 There are two theories to explain chromatography  Plate theory - older; developed by Martin & Synge in 1941    Rate theory - currently in use

Proposed by van Deemter in 1956 Accounts for the dynamics of the separation

 View column as divided into a number (N) of adjacent imaginary segments called theoretical plates  Within each theoretical plate analyte(s) completely equilibrate between stationary phase and mobile phase

Column Theoretical plate

Chromatographic principle

Mobile phase Sample mixture Equilibrium establishes at each point (ideally) Stationary phase The molecules of the mixture interact with the molecules of the Mobile and Stationary Phase Each molecule interacts differently with MP and SP Retardation of rate of movement of molecules Different distribution coefficients and different net rates of migration

 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 or height equivalent to theoretical plate (HETP)

 The number of theoretical plates that a real column possesses can be found by examining a chromatographic peak after elution by various methods like half-height method USP method

N is a ratio of t R and σ of Wb which is 4σ •N = 5.55 t R 2 / w 1/2 2 where: = 16 t R 2 / w 2 t R is retention time w1/2 is width at h 0.5

w is width measured at baseline

Where: N = Number of theoretical plates Ve = elution volume or retention time (mL, sec, or cm) h = peak height w1/2 = width of the peak at half peak height (mL, sec, or cm)

• N max = 0.4 * L/dp where: N max - maximum column efficiency L - column length dp - particle size • So, the smaller the particle size the higher the efficiency!

Band spreading - the width of bands increases as their retention time (t R ) or retention volume (V R ) increases

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

The smaller HETP, the narrower the eluted peak

• It is 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