Mobility of Polymer-Tethered Nanoparticles in Polymer Melts

A scaling theory is developed for the motion of a polymer-tethered nanoparticle (NP) in a polymer melt. Both NPs tethered with a single polymer chain (tail) and with multiple chains (tails) are studied. For a single-tail NP in a polymer melt, we identify two types of scaling regimes, particle-dominated regimes and tail-dominated regimes, that depend on the NP diameter d and the size of the tail R_tail. In a particle-dominated regime, a tethered NP moves as a bare NP, while the effects of the tethered tails on NP motion can be neglected. In a tail-dominated regime, the motion of a tethered NP is not significantly affected by the tails below a crossover time, but is dominated by the tails above the crossover time. For a multi-tail NP in an unentangled polymer melt, the boundaries separating the particle-dominated and tail-dominated regimes in the (d,R_tail) parameter space depend on the number of tails z. For a multi-tail NP in an entangled polymer melt, the motion of the entangled tails is described based on the dynamics of a star polymer entangled with the underlying polymer melt network. The mobility of such a multi-tail NP is approximated as the lower of the mobilities of the bare NP and of the branch point of the corresponding entangled star.