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Fig. 10 (a) Molecular model of a spiral SWCNT, obtained by insertion of pentagons and
heptagons within the hexagonal network. (b) +30 pentagon declination and
30 heptagon
inclination results in different local curvatures. Reprinted with permission from [ 37 ]
In summary, ( n , n ) armchair tubes are always metallic, ( n , m ) chiral and ( n ,0) zig-
zag tubes in which ( n
m ) is a multiple of 3 are semimetals displaying metallic
behavior, while chiral and zig-zag tubes where ( n
m ) is not a multiple of 3 are
always semiconductors.
Besides the helicity, the diameter also affects the electronic behavior of
CNTs [ 30 ]. It has been shown that as the tube radius ( R ) increases, semiconductors
and semimetal band gaps decrease with a 1/ R and 1/ R 2 dependence, respectively
[ 31 , 32 ].
Ultra-small-diameter SWCNTs have been found to exhibit superconductivity
properties after confinement inside inert porous AlPO 4 5 zeolite crystals (with
inner diameter of 0.73 nm), as a demonstration of the relationship between diameter
and electronic behavior of the tubes [ 33 ].
Another remarkable research investigation performed by Odom et al. in 1998,
permitted resolution by scanning tunneling microscopy (STM) of the hexagonal-
ring structure of the walls, revealing for the first time the explicit relationship
between the structure and the electronic properties. The local density obtained
from conductance measurements and the theoretical predictions was indeed found
to be in very good agreement [ 34 ].
Several studies have also confirmed that CNTs are not as perfect as they were
supposed to be. Different geometries like squares, pentagons, heptagons, and many
more spangle the honeycomb network, modifying drastically the electronic
properties of the whole structure. As a consequence, the explicit introduction of
defects (not necessarily non-hexagonal rings, but also vacancies or doping agents)
into the walls could be an interesting way to tailor the intrinsic properties of CNTs.
It has been shown that the pentagon-heptagon pair (Fig. 10 ) is the smallest
topological defect inducing minimal local curvature and preventing at the same
time the tube from collapsing or closing. Its incorporation within the hexagonal
network of a single carbon nanotube changes its helicity, and therefore the energy
gap between the electronic bands, providing the basis for the development of new
diodes for nano-electronics [ 35 , 36 ].
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