Kinetic distribution and dispersion of nanoparticles in polymer nanocomposites.

Dispersion and distribution of nanoparticles in polymer mixing processes are stumbling blocks to the production of nanocomposites. Dispersion, in polymer processing, refers to the structural breakup of agglomerates of nanoparticles while distribution involves spatial randomization. These two features of mixing respond to different viscous flow regimes: laminar flow and turbulent flow. Distributive mixing is difficult in laminar flow, while dispersive structural change can result from either laminar or turbulent flow. In kinetic mixing, agglomerates of immiscible nanoparticles or aggregates on the nanoscale are dispersively broken apart in proportion to the accumulated strain. Parallel to this structural change, turbulent flow, related to the Reynolds number, convectively redistributes the nanoparticles or aggregates. This redistribution optimally leads to the formation of macroscopic filler networks completing a structural hierarchy necessary for ionic and electrical conductivity, tear strength, and modulus enhancement. Both distribution and dispersion depend on the velocity of flow, but they have inverse dependencies on the flow gap size in the simplest geometry. We have adapted the random phase approximation and the van der Waals model to understand kinetic dispersion and distribution in polymer nanocomposites.