The chemical potential of a Lennard Jones fluid

TL;DR

This paper presents an analytical method to calculate the chemical potential of a Lennard Jones fluid, dividing the integration into two regions to avoid divergences, aiding studies of phase equilibrium in various physical systems.

Contribution

It introduces an analytical approach to compute the chemical potential of a Lennard Jones fluid, addressing divergence issues in the integration process.

Findings

Analytical expression for chemical potential derived.

Method applicable to phase equilibrium studies.

Potential relevance to planetary and astrophysical systems.

Abstract

The aim of this paper is to present an analytical calculation of the chemical potential of a Lennard Jones fluid. The integration range is divided into two regions. In the small distance region,which is $r\leq\sigma$ in the usual notation,the integration range had to be cut off in order to avoid the occurence of divergences.In the large distance region,the calculation is technically simpler. The calculation reported here will be useful in all kinds of studies concerning phase equilibrium in a $LJ$ fluid. Interesting kinds of such systems are the giant planets and the icy satellites in various planetary systems,but also the (so far) hypothetical quark stars.