Macromolecular Diffusion through a Polymer Matrix with Polymer-Grafted Chained Nanoparticles

Diffusion of deuterated polystyrene (dPS) is probed in PS matrices containing stringlike chained nanoparticles (cNP) grafted with PS. This investigation connects prior diffusion studies in model spherical and cylindrical NP systems and provides insight for technological applications, which typically involve irregularly shaped NPs such as carbon black. We report that the presence of chained NPs in PS matrices induces a minimum in the diffusion coefficient (<i>D</i>) with increasing cNP concentration when the key length scale, 2<i>R</i><sub>g</sub>/<i>L</i> ≤ 1.5, where <i>R</i><sub>g</sub> is the gyration radius of dPS and <i>L</i> is the mean length of the impenetrable core of the chained NPs. When 2<i>R</i><sub>g</sub>/<i>L</i> > 1.5, <i>D</i> decreases monotonically as the NP concentration increases. Note that in all cases 2<i>R</i><sub>g</sub> is larger than the diameter of these short-stringy NPs. The diffusion minimum is attributed to anisotropic diffusion in the vicinity of the chained NPs and requires that the long dimension of the cNP be comparable to or longer than the tracer molecule. Two normalizations are explored to provide insight about the diffusion mechanism: <i>D</i>/<i>D</i><sub>0</sub> where <i>D</i><sub>0</sub> is the diffusion coefficient in a pure homopolymer matrix and <i>D</i>/<i>D</i><sub>e</sub> where <i>D</i><sub>e</sub> is an effective diffusion coefficient that accounts for the distinct dynamics in the PS matrix and PS brush regions. For <i>D</i>/<i>D</i><sub>0</sub>, a sharp transition from a diffusion minimum to a monotonic decrease is observed as dPS molecular weight increases, while for <i>D</i>/<i>D</i><sub>e</sub> the transition is more gradual. These studies show not only that the NPs act as impenetrable obstacles for polymer diffusion but that the polymer brush grafted to the cNP provides an alternative pathway to control polymer dynamics.