
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 tR and σ of Wb which is 4σ
•N = 5.55 tR2/ w1/22 = 16 tR2/ w2
where:
tR is retention time
w1/2 is width at h0.5
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)
• Nmax = 0.4 * L/dp
where:
Nmax - 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 (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