Interacting hard-sphere fluids in an external field

TL;DR

This paper introduces a new method for analyzing equilibrium properties of interacting hard-sphere fluids in external fields, effective in one dimension and approximative in higher dimensions, capable of handling complex environments.

Contribution

The paper presents an exact analytical approach in one dimension and a good approximation method for higher dimensions for studying interacting fluids in external fields.

Findings

Exact solutions in one dimension match known results.

Method provides good approximations in higher dimensions.

Derives equations for pair distribution functions and thermodynamic quantities.

Abstract

We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary shape and limited range. Our method of analysis is exact in one dimension and provides demonstrably good approximations in higher dimensions. It can cope with homogeneous and heterogeneous environments. We derive an equation for the pair distribution function. The solution, to be evaluated numerically, in general, or analytically for special cases, enters expressions for the entropy and free energy functionals. For some one-dimensional systems, our approach yields analytic solutions, reproducing available exact results from different approaches.