Gauge cell method for simulation studies of phase transitions in confined systems

A method for Monte Carlo studies of phase equilibrium in confined systems is presented using an example of vapor-liquid equilibrium (capillary condensation and evaporation) in cylindrical pores. The method, named the gauge cell method, allows one to construct the full phase diagram of a confined fluid in the form of a van der Waals loop, which includes stable, metastable, and unstable equilibrium states. The phase coexistence is then determined by thermodynamic integration along the metastable and unstable regions of the phase diagram employing Maxwell's rule of equal areas. The simulation results agree with experimental data on the capillary condensation of nitrogen at its boiling temperature on mesoporous molecular sieves. The method can be applied to other phase transitions in confined systems such as fluid-fluid separation, layering, and freezing.