chapter 4
In this chapter, we examine 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 semi-grand 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
re-scaling 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. The results for the terminal polydispersity are consistent
with experiments performed on polydisperse colloidal suspensions.