Grand canonical ensemble simulation studies of polydisperse fluids

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. 54, 1523 (1971)) and Salacuse and Stell (J. Chem. Phys. 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. Typeset using REVTEX