Relative permittivity apparent

These properties are sometimes grouped as the dielectric properties but this is not entirely logical as dielectric simply means insulating. Relative permittivity of a material can, for practical purposes, be defined as the ratio of the capacitance of a condenser having the material as the dielectric to the capacitance of a similar condenser having air, or more precisely, a vacuum as the dielectric. The word relative is usually dropped and the property simply called permittivity and is the same thing as used to be called dielectric constant (this term is apparently still used in the USA). 

Polarisation effects at electrodes become most prominent when the material of a specimen shows some appreciable bulk conductivity. Characteristically, there is an apparent increase in the relative permittivity at low frequencies. The anomaly originates in a high-impedance layer on the electrode surface. This may be caused by imperfect contact between the metal electrode and the specimen, aggravated by the accumulation of the products of electrolysis, etc. At low frequencies there is sufficient time for any slight conduction through the specimen to transfer the entire applied field across the very thin electrode layers, and the result is an enormous increase in the measured capacitance. For a purely capacitive impedance Ce at the electrodes, in.series with the specimen proper (geometrical capacitance C0), Johnson and Cole (1951) showed that the apparent relative permittivity takes the approximate form ... 

Bisphenol-A carbonate has been widely studied by dielectric [8-26], dynamic mechanical [27 31] and thermally stimulated depolarization (TSD) [10- 13 32 35] techniques. However, differences in the compositions of the materials studied, and in their thermal history and pretreatment, have led to apparently conflicting results being reported in the literature, as discussed in detail in a recent paper [6]. In the present study contour maps of complex relative permittivity for both basic and u.v.-resistant grades of LEXAN have been obtained over an extended range of experimental conditions using a single apparatus, with each grade of material subject to the same thermal history. 

E t is the potential barrier for rotation about the bond i, Ni is the symmetry of the rotation (usually 2, 3, or 6), is the angle of rotation, r is the distance between atomic nuclei, and ej and are partial charges derived from the dipole moments of the bonds. The factor B contains the Coulomb energy and the apparent relative permittivities (dielectric constants). 8ij, dij, and bi j are parameters describing the potential energy of the contributions from nonbonded atoms. A 9-6 potential is often used instead of the Lennard-Jones 12-6 potential shown in equation (4-2). 

To induce a macroscopic polarization, an external electric field has to be applied, which promotes the displacement of the domain walls. For low electric fields, polarization is proportional to the field, which helps to define an apparent relative permittivity, function of the temperature (see Figure 11.16). This depends on the orientation of the electric field with respect to the crystallographic axes, as already stated earlier. For a ceramic sample, the relative permittivity measured is an average of all possible orientations. 

Figure 11.16. Variation of apparent relative permittivity ofBaTiO with temperature. Case of a single crystal...

Figure 11.21. Variation of apparent relative permittivity of PMN as a function of temperature for different measurement frequencies...

A real capacitance behavior is observed only for frequencies less than 1/(2jiRC). A wide frequency range is obtained by increasing the grain conductivity as much as possible. This is the reason why strontium titanate was preferred to barium titanate, with the mobihty of electrons being greater (see Table 11.4). Typically, conductivity is 10 Q l cm i and the cut-off frequency 1 GHz. The apparent relative permittivity is of the order of 20,000. 

From the preceding relation, it is apparent that 1/k is inversely proportional to the valence Z of the ions in the solution phase and to the square root of their concentrations. It is also directly proportional to the square roots of the absolute temperature and the relative static permittivity (or dielectric constant) of the medium. It is therefore to be expected that in a solvent of high dielectric constant, such as water, electrical effects extend much further into the solution phase than in a solvent of low dielectric constant, such as a hydrocarbon. Also, in the presence of an electrolyte, electrical effects have shorter ranges than in its absence—that is, the electrical double layer is compressed. 

The dielectric properties of soil determine the amount of RF power that can be dissipated in the soil. These properties are the relative dielectric constant (e ) and the loss-tangent. The loss-tangent, tan 6, is defined as o/oieQe where a is the apparent conductivity, w is the frequency of the applied electric field, radians/sec, and is the permittivity of free space which equals 8.85 X 10 Farads/meter. All the dielectric properties are a function of soil temperature, the frequency of the applied field, and the composition of the soil. 

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