Equivalent circuit, charge-transfer process

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

The selection of impedance or admittance for presentation of experimental results and data analysis is dependent on the type of equivalent electric circuit. For instance, for the analysis of -> charge-transfer processes and -> double-layer charging, the impedance may be preferred, while for the resonance circuits (e.g., in piezometric systems) the admittance may offer advantages. 

Figure 16. Equivalent circuit (a) and a simulated Nyquist plot (b) for the charge transfer pathway illustrated in Figure 15. The capacitance C represents that of the space-charge layer and the parallel branch components represent the Faradaic charge transfer process. Refer to the original work for further details. (Reproduced with permission from Ref. [84).)...

The electrical behavior of the electrode-solution interface and the processes which can take place at it, due to an electrochemical reaction, can be treated in terms of an electrical equivalent circuit. Such an equivalent circuit must represent the time-dependent behavior of the mechanism of the reaction but usually it is possible that more than one equivalent circuit can model the reaction behavior. The simplest equivalent circuit is (Cl) for a charge-transfer process not involving the production of an adsorbed intermediate, for example, for the case of an ionic redox reaction such as Fe(CN)e3- +e-- Fe(CN)6 - ... 

The equivalent circuit must usually include a solution resistance, / , in series with the combination of Qi and Rp. For the case of a charge-transfer process producing an adsorbed intermediate which can be desorbed (D) in a following step whose rate is characterized by a second reciprocal resistance Rd the equivalent circuit is written as... 

The resolution of the latter two steps in the overall interfacial process of hydrogen electrooxidation should be contrasted with the impedance spectrum for the ORR at a smooth Pt/Nafion membrane interface (see Fig. 6), that includes only a single feature associated with a single rate-limiting interfacial charge-transfer step. Figure 12 shows an equivalent circuit for the process at the smooth Pt/Nafion membrane... 

The so-called Randles equivalent circuit describes diffusion-controlled charge transfer processes (Figure 5.8). 

Figure 5.8 Randles equivalent circuit for a diffusion-controlled charge transfer process, Qj double layer capacitance, R charge transfer resistance, electrolyte resistance, and W Warburg impedance.

The electrochemical impedance for surface state-mediated charge transfer has been computed recently [78]. The key results are summarized in Fig. 16. Figure 16(a) contains the proposed equivalent circuit for the process and features a parallel connection of the impedance for the Faradaic process [Zf( )] (co = angular frequency, 2nf) and the capacitance of the semiconductor depletion layer, Csc- The... 

FIGURE 4.3.19. Equivalent circuit representation of an electrode-solution interface for a simple charge-transfer process. (A) Without adsorbed intermediates, and (B) with adsorbed intermediates. 

Thus, the equivalent circuit consists of a solution resistance, / s. in series with the double layer capacitance, Qi, and /fp, the Faradaic resistance associated with the charge-transfer process. However, if an adsorbed intermediate is involved in the charge-transfer process, such as ... 

Figure 2.1.14. The Randles equivalent circuit, which describes the response of a single-step charge-transfer process with diffusion of reactants and/or products to the interface.

Figure 4.3.17. The Randles equivalent circuit, with resistance of a charge-transfer process and the diffusional impedance Z. R f and CPE i are the high frequency resistance and the double layer distributed capacitance, respectively.

Figure 11.13 illustrates a basic equivalent circuit to represent a general electrochemical reaction. Rs represents the electric resistance, which consists of the ionic, electronic, and contact resistances. Since the electronic resistance is typically much lower than the ionic resistances for a typical fuel cell MEA, the contribution of the electronic resistance to Rs is often negligible. Cj is the double-layer capacitance associated with the electrode-electrolyte interfaees. Since a fuel cell electrode is three-dimensional, the interfaces include not only Arose between Are surfaces of the electrodes and the membrane but also those between the catalysts and the ionomer within the electrodes. Ret is the resistanee associated with the charge transfer process and is called charge transfer resistanee. Z is called the Warburg impedance it deseribes the resistance arising from the mass transport processes. 

In addition to the equivalent circuit method, the impedance results can also be analyzed using mathematical models based on physicochemical theories. Guo and White developed a steady-state impedance model for the ORR at the PEM fuel cell cathode [15]. They assumed that the electrode consists of flooded ionomer-coated spherical agglomerates surrounded by gas pores. Stefan-Maxwell equations were used to describe the multiphase transport occurring in both the GDL and the catalyst layer. The model predicted a high-frequency loop due to the charge transfer process and a low-frequency loop due to the combined effect of the gas-phase transport resistance and the charge transfer resistance when the cathode is at high current densities. 

Survila, A. and Baliukiene, V. (2001) Equivalent circuit of electrochemical processes involving two consecutive charge transfer steps. Chemija, 12 (3), 195-198. 

In the equivalent circuit analog, resistors represent conductive pathways for ion and electron transfer. As such, they represent the bulk resistance of a material to charge transport such as the resistance of the electrolyte to ion transport or the resistance of a conductor to electron transport. Resistors are also used to represent the resistance to the charge-transfer process at the electrode surface. Capacitors and inductors are associated with space-charge polarization regions, such as the electrochemical double layer, and adsorption/ desorption processes at an electrode, respectively. 

Figure 4.3 The equivalent circuit for an interface, showing the difference between the measured potential ac and the potential actually applied across the interface, Esc, which drives the charge-transfer process.

Note that the resistance R,j> is an integral part of the physical phenomenon that gives rise to the formation of the adsorption pseudocapacitance. It is a Faradaic resistance, since C< > is due to a charge-transfer process. The association of this charge-transfer process with the formation of an adsorbed intermediate, which can proceed only xmtil the appropriate coverage has been reached, is manifested by placing the resistor in series with the capacitor. It should also be borne in mind that both Cequivalent circuits representing the electrochemical interface... 

The equivalent circuit diagram used to model solar cell current-voltage characteristics is shown at the top of Figure 1.1. The schematic energy level diagram of a DSSC at the bottom of Figure 1.1 shows the various charge transfer processes that occur in photoelectrochemical cells and relates these processes to current pathways via components of the model circuit. An illumination current density /l is induced upon photoexcitation of the... 

Figure 1.1 Simple equivalent circuit (top) for modeling solar cell current-voltage characteristics and energy level diagram (bottom) mapping the various charge transfer processes in a DSSC to the current pathways of the model circuit. The dominant mechanisms are described by a current density Jl induced upon photoexcitation and electron injection into the conduction band of the metal oxide semiconductor surface MO, linear (Jsh) and nonlinear (/jj) reverse current densities in parallel with photocurrent source and a series resistance to account for electrode and ionic resistances. In Section 1.2.2 M0 = Ti02, Sn02, X = Br, I.

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