isocratic and gradient elution chromatography: a...

Journal of Chromatography A, 1109 (2006) 253–266

Isocratic and gradient elution chromatography: A comparison in terms ofspeed, retention reproducibility and quantitation

Adam P. Schellinger, Peter W. Carr ∗Department of Chemistry, Smith and Kolthoff Halls, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, MN 55455, USA

Received 22 August 2005; received in revised form 30 December 2005; accepted 11 January 2006Available online 3 February 2006

Abstract

Chromatographers are cautioned to avoid gradient elution when isocratic elution will do. In this work, we compared the analytical propertiesof gradient and isocratic separations of a sample which can be done quite readily under isocratic conditions. We found that gradient elution gavea shorter overall analysis with similar resolution of the critical pair compared to isocratic elution without sacrificing repeatability in retentiontime, peak area and peak height or linearity of the calibration curve. We also obtained acceptable repeatability in peak area/height and linearity ofcalibrations curves for a sample that required gradient elution using a practical baseline subtraction technique. Based on these results and relatedwtHp©

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ork which show that columns can be reequilibrated by flushing with less than two column volumes of the initial eluent, we conclude that many ofhe reasons given to avoid gradient elution deserve serious reconsideration, especially for those samples which are easily separated isocratically.owever, we believe isocratic elution will remain preferable when: (1) the sample contains less than 10 weakly retained components (i.e. the lasteak elutes with k′ < 5) or (2) the gradient baseline impedes trace analysis.

2006 Elsevier B.V. All rights reserved.

eywords: Gradient elution; Isocratic elution; RPLC method development; Quantitation; Baseline subtraction

. Introduction

After choosing the appropriate column (i.e. stationary phaseype and column dimensions) and eluent system (i.e. organic

odifier(s) and buffer), the next important step in RPLC methodevelopment involves choosing the elution mode (i.e. isocraticlution or gradient elution) that provides an adequate separa-ion within an acceptable analysis time. Dolan has suggestedhat a standard gradient elution scouting run be done to choosehe best elution mode for a specific column, eluent system andample [1]. He states that samples which occupy less than 20%f the separation space of this scouting run are better separatedy isocratic elution; conversely, he advises that samples whichccupy more than 40% of the separation space should be doney gradient elution. To a first approximation, these guidelinesake sense as gradient elution is required to solve the “general

lution problem” [2].

∗ Corresponding author. Tel.: +1 612 624 0253; fax: +1 612 626 7541.

When the sample occupies between 20 and 40% of the gra-dient scouting run, most chromatographers still prefer to useisocratic elution based on the criteria listed in Table 1. In termsof finding acceptable separation conditions, the optimization ofgradient elution is more complex as more variables influencethe selectivity (primarily gradient steepness and initial eluentstrength and secondarily dwell volume) compared to isocraticelution [3–7]. Also, the transfer of a gradient elution methodbetween columns, instruments and laboratories is notoriouslymore difficult than the transfer of an isocratic elution method[8–10]. In terms of separation speed, gradient elution is gen-erally considered to be an inherently slower technique thanisocratic elution since a widely accepted rule of thumb indi-cates that the column should be flushed (i.e. equilibrated) with atleast 10 column volumes of initial eluent before reliable reten-tion can be obtained in the next run [11]. Furthermore, manychromatographers have a phobia of “ghost” peaks [12–18], base-line noise [19–21] and other disturbances (e.g. eluent mixing)[22] associated with gradient elution that can lead to inaccuratevalues of peak area and peak height and impede quantitation.Also, gradient elution instrumentation is more complex and

E-mail address: [email protected] (P.W. Carr). requires more regular maintenance compared to isocratic elution

021-9673/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2006.01.047

254 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) 253–266

Table 1Current comparison of gradient and isocratic elution performancea

Metric Gradient elution Isocratic elution

Small k′ range (1 < k′ < 15) − ++Large k′ range (k′

max � 15) ++ − −Peak capacity (10 or more solutes) ++ −Method transfer − ++Quantitation (baseline disturbance) − ++Reequilibration time − − ++Method development − − +Instrumentation simplicity − − +

a Performance is judged qualitatively as excellent (++), good (+), fair (−) orpoor (− −).

instrumentation [23]. The main factors that drive chromatogra-phers to use gradient elution are multi-component samples, e.g.more than 10 components, which span a wide range in retention(k′

max/k′min � 15). That is, they seek to use the inherent higher

peak capacity of gradient elution [24] to handle more compli-cated samples or to overcome the general elution problem.

In prior work aimed at speeding up gradient elution by reduc-ing the reequilibration time, we developed strategies to achievevery good repeatability (i.e. standard deviation in retention timebetter than 0.002 min) and/or full equilibration of the columnsuch that the retention time for all peaks became independentof the reequilibration time [25]. We have shown that excellentrepeatability in retention time is possible for a sample of non-ionizable solutes, after the column is flushed with only a singlecolumn volume of unbuffered initial eluent [25]. In contrast fullequilibration with 1–2 column volumes of flushing was onlypossible when a small amount (1–3%, v/v) of an ancillary sol-vent (i.e. n-butanol) was added to the eluent [25]. The use ofan ancillary solvent, specifically n-propanol, was first suggestedby Dorsey [26,27]. Thus, when only 1–2 column volumes ofinitial eluent are required to reequilibrate the column, the timeneeded for reequilibration in gradient elution no longer has abig effect on analysis time (i.e. gradient time plus reequilibra-tion time). Consequently, the speed of a well-designed gradientelution separation may become comparable to and could oftenbe better than an isocratic separation.

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[19,33,34]. Zhu et al. [35] described a way to remove contam-inants from water-rich eluents which are a common source ofbaseline noise [14]. Also, problems with the instrumentation (i.e.poor eluent mixing or leaky valves) or UV detection below ornear the UV cut-off of the eluent also leads to baseline noise[20,22]. Further, Berry described the use of “Universal Liq-uid Chromatography” to detect many additional componentsusing UV detection between 190 and 210 nm under gradientconditions while minimizing baseline noise and ghost peaks[14,36–40]. Also, Winkler advised using the isobestic phe-nomenon in acetonitrile–water–trifluoroacetic acid mixtures tominimize baseline noise and obtain acceptable S/N for proteinsand peptides [41,42]. The use of perchloric acid to achieve lowpH with a very nearly transparent UV eluent should be consid-ered when mass spectroscopy is not to be done.

