Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions

Modern theories of electrolyte solutions are physically accurate but difficult to apply for real-life systems; a need therefore exists to theoretically derive simplified and practically useful mathematical expressions for thermodynamic excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Huckel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (beta) ion and a cloud (alpha) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a 'smaller-ion shell' (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller alpha ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Psi(b a, the SiS contributes an 'extra ionic attraction' and the overall extra-electrostatic energy, Psi(b>a)(kappa) declines monotonically with increasing kappa. The entire Psi contribution, Psi(+/-), is a linear combination of the Psi s of the two counter beta ions. The effectiveness of Psi(+/-) is demonstrated for real-life electrolyte systems, based on experimental mean ionic activity coefficients and their concentration dependencies. Fitting theory with experiment generates ion-size parameters that represent realistic interionic collision distances in solution, unlike parallel parameters based on other simplified theories.