Designing graphene structures with controlled distributions of topological defects: A case study of toughness enhancement in graphene ruga

A novel design methodology combining phase field crystal method and atomistic simulations is proposed to solve the inverse problem of finding the optimized distribution and type of topological defects that make a graphene sheet conform to a targeted arbitrary three dimensional (3D) surface. To demonstrate potential applications of the proposed method, we created a sinusoidal graphene structure with wavelength of 4 nm and amplitude of 0.75 nm, and then demonstrated using large-scale molecular dynamics (MD) simulations that the constructed graphene ruga1 has a fracture toughness around 25J/m2, which is about twice that of the defect-free graphene. The underlying toughening mechanisms include nanocrack shielding and atomic scale crack bridging. This study suggests a promising general methodology to tailor-design mechanical properties of graphene through controlled distributions of topological defects.