Dynamics of nanoparticles in polydisperse polymer networks: From free\n diffusion to hopping

Abstract

Using molecular dynamics simulations we study the static and dynamic\nproperties of spherical nanoparticles (NPs) embedded in a disordered and\npolydisperse polymer network. Purely repulsive (RNP) as well as weakly\nattractive (ANP) polymer-NP interactions are considered. It is found that for\nboth types of particles the NP dynamics at intermediate and at long times is\ncontrolled by the confinement parameter $C=\\sigma_N/\\lambda$, where $\\sigma_N$\nis the NP diameter and $\\lambda$ is the dynamic localization length of the\ncrosslinks. Three dynamical regimes are identified: i) For weak confinement ($C\n\\lesssim 1$) the NPs can freely diffuse through the mesh; ii) For strong\nconfinement ($C \\gtrsim 1$) NPs proceed by means of activated hopping; iii) For\nextreme confinement ($C \\gtrsim 3$) the mean squared displacement shows on\nintermediate time scales a quasi-plateau since the NPs are trapped by the mesh\nfor very long times. Escaping from this local cage is a process that depends\nstrongly on the local environment, thus giving rise to an extremely\nheterogeneous relaxation dynamics. The simulation data are compared with the\ntwo main theories for the diffusion process of NPs in gels. Both theories give\na very good description of the $C-$dependence of the NP diffusion constant, but\nfail to reproduce the heterogeneous dynamics at intermediate time scales.\n