Current potential curves, irreversible

In the case of an irreversible electrode reaction, the current-potential curve will display a similar shape, with... 

The question of the variation of a with potential is discussed further later first in Section 1.4.3, where it is shown that the variation can be neglected along an irreversible current-potential curve in most cases then in Section 1.4.4, where the experimental detection of this variation is discussed. 

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). 

The normalized current-potential curves are thus a function of the two parameters A and oc. An example corresponding to a = 0.5 is shown in Figure 1.19. Decreasing the parameter A as a result of a decrease in the rate constant and/or an increase in scan rate triggers a shift of the cathodic potential toward negative values and of the anodic potential in the reverse direction, thus increasing the irreversibility of the cyclic voltammetric response. When complete irreversibility is reached (i.e., when there is no anodic current underneath the cathodic current, and vice versa), a limiting situation is reached, characterized 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 pure kinetic conditions, which are achieved for large values of A, implies that bo = t/ q/x/A —> 0 and thus, from equation (6.40), i//2 = (//,. It follows that the current is exactly the double of the irreversible EC current obtained under pure kinetic conditions along the entire current-potential curve. 

As will become evident from an examination of the various voltammetric techniques, the electrochemical reversibility or irreversibility of a process influences the form of the relative current/potential curves. 

Fig. 5.6 Current-potential curves for the processes controlled by the mass transport of electroactive species. Curves 1 to 3 are for reversible processes in solutions containing (1) both Ox and Red, (2) Ox only, and (3) Red only. Curves 4 and 4 are for an irreversible reduction (curve 4) and oxidation (curve 4 ) in...

It will be clear that cyclic voltammetry is a powerful tool for a first analysis of an electrochemical reaction occurring at the surface of an electrode because it will reveal reversibility. Depending on whether the system is reversible, information will be obtained about half wave potential, number of electrons exchanged in the reaction, the concentration and diffusion coefficient of the electroactive species. However, these data can also be obtained for an irreversible system1113 but, in this case, the equations describing the current-potential curves differ somewhat from Equations 2.21 to 2.27. 

Moreover, the current-potential curves are affected by the disproportionation reaction therefore, other variables (the rate constant for the disproportionation reaction) must be taken into account. Since experimental results for many interesting systems show clear evidence of slow kinetics, ad hoc simulation procedures have typically been used for the analysis of the resulting current-potential curves [31, 38, 41, 48]. As an example, in reference [38], it is reported that a clear compropor-tionation influence is observed for an EE mechanism with normal ordering of potentials and an irreversible second charge transfer step. In this case, the second wave is clearly asymmetric, showing a sharp rise near its base. This result was observed experimentally for the reduction of 7,7,8,8-tetracyanoquinodimethane in acetonitrile at platinum electrodes (see Fig. 3.20). In order to fit the experimental results, a comproportionation rate constant comp = 108 M-1 s-1 should be introduced. 

Irreversibility — Figure. Quasireversible and irreversible behavior, a Current-potential curves and b lg j -E plots (Tafel plots) for a redox system at different angular velocities of a rotating disc electrode [Pg.374]

Fig. 21. Schematic current-potential curves for various categories of mixed couples, (a) Two irreversible couples (b) two reversible couples (c) two couples whose Em value lies within the plateau region of one of them.

For slow electron-transfer (irreversible) processes, the eventual extent of the electrode process will be governed by equilibrium considerations and the Nemst equation, but the rate of electrolysis will be small at the potentials predicted in the previous sections and long-duration electrolyses would result. For these processes, reduction must be carried out at somewhat more negative potentials the actual potential is usually selected on the basis of experimental current-potential curves taken under conditions near those for the intended bulk electrolysis. Processes that are controlled by the rate of a homogeneous reaction, such as... 

Figure 11.7.4 Theoretical cathodic current-potential curves for one-step, one-electron irreversible reactions according to (11.7.24) for several values of k. Curve A reversible reaction (shown for comparison). Curve B = 10 Curve C = 10 Curve D = 10" cm/s. The values assumed in making the plots were i = 2 mV/s, A = 0.5 cm, Cq = 1.0 mM, a - 0.5, V = 2.0 [From A. T. Hubbard, J. Electroanal Chem., 22, 165 (1969), with permission.]...

