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

Abstract

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 (R0), PEG volume fraction (ϕ), and molecular weight (Mw). Our results indicate that the radius of gyration, Rg, 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 D0/D = exp(α(R0/ξ)δ) for Rg > R0 and as D0/D = exp(α(Rg/ξ)δ) for Rg ≤ R0, where D0 is the diffusion coefficient in neat solvent, ξ is the correlation length, α = 1.63, and δ = 0.89. In size regime, ξ < R0 < a(ϕ), where a(ϕ) is the tube diameter for entangled polymer liquid, we found D ∼ ϕ–1.45 and independent of Mw. For R0 > a(ϕ), D ∼ ϕ–4 was obtained.