Impedance, faradaic

Chronoamperometry Linear sweep Polarography Rotating disk electrode Faradaic impedance... 

Figure 1.7 ORR impedance plots for a Pt electrode at several cathode DC currents, showing a low ftequency branch corresponding to slow increase of the rate (slow lowering of the faradaic impedance) following cathodic perturbation [Makharia et al., 2005].

The first estimations of for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the impedance under illumination could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the faradaic impedance was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 10 to 10 ms was estimated, corresponding to a rather unrealistic ket > 10 M cms . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid-liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. 

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

FIG. 6 Randles equivalent circuit for the ITIES Zq is the interfacial capacitance, Zy)v are the faradaic impedances of the charge transfer reactions, and is the solution resistance. 

Since the ion transfer is a rather fast process, the faradaic impedance Zj can be replaced by the Warburg impedance Zfy corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z and the imaginary Z" components of the complex impedance Z = Z —jZ " [/ = (—1) ] are given by [60]... 

Returning to the fundamental ac harmonic in Fig. 3.42, we wish to establish the relationship between I and the faradaic impedance Z( instead of considering a combination of a series resistance Rs and a pseudo-capacity C8, the alternative is to separate a pure resistance of charge transfer Rct and a kind of resistance to mass transfer Zw, the Warburg impedance the derivation of the polarogram39 then (for AEtc < 8/remV) leads to the equation... 

A modification of faradaic impedance measurement is a.c. polarography, where a small a.c. voltage is superimposed on the voltage polarizing the dropping mercury electrode (Fig. 5.181). 

There are several ways to present the Faradaic impedance data obtained at an electrode immobilized with an immunocomplex in the presence of a redox probe. For example, ZIm is plotted vs ZRe as a function of decreasing frequency to obtain a... 

E. Katz, L. Alfonta, and I. Willner, Chronopotentiometry and Faradaic impedance spectroscopy as methods for signal transduction in immunosensors. Sens. Actuators B 76, 134-141 (2001). 

In this case, a faradaic impedance Zf is placed in parallel with the capacitor Cd, based on the consideration that the current generated at the working electrode is the sum of the faradaic current (due to the redox process) and the capacitive current (due to the electrode/solution double layer). 

Figure 15. Faradaic impedance (Zp) of porous Pt electrodes on single-crystal zirconia in oxygen at zero bias, as determined from the total impedance (Z) using the methods of Berthier et aLF gQO and (b) 900 X. (c) Model...

Figure 34. Total impedance (2) and faradaic impedance (Zf) of unsintered porous LSM on YSZ measured in air at 850 °C. Electrolyte resistance (i ) has been subtracted from the total impedance, while both i e and the double-layer capacitance (Cdi) have been subtracted from Zp. (Reprinted with permission from ref 215. Copyright 1998 Elsevier.)...

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 ... 

Obviously, the faradaic impedance equals the sum of the two contributions f ct, the charge transfer resistance, and Zw = aco-1/2 (1 — i), the Warburg impedance. Again, the meaning of the parameters Rct and a is still implicit at this stage of the treatment and explicit expressions have to be deduced from an explicit rate equation, e.g. the expressions given in eqns. (51). 

Fig. 17. (a) The components of the faradaic impedance plotted against to. (b) The components of the faradaic admittance plotted against to1/2. System parameters fict = lficm1, p = 0.03. The solid parts of the plots indicate the frequency range that is normally accessible for meaningful analysis of data with the simple theory described in this section... 

In this section, a description of the state of the art is attempted by (i) a review of the most fundamental types of reaction schemes, illustrated by some examples (ii) formulation of corresponding sets of differential equations and boundary conditions and derivation of their solutions in Laplace form (iii) description of rigorous and approximate expressions for the response in the current and/or potential step methods and (iv) discussion of the faradaic impedance or admittance. Not all the underlying conditions and fundamentals will be treated in depth. The... 

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