Restricted primitive model of dianions and counterions within the mean spherical approximation: Integral equation and thermodynamic perturbation theory

Abstract

We present an analytical integral equation theory for dimers modeled as hard-sphere tangentially connected anions and cationic hard-sphere monomeric counterions embedded in a continuum dielectric medium. Each hard-sphere segment on the dimer and hard-sphere counterion is univalent with unit diameters. The model was formulated in the context of the two-density Ornstein–Zernike integral equation theory within the mean spherical approximation. Analytical algebraic solutions for the model were obtained except for one parameter which requires simple numerical computation. The contact values of the radial distribution functions, internal energy, Helmholtz energy, and osmotic pressure of the system were derived analytically as a function of density and Bjerrum length via the energy route. Radial distribution functions beyond contact predicted by the theory were calculated numerically using the Perram algorithm. Thermodynamic perturbation theory was used to predict the osmotic pressure of longer chains using the dimer thermodynamic and structural properties as a reference system. Predictions from the theory compared well with computer simulation data reported in the literature although no significant improvement over the monomer reference system was found.