Entropy of hydrophobic hydration: A new statistical mechanical formulation

A new statistical mechanical formulation is presented for the entropy of solution of simple molecules in water. The formulation is based on the Green-Wallace expansion for the entropy in terms of multiparticle correlation functions, which is derived here for rigid polyatomic fluids and for mixtures. In the latter case, the ideal (combinatorial) entropy of mixing is identified with the one-particle contributions, leading to an expression similar to that of Flory and Huggins. With a factorization assumption for the solute-water correlation function, we have been able to separate the translational and orientational contributions to the entropy of solution. This approach is applied to an infinitely dilute solution of methane in water. The required correlation functions are obtained by Monte Carlo simulation. The orientational contribution, which is due directly to the orientational asymmetry of water-water interactions, is found to be comparable to the translational contribution. We find that the large entropies and heat capacities of hydrophobic hydration are well accounted for by solute-water correlations alone and that large perturbations in water structure are not required to explain hydrophobic behavior.