Time-temperature superposition vertical shift factor

Tobol sky and co-workers who also modified it to account for proportionality of modulus to absolute temperature (3). This has the effect of creating a slight vertical shift in the data. Ferry further modified the time-temperature superposition to account for changes in density at different temperatures which has the effect of creating an additional vertical shift factor (4). The effect of the temperature-density ratio on modulus is frequently ignored, however, since it is commonly nearly unity. 

Lopes da Silva et al. (1994) found that the fiequeney-temperature superposition, analogous to time-temperature superposition in transient rheologieal experiments, was applieable to a 1 % locustbean (LB) gum dispersion so that master eurves at To = 25°C were obtained for G and G" (Figure 3-38). In eontiast, smooth master eurves could not be obtained for G and G" values of 3.5% high-methoxyl pectin dispersions either separately or for both simultaneously (Figure 3-39). The discrepancies were higher for a 3.5% low-methoxyl pectin dispersion. It was concluded that the time-temperature superposition technique was not applicable to the pectin dispersions due to their aggregated structure. For the studied samples, the vertical shift factor for the moduli (Topo/ T P) had a small effect on the master curve (Lopes da Silva et al., 1994). 

Figure 3. Tonperature shift ftu tors, log as a function of temperature. Table II. Vertical shift factors for time - temperature and time - strain superposition...

Fig. 2.33. A comparison of the retardation spectra L of a high molecular weight PS (filled triangles), a solution of 25% PS in TCP (open squares) and PIB (filled circles). The shift factors are arranged such that the maximum of the first peak occurs at the same reduced frequency for all three samples. Downward vertical shifts by 0.869 and 1.39 of logio L have been applied to data for PS and the 25% PS solution, respectively, in order to make all data have about the same height at the first maximum. The disparity in width of the softening dispersion of bulk PS and PIB is clear. The small peak near the bottom (dashed line) is the contribution to L from the local segmental motion in bulk PS. The inset shows isothermal tan 8 data of PIB in the softening region at -66.9 °C, and tan 8 of the solution of 25% PS in TCP obtained from a reduced recoverable-compliance curve after applying time-temperature superposition to the limited isothermal data.

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