Min

Figure 7.21 GC × GC-FID result for plasma FAMEs. Refer to Table 7.2 for peak identifi-cation. (From Tranchida, P. Q., Costa, R., Donato, P., Sciarrone, D., Ragonese, C., Dugo, P., Dugo, G., and Mondello, L., J. Sep. Sci., 31, 3347, 2008. With permission.)

DB5ω3

ω6

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C20

6.01

DB4DB3DB2DB1DB0

5.34

4.67

4.01

3.34

2.67

2.01

1.34

0.67

0.01

Sec

20.2 20.72 21.23 21.75 22.26 22.78 23.29 23.81 24.8424.33Min

Figure 7.22 Expansion relative to the 2D chromatogram shown in Figure 7.21, illus-trating the C20 FAMEs group (see Table 7.2 for peak assignment). (From Tranchida, P. Q., Costa, R., Donato, P., Sciarrone, D., Ragonese, C., Dugo, P., Dugo, G., and Mondello, L., J. Sep. Sci., 31, 3347, 2008. With permission.)

84534_CI.indd 9 11/5/09 11:00:59 AM

Di-aromatics

Mono-aromatics

7.5

5.0

2.5BP20

,2 t R (s)

BPX

-35,

2 t R (s)

0.013 25 38 50

DB-1, 1tR (min)63 75 88

0 10 20 30BP21, 1tR (min)

40 50 60 70

5

4

3

2

1

0

Alkanes

Di-aromaticsMono-aromatics

Alkanes

Figure 7.23 GC × GC–FID chromatograms of diesel oil obtained on two different column sets, namely, apolar–polar (top) and polar– medium polarity. (From Adahchour, M., Beens, J., Vreuls, R. J. J., Batenburg, A. M., and Brinkman UATh, J. Chromatogr. A, 1054, 47, 2004. With permission.)

100

80

60

Reco

very

(%)

40

20

00 2

Log Ko/w

4 6

SBSESPME

Figure 8.3 Maximum extraction yield of SPME and SBSE with different logKo/w values.

84534_CI.indd 10 11/5/09 11:01:11 AM

advances in chromatography: volume 48

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