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

Gold nanoparticles (Au NPs) were used 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$_{o}$ (2.5-10 nm), PEG volume fraction, $\phi $ (0-0.37) and molecular weight, M$_{w}$ (5 kg/mol and 35 kg/mol). Our results indicate that the radius of gyration, R$_{g}$ of the 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$_{o}$/D$_{ }$= exp ($\alpha $(R$_{o}$/$\xi )^{\delta })$ for R$_{g} \quad >$ R$_{o}$ and as D$_{o}$/D$_{ }$= exp ($\alpha $(R$_{g}$/$\xi)^{\delta })$ for R$_{g} \quad \le $ R$_{o}$, where D$_{o}$ is diffusion coefficient in the neat solvent, $\xi $ is the correlation length, $\alpha $ = 1.63 and $\delta $ = 0.89. In the intermediate size regime, $\xi \quad <$ R$_{o} \quad <$ a($\phi )$, where `a($\phi )$' is the tube diameter for entangled polymer liquid, we found that D $\sim \quad \phi ^{-1.45}$ and independent of M$_{w}$. For R$_{o} \quad >$ a($\phi )$, D$\sim \phi ^{-4}$ was obtained. The results were compared with currently available theories.