Master activity curves

The master activity curves determined by Sletmoe for solvents in dioctylphthalate and in alkyd monomer simulator were used in the present calculation to determine parameters for DCOO or the ester groups attached to the benzene rings of the alkyd backbone. 

Figure 9.11 represents the MMT content-dependent (wt%) flow activation energy (Ea) of pure PLA and various PLANCs obtained from an Arrhenius fit of the master curves [47]. It is clearly observed that the Ea value increases significantly for the nanocomposite containing 3 wt% MMT and then is almost unchanged with increasing MMT content. This result indicates that, in the presence of MMT, it is very difficult for the materials to flow. This behavior is also ascribed to the formation of a spatially linked structure in the nanocomposite in the molten state. 

Finally we compare the temperature dependencies reported for the structural relaxation and the self-motion of hydrogens studied by NSE. For PI, the shift factors used for the construction of the master curve on Q,T) (Fig. 4.17) are identical to those observed for the structural relaxation time [8]. This temperature dependence also agrees with DS and rheological studies. The case of PIB is more complex [ 147]. The shift factors obtained from the study of Teif(Q>T) (Fig. 4.14b) reveal an apparent activation energy close to that reported from NMR results (-0.4 eV) [136]. This temperature dependence is substantially weaker than that observed for the structural relaxation time (=0.7 eV, coinciding with rheological measurements) in the same temperature range (see Fig. 4.20). 

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the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data).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shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

One method is simple visual inspection of the generated master curve. If the fit of the individual data sets is poor, subsequent extrapolation is open to significant error. Another method is to determine an activation energy plot (of the shift of T with frequency) for the data set and compare temperatures or frequencies calculated from the resulting Arrhenius equation to those read from the nomograph. 

The master curve shows that the life-time is thermally activated. In Fig. 28, two Arrhenius plots for PMMA have been reproduced one from the mechanical P loss peak measurements and the other from the life-time measurements. The life-time plot is the same. Many authors have already associated the P loss peak with the fracture properties Here it is shown that the fibrils breakage itself is controll-... 

Finally, Fig. 33 shows the cyclic life-time versus temperature for the first material at different temperatures in a 1 Hz test, and Fig. 34 shows the master curve obtained by applying a shift corresponding to a thermal activation ener of 23 kcal/mol. As in the static loading case, the fibrils rupture process is thermally activated with the... 

Typical friction force data obtained at a constant load are shown in Fig. 4.17 (left). In these experiments, the applied load should be limited to <1 nN to ensure that the surface of the film to a depth of <2 nm is probed and that wear of the glassy PMMA film can be excluded. A clear maximum is observed that shifts to higher velocities with increasing temperature, in accordance with the time—temperature superposition principle [36]. From the master curve of friction force vs. velocity data for PMMA (shifted by aT to the reference temperature of 25°C) an activation energy of 35 kJ/mol can be estimated. 

In Figure 14.3c a normalization in a single master curve of E vs. tt data reflects the interfacial behavior of emulsifier adsorbed films for different emulsifier concentrations, at different adsorption times, and under different processing conditions (Nino and Patino, 2002 Nino et al., 2003). The plot suggests that interactions between adsorbed emulsifier molecules (residues) increase with tt. In fact, at lower tt values the slope of the -tt plot was close to 1, which corresponds to the behavior of an ideal gas with low emulsifier interactions. However, at higher tt values the slope changes, which implies an important nonideal behavior with higher molecular interactions as the amount of emulsifier at the interface increases. These data indicate that the interfacial activity and the surface dilatational modulus of emulsifier films are mainly a result of the amount of adsorbed emulsifier. 

The master plots of Fig. 5 show a remarkable relation between stmctural and JG relaxation both above and below Tg, demonstrating the interdependency of the two processes. Eq. (1) provides a rationale for the quantitative relation above Tg. As far as concerns below Tg, the master curve is possible since the activation energy Ejo of JG relaxation scales with P linearly with Tg(P). The activation energy of the intermolecular secondary process in the glassy state is scaling with the glass transition temperature, that is characteristic of the primary relaxation of the supercooled liquid. 

Figure 7. Results of time and temperature dependent studies of compression set in open-celled, porous M97 silicone foams. (A) % compression set as a function of time for the temperatures (°C) listed (B) Master curve at 21 °C derivedfrom a time-temperature-superposition analysis of the data in (A). The activation energy derived from this analysis was 78 kJ/mol.

The same procedure as for oxidation yield was applied to Sbet and to several porous textural parameters determined by the alpha method (total surface area, external surface area and micropore volume) on each sample oxidized in dry air. This led to the master curves at 673 K for the respective parameters shown on Fig. 21. All master curves for pore parameters were derived by using the same shift factors as for the oxidation yield (i.e., the same apparent activation energy). 

When a WLF master curve is generated the timescale it spans depends on the timescale of the ageing tests and on the activation energy. In some cases it is necessary to extrapolate the master curve to the time of interest which increases uncertainty. If the extrapolation needed is unreasonably large no prediction can be obtained from what appears to be perfectly good raw data. 

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 ...

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... 

To simplify SiC fiber mpture behavior for technical application and mechanistic understanding, two simple empirical approaches often used for metals and ceramics have been successfully developed. One approach is by use of Larson-Miller (LM) master curves or, equivalently, thermal-activation q-maps [16]. For this approach, measurements have been made on single fibers across a time range from -0.01 to over 100 hours using three types... 

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