On the Implementation of Chemical and Physical Ion Pairing in Electrolyte Models

Ion pairing, or ion-ion association, is a phenomenon that can be understood in different ways, such as the physical and the chemical association. In the former, only the electrostatic interactions and time-average of the relative positions of the ions define the association, while in the latter, a chemical bond between ions is considered, leading to the formation of ion pairs as a separate species. From Debye-Hückel and Born formalisms, considering electrolytes asymmetric in both size and charge, we demonstrate how the thermodynamics of electrostatic and chemical association relate to each other at the free energy and activity coefficient levels. We highlight how the definition of the ion pair parameters affects the results of activity coefficients. Our results reveal that the Bjerrum association constant can describe ionically bonded electrolytes but fails systematically for covalently bonded ones, establishing a fundamental physicochemical boundary for it. Finally, ion pair nonideality effects can be significant and should be considered alongside association approach and association constant choices, with relative importance varying by system.