Dielectric loss tangent tan

Polymer Dieleetrie permittivity e, eonventional polymer Dielectric permittivity e, plasma polymer Dielectric loss tangent tan S, eonventional polymer Dielectric loss tangent tan S, plasma polymer... 

Figure 11.15 Dielectric loss (tangent tan 8) versus fractal dimension (D) of the macromolecule section for copolyethersulfone formals with the content of formal blocks of 1 0, 2 5, 3 10, 4 30, 5 50 and 6 70 mol%. Measurement frequency 1 kHz.

The dielectric loss tangent (tan 6 ) analogous to the mechanical case is obtained from the ratio... 

The company s dielectric analyzer (DEA) measures capacitive and conductive properties over different frequencies, temperatures, and times to determine the permittivity e, loss factor e", dielectric loss tangent tan 8, and ionic conductivity. The DEA measures data at eight decades from 0.003 to 300,000 Hz [3]. Decades and octaves quantify frequency changes. 

The required properties for dielectric resonator materials are (a) high dielectric constant (b) low dielectric loss tangent tan and (c) low temperature coefficient of resonant frequency Xj. Many kinds of dielectric resonator materials have been developed since the 1970s 128-311. Table 5.1.5 shows the dielectric properties of some materials that are commercially available now. In the table, the quality factor Q is reciprocal of dielectric loss tangent Q = If tan As tan S is proportional to frequency for ionic paraelectric materials, the product of Q and frequency is the value inherent to each material. Some materials have high Q value equal to copper cavity and some have the temperature coefficient as stable as Inver cavity. The material with lower 8j. generally has higher Q value. 

Figure 8.13 Mechanical and dielectric loss tangent tan 8 and NMR absorption line width (maximum slope, in gauss) of polytrifluorochloroethylene (Kel-F) (41).

The real (s ) and imaginary (s ) parts of the dielectric constant as well as the dielectric loss tangent (tan ) can be extracted from equation (20),... 

As illustrated in Appendix 1 it can be proved that the relaxation time T2 corresponds to the frequency of the maximum in dielectric loss tangent (tan ). In this method the characteristic time constant T2 was chosen from the frequency at the maximum in tan( ). Hence, by using the relation T2 = T -JS equation (20) can be modified to... 

Fig. 6. The frequency dependent of imaginary part of the dielectric constant (e ) and dielectric loss tangent (tan = ) according to equation (24) for S = 2x 10 and T2 = 1.4 x 10 s.

Fig. 6 shows a typical example for dielectric loss tangent, tan, curve according to equation (36). The measured data for dielectric loss tangent can be fitted to equation (36) in order to estimate values for S and T2. In addition, to estimate S and T2 the coordinates at the peak value (maximum) in tan can also be used ( see Fig 6). The T2 can be calculated using the frequency corresponding to the maximum in tan and S can be estimated using the peak value of tan as described in Appendix 1. 

Fig. 11 shows the dielectric loss tangent, tan, as a function of frequency for l-methyl-3-propyl imidazolium iodide, at different temperatures. In order to estimate T2 and 5 this tan plots can also be employed. 

The heating characteristics of a particular material (for example, a solvent) under microwave irradiation conditions are dependent on the dielectric properties of the material. The ability of a specific substance to convert electromagnetic energy into heat at a given frequency and temperature is determined by the so-called loss tangent, tan <5. The loss factor is expressed as the quotient tan (3 = "/ , where e" is the dielectric loss, indicative of the efficiency with which electromagnetic radiation is... 

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

Dielectric measurements on PET [13], over a range of five different frequencies between 1 Hz and 10 kHz, at temperatures between - 120 and 80 °C, are shown in Figs. 12 and 13 for the dielectric constant, er> the loss tangent, tan <5, respectively. 

When an a.c. voltage is applied to a perfect capacitor, no energy is dissipated. However, a real capacitor dissipates energy because of lead and electrode resistances, d.c. leakage resistance and, most importantly, dielectric losses. These account for the capacitor s dissipation factor or loss tangent tan 3. It is sometimes convenient to regard the lossy capacitor as an ideal capacitor shunted by a resistance Rp or in series with a resistance rs, as shown in Fig. 5.5. 

In addition to high breakdown strength, the electrical insulators for superconducting magnets must have excellent dielectric properties at cryogenic temperatures. Chant reported the results of measurements on dielectric constant and loss tangent (tan 5) for several polymers over the temperature range from 4.2 to 300 K [83], The variation of dielectric constant of samples as a function of temperature is shown in Fig. 15. The dielectric constants of nonpolar polymers, such as polyethylene, polypropylene and polytetrafluoroethylene, are substantially independent of temperature, whereas those of polar polymers except polyimide decrease by a maximum of 20% as the temperature is reduced. The values of tan 8 at the frequency of 75 cps for nonpolar polymers decreased by... 

Several parameters are used to characterize the interaction of microwave radiation and matter the complex permittivity (e ), the dielectric constant O ). and the loss tangent (tan S). The dielectric constant, i-. can be thought of in a straightforward manner, as shown in Figure 5.15. Two parallel plates have a given capacitance, Co, when there is no material between them a vacuum. When the vacuum is replaced by a nonconducting medium, a dielectric, the new capacitance, C, is greater than Cq. The dielectric constant, e, is the ratio of these two capacitances ... 

The heating effect relies upon dielectric polarization [1], itself containing components of electronic, atomic, dipolar, and interfacial polarization, of which the last two have timescales which allow them to contribute to the overall heating effect at these frequencies. The loss tangent, tan 5, consists of two components, s, the dielectric constant, and s", the dielectric loss, where... 

The so-called loss tangent, tan 8, is a very useful dimensionless parameter and is a measure of the ratio of the electric energy loss to energy stored in a periodic field. The product x tan 8 is directly proportional to the dielectric loss of energy, e.g. in a high-voltage cable. 

At room-temperature, from the capacitance-frequency and loss tangent (tan S )-ffequency figures, it can be seen that the dielectric constant e and the loss tangent (tan 6 ) of BaTiOj ceramics can keep constant. Their properties are stable, at the range of certain frequency (200 150 000 Hz) (Fig. 5). Based on the equation ... 

The product of the dielectric constant and the loss tangent (tan 5) is called the loss factorP E", and is a relative measure of how easily a material will be heated by microwave energy. 

The electrical properties of polymers are important in many applications [1]. The most widespread electrical application of polymers is the insulation of cables. In recent years, high-performance polymers have become important in the electronics industry as encapsulants for electronic components, as interlayer dielectrics, and as printed wiring board materials. The dielectric constant (or permittivity) and the dissipation factor (or power factor or electrical loss tangent) tan 8, which are dimensionless quantities, are the key electrical properties. 

Figure 3. Dielectric loss (V j and loss tangent (tan l) as a function of frequency. Anionic polymer (Mn = 10s).

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