Unveiling Nanoparticle Diffusion Mechanisms Confined in Different Polymer Topologies

In this study, the diffusion dynamics of nanoparticles (NPs) in ring polymer-nanocomposites (RPNCs) is investigated using a coarse-grained molecular dynamics (CGMD) simulation system, which is compared with linear polymer-nanocomposites (LPNCs) in order to analyze the unique effects of the closed-loop topology. Both cross-linked and non-cross-linked cases are considered. Our results show that the dynamic behavior of NPs is influenced by NP size, and the larger size makes it more difficult to diffuse regardless of whether cross-linked network topological constraints are introduced. Due to the closed-loop structural features, the conformation of ring polymers is more compact compared to linear polymers with free ends. Additionally, the polymer chain length plays a critical role in regulating the diffusion dynamics of NPs in RPNCs and LPNCs. We found the existence of a critical chain length Nc ≈ 26. When N < Nc, NPs exhibit a superior diffusion behavior in LPNCs, whereas for N > Nc, the NP diffusion is more pronounced in RPNCs. The phenomenon of NP diffusion dynamics varying with chain length in these different topological systems is governed by the matrix motion characteristics and the number of entanglements. Upon the introduction of cross-linking points, RPNCs manifested a more densely packed cross-linked network compared to LPNCs. As cross-linking density increases gradually, the diffusion behavior of NPs in RPNCs is more significantly hindered compared to LPNCs, primarily due to the higher matrix viscosity induced by the compact network structure. This viscous restriction gives rise to the emergence of a critical cross-linking density threshold ρc ≈ 0.04, at which the relative diffusion dynamics of NPs between the two topological systems undergoes reversal. Beyond this threshold (ρ > 0.04), NP diffusion in RPNCs is more stringently constrained, further corroborating the pivotal role of topological constraints in governing NP dynamics. Meanwhile, we observe that when strongly bound, NPs diffuse via the hopping mechanism. This study provides new insights into the molecular-scale regulation of NP diffusion by the topology of ring polymers without free chain ends.