Relaxation peaks

Having suggested the connections between relaxation descriptors and the data it is now important to realize that here is sufficient information in isochronal scans that, with numerical analysis now readily carried out by computer, detailed parameters that describe relaxation can be determined jointly. Analysis is most conveniently carried out with the aid of a parameterized empirical phenomenological function. The method as implemented by us uses for each relaxation peak a Cole- Cole -like function (4) to represent the complex modulus,... 

Longitudinal relaxation measurements do not allow to establish whether the electron relaxation is constant or field-dependent. Transverse relaxation measurements, on the contrary, prove that the effective relaxation time is indeed field-dependent (see Sections I.A.l and II.A.4). The occurrence of a field-dependent electron relaxation time is confirmed by the longitudinal relaxation measurements in glycerol solution (62), as the typical high field relaxivity peak appears, with Af of 0.11 cm and of 7 x 10 s at 298 K. 

The NMRD profile of the protein adduct shows a largely increased relaxivity, with the dispersion moved at about 1 MHz and a relaxivity peak in the high field region. This shape is clearly related to the fact that the field dependent electron relaxation time is now the correlation time for proton relaxation even at low fields. The difference in relaxivities before and after the dispersion is in this case very small, and therefore the profile cannot be well fit with the SBM theory, and the presence of a small static ZFS must be taken into account 103). The best fit parameters obtained with the Florence NMRD program are D = 0.01 cm , A = 0.017 cm , t = 18x10 s, and xji =0.56 X 10 s. Such values are clearly in agreement with those obtained with fast-motion theory 101). 

More serious are the coherence transfer cross peaks in ROESY spectra because the coherence peaks are in phase with the genuine cross-relaxation peaks and thus may modulate intensity of the genuine peaks. To emphasize the effect of coherence transfer peaks (now TOCSY peaks) we do the ROESY experiment with Tm = 300 ms and with a spin-lock field of 5 kHz (fig. 4(C)). Besides positive diagonal peaks (thick contours), several pairs... 

Although two peaks of comparable amplitude are presented (see Fig. 2.1), only the first, denoted as Mi, is actually related to the carriers release from trap, the second, denoted as M2, is connected with dark conductivity variation with temperature (DC conductivity-determined relaxation peak related to the movement of equilibrium carriers). 

Such behavior of the TSDC peak is typical. On the other hand, the DC conductivity-determined relaxation peak shifts to lower temperatures when the band gap and/or preexponential factor decreases (Figs. 2.2 and 2.3). 

Thus, variation of the conductivity value a, mobility gap AE, and the activation energy of trap let us establish the range where TSDC peaks directly related to traps can be observed safely. For example, we can detect only traps with Ei < 0.6 eV if the dielectric relaxation peak locates close to the room temperature. 

Ultrasonic Pressure Transducers. Advantage is taken of the fact that pressure influences sound propagation in solids, liquids, and gases, but in different ways. In solids, applied pressure leads to so-called stress-induced anisotropy, In liquids, the effects of pressure are usually small (relative to effects in gases), but the frequency of relaxation peaks can be shifted significantly,... 

For the great majority of molecules, only one broad relaxation peak is observed and therefore it represents a continuum of the rotations of the molecule and the envelope cannot be delineated into rotations associated with specific bond groupings. There are some rare cases, however, where a more localised rotation is observed. For example, benzyl alcohol, which would be expected to have a relaxation time of more than 1000 ps on the basis of its volume, actually has a relaxation time of 188 ps and this has been attributed to a more localised rotation of the OH group relative to the larger benzyl... 

The contribution of the thermoelastic effect to energy dissipation in solids under transient or cyclic deformation was first studied by Zener and shown to account for mechanical relaxation peaks in some metals. 

FIGURE 18.11 Thermally stimulated depolarization currents of PVP K30 demonstrating two different global relaxation peaksPi is the (5-relaxation peak (representing molecular motion belfry, and P2 is the a-relaxation peak (representing mobility ). 

At 1 Hz, the main secondary relaxation peak is the ft peak, that appears at approximately - 70 °C. Furthermore, the peak has an asymmetrical shape, with a high-temperature side broader than the low-temperature side. The activation energy for the /3 peak is 70 8 kj mol-1 (Table 1). 

The associated activation energy (Table 1) is 56=bl0kJ, a value significantly lower than the one derived from mechanical measurements (Table 1). In the same way, the activation entropy (Table 2) of 53 d= 10 J K-1 mol-1 corresponding to the centre of the relaxation peak is lower that the value obtained from mechanical measurements. The symmetrical character of the dielectric P peak is also reflected in the constant value of ASa over the temperature range (Table 2). 

Fig. 21 Effect of different additives on the mechanical relaxation peak of PET at 1 Hz pure PET, 10% DMT, 10% TPDE and Q 20% TPDE (from [13])...

To examine in more detail the relaxation process suppressed by the additives, the relaxation peaks that were obtained from the PET/DMT blends have been subtracted from those obtained from pure PET. The result (Fig. 22) is a quite symmetrical peak, centred at - 60 °C for 1 Hz, which can be perfectly fitted with a Gaussian curve at each frequency, as shown in Fig. 22. The activation energy of the suppressed relaxation processes is approximately 70 kj mol-1. 

Fig. 22 Gaussian peaks that have been fitted to the suppressed relaxation peaks in PET at 1 Hz, + 3 Hz, A 10 Hz and 30 Hz (from [13])...

Fig. 24 Similarity between the dielectric relaxation peak in PET ( ) and the mechanical peak in a polymer/additive blend containing 10% DMT additive ( ) at 1 Hz (from [13])...

For the other reactive system for which T is lower than its Tgoo (= 177°C), the behavior is initially dominated by ionic conductivity and, as the reaction progresses, curves exhibit peaks due to vitrification (Fig. 6.9b). The higher the frequency, the lower the time at which this relaxation peak appears. 

In addition, from thermal and thermomechanical measurements, it is found that typical epoxy-amine networks exhibit one glass transition temperature, Tg, and one sharp well-defined relaxation peak. The same techniques were used for crosslinked polyurethanes based on triol and diisocyanate or diol and triisocyanate (Andrady and Sefcik, 1983). Similar conclusions to those found for epoxy-amine networks were attained. 

The P zone extend over a large temperature range. This is a characteristic of a secondary process which involve local motions of the lateral groups [155], They are more diversified movements with a large spectrum of relaxation times. Therefore, thermal cleaning of the t.s.c. global spectra is used to study the broad relaxation peaks of the low temperature secondary relaxation [42], This is effective because it allows one to excite only the specific transition of interest [155],... 

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