# Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

## TL;DR

This paper reviews analytical methods for calculating the structural and thermodynamic properties of hard-sphere liquids, improving upon Percus-Yevick theory and extending to related fluid systems.

## Contribution

It introduces a thermodynamically consistent analytical approach that enhances existing models and applies to various fluid systems beyond simple hard spheres.

## Key findings

- Improved analytical expressions for radial distribution functions.
- Enhanced equations of state for hard-sphere fluids.
- Extensions to sticky hard spheres and square-well fluids.

## Abstract

An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and square-well fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.