Chain diffusion based framework for modeling the welding of vitrimers

Unlike traditional thermosets, vitrimers with dynamic covalent bonds enable welding through thermally activated bond exchange reactions. The welding strength of such vitrimers highly depends on the chain diffusion across the interface. However, the understanding of diffusiontriggered welding of vitrimers still remains elusive. Herein, we study the welding of vitrimers through a combination of theory and experiment. We disentangle the welding of vitrimer into three processes: pressure-assisted surface contact, thermally induced chain diffusion across the interface, and chain association due to bond exchange reactions. Then we propose a framework for modeling the welding of vitrimers emphasizing the interfacial chain diffusion and interaction of the three processes. The framework identifies the associated chain ratio as a key intermediate parameter for scaling the welding efficiency and conditions. Based on this, a nonlinear eightchain model is derived that accounts for bond exchange reactions in the welded vitrimer for the subsequent stretching. As such, this model captures the effects of chain diffusion, welding pressure, and welding time on the tensile strength of welded vitrimers. The present model agrees well with experiments for hard glassy and soft rubbery vitrimers. We also formulate a contour diagram in the welding pressure- time space. This work will guide the welding of vitrimers, as well as contribute to the mechanics of welding.