Resistor polarity reference

An explanation of the observed relaxation transition of the permittivity in carbon black filled composites above the percolation threshold is again provided by percolation theory. Two different polarization mechanisms can be considered (i) polarization of the filler clusters that are assumed to be located in a non polar medium, and (ii) polarization of the polymer matrix between conducting filler clusters. Both concepts predict a critical behavior of the characteristic frequency R similar to Eq. (18). In case (i) it holds that R= , since both transitions are related to the diffusion behavior of the charge carriers on fractal clusters and are controlled by the correlation length of the clusters. Hence, R corresponds to the anomalous diffusion transition, i.e., the cross-over frequency of the conductivity as observed in Fig. 30a. In case (ii), also referred to as random resistor-capacitor model, the polarization transition is affected by the polarization behavior of the polymer matrix and it holds that [128, 136,137]... 

Figure 1 Influence of IR voltage error on Em in a three-electrode polarization cell. /f,pp is increased for both anodic and cathodic polarization. A larger /iapp than theoretical must be applied to achieve the same tme overpotential, T tl . The resistors between the working electrode (WE), reference electrode (RE), and counter electrode (CE) signify the finite solution conductivity.

In a second approach to determine the contribution of the spontaneous electric polarization to the total current, an experimental set-up was devised which simulates all other contributions to the induced current by an equivalent circuit. This set-up is referred to as compensation circuit, as the subtraction of the simulated signal from the measured signal compensates all irrelevant contributions. A sketch of this set-up is shown in Fig. 5.38. The resistance of the lyotropic liquid crystals was simulated with an adjustable resistor which is connected in parallel to an adjustable capacitor mimicking the capacity of the measurement cell. In addition, the resistance R o of the ITO layer has to be taken into account due to the small resistance of the lyotropic liquid crystal. In contrast to the other contributions to the total current, the resistance of the ITO layer has to be seen as connected in series. By subtracting the two signals only the contribution of the spontaneous electric polarization Ps to the total current should be left. As there are three adjustable... 

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