Maxwell-Wagner-Sillars

The interfacial or Maxwell-Wagner-Sillars (MWS) polarization is characteristic of heterogeneous systems. It is due to the piling up of space charges near the interfaces between zones of different conductivities. 

Interfacial polarization in biphasic dielectrics was first described by Maxwell (same Maxwell as the Maxwell model) in his monograph Electricity and Magnetism of 1892.12 Somewhat later the effect was described by Wagner in terms of the polarization of a two-layer dielectric in a capacitor and showed that the polarization of isolated spheres was similar. Other more complex geometries (ellipsoids, rods) were considered by Sillars as a result, interfacial polarization is often called the Maxwell-Wagner-Sillars (MWS) effect. 

Figure 17. Evidence of the Maxwell-Wagner-Sillars effect in the real permittivity of the composite system nematic E7 dispersed over hydroxypropylcellulose-type matrix. The interfacial polarization can be described by a double-layer arrangement. At lower frequencies and higher temperatures, the real permittivity increases further due to electrode polarization.

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. 

Dielectric spectroscopy is concerned with the dependence of complex permittivity on temperature and frequency. The relatively low level of d.c. conduction in polycarbonate ensures that the principal relaxations associated with polycarbonate s active C 0 dipole can be observed over a useful range of frequency and temperature. In multi-phase or multi-component polymers charge accumulation at the sub-structure interfaces leads to Maxwell-Wagner-Sillars (MWS) contributions to the overall polarization. 

Exceedingly large losses at low frequencies above 150°C are attributed to Maxwell-Wagner-Sillars (NWS) polarizations arising from conduction mismatches at the structural interfaces between a continuous matrix of amorphous polycarbonate and a crystalline or densified second phase. Provided that the discontinuous phase tends towards a two-dimensional aspect and has a conductivity less than that of the matrix, theory predicts substantial NWS losses even with a low concentration of the discontinous phase [37]. 

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 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. 

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). 

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.

Interfacial polarization, sometimes referred to as Maxwell-Wagner-Sillars (MWS) polarization, is a characteristic bulk phenomenon in polymer systems with a heterogeneous structure. This kind of polarization is due to the buildup of charged layers at the interface, resulting from unequal conduction currents... 

The complex dielectric constant of a suspension e of orientated ellipsoidal particles with the dielectric constant Cp at the particle volume fraction < ) dispersed in a continuous medium with a complex dielectric constant , can be calculated from the Maxwell-Wagner-Sillars equation [77] ... 

Numerical results from the above three type equations are compared by Banhcgyi [83]. The dielectric constant and loss of two-phase spherical particle mixture are calculated with the Maxwell-Wagner-Sillars equation, the Bottcher-Hsu equation, and the Looyenga equation using the parameters e i =2, p 8, S/m, CTp=10 S/m, and shown in Figure 23 against... 

Figure 23 The dielectric constant and loss vs. frequency calculated by using different models for spherical particle case at different particle volume fraction marked in the graphs, a) Maxwell-Wagner-Sillars equation b) Bdtlcher-Hsu equation c) Looyenga equation. Parameters are c , =2, p=8, Om=10 S/m, CTp=10 S/m. The particle volume fraction changes from 0.1 to 0.9 with the interval 0.2. Reproduced with permission from G. Banhegyi, Colloid Polym. Sci., 266(1988)11.

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