Dielectric mixing rules

Assuming the mixture of dielectrics and spherical pore with 3-0 connectivity, the dielectric constant (K) and loss quality (g) of (Pbo 5Cao.5)(Feo 5Tao.5)03 with different porosity were evaluated by the dielectric mixing rule. For the specimens with porosity, the ionic polarizabilities modified by Maxwell s Equation were closer to the theoretical values than those modified by Wiener s Equation. The predicted loss quality obtained from intrinsic ones and Maxwell s Equation agree with the observed ones. 

The surface tension is important for the calculation of mass transfer coefficients and the specific contact area (see Section 9.4.4). Depending on the availability of necessary parameters, the surface tension for a molecular species can be determined either with the simplest method of Hakim-Steinberg-Stiel or with a more complex DIPPR-method (see Ref. [52]). The mixture surface tension can be obtained via a mixing rule. A further extension to cover electrolyte mixtures is realized by the method of Onsager and Samaras (see Ref. [44]). The latter uses an additive term which can be estimated using the dielectric constant of the mixture and molar volumes of electrolytes. 

Inhomogeneous particles. For particles composed of a matrix and inclusions one approach for calculating optical properties is to assume an average dielectric coefficient (e) for the composed particle. A number of so-called mixing rules have been proposed a frequently used one is the Maxwell-Gamett mixing rule (cf. Bohren Huffman 1983). For a matrix with dielectric coefficient em, and a number of different kinds of inclusions with dielectric coefficients ej and volume fractions f) one uses... 

However, in most cases a limited miscibility (depending on Ni and k) (see Eq. 12.52) is observed leading to two phases enriched in mie compmient which can be described by a concentration Q. In principle the cmicepts developed in Sect. 12.4.2 can be employed to model the dielectric properties of each phase. In principle by analyzing the frequency position of the a-relaxati(Mi and its dielectric strength, the unknown concentration of each component can be estimated assuming appropriate mixing rules. In practical work this can be difficult. Of special interest is again the case where one component is dielectrically invisible as also discussed in Sect. 12.4.2. 

Dielectric analysis can determine concentrations of ingredients in mixtures based on differences in the electrical properties. Mixing rules describe how dielectric constant varies with concentration. For many materials, the relative permittivity e of a mixture containing volume fraction (pA of non-polar polymer A with relative permittivity ba and volume fraction (pB of additive material B with relative permittivity 6b is given by... 

In the composite, the dielectric constant is determined by the dielectric constant and volume fraction of the constituent material, and the complex form of the constituent material [31]. Table 2-5 shows the 4 different models of mixing rules for complex forms of the constituent materials. LTCC ceramics, being of the type with ceramic particles distributed in a glass matrix, fit the Maxwell model well. In order to achieve a lower dielectric... 

Impregnatioo of PVDF films with polar liquids such as propylene carbonate which exhibit large dielectric constants and dissipation factors reduces the breakdown tendency at application of strong electric fields (90,91). This is due to the smoothing of structural defects, and to the enhancement of dielectric strength by a mixing rule for the permittivities. 

III. DIELECTRIC PROPERTIES OF COMPOSITES A. Mixing Rules (or Permittivity... 

We present in this section the results of a few studies of dielectric properties of 0-3 polymer-ceramic composites and compare some of those with the mixing rules described in Section U. 

With regard to experimental data presented in Figures 21 and 22. we see that it is impossible to describe the dielectric constant (Fig. 21) and tan ft (Fig. 22) by the same mixing rules. Theoretical approaches to the linear response phase systems, even in the simplest noncoupled case, are based on various models of mixing rules [112]. A... 

The classical expressions for ai, pf , and up are similar to the pure-gas expressions with the slight added complication of having two sets of isolated-molecule parameters o oo, fio,. Fo, The determination of the mixed-pair parameters involved in uq is much more difficult. The determination of these parameters from mixed viscosities and pressure virial coefficients is hampered by a shortage of experimental data, and the usual procedure is to employ a set of empirical combining rules which relate the mixed parameters to those of the pure gases. A number of such rules have been proposed for the 6-12 potential, the most widely used for dielectric calculations being... 

The amount of free moisture in a substance greatly affects its dielectric constant since water has a high dielectric constant, approximately 78 at room temperature that of base materials is of the order of 2. Thus, with a larger percentage of water, the dielectric constant generally increases, usually proportionally. It should be emphasized that very complex phenomena occur when different dielectrics are mixed. However, a few rules of thumb may be applied ... 

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