Alpha-relaxation time

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... 

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... 

Hall DB, Hooker JC, Torkelson JM (1997) Ultrathin polymer films near the glass transition effect on the distribution of alpha-relaxation times as measured by second harmonic generation. Macromolecules 30 667-669... 

The F q, t) is calculated at a value corresponding to the first peak of structure factor S(q). The alpha relaxation time (t ) is obtained usually as the time at which the F q, t) decays by a factor of e. 

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,... 

Figure 26. Relaxation time of the alpha relaxation process (at 427 K) and the maximum temperature position of the alpha peak (at 0.3 Hz) as a function of film thickness. Inset The relaxation time distribution of POHOAc at 510 K for different thicknesses, as indicated.

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.

Much more pronounced effects are observed at higher temperatures The alpha relaxation peak of a thin PS film of 75 nm (measured at 122°C) is shifted to higher frequencies after keeping the sample at 180°C in ambient air (Fig. 33). Consequently, the average relaxation rate of the alpha relaxation process increases in time by more than one order of magnitude during this thermal treatment (inset, Fig. 33). 

For polymers, dielectric spectroscopy is sensitive to fluctuations of dipoles, which are related to the molecular mobility of groups, segments, or the polymer chain as well [38]. The molecular mobility is taken as a probe for structure. The basic quantity is the complex dielectric function e f) = t (f) - it"(f) as a function of the frequency/and the temperature T. s (/) is the real whereas e"(/) is the loss part i = >f ). A relaxation process is indicated by a step-like decrease of s (/) with increasing frequency and a peak in e"(/). From the maximum position of the peak a mean relaxation rate can be deduced, which corresponds to the relaxation time of the fluctuation of the dipole moment of a given structural imit. For details see reference [49]. All shown measurements were carried out isothermally in the frequency range from 10 to 10 Hz by an ALPHA analyzer (NovocontroF). The temperature of the sample is controlled by a Quatro Novocontrol system with stability better than 0.1 K. 

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). 

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) ... 

As we relax in preparation for and pass into sleep, the active desynchronised awake EEG characterised by the low-amplitude (5-10 pV) high-frequency (10-30 Hz) beta waves becomes progressively more synchronised giving larger (20-30 pV) and slower (8-12 Hz) alpha waves, and then even slower (1-4 Hz) and bigger (30-150 pV) delta waves. This so-called slow-wave sleep is interrupted at intervals of some 1-2h by the break-up and desynchronisation of the EEG into an awake-like pattern. Since this is accompanied by rapid eye movements, even though sleep persists and can be deeper, the phase is known as rapid eye movement, REM or paradoxical, sleep. It is a time when dreaming occurs and when memory may be secured. 

The Alpha Technologies MV 2000" Mooney viscometer can perform a stress relaxation test after completing the viscosity test (see condition 3. above). For example, an ML 1+4 test can be done on a raw rubber sample followed by a two-minute stress relaxation test. The stress relaxation portion of the test is initiated when the Mooney rotor is suddenly-stopped. The total test time would be seven minutes (or two minutes longer). Figure 36 shows two polymers that have the same Mooney viscosity yet have different stress relaxation profiles [132],... 

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