Size Effect of Nanoparticle Diffusion in a Polymer Melt

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 (2 R 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 2 R 0 ≈ 7–10 d t .