Diffusion of Nanoparticles in Entangled Poly(vinyl alcohol) Solutions and Gels

We studied the diffusion of gold nanoparticles within entangled solutions and gels formed by high molecular weight (Mw = 89000 g/mol) poly­(vinyl alcohol) (PVA) in water by using fluctuation correlation spectroscopy (FCS). The nanoparticle size (2R) was varied between 5 and 30 nm, and the PVA volume fraction (ϕ) was chosen to be in the entangled regime. We found that existing hydrodynamic and obstruction models are inadequate to describe the size dependence of the particle diffusion coefficient (D). For size ratios x = 2R/ae ≈ 0.5–2.5, where ae is the entanglement tube diameter in the solution, our results suggest a functional form for D ∼ exp­(−κx), where κ ≈ 1.4. This result qualitatively agrees with the scaling theory prediction of hopping motion for particles within entangled polymer solutions. For larger particles at higher volume fractions, an additional sharp slowing down of the particle motion was observed, which also exhibited an exponential dependence on the size ratio, but with a much higher value of κ ≈ 7.5. Such a rare hopping process can be explained qualitatively by recently developed force-based nonlinear Langevin theory.