Column performance longitudinal diffusion

First, we look at isocratic separations. Let us assume that the analysis can be accomplished within a retention factor of 10. We also suppose that the analysis is carried out with a typical reversed-phase solvent and a sample with a typical molecular weight of a pharmaceutical entity. In order to manipulate the analysis time, we will keep the mobile phase composition the same and vary the flow rate. The maximum backpressure that we will be able to apply is 25MPa (250 bar, 4000psi). In Figure 1, we have plotted the plate count as a function of the analysis time for a 5 J,m 15-cm column. We see that the column plate count is low at short analysis times and reaches a maximum at an analysis time of about 1 h. A further increase in analysis time is not useful, since the column plate count declines again. This is the point where longitudinal diffusion limits the column performance. The graph also stops at an analysis time of just under 5 min. This is the point when the maximum allowable pressure drop has been reached. 

This equation predicts that for maximum column performance we must minimize the contribution of each term while still maintaining a constant linear flowrate. The first term accounts for the geometry of the packing, the second for longitudinal diffusion in gas phase, and the third for resistance to mass transfer process. 

The plate theory assumes that an instantaneous equilibrium is set up for the solute between the stationary and mobile phases, and it does not consider the effects of diffusional effects on column performance. The rate theory avoids the assumption of an instantaneous equilibrium and addresses the diffusional factors that contribute to band broadening in the column, namely, eddy diffusion, longitudinal diffusion, and resistance to mass transfer in the stationary phase and the mobile phase. The experimental conditions required to obtain the most efficient system can be determined by constructing a van Deemter plot. 

At hi linear velocities, that is, at short analysis times, the column performance deteriorates as a result of resistance to mass transfer, while at long analysis times longitudinal diffusion is the limiting factor. 

Garg, D.R., and Ruthven, D.M., Performance of molecular sieve adsorption columns Combined effects of mass transfer and longitudinal diffusion, Chem. Eng. Sci., 30(9), 1192-1195 (1975). 

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