Chemistry Reference
In-Depth Information
Generally this method favors the growth of MWCNTs; however, Bai et al.
described specific conditions (810
C using Ar as inert gas) to promote the electro-
lytic conversion of graphite to SWCNTs [
28
].
Clear advantages of this approach are the use of mild reaction conditions, the
cheap materials employed, and the low consumption of energy.
3 Properties
3.1 Electronic Properties
As previously explained, carbon nanotubes can be thought of as a graphene sheet
which has been rolled up to form a cylinder. Their structure is mathematically
described by the chiral vector
C
h
, which expresses their circumferential periodicity,
together with the translation vector
T
, which is along the nanotube axis. In this way,
C
h
and
T
defines a one-dimensional rectangle of unrolled tube, represented by the
shaded areas in Fig.
7
.
Each possible wrapping of graphene into the tubular form could be predicted
knowing the values of the n,m integers, which are in turn connected to the a
1
and a
2
basic graphite vectors,
C
h
¼
ma
2
.
For instance, in Fig.
7a
, a (3,4) nanotube is under construction. The
corresponding final wrapping identifies a “chiral” tube, since
m
na
1
þ
6¼
n
. In turn, the
resulting tube will be “armchair” when
m
¼
n
and “zigzag” when
m
¼
0, as
described in Fig.
7b, c
.
The same differentiation into three classes is achievable knowing the chiral
angle
tan
1
[
θ ¼
3(
n
/(2
m
+
n
))] (
¼
30
for armchair,
¼
0
for zigzag, 0
<
√
θ <
30
for chiral nanotubes).
The theoretical categorization of nanotubes on the basis of the geometric
structure is of fundamental importance for the prediction of their electronic
properties [
6
]. Although graphene is a zero-gap semiconductor (Fig.
8
), carbon
nanotubes can be metals or semiconductors, depending on the helicity and
diameter.
To understand why, we should consider that in an isolated sheet of graphite two
energetic bands with linear dispersion (
*) meet at the Fermi level, generating
a K point in the Brillouin zone. Hereby, the whole Brillouin region is delimited by a
determined set of K,
ˀ
and
ˀ
, and M points, while the Fermi surface of an ideal graphite
layer consists of the six corner points K (Fig.
9
).
When forming a tube, only a certain set of states of the planar graphite sheet is
allowed, that may not include the K points. Whenever the K point is comprised into
the Brillouin area, the nanotubes are metallic (semimetals with zero band gap);
otherwise they are semimetals with tiny band gaps when (
n
ʓ
m
) is a multiple of 3, or
semiconductors with large gaps in all the other cases.