It is clear that regular instrument maintenance, high qualityeluents and the appropriate detection method all influence themagnitude of baseline noise/disturbances under gradient con-ditions. To further minimize the effect of the baseline on thequantification of analytes under gradient conditions, some inves-tigators have used advanced baseline correction algorithms [21].Although each of these algorithms has specific advantages anddisadvantages (see Ref. [21]), we use a commercially availablebaseline subtraction method to simplify correction of the base-line. Based on the repeatability in peak area and height, andlinearity of calibrations curves as criteria, we critically com-puedtr

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Although recently the speed, schemes for optimization andase of inter-instrument transfer [28,29] of gradient elutioneparations have been significantly improved, two importantuestions remain: (1) do gradient elution methods have anydvantages over isocratic elution for samples which are alsoasily separated isocratically? and (2) to what extent do theutative baseline complexities of gradient elution affect quan-ification compared to isocratic elution? Isocratic and gradientlution have been compared in terms of bandwidth [30], peakapacity [31] and method development strategies [32]. However,e believe this is the first work which critically compares the

dvantages and disadvantages of each elution mode for a sampleeliberately designed to be easily separated isocratically.

Many studies have been performed to address the issue ofaseline noise/disturbances in gradient elution chromatogra-hy. Obviously, the use of high purity solvents and reagentsre required to minimize baseline problems in gradient elution

are the affect of the baseline on the accuracy of quantificationnder gradient and isocratic conditions for a sample which isasily separated isocratically. These same criteria are used toetermine the affect of the baseline and a practical baseline sub-raction technique on the accuracy of quantification for a sampleequiring gradient elution.

Despite the plethora of ways to minimize baselineoise/disturbances under gradient conditions, the baseline mighttill be deleterious to trace analytical determinations. However,race analysis methods often involve a step to enhance the signal-o-noise ratio by (1) increasing the sample concentration, (2)erivatizing the solute(s) or (3) improving the sensitivity of theetection method to minimize the adverse affects of the iso-ratic or gradient baseline on quantitation. Unfortunately, inases where the quantity of sample is limited, the solute cannote labeled or the detection method is not adjustable, baselineoise/disturbance under gradient conditions can significantlympede quantitation. Although there are many factors whichnfluence the decision as to whether isocratic or gradient elutionill provide the “best” separation, the main goal of this work is

o show that many of the reasons to avoid gradient elution for aample easily separated isocratically are too conservative.

. Experimental

.1. Instrumentation

All chromatographic experiments were conducted using angilent 1100 chromatograph controlled by version A.10.01hemstation software (Agilent Technologies; Palo Alto, CA).his instrument was equipped with a vacuum degasser, low

A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) 253–266 255

pressure mixing chamber, autosampler, variable wavelength UVdetector and quaternary pump. The “intrinsic” dwell volume [29]of the instrument including all tubing required to connect the col-umn was determined to be 0.90 mL using the technique foundin chapter 8 of Ref. [43].

2.2. Reagents

The organic co-solvents in this study were used as obtainedfrom the manufacturer; acetonitrile was obtained from Burdickand Jackson (Muskegon, MI) and n-butanol was from Fisher(FairLawn, NJ). Trifluoroacetic acid (TFA; 99% purity) wasfrom Sigma-Aldrich (St. Louis, MO). HPLC grade water wasobtained in-house from a Barnstead Nanopure Deionizing sys-tem (Dubuque, IA). This water was boiled to remove carbondioxide and cooled to room temperature before use.

All eluents were prepared gravimetrically (±0.01 g) basedon the density (at 25 ◦C) of acetonitrile, n-butanol, water andtrifluoroacetic acid [44] where eluent composition is reported asthe v/v ratio. The eluents were stirred magnetically until theyreached room temperature. All eluents were passed through a0.45 �m nylon filtration apparatus (Lida Manufacturing Inc.;Kenosha, WI) immediately before use.

Uracil, acetophenone, butyrophenone, valerophenone, hex-anophenone, 1-(diphenylmethyl)-4-methylpiperazine, alpre-nolol, perphenazine, promethazine, amitriptyline, phenol,mnoptw

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injections. Thus, four injections of each solution were madeusing a specific mode of elution (isocratic or gradient elution)and wavelength of detection (214 or 254 nm). We also varied theinjection volume (from 0.5, 1.0, 2.0, 3.0, 5.0, 7.5 and 10.0 �L)of one solution (the 10–100 mL dilution of stock solution) togenerate calibration curves. Again, four replicates at each injec-tion volume were obtained using a specific elution mode anddetection wavelength.

2.4. Column

A 5 cm × 4.6 mm i.d. column with 5 �m Zorbax SB-C18 par-ticles and pore size of 80 A was used throughout this study. Theparticles were a gift from Agilent Technologies. The stainlesssteel column hardware was obtained from Isolation Technolo-gies (Hopedale, MA). The SB-C18 particles were slurried in2-propanol and sonicated (model PC3, L&R Manufacturing,Kearny, NJ) for 20 min before packing. The column was packedusing the downward slurry method technique at a packing pres-sure of 35 MPa using pure 2-propanol as the driving solvent anda Haskel 16501 high-pressure pump (Haskel International Inc.;Costa Mesa, CA).

2.5. Data analysis

Data analysis was performed as described in Ref. [25].

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ethylbenzoate, chlorpheniramine, meclizine, methapyrilene,itroethane, pheniramine and thioridazine were of reagent grader better and were used as obtained from Aldrich without furtherurification. These solutes were used to make two stock solu-ions in 100 mL volumetric flasks; all volumetric glassware usedas class A.The first stock solution contained approximately 50 �g/mL

racil, 150 �g/mL acetophenone and 300 �g/mL of 1-(diphenyl-ethyl)-4-methylpiperazine, alprenolol, perphenazine, promet-

azine, amitriptyline, phenol and methylbenzoate dissolved in1/20/78.9/0.1 (v/v/v/v) n-butanol, acetonitrile, water and tri-uoroacetic acid (TFA) eluent. The second stock solution con-

ained approximately 150 �g/mL of acetophenone, butyrophe-one, valerophenone and hexanophenone, 50 �g/mL of uracilnd 500 �g/mL of alprenolol, amitriptyline, phenol, chlorpheni-amine, meclizine, methapyrilene, nitroethane, pheniramine andhioridazine dissolved in a 1/10/78.9/0.1 (v/v/v/v) n-butanol,cetonitrile, water and TFA eluent. The mass of each solute wasecorded to ±0.0001 g.

