Shift factor compositional

Table 4. Effect of specific surface area of filler and its concentration on concentration shift factors aci and ac for composites copolymer + ash (the reference concentration 10%)...

Table 16. Composition", frequency (co) beginning from which one may achieve coincidence of the G values and the shift factors b(c) at 190 °C [344]...

Fig. 7. Value of the shift factor, aT, needed for superpositioning of bulk mechanical data as a function of temperature, 5>. The various compositions of the rubber-modified epoxies are indicated...

Fig. Z4 (a) Temperature ramp at a frequency a> = lOrads (strain amplitude A = 2%) for a nearly symmetric PEP-PEE diblock with Mn = 8.1 X 104gmol l, heating from the lamellar phase into the disordered phase. The order-disorder transition occurs at 291 1 °C, the grey band indicates the experimental uncertainty on the ODT (Rosedale and Bates 1990). (b) Dynamic elastic shear modulus as a function of reduced frequency (here aT is the time-temperature superposition shift factor) for a nearly symmetric PEP-PEE diblock with Mn = 5.0 X 1O g mol A Shift factors were determined by concurrently superimposing G and G"for w > and w > " respectively. The filled and open symbols correspond to the ordered and disordered states respectively. The temperature dependence of G (m < oi c) for 96 < T/°C 135 derives from the effects of composition fluctuations in the disordered state (Rosedale and Bates 1990). (c) G vs. G"for a PS-PI diblock with /PS = 0.83 (forming a BCC phase) (O) 110°C (A) 115°C ( ) 120°C (V) 125°C ( ) 130°C (A) 135°C ( ) 140°C ( ) 145°C. The ODT occurs at about 130°C (Han et at. 1995).

Master curves of G were constructed for all compositions of the five different binary systems using a reference temperature of ISO C. A typical result of a 6 master curve is given in Figure 4, which is a 40/60 blend of PE/EMA-Zn-20. As seen, satisfactory superposition is attained for 6 in these blends. Using the same shift factors as for G, superposition was attempted for G . As can be seen, there is a definite breakdown of the tlme-tenperature superposition principle at high frequencies (Fig. 4). Identical results were obtained for PE/EMA-Zn-40 and PE/EMA-Na blends. For these PE/EMA-salt systems, as the amount of lonomer present in the blend decreases, the frequency range over which superposition of G" is possible increases. As seen in a different perspective, the decrease in G" as a function of temperature at high frequencies is reduced upon the addition of PE to PE/EMA-salt binary systems. 

These a s can be translated into temperature shift factors At s according to the method of Shohamy and Eisenberg (40). These At s are given as a function of composition in Figure 14. As can be seen, there exists a linear relationship between the temperature shift factors and the composition in both the PE/EMA-Zn-40 and PE/EMA-Zn-20 systems. 

Creep behavior. Figure 5 shows the composite curve of the shift factors and also indicates that the shift factors in the glass transition region do not follow the WLF equation ... 

Figure 3. Composite curve of experimental shift factors as a function of (T —...

Figure 5. Composite plot of experimental shift factors for all epoxy specimens as a function of (1/T — 1/Tg) (symbols are as in Figure 2)...

The procedure for obtaining the shift factor was proposed to Williams et al.3 by Ferry8 through constructing a series of creep plots at different temperatures and then looking to see what shift is required to reconstruct the composite creep plot (Figure 6.14). 

Figure 6.14 Composite shift factor curve. (After Ward2 and Ferry.8)...

In these figures, the spectrum at a certain temperature is chosen for each sample as the reference (for instance 105°C for LIO), with which the line shapes of the spectra measured at different temperatures are matched over the glassy region to form a composite spectrum. From such a process, the time-scale shift factors aa with respect to the reference spectrum... 

A typical example of recent studies of time-temperature-modulus relationships may be found in papers by Moehlenpah et al. (1970, 1971), who examined crosslinked epoxy resins filled with glass beads, fibers, or air bubbles. The initial tangent modulus in compression was seen to increase with a decrease in strain rate flexural and tensile moduli were reported to behave in a similar fashion. The WLF shift factor was essentially independent of the type of filler used and of the mode of loading. Kerner s equation was found to hold for the particulate composites in the glassy range. 

Figure 12.10. Tensile yield stress vs. strain rate for epoxy composites (Tref = 50°C) (Moehlenpah et a/., 1970, 1971). The term oLjy is the WLF shift factor. (x) Continuous transverse (A) particulate-filled ( + ) unfilled (O) foam (J) brittle failure, range of ultimate strengths.

Figure 5. Calculated shift factors for various composites.

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

Figure 6.13 Composite curve obtained by plotting the data of Figure 6.12 with suitable shift factors, giving the behaviour over an extended frequency scale at temperature Tq. (Reproduced from Ferry, Viscoelastic Properties of Polymers (3rd edn), Wiley, New York, 1980, Ch. 11)...

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