Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles

TL;DR

This paper analytically investigates the effects of polydispersity on the stability, percolation, and phase coexistence of sticky hard sphere fluids using simplified closures, revealing that polydispersity generally stabilizes the fluid and reduces phase coexistence.

Contribution

It provides a full analytical study of the polydisperse Baxter model using the mMSA closure, including stability, percolation, and coexistence, with comparisons to Monte Carlo simulations.

Findings

Polydispersity inhibits instabilities and percolation.

Polydispersity increases the non-percolating phase.

Polydispersity diminishes the gas-liquid coexistence region.

Abstract

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified Mean Spherical Approximation (mMSA). This closure is known to be the zero-order approximation (C0) of the Percus-Yevick (PY) closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible sub-cases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the non percolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.