Fundamental measure theory for lattice fluids with hard core interactions

TL;DR

This paper extends Rosenfeld's fundamental measure theory to lattice models of hard hypercubes, providing an exact functional for one-dimensional cases and a generalized approach for higher dimensions, including nonadditive mixtures.

Contribution

It introduces the first functional for nonadditive mixtures of lattice hypercubes, generalizing the zero-dimensional cavities method for higher-dimensional lattice fluids.

Findings

Exact functional for 1D additive mixtures

Extension to nonadditive mixtures on lattices

Functional maintains correct dimensional crossovers

Abstract

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the one-dimensional exact functional form, we propose the extension to higher dimensions by generalizing the zero-dimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zero-dimensional limit. Some applications of the functional to particular systems are also shown.