Gibbs-ensemble Monte Carlo simulations mixtures

Gibbs-Ensemble Monte Carlo Simulations of Phase Equilibria in Supercritical Fluid Mixtures... 

Gibbs ensemble Monte Carlo simulation is predominantly used to simulate phase equilibrium for fluids and mixtures. Two fluid phases are simulated simultaneously allowing for particle moves between each phasel . 

Configurational-bias Monte Carlo in the Gibbs ensemble has been successfully applied to the calculations of single-component vapor-liquid phase equilibria of linear and branched alkanes [61,63-67], alcohols [68,69], and a fatty-acid Langmuir monolayer [70]. The extension to multicomponent mixtures introduces a case in which the smaller molecules (members of a homologous series) have a considerably higher acceptance rate in the swap move than do larger molecules. In recent simulations for alkane mixtures... 

Bolhuis and Frenkel have studied the phase behavior of a mixture of hard spheres and hard rods. In particular, Bolhuis and Frenkel used Gibbs-ensemble simulations to determine the vapor-liquid coexistence curve. In a Gibbs-ensemble simulation one simulates two boxes that are kept in equilibrium with each other via Monte Carlo rules. In this case the gas box has as a low density of hard spheres and the liquid box has a high density of spheres. Similarly to the phase equilibrium calculation of linear alkanes, the exchange step, in which particles are exchanged between the two boxes, is the bottleneck of the simulation. For example, the insertion of a sphere into the gas phase would almost always fail because of overlaps with some of the rods. Bolhuis and Frenkel have used the following scheme to make this exchange possible ... 

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