Reversible reaction potential step

Based on a general knowledge of base-catalyzed reactions of carbonyl compounds, a reasonable sequence of steps can be written, but the relative rates of the steps is an open question. Furthermore, it is known that reactions of this type are generally reversible so that the potential reversibility of each step must be taken into account. A completely... 

Figure 6.7 shows a typical special feature of the polarization curves. In the case of reversible reactions (curve 1), the anodic and cathodic branches of the curve form a single step or wave. In the case of irreversible reactions, independent, anodic and cathodic, waves develop, each having its own inflection or half-wave point. The differences between the half-wave potentials of the anodic and cathodic waves will be larger the lower the ratio fH. ... 

The behavior in the regions of moderate anodic or cathodic polarization depends on the relative positions of potentials E and Eq, which in turn depend on the relative values of constants and k 2- For E which are more positive than Eq (Fig. 13.1a), relation (13.20) for the cathodic CD remains valid at all values of cathodic polarization (except for the region of low values where the reverse reaction must be taken into account). At moderate values of anodic polarization, inequalities (la) and (2b) are found to be valid at potentials more negative than E, while step 2 becomes rate determining, which is the second step along the reaction path. In this case [see Eq. (13.10)], we have... 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Simulation of a Potential-Step Experiment for a Reversible E Reaction [1 ]... 

For each cathodic stripping mechanism, the dimensionless net peak current is proportional to the amount of the deposited salt, which is formed in the course of the deposition step. The amount of the salt is affected by the accumulation time, concentration of the reacting ligand, and accumulation potential. The amount of the deposited salt depends sigmoidally on the deposition potential, with a half-wave potential being sensitive to the accumulation time. If the accumulation potential is significantly more positive than the peak potential, the surface concentration of the insoluble salt is independent on the deposition potential. The formation of the salt is controlled by the diffusion of the ligand, thus the net peak current is proportional to the square root of the accumulation time. If reaction (2.204) is electrochemically reversible, the real net peak current depends linearly on the frequency, which is a common feature of all electrode mechanism of an immobilized reactant (Sect. 2.6.1). The net peak potential for a reversible reaction (2.204) is a hnear function of the log(/) with a slope equal to typical theoretical response... 

The motivation behind the considerable effort that was exerted in the development of DCV [42, 49, 50, 69] was based on the need to make CV and LSV quantitative tools for the study of electrode kinetics. At that time, there were three major problems that had to be overcome. These were (a) the precision in the measurement of Ep and AEp, (b) the problem with accurately defining the baseline for the reverse sweep and (c) the problem as to how to handle Rn in a practical manner. The development of DCV did indeed provide suitable solutions to all three of these problems, although the methods developed to handle the Ru problem [41, 42] only involve the derivative of the response in terms of precision necessary for the measurements. More recent work [55, 57] is indicative that the precision in Ep/2, Ep) and AEP measurements can be as high as that observed during DCV (see Sect. 3.4). Also, a recent study in which rate constants were evaluated using CV, DCV, and double potential step chronoamperometry for a particular electrode reaction showed that the precision to be expected frcm the three techniques are comparable when the CV baseline, after subtracting out the charging... 

As this chapter is primarily dedicated to the study of electrode kinetics, we wish to deal only briefly with the fundamental consequences of reactant adsorption for the methodology of the relaxation techniques, again confined to the potential step and the impedance methods. In addition, we will review briefly the potentialities of these methods with regard to the study of adsorption itself in the case of the reversible electrode reaction. 

Fig. 35. Time dependence of the surface excess Vq, after a potential step from E-t E° toEt

The potential response of the RDE to current steps has been treated analytically [3, 237, 251] and accurately by Hale using numerical integration [252] this enables the elucidation of kinetic parameters [185, 253]. A current density—transition time relationship at the RDE has been established which accounts for observed differences from the Sand equation [eqn. (218)] and which has been applied to EC reactions [254]. Other hydrodynamic solid electrodes have not been considered in detail, although reversible reactions at channel electrodes have been discussed [255, 256]. 

