Diffusive motion in polymer composites: coupling particle and polymer dynamics across scales

Understanding particle dynamics in polymer composites is essential to predicting their material properties. In composites with particles much larger than the polymers, the diffusive time scale of the particles is often longer than the polymer relaxation time. This separation of length and time scales regularly justifies coarse graining the polymer into a continuum viscoelastic fluid that is coupled to the particle, reducing modeling complexity. However, in polymer nanocomposites, the nanoscale particle size and the corresponding diffusive time scale are often smaller than those of the polymer. Whether the polymer can be coarse-grained in these systems, and in which circumstances this is a good approximation, remains an open question. In this work, we utilize the Generalized Langevin Equation and Fokker-Planck equation formalisms to study nanoparticle diffusive motion and determine whether coarse-graining the polymers into a nanoparticle coupled continuum accurately captures particles dynamics in nanocomposites. We find that the polymer can be coarse-grained into a continuum that couples to particle dynamics via the time-dependent friction (i.e. the memory Kernel). Furthermore, we outline the conditions under which coarse graining the polymer is a good approximation and test theory utilizing molecular dynamic simulations and Brownian dynamics simulations.