Maxwell-Wagner process

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... 

Biopolymers are both polar and ionic in character. They exhibit features characteristic of both polymeric solutes and of colloidal particles, giving complex behaviors difficult to describe simply. Enormous responses can occur at low frequencies. Minakata, Imai, and Oosawa have studied theory and experiment for solutions of the polyelectrolyte, tetra-JV-butylammonium polyacrylate (BU4NPA). They observed two low-frequency dielectric dispersion peaks, one at about 100,000 Hz, the other at about 1000 Hz. They suggest that the former is due to a bulk-bulk, Maxwell-Wagner process and that the later and slower process is... 

The low frequency absorption II originates from the Maxwell-Wagner effect already observed in dehydrated X-type zeolites (8). In the presence of water the enhanced cationic mobility intensifies this effect. This interpretation disagrees with that of Matron et al. (10). They ascribed their low frequency a-process to cations on site I and site II. This is improbable in view of the correspondence with the Maxwell-Wagner effect in dehydrated X-type zeolites, observed by us (8). 

The origin of this relaxation is in heterogeneity of the ceramic, in which anisotropically shaped grains exhibit strong variation in their piezoelectric and dielectric properties in different directions. As discussed in [17], in such heterogeneous materials Maxwell-Wagner like processes may lead to a behavior shown in Figure 13.6. 

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 three phase dielectric system backbone-waterlayer-air of a real RF aerogel is reduced to a two layer system. The third phase (air) is neglected because of its relative low influence (compared to the other two phases) on the compound dielectric permittivity according to its own material parameters e and k. In order to explain the measured spectra by Maxwell-Wagner polarization processes due to the absorbed water we propose the following model. ... 

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. 

The macroscopically observed transport is based on the quantum-mechanical interaction between the electron waves in neighbouring quantum metal particles , which is probably facilitated by the Maxwell-Wagner polarisation and thermally stimulated. Instead of hopping , the expression tunnelling may approximate more closely to the quantum mechanical fundamentals of this process. 

The erythrocyte and erythrocyte ghost suspensions are very similar systems. They differ in their inner solution (in the case of erythrocytes it is an ionic hemoglobin solution in the case of ghosts it is almost like the surrounding solution they were in while they were sealed). The cell sizes in a prepared suspension depend both on the ion concentration in the supernatant and in the cell interior (70). Thus, the dielectric spectra of erythrocytes and erythrocyte ghost suspensions have the same shape, which means that there are no additional (except Maxwell-Wagner) relaxation processes in the erythrocyte cytoplasm thus, the singleshell model (Eq. 89) can be applied. 

The time dependence of the dielectric properties of a material (expressed by e or CT ) under study can have different molecular origins. Resonance phenomena are due to atomic or molecular vibrations and can be analyzed by optical spectroscopy. The discussion of these processes is out of the scope of this chapter. Relaxation phenomena are related to molecular fluctuations of dipoles due to molecules or parts of them in a potential landscape. Moreover, drift motion of mobile charge carriers (electrons, ions, or charged defects) causes conductive contributions to the dielectric response. Moreover, the blocking of carriers at internal and external interfaces introduces further time-dependent processes which are known as Maxwell/Wagner/Sillars (Wagner 1914 Sillars 1937) or electrode polarization (see, for instance, Serghei et al. 2009). 

The time dependence of the dielectric response can be due to different processes like the fluctuations of dipoles (relaxation processes), the drift motion of charge carriers (conduction processes), and the blocking of charge carriers at interfaces (Maxwell/Wagner/Sillars polarization). In the following subchapters these effects will be discussed from a theoretical point of view. 

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