Abstract
Using molecular dynamics simulations, we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive and weakly attractive polymer–NP interactions are considered. It is found that for both types of particles, the NP dynamics at intermediate and long times is controlled by the confinement parameter C = σN/λ, where σN is the NP diameter and λ is the dynamic localization length of the cross-links. Three dynamical regimes are identified: (i) for weak confinement (C ≲ 1), the NPs can freely diffuse through the mesh; (ii) for strong confinement (1 ≲ C ≲ 3), NPs proceed by means of activated hopping; (iii) for extreme confinement (C ≳ 3), the mean-squared displacement shows on intermediate time scales a quasi-plateau because the NPs are trapped by the mesh for very long times. Escaping from this local cage is a process that depends strongly on the local environment, thus giving rise to an extremely heterogeneous relaxation dynamics. The simulation data are compared with the two main theories for the diffusion process of NPs in gels. Both theories give a very good description of the C dependence of the NP diffusion constant but fail to reproduce the heterogeneous dynamics at intermediate time scales.