(178q) Optimum Phase-Dependent Lennard-Jones Energy Cross-Parameters for Phase Equilibrium

A recent study [S. Moodley, E. Johansson, K. Bolton & D. Ramjugernath, Mol. Sim. DOI:10.1080/08927022.2012.659180 (2012)] investigated the effects of varying the Lennard-Jones (LJ) energy cross-parameter in each phase on the vapor-liquid equilibrium of a simple binary monatomic system (methane/xenon). The study proved that excellent agreement between simulation and experiment can be obtained at thermodynamic states when using “heterogeneous” cross-energy parameters where the otherwise conventional approach (i.e. using the same value of the cross-energy in each phase, a “homogeneous” parameter) fails to provide good agreement.
In this work, which is an extension of the aforementioned Gibbs ensemble Monte Carlo study (which was purely numerical and used a large number of simulations to obtain the optimized parameters), a method for calculating the optimum vapor and liquid LJ cross-energy parameters is presented. Equations are derived and it is shown that the optimized phase-dependent energy parameters can be obtained from much fewer simulations (approximately five times less than the original study), and that there are multiple solutions. Also, a better understanding of the effects of the heterogeneous parameters based on considerations of the vapor, liquid and overall system potential energies is provided. The method that is presented here can be used to good effect in systems for which an optimized homogeneous cross-energy parameter would provide good agreement with experiment in one phase, but poor agreement in the other phase.