Page 110 - Nanotechnology an introduction

some graphene.
9.2. Carbon Nanotubes

The synthesis and characterization of carbon nanotubes were first reported in the scientific literature by Iijima in 1991. Since then they have been
intensively studied both theoretically and experimentally. Great advances in fabrication techniques have been made, and nowadays it is possible to
produce high-quality carbon nanotubes in reasonable quantities at least for research purposes.
It was long known that carbon filaments are formed by passing hydrocarbons over hot metal surfaces, especially iron and nickel. The actual nature
of carbon nanotubes was however only established relatively recently (by Iijima in 1991): they are seamlessly rolled up tubes of graphene (Figure
9.2). The ends of the tubes may be open or “capped” with what is essentially a hemisphere of fullerene. Multiwalled carbon nanotubes (MWCNT)
most typically consist of several concentric tubes of graphene nested inside each other (Figure 9.3). A form in which graphene is rolled up to give a
spiral cross-section is also known.

Figure 9.2 A single walled carbon nanotube (SWCNT): a single graphene layer rolled into a seamless tube. Reproduced with permission from [24].

Figure 9.3 A multiwalled carbon nanotube (MWCNT): concentric single wall nanotubes of different diameters nested within each other. Reproduced with permission from [24].
An important feature of single walled carbon nanotubes (SWCNT) is the chiral (or wrapping or rollup) vector C , defined as
χ

(9.1)
where the unit vectors a and a have, respectively, the directions from the ith to the i + 2th carbon on any hexagon, and from the ith to the i + 4th
2
1
carbon; nm, where a C−C is the nearest-neighbor distance between two carbon atoms, and thus the magnitude of C is
χ
0.246 ; n and m are integers with m ≤ n. The chiral vector connects crystallographically equivalent sites on the graphene lattice; n
(≥ 3) (“twist”) and 0 ≤ m ≤ n (“countertwist”) are the integers required to ensure translational symmetry of the lattice. C defines the disposition of the
χ
hexagonal rings of the carbon nanotube or in other words describes how the graphene sheet is wrapped. If n = m the SWCNT is called armchair; if
m = 0 then the SWCNT is called zig-zag; otherwise it is simply called chiral. The diameter in nanometers is given by

(9.2)
the chirality by

(9.3)
and the chiral angle is

(9.4)

The ratio a /a provides a measure of helicity; it can range from zero (zig-zag) to 1 (armchair). The chirality ranges from zero (for zigzag and
2 1
armchair nanotubes) to 1 if a /a = 0.5. The corresponding chiral angles are 0 for armchair and 30° for zigzag.
2 1
The distance between the walls in multiwalled carbon nanotubes is about 0.34 nm, similar to the distance between graphene layers in graphite.

Single walled carbon nanotubes change their electrical properties depending on C . If n = m, then the nanotube is metallic and can bear an
k