Size-Dependent Particle Dynamics in Entangled Polymer Nanocomposites

Polymer-grafted nanoparticles with diameter <i>d</i> homogeneously dispersed in entangled polymer melts with varying random coil radius <i>R</i>₀, but fixed entanglement mesh size <i>a</i>_e, are used to study particle motions in entangled polymers. We focus on materials in the transition region between the continuum regime (<i>d</i> > <i>R</i>₀), where the classical Stokes–Einstein (S–E) equation is known to describe polymer drag on particles, and the noncontinuum regime (<i>d</i> < <i>a</i>_e), in which several recent studies report faster diffusion of particles than expected from continuum S–E analysis, based on the bulk polymer viscosity. Specifically, we consider dynamics of particles with sizes <i>d</i> ≥ <i>a</i>_e in entangled polymers with varying molecular weight <i>M</i>_w in order to investigate how the transition from noncontinuum to continuum dynamics occur. We take advantage of favorable enthalpic interactions between SiO₂ nanoparticles tethered with PEO molecules and entangled PMMA host polymers to create model nanoparticle–polymer composites, in which spherical nanoparticles are uniformly dispersed in entangled polymers. Investigation of the particle dynamics via X-ray photon correlation spectroscopy measurements reveals a transition from fast to slow particle motion as the PMMA molecular weight is increased beyond the entanglement threshold, with a much weaker <i>M</i>_w dependence for <i>M</i>_w > <i>M</i>_e than expected from S–E analysis based on bulk viscosity of entangled PMMA melts. We rationalize these observations using a simple force balance analysis around particles and find that nanoparticle motion in entangled melts can be described using a variant of the S–E analysis in which motion of particles is assumed to only disturb subchain entangled host segments with sizes comparable to the particle diameter