.3. Calibration curves

To generate calibration curves of peak area and peak heightersus the mass of solute injected, we diluted the stock solutionsy adding 10 mL of a stock solution (using a 10 mL volumet-ic pipette) to 25, 50, 100, 200, 250 and 500 mL volumetricasks. Data was collected by injecting 2 �L of each solution

n order from lowest to highest concentration. A blank run (i.e.he method was run without injecting a sample) was performedefore the first injection. This set of injections was repeated threeore times performing only one blank run between each set of

.6. Baseline subtraction

For sample 2 peak area and height were obtained by subtract-ng baseline noise/disturbances contained in the blank runs fromhe experimental gradient elution chromatograms with Chemsta-ion software. Peak area and peak height were obtained directlyrom the experimental chromatograms for sample 1.

. Results/discussion

.1. Gradient elution scouting runs

For this study, we used standard gradient elution scoutinguns and the current method development guidelines suggestedy Dolan [1] to determine which elution mode was best suitedor the samples. With a column volume of roughly 0.6 mL andflow rate of 1 mL/min; Dolan recommends a routine linear

radient elution scouting run from nearly 100% water to nearly00% acetonitrile in 18 min. After performing the scouting runs,e calculated the range in retention of the solutes divided by theradient time to be 0.27 for sample 1 (see Fig. 1) and 0.60 forample 2 (see Fig. 2). According to Dolan’s guidelines, sam-le 1 falls in the “grey area” where either elution method canrovide an acceptable separation. However, if one ignores thearliest solute, which is very well separated from other com-onents in the mixture, this sample only occupies 20% of theeparation space and isocratic elution is definitely the preferredode by conventional wisdom. For sample 2, we are confident

hat gradient elution is required as this sample occupies 60% ofhe separation space in the gradient scouting run.


Fig. 1. Gradient elution scouting run for sample 1. Conditions: 5 cm × 4.6 mmcolumn with 5 �m SB-C18 particles; 25 ◦C; 1 mL/min; 254 nm detection;1 �L injection of the stock solution of sample 1; eluent A: 1/98.9/0.1(v/v/v) n-butanol/water/trifluoroacetic acid; eluent B: 1/98.9/0.1 (v/v/v) n-butanol/acetonitrile/trifluoroacetic acid; 100/0 to 0/100 A/B to 100/0 in 18 and0.01 min; hold at 100/0 A/B for 7 min.

3.2. Locating acceptable isocratic and gradient elutionseparation conditions for a sample easily separated withisocratic elution

To simplify the method development process, we decided touse a fixed column format (i.e. the column dimensions and par-ticle type were not varied), a fixed flow rate (2 ml/min) and afixed eluent system (i.e. various amounts of acetonitrile/watercontaining a constant amount of n-butanol (1%, v/v) and triflu-oroacetic acid (0.1%, v/v) for both the isocratic and gradientseparations. We believe that holding the column, eluent sys-tem and flow rate constant allows for a fair comparison of theanalytical aspects of isocratic and gradient elution. Also, wewanted to avoid an exhaustive search for the “optimum” sta-tionary phase type and eluent system requiring a staggeringnumber of training runs. Clearly, finding the true global opti-mum is a rarity in chromatography and the effort is not justifiedin most practical work. However, we grant that our conclu-sions might change if the flow rate, column dimensions and

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Fig. 3. Isocratic retention data for components in sample 1 vs. the volume frac-tion of acetonitrile in the eluent. The acetonitrile–water eluent also containedn-butanol and trifluoroacetic acid at constant volume percents of 1% and 0.1%,respectively. The ln k′ data shown was obtained at 15 ◦C. The symbols and linesrepresent phenol (�), alprenolol (©), perphenazine (�), methylbenzoate (�),1-(diphenylmethyl)-4-methylpiperazine (�), acetophenone (�), promethazine(�) and amitriptyline (♦).

particle size were to be optimized for each of the two elutionmodes.

Overall, we performed nine isocratic experiments (i.e. train-ing runs) using three different eluent compositions at threedifferent temperatures to predict retention as a function of eluentstrength and column temperature. In principle one needs onlyfour runs to obtain the essential data to predict retention as afunction of eluent and temperature. We did nine training runsto obtain some idea of the goodness of fit of the model to thedata. We assumed that linear solvent strength theory (i.e. LSST,see Eq. (1)) is accurate where S is the slope of ln k′ (isocraticretention factor) versus

ln k′ = ln k′w − Sφ (1)

φ and ln k′w is the solute’s retention at φ = 0. Although there

is some curvature in the LSST plots (see Fig. 3), we assumeda straight line and used first order least squares regressions toobtain S and ln k′

w for each solute. To predict retention as afunction of column temperature, we generated plots of S andln k′

w as a function of temperature (see Fig. 4). We then generatedfits of the LSST parameters for each solute as a function oftemperature using the Pade approximation (see Eq. (2)) whereT is the

LSST parameter = A + BT

1 + CT(2)

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ig. 2. Gradient elution scouting run for sample 2. The conditions are describedn Fig. 1.

olumn temperature (in K) and A, B and C are dependent on theolute.

Choosing the appropriate gradient elution training runs isore complicated as five parameters (initial and final eluent

trength, temperature, dwell volume and gradient time) affecthe selectivity. However, the gradient scouting run provides anstimate of acceptable initial and final eluent strengths. Also,


Fig. 4. Isocratic data for the dependence of ln k′w and S values on column tem-

perature. The symbols and lines represent the same solutes as described in Fig. 3.

the effect of dwell volume on the selectivity is easily modeledonce we can predict gradient elution retention as a function ofeluent strength and column temperature. Thus, we only needto extract the gradient LSST parameters as a function of col-umn temperature to locate suitable gradient elution separationconditions.

To obtain the gradient S and ln k′w values at one temperature,

we choose appropriate initial and final eluent strengths, held thedwell volume constant and performed separations at three dif-ferent gradient times. We then used the Solver function in Excelto obtain the gradient LSST parameters by minimizing the sumof the squares of the residuals of tR, predicted against the exper-imental values (i.e.

∑ni=1(tR, predicted − tR, experimental)2

i). We fit

the gradient S and ln k′w values for each solute as a func-

tion of temperature (see Fig. 5) using the Pade approxima-tion (see Eq. (2)). Thus, method development for the iso-cratic and gradient elution separations was done as similarly aspossible.

