APPROXIMATE ANALYTICAL EXPRESSIONS FOR THE PROPERTIES OF AN ELECTRICAL DOUBLE-LAYER WITH ASYMMETRIC ELECTROLYTES - CYLINDRICAL AND SPHERICAL GEOMETRIES

Approximate analytical expressions for the electrical potential distribution, surface excess of co-ion, and double-layer free energy and entropy for both cylindrical and spherical surfaces are derived. The present analysis extends previous results in that asymmetric electrolytes are considered. The mathematical treatment of the Poisson-Boltzmann equation is based on a semi-empirical fourth-order polynomial function, along with a parameter reflecting the degree of asymmetry of electrolytes and a parameter measuring the effect of curvature of a surface. The result of numerical simulation reveals that the deviation of the present approximate result from the corresponding exact value for the double-layer properties under consideration is about 4%. The performance of the expression obtained by following a perturbation algorithm is also examined. It is found that for a relative thin to medium-thick double layer, the performance of two approaches are comparable; for a relative thick double layer, the present analysis yields a much better result. (C) 1994 Academic Press, Inc.