Temperature effects on the hydrophobic interaction of parallel plates in the framework of the probabilistic approach to hydrogen bonding.

Recently, we have proposed a probabilistic approach to examine the effect of water-water hydrogen bond networks around two foreign hydrophobic particles (immersed in water) on their interaction. Because of the proximity to a particle, a water molecule in the first hydration shell around it forms a smaller number of hydrogen bonds compared to a bulk molecule. The probabilistic approach allows one to analytically evaluate the former number if the latter is known (which is usually the case). On the other hand, the former bonds may be slightly (energetically) enhanced compared to the latter if at least one of the two bonded molecules lie in the first hydration shell and does not form a bond with a nearest neighbor site on the particle surface. When two hydrophobic particles are sufficiently close to each other, the overlap of boundary water-water hydrogen bond networks gives rise to an additional attractive force between them. In this paper we use the probabilistic approach to examine the effect of solvent temperature on the solvent-mediated interaction of two hydrophobic particles. Their hydrophobic attraction is affected by the solvent (water) temperature because the density of the solvent, strength of a hydrogen bonds, and number of hydrogen bonds per molecule are sensitive thereto (the pressure effects are not considered here). The probabilistic approach predicts that the solvent-mediated attraction of hydrophobic solutes is driven by the favorable entropic component ("-temperature x entropy") of the potential of mean force that dominates the unfavorable energetic component. This attraction decreases as the temperature increases.