Shift factors, determination

From the PDMS shift factors determined by Winter and Chambon, one may estimate that room temperature fluctuations affect the gel strength by no more than 5%. 

It is believed that the wide distribution of the relaxation time must be due to the heterogeneity [106] (see Sect. 6). It was also found [80] that the intermediate scattering functions 7(Q, t) can be scaled to a master curve using shift factors % determined from the temperature dependence of the viscosity as shown in Fig. 10 (upper curve). This result suggests that the neutron scattering can see the same a-process as that observed in macroscopic viscosity measurements and the relaxation mechanism does not change in the temperature range examined. 

In using the software, the recommended procedure is to first carry out the automatic shifting procedure. If the agreement between the computed shift factors and those obtained from automatic shifting is not satisfactory, the operator has the option to manually adjust the shift factors to agree completely with those calculated from an equation and generate a new master curve. The same shift factors should apply to each of the viscoelastic functions. This consistency criterion can be used to judge whether the shift factors determined need further adjustment. 

A.2 Shift Factor Determined Using the WLF Equation. Calculate the shift factor for PPS at 293 °C for a reference temperature of 330 °C using the WLF equation (Eq. 5.7) and compare it with the experimental value of 1.708. 

All amorphous polymers show remarkably similar results when values of log ay are plotted versus T - Tq. Manipulation of these data shows that the empirically determined shift factors can be fitted by the expression... 

Thus all the different temperature related data in Fig. 2.58 could be shifted to a single master curve at the reference temperature (7 ). Alternatively if the properties are known at Tref then it is possible to determine the property at any desired temperature. It is important to note that the shift factor cannot be applied to a single value of modulus. This is because the shift factor is on the horizontal time-scale, not the vertical, modulus scale. If a single value of modulus 7, is known as well as the shift factor ar it is not possible to... 

For easier reference to earlier work the shift for (239-240) was adopted as the reference for tabulation and where necessary derived from the (240-244) isotope shift by dividing the latter by 2.531, a constant factor determined by Blaise et al. (15). Over 9500 isotope shifts have now been measured, 50% of them in the infrared. 

If cation diffusion 1s Indeed Involved 1n the rate determining step, the dissolution rates at temperatures above Tg are expected to obey a WLF-type relationship (17). In the present context, the ratio of the dissolution rate at temperature T to that at Tg replaces the shift factor,... 

To obtain an estimate of lifetime, use the WLF equation to determine the shift factor from the reference temperature to the temperature of interest. Apply that shift factor to each of the points on the master curve to obtain the required property/time curve and read the time to reach the threshold value. 

Burnay [14] has developed a predictive model, which is based on the use of the superposition technique to determine thermal and dose rate shift factors relative to a master curve of compression set of a rubber seal versus time. The relation between the shift factors and environmental parameters of temperature and dose rate are given by ... 

However, because measurements are kinetically determined, this is a less accurate form of the equation. Very often it is observed that the measured shift factors, defined for different properties, are independent of the measured property. In addition, if for every polymer system, a different reference temperature is chosen, and ap is expressed as a function of T — rj, then ap turns out to be nearly universal for all polymers. Williams, Landel and Ferry believed that the universality of the shift factor was due to a dependence of relaxation rates on free volume. Although the relationship has no free volume basis, the constants and may be given significance in terms of free volume theory (Ratner, 1987). Measurements of shift factors have been carried out on crosslinked polymer electrolyte networks by measuring mechanical loss tangents (Cheradame and Le Nest, 1987). Fig. 6.3 shows values of log ap for... 

The above interpretation of the factors indicated by current theory to be important in determining proton and carbon-13 chemical shifts does not offer much encouragement for the optimistic statement that [carbon-13 chemical shifts] should provide a more reliable index of charge than the hydrogen shifts (Fraenkel and Farnum, 1968, p. 251). It is true that the other atom terms are a more serious perturbation on proton than on carbon-13 chemical shifts, and are difficult to evaluate. However it is also apparent that carbon-13 shifts are determined by a number of terms and 0 whose charge dependence may well be in... 

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

The preceding estimate is based on one-fermion theory, so the observed resonance frequency in a fermion beam may be different as a result of fermion-fermion interaction. Therefore, it is strongly advisable that I be tunable over a wide range to search for the actual resonance pattern. The same experiment can then be repeated in a proton, atomic or molecular beam and the RFR effect should be // 2-dependent with a pattern of resonance determined by the novel chemical shift factor Spin-spin interaction between fermions would split the spectrum as in ordinary NMR, but the RFR fingerprint would be unique. 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

The shift factors to align the plots at different temperatures with the plot for the chosen reference temperature are determined and then these are fitted to the WLF equation to find the constants. The equation can then be used to predict the response at service temperatures. The principle of constructing a master curve is illustrated ion Figure 15.8 and the plot of log aT against temperature in Figure 15.9. More details of fitting the WLF equation and possible problems with a discontinuity in the relation are considered in reference 49. 

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