Freezing and melting line invariants of the Lennard-Jones system

TL;DR

This paper demonstrates that structural and dynamical invariants observed along the freezing and melting lines of the Lennard-Jones system can be explained by isomorph theory, revealing these invariants are valid along all isomorphs, not just at phase boundaries.

Contribution

The study shows that the invariants along the freezing and melting lines are approximated by isomorphs and are consistent across all isomorphs, unifying empirical rules under isomorph theory.

Findings

Invariants are observed along the freezing/melting lines and other isomorphs.

Structural and dynamical properties are consistent with isomorph theory.

Empirical melting and viscosity rules are explained by isomorph invariants.

Abstract

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of the isomorph theory. First the freezing/melting lines for LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phase. Structure is probed by the radial distribution function and the structure factor and dynamics is probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties by reference to the isomorph theory explains why known single-phase melting criteria holds, e.g., the Hansen-Verlet and the Lindemann criterion, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from the isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.