Current potential curves, irreversible reversible

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... 

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. 

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.

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,...

Fig. 1.3.5 Quasi-reversible and irreversible behavior, (a) Current-potential curves and (b) log j — E plots (Tafel plots) for a redox system at different angular velocities of a rotating disc electrode ct>r = 50s (i) and Fe = O.OV, jo = O.OlAm, n = 1, = 5 x 10 m s, Dq =...

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. 

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. 

Curves 4 and 4 in Fig. 5.6 show an example of the current-potential relation obtained for an irreversible electrode process. For a reversible electrode process, the reduction wave appears at the same potential as the oxidation wave, giving an oxidation-reduction wave if both Ox and Red exist in the solution (curves 1, 2 and 3 in Fig. 5.6). For an irreversible process, however, the reduction wave (curve 4) is clearly separated from the oxidation wave (curve 4 ), although the limiting currents for the two waves are the same as those in the reversible process. The cur-rent-potential relation for the irreversible reduction process can be expressed by... 

Simpler forms of (5.5.24) are used for the reversible and totally irreversible limits. For example, consider (5.4.17), which we derived as a description of the current-time curve following an arbitrary step potential in a reversible system. That same relationship is available from (5.5.24) simply by recognizing that with reversible kinetics A is very large, so that F (A) is always unity. The totally irreversible limit will be considered separately in Section 5.5.1(e). 

We have discussed (1,5.1) the two factors, electron transfer and mass transport, which determine the rate of an electrode reaction. Figs. 1.5a and 1.5b illustrate the current/WE potential curves obtained for reactions which are said to be either reversible or irreversible. The basic factor which determines whether or not an electrode reaction is reversible is the rate of the electron transfer process. This is measured in terms of a rate constant (fc°) and in general if ... 

If the rate of electron transfer between the redox species and electrode is very slow, relative to the mass transport of solution species to the electrode, then, irrespective of the electrode potential, the observed current will not be a function of mass transport. In this case, the low rate of electron transfer results in a concentration ratio of the two forms of the redox couple at the electrode surface that does not conform with the Nernst equation. Current/voltage curves for these so-called irreversible processes are of limited analytical utility. In extreme cases the curve does not reach a peak or limiting value and so cannot be used for quantitative estimations of analyte concentrations. A reversible reaction may be rendered irreversible, simply by changing the rate of the mass transport to the electrode, and vice versa. An intermediate situation... 

Constant current techniques often prove to be useful for redox titrations involving couples of which at least one behaves in an irreversible manner, i.e., equilibrium is not established instantaneously at the electrode surface. As a result of this the potential jump in the region of the end-point is too small to be useful. The potentials of electrodes which behave irreversibly show considerable variation in value when they pass a current. The constant current required for such titrations has to be determined in a separate determination prior to the tittation itself. In Fig. 6.8 are shown current-voltage curves for two redox couples one of which behaves reversibly, the other irreversibly. It is... 

For quasi-reversible systems (with 10 1 > k" > 10 5 cm s1) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of k°/ JnaD (where a = nFv/RT). As k"/s/naD increases, the process approaches the reversible case. For small values of k°/+JnaD (i.e., at very fast i>) the system exhibits an irreversible behavior. Overall, the voltaimnograms of a quasi-reversible system are more drawn-out and exhibit a larger separation in peak potentials compared to those of a reversible system (Figure 2-5, curve B). 

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