THEORIES OF
CHROMATOGRAPHY
.
THE THEORETICAL PLATE
MODEL OF
CHROMATOGRAPHY
CONTENTS
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Introduction
Theory statement
Significance
Number of theoretical plates
Height equivalent to a theoretical plate
Predictions
INTRODUCTION
This theory was developed by Martin and Synge in 1941.
THEORY STATEMENT
This theory assumes that column is divided into a number
of adjacent imaginary segments called theoretical plates.
Within each theoretical plate, analyte(s) completely
equilibrate between stationary phase and mobile phase.
SIGNIFICANCE
The plates serve as a way of measuring column efficiency
by either;

Stating the number of theoretical plates in a column, N
(the more plates the better)
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Or by stating the plate height; the Height Equivalent to
a Theoretical Plate, HETP (the smaller the better)
NUMBER OF THEORETICAL
PLATES
The number of theoretical plates that a real column
possesses can be found by examining a chromatographic
peak after elution;
𝟓. 𝟓𝟓 𝐭 𝐑𝟐
𝐍=
𝟐
𝐰𝟏/𝟐
Where;
N
w1/2
tR
= Number of theoretical plates
= Peak width at half-height
= Retention time
HEIGHT EQUIVALENT TO A
THEORETICAL PLATE
Height equivalent to a theoretical plate is calculated using
following formula;
𝐋
𝐇𝐄𝐓𝐏 =
𝐍
Where;
L
N
= Length of column
= Number of theoretical plates
PREDICTIONS

The width of bands increases as their retention time or
retention volume increases

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
THE RATE THEORY
CONTENTS
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Introduction
Theory statement
Eddy diffusion
Longitudinal diffusion
Resistance to mass transfer
Van Deemter plot
INTRODUCTION
It was proposed by Van Deemter in 1956.
THEORY STATEMENT
The rate theory describes the process of peak dispersion
(band spreading) and provides an equation that allows the
calculation of the variance per unit length of a column (the
height of the theoretical plate, HETP) in terms of the
mobile phase velocity and other physical chemical
properties of the solute and distribution system.
Equation derivation
 This Theory
gives more realistic description of the
processes that work inside a column
 It takes account of the time taken for the solute to
equilibrate between the stationary and mobile phase
(unlike the plate model, which assumes that
equilibration is infinitely fast)
 States that the band shape or a chromatographic peak is
affected by the rate of elution.
 Band shape is affected by different paths available to
solute molecules as they travel between particles of the
stationary phase
𝐁
𝐇𝐄𝐓𝐏 = 𝐀 + + 𝐂𝐮
𝐔
Where;
U=
A=
B=
C=
Average velocity of the mobile phase
Eddy diffusion
Longitudinal diffusion
Resistance to mass transfer
The rate theory allows calculation of minimum plate
height at an optimum velocity and, thus, a maximum
efficiency.
Eddy diffusion
As the mobile phase moves through the column which is
packed with stationary phase, solute molecules will take
different paths through the stationary phase at random.
This will cause broadening of the solute band, because
different paths are of different lengths.
A is;
Independent of u
Depends on size of stationary phase.
Longitudinal diffusion
The concentration of analyte is less at the edges of the
band than at the center. So, analyte diffuses out from the
center to the edges. This causes band broadening.
If the velocity of the mobile phase is high then the analyte
spends less time on the column, which decreases the
effects of longitudinal diffusion.
.
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B = 2γ DM
γ = Impedance factor due to packing
DM = Molecular diffusion coefficient
This means that;
1- B term dominates at low u
This factor is very important in GC than LC since DM(gas)
> 104 DM(liquid) concentration
Resistance to mass transfer
The analyte takes a certain amount of time to equilibrate
between the stationary and mobile phase.
If the velocity of the mobile phase is high, and the analyte
has a strong affinity for the stationary phase, then the
analyte in the mobile phase will move ahead of the analyte
in the stationary phase. The band of analyte is broadened.
The higher the velocity of mobile phase, the worse the
broadening becomes.
H = A + B/u + u [CM +CS]
Cs: Stationary phase - Mass transfer
Cs = [(df)2]/Ds
df: stationary phase film thickness
Ds: diffusion coefficient of analyte in SP
CM: mobile phase – mass transfer
Packed columns, CM = [(dP)2]/DM
Open columns, CM = [(dC)2]/DM
dP: particle diameter
dC: column diameter
VAN DEEMTER PLOT
Such plot is of considerable use in determining the
optimum mobile phase flow rate.