Swelling Effect on the Yielding, Elasticity, and Fracture of Double-Network Hydrogels with an Inhomogeneous First Network

Typical double-network (DN) gels are formed by free radical polymerization, and the constituent network strands have a wide molecular weight distribution. It is important to clarify what determines the specific mechanical behaviors of DN gels with a strongly inhomogeneous first network, including the criteria for the occurrence of yielding and strain hardening during tensile deformation, as well as their impact on the fracture toughness. In this work, we first studied the influence of swelling ratio λs of the first network synthesized from radical polymerization on the yielding and strain hardening of DN and triple-network (TN) gels by tensile tests. We observed scaling relations for the yielding stretch ratio λy ∝ λs–1 and engineering yielding stress σy ∝ λs–2, like those found for DN hydrogels with a homogeneous first-network structure. Furthermore, we found a universal relationship λyσy ∝ λs–3 that is independent of the cross-linking structure of the first network. We found that these scaling relations agree well with the theoretical predictions derived from a simple one-dimensional affine model for the fracture of a homogeneous network, suggesting the affine swelling effect on the fracture of network strands. Next, we showed that swelling induces more tension in the inhomogeneous network than in the homogeneous network, suggesting non-affine swelling behavior at the network strand scale for the inhomogeneous network. We discussed the molecular origin of the discrepancy between the affine swelling effect on the fracture of network strands and the non-affine swelling behavior for strand tension. Finally, we investigated the influence of swelling ratio λs on the local yielding behavior ahead of the crack tip and the fracture toughness of the DN and TN hydrogels using pure shear tests. We found that crack-tip yielding zone size hy ∝ λs1 and fracture energy Γ ∝ λs–2. Furthermore, we found that the relationship Γhy∝λs−3 is also independent of cross-linking structure and obeys a universal relationship with the true yielding stress λyσy ∝ λs–3 determined from the tensile tests, which is in excellent agreement with nonlinear elastic fracture mechanics theory. This work provides important insight into the specific mechanical behaviors of the DN gels with an inhomogeneous first network.