Page 120 - Multidimensional Chromatography

112 Multidimensional Chromatography

where ( ) is the selectivity, which is a useful measure of relative peak separation
related to the discriminatory power of the chromatographic system, (b) is the reten-
tion, which expresses the retentive power of the chromatographic system, and (c) is
the efficiency, which measures the peak broading that occurs in the chromatographic
column (together with extra-column contributions, which in a well-designed system
are small). The three terms of equation (5.2) are essentially independent, so that we
can optimize first one, and then the others. The separation can be improved by vary-
ing the selectivity of the system ( ) by increasing N, and also by increasing the
retention factor by changing the solvent strength, until the term (k /(1 k )) reach a
plateau. Resolution is seen to be proportional to the term (k /(1 k )) of equation
(5.2), which corresponds to the fraction of the sample that is in the stationary phase.
Small values of k mean that the sample is largely in the mobile phase, and under
these conditions a poor separation of the sample is achieved. At high k values, the
factor (k /(1 k )) : 1 and it may therefore be thought that k should be high.
However, high k values lead to very long retention times, with the concomitant elu-
tion of excessively broad peaks which can be undetectable with available detectors.
It can be shown that k should not be much greater than 5 if reasonable analysis times
are to be obtained.
Therefore, the expression given in equation (5.2) suggests that when
1, in
order to optimize a given separation and to achieve a short time of analysis and good
sensitivity, the first factor to be optimized is k , and it may be shown that values
between 1.5 and 5 represent a reasonable compromise. Separation efficiency, as
measured by N, can be varied by changing the column length L or the solvent veloc-
ity u. N is usually chosen to provide the maximum efficiency compatible with a rea-
sonable analysis time. The operation of extended column lengths without increasing
the flow rate of the eluent necessarily increases the analysis time, and hence
decreases the throughput of samples. On the other hand, doubling the length of the
column will require a twofold increase in the flow rate of the eluent and conse-
quently a fourfold increase in inlet pressure, in order to maintain a constant retention
time. Moreover, as the term (c) of equation (5.2) shows, the resolution is not propor-
tional to N but increases with the square root of plate number, and thus the corr-
esponding increase in resolution with increasing plate number is not so great.
Up to this point, we have looked only at the separation of two-component mix-
tures. The optimization of separation becomes more complicated for samples that
contain many components of widely different k values.
As described above, resolution can be improved by variations in plate number,
selectivity or capacity factor. However, when considering the separation of a mixture
which contains several components of different retention rates, the adjustment of the
capacity factors has a limited influence on resolution. The retention times for the last
eluted peaks can be excessive, and in some cases strongly retained sample compo-
nents would not be eluted at all.
Improvement of column efficiency in terms of the number of theoretical plates
realized by increasing column length often yields marginal increases in resolution,
with a corresponding increase of analysis time to unacceptable levels. This