Electron transfer kinetics impedance

These electron transfer reactions are very fast, among the fastest known. This is the reason that impedance methods were used originally to determine the standard rate constant,13,61 at a time when the instrumentation available for these methods was allowing shorter measurement times (high frequencies) to be reached than large-amplitude methods such as cyclic voltammetry. The latter techniques have later been improved so as to reach the same range of fast electron transfer kinetics.22,63... 

In ACIS, a small-amplitude sine wave is superimposed on a constant potential, and the resulting current is recorded. The current lags behind the alternating potential by a degree proportional to the impedence of the SAM. From a plot of the imaginary versus real parts of the complex impedence, both the capacitance of the SAM and the electron-transfer kinetics can be extracted. Because the bulk of the studies described in this chapter make use of cyclic voltammetric or chromo-amperometric methods, ACIS is not discussed further here. Leading references are provided for the interested reader [23, 43, 76]. 

Impedance methods have been more useful in studying electron-transfer kinetics in electroactive monolayers in the absence of an electroactive solution species (71-73), such as alkylthiol layers with tethered electroactive groups (Section 14.5.2). The equivalent circuit adopted is shown in Figure 14.3.18, where the adsorbed layer is represented by Cads = (F AT)/4RT and the electron-transfer kinetics by = (2RT)/F ATkf, so that... 

Impedance spectroscopic methods and ac voltammetry can also be used, as described in Section 14.3.7, to study electron-transfer kinetics in systems like those discussed here (71-73). 

Electrochemical Impedance Spectroscopy (ElS) is a method used to characterize electron-transfer reactions by perturbing the system in a sinusoidal manner over a wide range of frequencies. This method, which is very sensitive to the properties of the electrode interface, provides information regarding electron-transfer kinetics, diffusion of charged species, charging/discharging, and system conductance. 

A typical impedance spectrum presented in the form of the Nyquist plot includes a semicircle portion at higher frequencies corresponding to the electron-transfer-limited process and a linear part at a lower-frequency range associated with the diffusion-limited process. The semicircle diameter in the impedance spectrum equals the electron-transfer resistance, R i, which is related to the electron-transfer kinetics of the redox probe at the electrode surface. As can be seen in Figure... 

The equation points out that as frequency increases (oo oo), the Faradaic impedance approaches R. At low frequencies (co — OUz) the Faradaic impedance can be viewed as two resistances connected in series—one related to electron-transfer kinetics, the other to mass transport toward the electrode. 

These expressions are designed for cyclic voltammetry. The expressions appropriate for potential step chronoamperometry or impedance measurements, for example, are obtained by replacing IZT/Fv by the measurement time, tm, and the inverse of the pulsation, 1/co, respectively. Thus, fast and slow become Af and Ah I and -C 1, respectively. The outcome of the kinetic competition between electron transfer and diffusion is treated in detail in Section 1.4.3 for the case of cyclic voltammetry, including its convolutive version and a brief comparison with other electrochemical techniques. 

Cyclic voltammetric, chronoamperometric and AC impedance spectroscopic (ACTS) methods have typically been used to determine the electron-transfer rates in SAMs. Laviron developed a simple method for determining electron-transfer rate constants by cyclic voltammetry [92], The method allows the determination of from the dependence of the cathodic/anodic peak separation, /SEp, upon sweep rate, but it is inherently inaccurate because it is based on Butler-Volmer kinetics [78, 93, 94]. 

The photoisomerization of a command interface resulting in different electrochemical kinetics of a soluble redox-probe also can be probed by faradic impedance spectroscopy. A small electron transfer resistance (R ) is found for the system when there is an attractive interaction between the charged redox-probe and the command interface, and a much larger one upon photoisomerization to the state when the repulsive interactions exist. This paradigm was demonstrated with a negatively charged redox-probe,... 

Figure 8.7.2 Equivalent circuit of cell with (a) Rfi, the solution resistance, Cd, the doublelayer capacitance, and Zf, the faradaic impedance. The faradaic impedance represents the effect of the heterogeneous electron-transfer process. Often Zf is broken down into the components shown in (b where the charge-transfer resistance R manifests the kinetics of heterogeneous charge transfer, and the components of the Warburg impedance,...

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