Energetic stability of graphene nanoflakes and nanocones

We investigate the relative energetic stability of a variety of nanographene structures such as graphene nanoflakes, nanoribbons, nanodisks, and nanocones. We calculate the cohesive energies with respect to hydrogen passivation, edge nature (zigzag versus armchair) and shape (triangular, rectangular, hexagonal). The cohesive energy is confirmed to increase with size for all these structures. We pay particular attention to optimally-compact circular flakes and compare our theoretical results with round disks produced in a plasma torch atmosphere. We find in the calculations that round shape does not have preferred relative stability. This suggests that the observed disks are grown under conditions where carbon atoms are highly mobile. For graphene nanocones we obtain a similar result. Experimentally, the open base of a 19-degree-cone is observed perpendicular to the cone axis, but this does not correspond to the most stable configuration as obtained by the calculations. Instead, we find that both, disks and cones, prefer minimal length of the edge termination rather than a maximum in the cohesive energy. With respect to our results we discuss for polycyclic aromatic hydrocarbons (PAH) and atomic clusters, as models for graphene flakes, the significance of the cohesive energy for the observed abundances.