Osmotic second virial coefficient of methane in water

A correlation-function-based scheme is proposed for calculating the osmotic second virial coefficient B for solutes that dissolve very little in a solvent. The short-distance contribution to B, a volume integral of the solute-solute pair correlation function h(r) from 0 to some finite distance r_c, is evaluated with h(r) obtained by molecular simulation. The remaining contribution to B from r_c to ∞ is calculated with an asymptotic form of h(r) (Evans, R.; et al. J. Chem. Phys. 1994, 100, 591). It is shown here that B for a model system of methane in water is obtained accurately in the temperature range between 238 and 373 K at 1 bar, with a result that B is a monotonically decreasing function of temperature, and the hydrophobic interaction between methane molecules measured by B is repulsive (B > 0) in supercooled water, virtually null (B ≲ 0) at around 0 C, and attractive (B < 0) at higher temperatures. It is also remarked that a nearly linear relation holds between B and the first-peak height of the solute-solute radial distribution function.