Close to the edge of Fundamental Measure Theory: density functional for hard sphere mixtures

TL;DR

This paper critically examines and extends the Fundamental Measure Theory for hard sphere mixtures, comparing various versions and proposing improvements for dimensional crossover and mixture modeling.

Contribution

It introduces an extension of the FMT to mixtures with different radii and proposes a new method to ensure exact 1D dimensional crossover.

Findings

Enhanced FMT for mixtures with different radii

Accurate modeling of wall-fluid interfaces

Successful dimensional crossover in 1D limit

Abstract

We analyze the structure of the Fundamental Measure Theory for the free energy density functional of hard sphere mixtures. A comparative study of the different versions of the theory, and other density functional approaches, is done in terms of their generic form for the three-points direct correlation function, which shows clearly the main advantages and problems of the different approximations. A recently developed version for the monocomponent case is extended to mixtures of hard spheres with different radii, and a new prescription is presented to obtain the exact dimensional crossover of those mixtures in the one-dimensional (1D) limit. Numerical results for planar wall-fluid interfaces and for the 1D fluid are presented.