Bridging dynamic regimes of segmental relaxation and center-of-mass diffusion in associative protein hydrogels

Hierarchy of relaxation times in supramolecular polymer model networks

“…The relaxation times are obtained by monitoring the Bragg-diffracted beam intensity created by a vanishing sinusoidal dye concentration profile. Similar to previously investigated protein-based P 4 -coils 11,15 and linear acrylamide chains with nickel-histidine coordination bonds, 12 a phenomenological superdiffusive regime with hti B d 2a (a o 1) is found in a range of d 2 = 0.3-200 mm 2 in the 10k gels. Beyond this range, terminal Fickian diffusion is observed in all tetra-arm PEGterpyridine networks at various temperatures (Fig.…”

“…By this model, real physical parameters are obtained, but the predictions overestimate several parameters such as the polymer radius of gyration by an order of magnitude. Very recently, 15 Rao and coworkers combined forced Rayleigh scattering (FRS) and neutron spin echo measurements on protein hydrogels to connect segmental polymer strand relaxations with the selfdiffusion of the network components, thereby spanning a huge length scale that ranges from nanometers to several micrometers. They found at least two length-scale dependent superdiffusive regimes that reflect a multitude of relaxation mechanisms and molecular states.…”

Mechanisms of Self-Diffusion of Linear Associative Polymers Studied by Brownian Dynamics Simulation

“…The effect of cross-link density in the network is explored by varying the chain concentration, the number of stickers per chain, and the binding equilibrium constant, resulting in differences in the topological structure that enable superdiffusive behavior via hopping even at high sticker densities. A comparison of the simulations with experimental self-diffusion measurements of analogous associative polymers 29,33 finds qualitative agreement, suggesting that this molecular model can successfully capture key dynamic behaviors of various associative systems across a range of length scales.…”

“…7,34,41 In addition, for most of the simulations, the sticker association rate was chosen to be slow compared to the Rouse time of the chain (i.e., k A ⟨F⟩/V ≪ (N 2 τ s ) −1 = 1/48 2 in the simulation units, where ⟨F⟩ is the average number of free stickers in the system). This separation in timescales is characteristic of a kinetics-limited system, 39 which applies to a large majority of experimental associative polymer gels 9,33 and is hypothesized to be crucial in enabling chain superdiffusive behavior via hopping. 37 All simulations were run at equilibrium, with the average chain conformations and sticker association states constant over time (to within fluctuations governed by the system size).…”

“…Recent experiments have shown that associative polymers with relatively few (∼10) stickers per chain, both in linear and branched architectures, can exhibit unexpected selfdiffusive behavior on different length scales, including apparent superdiffusion on length scales ∼10−1000 times the radius of gyration. 29,30,33,34 These anomalous dynamics have been proposed to arise due to the coexistence of multiple diffusive modes, which are largely not considered by current theories, including bound-state diffusion (e.g., "walking") and relatively free diffusion by complete detachment of all stickers from the network ("hopping"). 13,35−37 Mechanisms involving correlated sticker or chain motion in large clusters have also been proposed, though their role in quiescent-state dynamics is unclear.…”