theory of chromatographic separations

Introduction to and Theory of

Chromatographic Separations

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What is Chromatography? Chromatography is the separation of an

analyte from a complicated mixture of similar constituents for qualitative or quantitative identificationApplies to both organic and inorganic

compounds

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Basic Separation Principles and Terms Compounds (analytes) are separated from a

mixture by passing them through a stationary phase using a mobile phase carriermobile phase = solventstationary phase = column packing material

3

Basic Separation Principles and Terms Separations occur because analytes in the

mobile phase interact with the stationary phase at different ratesProduces varying migration rates for analytes

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Basic Separation Principles

Example: Column elution chromatography

Introduce two solutes (A & B) onto a packed column through which a mobil phase (i.e. solvent) or eluent is continuously pumped

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Basic Separation Principles Separations depend on the extent to which

solutes partition between the mobile and stationary phases

We define this interaction with a partition coefficient:

K = cs/cmWhere:cs = stationary phase concentration (molar)cm = mobile phase concentration (molar)

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Types of Chromatography

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ChromatographyPlanar Column

Liquid Gas Supercritical FluidPartition

Bonded PhaseAdsorption

Ion ExchangeSize Exclusion

Gas - LiquidGas – Bonded Phase

Gas - Solid

Classification of Column Chromatography Methods

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The Chromatogram

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Sample Mixture

Chromatogram

0 5 10 15 20Time (minutes)

Abun

danc

e AB

C

D

E

ChromatographThe time that a peak appears (it’s retention time) is diagnostic for a given compound

The relative size of a peak (area or height) is proportional to the relative abundance of the compound in the mixture

Chromatography Terms A number of terms can be defined from

the following chromatogram

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Chromatography Terms Retention Time (tR) = the time it takes after

injection for a solute to reach the detector Dead time (tM) = the time for an unretained

species to reach the detector Mobile phase velocity (u) = L/tM; the average

linear rate of movement of molecules in the mobile phaseL = length of chromatographic column

Linear Rate of solute migration ( ) = L/tR

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v

Chromatography Terms Retention Factor or Capacity Factor (k’A) = a

term used to describe the migration rate of solutes (analytes) on columns

Where:KA = is the distribution constant for species AVS = volume of stationary phaseVM = volume of the mobile phase

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M

SAA V

VKk '

Chromatography Terms The retention factor can be determined

directly from a chromatogram using:

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M

MRA t

ttk '

Chromatography Terms Interpreting the retention factor

If k’A < 1; the elution is too rapid for accurate determination of tR.

If k’A > approx. 10; the elution is too slow to be practical

The preferred range for k’A is between 1 and 5

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Chromatography Terms Selectivity Factor () = KB /KA

Where KB is the distribution constant of the more strongly retained species (so that >1

The selectivity factor can also be defined in terms of retention factors and retention times:

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MAR

MBR

A

B

tttt

kk

)()(

''

Chromatography Terms Zone Broadening or Band Broadening

Refers to the shape of a peak as a solute migrates through a chromatographic column; it will “spread out” and “shorten in height” with distance migrated

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Chromatography Terms Plate Height (H) and Theoretical Plates (N)

Terms used to quantitatively describe chromatographic column efficiency

Column “efficiency” increases as N increases

N = L/HWhere:

N = the number of interactions (i.e. transitions between mobile and stationary phases) that a solute has during its residence in the column

H= the distance through the column a solute travels between interactions (typically given in centimeters)

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Chromatography Terms Plate Theory – used to describe solute migration

through a column and the Gaussian shape of a peakIf the shape of a chromatographic peak is assumed to be

Gaussian, then the plate height can be defined in statistical terms involving standard deviation (σ)

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LH

2

Chromatography Terms Plate Theory (cont.)

H is defined as variance per unit length of column

H is the length of column that contains the fraction of analyte between L and L – σ

This is 34% of the analyte (1/2 of 1 std. dev.)

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Calculation of N From a Chromatogram

Where:W = magnitude of the

base of the triangle (in units of time)

tM = retention time of an unretained solute

tR = retention time of the solute

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2

16

WtN R

Chromatography Terms Rate Theory (or Kinetic Theory) – used to explain (in

quantitative terms) the shapes of chromatographic peaks and the effects of chromatographic variables on peaks as a solute migrates through a columnThe Gaussian shape of an peak can be attributed to the

additive combination of the random motions of individual solute molecules

The migration of an individual molecule through a column is irregular (based on “random walk” mechanism)

The time an individual molecule spends in a phase depends upon (accidentally) gaining sufficient thermal energy to change phases

Results in a symmetric spread of velocities around the mean

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Chromatography Terms Column Resolution (RS)

is a quantitative measure of the ability of a column to separate two analytes:

To increase resolution increase column length (L) Limitation: longer time and

broader bands Usually compromise

between resolution and speed of analysis

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BA

ARBRS WW

ttR

])()[(2

Summary of Important Terms

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Summary of Important Terms

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Variables Effecting Separation Efficiency in Column Chromatography

1. Particle Size of Packing (as size , Nand H)2. Immobilized Film Thickness (as film thickness , Nand H) -

due to faster diffusion rates in film3. Viscosity of Mobil Phase (as viscosity , Nand H)4. Temperature (as T , k' , but remains approximately

constant)5. Linear Velocity of Mobil Phase; u = L/tM (u is proportional to

1/tM because L = constant)6. Column Length (as L , N but H = constant, and separation

efficiency )

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In general, Separation (or Column) Efficiency In general, Separation (or Column) Efficiency , as N , as N and H and H

Variables Effecting Column Efficiency Mobile Phase Flow Rate

Optimum flow rate corresponds to minimum H

H is much smaller for HPLC than for GC (more efficient), but in practice GC columns are much longer than for HPLC - hence greater N for GC.

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Liquid Chromatography

Gas Chromatography

Variables Effecting Column Efficiency Particle Size of Column Packing

The smaller the packing particles, the greater the column efficiency.

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The General Elution Problem

It is often difficult to find a set of conditions which will resolve all peaks to the same degree and also permit reliable quantification

SolutionsMultiple runs at

different conditionsProgrammed elution

(i.e. change conditions during the run)

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