Processing time-temperature superposition shift

Time-temperature superposition (tTs) was carried out for these multi-temperature multi-frequency tests based on Williams-Landel-Ferry (WLF) relationship. It considers the equivalency of time and temperature in the context of free volume theory for an activated flow process in viscoelastic materials such as PET. It has been found the tTs holds for the whole temperature/frequenQr range. The master curve generated from tTs is shown in Figure 13 for the 10 wt. % bamboo-PET composite at the 25.0 C reference temperature. The time-temperature superposition shift factor follows Arrhenius temperature dqrendence according to the expression ... 

V = process line speed (m/min) used in the experiment to bond the felt layers, ax = time-temperature superposition shift further defined by the relationship ... 

The peak of the dielectric loss of this process reflects its viscoelastic nature by obeying the time-temperature superposition principle, wherein the peak is shifted to higher temperatures for shorter times (higher frequencies) and vice versa. This process has been described by the Havriliak-Negami empirical formula [106, 108]... 

For semi-crystalline polymers with melting points of more than 100 °C above the glass transition temperature and for amorphous polymers far above the glass transition temperature Tg (at around T = Tg + 190°C), the shift factors obtained from time-temperature superposition can be plotted in the form of an Arrhenius plot for thermally activated processes ... 

However, for thermorheologically simple materials, that is, for those materials for which the time-temperature superposition principle holds, the mechanical properties data can be shifted parallel to the time or frequency axis. This fact suggests an additional hypothesis that can be very useful in solving some specific thermoviscoelastic problems. According to this hypothesis, the net effect of temperature in the response must be equivalent to a variation in the rates of creep or relaxation of the material. Thus for T > Tq the process occurs at a higher rate than at Tq. 

An attempt will now be made to determine the activation energies of the two processes, since the identification of the mechanism is based primarily on this factor a study of all the stress relaxation curves has revealed that within experimental error time-temperature superposition is valid above a modidus of 10 dynes/cm , and that the shift factors are of the WLF form. Therefore, we can determine the constants of the WLF equation which were listed in Table 3 and also the corresponding activation energies. The values of the activation energies for the process which is governed by these shift factors, calculated for T —Tg + 30, ranges from 150 to 230 Kcal. This mechanism will, for the moment, be called the "first mechanism. 

The principle of time-temperature superposition is that there is a temperature-shift factor that allows all data to be plotted on a master curve. This presupposes that there is no change in mechanism during the reaction, so that Equation (3.8) applies (Prime, 1997b). Such superposition processes are regularly used in rheology and the WLF equation is routinely applied when the system is above temperature Tg. When the system is controlled by... 

Figure 6 shows the master curves for the PS films with M of 4.9k and 140k drawn by horizontal and vertical shifts of each curve shown in Fig. 5 at the reference temperatures of 267 and 333 K, respectively [26]. The master curves obtained from the dependence of lateral force on the scanning rate were very similar to the lateral force-temperature curves, as shown in Fig. 3. Hence, it seems plausible as a general concept that the scanning rate dependence of the lateral force exhibits a peak in a glass-rubber transition. Also, it is clear that the time-temperature superposition principle, which is characteristic of bulk viscoelastic materials [35], can be applied to the surface relaxation process as well. Assuming that Uj has a functional form of Arrhenius type [36, 37], the apparent activation energy for the aa-relaxati(Mi process, A//, is given by ...

Viscoelastic functions depend on both temperature and time. For many polymers, the logarithmic plot of a viscoelastic function at the temperature T may be obtained from that at the temperature Tq by shifting the curve along the logarithmic time axis by the amount of log (T)- This procedure is called time-temperature superposition. The ability to superpose viscoelastic data is known as thermorheological simplicity. Thermorheological simplicity demands that all the molecular mechanisms involved in the relaxation process have the same temperature dependencies. 

Zhang et al. have shown that the conductivity curves can be transposed to each other by means of time temperature superposition (TTS) [62]. Furthermore, an Arrhenius plot of the corresponding shift factors exhibits that the dynamic percolation is a thermally activated process. With regard to the considered polycarbonate-MWCNT example, the Arrhenius plot of the fit parameter 2/cFy leads to the same result (Figure 5.26(b)). Since Vy f xo 1 constant, this means the reaction rate depends only on the activation energy, which is approximately 115 kJ/mol for this system. 

The fundamental concept of the material clock or reduced time is similar to the principle described above in the discussion of time-temperature superposition. In the mechanical constitutive models, however, the change in the stress or deformation induces a shift in the material relaxation time. The fact that the time depends on the state of stress (or strain) or on its history leads to additional non-linearities in behavior from what is expected with, eg, the K-BKZ model. Physical explanations for the shifting material time are often based on free-volume ideas that are often invoked to explain time-temperature superposition. In addition, entropy changes have been invoked as have stress-activated processes. 

Partial master curves of 10 g.dL"l solutions of a,o)-alkaline earth dicarboxylato PBD in xylene at 297 K are reported in Figure 10, and result from a good frequency-temperature superposition of the experimental data.l7 Only the G" master curve of the solution of Be-based HTP is ill-defined due to the poor accuracy in the determination of the very small values of G". The shift factors support an apparent Arrhenius-type of dependence (Figure 11), from which the activation energy of the observed secondary ionic relaxation process was calculated and found to decrease as the radius of the alkaline earth cations increases (Figure 12). One also observes that the relaxation spectrum calculated by the first order approximation of Ninomiya and Ferry S is displaced along the time scale in relation with the cation size (Figure 13). The dynamic behavior of the 10 g.dL solution is obviously... 

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