Here, the electrode reaction is followed by a first-order irreversible chemical reaction in solution that consumes the primary product B and forms the final product C. The rate of this chemical reaction can be measured conveniently with cyclic voltammetry, double-potential-step chronoamperometry, reverse pulse voltammetry, etc. However, this is only true if the half-life of B is greater than or equal to the shortest attainable time scale of the experiment. 

A more elaborate version of the chronoamperometry experiment is the symmetrical double-potential-step chronoamperometry technique. Here the applied potential is returned to its initial value after a period of time, t, following the application of the forward potential step. The current-time response that is observed during such an experiment is shown in Figure 3.3(B). If the product produced during a reduction reaction is stable and if the initial potential to which the working electrode is returned after t is sufficient to cause the diffusion-controlled oxidation of the reduced species, then the current obtained on application of the reverse step, ir, is given by [63]... 

As shown in Chap. 2, attaining analytical explicit solutions is considerably more complex for nonplanar geometries. This section studies quasi-reversible and irreversible processes when a potential step is applied to a spherical electrode, since this solution will be very useful for discussing the behavior of these electrode reactions when steady-state conditions are addressed in the next section. Moreover, the treatment of other electrode geometries seldom leads to explicit analytical solutions and it is necessary in most cases to use numerical treatments. 

Substituent or solvent effects may be similar for concerted and stepwise processes. It has been shown that provided the rates of reverse reactions are almost independent of changes in oxidation potential, plots of E°, the standard reduction potential for the half cell (8) against log kf for a series of acceptors, Ox +, reacting with a hydride donor must have a slope of 30 mV/ log unit whether the rate-limiting step is hydride transfer, or hydrogen-atom transfer, or electron transfer (Kurz and Kurz, 1978). 

Chronoamperometry is often used for measuring the diffusion coefficient of electroactive species or the surface area of the working electrode. Some analytical applications of chronoamperometry (e.g., in vivo bioanalysis) rely on pulsing of the potential of the working electrode repetitively at fixed time intervals. Some popular test strips for blood glucose (discussed in Chapter 6) involve potential-step measurements of an enzymatically liberated product (in connection with a preceding incubation reaction). Chronoamperometry can also be applied to the study of mechanisms of electrode processes. Particularly attractive for this task are reversal double-step chronoamperometric experiments (where the second step is used to probe the fate of a species generated in the first one). 

This originated from a similar idea to that of the double potential step. A base potential at which all the electroactive species is electrolysed is applied, and the reverse reaction is carried out by normal pulse (Fig. 10.12). A good reason for using this technique is to diminish the problems caused by parallel electrode reactions of the initial species. 

Kq exceeds the value 1000, the boundary conditions are taken to be those for a reversible reaction. How these two different boundary conditions are applied to calculate the concentrations C. yo and Cb,o is described below. Note that before new concentrations are to be computed, ail old concentrations, including the boundary values, must be known. When a new potential is stepped to, it comes into effect only after the concentrations are renewed, after which Co is calculated. This might be thought of as less than satisfactory, but it is consistent with the explicit method. In Chaps. 8 and 9, more satisfactory methods will be presented. 

We have the following unknown boundary values the two species nearsurface concentrations Cyo and Cb,o, the two species fluxes, respectively G and G n, the additional capacitive flux Gc, and the potential p, differing (for p > 0) from the nominal, desired potential pnom that was set, for example, in an LSV sweep or a potential step experiment. Five of the six required equations are common to all types of experiments, but the sixth (here, the first one given below) depends on the reaction. That might be a reversible reaction, in which case a form of the Nernst equation must he invoked, or a quasi-reversible reaction, in which case the Butler-Volmer equation is used (see Chap. 6 for these). Let us now assume an LSV sweep, the case of most interest in this context. The unknowns are all written as future values with apostrophes, because they must, in what follows below, be distinguished from their present counterparts, all known. 

---