Volumetric properties of solvation in binary solvents

The volumetric properties of solutes, including partial molar volume, compressibility, and expansibility, are determined by and, therefore, sensitive to the entire spectrum of solute-solvent interactions. However, applications of volumetric measurements to the study of solvation of solutes in binary solvents consisting of the principal solvent and a cosolvent are almost nonexistent. This deficiency partially reflects the lack of an adequate theoretical framework to rationalize the measured volumetric observables in terms of solute-principal solvent and solute-cosolvent interactions. To address this deficiency, we present in this work a simple statistical thermodynamic model describing solute thermodynamics in binary solvents. Based on the model, we derive relationships that link the partial molar volumetric properties of solutes with the extent and intensity of interactions of a solute with the principal solvent and the cosolvent. If the approximation of homogeneous solvation is introduced, the derived formalism can be simplified to a form that can be readily employed for practical treatment of experimental volumetric data on small solutes and/or individual atomic groups. As an example, we use this simplified formalism to rationalize the volumetric properties of the zwitterionic amino acid glycine in concentrated urea solutions. In general, the theoretical development presented in this work opens the way for systematic applications of volumetric measurements to quantitative characterization of solute-solvent interactions in complex solvents.