The Wagner-Maxwell polarization

Polarization processes are extremely important in HR lluicls. Generally, there are four kinds of polarizations in a non-aqueous system containing no electrolytes or ions. They are electronic, atomic, Debye and the interfacial polarizations (the Wagner-Maxwell polarization). If the particulate material is an ionic solid, ionic displacement polarization should also be considered. The Debye and the intcrfacial polarizations arc rather slow processes as compared with electronic and the atomic polarizations. Usually, the former two polarizations arc called the slow polarizations, appearing at low frequency fields, whereas the last two are termed fast polarizations, appearing at high frequencies. 

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... 

In addition, the Wagncr-Maxwcll equation is able to adequately describe the dielectric property of ER fluids. Weiss [44] and Filisko [45] measured the dielectric constant and dielectric loss of ER fluids, and found that the Wagner-Maxwell equation is a suitable model to describe the dielectric property. The Wagner-Maxwell equation can also explain the frequency dependence of yield stress of ER fluids. As given in Figure 9 in Chapter 5, the frequency dependence of the yield stress and the dielectric constant follow a similar trend, further indicating that it is the Wagner-Maxwell polarization that controls the dielectric property of the ER suspension and then the ER effect. 

As the experimental facts indicated above, the importance of the Wagner-Maxwell polarization for the ER effect is obvious. However, it is still not clear how the interfacial polarization controls the ER effect, and how the material dielectric constant and dielectric loss correlate with the ER... 

Since the ER effect is determined by the Wagner-Maxwell polarization, the response time of the ER suspensions should be identical to the relaxation time of the Wagner-Maxwell polarization. That is, for a system where the conductivity of tlie dispersed particle is much larger than that of the dispersed medium and the conduetivity contribution from the dispersed medium is negligible, the relaxation time can be described by a simplified form as shown in Eq. (144) in Chapter 7. 

The conduction model is thought to be only valid for ER. suspensions in reaction with dc or low frequency ac fields. For high frequency ac fields, the polarization model is dominant [55,56]. As shown in Eq. (25) and (26), once the Wagncr-Maxwcll polarization is taken into account, the parameter P is detennined by the conductivity mismatch in dc or low frequency ac fields, and by the dielectric mismatch in high frequency fields (the low or high frequency is relative to the relaxation time of the Wagner-Maxwell polarization). The parameter p in the conduction model is ... 

The purpose of the dielectric investigation is to correlate the dielectric properties of the ER materials to the ER effect and to provide the predictive guidance for making high performance ER fluids. Before doing this, the following questions should be answered 1) Which kind of polarization should be responsible for the ER effect 2) Whether the Wagner-Maxwell... 

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). 

Finally, attempts are made on a theoretical basis to explain the unusually large dielectric increments and relaxation times of DNA. The discussion is limited to ionic-type polarizations in this report. The available theories, such as the Maxwell-Wagner theory 29) and the surface conductivity treatment, are reviewed and analyzed. These theories do not explain the dielectric relaxation of DNA satisfactorily. Finally, the counter ion polarization theory is described, and it is demonstrated that it explains most reasonably the dielectric relaxation of DNA. 

Figure 2.10 Dielectric spectra of chitin films with Maxwell-Wagner (MW) polarization at low frequency and high temperatnre. Interfacial polarization can be detected by the appearance of an extra semicircle. Source Reprodnced with permission from Gonzalez-Campos JB, Prokhorov E, Luna-Barcenas G, Mendoza-Galvan A, Sanchez IC, Nuno-Donlucas SM, Garcia-Gaitan B, Kovalenko Y. J Polym Sci B Polym Phys 2009 47 932 [5]. Copyright 2009 John Wiley and Sons, Inc.

Polarization current—caused by dipolar reorientation and accumulation of opposite charges at the electrodes and possible interfaces in the polymer (Friedrich et al. 1997, Wasylyshyn et al. 1996). Maxwell-Wagner-Sillars polarization arises in interfaces of heterogeneous systems like nanocomposites. 

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. 

In this context, the possibility to tune tire piezo- and pyroelectricity of specific composites (Floss et al. 2000) by means of separate poling of the inorganic particles and of the polymer crystallites should also be mentioned. In addition, piezo-, pyro-, and ferroelectric polymers such as PVDF and its relevant copolymers may be optimized by controlling fire poling of the amorphous and of the crystalline phase, as well as of the interface between fiiem (Maxwell-Wagner interface polarization) separately (Rollik et al. 1999). Furthermore, it is possible to follow the examples of the classical electret transducers (witti polymeric space-charge electrets) or of the dielectric-elastomer transducers (sometimes also called electro-electrets) and to... 

Among various mechanisms of the action of microwave field on solids, several classes of catalysts and processes that offer promise for use in practice can be identified. For instance, the Maxwell-Wagner interphase polarization mechanism can likely operate in mixed oxide catalysts (such as catalysts of partial oxidation based on vanadium and molybdenum oxides). For such catalysts, nontrivial and nonthermal effects can probably be expected. 

In addition to the Debye model for dielectric bulk materials, other dielectric relaxations expressed according to Maxwell-Wagner or Schwartz "interfacial" mechanisms exist. For example, the Maxwell-Wagner "interfacial" polarization concept deals with processes at the interfaces between different components of an experimental system. Maxwell-Wagner polarization occurs... 

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