Arrhenius equation, dielectric relaxation

The variation of tan 8a (referred to the polarizability a) as function of temperature is shown in Fig. 2.79. The activation energy value for this relaxation, calculated according to an Arrhenius equation for the five maxima, is 16kcal mol 1. This is a small value for a glass transition temperature, but not too much considering that in this case a small part of the macromolecule is activated from the dielectric point of view at higher temperatures than that of the p relaxation. 

If we make an Arrhenius plot of Equation 4.54 using the data reported in Table 4.11, we get that = 70 [kJ/mol] [125], The value measured for the activation energy (EJ for the cation-hopping mechanism of dielectric relaxation is similar to the values measured for the activation energies for... 

All the examples described above show that confinement in different cases may be responsible for nonmonotonic relaxation kinetics and can lead to a saddle-like dependence of relaxation time versus temperature. However, this is not the only possible reason for nonmonotonic kinetics. For instance, work [258] devoted to the dielectric study of an antiferromagnetic crystal discusses a model based on the idea of screening particles. Starting from the Arrhenius equation and implying that the Arrhenius activation energy has a linear dependence on the concentration of screening charge carriers, the authors of Ref. 258 also obtained an expression that can lead to nonmonotonic relaxation kinetics under certain conditions. However, the experimental data discussed in that work does not show clear saddle-like behavior of relaxation time temperature dependence. The authors of Ref. 258 do not even discuss such a possibility. 

The activation energy (E ) was calcnlated nsing the Arrhenius equation. Figure 8.17 shows the relationships between the reciprocal temperature of the tanS peaks shown in Fignre 8.15 and the logarithm of the measured frequencies. From the gradient of lines shown in Fignre 8.17, Ti s were calculated 512 kJ/mol for a dispersion and 59 kJ/mol for p dispersion. The value of the a dispersion was consistent with the main chain motion of polymers [64]. The E of the P dispersion was almost the same as that of the relaxation of water sorbed on wood, as estimated by the dielectric measurement [36]. 

In Figure 11.17 we show Arrhenius plots of the isobaric [t (7)]/> (F = 0.1 MPa) and isochoric [t (7)] v/ (vy = 20 to 30 mm /g) dielectric relaxation times of PMPhS, where the free volume Vf was obtained from the S-S equation of state. The slopes at the intersection of the isochoric and isobaric curves yield the respective activation enthalpies for ambient pressure. 

Relaxation Phenomena Hilczer et al. [2002] studied the relaxation behavior of nanoceramic-polymer composites. The smdy focused on a PVDF/PZT composite with 30-nm particles. The dielectric relaxation time of PVDF as well as that of the low-temperature component followed VFTH [Eq. (13.2)]. By contrast, the relaxation time of the high-temperature component obeyed the Arrhenius equation. It is interesting to note that the activation enthalpy increased strongly in composites. The effect was ascribed to the wide-angle oscillation of dipolar groups of PVDF. 

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. 

In this paper, we analyze the effect of fluorine substitution in the polymers listed above by dielectric analysis (DEA), dynamic mechanical analysis (DMA) and stress relaxation measurements. The effect of fluorination on the a relaxation was characterized by fitting dielectric data and stress data to the Williams, Landel and Ferry (WLF) equation. Secondary relaxations were characterized by Arrhenius analysis of DEA and DMA data. The "quasi-equilibrium" approach to dielectric strength analysis was used to interpret the effect of fluorination on "complete" dipole... 

Keywords dielectric relaxation, dielectric strength permittivity, dipole moment, polarization, relaxation, conductivity, relaxation time distribution, activation energy, Arrhenius equation, WLF-equation, Maxwell-Wagner polarization. 

Figure 8 Relaxation rates vp vs. inverse temperature for the dynamic glass transition of PMPS as obtained by the different techniques , dielectric spectroscopy , thermal spectroscopy , neutron spectroscopy. The data obtained from neutron scattering depend on the momentum transfer 0. In addition to the dynamic glass transition, the relaxation rates for the methyl group rotation for 0=1.8A ( ) are given. The line is a fit of the Arrhenius equation to the data of the methyl group rotation ( A=8.3kJmoL, log(L = 12.5 Hz). The inset gives dielectric loss vs. frequency for PMPS at different temperatures 212.2 K o, 215.2 K ), 219.2 K A, 225.2 K 0, 235.2 K V, 241.2 K +, 257.41 K , 283.1 K. The errors of the measurements are smaller than the size of the symbols. Lines are guides to the eyes.

Figure 12 Dielectric relaxation behavior of PMPS. (a) Relaxation map. Solid lines are fits of the VF equation to the low- and high-temperature data. The dash-dotted line is an MCT fit where the dashed line is an Arrhenius fit to the high-temperature data, (b) Derivative plot of the data shown in (a), (c) f As vs. 1/7. Lines are linear regressions to the low-and high-temperature data.

Kinetic information on the molecular conformational change can be extracted from dynamic mechanical studies, as described in Chapter 10, from the closely related acoustic relaxation experiments described in Chapter 11, and from dielectric relaxation covered in Chapter 12. In all of these, the observation of a transition in the frequency dependence of the property under study yields a relaxation time for the molecular process. This in turn transforms into the kinetics of the movement. Again, the activation energy associated with the conformational change is obtained from the effect of temperature on the relaxation time, using either the Arrhenius equation or a related analysis. 

In the study of dielectric relaxation, temperature is an important variable, and it is observed that relaxation times decrease as the temperature increases. In Debye s model for the rotational diffusion of dipoles, the temperature dependence of the relaxation is determined by the diffusion constant or microscopic viscosity. For liquid crystals the nematic ordering potential contributes to rotational relaxation, and the temperature dependence of the order parameter influences the retardation factors. If rotational diffusion is an activated process, then it is appropriate to use an Arrhenius equation for the relaxation times ... 

Thermally Stimulated Current (TSC) studies allow us to investigate the transition spectra of amorphous polymers. The relaxation modes observed around and above the glass transition T have common features (1) The TSC peak isolated around Tg corresponds to a distribution of relaxation times following an Arrhenius equation. The width of the distribution characterizes the distribution of the order parameter. (2) The TSC peak observed some 50° above Tg is well described by a Fiilcher-Vogel equation. This mode, which can also be distributed, has been associated with the dielectric manifestation of the liquid-liquid transition (Ty). 

The TSC spectrum of reference polystyrene, being complex, has been resolved by using fractional polarizations. The elementary spectra of Figure 2 correspond to the same polarization field as above with a temperature window of 10°C. A narrow distribution of relaxation times is found around Tg, while there is no distribution of these around T . Using eq. (5), the dielectric relaxation times were obtained as shown in the Arrhenius diagram in Figure 3. The three processes isolated around Tg follow an Arrhenius equation... 

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