Relaxation time Wagner-Maxwell polarization

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 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. 

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. 

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. 

Interfacial or Maxwell-Wagner polarization is a special mechanism of dielectric polarization caused by charge build-up at the interfaces of different phases, characterized by different permittivities and conductivities. The simplest model is the bilayer dielectric [1,2], (see Fig. 1.) where this mechanism can be described by a simple Debye response (exponential current decay). The effective dielectric parameters (unrelaxed and relaxed permittivities, relaxation time and static conductivity) of the bilayer dielectric are functions of the dielectric parameters and of the relative amount of the constituent phases ... 

To study the effects of interaction of starch with silica, the broadband DRS method was applied to the starch/modified silica system at different hydration degrees. Several relaxations are observed for this system, and their temperature and frequency (i.e., relaxation time) depend on hydration of starch/silica (Figures 5.6 and 5.7). The relaxation at very low frequencies (/< 1 Hz) can be assigned to the Maxwell-Wagner-Sillars (MWS) mechanism associated with interfacial polarization and space charge polarization (which leads to diminution of 1 in Havriliak-Negami equation) or the 5 relaxation, which can be faster because of the water effect (Figures 5.8 and 5.9). 

Keywords dielectric relaxation, dielectric strength permittivity, dipole moment, polarization, relaxation, conductivity, relaxation time distribution, activation energy, Arrhenius equation, WLF-equation, Maxwell-Wagner polarization. 

T is the relaxation time of the Maxwell-Wagner polarization, and can be expressed as ... 

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). 

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