A new correlation model for predicting the melting and boiling temperatures of the Lennard-Jones systems

Abstract

The Lennard-Jones (LJ) potential function is widely employed in molecular dynamics simulations. In this study, the LJ potentials under different characteristic diameter σ and characteristic energy ε were simulated, and the changes in properties such as number density, total energy, phase transition latent heat, and phase transition temperature were detailed. With the increase of σ, the melting and boiling temperatures of the LJ systems and the thermodynamic temperature range corresponding to liquid decrease, while with the increase of ε, the melting and boiling temperatures and the thermodynamic temperature range of liquid increase. Moreover, the phase transition latent heat hardly changes with the increase of σ, but significantly increases with ε. The number densities at the melting and boiling temperatures are only dependent on σ, and are not nearly influenced by ε. Furthermore, based on a modified Lindemann’s melting criterion, a new empirical correlation model is proposed to predict the melting and boiling temperatures of the LJ systems, where the phase transition points are in good agreement with the experimental values. For the melting point, the absolute error between the formula and the experimental measurement for inert gas and methane is no more than 10 K, and for the boiling point, the absolute error is less than 15 K. By this new presented model, some thermophysical properties of the LJ potential systems can be quickly obtained and evaluated.

100 Years of the Lennard-Jones Potential

“…184,185 The problem of overheating can be avoided if the solid and liquid phases are treated separately to obtain the free energies G solid (T) and G liquid (T) at selected temperatures near the melting point, where the two free energy curves cross, 161 or by algorithms such as the interface-pinning method, 186 which is however computationally very demanding. Comparisons of LJ melting and boiling points with experimental values for the rare gases have been provided by Sun et al 187 and Matsumoto, 188 which show generally good agreement with experiment. Melting temperatures can also be estimated from cluster simulations 189 and extrapolation of the cluster size to the bulk limit.…”