Solvent effects in weak electrolytes. I. Effect of a hard sphere solvent on the sticky electrolyte model with L=σ

Abstract

The Ornstein–Zernike (OZ) equations are solved for the sticky electrolyte model (SEM) with a hard sphere solvent using the hypernetted chain (HNC) approximation for the stickiness and the mean spherical (MS) approximation for the electrical interactions. Relations among the coefficients of Baxter’s q functions and the equation for the excess internal energy are given in the MS approximation for L≤σ, where σ is the molecular diameter, and L is the distance at which the oppositely charged ions can stick. The analytical results for L=σ in the HNC/MS and PY/MS approximations are presented in detail. When the charges are switched off, the results automatically lead to those of the sticky hard sphere system; when the stickiness is turned off and the discrete solvent is changed to a continuum, the results lead correctly to those of the restricted primitive model (RPM). The thermodynamic properties of the SEM in a hard sphere solvent for L=σ are calculated and compared with the properties in a continuum solvent; special attention is paid to the derivation of the osmotic coefficient in the McMillan–Mayer system for the SEM and for the corresponding uncharged system. By switching off the charge and the stickiness, the osmotic coefficient of an isotopic solute–solvent system is also obtained. The numerical results show that the hard sphere solvent has a strong packing effect on the structural and thermodynamic properties of the electrolyte and the association of the oppositely charged ions is greatly enhanced by the hard sphere solvent. The influence of a discrete solvent on the osmotic coefficient is quite subtle: for the charged system, the solvent tends to raise the osmotic coefficient; for the sticky hard sphere system, the solvent has just the opposite effect.