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of solute is placed at the midpoint of a tube filled with either a liquid or a gas the solute will slowly diffuse to either end of the tube. It will first produce a Gaussian distribution with a maximum concentration at the center and, finally, when the solute reaches the end of the tube, 'end' effects occur and the solute will continue to diffuse until there is a constant concentration throughout the length of the tube. The process is illustrated in Figure 5. Figure 5. Longitudinal Diffusion Before dispersion due to longitudinal dispersion is discussed some basic principles of diffusion need to be considered. The Diffusion Process Diffusion processes play important parts in peak dispersion. The process not only contributes to dispersion directly (i.e., longitudinal diffusion), but also helps to reduce the dispersion that results from solute transfer between the two phases. Consider the situation depicted in figure 6. Figure 6. The Diffusion Process

nbsp;      It is seen from equation (10) that the longitudinal diffusion term is a function of (k') the capacity factor of the solute. While this could be significant in an LC capillary column systems, where the film of stationary phase could be continuous along the length of the column, it will not be so in a packed column. The stationary phase in a packed column is broken into segments between each particles and between each pore in each particle so free continuousdiffusion in the stationary phase would be impossible. It follows that the longitudinal diffusion term for packed columns should be independent of the k' of the solute or, very nearly so, and in practice the effect of longitudinal diffusion in the stationary phase is ignored

on the quality of the packing. Longitudinal Diffusion Solutes when contained in a fluid naturally diffuse and spread driven by their concentration gradient. Thus, in a chromatographic column a discrete solute band will diffuse in the gas or liquid mobile phase. It also follows, that because the diffusion process is random in nature, a concentration curve that is Gaussian in form will be produced. This diffusion effect occurs in the mobile phase of both GC and LC columns. The diffusion process is depicted in figure 21.   Figure 21 Peak Dispersion by Longitudinal Diffusion

Diffusion Controlled Dispersion in the Stationary Phase The difference between diffusion controlled dispersion and dispersion resulting from adsorption and desorption processes is that the transfer process is concentration controlled. Reiterating equation (7), .  Thus, during solute transfer between the phases, (t) is now the average diffusion time (tD) and (s) is the mean distance through which the solute diffuses, i.e., the depth or thickness of the film of stationary phase (df

Note, this equation ignores the second order effect of any longitudinal diffusion that might be present in the stationary phase.In fact, in the original form, the equation was introduced by Van Deemter for packed GC columns and consequently, the longitudinal diffusion term for the liquid phase was not included and the function , was replaced by, . This was because  the diffusivity of the solute in a gas is four to five orders of magnitude greater than in a liquid. Thus, in the expression for longitudinal diffusion,       

nbsp; The longer the solute band remains in the column, the greater will be the extent of diffusion. The time the solute remains in the column is inversely proportional to the mobile phase velocity, so, the dispersion will also be inversely proportional to the mobile phase velocity. Van Deemter et al. derived the following expression for the variance contribution by longitudinal diffusion, (), to the overall variance/unit length of the column. (5) where (Dm) is the diffusivity of the