Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

TL;DR

This paper introduces a new density functional for hard-sphere mixtures based on an extension of the Carnahan-Starling equation, improving accuracy in inhomogeneous density predictions and consistency with scaled-particle theory.

Contribution

A novel density functional for hard-sphere mixtures that enhances accuracy and theoretical consistency over previous models, including the original White-Bear version.

Findings

Improved accuracy in inhomogeneous density distribution predictions.

Enhanced consistency with scaled-particle theory for pure fluids.

Higher consistency than both the original White-Bear and Rosenfeld's FMT.

Abstract

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.