Temperature and pressure dependence of methane correlations and osmotic second virial coefficients in water

We report methane's osmotic virial coefficient over the temperatures 275 to 370 K and pressures from 1 bar up to 5000 bar evaluated using molecular simulations of a united-atom description of methane in TIP4P/2005 water. In the first half of this work, we describe an approach for calculating the water-mediated contribution to the methane-methane potential-of-mean force over all separations down to complete overlap. The enthalpic, entropic, heat capacity, volumetric, compressibility, and thermal expansivity contributions to the water-mediated interaction free energy are subsequently extracted from these simulations by fitting to a thermodynamic expansion over all the simulated state points. In the second half of this work, methane's correlation functions are used to evaluate its osmotic second virial coefficient in the temperature-pressure plane. The virial coefficients evaluated from the McMillan-Mayer correlation function integral are shown to be in excellent agreement with those determined from the concentration dependence of methane's excess chemical potential, providing an independent thermodynamic consistency check on the accuracy of the procedures used here. At atmospheric pressure the osmotic virial coefficient decreases with increasing temperature, indicative of increasing hydrophobic interactions. At low temperature, the virial coefficient decreases with increasing pressure while at high temperature the virial coefficient increases with increasing pressure, reflecting the underlying hyperbolic dependence of the virial coefficient on temperature and pressure. The transition between a decreasing to increasing pressure response of the osmotic virial coefficient is shown to follow the response of the methane-methane contact peak to changes in pressure as a function of temperature, though a universal correlation is not observed.