Importance of the Relative Static Permittivity in electrolyte SAFT-VR Mie Equations of State

The influence and importance of the relative static permittivity (RSP) in electrolyte equations of state is examined for the case of aqueous sodium chloride. Using the SAFT-VR Mie model, the Debye-Hückel (DH) or Mean-Spherical Approximation (MSA) terms, as well as the Born-solvation term, are used to formulate an electrolyte equation of state. The RSP is obtained from a variety of models, each differing in their dependencies; we consider constant, temperature-, density- and composition-dependent models. For a fair comparison between different combinations of electrostatic and RSP models, all ion-related parameters are obtained a priori. A novel combining rule is proposed to obtain the unlike parameters between solvents and ions; its reliability is examined for a variety of electrolyte systems. We also compare its performance relative to parameterised electrolyte models. Both the DH and MSA terms yield similar results for almost all properties and conditions. The RSP models used have the more-significant impact. Liquid densities and solvent saturation pressures showed limited changes between RSP models whereas osmotic coefficients, mean ionic activity coefficients and carbon dioxide solubilities observed drastically different behaviour. Analysing the contributions of the various terms to the activities of each species in an electrolyte mixture reveals an important balance between the Born-solvation and the DH or MSA terms where the RSP models have a significant influence over this balance, particularly when these carry a solvent- or ion-composition dependence.