Totally irreversible electron transfer, potential

So, a totally irreversible process could be mistaken for a quasi-reversible one with a 0.5 (Fig. 7.17f). In order to discriminate the reversibility degree of the electrochemical reaction, it is necessary to take into account that for a quasi-reversible process the peak corresponding to more cathodic potentials in the second scan (denoted as RC by [29]) is higher than that located at more anodic ones (denoted as RA by [29]) when a 3> 0.5, whereas the opposite is observed for a fully irreversible electron transfer for any value of a (see also Table insert, Fig. 7.20). 

For irreversible systems the peak potential of a reduction process is shifted toward more negative potentials by about 0.030 V for a decade increase in the scan rate [Eq. (3.43)]. By analogy, a peak of an anodic process is shifted toward more positive potentials. The most characteristic feature of a cyclic voltammogram of a totally irreversible system is the absence of a reverse peak. However, it does not necessarily imply an irreversible electron transfer but could be due to a fast following chemical reaction. 

Fig. 7. Admittance vs. potential curves (phase-sensitive AC polarograms) for electrode reactions with different degrees of reversibility (A) Reversible, (B) Quasi-reversible. (C) Totally irreversible electron transfer. The dashed line is the blank.

For a totally irreversible electrochemical process, the heterogeneous rate constant ke for electron transfer at the CV peak potential Ep is given by... 

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 physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

This shows that for an irreversible process, the peak potential is shifted towards more negative (reduction reaction) or more positive (oxidation reaction) potentials by about 0.03 V per decade of increase in the scan rate. For a totally irreversible reaction, no return peak is observed due to the fact that the kinetics are so slow that the opposite reaction cannot occur. The activation energy, overcome by application of a potential, is so high that it is not possible to apply such a potential under experimental conditions. However, the absence of a return peak does not necessarily imply slow electron transfer, but can also be due to a fast following chemical reaction. 

Recently,the electron-transfer theory was extended in order to incorporate the slow and reversible chemically induced electron-exchange reactions, as observed for the fluorescer-catalyzed chemiluminescent decomposition of a-peroxylactones. It was argued that electron transfer is complete in the transition state for such a slow and irreversible endergonic electron-transfer reaction, but that the typically small slopes (— a/RT where a is about 0.3) of the In (intensity) vs. oxidation potential plot was due to the fact that only a fraction (a) of the total free-energy change manifests itself in the activation energy. 

In the case of irreversible reactions, the polarographic half-wave potential also depends on the standard potential (formal potential) however, the kinetics of the electrode reaction lead to strong deviation as an overpotential has to be applied to overcome the activation barrier of the slow electron transfer reaction. In the case of a totally irreversible electrode reaction, the half-wave potential depends on the standard rate constant ks of the electrode reaction, the transfer coefficient a, the number e- of transferred electrons, the diffusion coefficient T>ox, and the drop time t [7] as follows ... 

When the standard rate constant for electron transfer kP is very small, kf and are also both very small. Moreover, kf, becomes negUgible as the electrode potential is made increasingly negative to drive the reduction of O. In this case, the voltammogram is said to be totally irreversible and equation (11.2.50) reduces to equation (11.2.51). After substitution of kf and further rearrangement, the potential is expressed in terms of the current (equation (11.2.52)) ... 

Although the cyclic voltammograms appear to be irreversible, they should not be. In the case of a totally irreversible system, we cannot expect to determine the reduction potential. To understand this apparent anomaly more fully, a study of the reversibility of the system was performed. The electrochemical current corresponds to the difference between the rate of the forward electron transfer kf[Bi2a] and its rate kb[Bi2a] for the reverse process. The reversibility factor f, for the methylcobalamin system is described as follows ... 

If the adsorption coupled reaction (2.144) is totally irreversible, the voltammet-ric complexity is significantly reduced [111, 115]. For the totally irreversible case, the real net peak current is a linear function of the frequency, whereas the peak potentials depends linearly on log(/) with a slope of = 2-3 This slope enables estimation of the electron transfer coefficient, provided the number of exchanged electrons is known. Similarly, the same parameter can be inferred from the half-peak width, which is defined as A p/2 = (63.5 0.5) /% mV. 

The current-potential relationship of the totally - irreversible electrode reaction Ox + ne - Red in the techniques mentioned above is I = IiKexp(-af)/ (1+ Kexp(-asteady-state voltammetry, a. is a - transfer coefficient, ks is -> standard rate constant, t is a drop life-time, S is a -> diffusion layer thickness, and

logarithmic analysis of this wave is also a straight line E = Eff + 2.303 x (RT/anF) logzc + 2.303 x (RT/anF) log [(fi, - I) /I -The slope of this line is 0.059/a V. It can be used for the determination of transfer coefficients, if the number of electrons is known. The half-wave potential depends on the drop life-time, or the rotation rate, or the microelectrode radius, and this relationship can be used for the determination of the standard rate constant, if the formal potential is known. 

For some substances the half-wave potential of the oxidized form differs substantially from that of the reduced form. The shape of these waves, as well as the shifts of the half-wave potentials, are such as we would expect for a reversible process. Sometimes, the slope of the wave and the dependence of half-wave potentials on pH correspond to a transfer of a smaller number of electrons than is deduced from the limiting current. In such instances we assume that a part of the electrode process is mobile, but usually we describe such total processes as irreversible. Examples of such behaviour are the reductions of carbonyl compounds. For irreversible systems the exchange of water for an organic solvent, e.g. dioxane or dimethylformamide, can disclose whether or not, in the electrode process in aqueous solution, there is interaction with a molecule of water. 

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