Density functional for ternary non-additive hard sphere mixtures

TL;DR

This paper develops a density functional theory for three-component non-additive hard sphere mixtures, extending previous binary models, and validates it with simulation data.

Contribution

It introduces a Helmholtz free energy density functional for ternary non-additive mixtures, generalizing binary theories with complex diagrammatic structures.

Findings

Partial pair correlation functions match Monte Carlo simulations.

The functional accurately captures the structure of ternary mixtures.

Diagrammatic complexity increases with mixture components.

Abstract

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data.