Measurement partial equivalent circuit

Figure 19 Schematic Bode plots from EIS measurements and equivalent circuits that could be used to fit them for various possible corrosion product deposit structures (A) nonporous deposit (passive film) (B) deposit with minor narrow faults such as grain boundaries or minor fractures (C) deposit with discrete narrow pores (D) deposit with discrete pores wide enough to support a diffusive response (to the a.c. perturbation) within the deposit (E) deposit with partial pore blockage by a hydrated deposit (1) oxide capacitance (2) oxide resistance (3) bulk solution resistance (4) interfacial capacitance (5) polarization resistance (6) pore resistance (7) Warburg impedance (8) capacitance of a hydrated deposit.

Figure 1. A schematic diagram (a) and a partial equivalent circuit (b) are given for the LAPS. The components 4, Ci, Cdf Re, Vref and Vchem, respectively represent the applied bias potential, the insulator and depletion layer capacitances, the electrolyte resistance, the potential across the reference electrode, and a chemically sensitive surface potential. Ip represents the photogeneration of hole-electron pairs, and I the measured alternating photocurrent. Solution potential is maintained by a potentiostat using a Pt controlling electrode (CTL) and Ag/AgCl reference electrode (REF). The potential is defined as the potential from the output of the reference electrode to ground.

This equation was first postulated empirically by Wagner and Traud (1938). In Eq. (7-26), b+ and b are the slopes of the Tafel lines of the anodic and cathodic partial reactions. The fundamentals of polarization resistance measurements have been described in more detail by Mansfeld (1976). This concept has also been adopted for the interpretation of EIS (Mansfeld, 1981 Mansfeld et al., 1982). For the simplest case of a purely reaction controlled corrosion process, the Faraday impedance Zp in Fig. 7-3 may be replaced by a potential dependent charge transfer resistance / (( ), which is composed of the charge transfer resistances of the anodic and cathodic partial reactions. At the corrosion potential, the polarization resistance corresponds to Rp = R (Eco ) Th overall impedance of the equivalent circuit in Fig. 7-3 can then be described by... 

A different approach to impedance measurements of electrodes in CP conditions was assumed by Juchniewicz and Jankowski (1993). They elaborated a quantitative method, allowing the determination of the partial anodic current of polarized electrodes. They proposed an electric equivalent circuit of a polarized electrode describing the impedance characteristic of an electrode as a function of the applied potential. It has been assumed that on the electrode one activation controlled anodic reaction and one cathodic reaction with mixed activation-diffusion control proceeds. The adopted electric equivalent circuit is presented in Fig. 8-11. 

It was pointed out at the very beginning of this book that the impedance of the metal/ solution interface is partially capacitive. In simple cases, the equivalent circuit is that shown in Figure 8.1a. The double-layer capacitance Cdi and the Faradaic resistance Rp are inherent properties of the interface, which we measure experimentally and interpret theoretically. The solution resistance R is not a property of the interface. It can be viewed as an error term" arising from the fact that the potential in solution is always measured far from the interface on the molecular scale, typically at a distance oflO -lO nm. 

These dyes are spectrally and redox active, and must have redox potentials near that of the enzyme to function as a redox buffer . The potential of the enzyme is measured at equilibrium after a certain number of reducing equivalents have been transferred. The dye equilibrates with the partially reduced enzyme at open circuit to... 

From this table it is clear that we can work out all the needed derivatives if we have data on Cy and Cp and some way to evaluate the partial derivatives of v with respect to P and T. Values of Cy and Cp are measured in calorimeters. The derivatives of v are found from an equation of state. (Most modem equations of state are easy to solve for the derivatives of P and T with respect to v, but not for the v derivatives. For these equations we use some circuitous mathematical routes to provide the exact equivalents of the equations shown above.)... 

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