Implementation of the Gibbs ensemble using a thermodynamic model for one of the coexisting phases

Abstract

A Gibbs ensemble (GE) Monte Carlo technique to evaluate phase equilibria for systems in which a thermodynamic model describes accurately one of the coexisting phases is detailed. Such a simulation is conducted in much the same manner as a standard GE simulation: particles are moved about within one phase, and volume and particles are exchanged between the phases. However, with the proposed modification, one of the phases becomes a ‘virtual’ phase, and no account is made of particle positions within it. When formulating the acceptance criteria for particle and volume exchange, the residual free energy change of the virtual phase plays the role of the intermolecular potential energy change normally used in a GE simulation. We demonstrate the technique by computing the coexistence envelope of a van der Waals fluid. In the more interesting case of the Lennard-Jones fluid we show that when using a fifth-order virial model for the vapour, the technique accurately reproduces the phase envelope for temperatures to within 5% of the critical, while requiring substantially less computation than the standard GE simulation. Other potential benefits of the technique are discussed.