We investigate the mobility of polystyrene particles ranging from 100 to 790 nm in diameter in dilute and semidilute sodium polystyrene sulfonate (NaPSS) solutions using fluorescence microscopy. We tune the polymer conformations by varying the ionic strength of the solution. The nanoparticle mean-squared displacements evolve linearly with time at all time scales, indicating Fickian diffusive dynamics. In solutions of high ionic strength, chains adopt a random walk conformation and particle dynamics couple to the bulk zero-shear rate viscosity, according to the Stokes−Einstein picture. In solutions of low ionic strength, however, particle dynamics nonmonotonically deviate from bulk predictions as polymer concentration increases and are not accurately predicted by the available models. These nonmonotonic dynamics directly correlate with the non-Gaussianity in distributions of particle displacements, suggesting the emergence of a local confining length scale as polyelectrolyte concentration increases.

We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using x-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve as a function of normalized length scales. These results suggest that the soft interaction potential between polymergrafted nanoparticles and free polymer allows polymer-grafted nanoparticles to diffuse faster than predicted based on bulk rheology and modifies the coupling between grafted particle dynamics and the relaxations of the surrounding free polymer.Attaching polymers to surfaces modifies the interactions between nanoparticles and surrounding environments. Such fine-tuning of nanoparticle interactions is important to improve the biocompatibility of targeted drug delivery vectors, 1-4 control self-assembled structures in nanocomposites, 5-8 or stabilize emulsions. 9-11 For these applications, the efficacy of polymer-grafted nanoparticles (PGNPs) requires that the particles remain stable and transport effectively when dispersed into complex fluids. Whereas the long-time dynamics of large hard sphere colloids through complex fluids are well understood, multiple factors complicate predictions of the motion of PGNPs. First, PGNPs are often comparably sized to heterogeneities in the surrounding complex fluid, violating an assumption underlying microrheology theory. 12-14 Second, PGNPs are soft particles whose 'softness' can be characterized by their elastic deformability 15 or through the steepness and range of their repulsive interactions. [16][17][18] The combination of soft interactions between grafted polymers and hard interactions of the nanoparticle cores leads to elastic moduli and yield stresses for PGNP suspensions lower than those of hard sphere colloids and higher than those of "ultra-soft" star-like polymers or micelles. 16,19,20 Finally, the tethering of polymer to the particle surface significantly changes the grafted polymer relaxations 21-24 and may therefore affect the transport of PGNPs.Here, we investigate the dynamics of silica nanoparticles grafted with high molecular weight polystyrene so that the grafted polymer and silica core are comparably sized. The PGNPs are dispersed into solutions of free polystyrene and the dynamics of the PGNP center-of-mass are probed using x-ray photon correlation spectroscopy (XPCS). The PGNP diffusivity systematically depends on the free polymer molecular weight, diffusing faster in solutions with the same bulk viscosity but higher molecular weight. Although similar dependences have been observed for hard sphere nanoparticles, the PGNPs are much larger than the length scale at which hard spheres be...

We examine the coupling of the dynamics of flexible viral nanoparticles to the dynamics of comparably sized polymer chains. Using fluorescence microscopy, we quantify the dynamics of three filamentous viruses, potato virus M (PVM), M13, and pf1, that are suspended in semidilute solutions of partially hydrolyzed polyacrylamide. The dynamics of the viral nanoparticles are approximately diffusive on accessible time and length scales, but the distributions of displacements are non-Gaussian and exhibit increasingly extended tails as the aspect ratio of the viruses or the polymer concentration is increased. The long-time diffusion coefficients do not collapse onto a universal curve based on existing models for rodlike or spherical nanoparticles that are comparably sized to the polymer chains. Instead, the diffusivities appear to collapse as a function of the ratio of the polymer correlation length and a length scale intermediate between the virus radius and length, indicating that the hydrodynamic coupling to the polymer dynamics is affected by the virus anisotropy and flexibility.

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin–echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

We investigate the transport and localization of tracer probes in a glassy matrix as a function of relative size using dynamic X-ray scattering experiments and molecular dynamics simulations. The quiescent relaxations of tracer particles evolve with increasing waiting time, t w. The corresponding relaxation times increase exponentially at small t w and then transition to a power-law behavior at longer t w. As tracer size decreases, the aging behavior weakens and the particles become less localized within the matrix until they delocalize at a critical size ratio δ0 ≈ 0.38. Localization does not vary with sample age even as the relaxations slow by approximately an order of magnitude, suggesting that matrix structure controls tracer localization.