We first used Drylab 2000 Plus to locate reasonable val-ues of eluent strength and column temperature in isocraticelution. Drylab creates a map of the critical pair resolution(i.e. resolution of the worst separated pair of peaks) versusthe eluent strength and column temperature (see Fig. 6). Fromthis plot, the “best” separation conditions appeared to be atthe highest critical pair resolution (i.e. column temperature(T) of 30 ◦C and eluent strength of 1/21/77.9/0.1 (v/v/v/v)ns

Fig. 5. Gradient data for the dependence of ln k′w and S values on column tem-

perature. The symbols and lines represent the same solutes as described in Fig. 3.

Fig. 6. Plot of the isocratic critical pair resolution of sample 1 as a function ofthe volume fraction of acetonitrile in the eluent and column temperature. Thetraining runs used to generate Fig. 4 were input into Drylab 2000 Plus to obtainthis plot. The numbers in the legend represent the critical pair resolution; thus,the colors black, blue, yellow and orange correspond to critical pair resolutionsof 0, 1, 2, 3, and 4, respectively.

-butanol/acetonitrile/water/trifluoroacetic acid. However, thiseparation would take quite a long time and the last peak


would have k′ � 15. We are interested in a locating sepa-ration conditions providing reasonably robust resolution (i.e.Rs, critical pair � 2) in a short analysis time. Thus, a more effi-cient way to choose adequate separation conditions is to plotRs, critical pair divided by the time between two successive injec-tions as a function of the eluent strength or column temperature.

To make plots of the ratio of Rs, critical pair/analysis timeversus eluent strength or column temperature under iso-cratic conditions, we used an Excel-based Monte Carlosearch procedure that simultaneously varied the eluentstrength (from 1/10/88.9/0.1 to 1/35/63.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid) and the columntemperature (between 15 and 45 ◦C) to randomly generate15,000 separation “conditions”. This is clearly vast overkill butcertainly insures that we find the optimum conditions. We thendeleted those conditions that did not give reasonable resolutionof the critical pair (i.e. Rs, critical pair < 1.5); all situations pro-vided tolerable back pressures (i.e. �P < 38 MPa). We cautionthat acceptable situations under conditions outside the trainingdata range may be erroneous due to extrapolation errors.

Next, we made plots of Rs, critical pair/analysis time as afunction of eluent strength and column temperature (seeFig. 7). The regions of space in Fig. 7 (and Fig. 8, seebelow) which appear to be missing data correspond to con-ditions which do not satisfy the separation goals. After care-ful examination of Figs. 6 and 7, it is evident that the“tbsbaatas

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simultaneously vary gradient time (between 0.1 and 60 min),column temperature (between 15 and 35 ◦C), the initialand final eluent strength (from 1/0/98.9/0.1 to 1/35/63.9/0.1(v/v/v/v) and 1/20/78.9/0.1 to 1/60/38.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid, respectively)and the “effective” dwell volume [29] (between 0 and 5 mL)to generate 15,000 conditions. After removing those thatdid not meet our separation goals (i.e. Rs, critical pair > 1.5 and�P < 380 bar), we generated plots of Rs, critical pair/analysistime as a function of the initial eluent strength and columntemperature (see Fig. 8). Again, we caution that acceptableseparations predicted by extrapolation outside the gradienttraining runs should not be trusted. Examining Fig. 8, the“best” separation conditions appear to be at a column tem-perature of 25 ◦C and initial eluent strength of 1/31/64.9/0.1(v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid.Examination of the acceptable gradient elution situa-tions showed an “effective” dwell volume of 0.90 mL[29], final eluent strength of 1/42/56.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid and a gradienttime of 2 min give a very similar Rs, critical pair and shorter anal-ysis time compared to the “best” isocratic elution separation.

Given the narrow optimum range in the initial eluentcomposition and other variables (see Fig. 8) we could havegone on to a second round of searching over a narrowerset of conditions. For example we could have searched overt(tbtrpthdir

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best” isocratic elution separation is possible at a tempera-ure of 25 ◦C and eluent strength of 1/31/67.9/0.1 (v/v/v/v) n-utanol/acetonitrile/water/trifluoroacetic acid. Although Fig. 7hows that a higher ratio of Rs, critical pair/analysis time is possi-le at lower temperatures, we choose 25 ◦C as this temperatureppeared to provide a more robust separation (i.e. many accept-ble situations were generated around this as compared to loweremperatures). Furthermore, the Rs, critical pair at 25 ◦C is accept-ble (i.e. >2) and it gives a faster analysis time compared toeparations at lower temperatures.

To find acceptable gradient separation conditions for theame sample we used our Monte Carlo search program to

ig. 7. Ratio of critical pair resolution divided by the analysis time versus the veparation of sample 1. The Monte Carlo search program described in the text w

he range: gradient time (1–10 min), column temperature17–37 ◦C), the initial and final eluent strength (1/25/73.9/0.1o 1/35/63.9/0.1 and 1/30/68.9/0.1 to 1/50/48.9/0.1 (v/v/v/v) n-utanol/acetonitrile/water/trifluoroacetic acid, respectively) andhe “effective” dwell volume (0.5–1.5 mL). Assuming that aesolution of 1 min, 2 ◦C, 0.02, and 0.5 mL in gradient time, tem-erature, eluent strengths and “effective” dwell volume, respec-ively, is required to perform a reasonable grid search, one wouldave to generate 21,780 conditions. Although the number of con-itions needed for a systematic grid search is similar to that usedn our random search (i.e. 15,000), we found that as few as 500andomly generated conditions over the full multidimensional

e fraction of acetonitrile in the eluent and column temperature for the isocraticed to generate the data for these plots.


Fig. 8. Ratio of critical pair resolution divided by the analysis time vs. the volume fraction of acetonitrile in the initial eluent and column temperature for the gradientseparation of sample 1. Other details are described in Fig. 7.

space repeatedly found conditions which gave results within 5%of the optimum resolution per unit time revealed by either fullsearch. Clearly, it is improbable that the resolution of a system-atic search limited to only 500 possible sets of conditions wouldfind such a narrowly defined optimum in this five-dimensionalspace. Thus, the Monte Carlo method provides a simple buteffective way to locate reasonable gradient conditions. Futurework will more thoroughly investigate the use of Monte Carlosearch schemes in chromatographic optimization.

