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.

We investigated the dynamics of gold nanoparticles (NPs) within an entangled liquid of poly(n-butyl methacrylate) (PBMA) above the glass transition temperature (T g ). The experiments were performed by using a modified version of fluctuation correlation spectroscopy (FCS), which measured the translational diffusion (D) of the isolated NPs as a function of their size (2R 0 = 5−20 nm) and temperature (T). We probed the most interesting but sparsely investigated length regime where the particle size/tube diameter (d t ) ratio ranges between ∼1−4. This allowed us to put into direct test recently developed theories and simulations. By measuring the bulk viscosity of the melt, the ratio D/D SE was determined, where D SE is the continuum prediction from Stokes− Einstein (SE) relation. Our results indicate gradual recovery to SE behavior and full coupling to entanglement relaxation would require 2R 0 ≈ 7−10d t .

We study, using fluorescence correlation spectroscopy, translational diffusion in molecularly thin liquids confined within a surface forces apparatus. The diffusion coefficient decreases exponentially from the edges towards the center of the Hertzian contact and further suggests the presence of a small number of distinct diffusion processes. This holds alike a crystallizable fluid (OMCTS) and a glass-former (1,2-propane diol), both of which displayed static friction. We conclude that friction, the average of an ensemble of molecules, masked massively heterogeneous molecular mobility.

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