Irreversible reaction potential step

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. ... 

FIGURE 2.7. Double potential step chronoamperometry for an EC mechanism with an irreversible follow-up reaction, a Potential program with a cyclic voltammogram showing the location of the starting and inversion potentials to avoid interference of the charge transfer kinetics, b Example of chronoamperometric response, c Variation of the normalized anodic-to-cathodic current ratio, R, with the dimensionless kinetic parameter X. 

When pc —> oo, the catalytic loop is complete. The reaction sequence and the current-potential responses are the same as in the two-electron ECE homogeneous catalytic mechanism analyzed in the preceding subsection. When pc —> 0, deactivation prevails, and if the first electron transfer and the deactivation steps are fast, the same irreversible current-potential responses are obtained as in a standard EC mechanism. 

In an irreversible reaction, the rate controlling process is usually a single electron transfer step with a rate determined by Equation 1.8. The corresponding po-larographic wave is then described by Equation 1.18 where kconv is the rate constant for electron transfer at the potential of the reference electrode. For an irreversible... 

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],... 

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. 

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. 

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. 

For solution redox couples uncomplicated by irreversible coupled chemical steps (e.g. protonation, ligand dissociation), a standard (or formal) potential, E°, can be evaluated at which the electrochemical tree-energy driving force for the overall electron-transfer reaction, AG c, is zero. At this potential, the electrochemical rate constants for the forward (cathodic) and backward (anodic) reactions kc and ka (cms-1), respectively, are equal to the so-called "standard rate constant, ks. The relationship between the cathodic rate constant and the electrode potential can be expressed as... 

Hence, the correct thermodynamic criterion of the kinetic irreversibility at any step in the chemical transformation chain is a considerable (against quantity RT) change in the chemical potential of the reaction groups related to this step—that is, A j > RT. Note that the criterion is valid for both elementary and stepwise reaction, although in the latter case, one must consider the affinity for the stepwise transformation A,2 > RT. 

The homomediatory system is represented by equations (61) to (63), in which the mediator M is first oxidized to the cation radical at a relatively low oxidation potential. The next step involves a homogeneous electron transfer from S to to form S - this step is a reversible reaction. In the final step, S -is transformed to the products Pi and Pr by an irreversible reaction. 

In the presence of JV,JV -diphenyl-4,4 -phenylenediamine (DPPDA), a strong luminescence signal was observed when the potential was stepped between the reduction peak of the complex (—1.80 V) and the oxidation peak of the amine (+1.50 V), whereas in the presence of xanthone no significant signal was observed when the potential was stepped between the oxidation potential of Pt(tpy)2 (+0.85 V) and the reduction potential of xanthone (—1.68 V). These results show that DPPDA+ can play the role of X in reaction (20a), while apparently the xanthone anion radical cannot play the role of Y in reaction (21a). The most likely explanation for such a behavior is that Pt(tpy)2 undergoes fast decomposition, as suggested by the irreversible oxidation potential of Pt(tpy)2, before it can encounter the reduced xanthone. 

T. R. Mueller and R. N. Adams (see R. N. Adams, Electrochemistry at Solid Electrodes, Marcel Dekker, New York, 1969, p. 128) suggested that by measurement of ip/v for a nemstian linear potential sweep voltammetric curve, and by carrying out a potential step experiment in the same solution at the same electrode to obtain the limiting value of it, the n value of an electrode reaction can be determined without the need to know A, C, or Dq. Demonstrate that this is the case. Why would this method be unsuitable for irreversible reactions ... 

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,...

Since the forward reaction for a potential step to the limiting current region is unperturbed by the irreversible following reaction, no kinetic information can be obtained from the po-larographic diffusion current or the limiting chronoamperometric i-t curve. Some kinetic information is contained in the rising portion of the i-E wave and the shift of 1/2 with Wx- Since this behavior is similar to that found in linear potential sweep methods, these results will not be described separately. The reaction rate constant k can be obtained by reversal techniques (see Section 5.7) (32, 33). A convenient approach is the potential step method, where at = 0 the potential is stepped to a potential where Cq(x = 0) = 0, and at t = T it is stepped to a potential where Cr(x = 0) = 0. The equation for the ratio of (measured at time j.) to (measured at time Figure 5.7.3) is... 

Within the electrochemical framework of this classical example of a redox process whose rate is limited by the transport by diffusion, it was shown that, even for a reversible redox process, the derivation of the current response in the time domain is far from simple. In contrast, the impedance approach allows the more difficult case of an irreversible (finite reaction rate constants) redox process to be derived. Using the same approach, we will now examine the case of a multistep reaction, which is very difficult to investigate using techniques of potential step cyclic voltammetry. 

Cyclic voltammetry studies reveal striking differences between complex 13 and the analogous complex [HFe(depp)(dmpm)(CH3CN)f (17) in which the NMe group of 13 has been replaced by a methylene group. At normal scan rates the Fe " couple is reversible for complex 17, but irreversible for 13. Scan rate dependence measurements and potential step experiments indicated that this difference in behavior arises from a rapid transfer of the proton of the Fe hydride to the N atom of the pendant base with a rate constant of 1.1 x 10 s at room temperature. This proton transfer results in an irreversible Fe " " couple at low scan rates. A similar process cannot occur for 17, and the Fe " " couple remains reversible, even at slow scan rates in the presence of an external base. These results indicate that pendant bases in the second coordination sphere can facilitate the coupling of electron and proton transfer reactions. 

Chronoabsorptometry has been applied to the determination of heterogeneous electron-transfer parameters in single-step irreversible [55] and quasi-irreversible kinetics [56] and in double potential step modes [57]. In the case of a single potential step for the reaction... 

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. 

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