Aggregation of colloidal particles induced by polymer chains: The RISM integral equation theory

Using the reference interaction site model (RISM) integral equation technique we study aggregation of small colloidal particles in the environment of polymer chains. In particular, we are interested in the following two questions: (i) what is the effect of density of the polymer matrix, ϱp, and the chain length, Np, on the process of aggregation and (ii) how does the average cluster size depend on the polymer-particle interaction? The central object in our studies is the connectedness pair correlation function, hαβ+(r,r′), which gives the probability density that colloidal particle α has a position r and particle β in the same cluster has a position r′. The mean cluster (aggregate) size s is given by s = 1 + ϱclimq→0ĥαβ+(q), where ĥαβ+(q) denotes the spatial Fourier transform of hαβ+(r,r′) and ϱc is the number density of particles. It is shown that at higher density of the polymer medium aggregation of the colloidal particles is more intensive. With the chain length Np increasing, the effect of the polymer environment on the aggregation of the particles is diminished; however, at sufficiently large polymer densities and Np ∼ 103 convergence to the asymptotic limit is observed. In the case when polymer segments are adsorbed on the particles, the temperature dependence of the average aggregate size exhibits a nontrivial behavior: with temperature decreasing, the value of s first decreases and then begins to grow. The effect of varying colloid particle size and colloid density on the mean cluster size is also studied.