Ion Chromatography - Multi-path Diffusion
As the solute molecules pass through a packed column they describe a tortuous path between the particles and it is clear that some molecules will follow a shorter path than the average and others a longer path than the average.
Figure 8. The Process of Multi-path Dispersion
The differential movement of the solute molecules in a packed bed is depicted in figure 8. The magnitude of the resulting variance (s2M) was deduced by Van deemter to be,
Longitudinal Diffusion If a sample of solute is placed in the center of a tube filled with solvent it will slowly diffuse to the ends. Initially, the concentration curve will be Gaussianin in form but when the solute reaches the ends of the tube 'end effects' will take place and the Gaussian curve will flatted and eventually the tube will contain a constant concentration of solute along its entire length. This type of diffusion takes place in the mobile phase as the solute passes through a chromatographic column but as the solute is eventually eluted from the end of the column the 'end effects' are never observed. The diffusion process that produces the band dispersion is depicted in figure 9.
Figure 9. The Process of Longitudinal Diffusion It is clear that the longer the solute remains in the column the more the diffusion process will progress and the greater the dispersion of the peak. Since the residence time of the solute band in the column will be inversely proportional to the mobile phase velocity, the resulting dispersion will also be related to the reciprocal of the mobile phase velocity. Van Deemter derived the following expression for the dispersion due to longitudinal diffusion , (s2L),
where (Dm) is the diffusivity of the solute in the mobile phase,
(u) is the linear velocity of the mobile phase,
and (g) is a constant depending on the quality of the packing.
The effect of the longitudinal dispersion is represented at the left hand side of figure 9.