Time-temperature superposition significance

The successflil appHcation of time—temperature superposition (159) for polystyrene foam is particularly significant in that it allows prediction of long-term behavior from short-term measurements. This is of interest in building and constmction appHcations. 

Figure 3.13 shows the shift factors aT determined from time-temperature superposition as a function of temperature for melts of two semi-crystalline thermoplastics as well as the Arrhenius plot. For the two polyethylenes (HDPE, LDPE), the progression of log ax can be described with the Arrhenius equation. The activation energies can be determined from the slope as Ea(LDPE) 60 kj/mol and Ea(HDPE) 28 kj/mol. Along with polyethylenes (HDPE, LDPE, LLDPE), other significant semi-crystalline polymers are polypropylene (PP), polytetrafluoroethylene (PTFE) and polyamide (PA). 

The WLF equation applies to amorphous polymers in the temperature range of Tg to about Tg + lOO C. In this equation J is the reference temperature, these days taken to be the T, while and C2 are constants, initially thought to be universal (with Cx = 17.44 and C2 = 51.6), but now known to vary somewhat from polymer to polymer. These experimental observations bring up a number of interesting questions. What is the molecular basis of the time-temperature superposition principle What is the significance of the log scale and what does the superposition principle tell us about the temperature dependence of relaxation behavior And what about the temperature dependence of a7 at temperatures well below 2 ... 

The adhesive of this study has been designed for an automotive under-hood application. Accordingly, It was Important to understand the behavior of the adhesive over a wide frequency (engine RPM) and temperature range. Time-temperature superposition allows characterization beyond the frequency range of our Instrumentation (4). More significantly. It Is hoped to use time-temperature superposition data to explore the molecular weight Implications of Incomplete polymerization. 

Non-linear mechanical properties were observed for rubber eomposites and referred to as the Payne effect. The Payne effeet was interpreted as due to filler agglomeration where the filler clusters formed eontained adsorbed rubber. The occluded rubber molecules within filler elusters eould not eontribute to overall elastic properties. The composites behaved similarly to rubber composites with higher filler loading. Uniform and stable filler dispersion is required for rubber composites to exhibit linear viscoelastic behaviour. Payne performed dielectric measurements on SBR vulcanizates containing silica or carbon black. The dielectric data were used to construct time-temperature superposition master curves. The reference temperature increased with crosslinking but not significantly with filler. Comparison of dynamic mechanical and dielectric results for the SBR blended with NR was made and interpreted. ... 

A significant result in equations 29 and 30 is that the acoustic properties depend only on the product cor, not on either variable separately. Since r is a fimction of temperature, as shown in equation 31, the results of changing frequency are indistingmshable from those of changing temperature (neglecting any changes in Vo and Voo). The applicability of time-temperature superposition directly follows from the form of these equations. The analytic form of the temperature dependence of the relaxation time is, however, not specified in equations 29 and 30. 

Figures 9.4 and 9.5 show G and G" for two linear polymers, a poly(vinyl methyl ether) (PVME) with a molecular weight of 138,000 and a polystyrene (PS) with a molecular weight of 123,000, respectively. The data for each polymer have been moved horizontally along the frequency axis until they form a single curve. There is a substantial region of overlap, extending over three decades of frequency, so the superposition is clearly established. The shift factors needed to obtain overlap of the curves are shown as inserts. The reference temperature for each case was taken to be 84 °C this temperature has no significance other than being a convenient value for the particular application for which the data were obtained, which was a study of phase separation in blends of the two polymers. One of the significant uses of time-temperature superposition is made evident by focusing on the open and closed symbols in the PVME curves. The dynamic moduli are available over five orders...

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