Electrolyte mixing thermodynamics to probe ion-ion interactions

Abstract

In their study of solvent-averaged ion-ion pair potentials, Pettitt and Rossky show that, at least for the given underlying Born-Oppenheimer level model, there is a remarkable well in the potential of the solventaveraged Cl⁻−Cl⁻ interaction in water; it has a minimum below-kT and near 3.6Å, the Pauling diameter for the Cl⁻ ion. As Pettitt and Rossky also showed, the osmotic coefficient of aqueus NaCl solution as a function of ionic strength ϕ(I) could be insensitive to this remarkable feature, even when the well implies that there is a substantial concentration of dimers at 1M or higher stoichiometric concentration. Here it is argued that the thermodynamics of mixtures of aqueous NaCl with, say, aqueous NaClO₄, should be sensitive to the presence of the well in the Cl⁻−Cl⁻ interaction. Accordingly we apply the HNC approximation to calculate the mixing coefficients that characterize the excess free energy functions of several model aqueous NaCl−NaClO₄ mixed electrolyte solutions. For reference we use a model (V₆) in which all six ion-ion pair potentials have the simple ‘vanilla’ form: charged soft spheres supplemented by a dielectric image correction and an adjustable Gurney term that represents an interaction of the solvation structures about the ions. The six Gurney coefficients were adjusted to tune the model ϕ(I) close to the experimental for pure NaCl, pure NaClO₄, and an equimolar mixture, all in the range 0.1≤I≤2M. We find that the V₆ model gives mixing coefficients that agree closely with experiment. The calculations were also made for five models that incorporate, in varying degrees, the Pettitt-Rossky pair potentials. Comparison of the mixing coefficients for these models with the experimental data leads to the conclusion that the Cl⁻, Cl⁻ well is unrealistic, although a shallower well in the same place might be acceptable.