Conformation and Dynamics along the Chain Contours of Polymer-Grafted Nanoparticles

Abstract

Densely grafted polymer chains onto spherical nanoparticles produce a diverse range of conformations. At high grafting densities, the corona region near the nanoparticle surface undergoes intense confinement due to a high concentration of chains in the concentrated polymer brush (CPB) region, which results in strong stretching for portions of the chains located within. In contrast, a semi-dilute polymer brush (SDPB) forms farther away from the core and offers reduced confinement for the polymer and more ideal conformations. However, conventional experimental methods are limited in their ability to provide detailed information on individual segments of grafted polymers in these regions; hence, molecular dynamics (MD) simulations are essential for gaining comprehensive insights into the behavior of the grafted chains. This study aims to explore the variations in polymer structure and dynamics that occur along the contour of the grafted chains as influenced by spatial confinement. We focus on the motions and relative positions of each bead along grafted polymers. Our results show that only the initial few grafted beads near the nanoparticle surface exhibit the strong stretching attributed segments in the CPB region of the brush. Increased grafting density or decreased chain flexibility leads to more stretched grafted chains and more aligned bond vectors. As a result, the relaxation dynamics of local regions of the polymer are also strongly influenced by these parameters. Although the grafted beads in the interior of the CPB region are highly sensitive to these parameters, those farther from the nanoparticle core experience significantly diminished effects. In comparison to the Daoud–Cotton (DC) model’s predictions of CPB size, beads near the nanoparticle surface show slower dynamic decay, especially in high grafting densities, aligning with the DC model’s estimates. Finally, we compare our simulations to previous works for additional insight into polymer-grafted nanoparticles.

Confined Dynamics in Spherical Polymer Brushes

“…Further, assuming b = 1.28 for Kremer−Grest chains, 35,69 we estimate that ν̃= 0.28 from the slope of a linear fit to the data. This effective ν̃is close to the value ν̃= 0.30 estimated from experiments 34 and simulations, 48 and it suggests that the chains are strongly stretched on length scales below R i* due to the confinement imposed by their neighbors. Hence, our results indicate that the observed inflection in the MSDs is indicative of confined chain dynamics near the NP surface, and its presence delineates between the CPB-and SDPB-like regimes predicted by theory.…”

“…The relaxation time of monomers varies non-monotonically with monomer position, with monomers near the chain center exhibiting the slowest relaxations. , Additionally, the intrachain relaxations of grafted polymers do not follow simple exponential decays. ,, Instead, neutron spin–echo (NSE) measurements find that grafted chains are confined by their neighbors and do not fully relax on observable time scales. , By selectively contrast matching the grafted chains, NSE measurements reveal that dynamics are slower in the CPB region than in the SDPB region of a long brush . This behavior was confirmed in recent molecular dynamics (MD) simulations, which also showed that the relaxation time of individual chains increases with increasing confinement (i.e., increasing σ). , Although these investigations suggest that the relaxations of grafted polymers are affected by the local brush structure, a direct connection between the brush structure and dynamics has not yet been demonstrated.…”

“…This intermediate-time plateau is consistent with the confined dynamics observed in NSE experiments, 44,45 but it has not been scrutinized in previous computational studies of spherical brushes. 39,48 The plateau value increases with increasing monomer position and finally disappears for monomers sufficiently far from the particle surface, suggesting a continuous transition from confined to unconfined dynamics. To characterize this transition, we determine the monomer position at which the dynamic confinement disappears and show that this position is comparable to that of R CPB , which controls the structural transition between CPB and SDPB regimes.…”

“…The variation of this length scale with grafting density is in agreement with that predicted by the extended Daoud–Cotton model of Ohno et al for the critical radius associated with the transition from a concentrated to a semidilute polymer brush. While preparing our manuscript, a recent study was published on the dynamics and structure of chains in spherical polymer brushes under melt-like conditions . Using the theory of Ohno et al for solutions, they estimated the critical radius for the CPB regime and demonstrated that the grafted chains exhibit stretched conformations and slow segmental dynamics below this length scale.…”

“…46 This behavior was confirmed in recent molecular dynamics (MD) simulations, which also showed that the relaxation time of individual chains increases with increasing confinement (i.e., increasing σ). 47,48 Although these investigations suggest that the relaxations of grafted polymers are affected by the local brush structure, a direct connection between the brush structure and dynamics has not yet been demonstrated.…”