Application of the Gibbs ensemble to the study of fluid-fluid phase equilibrium in a binary mixture of symmetric non-additive hard spheres

Abstract

The ‘Gibbs’ Monte Carlo method introduced by Panagiotopoulos to study coexisting phases, is applied to the study of fluid-fluid phase equilibrium in a binary system of symmetric, non-additive hard spheres, previously studied by Melnyk and Sawford [1]. We find that the method is generally applicable, although requiring a significantly larger number of insertions per Monte Carlo step at higher densities than in the previously studied cases of gas-liquid binary mixtures. The coexistence curve calculated using this technique agrees qualitatively although not quantitatively with that obtained in [1]. In particular, in contrast to their results, the coexistence curve at high density is found to be significantly closer to the estimates from second order perturbation theory than those obtained from first order perturbation theory. The critical density η_cr is estimated to be η_cr = 0·2175^+0·0025 _-0·0075. However, near the critical density, relatively large long-time fluctuations render the calculation of the coexistence curve difficult. We also study the effects of different initial conditions in our simulations and the effects of varying system size (number of particles) on our results.