Page 92 - Carbon Nanotubes

Helically coiled and toroidal cage forms of graphitic carbon 81

@a40 6720 c600 c480 c360 c240

Fig. 7. Optimized structures of the tori shown by elongation to height: pentagons and heptagons are shaded;
top views and side views are shown in each case.

minimal at nl - n2 = 2 for n2 = 3,4, and 6. Contrary 4. HELICALLY COILED FORM
to the five-fold rotational symmetric surface, where OF GRAPHITIC CARBON
the upper and lower planes become convex and, hence,
increase the energy of the tori with nl , the surface re- 4.1 Expecting properties of helices
mains flat for the six-fold rotational symmetric case Helically coiled forms of the carbon cage on the
(k = 6) with increasing nl . However, the cohesive en- nanometer scale[ 141 concerned here have graphitic
ergy of the six-fold rotational symmetric torus in- layer (s), in contrast to the micron-order amorphous
creases with nl (if nl is larger than n2 + 2) (i.e., carbon fiber previously created by experimentsT283.
elongating nl). This increasing in energy with nl The motivation of studying the helical structure is as
arises from the increasing stress energy of the outer follows: (1) the electrical, magnetic, and elastic prop-
edges, where the number of hexagons that have fold- erties can be modulated by the tiling pattern of the
ing bonds at the edges increases linearly with nl . pentagons, hexagons, and heptagons and/or writhing

c288 c420 c576 c756

c1440 c1188 c960

Fig. 8. Optimized shallow toroidal structures: the subscripts indicate the number of the carbon atoms in
the torus; pentagons and heptagons are shaded.