Figure 7. Loss factor of the catalytically-grown multi-walled carbon
nanotube-reinforced epoxy composite at different temperatures.
The effect of temperature on the loss modulus is illustrated in Figure 8
for the catalytically-grown multi-walled carbon nanotube-reinforced
epoxy composite. Virtually all synthetic materials in existence are
viscoelastic, namely their behavior under mechanical stress lies
somewhere between that of a purely viscous liquid and that of a
perfectly elastic spring. Few materials behave like a perfect spring or
a pure liquid. Rather, the mechanical behavior of these materials is
generally time and temperature dependent and has led to such tests as
creep, stress relaxation, tear, and impact resistance. One of the more
important properties of materials sought is the materials' behavior
under dynamic conditions. To explore this, a material's response to a
cyclical stress as a function of temperature, time or frequency is
determined. If the viscoelastic solid is deformed and then released, a
portion of the stored deformation energy will be returned at a rate
which is a fundamental property of the material. That is, the
catalytically-grown multi-walled carbon nanotube-reinforced epoxy
composite goes into damped oscillation. A portion of the deformation
energy is dissipated in other forms. The greater the dissipation, the
faster the oscillation dies away. If the dissipated energy is restored,
the catalytically-grown multi-walled carbon nanotube-reinforced epoxy
composite will vibrate at its natural frequency. The resonant frequency
is related to the modulus of the catalytically-grown multi-walled carbon
nanotube-reinforced epoxy composite. Energy dissipation relates to such
properties as impact resistance, brittleness, and noise abatement.
Because of their viscoelastic nature, the stress and strain in
viscoelastic materials are not in phase, and, in fact, exhibit
hysteresis. If a plot is made of this relationship, the area enclosed by
the plot corresponds to the energy dissipated during each cycle of
deformation of the material. In order to accurately describe this
phenomenon, a complex modulus is often used to characterize the
material. The real part of the modulus corresponds to the amount of
energy that is stored in the strain and can be related to the spring
constant, the complex part corresponds to the energy dissipation or loss
and can be related to the damping coefficient used in second order
differential equations to define vibrating systems. All of these systems
place the catalytically-grown multi-walled carbon nanotube-reinforced
epoxy composite under test into vibration or oscillation utilizing
mechanical systems. These mechanical systems vibrate at a resonant
frequency determined primarily by the catalytically-grown multi-walled
carbon nanotube-reinforced epoxy composite. A drive transducer is used
to maintain the system in oscillation, a displacement transducer is used
to sense the displacement of the mechanical system, and a drive
amplifier is used to energize the drive transducer sufficiently to
maintain the system oscillating at resonance at a constant amplitude.
While many of these systems attempt to measure the elastic modulus, the
loss modulus is typically measured only on a relative basis by sensing
the power input to the system that is required to maintain a constant
oscillation amplitude. Unfortunately, this does not provide a calibrated
result in commonly accepted units. Other methods of determining the loss
modulus are by obtaining the logarithmic decrement by free decay of the
system. Unfortunately, this requires substantial additional
instrumentation. Another method of determining loss modulus is to use
the second order relationship that exists between oscillation frequency
and amplitude. This approach, while satisfactory, does not always
provide the results of the quality that might be desired.