The condition of microscopic reversibility in Gibbs ensemble Monte Carlo simulations of phase equilibria

Abstract

The condition of microscopic reversibility, also referred to as detailed balance, is examined in the context of Monte Carlo simulations in the Gibbs ensemble. The technique is used widely in the simulation of phase equilibria for liquids and their mixtures, and represents an invaluable tool in the area. The two coexisting phases are simulated as separate subsystems by performing three distinct Monte Carlo moves which include random displacements of particles in each subsystem, random changes in volume, and random transfers of particles between the two subsystems. Here, the particle transfer step of the Gibbs ensemble technique, as commonly implemented, is shown to be reversible. Other valid reversible criteria are presented for pure fluids and mixtures. The vapour-liquid equilibria of the pure square-well fluid with a range of 2 = 1'5 are examined with the various criteria. As expected, the choice of criteria makes little difference for pure fluids. The results are also presented of liquid-liquid immiscibility for a symmetrical square-well mixture with range 2 = 15 in which the unlike interactions are purely repulsive. For this mixture the various reversible algorithms for particle transfers give essentially equivalent results, although the efficiency in sampling phase space is sometimes quite different.