Long tail correlations between hydrophobic solutes in a model solvent

Abstract

Recently, a one-dimensional model with nearest-neighbour square-well interactions has been studied, in which parameters were chosen to mimic some of the thermodynamic properties of solutions of non-polar solutes in water. Here we investigate the properties of the pair distribution functions, comparing correlations between solvent molecules with those between solute molecules in the limit of infinite dilution. Under some appropriate thermodynamic conditions, both contain the same underlying–exponentially monotonic–decay, with a decay length that is characteristically long-tailed. But while this length is barely of interest for the pure solvent by virtue of the minuteness of the correlations at such long distances, and is almost undetectable for all practical purposes, it appears dramatically in the case of solute–solute correlations, becoming visible when one can access large length separations. The implications of this unexpected feature are discussed, also in relation to the mean force between solute molecules and the osmotic second virial coefficient for the solute. The case of square-well interactions is discussed at some length, and references are made to analogous results for the case of a triangular-well interaction potential.