Self-Diffusion in a Weakly Entangled Associative Network

Abstract

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.

Structure, Dynamics, and Rheological Behavior of Associative Polymers Formed by Hydrogen Bonds

“…However, when the hydrogen-bonding interaction is turned on, ⟨ Z ⟩ rises from 2.91, 2.97, 3.07, 3.19, and 3.37 to 3.52 with increasing N ag from 0, 2, 4, 6, 8, to 10, respectively. This indicates that the introduction of HBs improves the chain entanglements, which is also reported in the experiments. , Then, the average entanglement molecular weight ( N e ) and the average associated molecular weight ( N a ) are calculated via equations N e ≈ N /(< Z > + 1) and N a ≈ N /( N ag + 1), respectively. Here, N is the number of beads on the chain backbone.…”

“…The number of entanglements per chain gradually rises with increasing number of active stickers per chain. 47 The same result is observed for the supramolecular polymer networks formed from the poly(LMAran-HEMA) precursor copolymers equipped with ureidopyrimidinone groups. 48 In addition, the shear viscosity of poly(butyl acrylate) copolymers is nearly proportional to the number of HB, while the critical shear rate at the viscosity crossover is reduced.…”

“…This indicates that the introduction of HBs improves the chain entanglements, which is also reported in the experiments. 47,48 Then, the average entanglement molecular weight (N e ) and the average associated molecular weight (N a ) are calculated via equations N e ≈ N/(<Z> + 1) and N a ≈ N/(N ag + 1), respectively. Here, N is the number of beads on the chain backbone.…”

Structural and dynamic heterogeneity in associative networks formed by artificially engineered protein polymers

“…13,16,17,38 In contrast, the self-diffusion interconversion times τ off are 10–100 times greater than τ ex ≈ τ D , with no conclusive rheological signature for this relaxation process yet identified. 17,65 The results provide further evidence that self-diffusion and network relaxation are governed by fundamentally different processes, where network relaxation requires exchange of only single stickers on the time scale ∼ τ D while long-range self-diffusion requires a longer relaxation time ∼ τ off governed by the dissociation of all stickers on a molecule to begin a hopping event.…”

“…† The two-state model demonstrates that the interconversion between the two diffusive populations over a finite length scale range gives rise to apparent superdiffusive scaling, and the width of the superdiffusive regime is proportional to the ratio of the two diffusivities weighted by their relative populations. 17,65 In single-chain models, the two diffusive modes are shown to be molecular walking and hopping. 26,27 However, the two-state model does not assign a molecular origin for each diffusive mode, leaving open alternative hypotheses such as collective cluster motion.…”