Ion Pairing in ePPC-SAFT for Aqueous and Mixed-Solvent Alkali Halide Solutions

Short-range ion-solvent and ion-ion interactions need to be taken into account in molecule-based electrolyte equations of state. The ePPC-SAFT (electrolyte polar perturbed chain statistical associating fluid theory) model consists of hard chain, dispersion, association, multipolar, nonadditive hard sphere, mean spherical approximation, and Born contributions. Using Wertheim’s first-order thermodynamic perturbation theory for associating fluids to account for short-range cation-anion interactions offers significant advantages over models that use ion-ion dispersion interactions only. However, the ionic association framework assigns the same number of sites for ion-solvent and cation-anion interactions, assuming the formation of ion clusters. This work proposes a new association framework in which ion-ion and ion-solvent association sites are labeled, restricting the ion-ion association site number to one per ion to prevent the formation of larger ion clusters. This approach improves modeling accuracy compared to the original model, in which ion clustering was considered, without increasing the number of adjustable parameters. Furthermore, this work proposes a generalized Bjerrum theory with one adjustable parameter in the association strength function, as in Wertheim’s theory, and proposes an analytical approximation for the Bjerrum integral to speed up calculations. This work uses Wertheim’s theory for short-range ion-solvent interactions and compares Wertheim’s theory and Bjerrum’s theory for short-range ion-ion interactions, i.e., ion pairing. The new association framework with Wertheim’s theory for both short-range ion-ion and ion-solvent associations is demonstrated to be significantly more accurate compared to Bjerrum’s theory and slightly more accurate than the previous best practice. The model extends to mixed-solvent electrolyte solutions. Furthermore, the contributions of Helmholtz free energy terms and number of bonds of the ions are analyzed.