Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. I. Small Solvophobic Solutes.

We analyze the role of temperature, pressure, and solute's molecular size on the pattern of isochoric and isobaric solvation of small hard-sphere solutes in TIP4P/2005 water and in a water-like "Jagla" solvent exhibiting unusual thermodynamics. To this end, we employ molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy along isobaric and isothermal paths covering solvent's stable liquid and supercritical states as well as supercooled and "stretched" liquid states. Results are found to be consistent with the most primitive scaled-particle theory and the Gaussian model of small-length-scale solvation. The temperature and pressure dependence of solvation quantities embraces solvent's water-like unusual thermodynamic behavior: its density is reflected in the solvation free energy; the isochoric solvation energy and entropy; and the isothermal density derivative of the solvation free energy, its isobaric thermal expansivity in the isobaric solvation enthalpy and entropy, and its isothermal compressibility in the partial molecular volume. The solute's size or length-scale dependence is found to combine with solvent's water-like behavior to produce the "convergence thermodynamics" picture characteristic of aqueous solutions of nonpolar solutes, which is unequivocally found here to be the mapping of the water-like density maximum into the isobaric solvation enthalpy and entropy versus temperature curves for a set of solutes of varying sizes.