Chemistry Reference
In-Depth Information
3.2 Mechanical Properties
Carbon nanotubes are expected to have high axial strength as a result of the sp
2
carbon-carbon chemical bond of the rolled up graphene layer, which is one of the
strongest bonds known in nature for an extended system.
A great number of theoretical and experimental studies has been dedicated to the
investigation of mechanical properties of carbon nanotubes with the aim to develop
novel reinforced and stiff materials.
The mechanical properties of a material are described by the definition of its
Young's modulus (or tensile modulus) along a given direction, which is expressed
in Pascal (Pa) and defined as
2
E
@ε
1
V
eq
@
Y
¼
(1)
2
ε¼
0
where
E
is the total energy of the system,
V
eq
is the volume at the equilibrium, and
ε
is the strain. The Young's modulus defined for carbon nanotubes will be
2
E
@ε
1
S
eq
@
Y
¼
(2)
2
ε¼
0
where
S
eq
is the nanotube surface area at zero strain that is determined
unambiguously. A frequently applied convention is that
V
eq
¼
S
eq
h
, with
h
0.34 nm (the interlayer spacing in graphite).
In other words, the tensile modulus is a measure of the stiffness of a material,
expressed by dividing the tensile stress exerted over an object under tension by the
tensile strain, which in turn is defined as the amount by which the dimension of the
object changes because of the stress. In the light of this, materials such as rubber or
polystyrene present pretty low Young's modulus (0.1 and 3 GPa, respectively),
while graphene's and diamond's tensile modulus lie in the region of 1,000 GPa.
The elasticity of a body is directly related to the chemical bonding of
its constituent atoms, the reason why we expected CNTs' Young's modulus to
equalize that of graphene when the diameter is not too small to distort the C-C bond
significantly.
Much effort has been made towards the exact determination of the tensile
modulus of nanotubes. The first attempt to achieve a reliable value for MWCNTs
was reported in 1996 by Treacy et al., who measured the oscillation amplitude of
the intrinsic thermal vibrations of an MWCNTs' series by means of a TEM. They
found very high Young's moduli, with a mean value of 1.8 TPa [
38
].
Two years later the same team reported a subsequent study based on the same
experimental approach, but employing a larger sample of nanotubes. This time a
mean value of 1.25 TPa was achieved, which is in better agreement with the C
11
graphite basal plane tensile modulus [
39
].
¼
