Physical insight into the entropy-driven ion association

The ion association is widely believed to be dominated by the favorable entropy change arising from the release of water molecules from ion hydration shells. However, no direct thermodynamic evidence exists to validate the reliability and suitability of this view. Herein, we employ complicated free energy calculations to rigorously split the free energy including its entropic and enthalpic components into the water-induced contributions and ion-ion interaction terms for several ion pairs from monatomic to polyatomic ions, spanning the size range from small kosmotropes to large chaotropes (Na⁺ , Cs⁺ , Ca²⁺ , F^- , I^- , CO₃ ^2- , and HPO₄ ^2- ). Our results successfully reveal that though ion associations are indeed determined by a delicate balance between the favorable entropy variation and the repulsive enthalpy change, the entropy gain dominated by the solvent occurs only for the monatomic ion pairing. The water-induced entropic contribution significantly goes against the ion pairing between polyatomic anion and cation, which is, alternatively, dominated by the favorable entropy from the ion-ion interaction term, due to the configurational arrangement of polyatomic anions involved in ion association. The structural and dynamic analysis demonstrates that the entropy penalty from the water phase is primarily ascribed to the enhanced stability of water molecules around the cation imposed by the incoming anion. Our study successfully provides a fundamental understanding of water-mediated ion associations and highlights disparate lengthscale dependencies of the dehydration thermodynamics on the specific types of ions.