Resistivity balance

One of the major considerations for poling a composite (especially with 0 3 connectivity) is the ratio of the respective phase resistivities, and many attempts to produce a better poling effect rely on mechanisms for achieving a better resistivity balance, i.e. shifting the ratio Pceramic/ poiymer towards unity. This is described in more detail below. 

The application of an electric field can be assessed by applying the Maxwell-Wagner model, in which the composite is approximated as a two-layer capacitor (Fig. 6.8). 

When a DC voltage is suddenly applied to pole the composite, the initial field distribution corresponds to an electrostatic requirement of constant flux density. Under this condition, the ratio of the voltage Vi on phase 1 (ceramic) to the applied voltage Vq is given by 

This ratio is small because Si is usually much larger than 2- 

When a DC poling voltage is applied for a period longer than the system s relaxation time, the ratio Vi/Vq is given by 

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Figure 22.10. Schering bridge circuit. The capacitance being measured (the test capacitance) is represented by Cl and in series. R3 is a fixed resistance. Balance is obtained by adjustment of C3 and either Cl or R2. D is the detector.

The use of a parallel combination of R2 and C2, as in Fig. 1, is attractive because the value of C2 needed to compensate for the capacitance of the cell is quite low, and small capacitors are cheaper, more accurate, and less frequency dependent than large ones. By adjusting C2, and thus compensating for the phase shift in the cell, one can improve the balance of the bridge. The ideal detector is an oscilloscope since this permits separate observation of both the capacitive and the resistive balance and can also reveal any waveform distortion that might occur if there is serious polarization of the electrodes. 

Equation (19) is the familiar Wheatstone resistance balance condition, and Eq. (20) is a new condition that is needed when phase shifts can occur. Together, Eqs. (19) and (20) ensure that the alternating potential at points 5and Dm Fig. 15 will be equal in amplitude and exactly in phase at all times. 

Passive balancing is classified into two subtypes (1) resistance balancing, and (2) Zener diode balancing. 

Circuit of resistive balancing method for electrochemical supercapacitor stack. Source Linzen, D. et al. 2005. Electronics, 41,1135-1141. With permission.)... 

A more complex model for pool spread has been developed by Webber (1991). This model is presented as a set of two coupled diiSerential equations which models liquid spread on a flat horizontal and solid surface. The model includes gravity spread terms and flow resistance terms for both laminar and turbulent flow. Solution of this model shows that the pool diameter radius is proportional to t in the limit where gravity balances inertia, and as in the limit where gravity and laminar resistance balance. This model assumes isothermal behavior and docs not include evaporation or boiling effects. 

In general, the resistivity of the ceramic will be orders of magnitude lower than that of the polymer, making the potential across the ceramic a very small fraction of the applied potential. There are three obvious methods of producing a resistivity balance closer to unity ... 

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