Article

# A new Monte Carlo method to study the fluid-solid phase transition of polydisperse hard spheres

08/2008;

Source: arXiv

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**ABSTRACT:**We have established the solid-fluid coexistence region for a system of polydisperse hard spheres with near Gaussian diameter distributions, as a function of polydispersity. Our approach employs Monte Carlo simulation in the isobaric semigrand ensemble with a Gaussian activity distribution. Gibbs-Duhem integration is used to trace the coexistence pressure as a function of the variance of the imposed activity distribution. Significantly, we observe a ``terminal'' polydispersity above which there can be no fluid-solid coexistence. The terminus arises quite naturally as the Gibbs-Duhem integration path leads the pressure to infinity. This pressure divergence is an artifact of the method used to evaluate the freezing transition, because the sphere diameters vanish in this limit. A simple rescaling of the pressure with the average diameter brings the terminal pressure to a finite value. Nevertheless, the existence of this terminus only at infinite pressure precludes the construction of a continuous path from the solid to the fluid. At the terminus the polydispersity is 5.7% for the solid and 11.8% for the fluid while the volume fractions are 0.588 and 0.547 for the solid and fluid, respectively. Substantial fractionation observed at high values of the polydispersity (>~5%) implies that the ``constrained eutectic'' assumption made in previous theoretical studies is not generally valid. Our results for the terminal polydispersity are consistent with experiments performed on polydisperse colloidal suspensions.Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 08/1996; 54(1):634-643. - [Show abstract] [Hide abstract]

**ABSTRACT:**We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus be defined only for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find, in addition, that coexistence of several solids with a fluid phase is also possible.Physical Review Letters 09/2003; 91(6):068301. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.Physical Review Letters 03/2007; 98(8):085702. · 7.73 Impact Factor

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