Theory of electrolytes including steric, attractive, and hydration interactions

TL;DR

This paper develops a continuum electrolyte theory incorporating steric, attractive, and hydration interactions, deriving effective ion interactions and analyzing size-dependent effects consistent with experimental observations.

Contribution

It introduces a novel continuum model that includes solvent-mediated interactions and provides analytical expressions for ion correlations and activity coefficients.

Findings

Effective interactions depend on ion sizes due to steric and hydration effects.

Results align with experimental data and Collins' rule.

Provides approximate formulas for ionic interaction coefficients.

Abstract

We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional $\cal F$ for the coarse-grained solvent, cation, and anion densities, including the Debye-H\"uckel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution $\propto \exp(- {\cal F}/k_BT)$. Eliminating the solvent density deviation in $\cal F$, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. %where the latter are written in terms of the ion volumes %and are inversely proportional to the solvent compressibility. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density $n_{\rm s}$. Secondly, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model $[$J. Chem. Phys. {\bf 54}, 1523 (1971)$]$ for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule $[$Biophys. J. {\bf 72}, 65 (1997)$]$. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.