Time-temperature superposition. See

The viscosity functions of homopolymers and compatible polymer blends measured at different temperatures can be shifted together by displacement along a 45° axis to form a single curve (mastercurve) by time-temperature-superposition (see Fig. 3.12). This... 

Fig. 16. Reduced curve of creep compliance vs time for PEN showing lack of time-temperature superposition (see text for discussion). 30°C T 50°C 80°C <0> 100°C. After Cerrada and McKenna (45).

To determine the required time range, it is necessary to first compare the classically obtained times from the viscoelastic behaviour (Fig. 1). The situation is complicated by the fact that these times depend on the temperature. The usual glass time temperature superposition (see Sect. 2) has been checked in the 50s for rheological data the characteristic times T,, etc. depend on the temperature T by the same factor a(t) = 10(Cj(T — T )/Cj -F T — T. For the SANS data, a similar superposition has been proposed a form factor for t = tj at T, is compared to a form factor for (ij )t, at Tj. A satisfying overlapping is possible by a correct choice... 

In the interval between 198 K and 253 K, the form of the structural relaxation does not change114 as is evidenced by the success of the time-temperature superposition shown in Figure 21. One can also see from this figure that an additional regime intervenes between the short-time dynamics (first 10% of the decay at the lowest temperatures) and the structural relaxation (last 80% of the decay). We will identify this regime as the MCT (3-regime... 

The time-temperature superposition, implying that the functional form does not appreciably depend on temperature (see e.g. [34, 111]). For instance, mechanical or rheological data corresponding to different temperatures can usually be superimposed if their time/frequency scales are shifted properly taking a given temperature Tr as reference. 

The effects of strain rate and temperature are correlated, and can be modeled (Kinloch and Young, 1983, Kinloch, 1985). For different temperatures and strain rates, GIc and the time to failure, tf, were measured. Using the time-temperature superposition principle, shift factors (aT) applicable to the time to failure tf, were determine. Shift factors plotted against (T — Tg) are independent of the type of test used (Fig. 12.14). The construction of a typical master curve GIc versus tf/aT is shown in Fig. 12.15 (Hunston et al., 1984). The value of GIc may be predicted for any strain rate/temperature combination. This model can also be applied to rubber-modified epoxies (See chapter 13). 

As an example of the concentration dependence of viscoelastic properties in Fig. 16.11 the shear creep compliance of poly(vinyl acetate) is plotted vs. time for solutions of poly(vinyl acetate) in diethyl phthalate with indicated volume fractions of polymer, reduced to 40 °C with the aid of the time temperature superposition principle (Oyanagi and Ferry, 1966). From this figure it becomes clear that the curves are parallel. We may conclude that the various may be shifted over the time axis to one curve, e.g. to the curve for pure polymer. In general it appears that viscoelastic properties measured at various concentrations may be reduced to one single curve at one concentration with the aid of a time-concentration superposition principle, which resembles the time-temperature superposition principle (see, e.g. Ferry, General references, 1980, Chap. 17). The Doolittle equation reads for this reduction ... 

Fig. 24. G and G" obtained using small amplitude oscillatory strain for PCLC10 before and after large-amplitude shear. See text for conditions of large amplitude shear. Master curves obtained by application of time-temperature superposition and shifted to T0=55 °C. From Ref. [54].

For the moduli data, the time-temperature superposition fails at intermediate (0 between the segmental and global relaxation processes because these processes exhibit different Ojq at low T - (see, e.g., Adachi and Kotaka, 1993 Inoue et al., 1991, 1996 Kremer and Schonhals, 2003). (This failure is not well resolved in the compressed scale of the plots shown in Figure 3.3.) The superposition works separately at high and low ca where the viscoelastic data are dominated by one of these processes. In contrast, the dielectric data satisfy the superposition in the entire range of co because those data detect just the segmental relaxation process, although it fails in a close vicinity of... 

Both cis-polyisoprene (PI) and poly(vinyl ethylene) (PVE) have the type-B dipoles perpendicular to the chain backbone, and PI also has the type-A dipoles parallel along the backbone (cf. Figure 3.2). The dielectric relaxation detects the fluctuation of these dipoles, as explained in Section 3.2.2. The fluctuation of the type-B dipoles is activated by the fast, local motion of the monomeric segments, which enables the dielectric investigation of this motion. In contrast, the slow dielectric relaxation of PI due to the type-A dipoles exclusively detects the fluctuation of the end-to-end-vector R (see Equation 3.23). These dielectric features of PI and PVE are clearly noted in Figure 3.11, where the e" data are shown for a PI/PVE blend with the component molecular weights Mp, = 1.2 x 1(P and Mpyp = 6 x 1(P and the PI content rvpi = 75 wt% (Hirose et al., 2003). The data measured at different temperatures are converted to the master curve after the time-temperature superposition with the reference temperature of T, = -20°C, as explained later in more detail. The three distinct dispersions seen at high, middle, and low... 

As mentioned, the effects of time or temperature are very similar—suggesting a time-temperature superposition. This enables the use of data from measurements at various temperatures to prepare a master-curve versus extended time, (t/a), where "a" represents the horizontal shift on a logarithmic scale. See Figure 4-18. 

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