Density Functional Theory of Inhomogeneous Liquids: II. A Fundamental Measure Approach

TL;DR

This paper develops a density functional theory for inhomogeneous Lennard-Jones fluids by combining a fundamental measure approach with a model of the direct correlation function, accurately predicting interfacial properties and satisfying key exact conditions.

Contribution

It introduces a novel density functional theory integrating fundamental measure ideas with a correlation function model for Lennard-Jones fluids, improving predictions of inhomogeneous fluid behavior.

Findings

Accurately describes liquid-vapor interfaces

Predicts surface tension dependence on potential cutoff

Satisfies key exact conditions in density functional theory

Abstract

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid(Lutsko, JCP 127, 054701 (2007)). Here, this model is combined with ideas from Fundamental Measure Theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid-vapor interface, the fluid in contact with a hard wall and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: that relating the direct correlation function to the functional derivative of the free energy with respect to density, and the wall theorem.