Phase equilibria and fractionation in a polydisperse fluid

We describe how Monte Carlo simulation within the grand canonical ensemble 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 $\rho^\circ(\sigma)$ of the polydisperse attribute $\sigma$ is prescribed. Recently proposed computational methods facilitate determination of the chemical potential distribution conjugate to $\rho^\circ(\sigma)$. 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 ($\delta=40$) degree of polydispersity. Cloud and shadow curves are obtained, the latter of which exhibit a high degree of fractionation with respect to the parent. Additionally, we observe considerable broadening of the coexistence region relative to the monodisperse limit.