Maxwell-Wagner time

The effective polarizability should still be given by Eq. (8-2) when an ac field is applied whose frequency co is fast compared to the inverse of the Maxwell-Wagner time fMW required for the mobile charges to screen the particle dipoles. When /mww 1> however, should be given instead by Eq. (8-2a). The Maxwell-Wagner time is given by (Parthasarathy and Klingenberg 1996) ... 

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. 

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... 

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. 

Recently, Pollack derived, by adapting a simple procedure, a Maxwell-Wagner type of equation for a highly elongated ellipsoid of revolution (18). Although his procedure is considerably different from those of Fricke and Sillars, the final form is essentially the same. He derived the following equations for the relaxation time ... 

If the aqueous phase contains electrolytes, a relaxation due to the Maxwell-Wagner-Sillars effect will be observed. Since the electrolyte is not incorporated in the clathrate structures, an increased electrolyte concentration in the remaining free water will result, thus changing the dielectric relaxation mode. In Fig. 42 we note that the relaxation time r decreases from the initial 1000 100 ps to a final level of 200 20 ps during hydrate formation. The experimental value of 200 ps corresponds roughly to a 3% (w/v) NaCl solution, as compared with the initial salt concentration of 1% (w/v). 

The whole procedure of the human blood-cell suspension study is presented schematically in Fig. 50. The TDS measurements on the cell suspension, the volume-fraction measurement of this suspension, and measurements of cell radius are excecuted during each experiment on the sample. The electrode-polarization correction (see Sec. II) is performed at flie stage of data treatment (in the time domain) and then the suspension spectrum is obtained. The singlecell spectrum is calculated by the Maxwell-Wagner mixture formula [Eq. (88)], using the measured cell radius and volume fraction. This spectrum is then fitted to the single-shell model [Eq. (89)] in the case of erythrocytes or to the double-shell model [Eqs (94)-(98)] to obtain flie cell-phase parameters of lymphocytes. 

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. 

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. 

Figure 6.5. Schematic of an Arrhenius plot for mechanisms commonly observed in polymers. The lines correspond to Arrhenius [Eq. (6.8) for y, p, and Maxwell-Wagner-Sillars (MWS) relaxations] and Vogel-Tammann-Fulcher-Hesse [VTFH Eq. (6.10)], for a and normal-mode (n-) relaxation] temperature dependences for the relaxation time t(T). Relaxations ascribed to small, highly mobile, dipolar units appear in the upper right side of the plot, while those originating from bulky dipolar segments, slowly moving ions, and MWS mechanisms are located in the lower-left part of the plot.

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

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