14.3 Carbon Nanotubes
409
Fig. 14.15 Schematic
atomic arrangement in
graphene; the C–C bond
length is d C−C = 0.142 nm.
Several vectors for making
carbon nanotubes (cf.
Sect. 14.3) are shown
Fig. 14.16 Structure of
different types of carbon
nanotubes that have
similiar diameter of 0.8 nm.
a Armchair (6, 6), b zigzag
(8, 0) and c chiral
symmetry. Adapted
from [1247]
c h = n 1 a 1 + n 2 a 2 ≡ (n 1 , n 2 ) ,
(14.1)
where a 1 and a 2 are the unit vectors of the graphene sheet. The chiral vector denotes two crystallographic
equivalent sites which are brought together along the circumference of the nanotube. The possible
vectors are visualized in Fig. 14.15 for −30
◦
≤ θ ≤ 0
◦ . The fiber diameter is given by
d =
|c h |
π
=
a
π
n
2
1 + n 1 n 2 + n
2
2
,
(14.2)
with the graphene lattice constant a =
√
3 d C−C = 0.246 nm. Ab-initio calculations show that the
diameter becomes a function of the chiral angle below 0.8 nm; deviations from (14.2) are below 2%
for tube diameters d > 0.5 nm [1366]. The (n, 0) tubes (θ = 0) are termed ‘zig-zag’ and an example
is depicted in Fig. 14.16b. Nanotubes with θ = ±π/6, i.e. of the (n, n) (and (2n, −n)) type, are called
‘armchair’. All others are termed ‘chiral’.
The extension along the wire axis is large compared to the diameter. The tip of a nanotube is part of
a buckminster-fullerene type molecule (Fig. 14.17). When the nanotube if formed by rolling a single
sheet of graphene (SLG), a single-walled nanotube (SWNT) is formed. A FLG sheet creates a multiwalled nanotube (MWNT). For small number of layers they are called double-walled, triple-walled
and so forth.
409
Fig. 14.15 Schematic
atomic arrangement in
graphene; the C–C bond
length is d C−C = 0.142 nm.
Several vectors for making
carbon nanotubes (cf.
Sect. 14.3) are shown
Fig. 14.16 Structure of
different types of carbon
nanotubes that have
similiar diameter of 0.8 nm.
a Armchair (6, 6), b zigzag
(8, 0) and c chiral
symmetry. Adapted
from [1247]
c h = n 1 a 1 + n 2 a 2 ≡ (n 1 , n 2 ) ,
(14.1)
where a 1 and a 2 are the unit vectors of the graphene sheet. The chiral vector denotes two crystallographic
equivalent sites which are brought together along the circumference of the nanotube. The possible
vectors are visualized in Fig. 14.15 for −30
◦
≤ θ ≤ 0
◦ . The fiber diameter is given by
d =
|c h |
π
=
a
π
n
2
1 + n 1 n 2 + n
2
2
,
(14.2)
with the graphene lattice constant a =
√
3 d C−C = 0.246 nm. Ab-initio calculations show that the
diameter becomes a function of the chiral angle below 0.8 nm; deviations from (14.2) are below 2%
for tube diameters d > 0.5 nm [1366]. The (n, 0) tubes (θ = 0) are termed ‘zig-zag’ and an example
is depicted in Fig. 14.16b. Nanotubes with θ = ±π/6, i.e. of the (n, n) (and (2n, −n)) type, are called
‘armchair’. All others are termed ‘chiral’.
The extension along the wire axis is large compared to the diameter. The tip of a nanotube is part of
a buckminster-fullerene type molecule (Fig. 14.17). When the nanotube if formed by rolling a single
sheet of graphene (SLG), a single-walled nanotube (SWNT) is formed. A FLG sheet creates a multiwalled nanotube (MWNT). For small number of layers they are called double-walled, triple-walled
and so forth.