Clustering of binary colloidal suspensions: Theory

Recent experiments on binary colloidal suspensions have shown that particles of the first kind (e.g., alumina) can be induced to flocculate by the presence of particles of the second kind (e.g., polyacrylate), within a certain range of the density of the second species of particles. This is similar to the depletion flocculation and depletion stabilization of polymer-colloidal systems. We have thoroughly examined the binary-particle systems with numerical simulations (Monte Carlo) as well as with analytical equilibrium calculations [cluster variation method (CVM)]. The simulations show a peak in the flocculation rate as the number density of the second species particles is varied, in agreement with the experiments. The CVM calculations show a monotonic increase in cluster size as the particle 2 density is increased. Moreover, the simulations show an aging phenomenon at high particle 2 densities, i.e., the growth of the cluster size in the initially restabilized region, which has also been well observed in the experiment. We further show from free energy calculations that the flocculated state, including the seemingly restabilized state at high particle 2 densities, is metastable and the underlying thermodynamically stable state is phase separation. Therefore, the restabilization at high particle 2 densities is due to kinetics, namely the slowdown in particle movements, but not to thermodynamic reasons. Our calculations together with the experiments on binary colloids may shed some light on the understanding of polymer-colloidal systems.