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 (ϕ), 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(α( R 0 /ξ) δ ) for R g > R 0 and as D 0 / D = exp(α( R g /ξ) δ ) for R g ≤ R 0, where D 0 is the diffusion coefficient in neat solvent, ξ is the correlation length, α = 1.63, and δ = 0.89. In size regime, ξ < R 0 < a (ϕ), where a (ϕ) is the tube diameter for entangled polymer liquid, we found D ∼ ϕ –1.45 and independent of M w . For R 0 > a (ϕ), D ∼ ϕ –4 was obtained.