Accurate freezing and melting equations for the Lennard-Jones system

TL;DR

This paper derives accurate analytical equations for the freezing and melting points of the Lennard-Jones system, based on approximate methods and known thermodynamic limits, matching simulation data well.

Contribution

It introduces a unified functional form for the freezing and melting equations of the Lennard-Jones system, determined by high-temperature and triple point data.

Findings

Equations accurately predict phase coexistence points.

Good agreement with numerical simulation data.

Functional dependence of temperature on density established.

Abstract

Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional Lennard-Jones system. The emerging equations can be written as $T={\mathcal A}\rho^4+{\mathcal B}\rho^2$ in normalized units. We suggest to determine the values of the coefficients ${\mathcal A}$ at freezing and melting from the high-temperature limit, governed by the inverse twelfth power repulsive potential. The coefficients ${\mathcal B}$ can be determined from the triple point parameters of the LJ fluid. This produces freezing and melting equations which are exact in the high-temperature limit and at the triple point, and show remarkably good agreement with numerical simulation data in the intermediate region.