Helically coiled cage forms of graphitic carbon

Helically coiled forms of the carbon cage on the nanometer scale are theoretically proposed. The optimized surface construction for different types of helically coiled structures consisting of sevenfold, sixfold, and fivefold rings of carbon atoms is given. The thermal stability of various helical structures is studied by molecular-dynamics simulations, employing Stillinger-Weber-type potentials. The structures are found to be thermodynamically stable. It is found that the helically coiled structures derived from toroidal structues ${\mathrm{C}}_{360}$ and ${\mathrm{C}}_{1080}$ are stiff, so that the ring pattern of the surface changes with pitch length. On the contrary, the structure derived from torus ${\mathrm{C}}_{540}$ is found to be soft, i.e, a change in the pitch length does not change the ring pattern of the surface.