(373e) Mobility of Nanoparticles in Semi-Dilute Polymer Solutions

Understanding the diffusion of sub-micron particles in polymeric fluids impacts technological applications ranging from drug delivery to polymer nanocomposite processing. When the size of the particles is comparable to or smaller than length scales in the polymer solution, however, the solution cannot be treated a homogeneous continuum and the particle dynamics may not probe the bulk rheological properties of the fluid. Here, we explore the coupling between particle and polymer dynamics in this limit by measuring the mobility of nanoparticles at low concentrations in non-Newtonian dilute and semi-dilute aqueous solutions of high-molecular-weight polymers. Using optical microscopy, particle tracking, and differential dynamic microscopy, we characterize the mobility of 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 c^* to 100c^*, where c^* is the overlap concentration. For all samples, the effective diffusivity of the nanoparticles, extracted from the long-time limit of the MSD using the Stokes-Einstein relation, is greater than that calculated from the zero-shear-rate viscosity measured using bulk rheology. For concentrations c > 10c^*, 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 timescale 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 the Rouse time scale. Our results thus suggest that the nanoparticle dynamics are coupled to those of the polymers on a length scale intermediate between the blob size and the radius of gyration.