Making Sense of Band Broadening, Column Efficiency and Resolution
You might
already noticed that chromatographic peaks have a ‘normal distribution curve’
appearance. In the figure below, you will see the distribution of solute
molecules along the column at the time when the analyte peak reaches the end of
packing.
Relationship between Plate Height and Peak Area
In
this figure above, band broadening is proportional to the chromatographic term
plate height (H) which intern is inversely proportional to
column efficiency. The other related quantitative measure of column efficiency
is number of theoretical plates (N) and described as:
N = L/H
Details of
the theoretical model of plate theory of chromatography are discussed during the
lecture!
Now can you guess the
relationship between column efficiency and plate numbers?
A
further understanding of band broadening of chromatographic peaks can be
achieved by reviewing the rate theory of chromatography which mainly
relate to rate of elution. Here we consider The Eddy diffusion (A),
Longitudinal diffusion (B) and Resistance to mass transfer (C).
The relationship between these elution and band broadening parameters with
pate height is shown by the equation:
H = A +
B / u + C u where u is average velocity of mobile phase.
The resulting relationship between flow rate and plate height is shown in the
Van Deemter plot below.
Van Deemter Plot
Can you predict the effect of
the following conditions on band broadening or column efficiency?
1.
Flow rate of mobile phase
2.
Diffusion coefficient of solutes ((a) gas, (b) liquid mobile phase)
3.
Relationship between the above two conditions (1, and 2)
The relationship between plate numbers and retention time and peak broadening
can be shown mathematically as:
N
= 16 (tR/W)2 where W = width of the
peak at the base
The ability to separate analytes is called resolution Rs and
for two components A and B analytes in a mixture, Rs can be
defined as:
Have you noticed the difference between selectivity factor and
resolution?
From the equation below, one could further see
the relationship between resolution and number of plates, selectivity factor and
capacity factor.
Problem - A student tried to increase the resolution of his chromatogram
by doubling the length of his column. It didn't work! Explain why and give
alternatives approaches to achieve the goal.
From
the above resolution equation, you can see that there would be no resolution
if selectivity factor is reduced to unity! Suggest possible ways of
increasing selectivity?
Are you ready to further
review your study on column efficiency, selectivity and resolution? Sketch a
typical chromatogram for two compounds under the following conditions:
1. Poor
resolution and efficiency; adequate selectivity
2.
Good resolution, selectivity and efficiency
3.
Poor resolution, efficiency and selectivity
4.
Good resolution and selectivity, long analysis time and, poor
efficiency
5.
Good efficiency and selectivity, poor resolution
Further summary and exercise
1.
I expect you to know the definition of the following:
a)
Elution
b)
Mobile and stationary phase
c)
Partition ratio
d)
Retention time
e)
Capacity factor
f)
Selectivity factor
g)
Plate height and number of plates
h)
Resolution
2.
Based on the data below, calculate for each compound
a)
Capacity factor
b)
Partition coefficient
c)
Resolution
d)
Selectivity
e)
Number of plates
f)
Plate height
Length of column 30 cm
Flow rate 1 ml/min
VM
6 ml
VS
0.5 ml
|
Retention time |
Peak width (W), min. |
Solvent |
4 min |
- |
Compound A |
7 min |
0.5 |
Compound B |
22 min |
1.5 |
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