Page 94 - Carbon Nanotubes

Helically coiled and toroidal cage forms of graphitic carbon 83

Fig. 12. Elongated helical structures (a) helix C756 and (b)
helix C2,60.

helix Cz160 (nl = 12, n2 = 6, L = 1) can be generated
(see Fig. 12). In these cases, the flat part (i.e., the part
Fig. 10. Helically coiled form C,,,: one pitch contains a resembling the graphite layer) becomes wider and
torus C,,,.
wider with increasing nl. Thus, this type of helical
structure has minimal cohesive energy at nl - n2 =
0,2 as observed in the shallow tori.
was found to be stiffer than helix c360[14]. The dif-
ference in elasticity of the helically coiled forms of he- 4.4 Comparison with experiments
lices may be attributed to the difference in patterns of Ivanov et al.[31] and Van Tendeloo et al.[32] re-
the heptagons; these are sensitive to the geometric ported a synthesis of helically coiled multi-layered
properties, such as the ratio of the radii of the cross- form. They showed that: (1) cobalt on silica is the best
section and the curvature. catalyst-support combination for the production of
Because the tube diameter of the helix CSd0 is graphite tubes, such as straight tubes and coiled ones,
small compared to the helix c360, atoms at the open and (2) decreasing temperature from 973 to 873K
ends must bend inwards to cover the open end. The leads to strong decrease in the amorphous carbon pro-
open end is covered with six hexagons, one heptagon, duction. Also, (3) helically coiled carbon tubes were
one square, and one pentagon, see Fig. 11. The elec- obtained with inner and outer diameter of 3-7 and 15-
tronic structure of helices is strongly affected by the 20 nm, respectively, and up to 30 pm in length. The
end pattern of the rings because the end rings of odd size of the helical structure is orders of magnitude
numbers play a scattering center, such as a disclina- smaller than the helix-shaped fibers composed of
tion center as discussed by Tamura and Tsukada[30]. amorphous carbon[28]. Note their sizes are much
The edge effect may lead to adding an exotic electronic larger than that of the theoretical one[l4]. (4) Using
character to the helical structure which is not seen in TEM and the electron diffraction method, they sug-
the straight tubes. gested that the helically coiled tubes consist of a reg-
ularly polygonized structure, where the bend may be
4.3 Helices derived from elongated tori related to pairs of pentagon-hexagon carbon rings in
From elongated tori, such as type (C), type (D), the hexagonal network as suggested by ref. [14]. (5)
and type (E), helical structures are derived. For exam- As shown in Fig. 13, a helix-shaped nanotube with ra-
ple, from the type (c) elongated torus of Dbh, men-
tioned in 3.2.2, helix C756 (nl = 6, n2 = 3, L = 1) and
--

Fig. 11. Edge of the helix C540: (a) initial state and, (b) Fig. 13. TEM picture of a helix-shaped structure with radius
reconstructed form of the edge; the edge contains a square, of about 18 nm, pitch about 30 nm, containing 10 graphite
heptagon, pentagons and hexagons. tubes (after V. Ivanov et d.).