Related Experiment Video
Updated: Jun 3, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
Published on: September 17, 2021
Accurate freezing and melting equations for the Lennard-Jones system
Sergey A Khrapak1, Gregor E Morfill
1Max-Planck-Institut für extraterrestrische Physik, D-85741 Garching, Germany. skhrapak@mpe.mpg.de
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 (LJ) system. The emerging equations can be written as T=Aρ(4)+Bρ(2) in normalized units. We suggest to determine the values of the coefficients A at freezing and melting from the high-temperature limit, governed by the inverse 12th power repulsive potential. The coefficients 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.
Related Concept Videos
Phase Transitions: Melting and Freezing
Variables and Equations of State
Equation of State
The Clausius–Clapeyron Equation
Maxwell's Thermodynamic Relations
All thermodynamic potentials are exact differentials. Therefore, their second-order...
The Van der Waals Equation

