A growing focus in modern materials science is the attempt to transfer principles found in nature into new technological concepts with the goal of producing novel materials with tailored mechanical properties. One of these principles used in nature is the concept of sacrificial bonding (i.e. non-covalent cross-links that rupture prior to the protein backbone), which is associated with increased toughness in many biological materials. In the present work, the influence of the number and distribution of sacrificial bonds (SBs) on three main mechanical parameters-strength, work to fracture and apparent stiffness-is investigated in a simple model system using computer simulations. The results show that the work to fracture is mainly determined by the number of SBs present in the system, while the apparent stiffness and, to a lesser extent, the strength is altered when the distribution of SBs is changed. IntroductionIn contrast to engineered materials, biological organisms utilize a relatively limited selection of building blocks to synthesize materials (e.g. proteins, sugars, environmentally abundant ions). In spite of this, however, natural materials span an extremely wide range of mechanical properties, which is achieved by hierarchical structuring of the material over multiple length scales and by a combination of materials with opposing mechanical properties. One common and successful strategy to increase the toughness of protein-based biological materials is to use so-called sacrificial bonds (SBs).2 These non-covalent cross-links are weaker than the covalent bonds that comprise the protein backbone, and consequently, upon loading, they rupture before the covalent bonds fail. By doing so, SBs reveal hidden length (i.e. the length increase associated with unfolding of folded proteins) providing an efficient energy dissipation mechanism, while the overall material integrity survives.3 Furthermore, these bonds are reversible and may reform when the load is released, allowing for molecular repair. SBs have been found in a large variety of biologial materials like wood, 4 bone 5-7 and in some softer biological fibres such as silk, 8 whelk egg capsule 9 and mussel byssus threads. 10-13In materials such as silk, SBs are often weak hydrogen bonds combined in large numbers in regular protein conformations in order to collectively produce high stiffness 14 ; however, in the case of the mussel byssus, much stronger interactions between metal ions and proteins are employed. In this regard, the mussel byssus is an especially fascinating material. The mussel secretes the collageneous byssal threads as a means of creating a secure attachment in wave-swept rocky seashore habitats. Among the impressive properties of the mussel byssus are its high extensibility of over 100%, high stiffness and toughness, 10 its hard and wearresistant outer coating [15][16][17][18] and, last but not least, its ability to create strong and long-lasting underwater adhesion to a variety of surfaces.17 A fundamental aspect shaping each of these prope...

Sacrificial bonding is a ubiquitous cross-linking strategy for increasing toughness that is found throughout nature in various biological materials such as bone, wood, silk and mussel byssal threads. However, the molecular mechanism of sacrificial bonding remains only poorly understood. Molecular modeling possesses a strong potential to provide insights into the behavior of these crosslinks. Here we use Monte Carlo simulations to investigate the effect of reversible sacrificial binding sites on the mechanical properties of single linear polymer chains based on load-bearing metalloproteins found in the mussel byssus. It is shown that the topology of the bonds determines the position and spacing of sacrificial force peaks, while the height of these peaks is intimately tied to the magnitude of thermal fluctuations in the chain that are dependent on effective chain length. These results bear important implications for understanding natural systems and for the generation of strong and ductile biomimetic polymers.

Reversible cross-linking is a method of enhancing the mechanical properties of polymeric materials. The inspiration for this kind of cross-linking comes from nature, which uses this strategy in a large variety of biological materials to dramatically increase their toughness. Recently, first attempts were made to transfer this principle to technological applications. In this study, Monte Carlo simulations are used to investigate the effect of the number and the topology of reversible cross-links on the mechanical performance of a simple model system. Computational cyclic loading tests are performed, and the work to fracture and the energy dissipation per cycle are determined, which both increase when the density of cross-links is increased. Furthermore, a different topology of the bonds may increase the work to fracture by a factor of more than 2 for the same density. This dependence of the mechanical properties on the topology of the bonds has important implications on the self-healing properties of such systems, because only a fast return of the system to its unloaded state after release of the load ensures that the optimal topology may form.

Reversible cross-linking is an effective strategy to specifically tailor the mechanical properties of polymeric materials that can be found in a variety of biological as well as man-made materials. Using a simple model in this paper the influence of weak, reversible cross-links on the mechanical properties of aligned fiber bundles is investigated. Special emphasis in this analysis is put on the strength of the investigated structures. Using Monte Carlo methods two topologies of cross-links exceeding the strength of the covalent backbone are studied. Most surprisingly only two cross-links are sufficient to break the backbone of a multi chain system, resulting in a reduced strength of the material. The found effect crucially depends on the ratio of inter- to intra-chain cross-links and, thus, on the grafting density that determines this ratio.