A constitutive theory for large stretch behaviors of slide-ring gels by considering molecular frictions

Synthetic slide-ring hydrogels display excellent mechanical properties, including high extensibility, low viscosity, high toughness, etc. Here, by considering molecular frictions induced by sliding of rings on polymer chains, we have developed a nonaffine constitutive theory for large stretch behaviors of these hydrogels. In the theory, a represented volume element of a cube is employed with one chain aligning along each cubic edge, similar to the classical 3-chain model. Different from the classical 3-chain model, crosslinks at each corner of the cube are now mobile due to ring sliding so that contour lengths of chains within the cube would adapt upon loading. Based on the virtual work principle at each time step, the stress-stretch relationship is then obtained using an explicit method. With the theory, we predict viscoelastic behaviors of several slide-ring hydrogels, which are in agreement with experiments. Our analysis clearly indicates that sliding of rings is critical for their high fracture energy. Our analysis also suggests that the molecular friction coefficient for ring sliding on chains can be very small at small stretching but large at large stretch, which might strongly depend on the normal force occurring at the interface between rings and polymer chains. This work provides insights into the understanding of the high mechanical performance of slide-ring hydrogels.