Analytical Form of Forces in Hydrophobic Collapse

TL;DR

This paper derives an analytical expression for the forces between solvophobic solutes, revealing short-range attraction and long-range repulsion mediated by solvent effects, with implications for hydrophobic collapse.

Contribution

It provides a novel analytical formulation of solvent-mediated forces between solvophobic particles, including detailed force behavior and physical origin explanations.

Findings

Attractive forces at short range decrease linearly with surface separation

Long-range forces decay as 1 / s 4 and are repulsive

For Lennard-Jones solvent, forces follow the derived analytical form

Abstract

We calculate analytically the forces between two solvophobic solutes, considering a model system. We show that the effective interaction forces between two solvophobic solutes, mediated by the solvent, is attractive for short ranges, which decreases linearly with surface-to-surface separation s between the solutes and repulsive in the long range falling off as 1 / s 4 . The attraction originates from the unbalanced Laplace force at the liquid-gas interface, generated by the repulsive interaction with the solvent particles, around the solutes at small s. The long range part arises due to unbalanced osmotic pressure. We illustrate the calculations for the Lennard-Jones solvent. We discuss the general implication of our results in the context of hydrophobic collapse.