(317i) Hydrodynamic Flows in Unentangled Polymer Nanocomposites

Polymer nanocomposites are materials comprised of nanoscale particles immersed in a polymer matrix. They have a wide range of technological applications as functional materials, mechanically reinforced rubber, among others. Their improved properties are in part due to the nanoscale size of the particles, which makes them smaller than the surrounding polymer chains. Modelling particle dynamics in these materials is challenging in part because, in contrast to micron scale (colloidal) fillers, the polymer matrix cannot be assumed to be a continuum liquid a priori. 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. However, such couplings could result in polymer matrix mediated hydrodynamic interactions, which are well established to impact transport and rheology in composites with micron scale particles. In this work, we utilize scaling theory and simulations to study the flow propagated by particles in unentangled polymer nanocomposite. 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. Furthermore, we develop a scaling model that describes the spatial and time dependence of the flow induced by the nanoparticles via a modified Oseen tensor.