3.3. Comparison of the isocratic and gradient elutionseparations for a sample easily separated by isocraticelution

We performed the separations outlined above and obtainedthe isocratic and gradient chromatograms shown in Fig. 9. Theisocratic separation is acceptable as phenol (i.e. the first peakafter the dead time) is well retained (k′ ∼ 2), the last peak hasreasonable retention (k′ ∼ 14), and the critical pair resolution is2.10. However, the gradient separation requires less time whilegiving virtually the same critical pair resolution (1.90) withinexperimental error. The gradient elution analysis time was only3.4 min (2.4 min run time and 1 min instrument cycle time (i.e.data analysis and injection time) whereas the isocratic elutionanalysis time required 5 min at the same flow rate. The experi-mental values of Rs, critical pair/analysis time in each elution mode

Fig. 9. Optimized isocratic (A) and gradient (B) elution separations for sam-ple 1. Conditions: Eluent A: 1/31/67.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid; Eluent B: 1/60/38.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid; detection at 254 nm; 2 mL/min flow rate;2 �L injection of stock solution diluted 10–500 mL; 25 ◦C. (A) 100/0 A/B andrun ended at 4.0 min; critical pair: 3, 4. (B) 100/0 to 60/40 to 100/0 A/B in2 and 0.01 min and the run was ended at 2.4 min; critical pair: 8, 9. Solutes:uracil (1), phenol (2), 1-(diphenylmethyl)-4-methylpiperazine (3), alprenolol(4), perphenazine (5), acetophenone (6), promethazine (7), methylbenzoate (8)and amitriptyline (9).

are higher than predicted for both elution modes (0.42 and 0.56for isocratic and gradient elution, respectively) due to a conser-vative estimate of the plate count. Theoretically, increasing thegradient time from 2.0 min to 2.2 min would improve the gra-dient critical pair resolution to the value obtained in isocraticelution. Thus, gradient elution clearly provides a faster sepa-ration and similar critical pair resolution compared to isocraticelution for a sample that is easily separated isocratically.

Another advantage of separating sample 1 by gradient elutionis that the peak widths of the later eluting peaks are significantlynarrower compared to isocratic elution (see Figs. 9 and 10).Specifically, the peak width of amitriptyline is almost three timesless in gradient elution. Also, the peak width in gradient elution


Fig. 10. Comparison of the peak width obtained in isocratic and gradient elutionversus retention time. The minimum value of the peak width at half heightobtained in isocratic (�) and gradient (�) elution from all runs performed at214 and 254 nm was used to generate this plot.

remains almost constant for all solutes eluting after 1 min asthese analytes have a similar effective retention factor (k*) [45].Thus, gradient elution helps provide narrower peak widths whichdo not increase as a function of retention time as observed inisocratic elution.

At a flow rate of 2 mL/min, the instrument requires approxi-mately 1.2 min to flush 99% of the final eluent from the pumpingsystem [25]. Thus, the column inlet was flushed with less than acolumn volume of initial eluent before the next gradient analysiswas begun. Although this condition does not give “full” equili-bration as defined in our earlier work [25], in practice one onlyneeds to achieve acceptable repeatability in retention time [25].Therefore, we compared the repeatability of retention time inisocratic and gradient elution (see Fig. 11). Even with minimalreequilibration of the column, gradient elution and isocratic elu-tion provide similar and acceptable repeatability (see Fig. 11)and % RSD (data not shown) in retention time. It is important torealize that the addition of n-butanol to the eluent is not requiredto obtain acceptable repeatability in gradient elution [25]. Also,the addition of a fixed amount of n-butanol to the initial andfinal eluents does change the selectivity and increases the eluent

Fm(p

Fig. 12. Overlay of four blanks runs at 254 nm and 214 nm using the conditionsdescribed in Fig. 9B.

strength. The increased strength of the initial eluent decreasesthe gradient range (i.e. an initial eluent strength of pure water isno longer possible). Therefore, we urge that when an ancillarysolvent such as n-butanol is needed that it be used from the out-set. It is really only needed when fast, full equilibration of thecolumn is desired [25].

We then compared the accuracy and precision of quantita-tion in each elution mode. To investigate the degree of baselinenoise and disturbances in gradient elution, we overlaid repeatedbaselines from the blank runs (i.e. no sample was injected) per-formed at 214 and 254 nm (see Fig. 12). Obviously, the baselinechange with time is smaller in magnitude and more repeatableat 254 nm than at 214 nm. Also, the only region where baselinereproducibility is poor in gradient elution is between injectionand elution of uracil; this is where there is no separation possibleand thus no useful information can be collected. For practi-cal purposes, we believe that the gradient baselines are highlyrepeatable under the conditions used for sample 1. Furthermore,the results in Fig. 12 suggest that one can minimize baselinedisturbances due to the eluent components by collecting data at254 nm or another wavelength where an acceptable signal-to-noise ratio is obtained.

To further investigate the accuracy of quantitation, we com-pared the repeatability in peak area and peak height. All peakareas and peak heights were obtained directly from the exper-imental chromatograms (i.e. no baseline subtraction was per-foe

ig. 11. Repeatability of retention time in isocratic and gradient elution. Theedian value of the repeatability (n = 4) obtained in isocratic ( ) and gradient

) elution for all runs performed at 214 and 254 nm was used to generate thislot. The solutes are defined in Fig. 9.

ormed). To account for run-to-run variations in the volumef sample injected, we divided the peak area (or height) ofach solute by that of amitriptyline. Fig. 13 (note both axes


Fig. 13. Peak area and height repeatability as a function of the amount of sample 1 injected. The repeatability is the % RSD (n = 4) in the peak area or peak heightratio (i.e. peak area or height of the solute divided by the peak area or peak height of amitriptyline, respectively). The median repeatability of all solutes exceptamitriptyline was used to generate these plots. When varying the amount of sample injected, we either made 2 �L injections of various dilutions of the stock solutionor varied the injection volume of one solution (the 10–100 mL dilution of the stock solution). The symbols and lines represent isocratic elution at 214 nm (�), gradientelution at 214 nm (©), isocratic elution at 254 nm (�) and gradient elution at 254 nm (�). Other conditions are described in Fig. 9.

are logarithmic) compares the repeatability for both calibrationmethods used (see Section 2.3). In every case, the repeatabilitiesin both area and height ratios in gradient elution are similar tothose observed in isocratic elution. Furthermore, Fig. 13 indi-cates that the best way to improve the repeatability in peak areaand peak height is to inject more of the sample (i.e. mass orvolume). Unfortunately, column overload (i.e. peak tailing) willincrease the peak width to a similar extent in each elution modeas more mass is injected [43]. The linearity of plots of areaversus the amount of solute injected was compared via the cor-relation coefficient (see Table 2) and the precision in the slope(see Table 3). Table 2 shows that isocratic and gradient elutionprovide similar and acceptable correlation in calibration curvesof peak area versus solute mass for all peaks in sample 1. Table 3shows similar precision in the slope of the peak area calibra-tion curves for isocratic and gradient elution. Also, comparabletrends in the correlation coefficient and precision of the calibra-tion curve slope are obtained for calibration curves generatedusing the peak height (data not shown). Overall, the accuracy ofquantitation in gradient elution does not appear to be any worsethan isocratic elution for sample 1.

