Kinetics of bulk and interfacial ionic motion: microscopic bases and limits for the nernst—planck equation applied to membrane systems

Abstract

Criticisms of, limitations on, and alternatives to the Nernst—Planck equation for ionic transport are outlined in the context of motion into and through liquids, gels, ion-exchanger membranes, ionic crystals and polycrystalline materials, mainly in connection with their use as membranes. The origin of the equation from the point of view of Langevin and Onsager, and contributions of Schlögl provide a basis for discussion of limitations on applications to non-homogeneous materials. The surprising usefulness and wide applicability are demonstrated using correlations for diverse cases including coupled transport, association (ion pairing and clustering), adsorption and concentrated electrolytes. Some microscopic models for the friction coefficient, based on hole theory of liquid transport and vacancy transport in crystals are discussed in terms of atomic properties. These models were picked because they relate easily to the macroscopic Nernst—Planck equation. An attempt to show similarities of transport in liquid, semi-solid and crystalline membranes, and thereby to show why the Nernst—Planck equation seems to apply so widely, may fail to satisfy some specialists. Many complicated and subtle phenomena are discussed tersely and discussions rely on heuristic theories. New material on kinetic boundary conditions, slow ion exchange and ionic overpotential is presented.