Fatigue threshold of dual-crosslinking hydrogels

The fatigue threshold of covalent hydrogels follows the Lake-Thomas model, equating to the energy needed to break covalent bonds between crosslinks at the crack tip. Dynamic bonds are widely introduced as secondary crosslinks to toughen hydrogels. Previous studies have reported that dynamic bonds contribute to the fatigue threshold in some tough hydrogels but not in others, making their contribution unclear. In this work, we prepare dual-crosslinking hydrogels (PAV-M2+) by introducing ligands along covalent polymer chains, enabling dynamic coordination with various M2+ ions to tune the relaxation time. In such hydrogels, we propose that covalent bonds contribute to the fatigue threshold via the Lake-Thomas model, while dynamic bonds contribute based on the competition between relaxation time and the crack-tip strain rate. When the strain rate greatly exceeds the inverse of the relaxation time, dynamic bonds cannot re-associate and contribute little to fatigue threshold. Conversely, when the strain rate is much lower than the inverse of relaxation time, they re-associate reversibly and enhance the threshold. The fatigue threshold of PAV-Ni hydrogels (relaxation time ∼ 300 ms) is 10.5 J/m2 at a strain rate of 1 s−1 (consistent with the Lake-Thomas prediction, 9.4 J/m2), and increases to 17.7 J/m2 at 0.1 s−1. The fatigue threshold of PAV-Zn hydrogels (relaxation time ∼ 0.3 ms) is 39.8 J/m2 at 1 s−1 and 41.4 J/m2 at 0.1 s−1, due to the recovery of dynamic bonds during loading cycles. Based on these results, we propose a modified Lake-Thomas model that incorporates the contribution of dynamic bonds to fatigue threshold, capturing the competition between relaxation time and strain rate.