Low-frequency relaxations

Soil-Water Mixtures Figure 2 presents the dielectric spectra of clay-water mixtures (kaolinite and montmorillonite) after the influence of dc conductivity is removed. In addition to the orientational polarization of bulk water at 20GHz and adsorbed water at 10MHz, a low frequency polarization is observed at kHz to MHz frequencies. It should be noted that this low-frequency relaxation process cannot be generalized for all mineral-water... 

Figure 3.89. The two relaxations for a colloidal particle. The low-frequency relaxation is determined by diffusion in the far field, that at high frequency by Maxwell conduction in the double layer. The imaginary part "(fl)) has peaks at the two relaxations. Molecular relaxations, as considered in figs. 1.4,7 and 1.4.8 come on top of these and are observable at higher frequencies.

Relaxation in Insulating Crystals. The low-frequency relaxation of ionic materials consists typically of a set of simple decays arising from the motion of defects. - Some of these have freedom of extensive motion and contribute to the conduction current others are constrained to a few ndghbouring sites. Except at high temperature, the defects are remnants of the previous thermal and mechanical history of the sample. Their movement is a thermally activated process and relaxation times normally vary with temperature as exp AjkT). The e qierimental picture may be much complicated by the motion of electrons loosely bound to crystal defects. 

The Argand diagram of the 2.2 M solution of Et NCl shows three relaxation processes typical for aqueous electrolyte solutions (1) ion-pair relaxation (r l = tip), (2) low frequency relaxation (rj, as 8 ps) of water, (3) high frequency relaxation a 1 ps) of water, in contrast to that of the 2 M solution of Bu NBr where the relaxation process (2) splits up into two processes. Figure 7 shows the concentration dependence of the... 

Figure 7 Frequency dependence of the low frequency relaxation time r l of water in EttNCl solutions (curve 3) and splitting of in ButNBr solutions into (curve 1) and (curve 2), c. f. fig. 6.

Fig. 4.8 Plot of 8out against 8 using dielectric relaxation data for water in the frequency range 60 10 GHz [G5]. The solid line shows the contribution from the low-frequency relaxation process.

When ion pairing is present an additional relaxation is observed at low frequencies. A typical example is the MgS04 system in water. The ion pair has a dipole moment and therefore this species reorients in the alternating electrical field. The relaxation time associated with the reorientation is much longer than that associated with the reorientation of water molecules. It depends not only on reorientation of the ion-pair dipole but also on the kinetics of its formation and decomposition. For this reason, the parameter for the low-frequency relaxation process is strongly concentration dependent. 

F and NMF are also highly structured solvents as a result of hydrogen bonding. The low-frequency relaxation process in these systems can be attributed to the cooperative motion of hydrogen-bonded clusters. The process at the highest frequencies has a similar relaxation time to those observed in DMF and DMA. Thus, it is probably due to intramolecular rotation about the C-N bond in the monomer. The intermediate relaxation observed in NMF is attributed to rotational diffusion of a monomer. Relaxation parameters for F and NMF are also summarized in table 4.5. 

Urban, S., and Wurflinger, A. (2005) Thermodynamical scaling of the low frequency relaxation time in liquid crystalline phases, Phys. Rev. E 72,021707... 

In water/ice the LIB fraction describes the librational band, centered at 700—800 cm-1 and located near the border with the IR range. In the case of water the LIB fraction explains also the nonresonance low-frequency relaxation range. 

This drawback is avoided in the variant 2a + 2b, which concerns the second stage of our modeling. An explicit but very simplified consideration of the HB-related effects is now given in terms of a two-fraction model. Here the LIB fraction is involved similarly with the variant la. In the case of water, the variant 2a explains the low-frequency relaxation (Debye) and the libration bands. In the case of ice only the latter band is considered. 

