Frequency Dependence of the Dielectric Losses

Fig. 108 Frequency dependence of the dielectric loss, e", for two different samples of PMMA at several temperatures (from [75])...

A detailed analysis of the dielectric response of PMMA has been performed [75]. The frequency dependence of the dielectric loss, e"y at a few temperatures is shown in Fig. 108. An increase in temperature is associated with a shift towards higher frequency, as expected, but also with quite a significant increase in the height of the peak maximum. 

Fig. 2.12 Frequency dependence of the dielectric loss s" for (A) PCHEM at 125°C, ( ) PCHPM at 100°C and ( ) PCHBM at 90°C. The solid line indicate the conductive contribution with different slopes. (From ref. [33])...

Obviously in the limit of low and high frequencies the parameters of the two models determine the frequency dependence of the dielectric loss in the a relaxation [162,163],... 

Dielectric Loss. The frequency dependence of the dielectric loss (e"diel) oF liquid microemulsions (T=20°C) is reported in Figure 2. 

Figure 2. Frequency dependence of the dielectric loss of liquid microemulsion samples at T=20°C.

The frequency dependency of the dielectric properties The presence of relaxation effects makes the dielectric properties not only temperature but also frequency dependent. The data listed in Table 9.11 show the extent of this effect at room temperature. The curves in Figure 9.17 give an impression of the temperature and frequency dependency of the dielectric losses of PK terpolymer due to the B- and y-relaxation effects. 

Figure 11 shows the frequency dependence of the dielectric loss, normalized with respect to the peak position and height of the a-process, for four different annealing times during the isothermal annealing at Ta = 425 K for stacked thin films of 18-nm thick P2CS layers. The dielectric loss data in the frequency domain at... 

Figure 22 shows Arrhenius plots of the relaxation times for the a- and approcesses obtained by the peak frequency of the dielectric loss e" for P2CS thin films with d = 3.7 nm. The peak frequencies/ and/a, are evaluated fi-om the frequency dependence of the dielectric loss due only to the a- and approcesses that are reproduced from Eq. (12) with best-fit parameters. The peak frequency of As"(f, Ta) after isothermal aging at a given aging temperature Ta for 30 h and with... 

Fig. 37. Natural clinoptilolite. (a) Irradiation dose dependence of the dielectric constant c (b) frequency dependence of the dielectric loss, tmS, for different...

Thus, (2.5) describes the curve in Fig. 2.1 which represents the frequency dependence of the real component of e (the pure dielectric component), and the characteristic frequency /d = o /27r = (27rrD) - The frequency dependence of the dielectric losses, i.e., the imaginary part of e is also... 

Another failure of the Debye theory is that the frequency dependence of the dielectric loss predicted by Eq. (8) is not what is observed experimentally. Experimental loss-log(frequency) curves are generally broader... 

As already stated, the addition of metallic fillers to a formulation serves to decrease the electrical insulation, but there may be other effects on the compound s electrical properties that may need to be taken into account. The frequency dependence of the dielectric loss factor increases as the metallic particles offset the low loss factors of the binder system. The loss factor is defined as the product of the power factor and the dielectric constant and is a measure of the signal absorption by the compound. Normally, low loss factors are desirable, particularly where a material is to be used in devices operating at high speed such as gallium arsenide based semiconductors, and this should be taken into account when formulating with conductive extenders. 

Figure 7.10 Frequency dependence of the dielectric loss factor of 164 kDa cis-polyisoprene in (a) benzene at concentrations (O) 1-91 and (0) 31.3 wt%, and (b) dioxane at concentrations (O) 0.85 and (0) 26.1 wt%, from original measurements by Adachi and Kotaka(6).

Figure 7.11 Frequency dependence of the dielectric loss function of cis-polyisoprenes in toluene at concentrations near 50 wt%, namely (x) 5 kDa, 52 wt% ( ) 14 kDa, 49 wt% (0) 32 kDa, 52 wt% and (O) 53 kDa, 52 wt%, using original measurements by Adachi, et a/. (31). Lines represent stretched exponentials, power laws, and their sums as described in the text.

Figure 3.2 Frequency dependence of the dielectric loss at 270 K for the homopolymers PVE and PI and for the blend 50%PVE/50%PI. Lines correspond to the estimated contributions of the a-relaxation to the spectra. Reproduced from Reference [5],...

Dielectric Measurements. The dielectric properties of Resin 5208 were followed for isothermal cures of 110, 125, 137, 148, and 162"C at several frequencies. Figure 7 shows the time dependence of the dielectric loss tangent for the combination of the PTFE... 

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.)...

