Size-Dependent Dynamics of Nanoparticles in Unentangled Polyelectrolyte Solutions

The mobility of polystyrene nanoparticles ranging in diameter from 300 nm to 2 μm was measured in dilute and semidilute solutions of partially hydrolyzed polyacrylamide. In this model system, the ratio of particle to polymer size controls the long-time diffusivity of nanoparticles. The particle dynamics transition from subdiffusive on short time scales to Fickian on long time scales, qualitatively similar to predictions for polymer dynamics using a Rouse model. The diffusivities extracted from the long-time Fickian regime, however, are larger than those predicted by the Stokes–Einstein equation and the bulk zero-shear viscosity and moreover do not collapse according to hydrodynamic models. The size-dependent deviations of the long-time particle diffusivities derive instead from the coupling between the dynamics of the particle and the polymer over the length scale of the particle. Although the long-time diffusivities collapse according to predictions, deviations of the short-time scaling exponents and the crossover time between subdiffusive and Fickian dynamics indicate that the particles are only partially coupled to the relaxation modes of the polymer

Mobility of Nanoparticles in Semidilute Polyelectrolyte Solutions

We measure the mobility of nanoparticles at low concentrations in non-Newtonian semidilute aqueous solutions of high-molecular-weight polyelectrolyte polymers. Using optical microscopy and particle tracking algorithms, we image and track hydrophilic polystyrene nanoparticles of diameter 400 nm moving in aqueous solutions of partially hydrolyzed polyacrylamide of molecular weight 8 000 000 Da and concentration of 0.0424.2 g/L. The effective diffusivity of the nanoparticles in the semidilute polymer solutions, extracted from the long-time limit of the mean-squared displacement using the Stokes–Einstein relation, is greater than that calculated from the zero-shear-rate viscosity measured using bulk rheology. For concentrations <i>c</i> > 0.42 g/L, the mean-square displacements (MSD) of particles measured as a function of lag time revealed that the particle dynamics are subdiffusive at short time scales and are Fickian on long time scales. The time scale for the crossover from subdiffusive to Fickian dynamics increases with increasing polymer concentration; moreover, it is longer than the relaxation time scale for polymer blobs and shorter than that for the chain. Our results suggest that the nanoparticle dynamics are coupled to those of the polymers on a length scale intermediate between the blob size and the end-to-end distance of the polymer

Confined Dynamics of Grafted Polymer Chains in Solutions of Linear Polymer

We measure the dynamics of high molecular weight polystyrene grafted to silica nanoparticles dispersed in semidilute solutions of linear polymer. Structurally, the linear free chains do not penetrate the grafted corona but increase the osmotic pressure of the solution, collapsing the grafted polymer and leading to eventual aggregation of the grafted particles at high matrix concentrations. Dynamically, the relaxations of the grafted polymer are controlled by the solvent viscosity according to the Zimm model on short time scales. On longer time scales, the grafted chains are confined by neighboring grafted chains, preventing full relaxation over the experimental time scale. Adding free linear polymer to the solution does not affect the initial Zimm relaxations of the grafted polymer but does increase the confinement of the grafted chains. Our results elucidate the physics underlying the slow relaxations of grafted polymer