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

TL;DR

This study uses molecular dynamics simulations to explore how spherical nanoparticles move within polydisperse polymer networks, revealing three distinct dynamical regimes influenced by confinement and highlighting the heterogeneity of relaxation dynamics.

Contribution

The paper introduces a detailed analysis of nanoparticle dynamics in polydisperse networks, identifying three regimes and comparing simulation results with existing theories, emphasizing the role of confinement.

Findings

Diffusion is governed by the confinement parameter C.

Three dynamical regimes: free diffusion, activated hopping, and trapping.

Heterogeneous relaxation dynamics are observed at intermediate times.

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 (RNP) as well as weakly attractive (ANP) polymer-NP interactions are considered. It is found that for both types of particles the NP dynamics at intermediate and at long times is controlled by the confinement parameter $C=\sigma_N/\lambda$, where $\sigma_N$ is the NP diameter and $\lambda$ is the dynamic localization length of the crosslinks. Three dynamical regimes are identified: i) For weak confinement ($C \lesssim 1$) the NPs can freely diffuse through the mesh; ii) For strong confinement ($C \gtrsim 1$) NPs proceed by means of activated hopping; iii) For extreme confinement ($C \gtrsim 3$) the mean squared displacement shows on intermediate time scales a quasi-plateau since 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.