Reversible reaction current step

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 decomposition mode of the adducts has early been noticed to be associated with redox reactions (60,77), and is currently under scrutiny because of its great bioinorganic relevance. It has been shown that the reduction of NP to the EPR-active [Fe(CN)5NO]3 ion occurs in the reaction with cysteine, which is oxidized to cystine (60). In this reaction, NP showed to behave catalytically with respect to the autoxidation of cysteine to cystine, provided enough oxygen was present. A recent kinetic and mechanistic study has thrown more light on the complex mechanistic details comprising the decompositions of the red adducts formed by NP with cysteine, A-acetylcysteine, ethyl cysteinate, and glutathione (120). Under conditions of excess of NP, in anaerobic medium, the reversible adduct formation step is shown by Eq. (26) ... 

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]. 

Cyclic chronopotentometry — A controlled current technique where the applied - current step is reversed at every transition time between cathodic and anodic to produce a series of steps in the potential vs. time plot - chronopotentiogram. The progression of transition times is characteristic of the mechanism of the electrode reaction. For example, a simple uncomplicated electron transfer reaction with both products soluble and stable shows relative -> transition times in the series 1 0.333 0.588 0.355 0.546 0.366... independent of the electrochemical reversibility of the electrode reaction. 

The kinetics of the C step are not always first order or pseudo-first order. A second-order reaction will produce qualitatively similar effects to those described above. However, the relative magnitude of the reverse peak current associated with the E step and hence the extent of reversibility and the shift in peak potential will depend on the concentration of the electroactive species for an EC2 mechanism. A process of this type will have a reversible E step at low concentrations or fast scan rates and an irreversible E step at high concentrations or slow scan rates. An example of an EQ-type reaction (Bond et al., 1983, 1989) is the electrochemical oxidation of cobalt (III) tris(dithiocarbamates) (Co(S2CNR2)3) at platinum electrodes in dichloromethane/0.1 M (C4H9)4NPp6 [equations (44) and (45)]. 

In order to demonstrate the mathematical approch to describing the electrode process we can consider the potential-step experiment for a reversible charge transfer without kinetic complications. In this case there are two diffusing species, A and B in (1). However, if the potential of the electrode is sufficiently greater than the reversible potential for reaction (1), the reverse reaction can be neglected so that only the diffusion of A contributes to the current. The equation to be solved results from Pick s second law and is given by (7). The... 

Yet when applied to current reversal techniques, such as double-step chronampero-metry of cyclic voltammetry, these methods require that an appreciable current be observed during the backward perturbation, that is, for t > 0, in potentiostatic methods or after the potential scan inversion in cyclic voltammetry. This requires that the characteristic time 0 of the method is adjusted to match the half-life ti/2 of the electrogenerated intermediate. Today, owing to the recent development of ultramicroelectrodes, 0 can be routinely varied from a few seconds to a few nanoseconds [102]. Yet with basic standard electrochemical equipment, 0 is usually restricted from the second to the low millisecond range. Thus for experimental situations involving faster chemical reactions, current rever-... 

At this point, the surface activities of the reactant and product intermediates of the rds in Eq. (22) have unknown potential dependencies, but these can usually be evaluated by use of the quasi-equilibrium method. For the cathodic, forward direction, this potential dependence may be built up progressively in terms of the initial reactant of the reaction scheme, that is, Ai. Thus the rate of step 1 (in Scheme 1) is limited by the rds and according to the above assumptions is considered to be in quasi-equilibrium. Therefore the rates (as current density) of the forward and reverse reactions of this step may be equated as... 

With faster scan cyclic voltammetry, a new two-electron anodic peak was detected, at more negative potentials, for the first stage of the oxidation process, with an accompanying cathodic peak on the reverse scan (11). The ratio of the forward to the reverse peak currents increased towards unity as the scan rate was raised to —200 V s 1 (Fig. 15). This behavior was attributed to the initial two-electron process being accompanied by a fairly rapid follow-up chemical reaction and was successfully analyzed in terms of an EqCi process (quasi-reversible electron transfer followed by a first-order irreversible chemical process), with a rate constant for the chemical step, k, = 250 s 1. 

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,...

Note that equations need not be written for species Y, since its concentration does not affect the current or the potential. If reaction (12.2.2) were reversible, however, the concentration of species Y would appear in the equation for 5Cr(x, t) dt, and an equation for 5Cy(, t) dt and initial and boundary conditions for Y would have to be supplied (see entry 3 in Table 12.2.1). Generally, then, the equations for the theoretical treatment are deduced in a straightforward manner from the diffusion equation and the appropriate homogeneous reaction rate equations. In Table 12.2.1, equations for several different reaction schemes and the appropriate boundary conditions for potential-step, potential-sweep, and current-step techniques are given. 

So far, the most popular solution for this problem has been to sample the current in SCV not at the end of the pulse but at an appropriate time (sampling time, ts) so that the SCV voltammogram is equivalent to the CV one. The optimal value for the sampling time depends on the experimental system (electrode kinetics, reaction mechanism, step potential, etc.) and it has been established for some frequent situations. For example, for a reversible E mechanism at a macroelectrode there is an acceptable agreement between SCV and CV for Ea [Pg.81]

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. 

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