3.4. Revised RPLC method development guidelines

Considering that sample 1 is somewhat better and morequickly separated using the gradient elution method whereasthe current guidelines clearly indicate that it should be doneby isocratic elution suggest that the current RPLC guidelinesshould be revised [1]. We advise that isocratic elution is thebest choice for samples less than only 10%, not 20%, of theseparation space of the gradient scouting run and for samplescontaining solutes that span a very narrow range in retention(i.e. k′

max < 5). However, samples occupying more than 10%but less than 20% of the separation space are equally well andprobably better separated with gradient elution. The final choicedepends not only on the sample and chromatographic condi-tions, but also on the goals of the chromatographer and availableresources (i.e. instrumentation and optimization/computer sim-ulation programs). However, we have shown here that manyof the reasons why gradient elution is avoided, most espe-cially the presumed longer analysis time (i.e. slower samplethrough-put) and retention reproducibility, should be seriouslyreconsidered.


Table 2Linearitya of the peak area calibration curves for sample 1b

Solute 214 nm 254 nm

Injector Solution Injector Solution

Gradient Isocratic Gradient Isocratic Gradient Isocratic Gradient Isocratic

1-(Diphenylmethyl)-4-methylpiperazine 0.07 0.34 0.11 0.06 0.25 0.61 0.10 0.12Acetophenone 0.43 4.66 0.66 0.09 0.02 0.01 0.01 0.01Alprenolol 0.12 0.84 0.09 0.05 0.19 0.31 0.05 0.11Amitriptyline 0.02 0.05 0.03 0.02 0.03 0.02 0.01 0.04Methylbenzoate 0.05 0.08 0.02 0.04 0.0 0.14 0.05 0.09Perphenazine 0.06 0.07 0.04 0.05 0.12 0.05 0.04 0.03Phenol 0.02 0.33 0.03 0.01 0.02 0.11 0.01 0.03Promethazine 0.04 0.05 0.03 0.02 0.07 0.07 0.03 0.01Average 0.10 0.80 0.13 0.04 0.14 0.17 0.04 0.06Median 0.05 0.21 0.04 0.04 0.09 0.09 0.03 0.04

a Linearity is reported as (1 − R2) × 1000 where R2 is the correlation coefficient.b Calibration curves generated by varying the injection volume used n = 26 data points; calibration curves generated by varying the solution concentration used

n = 30 data points (see Section 2.3).

Table 3Precisiona in the peak area calibration curve slope for sample 1b

Solute 214 nm 254 nm

Injector Solution Injector Solution

Gradient Isocratic Gradient Isocratic Gradient Isocratic Gradient Isocratic

1-(Diphenylmethyl)-4-methylpiperazine 0.17 0.36 0.19 0.14 0.31 0.49 0.18 0.20Acetophenone 0.41 1.34 0.47 0.17 0.08 0.05 0.05 0.04Alprenolol 0.22 0.57 0.17 0.13 0.27 0.35 0.13 0.19Amitriptyline 0.09 0.12 0.09 0.07 0.13 0.10 0.09 0.10Methylbenzoate 0.13 0.17 0.09 0.12 0.39 0.23 0.13 0.17Perphenazine 0.15 0.17 0.12 0.12 0.11 0.14 0.11 0.11Phenol 0.08 0.36 0.11 0.04 0.08 0.20 0.05 0.10Promethazine 0.12 0.14 0.1 0.08 0.16 0.16 0.10 0.07Average 0.17 0.40 0.17 0.11 0.21 0.21 0.11 0.12Median 0.14 0.27 0.1 0.12 0.18 0.18 0.10 0.10

a The precision was calculated by multiplying the standard error in the slope by 100% and then dividing by the slope.b Calibration curves were generated as described in Table 2.

Table 4Linearity of the peak area and peak height calibration curves for sample 2a

Solute Peak area Peak height

214 nm 254 nm 214 nm 254 nm

Injector Solution Injector Solution Injector Solution Injector Solution

Phenol 0.23 1.12 0.01 0.02 0.14 0.18 0.28 0.20Pheniramine 0.25 1.92 0.04 0.04 0.15 0.75 0.07 0.45Methapyrilene 0.16 0.29 0.01 0.01 0.04 0.25 0.06 0.27Chlorpheniramine 0.09 0.15 0.37 0.01 0.08 0.16 0.08 0.33Nitroethane 0.54 0.37 0.02 0.07 0.36 0.35 0.22 0.30Alprenolol 0.05 0.06 0.55 0.12 0.120 0.58 0.16 0.16Acetophenone 0.02 0.03 0.02 0.08 0.28 1.14 0.38 1.99Amitriptyline 0.03 0.06 0.030 0.10 0.57 2.59 0.36 1.95Thioridazine 0.02 0.03 0.020 0.02 0.15 0.62 0.21 1.09Butryophenone 0.52 0.51 0.11 0.07 0.070 0.47 0.45 0.48Meclizine 0.02 0.01 3.67 0.18 0.26 1.14 0.34 0.99Valerophenone 6.07 2.26 0.070 0.07 0.82 0.41 0.67 0.54Hexanophenone 1.60 0.43 0.50 0.14 1.15 0.41 1.08 0.49Average 0.74 0.56 0.43 0.07 0.37 0.70 0.34 0.71Median 0.16 0.29 0.04 0.07 0.26 0.47 0.28 0.48

a The definition of linearity and method for generating the calibration curves are described in Table 2.


