Page 172 - Multidimensional Chromatography

164 Multidimensional Chromatography

perfectly suitable to start development of a separation by using HPLC, particularly if
there is history of the problem at hand and an earlier solution on which to build.
Then we can simply investigate the possibilities of changing temperature, pressure,
and mobile-phase composition in our search for achieving our goals for separation in
the least possible time.

7.5 COLUMN EFFICIENCY AND PLATE HEIGHTS
IN UNIFIED CHROMATOGRAPHY

The plate height in chromatography, H, is a useful indicator of the rate of peak
broadening. The local plate height at any point on a column is given by the follow-
ing:

2
H d( ) dz (7.1)
2
where is the spatial variance of the peak along the column axis and z is the dis-
tance of the peak center from the column inlet (32). If H is constant and there are no
gradients, then:

2
H L (7.2)
2
where is determined at the column outlet and L is the column length.
There have been a few reports of column efficiency and reduced plate height mea-
surements in several unified chromatography techniques. These have been based on
the apparent plate height observed at the column outlet. In the notation used by
ˆ
Giddings (32) the apparent plate height, H, is given by the following:
2

ˆ (7.3)
H L
t R
where L is the column length, t R is the retention time of the peak in question, and is
the standard deviation of the retention time. (This standard deviation is a measure of
the width of one peak in time units, and not our ability to reproduce a t R value with
repeated trials of the same experiment.)
Chromatographers know well that plate height measurements carried out in the
manner of equation (7.3) are indicative of the actual column plate height only when
the column is completely uniform, that is, when there are no gradients. In practice,
this no-gradient rule is often erroneously interpreted as a no-program rule: if all of the
adjustable experimental parameters are kept constant, then we, too frequently, assume
we can accurately measure the column plate height or efficiency by observing the
peaks and their widths at the column outlet. Giddings and co-workers showed that this
is not true in GC because of the velocity gradient that exists in the column (33).
This velocity gradient arises from the pressure gradient necessary to create
mobile-phase flow. The pressure drops as we travel from the column inlet to the