The Electrostatic "Leash" and Coupling Effects in Diffusion of Ionic Species

Using the thermodynamics of irreversible processes as starting point, the Maxwell-Stefan (M-S) formulation for diffusion of charged species under the influence of electrostatic force fields is derived. The M-S diffusion formulation, that is generally applicable to concentrated ionic solutions, simplifies to yield the Nernst-Planck equations for systems in which the ionic species are present in dilute solutions. The requirements of electro-neutrality and the no-current prescription, combined with the differences in the mobilities of individual ionic species results in the creation of an electrostatic potential gradient, that acts as a "leash" in a manner so as to speed-up or slowdown an ionic species, depending on the sign of the charges. The net result is that diffusion of ionic species is, in general, strongly coupled to one another. Published experimental data for a wide variety of systems are used to highlight several features of ionic diffusion such as transient overshoots, and uphill diffusion during equilibration in bulk electrolyte solutions, permeation across cation-exchange membranes, and uptake in ion-exchange particles.