Maxwell-Wagner losses

A third relaxation type mechanism, which once again hsis its strongest influence in the radio frequency range, is a loss due to space charges in interfaces between different dielectric materials, referred to as Maxwell-Wagner loss. It may be assumed that at the low frequencies where these losses are important, the conductivity loss mechanism referred to above will be the dominant one for ceramic materials and therefore losses due to Maxwel1-Wagner polarisation will not be considered any further. 

Another type of polarization arises from a charge build-up in the contact areas or interfaces between different components in heterogeneous systems. This phenomenon is also known as interfacial polarization and is due to the difference in the conductivities and dielectric constants (see below) of the materials at interfaces. The accumulation of space charge is responsible for field distortions and dielectric loss and is commonly termed Maxwell-Wagner polarisation . 

We would expect intuitively that tan 0 emd the Deborah number De are related, since both refer to the ratio between the rates of an imposed process and that (or those) of the system. The exact shape of this relationship depends on the number and nature(s) of the releixation process(es). So let us anticipate [3.6.4 la] for the loss tangent of a monolayer in oscillatory motion, which describes a special case of [3.6,12], namely -tan0 = t]°(o/K°. Here, (o is the imposed frequency, equal to the reciprocal time of observation, t(obs) =< . The quotient K° /t]° also has the dimensions of a time in fact it is the surface rheological equivalent of the Maxwell-Wagner relaxation time in electricity, (Recall from sec. 1.6c that for the electrostatic case relaxation is exponential ith T = e/K where e e is the dielectric permittivity and K the conductivity of the relaxing system. In other words, T is the quotient between the storage and the dissipative part.) For the surface rheological case T therefore becomes The exponential decay that is required for such a... 

The impedance spectrum of the RF aerogels in the density range of 340 kgW up to 880 kg/m is clearly dominated by losses due to relaxation processes. Considering the so called Maxwell-Wagner polarisation we were able to attribute these losses to adsorbed water layers. 

The a process appears most clearly at the higher frequencies whereas at the lower frequencies it is hidden by the rapid increase in both dielectric constant and loss due to the Maxwell-Wagner effect The p process on the other hand is easily revealed in the whole frequency range. 

C yielded a loss mechanism in the mHz region in polyethylene and in the kHz region for polycarbonate that was Interpreted as a Maxwell-Wagner effect. 

In the interpretation of the loss factor tg 8, it is not easy to make a distinction between a dipole relaxation and the interfacial polarization. With metallic electrodes, both effects are superposed on the ionic part of the dielectric loss and not necessarily distinguishable from it. With blocking electrodes, the relative intensity of the dipole relaxation and the Maxwell-Wagner effect depends on the ratio of the thickness of the blocking layers and the zeolite pellets (15). 

The dielectric constant at 20°C increased from 3.39 to 3.84 due to the 1.7 %wt. moisture (2.0 %v.). The calculated increase of the dielectric constant from 3.39 to 3.60 is only about 50 % of the total effect. The Maxwell-Wagner theory thus seems to describe roughly the frequency/temperature location of the dielectric loss maximum due to absorbed moisture. However, it does not adequately describe the increase of the dielectric constant due to the moisture uptake from the air. A possible reason for this discrepancy might be that one of the assumptions does not hold, viz. that the conductivity of the resin matrix is negligibly small. 

Dielectric relaxation and dielectric losses of pure liquids, ionic solutions, solids, polymers and colloids will be discussed. Effect of electrolytes, relaxation of defects within crystals lattices, adsorbed phases, interfacial relaxation, space charge polarization, and the Maxwell-Wagner effect will be analyzed. Next, a brief overview of... 

If the dielectric material is not homogeneous but could be regarded as an association of several phases with different dielectric characteristic, new relaxation processes could be observed. This relaxation processes called Maxwell-Wagner processes occur within heterogeneous dielectric materials. An arrangement comprising a perfect dielectric without loss (organic solvent) and a lossy dielectric (aqueous... 

Exceedingly large losses at low frequencies above 150°C are attributed to Maxwell-Wagner-Sillars (NWS) polarizations arising from conduction mismatches at the structural interfaces between a continuous matrix of amorphous polycarbonate and a crystalline or densified second phase. Provided that the discontinuous phase tends towards a two-dimensional aspect and has a conductivity less than that of the matrix, theory predicts substantial NWS losses even with a low concentration of the discontinous phase [37]. 

Numerical results from the above three type equations are compared by Banhcgyi [83]. The dielectric constant and loss of two-phase spherical particle mixture are calculated with the Maxwell-Wagner-Sillars equation, the Bottcher-Hsu equation, and the Looyenga equation using the parameters e i =2, p 8, S/m, CTp=10 S/m, and shown in Figure 23 against... 

Figure 23 The dielectric constant and loss vs. frequency calculated by using different models for spherical particle case at different particle volume fraction marked in the graphs, a) Maxwell-Wagner-Sillars equation b) Bdtlcher-Hsu equation c) Looyenga equation. Parameters are c , =2, p=8, Om=10 S/m, CTp=10 S/m. The particle volume fraction changes from 0.1 to 0.9 with the interval 0.2. Reproduced with permission from G. Banhegyi, Colloid Polym. Sci., 266(1988)11.

Direct differentiation on the contribution of the Debye or the Wagner-Maxwell polarization to the ER effect was carried out by Hao [35]. The strategy employed in Hao s paper is to compare the temperature dependence difference of the dielectric loss tangent maximum values of commonly encountered thrcc-lypc polarizations, the ionic polarization, the Debye polarization, and the interfacial polarization. As shown in Eq.(147) in Chapter 7, for the Maxwell-Wagner polarization (also called the interfacial polarization) the dielectric loss tangent can be expressed as follows if the particle conductivity Op is much larger than that of the medium... 

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