Introduction to Chromatography Theory

akashmarathakam@gmail.com

The Theory of Chromatography

• Plate theory - older; developed by Martin & Synge

• Rate theory - currently in use today

Plate Theory - Martin & Synge 1954 Nobel Laureates

• View column as divided into a number (N) of adjacent imaginary segments called theoretical plates

• within each theoretical plate complete equilibration of analytes between stationary and mobile phase occurs

Plate Theory - Martin & Synge 1954 Nobel Laureates

• Significance?Greater separation occurs with:– greater number of theoretical plates (N)– as plate height (H or HETP) becomes smaller

• L = N H or H = L / Nwhere L is length of column, N is number of plates, and H is height of plates

N can be Estimated Experimentally from a

Chromatogram• N = 5.55 tr

2 / w1/22 = 16 tr

2 / w2

where:tr is retention time;w1/2 is full width at maximumw is width measured at baseline

Choice of Column Dimensions• Nmax = 0.4 * L/dp

where:N - maximum column efficiencyL - column lengthdp - particle size

• So, the smaller the particle size the higher the efficiency!

Efficiency Relative to Analysis Time

N

Analysis Time, min

1970’s300 mm L10 um

today150 mm L5 um

today90 mm L3 um

10 100

First Important Prediction of Plate Theory

Bandspreading - the width of bands increases as their retention time

(volume) increases

Problem:

• A band exhibiting a width of 4 mL and a retention volume of 49 mL is eluted from a column. What width is expected for a band with a retention volume of 127 mL eluting from the same analyte mixture on the same column?

• ANS: 10.4 mL

Second significant prediction of plate theory

The smaller HETP, the narrower the eluted peak

Plate Theory - Practical Considerations

• Not unusual for a chromatography column to have millions of theoretical plates

• Columns often behave as if they have different numbers of plates for different solutes present in same mixture

Rate Theory• Based on a random walk mechanism for the

migration of molecules through a column

• takes into account:– band broadening– effect of rate of elution on band shape– availability of different paths for different

solute molecules to follow– diffusion of solute along length

Van Deemter Equation

• H = A 1/3 + B/ + C

where:

H is HETP (remember want a minimum!) is mobile phase velocityA, B, and C are constants

Van Deemter Equation• H = A 1/3 + B/ + C

– first term - rate of mobile phase movement through column (often just a constant)

– second term - longitudinal solute diffusion; solute concentration always lower at edges of column so solute diffuses longitudinally

– third term - equilibration is not instantaneous

Resolution• Ideal chromatogram exhibits a distinct

separate peak for each solute

• reality: chromatographic peaks often overlap

• we call the degree of separation of two peaks:

• resolution = peak separation average peak width

Resolution• Resolution = tr / wavg

• let’s take a closer look at the significance of the problem:

Resolution

• So, separation of mixtures depends on:

– width of solute peaks (want narrow)efficiency

– spacing between peaks (want large spacing)selectivity

Example

• What is the resolution of two Gaussian peaks of identical width (3.27 s) and height eluting at 67.3 s and 74.9 s, respectively?

• ANS: Resolution = 2.32