A model with contact maps at both polymer chain and network scales for tough hydrogels with chain entanglement, hidden length and unconventional network topology

Tough hydrogels with unconventional polymer network architectures often show superior mechanical properties because of the microstructures at the polymer chain and network scales. In this study, a single-chain based model, or called the network topology with hidden length and entanglement (NeTHE) model for the tough hydrogels with chain entanglement, hidden length and unconventional network topology, is developed by imposing contact maps at both polymer chain and network scales on the Arruda-Boyce model. In particular, the contact map is imposed at the polymer chain scale to characterize both entanglement and hidden length simultaneously, while the contact map is imposed at the polymer network scale to consider different polymeric network topologies. The present NeTHE model is validated well by comparing published experimental results of a highly entangled hydrogel and two soft regular hydrogels with hidden lengths. It is confirmed that the present model is able to characterize the hardening, softening, swelling, and damage of the hydrogels. By simplifications, the NeTHE model is reduced directly to the pseudo-elasticity model [1]. Furthermore, the model is able to cover the exponential or scaling law type of damage behaviors of the hydrogels. Finally, several parameter studies are conducted for the swelling and hysteresis of the hydrogels. It is observed theoretically that the constraints of polymer chains due to entanglements result in the high swelling resistance of highly entangled hydrogels, while the hidden length facilitates the swelling of soft regular hydrogels. It is also found that, regarding the hysteresis of hydrogels with different polymer network topologies, the ideal polymer network possesses the highest damage tolerance when compared with both the random and high-functionality crosslinked polymer networks. Regarding the effects of entanglements and hidden lengths on the hysteresis, the highly entangled hydrogel shows a lower stress–stretch hysteresis due to the energy dissipated partially to harden polymer chains when compared with the soft regular hydrogel of which the energy is dissipated fully to fracture the polymer chains.