Carbon Nanotube Reinforced Composites: Metal and Ceramic ...

4j 1 Introduction
Figure 1.3 Schematic diagram showing chiral vector and chiral
angle in a rolled graphite sheet with a periodic hexagonal
structure. Reproduced with permission from [15]. Copyright Ó
(2001) Elsevier.
where~a 1 and~a 2 are unit vectors in a two-dimensional hexagonal lattice, and n and m
are integers. Thus, the structure of any nanotube can be expressed by the two integers
n, m and chiral angle, q (Figure 1.3). When n ¼ m and q ¼ 30 , an armchair structure
is produced. Zig-zag nanotubes can be formed when m or n ¼ 0 and q ¼ 0 while
chiral nanotubes are formed for any other values of n and m, having q between 0 and
30 [15]. Mathematically, the nanotube diameter can be written as [16]:
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a m
d ¼ 2 þ n2 p
þ nm
ð1:2Þ
p
where a is the lattice constant in the graphene sheet, and a ¼ ffiffi p
3aC-C;
aC-C is the
carbon–carbon distance (1.421 A). The chiral angle, q, is given by:
pffiffiffi 3m
tan q ¼
ð1:3Þ
2n þ m
The electrical properties of CNTs vary from metallic to semiconducting, depending
on the chirality and diameter of the nanotubes.
The demand for inexpensive carbon-based reinforcement materials is raising
new challenges for materials scientists, chemists and physicists. In the past decade,
vapor grown carbon nanofibers (VGCFs) with diameters ranging from 50 to 200 nm
have been synthesized [17]. They are less crystalline with a stacked cone or cup
structure, while maintaining acceptable mechanical and physical properties. Compared
with SWNTs and MWNTs, VGCFs are available at a much lower cost because
they can be mass-produced catalytically using gaseous hydrocarbons under relatively
controlled conditions. VGCFs have large potential to override the cost barrier that has
prevented widespread application of CNTs as reinforcing materials in industries.