110th Anniversary: Theory of Activity Coefficients for Lithium Salts in Aqueous and Nonaqueous Solvents and in Solvent Mixtures

On the basis of work by Bernard and Blum [Bernard, O.; Blum, L. Binding Mean Spherical Approximation for Pairing Ions: An Exponential Approximation and Thermodynamics. J. Chem. Phys. 1996, 104, 4746-4754], Barthel et al. [Barthel, J.; Krienke, H.; Holovko, M.; Kapko, V.; Protsykevich, I. The Application of the Associative Mean Spherical Approximation in the Theory of Nonaqueous Electrolyte Solutions. Condens. Matter Phys. 2000, 3, 23], and Simonin et al. [Simonin, J.-P.; Bernard, O.; Blum, L. Real Ionic Solutions in the Mean Spherical Approximation. 3. Osmotic and Activity Coefficients for Associating Electrolytes in the Primitive Model. J. Phys. Chem. B 1998, 102, 4411-4417], this work presents and validates a molecular-thermodynamic model for lithium salt activity coefficients in aqueous and nonaqueous single- and mixed-solvent systems. The Binding Mean Spherical Approximation gives electrolyte activity due to long-range electrostatic forces, short-range hard-sphere repulsion, and ion-pair formation. The theory shows good agreement with measured salt activities up to 3 molar in aqueous and nonaqueous solvents using a solvent-dependent, concentration-independent, center-to-center distance of closest approach between ions as the single fitting parameter for each electrolyte system. For mixed-solvent electrolytes, the local solvation environment around the ions dictates short-range interactions. To account for preferential ion solvation in a mixed solvent, the center-to-center distance is obtained from Wang and co-workers' Dipolar Self-Consistent-Field Theory [Nakamura, I.; Shi, A.-C.; Wang, Z.-G. Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization. Phys. Rev. Lett. 2012, 109, 257802]. For a particular salt in a binary solvent mixture at fixed temperature, the model predicts salt activity coefficients using only the fitted single-solvent distances-of-closest approach