Zone and boundary diffusion in electrophoresis.

In chromatography, electrophoresis and sedimentation, an irreversible zone or boundary spreading is often observed which is greater than that attributable to ordinary molecular diffusion and to dispersion caused by flow in porous media. The additional spreading can often be identified with kinetic processes such as adsorption, partition, and chemical interconversion. The existence of this kinetic or rate effect has been especially observed in gas chromatography (1). The effect is found whenever a species is capable of existing in two or more states, each moving with a different velocity (2). The extent of the spreading is governed by the rate of interconversion between the states. Thus if an ion obtains a different mobility, perhaps by association, a spreading will result which is a function of the association-dissociation rates. This effect has been described before for simple reactions involving a single forward and reverse process (3, 4). The phenomenon has been called electrodiffusion (3), and it is found that an “effective” diffusion coefficient describes the spreading. The effective diffusion coefficient, D,, is comparable to the ordinary molecular diffusion coefficient, with the same dimensionality and relationship to flux and concentration gradient. The object of the present work is to extend the theoretical analysis to more realistic processes than those involving only two steps, and to estimate the order of magnitude of the effects. A mathematical description of the “diffusion” of chromatographic zones has been developed for rate processes of any degree of complexity (2). The value of D, obtained by this method can be written as