Page 175 - Multidimensional Chromatography

Unified Chromatography 167
Expressing the averages in equation (7.4) with integrals, we obtain:
L L
ˆ
2 2
H L H(1 k) dz [(1 k) dz] 2 (7.5)
0 0
What conditions would be necessary for the apparent plate height to match the
true plate height? The first immediately obvious instance is when H, k and are all
constant. Then, the right-hand side of equation (7.5) reduces to H. If k and were
ˆ
constant, or if the product (1 k) were constant, then H would equal the spatial
average of H.
The only unified chromatography technique in which k and are both constant is
LC. For all of the other unified chromatography techniques, k and are not constant
until reaching the other limiting case, i.e. GC, where k becomes constant again.
Considerable effort would be required to express H, k, and in terms of z (or to
change the variables, if necessary to make integration easier, or even possible) before
ˆ
ˆ
being able to calculate a value for H. Thus, it is not obvious if H would be smaller or
larger than the spatial average H or some particular local H value. However, it is
ˆ
unlikely that H would provide any useful measure of column performance without
sorting out all of these complications.
The point of all this is simply that we must not use the apparent plate height or the
apparent plate number as performance criteria in the unified chromatography tech-
niques on the justification that they already work well for LC and that they work well
for GC when a pressure correction is applied. A considerable expansion of theory
and an effective means for evaluating equations (7.4) or (7.5) are required first.
Likewise, as we consider multidimensional chromatography involving techniques
existing between the extremes of LC and GC, we must not build judgments of the
multidimensional system on unsound measures of the individual techniques
involved.

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