Application of excluded volume map sampling to phase equilibrium calculations in the Gibbs ensemble

An improved method for studying liquid-liquid phase equilibria in the Gibbs ensemble is described. The improvement is based on the excluded volume map sampling (EVMS) technique, recently introduced by Deitrick et al, which has been shown to increase the liquid density range over which the Widom particle insertion method can be applied for the calculation of the chemical potential. Application of EVMS in the Gibbs ensemble greatly improves the efficiency of the particle interchange moves in a Gibbs simulation. We first demonstrate the improved method with Gibbs simulations of liquid-liquid phase equilibria in a two-component Leonard-Jones fluid. The map method results in a significant reduction in the computing time required for these simulations when the number of attempted interchanges is large. A detailed simulation study of fluid-fluid phase equilibria in a model nitrogen-helium mixture was performed using the EVMS Gibbs technique. Typically, a Gibbs simulation of liquid-liquid equilibrium in this fluid, using the map method, requires only 40% of the time used by a conventional Gibbs ensemble simulation. The results demonstrate that it is possible to determine the form of complex phase diagrams using computer simulation. In this work we calculate the pressure-composition sections of the phase diagram close to the temperature minimum of gas-gas immiscibility. The potential model we used was a Lennard-Jones plus quadrupole interaction, with parameters the same as in a recent theoretical study of this fluid mixture. Comparison of our simulation results with the theoretical work shows that the perturbation theory consistently overestimates the mole fraction of nitrogen in the coexisting phases. At the temperatures and pressures studied the simple potential model predicts thermodynamic properties in surprisingly good agreement with experimental data, even though the potential parameters were not adjusted in any way.