Hydrodynamic flows and interactions in unentangled polymer nanocomposites

Polymer nanocomposites are materials comprised of nanoscale particles in a polymer matrix. They have numerous technological applications, for example being used as mechanically reinforced rubber. Their improved properties are in part due to the nanoscale size of the particles, which makes them smaller than the surrounding polymer chains. Recent models predicting transport and rheology in polymer nanocomposites focus on the particle-to-polymer coupling on length scales on the order of the particle size. This coupling impacts particle self-diffusion and their leading order contribution to mechanical properties such as viscosity. The coupling of the particle to the polymer on larger length scales has received much less attention in the literature, even though such coupling could result in solvent-mediated hydrodynamic interactions well established to impact transport and rheology in composites with micron-scale (colloidal) particles. In this work, we utilize scaling theory and simulations to study the flow propagated by particles in unentangled polymer nanocomposites. By measuring pair correlations, we determine the hydrodynamic flow propagated by a nanoparticle in an unentangled polymer melt. Interestingly, we find the flow propagates with a slow 1/r decay, characteristic of long-range hydrodynamic interactions, even for particles with a size smaller than the polymer. Utilizing a modified Oseen tensor, we develop a scaling model that describes the induced flow.