Page 173 - Multidimensional Chromatography

Unified Chromatography 165
outlet. The gaseous mobile phase expands according to Boyle’s law as it decom-
presses. Thus, the mobile-phase velocity increases monotonically from the column
inlet to the outlet. Giddings and co-workers derived two new factors to correct the
velocity-independent and velocity-dependent terms of the plate-height equations for
predicting the observed plate height on columns with pressure drops (33). This cor-
rection is small in GC, usually amounting to only a few percent (33).
Pressure-drop correction is totally unnecessary in HPLC because, although there
is a huge pressure drop in comparison to GC, the mobile phase is nearly incompress-
ible. Thus, no significant velocity gradient results. However, in unified chromatogra-
phy the departure of the apparent plate height from any meaningful measure of
column performance is more likely than in LC or GC. We must not use equation
(7.1) recklessly to estimate the true plate height or any average. Let’s look into this a
little more closely.
First, we need to distinguish between two kinds of gradients, i.e. temporal and
spatial. Temperature programming in GC is an example of a pure temporal gradient.
The column temperature is changed as a function of time, and at any particular time
the column temperature is the same, spatially, over the entire column. Since local
retention factors for a solute vary only as a function of temperature on any particular
GC column if it is uniformly coated or packed, the retention factor for a given solute
will be the same at all locations on such a column held at a constant temperature.
This means that the ratio of the average velocity of the solute molecules relative to
the local mobile-phase velocity will also be constant everywhere on the column.
Likewise, if we look at a single peak while it is on the column, and examine the local
retention factor spatially across the width of the peak, we would find the retention
factor is constant over the entire peak. There is no spatial component in a tempera-
ture program in (conventional) GC.
This is not the case in gradient-elution LC. Here the gradients are obviously temporal
since the mobile-phase composition is programmed to change as a function of time.
However, there is also a spatial component: at any given time, the mobile phase at a ref-
erence point on the column is older than the mobile phase upstream from that point. If a
(temporal) gradient of the modifier solvent is programmed at 5%/min, then the mobile
phase that is one minute upstream from our reference point will be 5% stronger. If we
examine a peak on an LC column at a particular location and point in time while it is in
the midst of a gradient, we would find, as we look downstream toward the leading edge
of the peak, that the mobile phase would weaken. Similarly, looking upstream toward
the trailing edge of the peak, the mobile phase would be increasingly stronger.
The consequence of this spatial component of the gradient is that the local reten-
tion factor of the solute will be lower on the peak’s leading edge than on its trailing
edge. If we assume the LC mobile phase is not compressible so that the mobile-
phase velocity is uniform, and if we temporarily disregard peak broadening phenom-
ena, then the local value of the solute velocity would be faster on the trailing edge of
the peak than on the leading edge. This means that the application of a mobile-phase
gradient in HPLC contributes to a narrowing of the peaks spatially and temporarily.
Of course, the peak-broadening processes are still at work in the column, opposing