Dynamic polymer networks utilize weak bonding interactions to dissipate the stored energy and provide a source of self-healing for the material. Due to this, tracking the progression of damage in these networks is poorly understood as it becomes necessary to distinguish between reversible and irreversible bond detachment (by kinetic bond exchange or chain rupture, respectively). In this work, we present a statistical formulation based on the transient network theory to track the chain conformation space of a dynamic polymer network whose chains rupture after being pulled past a critical stretch. We explain the predictions of this model by the observable material timescales of relaxation and self-healing, which are related to the kinetic rates of attachment and detachment. We demonstrate our model to match experimental data of cyclic loading and self-healing experiments, providing physical interpretation for these complex behaviors in dynamic polymer networks.

Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the Transient Microsphere Model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker-Planck equation which incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.

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We investigate the mechanical properties of a magnetic temperature-sensitive hydrogel at varying concentrations of covalent and physical cross-linking. The hydrogel consists of covalently cross-linked poly(N-isopropylacrylamide) (PNIPAAm), physically interacting nanoclay particles, and magnetic ferric oxide nanoparticles. The physical nanoclay network exhibits strong viscoplastic behavior, and we find that increasing nanoclay content improves both strength and toughness in the double network materials. We investigate the behavior of the gels using a nonlinear viscoplasticity model with a modified rule of mixtures approach and attribute the observed trends to two factors: (a) the yield-stress behavior of the nanoclay network and (b) load-sharing interactions between the PNIPAAm and the nanoclay. Our findings indicate a strong correlation between the mass ratio of covalent cross-linker used and fractional percolation of the PNIPAAm network.