Self-healing polymers crosslinked by dynamic bonds have shown great potential in various engineering applications ranging from electronics to robotics. Due to the intrinsic weakness of dynamic bonds, most of the existing self-healing polymers have relatively weak mechanical strengths. To address this drawback, it is proposed to incorporate crystalline domains within the polymer matrix during the synthesis to make tough and strong self-healing thermoplastic elastomers with semi-crystalline phases. Despite the success in the polymer synthesis, the theoretical understanding of self-healing thermoplastic elastomers remains elusive. In this paper, we develop a theoretical framework to model the constitutive and healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and semi-crystalline phases. We model the virgin thermoplastic elastomer by using a spring-dash model that couples the soft rubbery phase and the stiff crystalline phase. The rubbery polymer network is formed by layering the body-centered unit cubes that link polymer chains via dynamic bonds. Then, the healing is considered as a coupling of polymer chain diffusion and dynamic-bond binding, leading to an effective diffusion-reaction model. Based on the theoretical framework, we can model the stress-strain behavior of the virgin and healed polymers and theoretically explain the relationship between the healing strength and the healing time. The model can consistently explain our own experiments on self-healable thermoplastic elastomers polyurethane and the documented experiments on self-healable thermoplastic elastomers with disulfide bonds and pi-pi interactions. 

Modeling Self-Healing Mechanics: Self-Healing Thermoplastic Elastomers

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