A model for weak electrolytes

Abstract

The structural and thermodynamic properties of a model electrolyte in which oppositely charged ions bind at a distance L through a delta function interaction are reviewed. The sticky electrolyte model (SEM), as it is called, mimics the behavior of a weak electrolyte and requires a theory (or approximations) for the stickiness (or bonding) between the ions and for the electrical interactions between them. Analytic solutions for charged hard spheres of diameter σ with L = σ/n where n=1, 2, 3, 4, and 5 have been obtained when the hypernetted chain (HNC) approximation was used for the correlation functions inside the hard core and the mean spherical approximation (MS) was employed outside this region. Numerical solutions to the HNC approximation applied to both these regions show only small changes in the internal energy and the degree of association as a function of the concentration. The effect of a solvent on the association of a weak electolyte is assessed from the analytic solutions to the HNC/MS approximation in the presence of a hard sphere solvent and a dipolar solvent. It is found that the degree of association of the weak electrolyte is considerably enhanced by the packing effect of a solvent and is decreased by ion solvation. In the limit of complete association, the system consists of dumbells with extended dipoles provided L<σ/2 when polymerization is averted by the repulsion between the hard cores of like ions. The energies of the systems of extended dipoles are found to have a simple analytic form when they are calculated according to the mean spherical approximation.