Nearly monodisperse fluids. I. Monte Carlo simulations of Lennard-Jones particles in a semigrand ensemble

A hybrid, semigrand ensemble is applied to the simulation of mixtures of very many components. The independent variables are temperature, density, and the distribution of activity ratios. The system samples different compositions, with particles changing species identities during the simulation. Thus, the method is particularly well suited for applications to polydisperse mixtures. Results are presented for the simulation of mixtures of Lennard-Jones particles continuously varying in size and energy parameters. Four system sizes are used: 108, 216, 343, and 512 particles. The effect of degree of polydispersity is investigated by varying the width of the imposed distribution of activity ratios, which is Gaussian. It is found that very large systems are needed to describe wide distributions, due to the presence of ever-larger particles. A limit on sizes eventually arises from the competition of energetic and entropic effects. Methods for determining phase equilibrium for these mixtures are also discussed.