Dynamics of Dual Networks: Strain Rate and Temperature Effects in Hydrogels with Reversible H-Bonds

Combining high concentration of reversible hydrogen bonds with a loosely cross-linked chemical network in poly(N,N-dimethylacrylamide-co-methacrylic acid) hydrogels produces dual-network materials with high modulus and toughness on par with those observed for connective tissues. The dynamic nature of the H-bonded cross-links manifests itself in a strong temperature and strain rate dependence of hydrogel mechanical properties. We have identified several relaxation regimes of a hydrogel by monitoring a time evolution of the time-average Young's modulus ⟨E(t)⟩ = σ(t)/ε̇t as a function of the strain rate, ε̇, and temperature. At low temperatures (e.g., 3 °C), ⟨E(t)⟩ first displays a Rouse-like relaxation regime (⟨E(t)⟩ ∼ t–0.5), which is followed by a temporary (physical) network regime (⟨E(t)⟩ ∼ t–0.14) at intermediate time scales and then by an associating liquid regime (⟨E(t)⟩ ∼ t–0.93) at the later times. With increasing temperature to 22 °C, the temporary network plateau displays lower modulus values, narrows, and shifts to shorter time scales. Finally, the plateau vanishes at 37 °C. It is shown that the energy dissipation in hydrogels due to strain-induced dissociation of the H-bonded cross-links increases hydrogel toughness. The density of dissipated energy at small deformations scales with strain rate as UT ∼ ε̇0.53. We develop a model describing dynamics of deformation of dual networks. The model predictions are in a good agreement with experimental data. Our analysis of the dual network's dynamics provides general frameworks for characterization of such materials.