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The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiplescales and system-specific variables, has posed a long-standing challenge onits theoretical description. In this paper, we construct a microscopic theoryfor polymer diffusion in the mixtures based on a combination of generalizedLangevin equation, mode-coupling approach, and polymer physics ideas. Theparameter-free theory has an explicit expression and remains tractable on paircorrelation level with system-specific equilibrium structures as input. Takinga minimal polymer-NP mixture as an example, our theory correctly captures thedependence of polymer diffusion on NP concentration and average interparticledistance. Importantly, the polymer diffusion exhibits a power law decay as thepolymer length increases at dense NPs and/or long chain, which marks theemergence of entanglement-like motion. The work provides a first-principletheoretical foundation to investigate dynamic problems in diverse polymernanocomposites.

Theory of polymer diffusion in polymer-nanoparticle mixtures: effect of nanoparticle concentration and polymer length