Anomalous scaling law of strength and toughness in polymers with strong interfacial secondary bonds

In materials design, the increase of toughness usually leads to the decrease of strength, which is a long-standing challenge. Polymeric materials with strong interfacial secondary bonds have recently emerged as promising solutions due to their remarkable capabilities to increase toughness and strength simultaneously. Nevertheless, a quantitative understanding on how toughness increases with strength is unavailable, posing challenges for deeper understanding and on-demand design for stronger and tougher advanced materials. In this work, we reveal a quadratic scaling law of simultaneously increased strength and toughness that unifies multiscale evidences from theories, computations and experiments across multiple material systems, where the deformation mechanisms are dominated by breaking and reforming of interfacial secondary bonds. Our results highlight the significance of interfacial secondary bonding combined with topology design to enable a wide range of strong and tough advanced materials.