Cyclic voltammetry irreversible electron transfer

Similar equations can be derived for the peak current for voltammetric responses for irreversible electron transfer ( irrev mechanism - Eirrev diagnostics in cyclic voltammetry) or for other mechanistic cases. 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

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 ... 

The two cyclic voltammograms shown in Fig. 13 of [Scm(LBu2)] (b) and Scln(LMe-)] (a) show an important feature. Whereas the cyclic voltammetry (CV) of the former compound displays three reversible one-electron transfer waves, the latter shows only two irreversible oxidation peaks. Thus methyl groups in the ortho- and para-positions of the phenolates are not sufficient to effectively quench side reactions of the generated phenoxyls. In contrast, two tertiary butyl groups in the ortho- and para-positions stabilize the successively formed phenoxyls, Eq. (5)... 

FIGURE 1.17. Cyclic voltammetry of slow electron transfer involving immobilized reactants and obeying a Butler Volmer law. Normalized current-potential curves as a function of the kinetic parameter (the number on each curve is the value of log A ) for a. — 0.5. Insert irreversible dimensionless response (applies whatever the value of a). 

FIGURE 2.5. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying the Butler-Volmer law (with a = 0.5) and an irreversible follow-up reaction, a Variation of the peak potential with the scan rate, b Variation of the peak width with scan rate. Dots represent examples of experimental data points obtained over a six-order-of-magnitude variation of the scan rate. 

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. 

The cyclic voltammetry behavior of the Cu(II) rotaxane, 4(5)2+ (Fig. 14.8b), is very different from that of 4, t l +. The potential sweep for the measurement was started at - 0.9 V, a potential at which no electron transfer should occur, regardless of the nature of the surrounding of the central Cu(II) center (penta- or tetracoordinate). Curve i shows two cathodic peaks a very small one, located at + 0.53 V, followed by an intense one at —0.13V. Only one anodic peak at 0.59 V appears during the reverse sweep. If a second scan ii follows immediately the first one i, the intensity of the cathodic peak at 0.53 V increases noticeably. The main cathodic peak at —0.15 V is characteristic of pentacoordinate Cu(II). Thus, in 4(5)2+ prepared from the free rotaxane by metalation with Cu(II) ions, the central metal is coordinated to the terdentate terpyridine of the wheel and to the bidentate dpp of the axle. On the other hand, the irreversibility of this peak means that the pentacoordinate Cu(I) species formed in the diffusion layer when sweeping cathodically is transformed very rapidly and in any case before the electrode potential becomes again more anodic than the potential of the pentacoordinate Cu2 + /Cu+ redox system. The irreversible character of the wave at —0.15 V and the appearance of an anodic peak at the value of + 0.53 V indicate that the transient species, formed by reduction of 4(5)2 +, has undergone a complete reorganization, which leads to a tetracoordinate copper rotaxane. The second scan ii, which follows immediately the first one i, confirms this assertion. 

In aprotic solvents, the radical anion, RX , for aryl halides has been detected as intermediate. In cyclic voltammetry of aryl halides, though an irreversible two-electron reduction occurs at low scan rate, a reversible one-electron reduction occurs at high scan rate. Thus, it is possible to get the values of the standard potential ( °) for the RX/RX couple and the rate constant (k) for RX -> R (therefore, the lifetime of RX ). In Fig. 8.18, the relation between ° and log k for aryl bromides in DMF is linear with a slope of 0.5 [5If], It is apparent that the lifetime of RX , obtained by 1/k, increases with the positive shift of E0. In contrast, the existence of RX for alkyl monohalides has never been confirmed. With these compounds, it is difficult to say whether the two processes, i.e. electron transfer and bond cleavage, are step-wise or concerted (RX+e -> R +X ). According to Sa-veant [5le], the smaller the bond dissociation energy, the larger the tendency for the concerted mechanism to prevail over the step-wise mechanism. 

Electron transfer reactions are classified as reversible, quasi-reversible or irreversible depending on the ability of the reaction to respond to changes in E, which, of course, is related to the magnitude of k°. The distinction is important, in particular, for the (correct) application of linear sweep and cyclic voltammetry, and for that reason further discussion of this classification will be postponed until after the introduction of these techniques in Section 6.7.2. 

The irreversibility of the reduction peak of 16 2+, combined with the appearance of a reversible peak corresponding to tetracoordinated copper, suggests that the reorganization of the rotaxane in its pentacoordinated form 16(S)+ (i.e., with the copper coordinated to terpy and to dpp units) to its tetracoordinated form (16 +, in which the copper is surrounded by two dpp units) occurs within the timescale of the cyclic voltammetry. Indeed, the cyclic voltammetry response located at -0.15 V becomes progressively reversible when increasing the potential sweep rate, as expected for an electrochemical process in which an electron transfer is followed by an irreversible chemical reaction (EC). Following the method of Nicholson and Shain, 9S the rate constant value, k, of the chemical reaction, i.e., the transformation of pentacoordinated Cu(i) into tetracoordinated Cu(i), was determined. A value of 17 s 1 was... 

Electron transfer properties of polyhalogenated biphenyls were investigated by cyclic voltammetry. The primary reduction peak of 4,4 -dichlorobiphenyl, involving replacement of halide with hydrogen in an irreversible ECE- type reaction, are under kinetic control of the initial ET step. Electrochemical transfer coefficients, standard potentials and standard heterogeneous rate constants were also estimated from the voltammetric data230. 

Eirrev diagnostics in cyclic voltammetry — For electrochemical systems with kinetic constraints in the heterogeneous electron transfer reaction (- irreversibility)... 

ErevCirrev diagnostics in cyclic voltammetry — Assuming that the product (R) of an electrochemically reversible electron transfer reaction (E step) is involved in additional irreversible chemical reaction (C step), according to the scheme ... 

Peak potential — is a term used in -> voltammetry for the potential of the working (indicator) electrode at which the peak current is attained. In the cyclic voltammogram of a reversible redox couple, anodic and cathodic peak p. are separated by 2.2RT/nF, which is considered as a diagnostic feature and gives a possibility to determine the formal p. as a mid-peak p. For irreversible couples, quantitative relations exist, interconnecting peak p. and the rate constant of the -> electron transfer. 

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