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The two-dimensional crystalline structures in graphene challenge the applicability of existing theories that have been used for characterizing its three-dimensional counterparts. It is crucial to establish reliable structure-property relationships in the important two-dimensional crystals to fully use their remarkable properties. With the success in synthesizing large-area polycrystalline graphene, understanding how grain boundaries (GBs) in graphene alter its physical properties is of both scientific and technological importance. A recent work showed that more GB defects could counter intuitively give rise to higher strength in tilt GBs (ref. 10). We show here that GB strength can either increase or decrease with the tilt, and the behaviour can be explained well by continuum mechanics. It is not just the density of defects that affects the mechanical properties, but the detailed arrangements of defects are also important. The strengths of tilt GBs increase as the square of the tilt angles if pentagon-heptagon defects are evenly spaced, and the trend breaks down in other cases. We find that mechanical failure always starts from the bond shared by hexagon-heptagon rings. Our present work provides fundamental guidance towards understanding how defects interact in two-dimensional crystals, which is important for using high-strength and stretchable graphene for biological and electronic applications.

The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene