Maxwell-Wagner

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). 

Maxwell-Wagner piezoelectric relaxation and clockwise hysteresis... 

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. 

Dominant contributions are responsible for the a, fi, and y dispersions. They include for the a-effect, apparent membrane property changes as described in the text for the fi-effect, tissue structure (Maxwell-Wagner effect) and for the y-effect, polarity of the water molecule (Debye effect). Fine structural effects are responsible for deviations as indicated by the dashed lines. These include contributions from subcellular organelles, proteins, and counterion relaxation effects (see text). 

Three categories of relaxation effects are listed as they contribute to gross and fine structure relaxational effects. They include induced dipole effects (Maxwell-Wagner and counterion) and permanent dipole effects (Debye). 

Table III attempts to summarize at what level of biological complexity the various mechanisms occur. Electrolytes display only the y-dispersion characteristic of water. Biological macromolecules in water add to the water s Y-dispersion a 6-dispersion. It is caused by bound water and rotating side groups in the case of proteins, and by rotation of the total molecule in the case of the amino acids and, in particular, proteins and nucleic acids add further dispersions in the 6 and a-range as indicated. Suspensions of cells free of protein would display a Maxwell-Wagner 6-dispersion and the Y-dispersion of water.

The dielectric properties of tissues and cell suspensions will be summarized for the total frequency range from a few Hz to 20 GHz. Three pronounced relaxation regions at ELF, RF and MW frequencies are due to counterion relaxation and membrane invaginations, to Maxwell-Wagner effects, and to the frequency dependent properties of normal water at microwave frequencies. Superimposed on these major dispersions are fine structure effects caused by cellular organelles, protein bound water, polar tissue proteins, and side chain rotation. 

The specific carrier-wave amplitudes (field intensities) which have been found to be effective in producing Ca ion efflux are discussed in terms of tissue properties and relevant mechanisms. The brain tissue is hypothesized to be electrically nonlinear at specific field intensities this nonlinearity demodulates the carrier and releases a 16 Hz signal within ljie tissue. The 16 Hz signal is selectively coupled to the Ca ions by some mechanism, perhaps a dipolar-typ +(Maxwell-Wagner) relaxation, which enhances the efflux of Ca ions. The hypothesis that brain tissue exhibits a slight nonlinearity for certain values of applied RF electric field intensity is not testable by conventional measurements of e because changes... 

For non-conducting fibers, such as glass, the matrix resin is the more conductive phase, at least early in cure, and one would expect some internal polarization effects to be visible in parallel-plate data. However, in spite of a large body of literature on glass fiber composites (see Sect. 5), we have found no clearly documented cases of Maxwell-Wagner effects in fiber-reinforced composites. We speculate that... 

Theoretical and semi-empirical equations were derived for gas emulsions (as well as for suspensions of non-conducting spherical particles and O/W emulsion), specifying Eq. (8.33) . A relation for coefficient B can be derived from Maxwell-Wagner equation [45,46]... 

Two other approaches have been taken to modelling the conductivity of composites, effective medium theories (Landauer, 1978) and computer simulation. In the effective medium approach the properties of the composite are determined by a combination of the properties of the two components. Treating a composite containing spherical inclusions as a series combination of slabs of the component materials leads to the Maxwell-Wagner relations, see Section 3.6.1. Treating the composite as a mixture of spherical particles with a broad size distribution in order to minimise voids leads to the equation ... 

Could this be behavior in terms of the Maxwell-Wagner dispersion, which would arise through conductivity in the double layer near the polyanion. In support of this, the dielectric constant falls as the frequency increases (Fig. 2.79). 

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 . 

For the very simplified situation that the sphere behaves electrically as a pure capacitor, and the solution as a pure resistance, the relaxation can be described by a Maxwell-Wagner mechanism, with T = e e/K, see (1.6.6.321. Although some success has been claimed by Watillon s group J to apply this mechanism for a model, consisting of shells with different values of e and K, generally a more detailed double layer picture is needed. In fact, this Implies stealing from the transport equations of secs. 4.6a and b. generedizing these to the case of a.c. fields. 

The behavior of the relaxation times as a function of temperature for aniline in CPG of 7,5 nm pore size are depicted in Fig. 3. For temperatures greater than 246 K (melting point inside the pores), there are two different relaxations. The longer component of the relaxation that is of the order of lOx 10" s is divided into three regions. The response in the region T > 267K is due to Maxwell-Wagner polarization. 

---