Mode Expansion in Equilibrium Statistical Mechanics. II. A Rapidly Convergent Theory of Ionic Solutions

The mode expansion theory, which was derived in a previous paper, is applied to the calculation of thermodynamic properties of an ionic solution. The specific system investigated is the 1–1 restricted primitive model aqueous electrolyte. In this model, the effective interactions (potentials of mean force at infinite dilution) between ions are a sum of pair potentials, and the pair potentials are hard-core repulsions (all with diameter 4.6 Å) plus a positive or negative Coulomb potential reduced by the dielectric constant of water. For this system, the mode expansion converges rapidly. At salt concentrations between 0.05 and 1.0M, only the first three terms in the expansion are needed to obtain osmotic coefficients and activity coefficients which agree very well with the accurate results obtained by integral equation methods. Due to the computational simplicity of the mode expansion, it is argued that the theory provides a convenient method for studying more realistic models for electrolytes.