Increasing the elastic modulus of graphene by controlled defect creation

The extraordinary strength, stiffness(1) and lightness of graphene have generated great expectations of its application in flexible electronics and as a mechanical reinforcement agent. However, the presence of lattice defects, unavoidable in sheets obtained by scalable routes, might degrade its mechanical properties(2,3). Here we report a systematic study on the elastic modulus and strength of graphene with a controlled density of defects. Counter-intuitively, the in-plane Young's modulus increases with increasing defect density up to almost twice the initial value for a vacancy content of similar to 0.2%. For a higher density of vacancies, the elastic modulus decreases with defect inclusions. The initial increase in Young's modulus is explained in terms of a dependence of the elastic coefficients on the momentum of flexural modes predicted for two-dimensional membranes(4,5). In contrast, the fracture strength decreases with defect density according to standard fracture continuum models. These quantitative structure-property relationships, measured in atmospheric conditions, are of fundamental and technological relevance and provide guidance for applications in which graphene mechanics represents a disruptive improvement.