(390j) Constraint Release Leads to Size-Dependent Diffusivity of Nanoparticles in Solutions of Unentangled Polyelectrolytes

Using a polyelectrolyte model system, we show that polymer mobility controls the size-dependent deviations from Stokes-Einstein behavior for nanoparticles diffusing in unentangled polymer solutions. We measure the long-time diffusivity of fluorescent polystyrene nanoparticles ranging in diameter from 300 nm to 2 μm in dilute and semidilute solutions of partially hydrolyzed polyacrylamide. At short time scales, the particles exhibit subdiffusive behavior characterized by MSD ~ t^α where α < 1. On long time scales, the particles exhibit Fickian diffusion (α=1) from which the diffusivities are extracted. Whereas diffusivities of the large particle agree with predictions using the Stokes-Einstein equation and bulk zero-shear viscosity, the smaller particles diffuse much faster than predicted. To capture the particle- and polymer-size dependence of the long-time diffusivity, we propose a model in which particles diffuse in a matrix with relaxing constraints caused by the diffusion of polymer segments. We derive an effective length scale that collapses the long-time diffusivities onto a single curve and cleanly captures a smooth crossover to bulk behavior when the particles are much larger than the polymer chains. Furthermore, the effective length scale controls the crossover time scale between subdiffusive and Fickian behavior for all particle sizes and polymer concentrations. Our model generates new physical insight into the effect of length scales on diffusion through dynamic, heterogeneous media.