A dynamic model of complexly mechanoresponsive chain-poly[n]-catenations in double-network polyampholyte hydrogels

Polyampholytes have been widely used to improve mechanical performance of double-network (DN) hydrogels, however, the complex mechanisms of electric charge reactions and chain catenations have not been well understood. In this study, a collective and cooperative model is developed to describe the dynamics and constitutive relationships of complexly mechanoresponsive chain-poly[n]-catenations in polyampholyte DN hydrogels. The freely jointed chain (FJC) model and Flory-Huggins theory are firstly employed to formulate mechanochemical behaviors of the DN hydrogels, in which the stretchable network undergoes a folding-to-unfolding transition and the brittle one undergoes a reversibly mechanochemical transition. The worm like chain (WLC) model is then introduced to describe the chain-poly[n]-catenations, of which the strong and weak ionic bonds have been modeled based on the entanglement and dangling effects, respectively. Finally, a free-energy equation is developed to describe their collective and cooperative dynamics. Effectiveness of the newly proposed model is verified by applying it to predict the experimental results of the polyampholyte DN hydrogels reported in literature.