Introduction To Chromatography Theory.ppt

Introduction to Chromatography Theory

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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 / N where 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 tr2 / w1/22 = 16 tr2 / w2 where: tr is retention time; w1/2 is full width at maximum w is width measured at baseline

Choice of Column Dimensions • Nmax = 0.4 * L/dp where: N - maximum column efficiency L - column length dp - particle size • So, the smaller the particle size the higher the efficiency!

Efficiency Relative to Analysis Time

today 90 mm L 3 um

today 150 mm L 5 um

N

1970’s 300 mm L 10 um

10

100

Analysis Time, min

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=Aν

1/3

+ B/ν + C ν

where: H is HETP (remember want a minimum!) ν is mobile phase velocity A, B, and C are constants

Van Deemter Equation • H=Aν

1/3

+ B/ν + C ν

– 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