Dielectric relaxation loss function

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

Figures 3-5 that the dielectric relaxation again reveals only a single a relaxation for the mixtures. These are, however, noticeably broader than the a relaxation of the pure polymers. The temperatures of the loss maxima, when plotted (Figure 7) as a function of wu the weight fraction of PPO in the mixtures, do not display the smooth monotonic increase in T0 vs. Wi that was shown by both the Vibron and the DSC results. Instead, there is a pronounced increase in Tg above = 0.5 to give a sigmoid curve for this relation. Some reservations should be attached to this observation inasmuch as data for only three polyblend compositions are available nevertheless a qualitatively similar phenomenon is observed in the analysis of the intensity of the y peak (below). Further, if only the stronger maxima in the dynamical mechanical data are considered— i.e.y if the secondary peaks and shoulders which led to the identification of two phases are omitted—then a similar sigmoid curve is found. The significance of this observation is discussed later.

Figure 2 Dielectric loss as a function of frequency for systems permitting chemically induced dielectric relaxation d) Schematic curves...

Figure 4.3 Frequency-dependence of the imaginary (loss) part of the dielectric relaxation function for PDE at different temperatures. The lines are fits by the Cole-Davidson function, Eq. (4-2), with cu = 2nf and temperature-dependent exponent given in Fig. 4-4. (Reprinted from Physica, A201 318, Stickel et al. (1993), with kind permission from Elsevier Science - NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

It has to be mentioned that such equivalent circuits as circuits (Cl) or (C2) above, which can represent the kinetic behavior of electrode reactions in terms of the electrical response to a modulation or discontinuity of potential or current, do not necessarily uniquely represent this behavior that is other equivalent circuits with different arrangements and different values of the components can also represent the frequency-response behavior, especially for the cases of more complex multistep reactions, for example, as represented above in circuit (C2). In such cases, it is preferable to make a mathematical or numerical analysis of the frequency response, based on a supposed mechanism of the reaction and its kinetic equations. This was the basis of the important paper of Armstrong and Henderson (108) and later developments by Bai and Conway (113), and by McDonald (114) and MacDonald (115). In these cases, the real (Z ) and imaginary (Z") components of the overall impedance vector (Z) can be evaluated as a function of frequency and are often plotted against one another in a so-called complex-plane or Argand diagram (110). The procedures follow closely those developed earlier for the representation of dielectric relaxation and dielectric loss in dielectric materials and solutions [e.g., the Cole and Cole plots (116) ]. 

In the previous subsection, we have provided conceptually the rationale and experimentally some data to justify the expectation that the primitive relaxation time To of the CM should correspond to the characteristic relaxation time of the Johari-Go Id stein (JG) secondary relaxation Xjg- Furthermore, it is clear from the CM relation, Ta = ( "to)1 1- , given before by Eq. 6 that To mimics Ta in behavior or vice versa. Thus, the same is expected to hold between Xjg and Ta. This expectation is confirmed in Section V from the properties of tjg- The JG relaxation exists in many glass-formers and hence there are plenty of experimental data to test the prediction, xjG T,P) xo(T,P). Broadband dielectric relaxation data collected over many decades of frequencies are best for carrying out the test. The fit of the a-loss peak by the one-sided Fourier transform of a Kohlrausch function [Eq. (1)] determines n and Ta, and together with tc 2 ps, To is calculated from Eq. 6... 

The relaxation map of Fig. 55 shows the temperature dependence of the most probable relaxation times xa, xp, and xy of neat EPON828 obtained. The dielectric ot-loss peak of neat EPON828 was well-fitted by the one-sided Fourier transform of the KWW function with n = 0.47. It is temperature-independent near Tg and together with xa(I), the corresponding Tq(T) is calculated by Eq. (10). The calculated values of xo(7) at 7 256 and 259 K near Tg are... 

Dielectric relaxation (DR) experiments measure the collective polarization response of all the polar molecules present in a given system. The DR time provides a measure of the time taken by a system to reach the final (equilibrium) polarization after an external field is suddenly switched on (or off). DR measures the complex dielectric fimction, s(w), that can be decomposed into real and imaginary parts as efca) = s (o) — is" (o) where s (co) and s fo ) are the real (permittivity factor) and imaginary (dielectric loss) parts, respectively. The total dipole moment of the system, at any given time t, M(t) = fift) where N is the total number of dipolar molecules and /Af is the dipole moment vector of the ith molecule. The complex dielectric function e((w) is given by the following relation. 

The dynamic dielectric constant s (a)) and the dielectric loss e"(co) appearing in Equation (3.12) are expressed in terms of the normalized dielectric relaxation function 0(f) as... 

The dielectric loss factors d of the pure polypropylene and the composites containing the lignocellulosic materials derived from hemp and flax are presented in Figs. 14 and 15 as a function of the temperature for the frequency of 1000 Hz. Pure polypropylene is known to exhibit two characteristic features (Kotek et al., 2005) a glass relaxation p>eak around 263 K and a high - temperature ( 323 K) shoulder associated with chain relaxation in the crystalline phase. These features cannot be detected by the Dielectric Relaxation... 

Here eo - oo (= Ae, say) is the relaxation strength. Figure 2 shows plots of and e" against log cot for eo = 13, eco = 3 for equations 6,7 [the single relaxation time (SRT) function], tomax = 1 at the loss peak. Thus dielectric relaxation is characterized by Ae and r for this function. The steady ionic conductivity ao contributes an additional, rising loss at low frequencies given by e/ = uo/wev, but this process makes no contribution to s (co) in this case. 

Figure 2 includes curves for and " calculated using equation 4 and the KWW function for = 0.50. The loss curve is broad and nonssrmmetrical, with a total half-width A1/2 2.2 (cf 1.14 for the SRT process). The dielectric data for glycerol conform approximately to the KWW function (fi increases from about 0.6 to 0.95 as temperature is increased). Thus dielectric relaxation in polymers and other materials is characterized by the shapes of the b and b" curves in addition to Ab and (t). 

As with the dynamic mechanical relaxations, it is also possible to check the dielectric behavior of the sample. In this case the thermal analysis is carried out measuring the dielectric constant, dissipation factor, loss index, and phase angle as a function of temperature and frequency. In order to see a dielectric effect, a dipole must be connected with the molecular motion. In this way dielectric relaxation may be more specific than DMA. A combination of DMA, dielectric measurements, and DSC is often needed for a detailed interpretation of the properties of the materials. ... 

Here e( )) is the complex dielectric function, co) and e"(dynamic dielectric constant and the dielectric loss, oo is the high-frequency dielectric constant, and Ae is the dielectric relaxation intensity. 

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