Electrode equivalent circuit models

FTEIS is an experimentally convenient technique for such potentiodynam-ic impedance measurements. In this approach, a series of Nyquist (or Bode) spectra is obtained in parallel with the recording of CV data. DC voltage-dependent electrode equivalent-circuit models can be developed through CNLLS analysis of the impedance spectra. However, in FTEIS postexperiment processing is often cumbersome and inconvenient, and FTEIS limits the amplitude of the excitation signal to imder 10 mV (for aqueous solutions) because of the nonlinearity of the electrochemical system. 

Figure 53. Idealized half-cell response of a thin solid electrolyte cell, (a) Cell geometry including working electrodes A and B and reference electrode (s). (b) Equivalent circuit model for the cell in a, where the electrolyte and two electrodes have area-specific resistances and capacitances as indicated, (c) Total cell and half-cell impedance responses, calculated assuming the reference electrode remains equipotential with a planar surface located somewhere in the middle of the active region, halfway between the two working electrodes, as shown in a.

When we begin to investigate an electrochemical system, we normally know little about the processes or mechanisms within the system. Electrochemical impedance spectroscopy (EIS) can be a powerful approach to help us establish a hypothesis using equivalent circuit models. A data-fitted equivalent circuit model will suggest valuable chemical processes or mechanisms for the electrochemical system being studied. From Chapter 1, we know that a fuel cell is actually an electrochemical system involving electrode/electrolyte interfaces, electrode reactions, as well as mass transfer processes. Therefore, EIS can also be a powerful tool to diagnose fuel cell properties and performance. 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

In the previous section we considered the conditions under which mechanical resonances would occur in a TSM resonator. In considering only the mechanical properties of the crystal, however, we neglected consideration of how these resonances would actually be excited or detected. The device uses a piezoelectric substrate material in which the electric field generated between electrodes couples to mechanical displacement. This allows electrical excitation and detection of mechanical resonances. In constructing a practical sensor, changes in resonant frequency of the device are measured electrically. The electrical characteristics of the resonator can be described in terms of an equivalent-circuit model that describes the impedance (ratio of applied voltage to current) or admittance (reciprocal of impedance) over a range of frequencies near resonance. 

Yang and Thompson [21] have noted that when a TSM resonator is operated in a liquid, fringing electric fields can enter the liquid, making Co sensitive to the dielectric properties of the liquid. This sensitivity, which can be considered to arise from changes in the parasitic capacitance Cp, is especially pronounced when both electrodes are immersed. Tiean et al. [22] have noted that under these circumstances, a parallel conductance must be added to the equivalent-circuit model to account for conduction through the liquid between electrodes. 

Figure 29. Equivalent-circuit model of the electrode in the presence of adsorption. ...

Figure 2. Diagram showing the equivalent circuit model for a cell in suspension. The electrical double layer (EDL) on the surface of the electrodes is model as a capacitor C i.

This model is known as the model of the common diffuse layer (CDL) [27]. As shown in Ref. [30], both models can describe only some limiting cases and the exposition for the total capacity of the PC electrode (equivalent circuit) investigated depends on the relationship between the three lengths (1) the characteristic size of the individual planes at a PC electrode surface (2) the effective... 

The impedance of a modified electrode depends on the impedance of each of the bulk phases and on interfacial properties as well. The equivalent circuit model (ECM) is used to elucidate the contribution of different charge transfer or transport processes to the overall impedance of electrodes. The equivalent circuit modeling concern finding equivalent electrical elements best representing physical processes within a range of frequencies by assuming each element... 

In the case of the impedimetric IME sensor, the two sets of electrodes of the IME can be two poles in a two-electrode configuration for electrical impedance measurements. Figure 4 shows 4a a picture, 4b a schematic, 4c the equivalent circuit model for the IME device, and 4d the Bode plot of the electrochemical impedance spectram obtained in aqueous 0.01 M phosphate-buffered saline containing 10 mM ferricyanide at room temperature. The equivalent circuit for the IME device in Fig. 4c consists of an ohmic resistance (/ s) of the electrolyte between two sets of electrodes and the double-layer capacitance (Cdi), an electron transfer resistance (Ret), and Warburg impedance (Z, ) around each set of electrodes [2], Rs and the two branch circuits are connected... 

A picture of a microfabricated interdigitated microsensor electrode, (b) a schematic illustration of the IME, (c) the Bode plot of I Z I and 9 obtained from the frequency-dependent interrogation of an IME 1525.3 ITO device in 0.01 M PBS containing 10 mM [Ee(CN)e] (solid line, 10 mV p-t-p, offset = 0) and the corresponding fitting data (dotted line), and (d) the equivalent circuit model derived from the NLLS fitting of the impedance data... 

Based on equivalent circuit models of the cell component resistances [66], maximum ceU performance of SC-SOFCs with coplanar electrodes is predicted for very small electrode widths (6-10 pm) and gap sizes (2-12 pm). Performance comparisons of macro-, miUi-, and microcells [71] revealed a 10 times higher power density for the micro SC-SOFC which had smaller inter-electrode gaps and electrode widths. As closely spaced small-scale electrodes lower the ohmic resistance and the inter-digitated electrode pattern maximizes the electrode surface area, miniaturization of SC-SOFCs with coplanar, interdigitated electrodes is expected to yield suitable cell performance for small- and microscale power applications. The fabrication of microcells (Figure 2.3) presents many challenges and requires the manufacturing of coplanar microscale electrode patterns from multicomponent ceramic materials. 

An electrical equivalent circuit model, composed of a resistor and a capacitor which were connected in series, was adopted to represent the soymilk-electrode system. High frequency impedance measurements presented an increase in resistance and constant value in reactance for different coagulation times. This resistance is attributed to the bulk resistance of soymilk mixture and changed minimally when the coagulation process is finished [50]. 

FIGURE 12.11 Nyquist plots of methanol oxidation at 80 °C and 0.35 V, 0.45 V, 0.55 V, and 0.65 V (vs. NHE) for an electrode with 40 wt.% Pt Ru (1 1 atomic ratio) on Vulcan XC-72 in l.Omoldm methanol and l.Omoldm sulfuric acid. Experimental data (symbols) and fitted results for equivalent circuit model (ECM) curves (solid lines) [24]. (For color version of this figure, the reader is referred to the online version of this book.)... 

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