Understanding and predicting apolar solvation in mixed aqueous solvents is of fundamental and practical importance in applications such as pharmaceutical product development, food science, and chemical separations. Most recent theoretical approaches are based on preferential interaction models or, equivalently, on Kirkwood-Buff solution theory. As such, many of the parameters in these models are difficult if not impossible to accurately predict for most systems of practical interest. The work presented here offers an alternative approach based on analyzing the isothermal, isobaric process of transferring a solute (2) at infinite dilution from pure water (1) to a mixture of cosolvent (3) and water in terms of a two-step, thermodynamic cycle. The first step is an isothermal change in composition at fixed mass density that yields the final water-cosolvent weight fractions, but at a pressure above or below atmospheric depending on the binary 1-3 interactions. The second step is an isothermal expansion or compression step at fixed composition, to recover atmospheric pressure for the overall process. The cycle was designed to help separate and highlight the strong role that solvent density (i.e., the equation of state) and the work of cavity formation can play in determining the chemical potential of dissolved solutes (m₂) and the transfer free energy of the solutes between water and water-cosolvent mixtures (Dm₂^tr). Two model systems are used to illustrate the approach and the insights it provides regarding the relative importance of the solvent-exchange vs. density-adjustment steps. The first is methane solvation at infinite dilution in water-sorbitol and water-methanol cosolvents, based on recent results from molecular dynamics simulations over a broad range of temperatures, pressures, and binary cosolvent compositions.¹ The second is the unfolding thermodynamics of RNase A as a function of temperature in water-sucrose and water-ethanol mixtures based on available experimental data.²

For methane solvation in methanol-water mixtures, Dm₂^tr is negative at high temperature across all methanol concentrations, while at low temperatures it changes sign from positive to negative as methanol concentration increases. Under conditions where Dm₂^tr is negative (i.e., the transfer from water to methanol-water is favorable), the density adjustment or EoS contribution to solvation is dominant and primarily entropic. When Dm₂^tr is positive, the unfavorable solvent-exchange step is dominant and primarily enthalpic. Conversely, Dm₂^tr for methane in sorbitol-water mixtures is positive over a broad range of temperatures and compositions, and is dominated by the EoS contribution which is primarily enthalpic. From a more general perspective, we find that the changes in m₂ during the constant-density, solvent-exchange step for both methanol- and sorbitol-water systems can be captured by a common profile. If this behavior holds to other water-cosolvent systems, it suggests Dm₂^tr can be predicted for a range of water-cosolvent mixtures based almost purely on binary EoS data or calculations. A similar analysis of RNase A unfolding thermodynamics within this thermodynamic cycle framework illustrates the stabilizing behavior of sucrose-water mixtures at all temperatures and the conflicting stabilizing/destabilizing behavior of ethanol-water mixtures at low vs. high compositions and temperatures. The results of the thermodynamic cycle analysis for RNAse A also highlight a natural thermodynamic connection between the processes of solvent-mediated stabilization or unfolding, and those of pressure-induced unfolding of proteins.

(1) Shah, P. P.; Roberts, C. J. “Molecular solvation in water-methanol and water-sorbitol mixtures: the roles of preferential hydration, hydrophobicity, and the equation of state”. Journal of Physical Chemistry B 2007, 111, 4467.

(2) Mitra, L.; Smolin, N.; Ravindra, R.; Royer, C.; Winter, R. Pressure perturbation calorimetric studies of the solvation properties and the thermal unfolding of proteins in solution-experiments and theoretical interpretation”. Physical Chemistry Chemical Physics 2006, 8, 1249.