Enhanced Nanorod Diffusion in Polymer Melts

Using Rutherford backscattering spectroscopy (RBS), the translational diffusion of titanium oxide (TiO$_{2})$ nanorods ($l=$43.1 nm and $d=$4.6 nm) is measured in entangled and unentangled polymer melts, polystyrene (PS; $M_{n}=$9-2000 kg/mol). Nanorods in entangled systems ($M_{n}=$160, 650, and 2000 kg/mol) are found to diffuse up to two orders of magnitude faster than predicted by classical theory. However, diffusion of nanorods in unentangled systems ($M_{n}=$9 and 65 kg/mol) is captured by this continuum theory. Below or near the entanglement limitation, $M_{n} \quad \le \quad M_{e}$ ($M_{e}$: entanglement molecular weight), unentangled polymer melts described by Rouse dynamics can be modeled as a continuum matrix against nanoscale inclusions. However, in highly entangled systems ($M_{n}$ \textgreater \textgreater $M_{e})$ the standard continuum models are no longer valid and lead to local non-hydrodynamic friction at the length scale of the tube diameter (i.e., $d_{t}=$8 nm for PS) [1]. Thus, enhanced diffusion of nanorods parallel to the tubes may be responsible for the faster than expected translational diffusion in entangled polymer melts. These experiments provide new insight into the relevant parameters that govern the diffusion of anisotropic nanoparticles in complex fluids. [1] Yamamoto et. al., J. Chem. Phys., 135, 224902 (2011).