Faradaic impedence potential dependence

Sluyters and coworkers [34] have studied the mechanism of Zn(II) reduction on DM E in NaCl04 solutions at different water activity (uw) using faradaic impedance method. Dqx and E p were determined from dc polarographic curves. Hydration numbers of Zn(Il) ion were estimated from the dependence of E[p on In Uw The obtained standard rate constant was changing with a NaCl04 concentration and the slope of the dependence of In k on potential was changing with potential (see Fig. 1). Therefore, the following mechanisms were proposed ... 

Thus, the fundamental difference between N-NDR and HN-NDR systems is that the former s stationary polarization curve exhibits a range of negative real impedance, whereas for the latter the zero-frequency impedance is strictly positive in the potential region of interest. From this observation one might get the impression that the mechanisms of electrode reactions are fundamentally different for systems in the two groups. But in fact it is only a small step, or more precisely, one additional potential-dependent process, that transforms an N-NDR system into an HN-NDR system. Formally, any HN-NDR system is composed of a subsystem with an N-shaped stationary polarization curve whose NDR is hidden by at least one further slow and potential-dependent step of the interfacial kinetics of the total system. This step dominates the faradaic impedance at low perturbation frequencies, whereas at higher... 

The general expression (10.3) guides development of impedance models from proposed reaction sequences. The reaction mechanisms considered here include reactions dependent only on potential, reactions dependent on both potential and mass transfer, coupled reactions dependent on both potential and surface coverage, and coupled reactions dependent on potential, surface coverage, and mass transfer. The proposed reaction sequence has a major influence on the frequency dependence of the interfacial Faradaic impedance described in Qiapter 9. 

Experimentally measured ac current or total admittances are functions of the electrode potential. Figure 17 presents the dependence of the total admittances of a process limited by the diffusion of electroactive species to and from the electrode and the kinetics of the charge-transfer process, on the electrode potential. Information on the kinetics of the electrode process is included in the faradaic impedance. It may be simply... 

Figure 18. Dependence of real and imaginary parts of the faradaic impedance of a diffusion-kinetic process on at a constant potential.

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

To obtain the total impedance, the faradaic impedance, Eq. (5.19), must be inserted into the total impedance (Fig. 4.1b). The complex plane and Bode plots of the total impedance are as in Fig. 2.35. The circuit parameters R i and Cp depend on the potential, as illustrated in Fig. 5.1. The charge transfer resistance displays a minimum at Ep and its logarithm is linear with the potential further from the minimum, while the pseudocapacitance displays a maximum. These values at the potential Ep are... 

Figure 4.5.25. Complex-plane or Nyquist plots for the impedance spectrum of a double-layer capcitance in parallel with a potential-dependent (/ ) Faradaic resistance,...

The increase in phase angle is the more considerable, the more rapid the adsorption process [29]. These qualitative considerations are at present illustrated in a number of theoretical and experimental papers. Faradaic impedance with allowance for adsorption of electrochemically active substances at the equilibrium potential was frequently [30-35] investigated theoretically. Originally [30, 35] it was assumed that the adsorption of the reaction components can be described by the Langmuir isotherm and that the adsorption and desorption rate constants did not depend on the potential. A more general analysis avoiding these assumptions was made by Senda and Delahay [31] on the supposition that only adsorbed particles were electrolyzed and by Lorenz [32], who took account... 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

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