Nanoparticle Mobility within Permanently Cross-Linked Polymer Networks

Coarse-grained molecular dynamics simulations were performed to investigate the mobility of nanoparticles (NPs) embedded in end-linked polymer networks, considering both the entangled and unentangled cases. For the entangled case, where the network strand length N-x is longer than the entanglement length N-e, the strand dynamics exhibits a heavily entangled subdiffusive feature before being restricted within the fluctuation distance d(fluct) by the permanent cross-links. The dynamics of NPs with size d(NP) smaller than the entanglement tube length d(T) in such network follows the same behavior as that in entangled linear polymers, while for NPs with size comparable to d(T), their motion is suppressed by the entanglements. The constraint release of the entanglements would allow the particles to pass through but is slightly restricted by the permanent network junctions. For the unentangled case, where N-x/N-e < 1, the network strands can move only locally with suppressed subdiffusive behavior due to the restrictions imposed by the adjacent network junctions. Consequently, the coupled NP dynamics is also reduced. In addition, when d(NP) is larger than the strand fluctuation distance d(fluct), the NPs are trapped by the network cages and can diffuse at long times through hopping, which is partially masked by the NP thermal fluctuations, as reflected from the NP trajectories. Such hopping fashion of NP motion becomes more apparent with increasing the network confinement ratio before being permanently localized within the network. Increasing the NP-polymer attraction would further hamper the NP mobility. In general, this work provides some insights into understanding how the permanent cross-links affect the network dynamics and thereby the coupled NP mobility.