On the analysis of the effective adhesion in colloidal dispersions in the sticky hard sphere model

Abstract

Structural trends in multicomponent mixtures of adhesive spheres are analyzed by using the Baxter formalism and the Percus–Yevick approximation (PYA). The Orsnstein–Zernike (OZ) equations in q space are cast in a form which allows a fully analytical expression of the effective adhesiveness coefficient of the large (solute) spheres in the asymptotic limit of vanishing size ratio and no solute self-stickiness. This allows a simple discussion of the factors which determine the effective solute adhesiveness and suspension stability: while the steric effect and like particles stickiness are found to favor suspension instability, hetero stickiness is found to act in one side or in the opposite depending on the concentration of the smaller species. These qualitative predictions are paralleled with studies on solvent effects in ordinary colloidal solute–solvent systems and with the behavior of pseudobinary systems such as colloid–polymer or bidisperse colloidal mixtures. Results from the literature for hard sphere mixtures and calculations in the PYA including solute self-stickiness at nonzero size ratio are finally used to discuss the reliability of the trends deduced from the asymptotic limit.

How “sticky” are short-range square-well fluids?

“…5 Given its simplicity and the fact that it can be exactly solved within the Percus-Yevick (PY) approximation, 4,6 the SHS model has received considerable attention as a convenient model of colloidal suspensions. 7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 It is obvious that the thermodynamic and structural properties of the SW fluid must approach those of the SHS fluid as λ → 1 at fixed η and τ . This has been tested, for instance, in the case of the vapour-liquid critical point.…”

Simple statistical thermodynamic model of the heteroaggregation and gelation of dispersions and emulsions

“…Clustering occurs only through unlike interactions of type A-B. Based on the solution of the Percus-Yevick integral equation for a binary mixture of equal-sized spheres with sticky unlike interactions and non-sticky like interactions, the average cluster size of the connected particles is given by [28][29][30]:…”

“…This purely analytical approach is derived from a qualitatively reasonable statistical description of the liquid state, i.e., the Percus-Yevick solution of the Baxter sticky sphere model [27]. The theory has been extended to mixtures of spheres of different sizes with variable degrees of stickiness [28,29]. An appealing feature of this model for colloids is that it embraces an unambiguous criterion for the aggregation state of the particles, including the fully interconnected gel-like state where the average cluster size diverges to macroscopic dimensions (the so-called percolation threshold) [30,31].…”

Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions

“…In general, the indirect, solvent-mediated, solute-solute interactions depend on both the solute-solvent and solvent-solvent ones, and thus may be very difficult to evaluate [6,7,20,28,29]. We will now report several very simplified cases.…”

“…Several other studies of depletion forces, which go beyond the entropic HS approach by taking into account more refined representions of the solute-solvent and solvent-solvent interactions, are also available in the recent literature [6,7,20,28,29].…”