Figure 11.7.5 Theoretical cathodic current-potential curves for one-step, one-electron irreversible reactions for several values of a. Curve A reversible reaction. Curve B a = 0.75,...

In this section, the behavior of a redox system at the equilibrium potential has been discussed. It should, however, be noted that impedance spectroscopy of irreversible systems can also yield useful information. For example, the charge-transfer resistance determined at the corrosion potential corresponds to the slope of the current-potential curve (/ ct = dV(t)/dI (t) at that potential and allows calculation of the rate of corrosion [1]. 

Numerous terms are put to use in the field of electrochemical kinetics to characterise typical situations which are limiting cases with particular shapes for the corresponding current-potential curves. In scientific literature, these terms are not always applied with the greatest rigour. In the forthcoming sections we will give a precise definition for the common terms nernstian redox systems in section 4.3.2.4 reversible/irreversible redox reactions in section 4.3.2.S slow/fast redox systems in section 4.3.2.6. 

This half-wave potential is very useful in evaluating the electrochemical reaction based on the measured current-potential curves by RDE technique. Note that Eqn (5.21) is for the case of reversible reactions. As a rough estimation, this half-wave potential may be useful for those pseudoreversible reactions. However, one should be careful when using this half-wave potential to evaluation the irreversible electrochemical reactions. 

The net current is the algebraic sum of the cathodic and anodic currents (see Section 4), corresponding to the reduction and oxidation reactions. However, in polarography the solution usually contains only one electroactive species and the contribution from the reverse reaction can usually be neglected in the case of many organic reactions which behave irreversibly. It can be seen that as the applied potential is increased the cathodic current increases exponentially until it becomes diffusion limited, and this is shown in the current-potential curve, or polarogram (Figure 5). 

However, only a few organic compounds behave in a polarographically reversible manner although many may involve a reversible electron transfer step, this is often followed by irreversible chemical reactions. Irreversible processes are those for which the current is limited mainly by the kinetics of the process at the electrode surface and not by diffusion. The nature of such current-potential curves can be described by reference to Figure 6. If electrochemical equilibrium obtains at the electrode surface, then a reversible wave is obtained (curve a). The irreversible wave (curve b) is more drawn out, i.e., for a given current, say, /i or I2, a higher cathodic potential is required. 

The current-potential curves for a totally irreversible process have also been derived by Delahay and the expression for the peak current is then... 

There are well-defined criteria for this "reversible" system in terms of peak separation, wave shape, etc. and the maximum current scales inversely with the square root of the scan rate. The half-wave potential of a "reversible" redox process may readily be obtained from the voltammogram. If, however, the electron transfer produces a species that is chemically reactive on the experimental time scale, then the return wave is missing and the peak potential shifts as a function of the kinetics of the follow-up processes. The peak is not as well defined, and without a proper return wave it is now not straightforward to obtain thermodynamic half-wave potentials from the trace of such an irreversible system. Furthermore, if a disk electrode is used of micrometer-dimensions, then hemispherical diffusion now takes place and a sigmoidal current-potential curve is obtained [Fig. 4(b)]. 

The current-potential curves of the catalytic oxidation current mediated by the mixed-in mediators depend on the electrode reaction properties of the mediator used, as theory has predicted those which gave reversible cyclic voltammograms, such as, 1,2-naphthoquinone and 2,6-dichloro-p-benzoquinone produced reversible catalytic current-potential curves, as shown in Figure 7, whereas those which gave quasi-reversible or irreversible cyclic voltammograms, such as BQ and 2-methyl-p-benzoquinone, gave quasi- or irreversible drawn-out waves, as seen in Figure 1. The half-wave potential of the catalytic current nearly coincided with the mid-potential for the former "reversible compounds, whereas it was shifted to more positive potential than the mid-potential for the latter. In the same way, the enzyme kinetics should also influence the dependence of the catalytic current on the electrode potential. 

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