Computations for Higher Valence Electrolytes in the Restricted Primitive Model

Abstract

A detailed account of the hypernetted chain (HNC) equation for 1–1, 2–1, 3–1, and 2–2 electrolytes in the restricted primitive model (charged hard spheres of equal size) is given, and comparisons are made with some other approximations for the excess thermodynamic functions. On the basis of self‐consistency tests, it is concluded that at a given concentration, the osmotic coefficients from the HNC approximation decrease in accuracy as the charges on the ions are increased. By comparison with the Monte Carlo results of Card and Valleau, it is concluded that the excess energy functions for all of these electrolytes are accurate to within a few percent. It is found that the HNC and $\mathrm{DHLL}+{\mathrm{B}}_2$ approximations show certain anomalies in the thermodynamic functions of 2–2 electrolytes which also occur in real electrolytes but are not predicted to occur in some of the other theories developed recently. The charge densities around ions, derived from the HNC theory, are compared with the well‐known predictions of Debye and Hückel. Oscillations in these charge densities are found to occur at sufficiently high concentrations for all of the model electrolytes considered in this study.