Dielectric frequency dependence, fractal

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

FIGURE 2.1 The dependence of dielectric losses angle tangent tgd on fractal dimension of chain part between clusters for copolymers SP - OPD at frequencies 1(1) and 10 kHz [7]. 

Figure 2.2 The dependence of the dielectric losses angle tangent tg 8 on the fractal dimension D of the macromolecule part between entanglements for copolyethersulfoneformale with formal blocks contents (1) 0 (2) 5 (3) 10 (4) 30 (5) 50 and (6) 70 mol%. The measurement frequency is equal to 1 kc [57]...

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