Carbon Nanotube-Based Sensor Platform for Bioelectronic Nose - Bioelectronic Nose: Integration of Biotechnology and Nanotechnology - page 217

Fig. 12.1 Honeycomb lattice
of carbon atoms in graphene.
A graphene piece with differ-
ent direction was rolled up to
form a CNT

materials. Such atomic structures can be specified by a vector which corresponds to
the section of the SWCNT perpendicular to the tube axis. As shown in Fig. 12.1 , the
translational vector T is the direction of a nanotube axis. The C h is a chiral vector
which can be specified by the pair of integers ( n , m ), and the a 1 and a 2 represent
each unit vectors. Then, the chiral vector can be written like

(12.1)

C

= + ≡ n a m a ( , nm ), ( , nm are integer, 0 ≤≤ m n )

1 2

The chiral angle θ is defined by taking the inner product of C h and a 1 , yielding an
expression for cos θ ,

� �

Ca · 2 nm +

(12.2)

h 1

cos θ = = �

�

Ca -

2 2

2 n ++ m nm h 1

In particular, if n equals to m in the chiral vector C h ( θ = 30°), the tube is called an
armchair tube. If m equals to zero ( θ = 0°), then we call the tube a zigzag tube. For
all other configurations, the tubes are known as chiral tubes (Fig. 12.1 ).
The electrical properties of SWCNTs can be predicted by periodic boundary
conditions from the chiral vector C h . Briefly, if n − m is the integer multiple of
three, then the SWCNT has metallic properties else it possesses semiconducting
properties [ 1 ]. The electrical properties of the SWCNTs can also be predicted by the
atomic structures of the SWCNTs. For example, the armchair SWCNTs always ex-
hibit metallic properties, whereas zigzag and chiral SWCNTs exhibit either metallic
or semiconducting properties [ 1 ].
Due to the versatile electrical properties of CNTs, they exhibit many interesting
phenomena such as a single electron tunneling, a spin-polarized electron transport,