Dynamic study of the aggregation of nanoparticles immersed in a ternary mixture of polymers

The physical system we consider is a ternary polymers solution made by two chemically incompatible polymers and a good solvent. The mixture is assumed to be in the presence of identical nanoparticles. At temperatures close to the critical point of the free mixture, the fluctuations of the composition induce a critical Casimir force between colloids. This force is responsible for the colloidal aggregation. In this paper, we propose to study the dynamics of such transition leading colloids from dispersed phase to dense phase, like the gas-liquid transition for fluids. Using field theory, we compute the relaxation rate of this transition. In the order to understand the solvent role effect on the relaxation rate, we compare the obtained results of the binary polymer mixture and those of the ternary polymer solution.