Band broadening longitudinal diffusion

Considering a chromatographic process controlled by a partition equilibrium and neglecting extracolumn effects (i.e., band broadening caused by factors outside the column, e.g., tubings, detector etc.), several factors can contribute to the overall solute band broadening eddy diffusion, longitudinal diffusion, and resistance to mass transfer in mobile and stationary phase. 

Schematics illustrating the contributions to band broadening due to (a) multiple paths, (b) longitudinal diffusion, and (c) mass transfer.

To determine how the height of a theoretical plate can be decreased, it is necessary to understand the experimental factors contributing to the broadening of a solute s chromatographic band. Several theoretical treatments of band broadening have been proposed. We will consider one approach in which the height of a theoretical plate is determined by four contributions multiple paths, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase. 

Here, A is the random path, B the longitudinal molecular diffusion and C the RTMT contributions with the velocity of the mobile phase u shown separately. H is referred to as the Height Equivalent to a Theoretical Plate and is terminology borrowed from distillation. While the distillation HETP is not truly applicable, the terminology has persisted. It can be shown that the H in this expression is the equivalent to variance/unit length. This is the expression introduced by Van Deemter and co-workers in 1956 in a discussion of band broadening. 

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. 

Neglecting all other sources of band-broadening, the maximum theoretical efficiency (lVmax) due to longitudinal diffusion alone is... 

The major source of band-broadening in CZE is longitudinal diffusion. Longitudinal diffusion refers to the axial diffusive spreading of the solute from the solute zone into the bulk solution as it travels down the capillary. The variance in peak width contributed by longitudinal diffusion is given by... 

The typical appearance of a van Deemter plot is shown in Figure 5.6. At low flow rates an axial longitudinal diffusion results in band broadening (the analyte can diffuse against the... 

In capillary gel electrophoresis, one of the major contributors to band broadening, besides the injection and detection extra-column effects, is the longitudinal diffusion of the solute molecules in the capillary tube [14], The theoretical plate number (N) is characteristic of column efficiency ... 

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

The contribution of longitudinal diffusion and other factors to band broadening in liquid chromatography can be quantitatively described by the following equation, which relates the column plate height H to the linear velocity of the solute, jU- ... 

The second term in Eq. (3), Blfi, describes the contribution of longitudinal diffusion to band broadening of the solute as it passes through the chromatographic system. This is the only term in the equation inversely proportional to the linear velocity of the mobile phase the other terms increase in value as the linear velocity increases. Giddings and others have also shown that this term is also directly proportional to the diffusion coefficient D , of the solute in the mobile phase according to the following equation, where Q is a constant [3] ... 

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