Modulus-temperature data

Other penetrometer-indentometers include transducers to sense the position and movement of the probe and microprocessors for temperature control and data collection and reduction. These instruments are used mainly to measure softening points, which are not glass transitions but are usually close to those values. Because a softening point is indicative of behavior under load, it is often more useful for predicting performance than the Tg. Penetrometer-indentometers can also be used to measure indentation hardness, creep, creep recovery, and modulus. Examples of such instruments include the TA Instruments, Mettler, Perkin-Elmer, Seiko, and Shimadzu thermomechanical analyzers (TMAs). They can be used to generate modulus and modulus-temperature data from indentation-time plots by applying the Hertz equation (eq. 36) (170,296), where E is the elastic or Young s modulus, jx the Poisson s ratio, r the radius of the hemispherical indentor, P the force on the indentor (mass load x g), h the indentation, and ifk the indentation hardness. 

Crystal crystal transitions sometimes can appear on the DMA curves. Figure 5.37 shows the storage modulus-temperature data for an as-spun monofilament and a drawn monofilament prepared frompoly(2-methylpenta-... 

Two very important temperatures are indicated in Fig. 3.15 and are the melt temperature (or first order transition temperature), T j and the glass transition (or second order transition temperature) Tg. The T and Tg can only be determined approximately from isochronous modulus-temperature data similar to that given in Fig. 3.15. Often, manufacturers specification... 

We wish to acknowledge discussions with and the assistance of Drs. N. J. McCarthy and 0. Olabisi in respectively supplying the samples of phenolic dispersion and the modulus-temperature data. 

This is very useful for generating modulus versus temperature data on rubber compounds. The effects of temperature on this important material property can be obtained over a wide temperature range (typically -150 to +200 °C), along with the glass transition temperature and information on thermal stability. 

For the PVN-PEO polyblends, volume changes at melting temperature (Figure 6) as well as x-ray data at room temperature (2) show that the 25% (PEO) blend is completely amorphous, and that the 50 and 75% blends contain significant amounts of amorphous PEO. Calculations based on specific volume data indicate that the crystalline part of both the 50 and 75% blends consists of PEO, whereas the amorphous part contains 46% PEO and 54% PVN. Another important result is that the unusual phenomenon of a well in the modulus temperature curves (Figure 1) was observed only for the blends which exhibit crystallinity. Based on these observations, the behavior of blends could be interpreted by postulating that the amorphous PEO forms a complex phase with PVN in the ratio of 3 to 1 monomer units (i.e., 46 wt. % PEO to 54 wt. % PVN), respectively. 

To apply Equation 1, the model parameters A and 0 have to be determined. They are derived from the calculated modulus-temperature curves which best fit the experimental data of Figure 4. To perform these calculations, one of the components has to be taken as the continuous phase. For the 75/25 and 50/50 blends, PC was taken as the continuous phase while for the 25/75 blend, PST was taken as this phase. This choice is based on the morphological study and the mechanical behavior reported earlier. The A and 0 values used to fit the data are reported in Table II. A fairly good agreement is found in the temperature range between 95° and 140°C. 

Viscoelastic data are commonly represented in the form of a master curve which allows the extrapolation of the data over broad temperature and frequency ranges. Master curves have, historically been presented as either storage modulus and loss modulus (or loss tangent) vs. reduced frequency. This representation requires a table of conversions to obtain meaningful frequency or temperature data. 

Figure 4. Values of lossy modulus, E". Data from references 1, 5, and 8. The data for PEMA was obtained from 3G" at 1 Hz and converted to 110 Hz. The PEMA homopolymer is seen to have a very high E" value over a broad temperature range brought about by the strong secondary transition. With no common comonomer the loss peaks and also tan S peaks (Figure 5) of the IPN s tend to be bimodal.

The glass transition temperature, T, was also determined for some of the test materials. Values given in this paper are somewhat higher than reported literature values as they were obtained from the temperature location of the principal maximum in the loss modulus vs. temperature data from tests made at 3 Hz. 

The data for the modulus-temperature curve are most often gathered in the dynamic mode at a fixed frequency of around 1 rad/s, either in shear or flex, depending on the stiffness range of the test material over the desired temperature range. See Appendix 3 of Chapter 2. 

Assuming that the WLF equation does indeed describe the time-temperature shifts, the complete viscoelastic response of any polymer under any experimental conditions may be obtained from knowledge of any two of the following three functions the master curve at any temperature, the modulus-temperature curve at any time, and the shift factors relative to some reference temperature. For example, suppose we are given the constants Cj, and C2 for a polymer whose master curve is known. (The values given for C, and C2 are those that result from fitting equation (4-6) to the aT vs. T data.5) For simplicity, we can assume that the master curve is at the same reference temperature as that in the WLF equation, perhaps Tg. Suppose it is desired to calculate the 10-second modulus-versus-temperature curve for this polymer. 

