Whether the mean-field two-length scale theory of hydrophobic effect can be microscopically approved?

TL;DR

This paper investigates whether the mean-field two-length scale theory of the hydrophobic effect can be justified microscopically by deriving solvation free energy and solvent density equations from a microscopic particle-based approach.

Contribution

It provides a microscopic derivation of the hydrophobic effect and examines the consistency of the two-length scale mean-field theory with this microscopic foundation.

Findings

Derived an expression for solvation free energy for arbitrary-shaped solutes.

Formulated a nonlinear equation for the mean solvent density around the solute.

Identified inconsistencies between microscopic derivation and mean-field theory.

Abstract

We discuss the simple microscopic derivation of a hydrophobic effect. Our approach is based on the standard functional representation of the partition function of interacting classical particles and subsequent passage to collective variables (local densities of the solvent). We get an expression for the solvation free energy of solute molecule of any arbitrary shape and derive the nonlinear equation for the mean solvent density surrounding the solvated object. We pay a special attention to some inconsistencies between the microscopic consideration and the two-length scale mean-field theory of hydrophobic effect.