Relaxations dielectric strength

Keywords dielectric relaxation, dielectric strength permittivity, dipole moment, polarization, relaxation, conductivity, relaxation time distribution, activation energy, Arrhenius equation, WLF-equation, Maxwell-Wagner polarization. 

The s parameter following this procedure is found to be between 0.91 and 0.95 and the conductivity increases x 10 x S cm-1. The activation energy, for this conductive process, obtained from the Arrhenius plot was equal to 100.5 kJ mol-1 (1.04 eV). As usual, the dielectric strength of the a -relaxation Ae = eoa — < coa, decreases when the temperature increases. The shape parameter for both parameters are nearly temperature independent. 

In order to obtain the excellent dielectric properties desirable for electronic applications the growth rate of coatings is limited to about 10 pm per hour at 300 °C, but well adherent layers can be grown at much higher rates if the requirements on dielectric strength are relaxed and temperatures of 400-500 °C allowed147. Since the depostion takes place simultaneously on the whole surface, only several hours should be necessary to redeposit a 100200 pm thick coating 34). 

Here, Ae is the dielectric strength and x the mean relaxation time. The parameters a and /i describe the symmetric and asymmetric broadening of... 

Electrical properties — dielectric constant (e), representing polarization dissipation factor (tan 8), representing relaxation phenomena dielectric strength (EB), representing breakdown phenomena and resistivity (pv), an inverse of conductivity — are compared with other polymers in Table 5.14.74 The low dielectric loss and high electrical resistivity coupled with low water absorption and retention of these properties in harsh environments are major advantages of fluorosilicone elastomers over other polymeric materials.74... 

The static value s is called the relaxed dielectric constant and the short-time (or high-frequency) value lDO the non-relaxed dielectric constant es — e,x, is called the dielectric strength. They are equal to... 

Figure 49. Temperature dependence of the dielectric strength As for sample C. Symbols represent experimental data corresponding to the relaxation times presented in Fig. 48 unfilled circles correspond to the data presented early in Fig. 46 filled circles represent the experiment with reduced water content [78]. The lines mark values of the averaged dielectric strength Asav for these experiments. (Reproduced with permission from Ref. 78. Copyright 2004, The American Physical Society.)...

Figure 49. Dielectric strength As as well as the thermal capacity ACp of the a-relaxation of PDMS normalized to the bulk values are plotted against pore size. The data show mark decrease of Ae and A(. from the bulk value on decreasing the pore size.

Figure 27. Dielectric strength of the alpha relaxation process of POHOAc at 500 K as a function of film thickness. Inset Refractive index of POHOAc at X — 630 nm in dependence on the film thickness.

Figure 9. Dielectric strengths ASaCmd Aspof the mixture of 16 wt.% tert-butyl-pyridine (TBP) in tristyrene. Full symbols are for Ae of the a-relaxation (right axis) and open symbols for Asp of the JG f-re taxation (left axis). Dotted lines are linear fits of ASp below and above Tg. Dashed vertical line indicates T=211.5 K [where logjQ(zJs) 3] and is near the temperature at which occurs the crossover of temperature dependence of Asp with an elbow-shape.

Figure 3. (a) Comparison of the dielectric loss spectra measured for lactose (filled symbols) and octa-O-acetyl-lactose (open symbols) obtained below their Tg at three indicated temperatures, (b) Temperature dependence of dielectric strengths of the y- relaxation processes of lactose and its acethyl derivative. 

Here Ae is the dielectric strength and t the mean relaxation time. The parameters a and P describe the symmetric and asymmetric broadening of the relaxation process. The temperature dependencies of the relaxation times of the observed a-relaxation process for pure PPX, PPX + Cu, and PPX + Zn samples demonstrate an Arrhenius behavior with the energies of activation 196 kJ/mol, 187kJ/mol, and 201kJ/mol, respectively, and correlate with the activation energies of the a-process in most known polymer materials [75]. 

The dielectric strength. As, which is proportional to the area under the loss peak, is much lower for the secondary processes, relative to the a relaxation analysed in the next section. This is a common pattern foimd in both polymer materials and glass formers. The P secondary process is even more depleted in linear polymers that contain the dipole moment rigidly attached to the m chmn, such as polycarbonate [78-80] and poly(vinyl chloride) (the behaviour of this polymer was revisited in ref [81] where the secondary relaxation motions are considered as precursors of the a-relaxation motions). Polymers with flexible polar side-groups, like poly(n-alkyl methacrylate)s, constitute a special class where the P relaxation is rather intense due to some coupling vnth main chain motions. 

However, the expected increase of the intensity of Af with temperature for secondary relaxations is not always observed as is evidenced by data relative to two epoxy resins poly[(phenyl glycidyl ether)-co-formaldehyde] (PPGE) and DGEBA, where the dielectric strength of the P process decreases with temperature [74]. The additionally detected y secondary process follows the usual pattern. In these systems the y relaxation is more intense than the P process, as was also found in n-ethyleneglycol dimethaciylate monomers with [47]. For the poly(n-alkyl... 

Figure 9. Temperature dependence of dielectric strengths for DEGMA evidencing the change of slope for the secondary relaxations around Tg The p process is merged under the main alpha process and so is only detected in a limited temperature range (adapted from reference [47]).

The study of the aP coupling is advantageous in poly( -alkyl methacrylate)s due to the accessibility to the crossover region by both dielectric and mechanical spectroscopies and to the fact that both secondary and main processes are associated with high dielectric strength values, in contrast to a variety of other materials where the P relaxation is much less intense,. 

In this paper, we analyze the effect of fluorine substitution in the polymers listed above by dielectric analysis (DEA), dynamic mechanical analysis (DMA) and stress relaxation measurements. The effect of fluorination on the a relaxation was characterized by fitting dielectric data and stress data to the Williams, Landel and Ferry (WLF) equation. Secondary relaxations were characterized by Arrhenius analysis of DEA and DMA data. The "quasi-equilibrium" approach to dielectric strength analysis was used to interpret the effect of fluorination on "complete" dipole... 

From the experimental point of view, all relevant parameters like the relaxation rate (or time), the dielectric strength, and the shape parameters can be estimated by fitting the HN function to the data (for details see references Schlosser and Schihihals 1989 Schonhals and Kremer 2003). As an example Fig. 12.5 gives the dielectric loss for poly(vinyl acetate) at the dynamic glass transition versus frequency at a temperature of T = 335.6 K. Only the HN function is able to describe the data correctly. 

In the following the properties of the p-relaxation are briefly given in terms of its relaxation rate, its dielectric strength, and the shape of the relaxation function. 

Dielectric relaxation and dielectric strength of pol)rpropylene and its composites... 

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