Local Carbon Concentration Determines the Graphene Edge Structure

Although the structures and properties of various graphene edges have attracted enormous attention, the underlying mechanism that determines the appearance of various edges is still unknown. Here, a global search of graphene edge structures is performed by using the particle swarm optimization algorithm. In addition to locating the most stable edges of graphene, two databases of graphene armchair and zigzag edge structures are built. Graphene edge self-passivation plays an important role in the stability of the edges of graphene, and self-passivated edge structures that contain both octagons and triangles are found for the first time. The obvious apical dominance feature of armchair edges is found. The appearance of the experimentally observed ac(56), ac(677), and Klein edges can be explained by the local carbon concentration. Additionally, the graphene edge database is also significant for the study of the open end of nanotubes or fullerenes.