Multi-scale model for binary mixtures containing nanoscopic particles

We develop a computer simulation for the dynamic behavior of a phase-separating binary mixture that contains mobile, solid particles. The system models "filled polymers", which contain not only a blend of different macromolecules, but also solid fillers. We focus on the case where one of the components preferentially wets the surface of the particles. By combining a mesoscopic, coarse-grained description of the fluids with a discrete model for the particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. To probe the late-stage properties of the system, we also develop a mean-field rate-equation model for the mixture. The results indicate that the phase separation is arrested in the late stage; the "steady-state" domain size depends strongly on both the particle diffusion constant and the particle concentration. To obtain insight into the effects of processing on the properties of such composites, we also investigated the behavior of the binary fluid/particle mixture under shear. For sufficiently large particle densities, we find that the anisotropic growth caused by the imposed shear is destroyed by the randomly moving particles, and the domains are isotropic in shape even for large shear strains. Finally, we apply our models to mixtures of diblock copolymers and fillers. Overall, our findings reveal how the solid additives can be used to tailor the morphology of the complex mixture, and thereby control the macroscopic properties (such as mechanical integrity) of the composite.