Connectedness-in-probability and continuum percolation of adhesive hard spheres: Integral equation theory

Abstract

Integral equation theory was employed to study continuum percolation and clustering of adhesive hard spheres based on a ''connectedness-in-probability'' criterion. This differs from earlier studies in that an ''all-or-nothing'' direct connectivity criterion was used. The connectivity probability may be regarded as a ''hopping probability'' that describes excitation that passes from one particle to another in complex fluids and dispersions. The connectivity Ornstein-Zernike integral equation was solved for analytically in the Percus-Yevick approximation. Percolation transitions and mean size of particle clusters were obtained as a function of connectivity probability, stickiness parameter, and particle density. It was shown that the pair-connectedness function follows a delay-differential equation which yields analytical expressions in the Percus-Yevick theory.

Specific Ion-Dependent Attraction and Phase Behavior of Polymer-Coated Colloids

“…The “adhesive sphere” (AS) potential due to Baxter is convenient for modeling equilibrium phase behavior of colloids with short-range attractive interactions. A number of analytical expressions − and Monte Carlo (MC) simulation results − are readily available in the literature for comparison with experimental results. The AS potential can be written in a similar form to eq 1 with a repulsive hard-wall term, an attractive surface adhesion term, and a noninteraction term for separations beyond the range of the surface adhesion as 19 where τ characterizes the magnitude of the contact adhesion and all remaining variables are defined in Figure .…”

Solvent Quality Dependent Continuum van der Waals Attraction and Phase Behavior for Colloids Bearing Nonuniform Adsorbed Polymer Layers

“…Adhesive Sphere Potential and Phase Behavior. The “model” adhesive sphere (AS) potential due to Baxter 30 provides convenient analytical expressions − and Monte Carlo simulation results − for predicting solvent quality dependent phase behavior of polymer coated colloids with the “real” potential in eq 1. The AS potential can be written in a form analogous to eq 1 with a repulsive hard wall term, an attractive surface adhesion term, and a term indicating no interaction for separations beyond the range of the surface adhesion as 30 where τ characterizes the contact adhesion due to an infinitely deep square well with zero width.…”

Precise determination of the critical percolation threshold for the three-dimensional “Swiss cheese” model using a growth algorithm

“…Different types of continuum percolation have been the topic of recent literature including the distribution of rods, [1][2][3][4] the distribution of squares, 5 and the distribution of disks or spheres. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] In this paper, we study the continuum model that consists of a system of spatially uncorrelated, equal-sized spheres, whose centers are distributed by a Poisson process within the three-dimensional LϫLϫL system. If the spheres are thought to be removed from the system, it can be seen why this has been given the nickname, the ''Swiss cheese'' model.…”