Modulated Force Thermomechanometry

 

Modulated force thermomechanometry (or its alternative term dynamic mechanical analysis) involves the measurement of the effect of temperature on a sample that is subject to a sinusoidal applied force. If the sample is allowed to continue vibrating after the applied sinusoidal thrust is removed, the response of the sample will be a damped form of the applied sinusoidal force.

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Figure 19. The Basic Modulated Force Thermomechanometry Apparatus

 

The damping effect will introduce a phase difference between the original applied sinusoidal force and the sinusoidal response by the sample. From the phase difference and other factors the sample heat dissipation capacity can be calculated. From the same data an indication as to the ’so-called’ stiffness of the sample can also be determined. The basic apparatus is depicted in figure 19,

 

The sample, which may be in the form of a wire or a strip, is attached to a rigid frame at one end or side and the other end or side to a connecting rod (using securing bars) and thence to a magnetic transducer. The other end of the transducer rod is connected to a sinusoidal thrust driver, which is also connected to the supporting frame. The sample is situated in an oven so the sample temperature can be selected or programmed as desired.

 

If at a given temperature the frequency of the thrust driver is programmed the resonant frequency will be identified as a maximum in the curve relating the amplitude of the sinusoidal waveform to the frequency of the applied oscillation.

 

Young’s Modulus is given by the following equation,

 

 

                  where (l) is a sample length (between the securing bars)

                            (d) is the sample thickness

                            (r) is the sample density

                            (n) is the Resonance frequency

                     and (c) is a constant

 

If the sample is allowed to oscillate without thrust then it will do so at the resonance frequency with decreasing amplitude as shown in figure 20.

 

 

Figure 20. A Damped Sinusoidal Waveform

 

The damping of the sinusoidal wave is given by,

 

 

            where (a₁), (a₂), (a₃) and (a₄) have the meanings defined in figure 20.

 

An example of the results obtained from the examination of an alkane polymer is shown in figure 21.

 

Figure 21. Frequency and Damping Curves Obtained for an Alkane Polymer

 

The two curves clearly show two separate phase transitions taking place at two distinct temperatures. Such data allows the physical performance of the plastic to be predicted with changes in environmental temperature.