Phase equilibria by simulation in the gibbs ensemble alternative derivation, generalization and application to mixture and membrane equilibria

The Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos [1] is generalized and applied to mixture and membrane equilibria. An alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented. The method is then generalized for the calculation of phase equilibria of mixtures by simulation in a constant-pressure Gibbs ensemble and the calculation of equilibria across semipermeable membranes with an imposed osmotic pressure difference. The method is used to calculate phase equilibria for binary mixtures of Lennard-Jones molecules. Good agreement is found with published results obtained using other simulation techniques. The computer time required for the Gibbs method is only a small fraction of the corresponding requirement for previously available simulation techniques. Calculations for simple osmotic systems are performed for the first time by simulation, with results in agreement with exact theoretical predictions.