Diffusion of Nanoparticles in Semidilute Polymer Solutions: Effect of Different Length Scales

We used gold nanoparticles (NPs) to investigate the length-scale-dependent dynamics in semidilute poly(ethylene glycol) (PEG)-water solutions. Fluctuation correlation spectroscopy was used to measure the diffusion coefficients (D) of the NPs as a function of their radius (R-0), PEG volume fraction (phi), and molecular weight (M-w). Our results indicate that the radius of gyration, R-g, of polymer chain is the crossover length scale for the NPs experiencing nanoviscosity or macroviscosity. The reduced diffusivity can be plotted on a single master curve as D-0/D = exp(alpha(R-0/xi)(delta)) for R-g > R-0 and as D-0/D = exp(alpha(R-g/xi)(delta)) for R-g <= R-0, where D-0 is the diffusion coefficient in neat solvent, xi is the correlation length, alpha = 1.63, and delta = 0.89. In size regime, xi < R-0 < a(phi), where a(phi) is the tube diameter for entangled polymer liquid, we found D similar to phi(-1.45) and independent of M-w. For R-0 > a(phi), D similar to phi(-4) was obtained.