Graphitic cones and the nucleation of curved carbon surfaces

The nucleation and growth of curved carbon structures, such as fullerenes, nanotubes and soot, are still not well understood. A variety of models have been proposed, and it seems clear that the occurrence of pentagons, which yield 60°disclination defects in the hexagonal graphitic network, is a key element in the puzzle. The problem of nucleation has been complicated by the great variety of structures observed in any one sample. Here we report an unusual carbon sample generated by pyrolysis of hydrocarbons, consisting entirely of graphitic microstructures with total disclinations that are multiples of +60°. The disclination of each structure corresponds to the presence of a given number of pentagons in the seed from which it grew: disks (no pentagons), five types of cones (one to five pentagons), of which only one was known previously, and open tubes (six pentagons). Statistical analysis of these domains shows some unexpected features, which suggest that entropy plays a dominant role in the formation of disclinations. Furthermore, the total disclination of a domain is determined mainly at the nucleation stage.