Electron transfer kinetics from cyclic voltammetry

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

As discussed before in the case of nucleic acids the authors have also considered the incidence of the interfacial conformation of the hemoproteins on the appearance of the SERRS signals from the chromophores. Although under their Raman conditions no protein vibration can be observed, the possibility of heme loss or protein denatura-tion are envisaged to explain a direct interaction of the heme chromophores with the electrode surface in the case of the adsorl Mb. extensive denaturation of Cytc at the electrode appears unlikely to the authors on the basis of the close correspondence of the surface and solution spectra. Furthermore, the sluggish electron transfer kinetics measured by cyclic voltammetry in the case of Cytc is also an argument in favour of some structural hindrance for the accessibility to the heme chromophore in the adsorbed state of Cytc. This electrochemical aspect of the behaviour of Cytc has very recently incited Cotton et al. and Tanigushi et al. to modify the silver and gold electrode surface in order to accelerate the electron transfer. The authors show that in the presence of 4,4-bipyridine bis (4-pyridyl)disulfide and purine an enhancement of the quasi-reversible redox process is possible. The SERRS spectroscopy has also permitted the characterization of the surface of the modified silver electrode. It has teen thus shown, that in presence of both pyridine derivates the direct adsorption of the heme chromophore is not detected while in presence of purine a coadsorption of Cytc and purine occurs In the case of the Ag-bipyridyl modified electrode the cyclicvoltammetric and SERRS data indicate that the bipyridyl forms an Ag(I) complex on Ag electrodes with the appropriate redox potential to mediate electron transfer between the electrode and cytochrome c. 

In cyclic voltammetry a redox-active molecule is placed in an electroanalytical cell and the electrode potential is raised from a starting value at which there is no electroactivity. When electron transfer occurs a current is measured, and the shape of the trace depends upon, among other factors, the size and shape of the electrode. Thus, at a disk or wire of millimeter-sized dimensions (millielectrode) under conditions of linear diffusion, an initial current increase imder the control of electron-transfer kinetics meets a current decrease under diffusion control towards an effectively planar surface, and a characteristic peak shape is observed [Fig. 4(a)]. If the electron-transfer reaction produces a relatively stable species, then on reversing the scan direction a current is observed in the opposite direction. 

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions. The power of cyclic voltammetry results from its ability to rapidly provide considerable information on the thermodynamics of redox processes, on the kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or adsorption processes. Cyclic voltammetry is often the first experiment performed in an electroanalytical study. In particular, it offers a rapid location of redox potentials of the electroactive species, and convenient evaluation of the effect of media upon the redox process. 

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

FIGURE 2.6. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying a MHL kinetic law (Xt — 0.7 eV, koo — 4 x 103 cms-1, implying that kg = 0.69 cms-1) and an irreversible follow-up reaction (from bottom to top, k+ = 103, 105, 107, 109s 1). Temperature, 25°C. a Potential-dependent rate constant derived from convolutive manipulation of the cyclic voltammetric data (see the text), b Variation with potential of the apparent transfer coefficient (see the text) obtained from differentiation of the curves in part a. 

Although separate determination of the kinetic and thermodynamic parameters of electron transfer to transient radicals is certainly important from a fundamental point of view, the cyclic voltammetric determination of the reduction potentials and dimerization parameters may be useful to devise preparative-scale strategies. In preparative-scale electrolysis (Section 2.3) these parameters are the same as in cyclic voltammetry after replacement in equations (2.39) and (2.40) of Fv/IZT by D/52. For example, a diffusion layer thickness S = 5 x 10-2 cm is equivalent to v = 0.01 V/s. The parameters thus adapted, with no necessity of separating the kinetic and thermodynamic parameters of electron transfer, may thus be used to defined optimized preparative-scale strategies according to the principles defined and illustrated in Section 2.4. 

In cyclic voltammetry, the current-potential curves are completely irreversible whatever the scan rate, since the electron transfer/bond-breaking reaction is itself totally irreversible. In most cases, dissociative electron transfers are followed by immediate reduction of R, as discussed in Section 2.6, giving rise to a two-electron stoichiometry. The rate-determining step remains the first dissociative electron transfer, which allows one to derive its kinetic characteristics from the cyclic voltammetric response, ignoring the second transfer step aside from the doubling of the current. 

Application of these curves may have as other objective to uncover the kinetic characteristics of the electrode electron transfer. This cannot be done in the absence of catalysis since the RDEV response is nil insofar as the steady-state response of an attached species is nil. Cyclic voltammetry could be used instead. The response is not nil, but the signal is in general small, often hardly emerging from the baseline current. Determining the standard potential under these conditions is generally feasible, but an accurate... 

Several classes of coordination compound undergo several successive, reversible one-electron-transfer reactions. These comprise a so-called electron-transfer chain or series .8 Cyclic voltammetry is particularly useful for recognizing such behaviour and an example is illustrated by Figure 2. This shows the four members of the electron-transfer chain [Fe4S4(SPh)4]"-, n = 1-4.5 An electron-transfer series provides the coordination chemist with a means of examining the consequence of systematic addition (or removal) of electrons from a nominally fixed geometry thermodynamic, kinetic and spectroscopic relationships between members of a series can be explored.9... 

An interesting study [52] of the protonation kinetics and equilibrium of radical cations and dications of three carotenoid derivatives involved cyclic voltammetry, rotating-disk electrolysis, and in situ controlled-potential electrochemical generation of the radical cations. Controlled-potential electrolysis in the EPR cavity was used to identify the electrode reactions in the cyclic volt-ammograms at which radical ions were generated. The concentrations of the radicals were determined from the EPR amplitudes, and the buildup and decay were used to estimate lifetimes of the species. To accomplish the correlation between the cyclic voltammetry and the formation of radical species, the relative current from cyclic voltammetry and the normalized EPR signal amplitude were plotted against potential. Electron transfer rates and the reaction mechanisms, EE or ECE, were determined from the electrochemical measurements. This study shows how nicely the various measurement techniques complement each other. 

The chronocoulometry and chronoamperometry methods are most useful for the study of adsorption phenomena associated with electroactive species. Although less popular than cyclic voltammetry for the study of chemical reactions that are coupled with electrode reactions, these chrono- methods have merit for some situations. In all cases each step (diffusion, electron transfer, and chemical reactions) must be considered. For the simplification of the data analysis, conditions are chosen such that the electron-transfer process is controlled by the diffusion of an electroactive species. However, to obtain the kinetic parameters of chemical reactions, a reasonable mechanism must be available (often ascertained from cyclic voltammetry). A series of recent monographs provides details of useful applications for these methods.13,37,57... 

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