Grand canonical ensemble simulation studies of polydisperse fluids

Abstract

We describe a Monte Carlo scheme for simulating polydisperse fluids within the grand canonical ensemble. Given some polydisperse attribute $σ$, the state of the system is described by a density distribution $ρ(σ)$ whose form is controlled by the imposed chemical potential distribution $μ(σ)$. We detail how histogram extrapolation techniques can be employed to tune $μ(σ)$ such as to traverse some particular desired path in the space of $ρ(σ)$. The method is applied in simulations of size-disperse hard spheres with densities distributed according to Schulz and log-normal forms. In each case, the equation of state is obtained along the dilution line, i.e. the path along which the scale of $ρ(σ)$ changes but not its shape. The results are compared with the moment-based expressions of Boublik et al (J. Chem. Phys. {\bf 54}, 1523 (1971)) and Salacuse and Stell (J. Chem. Phys. {\bf 77}, 3714 (1982)). It is found that for high degrees of polydispersity, both expressions fail to give a quantitatively accurate description of the equation of state when the overall volume fraction is large.