CE mechanisms

In the CE electrode mechanism the electroactive reactant is produced by means of a preceding homogeneous chemical reaction [15,55,60], Assuming an oxidative mechanism, the simplest form of the CE scheme is as follows  

For the sake of simplicity, hereafter the charge of the species is omitted. The preceding chemical reaction is assumed to be a chemically reversible process attributed with first-order forward (s ) and backward kb (s ) rate constants. In the real experimental systems, the forward chemical reaction is most frequently a second-order process  

To take into account the chemical transformation of R, the common diffusion equation is modified as follows  

This equation can be solved in combination with the differential equation describing the mass transport and chemical transformation of Y  

For the sake of simplicity, a common diffusion coefficient D is assumed for all species. The mass transport of the O form is described by the common diffusion equation (1.2). 

Assume that the electrochemical reduction of B to C is fully reversible, and further that the forward rate constant for the chemical step is very large, to ensure that the species A and B are always at equilibrium on the timescale of the experiment. Explain why the reversible voltammetric wave shifts negatively as the value of IQq is decreased from a value of 1 to 10 .  

The shift in the voltammetric feature is mirroring the change in the equilibrium potential of the reduction of B to C as a function of K q. This may be shown mathematically through consideration of the Nernst equation for the reduction of B to C. 

From Eq. 7.4, as the value of Kgq is decreased, the apparent equilibrium potential for the reduction of B to C becomes more negative. 

With the aid of sketches, describe how the voltammetric response of this system will differ in the presence and absence of an excess of species X. 

The increase in the peak current is due to the reoxidation of B to A by species X. During the forward scan the A/B redox system cycles around such that it is possible for any one molecule to be reduced at the electrode surface multiple times. The 

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Other reaction mechanisms can be elucidated in a similar fashion. For example, for a CE mechanism, where a slow chemical reaction precedes the electron transfer, the ratio of is generally larger than unity, and approaches unity as the scan rate decreases. The reverse peak is usually not affected by the coupled reaction, while the foiward peak is no longer proportional to the square root of the scan rate. 

For the CE mechanism equations for k and id have been derived20 that for ik contains the term m2/3<2/3, which means that, as is approximately... 

In the CE mechanism (Scheme 2.2), a first-order (or pseudo-first-order) homogeneous reaction precedes the electron transfer step. In the case where the initial electron transfer is fast enough not to interfere kinetically, the electrochemical response is a function of two parameters the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic... 

A reaction scheme frequently encountered in practice, the so-called square scheme mechanism, consists of the association of two EC reaction schemes as shown in Scheme 2.3 (which may as well be viewed as an association of two CE mechanisms). In the general case, the cyclic voltammetric response may be analyzed by adaptation and combination of the treatments given in Sections 2.2.1 and 2.2.2. A case of practical interest is when the follow-up reactions are fast and largely downhill. A and D are then stable reactants, whereas B and C are unstable intermediates. When the starting reactant is A (reduction process), the reaction follows the A-B-D pathway. The reoxidation preferred pathway is D-C-A. It is not the reverse of the forward... 

There is a clear antiperiplanar preference for the reaction (Scheme 4.2) due to the stabilization of the radical by coupling of the unpaired electron with bromine (ESR) in the first case. The weaker bond dissociation energy leads to a more favorable standard potential and a weaker intrinsic barrier. When the two conformers are present and can convert one into the other, the reduction follows a CE mechanism (Section 2.2.2), which goes through the more reducible of the two.1 2... 

A similar process is indicated as a CE mechanism, or more specifically as a CrEr mechanism (where the subscript r indicates the reversibility of the respective process). 

Both partners of the preequilibrium are not always electroactive (CE mechanism). 

Experimental studies of CE mechanisms with SWV are scarce. Santos et al. [65] studied two experimental systems, i.e., the reduction of Cd + ion in the presence of nitrilotriacetic acid (NTA) and aspartic acid (ASP). For the first experimental system, the preceding chemical reaction is described by the scheme ... 

The electrode reaction (2.46) is followed by a first-order homogeneous chemical reaction (2.47), in which the product of the electrode reaction O is converted to a final electroinactive product Y. By analogy with the CE mechanism, the chemical step can proceed as ... 

The meaning of all symbols is equivalent as for CE mechanism (Sect. 2.4.1). Combining (2.54) and (2.55) with the Nemst equation (1.8) yields an integral equation, as a general solution for a reversible EC mechanism. The numerical solution reads ... 

The ECE mechanism [54] unifies the previously elaborated EC and CE mechanisms. It is represented by the following scheme ... 

The convolution-deconvolution voltammetry, combined with digital simulation techniques, was applied [36] to determine the electrochemical and chemical parameters for the Cd(II)/Cd(Hg) system in aqueous NaNOs solution. The agreement between experimental and theoretical data indicated that the reduction mechanism at the mercury electrode proceeds via consisting in chemical step (C) followed by charge transfer step (E)-so-called CE mechanism [37]. 

Electroreduction of Cd(II)-nitrilotriace-tic acid and Cd(II)-aspartic acid systems was studied on DME using SWV [73]. The CE mechanism in which the chemical reaction precedes a reversible electron transfer was established. Also, the rate constants of dissociation of the complexes were determined. Esteban and coworkers also studied the cadmium complexes with nitrilotriacetic acid [74, 75] and fulvic acid [76]. The complexation reaction of cadmium by glycine was investigated by different electrochemical methods using HMDE and mercury microelectrode [77, 78]. 

Scheme 3.2 CE mechanism for the one-electron oxidation of FcCOO in the presence of P-CD.

A limiting current insensitive to changes in electrode potential and below the convective-diffusion limiting current indicates that a chemical step is rate-determining and precedes the charge transfer step in the overall electrode reaction (CE mechanism). 

The three limiting cases clearly show up in a plot of — r1/2 vs. —as an example, the result for the CE mechanism has been reproduced in Fig. 37. 

On varying the frequency, it may happen that the first condition is met at the lower frequencies and the third condition at the higher frequencies. This is schematically visualized in Fig. 39, where ZY is plotted in the complex plane, assuming the presence of a CE mechanism with KA — 1, while kA is given some appropriate values. 

Fig. 13. Diagnostic plots for electrode reactions with coupled homogeneous reactions, illustrated for the RDE. (a) CE mechanism. Curve A, no effect from chemical reaction (5k = 0) curve B, effect of preceding chemical reaction (5k >0). (b) Catalytic mechanism. Curve A, in the absence of parallel chemical reaction curve B, experimental dependence predicted from eqn. (175).

The convective-diffusion equations and boundary conditions for z = °° will be exactly the same as for the CE mechanism. However, at z — 0 we have... 

In the CE mechanism (or preceding chemical reaction) the electroactive species is generated from an electroinactive species by a chemical reaction ... 

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