Mechanism of Soft Nanoparticle Diffusion in Entangled Polymer Melts

While there is an emerging good theoretical understanding of how hard impenetrable spherical nanoparticles diffuse in unentangled and entangled polymer liquids, the analogous problem for soft permeable nanoparticles is far less well understood due to their unique topology and flexibility. It also has proven difficult to experimentally quantify the motion of such very slow moving soft nanoparticles (SNP) in entangled polymer melts. To address these problems, we have combined a protocol to measure the tracer diffusion coefficient of soft nanoparticles in a linear polymer matrix with recently developed synthetic control over their structure to independently elucidate the effects of SNP and entangled linear chain matrix molecular weight, nanoparticle softness, and temperature on its diffusive behavior. We find the surprising result that the molecular weight (MSNP) dependence of the SNP diffusion constant is very weak, ca. D-SNP similar to M-SNP(-1). Moreover, DSNP varies strongly with both its internal cross-link density and polymer matrix molecular weight. A simple and predictive statistical mechanical model captures the observed rich behavior by invoking the threading of linear polymer chains through the loops that exist near the cross-linked SNP surface which act as topological constraints that inhibit its center-of-mass motion. The theory predicts D-SNP scales inversely with the product of SNP molecular weight and internal cross-link density and is proportional to the entangled matrix chain center-of-mass diffusivity. The experimental results for the SNP tracer diffusion reported here and in our previous publications agree with this prediction over 2 orders of magnitude variation of D-SNP. Our combined experimental and theoretical insights may also be relevant to understanding diffusive motion in other soft materials such as dense microgel and nanogel suspensions and linear/ring polymer blends.