Differential Coupling of Nanoparticle Translational and Rotational Diffusion to Polymer Relaxation Modes in Unentangled Polymer Melts

Abstract The diffusion of spherical nanoparticles (NPs) in unentangled polymer melts is investigated using coarse-grained molecular dynamics simulations. We show that for both translational and rotational diffusion, when the NP diameter d is smaller than a characteristic length lc, the continuum Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations, based on macroscopic viscosity, break down and substantially underestimate the diffusion coefficients. For translational diffusion, the polymer chain size ⟨Ree2〉1/2 defines the relevant length scale, with the characteristic size lcT being a few times ⟨Ree2〉1/2; the SE relation accurately describes the translational diffusion coefficient DT when d>lcT. In contrast, the polymer contour length Nl0 serves as the relevant length scale for rotational diffusion. Recovery of the SED relation is not observed within the simulated NP size range, while extrapolation of the fitted relation to a 90% recovery criterion yields a characteristic recovery length of lcR∼80Nl0, substantially larger than lcT. Analysis of the dynamical coupling between NP motion and polymer relaxation modes reveals that translational and rotational motion exhibits differential coupling behaviors, with rotational diffusion being less strongly coupled to the macroscopic viscosity of the polymer melts. Furthermore, this differential coupling can be modulated by NP–polymer affinity and NP surface bead density. Our findings provide fundamental insights into the mechanisms governing NP dynamics in polymer melts.