Biomedical Engineering Reference
In-Depth Information
C
na
ma
(9.1)
1
2
where
the unit cell vectors of
two-dimensional lattice formed by the graphene sheets.
The angle between the chiral vector and zigzag nanotube axis is
the chiral angle
n
and
m
are integers; while
a
and
a
1
2
θ
(Fig. 9.2). It is defined as follows:
1
tan [( 3)/( 2 )]
q
m
m
n
.
(9.2)
) which
is related to the chiral vector. Three types of CNTs are revealed with
these values:
•
Nanotubes are only described by the pair of integers (
n, m
θ
= 0°
when
n = m
, the nanotube is called
armchair
(
);
•
θ
= 30°
when
m = 0
, then it is called
zigzag
(
);
• when
n
≠
m
, it is a
chiral
tube (0° <
θ
< 30°
).
Figure 9.2
Carbon nanotubes are made by rolling a graphene sheet into
a cylinder. The tubes are uniquely determined by their lattice
vector
C
h
, which is constructed from basis set
a
and
a
, as
1
2
q
shown in the top-frame. The chiral angle is denoted by
, while
a
denote the unit vectors of graphite. The bottom frame
shows possible vectors for nanotubes with different chiralities.
The larger and smaller dots denote, respectively, metallic and
semiconducting behavior for each nanotube. Reprinted with
permission from AIP [44].
and
a
1
2
