Standard rate constant cyclic voltammetry

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

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... 

By using cyclic voltammetry, Schiffrin and coworkers [26, 186, 187, 189] studied electron transfer across the water-1,2-dichloroethane interface between the redox couple FefCNls /Fe(CN)6 in water, and lutetium(III) [186] and tin(IV) [26, 187] diphthalocyanines and bis(pyridine)-me50-tetraphenylporphyrinato-iron(II) or ru-thenium(III) [189] in the organic solvent. An essential advantage of these systems is that none of the reactants or products can cross the interface and interfere with the electron transfer reaction, which could be clearly demonstrated. Owing to a much higher concentration of the aqueous redox couple, the pseudo-first order electron transfer reactions could be analyzed with the help of the Nicholson-Shain theory. However, though they have all appeared to be quasireversible, kinetic analysis was restricted to an evaluation of the apparent standard rate constant o. which was found to be of the order of 10 cm s [186, 189]. Marcus [199] has derived a relationship between the pseudo-first-order rate constant for the reaction (8) and the rate... 

Assuming that standard rate constants (i.e., kf at AG° = 0) are similar, the differences in ET rates for these reactants may only be due to the different AE° values. The formal potentials of Ru(CN)s , Mo(CN)g , and Fe(CN)s- couples measured by cyclic voltammetry are 750, 590, and 235 mV versus Ag/AgCl, respectively. Accordingly, the feedback current obtained with Mo(CN)g in water was higher than with Ru(CN)g . With Fe(CN)s, the ET rate is much higher, and the overall process was diffusion-controlled at any [CKT]] ... 

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 ... 

FIGURE 4.3. Redox and chemical homogeneous catalysis of trans-1,2 dibromocyclohexane. a cyclic voltammetry in DMF of the direct electrochemical reduction at a glassy carbon electrode (top), of redox catalysis by fhiorenone (middle), of chemical catalysis by an iron(I) porphyrin, b catalysis rate constant as a function of the standard potential of the catalyst couple aromatic anion radicals, Fe(I), a Fe(0), Co(I), Ni(I) porphyrins. Adapted from Figures 3 and 4 of reference lb, with permission from the American Chemical Society. 

The experimental kinetic data obtained with the butyl halides in DMF are shown in Fig. 13 in the form of a plot of the activation free energy, AG, against the standard potential of the aromatic anion radicals, Ep/Q. The electrochemical data are displayed in the same diagrams in the form of values of the free energies of activation at the cyclic voltammetry peak potential, E, for a 0.1 V s scan rate. Additional data have been recently obtained by pulse radiolysis for n-butyl iodide in the same solvent (Grim-shaw et al., 1988) that complete nicely the data obtained by indirect electrochemistry. In the latter case, indeed, the upper limit of obtainable rate constants was 10 m s", beyond which the overlap between the mediator wave and the direct reduction wave of n-BuI is too strong for a meaningful measurement to be carried out. This is about the lower limit of measurable... 

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 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. 

In this experiment, the electrochemistry of both [Co(en)3]3+/2+ and [Co(ox)3]3+/2+ will be investigated using cyclic voltammetry, and the standard reduction potential (E°, V) for the [Co(en)3]3+/2+ couple will be measured. For metal complex stability reasons discussed below, it is not possible to use this technique to obtain reduction potentials for the mixed ligand cobalt systems an exercise at the end of this experiment helps to estimate these. The E° values obtained will be important for experiment 5.6, in which outer-sphere electron transfer rate constants between [Co(en)3)]2+ and [Co(en)2)(ox)]+ will be mathematically modeled using Marcus theory. 

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