Variational perturbation calculations for the phase diagram of systems with short-ranged interactions

Abstract

A variational perturbation theory based on the Gibbs–Bogoliubov inequality is used to predict the phase behavior of systems with short-ranged interactions. We are primarily concerned with the disappearance of a stable liquid phase and the occurrence of an isostructural solid–solid transition, and consider two model systems interacting via a hard-sphere attractive Yukawa (HSAY) potential and a so-called m−n potential, a natural extension of the 12−6 Lennard-Jones potential to higher powers. In the variational calculations, a consistent treatment of the fluid and solid phases is aimed at and the hard-sphere system is used as the reference system for both phases. The predicted phase diagrams for the HSAY system with not very short-ranged potential are confirmed to be in good agreement with essentially the same calculations by Hagen and Frenkel [J. Chem. Phys. 101, 4093 (1994)]. The predicted isostructural solid–solid transition for this system, which occurs for a very short-ranged potential, are somewhat different from the Monte Carlo (MC) simulations by Bolhuis et al. [Phys. Rev. E 50, 4880 (1994)]. In particular, the predicted critical range of the potential for the occurrence of this transition is much shorter than the MC result. For the m−n potential system, a stable liquid phase is found to disappear when the attractive potential range becomes comparable to that of C60. The critical temperature for the m−n potential system, at which the isostructural solid–solid transition terminates, is consistently higher by about 50% than that for the HSAY system, which is interpreted as an effect of the softness of the repulsive core. The solid–solid transition in the high density limit, which could occur for an infinitesimally short-ranged potential, is discussed in some detail for both systems within the framework of the present method.