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.