Time dependence alpha-relaxation

Using the usual fitting procedure [ 1 ], the dependence of the relaxation rate on the inverse temperature for the alpha and beta relaxation process is extracted (Fig. 25). The dynamic glass transition becomes more than one order of magnitude faster with increasing confinement, corresponding to a shift of 36 K to lower temperatures (Fig. 26). The thickness dependence of both the alpha relaxation time (at a constant temperature of 427 K) and the maximum... 

Figure 33. Normalized dielectric loss versus frequency at 122°C, showing the alpha relaxation process of a thin PS film of 75 nm as prepared, and after different annealing times at 180°C in air, as indicated. Inset. The corresponding relaxation rate in dependence on the annealing time at 180°C in air.

Cerveny investigated the development of the dynamic glass transition in styrene-butadiene copolymers by dielectric spectroscopy in the frequency range from 10 to 10 Hz. Two processes were detected and attributed to the alpha- and beta-relaxations. The alpha relaxation time has a non-Arrhenius temperature behavior that is highly dependent on styrene content... 

In addition, a power law contribution (cx was used to accoxmt for the normal mode contribution at low frequencies, which is the frequency dependence expected from the Rouse model for frequencies larger than the characteristic one of the shortest mode contribution. Thus, we assumed that the high frequency tail of the normal mode follows a C jon law and superimposes on the low frequency part of the alpha relaxation losses, being C a free fitting parameter at this stage. The (t-relaxation time corresponding to the loss peak maximum was obtained from the parameters of the FIN function as follows Kremer Schonals (2003) ... 

Fig. 3.1 a Tempraatme dependence of volume or enthalpy for an amtnphous polymer. The vertical lines denote Tg determined using fast and slow cooling rates. The vatical arrow denotes glassy-state structural relaxation (physical aging) of the glass ftnmed on slow cooling, b Normalized Arrhenius plot of the average alpha-relaxation time fra- an amorphous polymer. Above Tg, polymer relaxation exhibits a non-Anhenius tempaature dependence while below Tg, polymer relaxation exhibits an Arrhenius temperature dependence... 

Until 1984, all of the stopped-flow and temperature-jump kinetic studies of alpha cyclodextrin inclusion-complex formation were explainable in terms of a single-step, binding mechanism. According to this mechanism, the observed rate constant, kobs, (for stopped-flow) and the reciprocal relaxation time, 1/t, (for temperature-jump) should show a linear dependence on the edpha cyclodextrin concentration. Sano and coworkers, however, in the case of the iodide-alpha cyclodextrin interaction, and Hersey and Robinson,in the case of various azo dye-alpha cyclodextrin interactions (see Fig. 7), found that certain guest species exhibit a limiting value of kobs and 1/t at high concentrations of alpha cyclodextrin. This behavior can most simply be explained in terms of a mechanism of the type,... 

A related issue is that the modulus is a viscoelastic property, as evidenced by the temperature/strain-rate dependence, and that for most poljnners (at least those without a large beta transition near the alpha transition) time-temperature superposition of, for example, the shear relaxation modulus is valid (80). Further, G Sell and McKenna (81) have shown that the 5neld stress vs strain rate also seems to obey time-temperature superposition. Hence there is a correlation between the viscoelastic properties and the yield response of pol5uners, though one that is not generally stated explicitly. We note that some of the models mentioned previously, such as those of Caruthers group (41,42), Tervoort and co-workers (40), and Knauss and Emri (35), are (nonlinear) viscoelastic models that have yield arising due to the nonlinear response induced by the material clock (see Viscoelasticity). 

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