The effective interaction between colloidal hard sphere particles in a polymerizing solvent. Application of Wertheim's theory of association

Abstract

The effective interaction between colloidal particles in a solvent of hard spheres, which can polymerize with the formation of chains and rings, is studied. Polymerization results in changes of the effective interaction between the colloid particles, compared with the effective interaction for unpolymerized solvents that has been extensively studied in previous publications. To describe the mixture, we use the associative Percus-Yevick approximation for Wertheim's Ornstein-Zernike integral equation. Both the infinite dilution and the nonvanishing concentration limits for the colloid species are considered. It is shown that, in the model of Wertheim for polymerization, the intercolloidal potential of mean force (PMF) depends primarily on the solvent density and to a lesser extent on the degree of polymerization. A depletion of the solvent density around the colloid particles is observed. If the solvent consists of longer chains, compared with hard spheres, the correlations between the colloid particles are of longer range. The oscillations of the PMF depend upon the average chain length but not so strongly as in the model with chains having a fixed number of beads; this is probably due to the flexibility of the chain conformations in Wertheim's model. We also study the effect of the size ratio of the colloid spheres and the solvent monomers. We observe that the polymer hypernetted chain closure is difficult to apply to the systems under study. This closure shares difficulties, especially near the critical point, that are well known in the study of the phase diagram of fluids with both repulsive and attractive interactions. For large colloidal particles, the mixed closure of Henderson is useful.