The two different temperature dependencies described above for giass-forming liquids are present in a-chitin, and the simiiarity between dc conductivity and relaxation time for the two low frequency relaxations is clearly observed in Figure 2.12a and b. Both dependencies (dc conductivity (a, .) and relaxation time (t) versus T plots) show the same features an Arrhenius type relaxation will yield a straight line above 80 °C, whereas a non-Arrhenius relaxation will manifest as a curved line that suggests a VFTH type or glass transition below 80 °C in dry annealed samples. For wet and dry samples, the decrease of conductivity as the temperature is increased from 20 to 80 °C is likely due to the motion of water-polymer complex since water could be modifying the relaxation mechanism of the matrix material. 

TABLE 2.1 Parameter Values for the Arrhenius-iype Dependence in Relaxation Time. Low Frequency Relaxation in the 80-210 °C Range... 

Low Frequency Relaxations The Influence of Moisture Content on Dielectric Measurements... 

Fig. 2.3.10. Expected form of the dispersion of the principal dielectric constants of 4,4 -di-n-alkoxyazoxybenzenes. The suffix 0 refers to the static values and the suffix CO to the optical values, shows the low frequency relaxation and both s, and show the normal Debye high frequency relaxation. (After Maier and Meier. )...

Figure 13.7b shows the imaginary part of the dielectric modulus, M", versus/of a PA-11/BT 700-nm nanocomposite at 72°C for volume fractions / = 0.03,0.1, and 0.2. The maximum of M" decreases when the filler content increases, due to the increase in permittivity e. The filler content does not affect the frequency dependence of the three relaxations. However, the ratio between the maximum value of the a -mode versus the maximum value of the a-mode increases with increasing filler content, indicating the interphase effects between the polymer and the nanoparticles. The low-frequency relaxation associated with the MWS phenomena become more pronounced with increasing volume filler fraction compared to the other relaxations. This evolution is attributed to the increase in interfacial effects around the particles. 

It is considerably larger in the confined liquid crystals above Tni than in the bulk isotropic phase. The additional relaxation mechanism is obviously related to molecular dynamics in the kHz or low MHz frequency range. This mechanism could be either order fluctuations, which produce the well-known low-frequency relaxation mechanism in the bulk nematic phase [3], or molecular translational diffusion. Ziherl and Zumer demonstrated that order fluctuations in the boundary layer, which could provide a contribution to are fluctuations in the thickness of the layer and director fluctuations within the layer [36]. However, these modes differ from the fluctuations in the bulk isotropic phase only in a narrow temperatnre range of about IK above Tni, and are in general not localized except in the case of complete wetting of the substrate by the nematic phase. As the experimental data show a strong deviation of T2 from the bulk values over a broad temperature interval of at least 15K (Fig. 2.12), the second candidate, i.e. molecular translational diffusion, should be responsible for the faster spin relaxation at low frequencies in the confined state. 

Here, Cg and Cj f are capacities in the low- and high-frequency limits, respectively. Incidentally, a CPE is an empirical admittance function of the type A(i ) , which reduces to a pure conductance, A = 1/2 , when a = 0 and to a pure capacity when a = 1 its use is justified if the relaxation time of the process under study is not single valued, but is distributed continuously around a mean [27]. In Eq. (1), a p value <1 was ascribed to a certain roughness at the interphase, while an a value <1 was ascribed to a continuous distribution of low-frequency relaxation phenomena. The physical significance of these two CPEs is not entirely clear. At any rate, over the potential range of the capacity minimum (i.e. between —0.4 and —0.7 V/SCE) both a and P were found to be very close to unity, thus denoting that the behavior of the SAM approaches that of a simple series RC network closely. Nelson and... 

Impedance Spectra with Inductive Behavior at Low Frequencies Relaxation Impedance. Based on the concept of impedance elements, Gdhr [1986] described the Faradaic impedances as connections of impedance elanents each of which is associated with a single process. One of such an impedance element is the relaxation impedance, desalbing the surface relaxation of the interface and explaining the development of the pseudoinductive behavior in the low frequency range (frequency < 3 Hz) in the impedance spectra of the fuel cell. This behavior was first found by Muller et al. [1999] during poisoning the anode of a PEFC with... 

Low Frequency Relaxation in the Series of Ribose Phosphate Compounds Compound Cone. fr(MHz) Ax 10 A/mxlO ... 

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