Page 50 - Tandem Techniques

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Longitudinal Diffusion

Dispersion due to longitudinal diffusion ensues from the fact that, while the solute is in the mobile
phase, the band will spread as a result of the normal diffusion processes driven by concentration
gradients that occur in any fluid. Obviously the longer the solute remains in the column, the more the
solute will diffuse, and thus the variance of the band due to this effect will be inversely proportional to
the linear mobile phase velocity. Van Deemter proposed the following function to describe the
contribution to variance from longitudinal diffusion:

where (DM) is the diffusivity of the solute and (g) is a constant.

Resistance to Mass Transfer

The third dispersion process that Van Deemter considered to contribute to (H) and which, at high
mobile phase velocities, becomes the major contribution to peak variance, is the resistance to mass
transfer between the two phases. This dispersion process results from the finite time necessary for a
solute molecule to pass through the mobile phase to enter the stationary phase and conversely to pass
through the stationary phase and enter the mobile phase. It follows that some molecules are stationary in
the column during the period that the transfer processes are taking place, while those molecules in the
mobile phase continue to move along the column. As a consequence band dispersion takes place. The
two functions proposed by Van Deemter to describe the resistance to mass transfer between the two
phase were as follows:-

where (k') is the capacity factor of the solute,
(df) is the film thickness of the stationary phase,
and (Ds) is the diffusivity of the solute in the stationary phase.