Non-local Shortest Paths: Microstructural Evolution controls Macroscopic Response for Dynamic Polymer Networks

Highly stretchable and self-healable supramolecular elastomers are promising materials for future soft electronics, biomimetic systems, and smart textiles, to name a few, due to their dynamic cross-linking bonds. The dynamic or reversible nature of the cross-links gives rise to interesting macroscopic responses in these materials such as self-healing and rapid stress-relaxation. However, the relationship between bond activity and macroscopic mechanical response, and the self-healing properties of these dynamic polymer networks (DPNs) remains poorly understood.

We developed a coarse-grained molecular dynamics (CGMD) model for DPNs and demonstrated that it successfully captures the stress-strain hysteresis and self-healing behaviors. By contrasting its behavior against irreversible cross-linked polymeric model, we show that these behaviors are the result of dynamic bond breaking and re-formation. Furthermore, we reveal a fundamental connection between the macroscopic behaviors of DPNs and the shortest paths between distant nodes in the polymer network. Notably, the trajectories of the material on the shortest path-strain map provide key insights into understanding the stress-strain hysteresis, anisotropy, stress relaxation, and self-healing of DPNs. Based on CGMD simulations under various loading histories, we formulate a set of empirical rules that dictate how the shortest path interacts with stress and strain. This lays the foundation for the development of a physics-based theory centered around the non-local microstructural feature of shortest paths to predict the mechanical behavior of DPNs.