Figure 25. Temperature dependence of the dielectric loss at four different frequencies Indicated in logarithmic value. Isothermal frequency spectra for the Y and 0 relaxations are shown In the Insets. Reproduced from Ref. 45. Copyright 1978 American Chemical Society.

In Figs. 27a and 27b we show the low-frequency dependences of the dielectric constant sf and the loss s", calculated from Eqs. (75) and (80). Here the solid lines... 

The computed absorption and loss factor are shown, respectively, in Figs. 31a and 31b Fig. 31c represents the low-frequency wing of the /r(v) curve characteristic for the non-resonance loss spectrum. Fig. 32 represents the frequency dependence of the dielectric constant s (v) and the Cole-Cole plot s"[s (v)]. The latter two graphs also agree with experiment. We see that our theory agrees reasonably well with the spectra observed by Bertie et al. [51]. Note the empirical formulas (72)-(74) by Hufford [20] could be applied for describing of the far IR ice loss spectrum (viz., at v < 100 cm-1), if the constant cfit in Eq. (72) is fitted properly (see Fig. 33). For T = 100 K cfit 17. 

Dielectric Loss in the Presence of an External Magnetic Field. Figure 2 shows the temperature dependence of the dielectric loss at a microwave frequency of 24 kMc. (3). The upper curve represents the loss in a field of 2800 gauss perpendicular to the microwave electric field, hence a molecular... 

Figure 2.17. Three-dimensional plot of the frequency and temperature dependence of the dielectric losses e" for the sample PPX + Cu, 8 vol. %. The accuracy of the measured dielectric losses is estimated to be better than 3%.

Table 5 Best-fit parameters for the frequency and temperature dependence of the dielectric loss g" observed for the P2CS ultrathin films of thickness d... 

When a polymer exhibits a maximum in the imaginary part of the dielectric permittivity (the loss permittivity, e") at frequencies less than 200 Hz, it becomes possible to make comparisons with the frequency dependence of shear moduli and most specifically with the loss shear modulus, G". This has been done for polypropylene diol, also called poly(oxypropy-lene), where there is reported a near perfect superposition of the frequency dependence of the normalized loss shear modulus with that of the normalized loss permittivity as reproduced in Figure 3. The acoustic absorption frequency range of interest here is 100 Hz to 10 kHz, yet present macroscopic loss shear modulus data can be determined at most up to a few hundred Hz. Nonetheless, for X -(GVGIP)32o there is a maximum in loss permittivity, e", near 3 kHz that develops on raising the temperature through the temperature range of the inverse temperature transition. With the width of the loss permittivity curve a distinct set of curves as a function of temperature become... 

Temperature and frequency dependence of the dielectric constant (e) and the dielectric loss tangent (6) of poly crystalline p-BN are depicted in Fig. 4-6, p. 30 [38]. 

Figure 12 shows the temperature dependence of the dielectric loss e" at a frequency of IkHz for each copolymer. 

Figure 15 Dependence of the dielectric loss on the logarithm of frequency during isothermal crystallization process for the elapsed times of 0,60,100, and 420 min. The open circles represent observed values, and the solid line overlapping with the open circles is given by a fit to the Havriliak-Megami equation. The dotted line, dotted-broken line, and broken line are the contributions from the a-process, oo-process, and p-process, respectively. The contribution on the lower frequency side is that from the DC conductivity due to impurities. This is represented by the solid line. With permission from Fukao, K. Miyamoto, Y. Phys. Rev. Lett. 1997, 79, 4613. ...

In conclusion, complex perovskite relaxor ceramics are characterized by a very diffuse range of the ferroelectric-paraelectric OD phase transition, owing to nano-scopic compositional fluctuations. The minimum domain size that stiU sustains cooperative phenomena leading to ferroelectric behavior is the so-called Kiinzig region (Kanzig, 1951), and is on the order of 10 to lOOnm in PMN. In contrast to normal ferroelectric ceramics, relaxor ceramics show a frequency dependence of the dielectric permittivity as well as the dielectric loss tangent, which presumably is caused by the locally disordered structure that creates shallow, multipotential wells. 

Fig. 5.19. Frequency- and temperature dependence of the dielectric loss in cis-PIP (M = 1.2 10 ), indicating the activity of two groups of relaxatory modes. Spectra obtained by Boese and Kremer [58]...

The frequency dependence of the dielectric constant and the loss tangent of BoSPS is shown in Figure 13.20. In BoSPS, the low dielectric constant and the small loss tangent are unchanged over the wide range of frequency. 

Fig. 6.30. Frequency dependence and temperature dependence of the dielectric loss associated with the /3-process in PEcVA with 17% per weight of VA units (83)...

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