Phase equilibria and fractionation in a polydisperse fluid

We describe how Monte Carlo simulation within the grand canonical ensemble 1 can be applied to the study of phase behaviour in polydisperse fluids. Attention is focused on the case of fixed polydispersity in which the form of the "parent" density distribution ρ°(σ) of the polydisperse attribute σ is prescribed. Recently proposed computational methods facilitate determination of the chemical potential distribution conjugate to ρ°(σ). By additionally incorporating extended sampling techniques within this approach, the compositions of coexisting ("daughter") phases can be obtained and fractionation effects quantified. As a case study, we investigate the liquid-vapor phase equilibria of a size-disperse Lennard-Jones fluid exhibiting a large (δ = 40%) degree of polydispersity. Cloud and shadow curves are obtained, the latter of which exhibit considerable fractionation with respect to the parent. Additionally, we observe a surprisingly large degree of broadening of the coexistence region relative to the monodisperse limit.