the theory of chromatography

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 phaseand mobile phase

ColumnTheoretical plate

Chromatographic principle

The molecules of the mixture interact with the molecules of the Mobile

and Stationary Phase

Retardation of rate of movement of

molecules

Each molecule interacts differently

with MP and SP

Different distribution coefficients and different

net rates of migration

Stationary phase

Mobile phaseSamplemixture Equilibrium

establishes at each point (ideally)

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 = 5.55 tR2/ w1/2

2 = 16 tR2/ w2

where: tR is retention timew1/2 is width at h0.5 w is width measured at baseline

N is a ratio of tR and σ of Wb which is 4σ

Where: N = Number of theoretical platesVe = elution volume or retention time (mL, sec, or cm)h = peak heightw1/2 = width of the peak at half peak height (mL, sec, or cm)

• Nmax = 0.4 * L/dp where:Nmax - maximum column efficiencyL - column lengthdp - particle size

• So, the smaller the particle size the higher the

efficiency!

Band spreading - the width of bandsincreases as their retention time (tR) or retention volume (VR) 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