Model of the hydrophobic interaction

Abstract

The potential of mean force between interstitial solute molecules in Ben-Naim's one-dimensional, many-state lattice model (related to the one-dimensional q-state Potts model) is calculated. Since the model is exactly soluble, all results are explicit and analytic. It is found that the magnitude of the effective attractive force between solutes and the range of that attraction vary inversely with each other: the strength of the attraction, as expected, increases with increasing magnitude of the (entropically unfavorable) free energy of “hydrogen-bond’' formation, but at the same time the range decreases. Conversely, when the unfavourable entropy and favourable energy of “hydrogen-bond’' formation are nearly in balance, the attraction between hydrophobes, while then weak, is of very long range. It is remarked that solubility in a one-dimensional solution model, when the direct intermolecular interactions are of short range, can only be defined osmotically. The solubility of the hydrophobe, as so defined, is calculated with the present model. It is found to decrease with increasing temperature, as expected for a hydrophobic solute.