10.2 Carbon Nanotubes 235
cations. In particular, as it is possible to produce quite long imogolite fibers with
diameters that are adjustable in a wide range, such products may have a great
future in technological applications.
10.2
Carbon Nanotubes
As already explained in Chapter 5, depending on their chirality, some types of
carbon nanotubes show metallic electric conductivity. As long as the length is
limited, this is ballistic conductivity, as was demonstrated experimentally and
depicted in Figure 10.5. Interestingly, multiwalled carbon nanotubes [2] and single
layers of graphene [5] show a similar voltage dependency of the electric conductivity. In both cases, it was found experimentally that, above 100 mV, the conductivity
increases with increasing voltage. For voltages below ca. 100 mV, the conductance
is G 0 .
G G
V
G G
V
V
=
≤
=
+
(
)
>
0
0
0 1
0 1
.
.
.
V
V
α β
(10.5)
The quantities α and β are specimen-dependent factors ranging from 0.25 up to
maximal 1.0. According to Eq. (10.5), a graph of the conductance is symmetric
against V = 0 V. Such a graph for multiwalled carbon nanotubes is depicted in
Figure 10.8. Because of unavoidable contact resistance, the constant contribution
to conductance is smaller than G 0 . Furthermore, because of the thermal excitation
observed at temperatures significantly above 0 K, the theoretically expected steps
of the electrical conductivity (see Figure 10.3) are not observed.
Figure 10.8 Electric conductivity of multiwall
nanotubes [2]. For voltages above ca.
100 mV, the electric conductivity follows Eq.
(10.5). Below that limit, the conductivity is
constant. Single graphene layers show a
similar behavior [5]. Because of unavoidable
contact resistance, the minimum value of the
conductivity is less than 1 G 0 .
–4
–2
0
2
4
voltage [V]
0
0.25
0.5
0.75
1
1.25
1.5
conductivity
[G 0
]
cations. In particular, as it is possible to produce quite long imogolite fibers with
diameters that are adjustable in a wide range, such products may have a great
future in technological applications.
10.2
Carbon Nanotubes
As already explained in Chapter 5, depending on their chirality, some types of
carbon nanotubes show metallic electric conductivity. As long as the length is
limited, this is ballistic conductivity, as was demonstrated experimentally and
depicted in Figure 10.5. Interestingly, multiwalled carbon nanotubes [2] and single
layers of graphene [5] show a similar voltage dependency of the electric conductivity. In both cases, it was found experimentally that, above 100 mV, the conductivity
increases with increasing voltage. For voltages below ca. 100 mV, the conductance
is G 0 .
G G
V
G G
V
V
=
≤
=
+
(
)
>
0
0
0 1
0 1
.
.
.
V
V
α β
(10.5)
The quantities α and β are specimen-dependent factors ranging from 0.25 up to
maximal 1.0. According to Eq. (10.5), a graph of the conductance is symmetric
against V = 0 V. Such a graph for multiwalled carbon nanotubes is depicted in
Figure 10.8. Because of unavoidable contact resistance, the constant contribution
to conductance is smaller than G 0 . Furthermore, because of the thermal excitation
observed at temperatures significantly above 0 K, the theoretically expected steps
of the electrical conductivity (see Figure 10.3) are not observed.
Figure 10.8 Electric conductivity of multiwall
nanotubes [2]. For voltages above ca.
100 mV, the electric conductivity follows Eq.
(10.5). Below that limit, the conductivity is
constant. Single graphene layers show a
similar behavior [5]. Because of unavoidable
contact resistance, the minimum value of the
conductivity is less than 1 G 0 .
–4
–2
0
2
4
voltage [V]
0
0.25
0.5
0.75
1
1.25
1.5
conductivity
[G 0
]