Wagner-Maxwell-Sillar equation

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 ... 

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.

Dielectrie impedance is another method used to detect the phase separation. The permittivity and conductivity changes during the second-phase growing and interface formation. The effect is desalbed for Maxwell-Wagner-Sillars equation (1.1). 

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). 

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