Dielectric loss peak

Figure 2. Secondary dielectric loss peaks (1 kHz) in cured I.

The temperature dependence of e and k in a roll-drawn and polarized PVDF was measured by Oshiki and Fukada (1971) and is illustrated in Fig. 28. Both quantities have maxima at — 20° C and 50° C where dielectric loss peaks are observed, due to primary and crystalline relaxations, respectively (Sasabe and others, 1969). 

FIG. 13.29 Frequency-temperature correlation map for polystyrene, (o, ) mechanical loss peaks ( , ) dielectric loss peaks (A, ) NMR narrowing and T, (i.e. spin-lattice relaxation time) minima for (open symbols) atactic an (filled symbols) isotactic polystyrenes. From Yano and Wada (1971). Courtesy John Wiley Sons, Inc. 

The CD function indicates that the dielectric loss (e") of glycerol follows the power law e" /Pcd at high frequencies (f fmx), where/max is the frequency corresponding to the dielectric loss peak. However, the high-frequency experimental data in Fig. 24 demonstrate a significant deviation from the expected asymptotic behavior both for CD and KWW functions, e" values... 

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],... 

These observations underlie many of the empirical functions commonly used to describe dielectric loss peaks, for instance, the ones proposed by Cole and Cole (100), Davidson and Cole (101), and Havriliak and Negami (102). In the time domain, the empirical KWW relaxation function 0(t) oc exp[—(t/t) ] often provides a reasonable description of experimental data (103). Since the response function is calculated as the negative derivative of 0(t), it behaves as a power law for short times. Moreover, the ubiquitous occurrence of power laws in (dielectric) spectra explains why log-log representations often are preferable power laws present themselves as straight lines when a log-log scale is used. 

The dielectric loss behavior of both polyethylene s Y transi-tion and polycarbonate s 0-transltion was enhanced by the presence of unassociated water. The area under the associated loss peak was found to increase in direct proportion to the concentration of unassociated water. In addition a secondary dielectric loss peak associated with frozen clustered water occurred in polycarbonate about 40°C below Its g-transition. Liquid clustered water at... 

In view of Table II the main difference of the parameters, fitted for HW, from those, fitted for OW, concerns (i) some increase of the libration amplitude / , (ii) decrease of the form factor /, (iii) decrease of the frequency vq (the center frequency of the T-band) and increase of the moment nq, responsible for this band, and (iv) decrease of the intensity factor gj, which strongly influences the THz band. Comparison of curves 3 in Figs. 4h and 5h shows that the partial dielectric loss peak g"max of HW, located at v near 150 cm-1 and stipulated by harmonic longitudinal vibration of HB molecules, substantially exceeds such a peak of OW, since the elastic dipole moment / (D20) 8.8 D exceeds the moment / (H20) 3.5 D. 

Figure 14.12 (a) Effect of temperature on dielectric loss peak in an Li20-Si02 glass. As the temperature increases, the frequency at which the maximum in loss occurs also increases, since the mobility of the ions increases, (h) Temperature dependence of frequency at which maximum in dielectric-loss peak occurs. 

In one investigation, using a viscoelastometer, crystal mats of polyoxymethylene from cyclohexanol solution showed a 7-loss modulus peak at 200°K. ( 102 c.p.s.) (40), reduced in magnitude but at approximately the same temperature as that for melt-crystallized material. However, results obtained for crystals, grown at 97°C. from a 1% Delrin 500 solution in a 3 1 phenol-ethanol mixture (5), indicated that the attenuation peak for crystals suspended in methanol and the associated dielectric loss peak are at lower temperatures than that for the loss peak in melt-crystallized material, in agreement with results for polyethylene. A sample prepared by... 

Chiu (116) used the apparatus previously described to study the thermal decomposition of selected polymers such as polyethylene terephthalate), po y(vinyl fluoride), po y(vinylidene fluoride), and others. The dielectric constant curves of a group of fluorocarbon polymers are shown in Figure 11.33. As illustrated, the more polar polymers such as poly(vinylidinefiuoride) (PVDF) and poly(vinyl fluoride) (PVF) show characteristic dielectric loss peaks that are distinguishable from the relatively featureless and low-loss curves of the other polymers. For PVF, the low-temperature process is due... 

The dielectric loss peak of secondary relaxations is extremely broad due to the variety of molecular environments (structural heterogeneity) of the relaxing unit, and, consequently, a variety of energy barriers, being more or less symmetrical. 

K and the peak height decreases with decreasing film thickness. In addition to this behavior, another process around 320 K is evident rally for the d = 3.7 nm thin film. This peak of e" due to another process is also observed for thin films of both PS and PS labeled with the dye DRl (disperse red one) [27, 78]. This extra loss peak was attributed to the segmental motion of a liquid-like layer near the surface or interface, which we have called the approcess. The loss peak observed for ultrathin P2CS films may also be attributed to the approcess. If the thickness of the liquid-like layer is independent of the overall thickness, then the contribution of the liquid-like layer becomes more appreciable as the thickness decreases. Figure 18 shows that the dielectric loss peak due to the a-process is reduced and, accordingly, that of the approcess becomes more appreciable as the film thickness is decreased to d = 3.7 nm. 

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. 

An analogous expression for the dielectric loss in terms of the derivative of the permittivity is commonly used to avoid the problem of dielectric loss peaks being masked by dc conductivity (the latter not contributing to the in-phase response) (Wubbenhorst and Van Tumhout, 2002). 

Do these critical frequencies associated with reproduction processes (or their ranges) correspond to the frequency of the dielectric loss peaks of... 

Table III. Dielectric Loss Peaks Observed at Several kHz of...

---