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

The Lennard-Jones (LJ) potential function is widely employed in molecular dynamics simulations. In this study, the LJ potentials under different characteristic diameter sigma and characteristic energy epsilon 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 sigma, the melting and boiling temperatures of the LJ systems and the thermodynamic temperature range corresponding to liquid decrease, while with the increase of epsilon, 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 sigma, but significantly increases with epsilon. The number densities at the melting and boiling temperatures are only dependent on sigma, and are not nearly influenced by epsilon. 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