Thermodynamics of Extra-Toughness and Hidden-Length in Polymeric Materials with Sacrificial Bonds

Sacrificial bonds have been observed in several biological materials and structures and can increase their toughness, i.e., their resistance to fracture. They provide a reversible mechanism for dissipating mechanical energy before the possible system rupture. From a structural point of view, sacrificial bonds consist of short polymer chains that short-circuit parts of a main macromolecular chain (generating hidden lengths) and absorb energy by breaking them instead of the main chain. The toughness increase due to the presence of sacrificial bonds is typically named extra-toughness. Here, we developed a statistical mechanics and thermodynamics-based theory able to estimate the force–extension relation for chains with sacrificial bonds and to calculate the corresponding extra-toughness. The model is useful to better understand the sacrificial bond effects in biomaterials but also to apply the biomimetic paradigm and foster the development of high-performance artificial polymeric materials.