Table 5Precisiona in the peak area and peak height calibration curve slope for sample 2b

Solute Peak area Peak height

214 nm 254 nm 214 nm 254 nm

Injector Solution Injector Solution Injector Solution Injector Solution

Phenol 0.29 0.61 0.06 0.08 0.23 0.24 0.33 0.26Pheniramine 0.31 0.80 0.13 0.11 0.24 0.50 0.17 0.39Methapyrilene 0.25 0.31 0.07 0.07 0.13 0.29 0.15 0.30Chlorpheniramine 0.19 0.22 0.38 0.05 0.18 0.23 0.18 0.33Nitroethane 0.46 0.35 0.09 0.16 0.37 0.34 0.29 0.31Alprenolol 0.14 0.14 0.46 0.20 0.20 0.44 0.24 0.23Acetophenone 0.09 0.10 0.10 0.16 0.33 0.62 0.38 0.81Amitriptyline 0.10 0.14 0.03 0.18 0.47 0.93 0.37 0.81Thioridazine 0.09 0.10 0.04 0.07 0.24 0.45 0.29 0.60Butryophenone 0.45 0.41 0.21 0.15 0.52 0.40 0.42 0.40Meclizine 0.10 0.06 1.19 0.25 0.32 0.62 0.36 0.58Valerophenone 1.53 0.87 0.34 0.15 0.56 0.37 0.51 0.42Hexanophenone 0.78 0.38 0.44 0.22 0.67 0.37 0.64 0.40Average 0.37 0.35 0.27 0.14 0.34 0.45 0.33 0.45Median 0.25 0.31 0.13 0.15 0.32 0.40 0.33 0.40

a The precision was calculated as described in Table 3.b Calibration curves were generated as described in Table 2.

3.5. Robustness of a gradient elution separation for asample requiring gradient elution

Gradient elution clearly gave a better separation than isocraticelution for sample 1. However, in this case the gradient requiredonly a relatively small range in eluent strength which helpedminimize baseline disturbances. When a sample contains solutesthat span a wider retention range, such as sample 2, a larger rangein eluent strength is required to provide an acceptable gradientseparation. In this case, we expect that the repeatability in peakheight or peak area along with the linearity of the calibrationcurves will worsen, mainly due to increased baseline distur-bances. Thus, we investigated the accuracy of quantification forthe gradient separation of sample 2.

Fig. 14 shows the gradient elution separation of this sample.We used a conventional baseline subtraction technique to “cor-rect” the baseline of the experimental chromatograms. Althoughthe blank and experimental runs were performed as much as80 min apart, Fig. 14 shows that baseline subtraction providesa chromatogram with only minor baseline disturbances. Thisbaseline-corrected chromatogram allowed us to obtain peakarea/height values automatically without manual integration ora tedious search for appropriate integration parameters.

The repeatabilities in area and height after baseline subtrac-tion are given in Fig. 15. Clearly they are both worse than thoseobtained in the isocratic and gradient elution separations of sam-ptrbrtnww

We calculated the correlation coefficient (see Table 4) andprecision of the slope (see Table 5) for the area and height cal-ibration curves. Again, we believe that baseline disturbances(see Fig. 16) contribute to the lower correlation coefficients and

Fsubtracting the baseline from the experimental chromatogram (i.e. A). Condi-tions: Eluent A: 1/10/88.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoro-acetic acid; Eluent B: 1/90/8.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid; 100/0 to 0/100 to 100/0 A/B in 5 min and 0.01 min; runended at 8 min; detection at 254 nm; 2 mL/min flow rate; 2 �L injection of stocksolution diluted 10–500 mL; 25 ◦C.

le 1 (see Fig. 13). We attribute most of the decrease in precisiono the increased baseline disturbances resulting from the largerange in eluent strength (see Fig. 16); the reproducibility of theaseline is acceptable but slight changes in the baseline fromun-to-run do affect the accuracy of the baseline subtractionechnique. Overall, the repeatabilities in area and height wereo worse than 2% RSD when reasonable amounts of sample 2ere injected; in most cases, the precision in the area and heightas better than 1% RSD.

ig. 14. Gradient elution separation of sample 2 before (A) and after (B)


Fig. 15. Peak area and height repeatability as a function of the amount of sample 2 injected. The repeatability in the peak height and peak area ratios was calculatedas described in Fig. 13. The symbols and lines represent detection wavelengths of 214 nm (�) or 254 nm (©); other conditions are described in Fig. 14.

poorer precision, especially at 214 nm, compared to the valuesobtained for sample 1. However, the correlation coefficients formany of the solutes are still acceptable. Furthermore, the solutesthat have relatively low correlation coefficients (R2 < 0.999)or relatively poor precision in the calibration curve slope (%RSDslope > 0.30) are located in sections of the chromatogramwhere baseline disturbances are large or the repeatability of thebaseline (see Fig. 16) is poor.

Although baseline subtraction offers a reasonable way toaccount for baseline disturbances for the majority of the solutesin sample 2, this technique is not practical for all methodsas additional analysis time is required and sample carry-overmight be problematic. One way to avoid baseline subtrac-tion and reduce the effect of baseline disturbances is to use awavelength or detection method which is insensitive to com-ponents of the eluent but provides an acceptable signal-to-noise ratio for the analytes. For example, working at 254 nmcompared to 214 nm significantly reduces the magnitude ofthe baseline disturbances while simultaneously improving therepeatability of the baseline (see Fig. 16). We also stronglyadvise the use of dilute perchloric acid (10 mM) instead of0.1% TFA when mass spectrometry is not to be done and alow detection wavelength is required. Perchlorate is virtuallytransparent even at 210 nm. It is a stronger ion pairing agentthan TFA [46–50] thus requiring a bit higher initial eluentstrength.

Fig. 16. Overlay of eight blanks runs (i.e. no injection made) at 254 and 214 nmusing the conditions described in Fig. 14.


4. Conclusions

Many of the reasons for avoiding gradient elution listed inTable 1 have been addressed for a sample which contains solutesthat are easily separated isocratically. For this sample, gradientelution provides an overall faster analysis, narrower peaks andsimilar resolution of the critical pair compared to isocratic elu-tion without loss in repeatability of retention time, peak area,peak height, or linearity of the calibration curve. While theresults were obtained with only a single sample we believe thatmost of the findings especially those concerning peak width anddetection are general and will hold up for many samples. It isour belief that the fact that because gradient elution inherentlyinvolves more parameters that impact selectivity (gradient steep-ness > initial solvent composition > dwell volume) as comparedto isocratic composition (eluent strength) that gradient elutionwill generally be able to provide better selectivity. In combina-tion with the inherently narrower peak width for later elutingspecies we infer that resolution in gradient elution will rathergenerally, certainly not invariably, exceed that of isocratic elu-tion. Furthermore, when gradient reequilibration time is short,say 1–2 column volumes, the overall time from injection to injec-tion will probably be less than that for isocratic elution becausewe can trade higher resolution for shorter analysis time. Also,we found that a simple random search algorithm is a very effi-cient way to locate acceptable gradient conditions when a largemrtt

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to recognize the impact of two very perceptive reviewers whosecomments greatly benefited the final manuscript.

