Solvent effects in weak electrolytes. II: Dipolar hard sphere solvent and the sticky electrolyte model with L=σ

The sticky electrolyte model in a dipolar solvent is studied in this paper. A detailed separation of the Ornstein–Zernike (OZ) equations and their solution in the mean spherical (MS) approximation for binding (or stickiness) at L=σ are given. The results derived earlier by Adelman and Deutch, Blum et al. and by Ho/ye et al. in this approximation are reproduced when the stickiness is switched off. Also when the density of the solvent goes to zero, the results reduce to those of the sticky electrolyte model (SEM) in a continuum solvent. It is found that the PY/MS approximation gives negative solutions for the association parameter λ, while the HNC/MS approximation works in a narrow interval of the sticky potential well depth ε2 between the positive and negative ions. As expected, the ion association increases when sticky potential well becomes deeper, but the dipole moment of the solvent is found to have a strong screening effect on this association. The study of the radial distribution functions of this system shows that the probability of a free ion appearing near a counter ion is greatly decreased when binding occurs between the oppositely charged ions at the contact; the opposite happens for ions of the same sign. The absolute value of the ion solvation energy becomes smaller as the electrolyte concentration increases and when stickiness between oppositely charged ions is introduced.