Computer) The Figure 4-2 data for amorphous polycarbonate is listed in file PC 4 OkDa. TXT in the CD. As explained in the footnote of Figure 4-2, these data are actually 1/7(10 s). Using the WLF constants for polycarbonate of C, = 16.4 and C2 = 54.3, with Tg = 150.8 °C, correct these data using the approximation of Problem 2-5. Plot on the same graph the modulus-temperature curves based on your G(10 s) and the original 1/7(10 s), and comment on the differences. 

The Young s modulus vs. temperature data plotted in Figures 1 and 2 were obtained on a special apparatus (5). 

Fortunately for linear amorphous polymers, modulus is a function of time and temperature only (not of load history). Modulus-time and modulus-temperature curves for these polymers have identieal shapes they show the same regions of viscoelastic behavior, and in each region the modulus values vary only within an order of magnitude. Thus, it is reasonable to assume from such similarity in behavior that time and temperature have an equivalent effect on modulus. Such indeed has been found to be the case. Viscoelastic properties of linear amorphous polymers show time-temperature equivalence. This constitutes the basis for the time-temperature superposition principle. The equivalence of time and temperature permits the extrapolation of short-term test data to several decades of time by carrying out experiments at different temperatures. 

The aforesaid extrapolations make use of a time-temperature superposition principle which is based on the fact that time and temperature have essentially equivalent effects on the modulus values of amorphous polymers. Figure 3.19 shows modulus data taken at several temperatures for poly(methyl methacrylate) [8]. Because of the equivalent effect of time and temperature, data at different... 

Figure 3.24 shows some typical experimental data. It is seen that Tg is easily identifiable as a peak in the tan (5 or the loss modulus trace. These maxima do not coincide exactly. The maximum in tan d is at a higher temperature than that in G" (o), because tan 6 is the ratio of G (w) and G (oj) (see Equation 3.96) and both these moduli are changing in the transition region. At low frequencies (about 1 Hz) the peak in tan (5 is about 5°C higher than Tg from static measurements or the maximum in the loss modulus-temperature curve. 

Radiation damage effects are likely to be of prime importance in organic matrix composites. Screening measurements to assess the severity of the problem are needed. For most of these materials, there is no low-temperature data base. Specifications for industrial laminates (NEMA/ASTM) are generally electrical in nature, and mechanical specifications may be necessary additions for low-temperature applications. Very few 4 K data exist for the advanced (high-modulus) composites and specialty fiberglass composites, which may be needed for low-temperature structural applications near pulsed coils. 

Thus far four composites listed in Table I have been studied. NbTi/Cu is discussed briefly here. From its microstructure and manufacture, a rectangular cross-section bar, it was assumed that this composite has orthorhombic (orthotropic) symmetry in its physical properties. Materials with this symmetry have nine independent elastic constants. While deviations from elastic behavior were small, nine independent elastic constants were verified. Four specimens were prepared (Fig. 16) and 18 ultrasonic wave velocities were determined by propagating differently polarized waves in six directions, (100) and (110). An example cooling run is shown in Fig. 17 for E33, Young s modulus along the filament axis. These data typify the composites studies a wavy, irregular modulus/temperature curve. 

Fig. 3. Isochronous modulus-strain data for specimens cut at various angles, 6, to the fibre axis of cold-drawn LDPE, draw ratio 4-2. In all diagrams, except where explicitly stated otherwise, test temperature was 20 C. (After Darlington and...

Both the modulus-temperature relationships presented in the preceding sections and the tensile data presented above are strikingly similar to those demonstrated for other rubber-plastic combinations, such as the thermoplastic elastomers (see Chapter 4 and the model system presented in Section 10.13) and the impact-resistant plastics (Chapter 3). The IPN s constitute another example of the simple requirement of needing only a hard or plastic phase sufficiently finely dispersed in an elastomer to yield significant reinforcement. Direct covalent chemical bonds between the phases are few in number in both the model system (Section 10.13) and present IPN materials. Also, as indicated in Chapter 10, finely divided carbon black and silicas greatly toughen elastomers, sometimes without the development of many covalent bonds between the polymer and the filler. 

To test the results of the model developed here, results are compared with room temperature tensile loading data for a porous cordierite. The modulus-temperature behavior for this ceramic is shown in Figure 2. From this data, values for and were computed. The coefficient of friction for this material is not known, but reported values for ceramics range from 0.6 -1.8 For this work, a nominal value of / = 1.0 was selected. The other needed parameters of interest are given in Tabie 1 along with the method nsed for determining their values. 

The dynamic storage modulus (G ) vs. temperature data are displayed in Figs. 1-4. The low temperature torsion data (Figs. 1 and 2) show a distinct transition zone at... 

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