References

[1] J.W. Dolan, LC–GC 13 (2000) 388.[2] L.R. Snyder, Gas chromatography, in: Proceedings of the Interna-

tional Symposium on Gas Chromatography (Europe), vol. 8, 1971,p. 81.

[3] M.A. Stadalius, M.A. Quarry, L.R. Snyder, J. Chromatogr. 327 (1985)93.

[4] U.D. Neue, J.R. Mazzeo, J. Sep. Sci. 24 (2001) 921.[5] J.H. Zhao, P.W. Carr, Anal. Chem. 71 (1999) 2623.[6] Y. Baba, M.K. Ito, J. Chromatogr. A 485 (1989) 647.[7] P. Jandera, J. Chromatogr. A 485 (1989) 113.[8] L.R. Snyder, J.W. Dolan, LC–GC 8 (1990) 524.[9] J.W. Dolan, LC–GC 20 (2002) 940.

[10] S.D. Patterson, J. Chromatogr. 592 (1992) 43.[11] J.W. Dolan, LC–GC 21 (2003) 968.[12] V.V. Berry, J. Chromatogr. 199 (1980) 219.[13] V.V. Berry, Adv. Chromatogr. 15 (1980) 219.[14] V.V. Berry, R.E. Shansky, J. Liq. Chromatogr. 7 (1984) 943.[15] J.W. Dolan, LC–GC 6 (1988) 112.[16] J.W. Dolan, LC–GC 8 (1990) 516.[17] S. Williams, J. Chromatogr. A 1052 (2004) 1.[18] H. Engelhardt, H. Elgass, J. Chromatogr. 112 (1975).[19] J.W. Dolan, LC–GC 11 (1993) 498.[20] J.W. Dolan, LC–GC 13 (1995) 374.[21] H.F.M. Boelens, R.J. Dijkstra, P.H.C. Eilers, F. Fitzpatrick, J.A. West-

[

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[[[[

[

[

[

[

[

[

[[[[[[[

[

[[

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ultidimensional space is searched. Thus, many of the previouseasons for avoiding gradient elution (i.e. long reequilibrationimes, poor precision and difficult optimization) appear muchoo pessimistic. We are currently studying additional samples.

For sample 2, which required a wide range gradient, we havehown that simple baseline subtraction is a convenient way tobtain acceptable quantitative precision (i.e. linearity of a cal-bration curve and repeatability of peak area and peak height).owever, more advanced detection methods or baseline sub-

raction algorithms [21] may be needed to improve precision toetter than 1% RSD and eliminate the need for numerous blankuns.

Based on these findings, we have moderately relaxed thePLC method development guidelines suggested by Dolan [1].or example, isocratic elution appears more preferable when

he sample occupies less than 10%, not the previously recom-ended 20%, of the separation space of the standard gradient

couting run. Alternatively, isocratic elution is preferred for sim-le samples (i.e. less than 10 components) where the last peaklutes at k′ less than 5. Samples occupying more than 40% of theeparation space certainly require gradient elution. However, foramples occupying between 10 and 40% of the separation space,ither elution technique could be used but the only pragmaticeasons to avoid gradient elution is that gradient elution instru-entation is not available or the gradient baseline limits trace

nalysis.

cknowledgements

The authors acknowledge financial support from the Nationalnstitutes of Health (grant # 5R01GM054585-09). We also wish

erhuis, J. Chromatogr. A 1057 (2004) 21.22] H.E. Schwartz, B.L. Karger, P. Kucera, Anal. Chem. 55 (1983)

1752.23] J.J. Gilroy, J.W. Dolan, LC–GC 22 (2004) 982.24] C. Horvath, Anal. Chem. 39 (1967) 1893.25] A.P. Schellinger, D.R. Stoll, P.W. Carr, J. Chromatogr. A 1064 (2005)

143.26] L.A. Cole, J.G. Dorsey, Anal. Chem. 62 (1990) 16.27] D.L.D. Warner, G. John, LC–GC 15 (1997) 254.28] J.W. Dolan, L.R. Snyder, J. Chromatogr. A 799 (1998) 21.29] A.P. Schellinger, P.W. Carr, J. Chromatogr. A 1077 (2005)

110.30] M.I. Aguilar, A.N. Hodder, M.T.W. Hearn, HPLC Proteins, Pept. Polynu-

cleotides, 1991, p. 199.31] J.W. Dolan, L.R. Snyder, N.M. Djordjevic, D.W. Hill, T.J. Waeghe, J.

Chromatogr. A 857 (1999) 1.32] P. Jandera, Handbook of Analytical Separations, vol. 1, 2000,

p. 1.33] S.M. McCown, D. Southern, B.E. Morrison, J. Chromatogr. 352 (1986)

493.34] S.M. McCown, B.E. Morrison, D.L. Southern, Am. Lab. 16 (1984)

82.35] P.L. Zhu, L.R. Snyder, J.W. Dolan, J. Chromatogr. A 718 (1995)

429.36] V.V. Berry, J. Chromatogr. 236 (1982) 279.37] V.V. Berry, R.E. Shansky, J. Chromatogr. 284 (1984) 303.38] V.V. Berry, R.E. Shansky, J. Chromatogr. 290 (1984) 143.39] V.V. Berry, LC Magazine 2 (1984) 100.40] V.V. Berry, J. Chromatogr. 321 (1985) 33.41] G. Winkler, LC–GC 5 (1987) 1044.42] G. Winkler, P. Wolschann, P. Briza, F.X. Heinz, C. Kunz, J. Chromatogr.

347 (1985) 83.43] L.R. Snyder, J.L. Glajch, J.J. Kirkland, Practical HPLC Method Devel-

opment, Wiley-Interscience, New York, 1996.44] R.L. Schneider, Eastman Org. Chem. Bull. 47 (1975) 1.45] L.R. Snyder, J.W. Dolan, Advances in Chromatography, Marcel Dekker,

New York, 1998, p. 115.46] J. Dai, P.W. Carr, J. Chromatogr. A 1072 (2005) 169.


[47] J. Dai, S.D. Mendonsa, M.T. Bowser, C.A. Lucy, P.W. Carr, J. Chro-matogr. A 1069 (2005) 225.

[48] A. Jones, R. LoBrutto, Y. Kazakevich, J. Chromatogr. A 964 (2002)179.

[49] R. LoBrutto, A. Jones, Y.V. Kazakevich, J. Chromatogr. A 913 (2001)189.

[50] R. LoBrutto, A. Jones, Y.V. Kazakevich, H.M. McNair, J. Chromatogr.A 913 (2001) 173.

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