Dielectric loss peak, width

As illustrated in some of these figures, all the a-loss peaks are well-fitted by the one-sided Fourier transform of the KWW over the main part of the dispersion. Thus, the experimental fact of constant dispersion at constant xa can be restated as the invariance of the fractional exponent KWW (or the coupling parameter n) at constant xa. In other words, xa and (or n) are co-invariants of changing thermodynamic conditions (T and P). If w is the full width at half-maximum of the dielectric loss peak normalized to that of an ideal Debye loss peak, there is an approximate relation between w and n given by n= 1.047(1 — w-1) [112],... 

The width of the dielectric loss peak given by equation (9.28b) can be shown to be 1.14 decades (see problem 9.3). Experimentally, loss peaks are often much wider than this. A simple test of how well the Debye model fits in a particular case is to make a so-called Cole-Cole plot, in which s" is plotted against e. It is easy to show from equations (9.28) that the Debye model predicts that the points should lie on a semi-circle with centre at [(fis + oo)/2, 0] and radius (e — Soo)/2- Figure 9.3 shows an example of such a plot. The experimental points lie within the semi-circle, corresponding to a lower maximum loss than predicted by the Debye model and also to a wider loss peak. A simple explanation for this would be that, in an amorphous polymer, the various dipoles are constrained in a wide range of different ways, each leading to a different relaxation time r, so that the observed values of s and e" would be the averages of the values for each value of r (see problem 9.4). 

Show that, according to the Debye model, the width of the dielectric loss peak e" plotted against frequency is 1.14 decades measured at half the peak height. 

CONCEPTS More about relaxation process within solids Typical loss peaks are broader and asymmetric in solids, and frequency is often too low compared with Debye peaks. A model using hypotheses based on nearest-neighbor interactions predicts a loss peak with broader width, asymmetric shape, and lower frequency [27]. This behavior is well suited to polymeric, glassy materials and ferroelectrics. Low temperature loss peaks typically observed for polymers need many-body interactions to be obtained. Although current understanding of these processes is not yet sufficient to enable quantitative forecasting the dielectric properties of solids may offer insight into the mechanisms of many-body interactions. 

In the frequency domain, the dielectric -relaxation displays a broad and in the most cases symmetric loss peak with half widths of four to six decades [41]. The variety of molecular environments (structural heterogeneity) of the... 

Thus, from both the DSC and the dielectric relaxation data cited earlier, the crossover of r y of PI in the HAPB of 35% and 20% PI with PtBS from VFT to Arrhenius dependences is not found at any temperature. This is the most direct proof that the confinement scenario is unreal. Arrese-lgor et al. (2010) admitted that the crossover predicted by the confinement scenario is not observed on Xaf of PI in the HAPB, but still maintained a vestige of confined dynamics by invoking the marked decrease of the intensity and increase of width as temperature decreases of the a-loss peak of PI in the 20% PI blend. 

During the isothermal ciystallization of PET at 97.5 ° C, that is, about 20 °C above its calorimetric glass transition temperature, the peak of the a-process is positioned at 104 Hz, and the shape of the dielectric loss curve is asymmetric as it is typically observed for the a-process of amorphous polymets. Hgure 15 shows contributions from the DC conductivity on the lower frequency side and a tail of the subglass p-process, whose peak exists above 1 MHz. As time passes, the peak value of the a-process deaeases and another peak appears at 10-100 Hz. The shape of the dielectric loss curve of the oo-process is quite different from that of the a-process the peak width is much broader than that of the a-process, and the peak shape is symmetric. Figure 16 shows that Ae of the a-process deaeases with time and eventually... 

This function is assumed to represent the superposition of many Debye functions [Eq. (6.5)] with various relaxation times (Bottcher and Bordewijk 1978). In terms of the Havriliak-Negami model, a complete description of a real (non-Debye) relaxation process in a polymer requires calculation of four parameters the dielectric strength (Ae), a parameter related to the relaxation time of the process at the temperature of the scan (xhn), and two shape parameters (0 < ttHN < 1 and 0 < Phn 1). The latter describe the width and the asymmetry of the loss peak, respectively, but lack a physical meaning. 

The dielectric loss characteristics of polar polymers are much more complicated, as would be expected from the theoretical aspects described above. The range of values in the dissipation factor for a variety of plastic material is tremendous (see Figs. 35 and 36). The absorption peaks also vary greatly in width. In general, the dissipation factor at a given frequency and temperature cannot be predicted for other conditions. The common practice of providing one value at perhaps 1000 Hz is obviously completely inadequate in the functional sense. For a meaningful evaluation, it is necessary to obtain dissipation factor values over... 

These relationships are known as the Debye formulae. The Debye process has a relaxation time distribution, which is symmetrical around /niax= niax/2n and has a full width at half-maximum of 1.14 decades in frequency for the dielectric loss. In most cases, the half width of measured loss peaks is much broader than the predicted by eqn [26] and in addition, their shapes are asymmetric and with a high-frequency tail. This is the non-Debye (or nonideal) relaxation behavior found in many glass formers. In the literature, several empirical model funaions, mostly generalization of the Debye function, have been developed and tested which are able to describe broadened and/or asymmetric loss peaks. Among these empirical model functions, the most important are the Kohlrausch-Williams-Watts (KWW), Cole-Cole (CC), Cole-Davidson (CD), and the Havriliak-Negami (HN) function. The HN function, with two shape parameters, is the most commonly used funaion in the frequency domain. 

Various model available to fit the non-Debye relaxation profiles Width of loss pe also provide the measure of dynmnic heterc eneity Dielectric intensity/strength or a-peak decreases as crystallization progresses with time) Exact identity of molecular relaxor needs complementary analysis... 

---