Nanotubes structures

Fig. 7. Strain energy per carbon (total energy minus total energy extrapolated for the graphite sheet) as a function of nanotube radius calculated for unoptimized nanotube structures (open squares) and optimized nanotube structures (solid circles). Solid line depicts inverse square relationship drawn through point at smallest radius.

As an example of a nanotube representative of the diameters experimentally found in abundance, we have calculated the electronic structure of the [9,2] nanotube, which has a diameter of 0.8 nm. Figure 8 depicts the valance band structure for the [9,2] nanotube. This band structure was calculated using an unoptimized nanotube structure generated from a conformal mapping of the graphite sheet with a 0.144 nm bond distance. We used 72 evenly-spaced points in the one-... 

Carbon nanotubes are also of considerable interest with regard to both reinforcement and possible increases in electrical conductivity [237-239]. There is considerable interest in characterizing the flexibility of these nanotube structures, in minimizing their tendencies to aggregate, and in maximizing their miscibilities with organic and inorganic polymers. 

In most publications, Iijima is given credit for the discovery in 1991 of the nanotube structure of carbon (Iijima, 1991 Bethune et al., 1993 Iijima and Ichihashi, 1993). However, it has been said that Oberlin et al. (1976) also imaged carbon nanotubes, perhaps even SWNTs. Incredibly, nearly a century earlier, there was a study on the thermal decomposition of methane that resulted in the formation of long carbon strands, which were proposed at the time as a candidate for filaments in light bulbs (see Bacon and Bowman, 1957). 

The structure of carbon nanotubes depends upon the orientation of the hexagons in the cylinder with respect to the tubule axis. The limiting orientations are zigzag and arm chair forms, Fig. 8B. In between there are a number of chiral forms in which the carbon hexagons are oriented along a screw axis, Fig. 8B. The formal topology of these nanotube structures has been described [89]. Carbon nanotubes have attracted a lot of interest because they are essentially onedimensional periodic structures with electronic properties (metallic or semiconducting) that depend upon their diameter and chirality [90,91]. (Note. After this section was written a book devoted to carbon nanotubes has been published [92], see also [58].)... 

Bandaru PR (2007) Electrical properties and applications of carbon nanotube structures. JNanosci Nanotechnol 7 1239-1267. 

When the graphene sheet is rolled up forming a nanotube, the two ends of the chiral vector meet one another. The chiral vector thus forms the circumference of the CNTs circular cross-section. Different values of n and m give different nanotube structures with different diameters (Figure 12.9). 

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