Activation energies of the relaxation process

Dynamic mechanical response spectra of elastin145 (insoluble protein of vessels and ligaments), poly(ethylene terephthalate)141 and polycarbonate based on Bisphenol A (4,4 -dihydroxydiphenylmethane)141 show that incorporated water brings about enlargement of the existing secondary loss peak and its displacement toward lower temperatures. In conformity with the latter result, the activation energy of the relaxation process of elastin decreases. So far, no detailed data on this type of relaxation have been collected so that the copartidpation of water in the molecular motion cannot be specified more accurately. 

The resultant data are plotted in Arrhenius form in Figure 1 and the resultant values for the activation energies of the relaxation processes are listed in Table I. 

Energies required for main-chain and side-group motions can be obtained by determining the effect of frequency on the maximum temperatures of the loss or tan 8 peaks. The temperature at the peak maxima, Tmax, increases with increasing frequency and the activation energy, of the relaxational process may be determined from the slope of a semilog plot of frequency (/) versus reciprocal peak-temperature (l/Tmax) as... 

Estimate the activation energy of the relaxation process responsible for the deformation of polycarbonate from figure 8.9 ... 

From the temperature dependence of tan 8 it follows that for the 65 35 IPN the continuous phase is the PU-enriched phase, whereas for the 50 50 IPN the continuous phase is PBMA-enriched phase. From the temperature dependence of tan 8 at various frequencies the activation energies of the relaxation processes in IPNs have been calculated [192] using the Arrhenius equation ... 

An attempt will now be made to determine the activation energies of the two processes, since the identification of the mechanism is based primarily on this factor a study of all the stress relaxation curves has revealed that within experimental error time-temperature superposition is valid above a modidus of 10 dynes/cm , and that the shift factors are of the WLF form. Therefore, we can determine the constants of the WLF equation which were listed in Table 3 and also the corresponding activation energies. The values of the activation energies for the process which is governed by these shift factors, calculated for T —Tg + 30, ranges from 150 to 230 Kcal. This mechanism will, for the moment, be called the "first mechanism. 

No significant effect of either water or sucrose content was observed on the activation energy of the relaxation E 480 kj/mol) in the concentration range studied. This could be due to the actual merging of sub-Tg processes, dehydration artifacts, and a relaxation features, which caused some difficulties in the accurate determination of the peak maximum at different frequencies. 

Here Ae is the dielectric strength and t the mean relaxation time. The parameters a and P describe the symmetric and asymmetric broadening of the relaxation process. The temperature dependencies of the relaxation times of the observed a-relaxation process for pure PPX, PPX + Cu, and PPX + Zn samples demonstrate an Arrhenius behavior with the energies of activation 196 kJ/mol, 187kJ/mol, and 201kJ/mol, respectively, and correlate with the activation energies of the a-process in most known polymer materials [75]. 

Here tq is the relaxation time at equilibrium (Tf = T) at high temperatures, x is a structural parameter and measure of nonlinearity, with values 0 < x < 1, and AE is the activation energy for the relaxation processes and has an Arrhenius temperature dependence. The models also use the stretched exponential function of Kohlrausch, Williams, and Watts [1970] (KWW) to describe the distribution of relaxation times as... 

In most supramolecular structures, the temperature dependence of the characteristic dielectric relaxation time follows the Arrhenius equation, r = Toexp(A dip/ T). where tq is the preexponential factor that is often of the magnitude of the vibrational time scale and A dip is the activation energy of the dipolar process.The dipolar process of the host lattice and the trapped molecules follows this behavior, but A trapped molecules is less than that for the host lattice molecules. In ice ciathrates, the dipolar processes of the water molecules that form the host lattice and the guest molecules inside the cages of this lattice occur at widely different time scales. This allows for a reliable attribution of the dielectric spectra features to water molecules and to the guest molecules. As an example of the magnitude of the dielectric properties of supiainolecular structures, the data on selected ice clathrates and other inclusion compounds are summarized in Tables 1 and 2. 

By varying an external parameter, such as the temperature, the pressure, or an applied magnetic field, the relaxation time may be varied and its value obtained from the Mossbauer spectra by modeling the line shape profile. An Arrhenius plot of the temperature or pressure dependence of the relaxation time yields the activation energy for the relaxation process. 

As the activation energies of different relaxation processes differ, their relaxation time also differs. This is the reason why the simple spring-and-dashpot model from section 8.2.1 cannot be used to make quantitative predictions. This would require coupling several such elements [97] with relaxation times chosen to fit their respective processes. 

We already saw in section 8.1.1 that the activation energy of some relaxation processes is so low that it can be overcome by thermal activation already at temperatures as low as a few kelvin. At room temperature, their relaxation... 

The relaxation times of the E-process are intermediate between the fast process and the a-process below about 320 K, while they almost agree with those of the a-process above -320 K. The activation energy of the E-process, which was evaluated above -300 K,is 2.5 kcal/mol (see Fig. 23). This value corresponds to the barrier height of a single C-C bond rotation. Similarly, the activation energies of the E-process for PCP and PIB were obtained as 2.6 kcal/mol and 2.9 kcal/mol, respectively. These values are close to the activation energy pre-... 

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