Activation energy dielectric relaxation

Detailed examination of the relaxations requires isothermal scans of relative permittivity and dielectric loss factor as a function of frequency/ so that effective dipole movements and activation energies of relaxation times may be obtained. A typical pair of plots of d and e" values against log/is shown in Fig. 3.7. Graphs of dielectric data of this kind are sometimes called, rather... 

The resonance DMR method applied in this work does not allow one to estimate the activation energy of relaxational transitions. Naoki and Akira (26) studied thermotropic LC polyester, whose chemical stmcture was similar to that of CPE-1 however, the ratio between the components involved was somewhat different 33.3 mol % NPA, 33.3 mol % HBA,and 33.3 mol % PHQ. The methods of DMR and dielectric relaxation (DR) were applied to investigate the two principal relaxational transitions that take place in the same temperature intervals as the relaxation transitions in... 

Finally, recently depolarized light scattering spectra [191] display an additional process that shows a much faster characteristic time and a much weaker temperature dependence than the dielectric j0-relaxation (more than three orders of magnitude faster time at -200 K and an activation energy of 0.16 eV, about half of the dielectric value). Also atomistic simulations on PB have indicated hopping processes of the frans-double bond [192,193] with an associated activation energy of -0.15 eV. Whether these observations may be related with the discrepancy in the apparent time scale of the NSE and dielectric experiments remains to be seen. 

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. 

Figure 2.3 Dielectric relaxation maximum as a function of DC conductivity activation energy E .

Activation energies of the viscous flow, dielectric relaxation process and orientational process in an electric field... 

The transition has also been detected in dielectric studies at frequencies from 103 to 107 cps (Mikhailov, Kabin, and Smolyanskii). The activation energy for the transition is 18 kcal per mole, and the activation entropy is 45 entropy units per mole. From the breadth of the loss peak in Fig. 8, it has been determined that more than a single relaxation time is required. 

In Equation 1, R and V refer to the relaxed (low frequency) and unrelaxed (high frequency) dielectric constants, and AH is the measured activation energy for the y process. The latter was nearly independent of blend composition an average value of 8.7 kcal/mole was used. The integral in Equation 1 was found to be approximately independent of frequency in the range studied. The loss peak in absolute terms is rather weak, and values of eR — V were of the order of 10"2 and less. From these values, it was also possible to calculate the apparent dipolar density, Np2, using the Onsager relation (9) ... 

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). 

The frequency analysis of this peak has been performed [18] and is shown in Fig. 27 in the temperature range - 112 to - 38 °C. In addition to the expected shift of the frequency at the peak maximum with increasing temperature, there was a large increase of ax, as we as a narrowing of the peak. Such a behaviour indicates that the dielectric / relaxation does not correspond to a unique process, but contains different processes with various activation energies, which gradually merge when the frequency is increased. 

It is worth noting that the relaxation observed from dielectric measurements (Fig. 77) occurs at the same temperature as the one from dynamic mechanical measurements. In addition, the activation energies derived from the maximum of the mechanical /3 peak (Table 7) are close to those obtained from dielectric relaxation (Table 6). 

Furthermore, the comparison between dynamic mechanical results and NMR mobility observations will be more delicate since it requires extrapolation of the mechanical response over about 5 decades, and must take into account the experimental uncertainty of the activation energy values. In the other reported polymers, the use of dielectric relaxation techniques, which cover a frequency range up to 105 Hz, overcame the extrapolation difficulty. Consequently, for the epoxy resins the comparison will remain more qualitative [63]. 

Furthermore, the activation energies (83 =t 5 kj mol-1 from mechanical analysis and 82 2 kj mol-1 from dielectric relaxation) as well as the activation entropies (51 3 J K-1 mol-1 from mechanical analysis and 58 33 J K-1 mol-1 from dielectric relaxation) are identical, confirming that the processes are the same. 

Figure 5.3 shows the measured temperature dependence of the loss tangent of LaA103 single crystals and a fit employing the skm model plus a Debye relaxation term. The best fit was achieved for an activation energy of 31 meV, the estimated defect concentration is only 1016/cm3. It was suggested that aluminium atoms on interstitial lattice positions are responsible for the observed relaxation phenomena. This indicates, that the dielectric losses are extremely sensitive to very small concentrations of point defects [21],... 

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