Effective interaction between hard sphere colloidal particles in a polymerizing Yukawa solvent

Abstract

The effective interaction between colloidal hard sphere particles in a Yukawa solvent that can polymerize with the formation of chains and rings is studied and compared with the corresponding results for colloidal hard sphere particles in a solvent of polymerizing hard spheres. The attractive nature of the polymerizing Yukawa solvent particles induces significant changes in the effective interactions between the colloid particles as compared to a polymerizing solvent of hard spheres that was investigated in previous studies. The results for the colloid–solvent mixture are obtained using the associative Percus–Yevick approximation for Wertheim’s Ornstein–Zernike integral equation; the colloidal species are taken at a nonvanishing but very small concentration throughout this article. We present the effects of the size ratio of colloid spheres to solvent spheres, the degree of polymerization, and the solvent density on the effective interactions between colloid and solvent particles. The intercolloidal potential of mean force (PMF) is found to be highly dependent on these parameters for Wertheim’s model. It is found that the correlations between colloid particles obtained using the Yukawa solvent model are longer ranged and more attractive than those found using the hard sphere solvent model. A greater depletion of the solvent density around the colloidal particles is also observed for the Yukawa solvent model as compared to the hard sphere model; an increased polymer chain length also enhances the depletion of the solvent density. The PMF is found to be oscillatory in structure. The oscillatory structure also depends upon the average polymer chain length, specifically, the oscillatory structure in the PMF is strongly diminished as the average polymer chain length increases. Additionally, as the average polymer length increases, the attraction at the colloid–colloid contact distance decreases.