Potential step irreversible system

To impose the diffusion-controlled conversion of O to R as described earlier, the potential E impressed across the electrode-solution interface must be a value such that the ratio Cr/Cq is large. Table 3.1 shows the potentials that must be applied to the electrode to achieve various ratios of C /Cq for the case in which Eq R = 0. For practical purposes, C /C = 1000 is equivalent to reducing the concentration of O to zero at the electrode surface. According to Table 3.1, an applied potential of -177 mV (vs. E° ) for n = 1 (or -88.5 mV for n = 2) will achieve this ratio. Similar arguments apply to the selection of the final potential. On the reverse step, a small C /Cq is desired to cause diffusion-controlled oxidation of R. Impressed potentials of +177 mV beyond the E° for n = 1 (and +88.5 mV for n = 2) correspond to Cr/Cq = 10"3. These calculations are valid only for reversible systems. Larger potential excursions from E° are necessary for irreversible systems. Also, the effects of iR drop in both the electrode and solution must be considered and compensated for as described in Chapter 6. 

Nernstian boundary conditions, or those for quasireversible or irreversible systems. All of these cases have been analytically solved. As well, there are two systems involving homogeneous chemical reactions, from flash photolysis experiments, for which there exist solutions to the potential step experiment, and these are also given they are valuable tests of any simulation method, especially the second-order kinetics case. 

When the potential step is small and the system is chemically reversible three cases of interest are analyzed. First, when the reaction is kinetically sluggish (electrochemi-cally -> irreversible or quasireversible) and the -> mass transport effects are negligible. 

Note that this relation could also have been derived under the conditions Cq= 0 and Cr = 0 without requiring nemstian behavior. It therefore holds also for irreversible systems, provided large enough potential steps are employed. 

Recently, a method for the analysis of the DPP curves arising from slow electrode reaction has been presented [68, 69]. The influence of the first polarization time, of the pulse duration and potential step amplitude on the recorded current was clearly manifested. The solution may be applied to the static as well as to the dropping mercury electrodes. It was verified for the quasi-reversible system Cd(Hg)/Cd(II) in the presence of 2-(a-hydroxybenzyltriamine), a substance of biological interest. Also the irreversible system Cr(VI)/Cr(III) in NaOH medium (characterized by k° 10" m s" ) was followed according to this concept. 

The single potential step chronoabsorptometry technique has been employed to determine the heterogeneous electron transfer kinetic parameters of myoglobin [36], horse heart cytochrome c [37] and soluble spinach ferredoxin [38]. In every case, the chronoabsorptometric data were analysed according to the irreversible model (the reverse reaction is ignored). The error associated with the use of this model for the kinetic analysis of these systems is most pronounced at low overpotentials, long transient times, and large reaction rates. 

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... 

The passage from one control to the other is pictured in Figure 2.5 for the cathodic peak potential and the peak width as a function of the scan rate and of the intrinsic parameters of the system. We note that increasing the scan rate tends to move the kinetic control from the follow-up reaction to the electron transfer step. It thus appears that the overall reaction may well be under the kinetic control of electron transfer, even if this is intrinsically fast, provided that the follow-up reaction is irreversible and fast. The reason is that the follow-up reaction prevents the reverse electron transfer from operating, thus making the forward electron transfer the rate-determining step. 

The second experimental system explored the reduction mechanism of another azo-dye, known as Sudan III (I-(4-pheuyIazophenyIazo)-2-naphthoI) [91]. Sudan III contains two azo groups rendering two successive two-electron, two-proton reduction steps at the mercury surface. Figure 2.68 shows a typical SW voltammetric response of Sudan III recorded in a borate buffer at pH 10.00. The first reduction step is chemically reversible, while the second one is irreversible. More importantly, the second reduction step proceeds at potential about 230 mV more negative than the first one, thus causing a well-separated voltammetric peak. The overall mechanism... 

The CV of [MoOX2(dtc)2] 2 in MeCN showed that the complex reduces in an irreversible two-electron step, with the elimination of both halide ligands (Sch. 2). The metal product of the electrochemical reduction, [MoO(dtc)2], detected by CV through its reduction and oxidation systems, was obtained by controlled-potential reduction of 2 (2 F mol 2). 

In addition, electrode reactions are frequently characterized by an irreversible, i.e., slow, electron transfer. Therefore, overpotentials have to be applied in preparative-scale electrolyses to a smaller or larger extent. This means not only a higher energy consumption but also a loss in selectivity as other functions within the molecule can already be attacked. In the case of indirect electrolyses, no overpotentials are encountered as long as reversible redox systems are used as mediators. It is very exciting that not only overpotentials can be eliminated but frequently redox catalysts can be applied with potentials which are 600 mV or in some cases even up to 1 Volt lower than the electrode potentials of the substrates. These so-called redox reactions opposite to the standard potential gradient can take place in two different ways. In the first place, a thermodynamically unfavorable electron-transfer equilibrium (Eq. (3)) may be followed by a fast and irreversible step (Eq. (4)) which will shift the electron-transfer equilibrium to the product side. In this case the reaction rate (Eq. (5)) is not only controlled by the equilibrium constant K, i.e., by the standard potential difference be-... 

Pulsed-current techniques can furnish electrochemical kinetic information and have been used at the RDE. With a pulse duration of 10-4 s and a cycle time of 10-3 s, good agreement was found with steady-state results [144] for the kinetic determination of the ferri-ferrocyanide system [260, 261], Reduction of the pulse duration and cycle time would allow the measurement of larger rate constants. Kinetic parameter extraction has also been discussed for first-order irreversible reactions with two-step cathodic current pulses [262], A generalised theory describing the effect of pulsed current electrolysis on current—potential relations has appeared [263],... 

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