Physicochemical insight into gap openings in graphene

Based on a newly developed size-dependent cohesive energy formula for two-dimensional materials, a unified theoretical model was established to illustrate the gap openings in disordered graphene flakes, involving quantum dots, nanoribbons and nanoporous sheets. It tells us that the openings are essentially dominated by the variation in cohesive energy of C atoms, associated to the edge physicochemical nature regarding the coordination imperfection or the chemical bonding. In contrast to those ideal flakes, consequently, the gaps can be opened monotonously for disordered flakes on changing their sizes, affected by the dimension, geometric shape and the edge saturation. Using the density functional theory, accordingly, the electronic structures of disordered flakes differ to the ideal case because of the edge disorder. Our theoretical predictions have been validated by available experimental results, and provide us a distinct way for the quantitative modulation of bandgap in graphene for nanoelectronics.