Statistical mechanical study of hydrophobie interaction. II. Interaction among a set of M identical, spherical, and nonpolar solute particles

The tendency of a set of M solute particles to adhere to each other in various solvents is examined within the framework of classical statistical mechanics. The free energy change associated with the process of bringing M solute particles from infinity to a close configuration is split into two parts: a direct work against the intermolecular potential operating among the set, and an indirect part originating from the solvent properties. Various close configurations, for which pertinent experimental results are available, are examined. It is established that the indirect part of the free energy change, referred to as the hydrophobic part, is definitely anomalous in water compared with two relatively simpler solvents. The relative probabilities of clusterization of nonpolar solutes in water and in simple solvents is found to be greater, the larger the number of solute particles.