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

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 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 subcases 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 nonpercolating 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.

Connectivity percolation of polydisperse anisotropic nanofillers

“…With these model ingredients we find an analytical expression for the PT from the nanofiller fraction at which the cluster size diverges. Similar to what was found previously for the geometrically much simpler case of spherical particles, 24 the PT that we obtain is a function only of higher-order moments of the full size distribution notwithstanding the presence of angular correlations between the filler particles caused by translation-rotation coupling.…”

“…A similar result was found for spherical particles, although these obviously do not exhibit angular correlations. 24 That these are important for rods is straightforward to illustrate by means of a so-called contact-volume argument. 7 This implies that we presume that percolation requires that there is about one rod per average contact or overlap volume, which is equal to L 2 k λ eff γ kγ π/2.…”

Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

“…Indeed, the matter is complicated by the fact that there is no unique model for polydispersity in such a system. Very recently, however, a number of physically reasonable models for polydispersity in AHS system have been proposed by Fantoni et al [44], who investigated the corresponding phase behaviour using integral equation theory. From ref.…”

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

“…This possibility was used to describe the properties of polydisperse hard-sphere fluid utilizing Percus-Yewick (PY) approximation [1][2][3][4] and polydisperse Yukawa hard-sphere fluid using mean spherical approximation [5][6][7] (MSA). More recently the MSA was used to study the phase behavior of polydisperse hard-sphere mixtures with Yukawa [8], Coulombic [9][10][11], and sticky [12] interactions outside the hard core. In the case of Yukawa and sticky potentials application of the MSA is restricted to the systems with factorized version of interaction, i.e.…”