Introduction to Polymer Science and Technology

Thermal properties

(to lower frequencies), while those above will be shifted to the right (to higher frequencies) to bring them to lie on the progressively forming master curve. During the shifting, the computer stores the shift factors, a_r After all of the individual data points are shifted, the complete master curve is formed as shown in Figure 7.14.

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Log [frequency(Hz)]

Figure 7.14Master curve of loss modulus (E") vs. frequency at reference temperature of 145 °Cfor PC (source: ТА lnstruments-1)

This curve shows the variation of the loss modulus with frequency over a wide frequency range (8 orders of magnitude), whereas the tests were only conducted over 10~² to 10° frequency range. The maximum energy dissipation occurs at a frequency of 0.31 Hz at 145°C, represented by the peak maximum.

The experimental shift factors are plotted against the temperature as in Figure 7.15, and the data was fitted with WLF predictions, shown by the solid line, the WLF constants of C_l = 22.9 and C₂ = 78.8 produce the best fit. Once the WLF constants are determined the equation can be used to predict material response at other than the reference temperature: the master curve can be transposed to any desired/service temperature by applying the model and, therefore establishing the frequency at which the maximum energy dissipation occurs at the given temperature. It is recommended, though, that the master curve be shifted only to temperatures in the range in which the data was collected.

Introduction to Polymer Science and Technology

Thermal properties

A master curve for any of the other dynamic mechanical properties can be constructed; Figure 7.16 displays the master curve generated from the storage modulus data for polycarbonate. It shows the effects of frequency on the modulus of PC at 145 °C, the reference temperature. At very low frequencies (or long times) the material exhibits a low modulus and behaves similar to a rubber. At high frequencies (or short times) the PC behaves like an elastic solid and has a high modulus. This master curve again demonstrates that data collected over only two decades of frequency can be superimposed to cover eight decades.

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Log [frequency (Hz)]

Figure 7.16Master curve for the storage modulus (E') vs. frequency at of 145 °Cfor PC (source: ТА lnstruments-1)

Introduction to Polymer Science and Technology Thermal properties

Master Curves can be generated for other viscoelastic properties, e.g. stress relaxation and creep, as well as the dynamic mechanical properties measured at fixed frequencies.

7.4.1.3 Establishment of service temperature limits

DMTA provides very useful information that can help users to decide the suitability of a polymeric material for applications, particularly with respect to prevailing temperatures. An example of this is given in the PerkinElmer application notes for polyurethane foam tested under compression at 1 Hz from -80 °C to 100 °C at a heating rate of 5 °C/min.

Polyurethane foam is used for various applications, such as packaging, footwear, furnishings, that require impact absorption properties. In order to absorb energy, it is important that the foam is in its rubbery state. In glassy state, the material will be rigid and very friable due to the large proportion of void space in the structure. It is therefore important to accurately determine the T . Figure 7.17 shows the tan 8 and modulus response from the polyurethane sample. The T is at approximately -40 °C, where the desirable rubbery properties change significantly: as temperature falls the elastic modulus increases from less than 1 MPa to above 100 MPa. This material will require a low modulus to operate effectively

Date: 2015-12-11; view: 846