(32i) Role of Chain Walking and Hopping on Anomalous Self-Diffusion in Linear Associative Polymer Gels

Associative polymer gels based on reversible cross-links have attracted wide attention for applications in biomedicine and soft robotics due to their tunable viscoelastic properties and stimuli-responsive abilities. Engineering the macroscopic behavior of such materials for different applications requires a fundamental understanding of the internal chain dynamics on various length scales, which govern key material properties such as the rates of stress relaxation and mechanical actuation. However, the interplay between transient binding and segmental motion in such systems has been found to result in unexpected transport phenomena, including observations of apparent superdiffusive chain motion on length scales 10-100 times the radius of gyration. This surprising behavior is not captured by existing theories of associative polymer gels, suggesting that our understanding of chain dynamics in such systems is incomplete. Recent studies of associative star polymers have suggested that superdiffusive behavior can arise from an interplay between different diffusive modes such as “walking” and “hopping” in the gel. However, in the more common case of associative linear polymers, the presence and contributions of these dynamic modes toward superdiffusive behavior are largely unknown. In addition, the effect of parameters such as number of stickers per chain and the sticker binding kinetics in these systems have been largely uninvestigated to date, limiting their capacity for design.

In this work, a Brownian dynamics model of linear polymers with regularly spaced stickers is developed to explore the interplay between diffusive modes such as walking and hopping in unentangled gel networks over a range of length scales, from smaller than the radius of gyration up to the macroscopic Fickian regime. Polymers are coarse-grained as bead-spring chains that can reversibly bind through interaction with a mean-field background or formation of intramolecular loops. Chain trajectories are calculated using overdamped Langevin dynamics, with sticker binding reactions handled by a kinetic Monte Carlo scheme. An analysis of the self-intermediate scattering function reveals the presence of multiple chain relaxation modes, depending on the length scale probed. By examining the relaxation time as a function of the length scale, the simulations demonstrate several different self-diffusive regimes on different length scales, including two distinct regimes of superdiffusive scaling. Surprisingly, the two superdiffusive regimes are found to result from different physical origins: while one occurs due to a transition from walking to hopping, the second arises from the walking mechanism alone. An analysis of the walking mechanism suggests that this second superdiffusive regime results from the increase in the strand contour length after dissociation of a sticker, which increases the chain’s mean-square center-of-mass displacement during a walking step compared to smaller timescales when chains are more strongly confined by binding. The simulations also reveal a strong sensitivity of the extent of superdiffusive behavior to the sticker density, chain concentration, and binding kinetics. The effect of sticker concentration is found to depend on sticker connectivity: increasing the sticker density on a chain promotes loop formation and enables superdiffusive scaling through hopping, even for a chain with 49 stickers, while increasing the chain concentration overall promotes intermolecular binding and suppresses hopping. Finally, the simulation results are compared with experimental self-diffusion measurements of analogous associative linear polymers with good qualitative agreement, providing a molecular understanding of the diffusive regimes observed experimentally. Overall, this work provides key insight into the interplay between sticker binding and chain diffusion in associative polymer gels and reveals design criteria to tune the transport properties of these systems for various applications spanning biomedicine, soft robotics, and self-healing materials.