Diffusion of Polymer-Grafted Nanoparticles with Arm Retraction in Entangled Polymer Melts

Diffusion of nanoparticles loosely grafted with polymer chains of varied lengths in entangled melts of linear polymers was investigated by means of molecular dynamics simulations. The study showed that for nanoparticles with short graft chains that are unentangled with the matrix polymer, their transport is controlled by the frictions experienced by the nanoparticle core and the graft chains from the surrounding matrix; that is, the grafted nanoparticle can diffuse through dragging the grafts with it. At longer graft length N_g, when they are entangled with the matrix, a severe suppression of the polymer-grafted nanoparticle diffusivity was observed. For particles grafted with only two chains, the diffusivity decreases with N_g as D ∼ N_g^–2, suggesting a “snake-like” motion of the two-chain-grafted nanoparticles, like a linear chain. When multiple chains were grafted onto the nanoparticle, the decrease of D with N_g is more rapid than a power law, showing an exponential dependence on N_g, i.e., D ∼ exp(−αN_g), where α is a constant, due to the presence of extra grafts, blocking the reptation of the grafted nanoparticle. Instead, the multiple-chain-grafted nanoparticles can diffuse through one by one, rather than simultaneously, retractions of the graft chains. At much higher N_g, the “tube-renewal” effect of the surrounding matrix polymer emerges and gradually dominates the particle diffusion, as it becomes faster than the graft chain “retraction” process. Consequently, the diffusion coefficient deviates from the exponential relation and shows a progressively weaker dependence on N_g, until D ∼ N_g^–1 at sufficiently high N_g. Finally, we also observed non-Gaussian dynamics at the crossover from the subdiffusive to diffusive stages due to the slowly varying, spontaneous fluctuations of the surrounding matrix polymer. Our findings could advance the fabrication of high-performance polymeric nanocomposites and inform innovative design strategies for precision-engineered drug delivery platforms.