HELICALLY COILED AND TOROIDAL CAGE FORMS OF GRAPHITIC CARBON

Toroidal forms for graphitic carbon are classified into five possible prototypes by the ratios of their inner and outer diameters, and the height of the torus. Present status of research of helical and toroidal forms, which contain pentagons, hexagons, and heptagons of carbon atoms, are reviewed. By molecular-dynamics simulations, we studied the length and width dependence of the stability of the elongated toroidal structures derived from torus C-240 and discuss their relation to nanotubes. The atomic arrangements of the structures of the helically coiled forms of the carbon cage for the single layer, which are found to be thermodynamically stable, are compared to those of the experimental helically coiled forms of single- and multi-layered graphitic forms that have recently been experimentally observed.