Anomalous self-diffusive behavior in associative polymer gels has been attributed to the presence of multiple diffusive mechanisms on different length scales; however, the role of these dynamic modes in networks of linear polymers with pendant stickers remains unknown, particularly at sticker densities below the meanfield limit. Here, a generalized Brownian dynamics model is developed to study the effect of transient binding on self-diffusion of unentangled linear polymers with regularly spaced stickers, selected as a prototypical associative network model with wide experimental relevance. The simulations reveal an interplay between several diffusive mechanisms, including segmental fluctuations, "walking" diffusion, and "hopping" diffusion, each governed by a molecule's connectivity to the network. These dynamic modes combine to result in multiple self-diffusive regimes on different length scales, including two distinct regimes of apparent superdiffusion before terminal Fickian diffusion, consistent with experiments. The two superdiffusive regimes have different physical origins: while one occurs due to a transition from walking to hopping, the second occurs from walking alone on smaller length scales, even in the absence of hopping. This second superdiffusive regime is proposed to arise from an increase in the chain pervaded volume upon sticker detachment, which increases the walking step size compared to the "cage" formed by binding. Each self-diffusive regime is highly sensitive to the sticker concentration, equilibrium constant, and association/dissociation kinetics due to their effects on the walking and hopping modes. Notably, increasing a chain's sticker density promotes intramolecular loops and enables superdiffusive scaling through hopping; in contrast, increasing the chain concentration promotes intermolecular binding and suppresses hopping, resulting in dynamics approaching the mean-field limit of Fickian centerof-mass diffusion on all length scales. Analytical predictions for the hopping and walking diffusivities demonstrate a link between the static network structure, bond lifetime, and the contribution of each dynamic mode, with qualitative agreement with simulation.
The presence of entanglements in associative polymer gels has been shown to impart enhanced mechanical strength, toughness, and extensibility; however, the interplay between topological and binding interactions in these systems remains poorly understood. Here, the effect of entanglements on chain dynamics in a model associative network is investigated in the weakly entangled regime, corresponding to 1.1−3.1ϕ e , where ϕ e is the characteristic concentration for the onset of entanglement. The associative network is formed by a linear random copolymer of N,N-dimethylacrylamide and a histidinefunctionalized monomer crosslinked with Ni 2+ ions. Rheological characterization indicates that the concentrations investigated span the transition from unentangled to the weakly entangled regime, resulting in a subtle broadening of their relaxation spectrum. Selfdiffusion measurements using forced Rayleigh scattering demonstrate a pronounced suppression of apparent superdiffusive behavior with increasing concentration, revealing a stronger impact of topological entanglement on self-diffusion compared to overall network relaxation. This suppression in superdiffusive behavior is attributed to a reduction in the contribution of "hopping" diffusion due to the presence of entanglements, resulting in an approach to purely Fickian diffusion governed by a single "walking" diffusive mode at the highest concentration probed. These results demonstrate the marked effects of entanglements on self-diffusion and relaxation in associative networks, providing insight into the network response beyond that accessible by rheology alone.
This work investigates static gel structure and cooperative multi-chain motion in associative networks using a well-defined model system composed of artificial coiled-coil proteins.
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