On the coexistence of phases in a Lennard Jones liquid:first results

The aim of this paper is to investigate the conditions for the coexistence of phases in a Lennard Jones fluid. The calculation has been performed within the virial developement mathod and, as a result, a simple approximate relation has been obtained between the number densities of two coexisting densities and the interparticle potentials in them. The calculation is preliminary,in the sense that it does not take into account the equality of the chemical potentials. The results of this work may have implications for modelling of the giant planets. More than 300 exoplanets have been discovered, so this has become more important than ever.

💡 Research Summary

The paper tackles a classic problem in statistical mechanics – determining the conditions under which two distinct phases can coexist in a fluid whose particles interact via the Lennard‑Jones (LJ) potential. Rather than following the conventional route of enforcing equality of temperature, pressure, and chemical potential (μ) across phases, the authors deliberately limit their analysis to temperature and pressure equality, using the virial expansion as their primary theoretical tool. This “preliminary” approach yields a simple, approximate relationship linking the number densities of the coexisting phases (ρ₁ and ρ₂) directly to the LJ parameters ε (depth of the potential well) and σ (characteristic distance).

The methodology begins with the standard LJ pair potential:
U(r) = 4ε