Unified Theory of Equilibrium Thermodynamics and Ion Association in Aqueous and Nonaqueous Electrolytes with Explicit Hard-Core Size

Within the framework of a functional integral formalism incorporating ionic charge and hard-core (HC) interactions on an equal footing, we formulate a unified theory of equilibrium thermodynamics and ion association in charged solutions. Via comparison with recent Monte-Carlo (MC) simulation results (J. Forsman et al., PCCP <b>26</b>, 19921 (2024)), it is shown that our approach is able to predict with quantitative precision the pair distributions of monovalent ions with the typical hydrated sizes <i>d</i> = 3.0 Å and 4.0 Å up to the molar concentration <i>n</i>_<i>i</i> ≈ 2.0 M. Moreover, comparison with additional simulation data from the literature indicates that within the characteristic regime of ionic packing fraction η ≲ 0.1, the theory can accurately account for the ion size dependence of the excess energy and pressure from <i>d</i> = 14.3 Å down to <i>d</i> = 1.6 Å. Via the adjustment of the hydration radius, our electrostatic formalism can also reproduce the nonmonotonic salt dependence of the experimentally measured osmotic coefficients of various aqueous and nonaqueous solutions. In accordance with AFM experiments involving weakly polar nonaqueous electrolytes, the underlying sharp competition between the particularly strong opposite charge attraction and the excluded volume constraint is shown to limit the occurrence of substantial ionic pair formation to the submolar concentration regime <i>n</i>_<i>i</i> ≲ 50 mM; at larger concentrations, HC repulsion hinders ion association and results in the quasi-saturation of the pair fraction curves.