Phase equilibrium of colloidal suspensions with particle size dispersity: A Monte Carlo study

Abstract

We have studied the crystalline-amorphous coexistence for systems of polydisperse soft spheres that interact via a purely repulsive power law potential. Potential softness quantified by the exponent of the potential was a primary input in our simulations. Simulations were performed in the isobaric semigrand statistical ensemble, i.e., the composition of the parent distribution was not fixed in our systems. Gibbs-Duhem integration was used to trace the coexistence pressure as a function of potential softness for monodisperse systems. A second Gibbs-Duhem integration, initiated from the monodisperse coexistence curve, was employed to determine coexistence pressure versus imposed variance of the activity distribution. Amorphous-crystalline coexistence densities and volume fractions were determined to be monotonically increasing functions of the breadth of particle size dispersity. Semigrand ensemble simulations testified to the existence of a terminal diameter dispersity, i.e., a dispersity above which no amorphous-crystalline phase coexistence was observed. At the terminus size dispersity increases from 5.8% to 6.1% to 6.4% and to 6.7% and 6.5% for the crystalline phase as the steepness parameter n, takes on smaller values: from 100 to 50 to 12 to 10 and 8, respectively. In sharp contrast to the crystalline phases' enhanced, by potential softness, allowable size dispersity the amorphous phase exhibits an opposite trend, as potential interactions soften. Furthermore, amorphous phases accommodate, on average, smaller particles than those of the ordered (fcc) phase. Contrary to widely accepted intuition crystalline phases composed of size-disperse particulates exhibit a higher degree of local order than their monodisperse counterparts, admittedly at differing thermodynamic conditions.