Coupled homogeneous electrode reactions constants

The popularity of the cychc voltammetry (CV) technique has led to its extensive study and numerous simple criteria are available for immediate anal-j sis of electrochemical systems from the shape, position and time-behaviour of the experimental voltammograms [1, 2], For example, a quick inspection of the cyclic voltammograms offers information about the diffusive or adsorptive nature of the electrode process, its kinetic and thermodynamic parameters, as well as the existence and characteristics of coupled homogeneous chemical reactions [2]. This electrochemical method is also very useful for the evaluation of the magnitude of imdesirable effects such as those derived from ohmic drop or double-layer capacitance. Accordingly, cyclic voltammetry is frequently used for the analysis of electroactive species and surfaces, and for the determination of reaction mechanisms and rate constants. 

In such timescales, it is possible to study very fast heterogeneous electron transfer rate constants [48]. Diffusion layers as thin as a few nanometers are characteristic for such fast scan rates [50]. Coupled homogeneous chemical reaction steps become less important, and highly reactive intermediates can be detected [48]. The chemical reversibility of electrode reactions increases and thus redox potentials of electron transfer reactions involving extremely unstable species become available [48]. 

As will now be clear from the first Chapter, electrochemical processes can be rather complex. In addition to the electron transfer step, coupled homogeneous chemical reactions are frequently involved and surface processes such as adsorption must often be considered. Also, since electrode reactions are heterogeneous by nature, mass transport always plays an important and frequently dominant role. A complete analysis of any electrochemical process therefore requires the identification of all the individual steps and, where possible, their quantification. Such a description requires at least the determination of the standard rate constant, k, and the transfer coefficients, and ac, for the electron transfer step, or steps, the determination of the number of electrons involved and of the diffusion coefficients of the oxidised and reduced species (if they are soluble in either the solution or the electrode). It may also require the determination of the rate constants of coupled chemical reactions and of nucleation and growth processes, as well as the elucidation of adsorption isotherms. A complete description of this type is, however, only ever achieved for very simple systems, as it is generally only possible to obtain reliable quantitative data about the slowest step in the overall reaction scheme (or of two such steps if their rates are comparable). 

We consider three simple schemes, shown in Fig. 6.11, and examine the effect of homogeneous coupled reactions on the current at the electrode they are CE, EC, and EC, where E represents an electrochemical step (at the electrode) and C a chemical step (in solution). The equations to calculate the rate constants from experimental measurements for the various types of electrode can be found in the specialized literature. In most studies the electrochemical step has been considered reversible—thus, in the following, the rate constant for the electrode reaction is not indicated. 

In all these schemes for coupled homogeneous reactions, it is useful to consider in the deduction of the equations the concept of a reaction layer associated with the homogeneous reaction all the homogeneous reaction occurs within a distance equal to the thickness of the reaction layer from the electrode. When the thickness of the layer is significantly smaller (<10 per cent) than the thickness of the diffusion layer the two layers can be considered as being independent, which simplifies the mathematical treatment. The thickness of the reaction layer depends on the values of the homogeneous rate constants kx and k x. 

Note that the homogeneous chemical reactions (C steps) coupled to the electrode process alter the concentration profiles of the electroactive species and therefore the electrochemical response of the system. Thus, electrochemical methods enable the characterisation of the chemical reaction in solution, that is, the determination of the mechanism as well as the rate and equilibrium constants. 

In the preceding three sections reaction mechanisms in which the homogeneous chemical reaction was coupled with the electrode process were discussed. This coupling enables exceptionally fast chemical reactions to be investigated and their rate constants determined. Nevertheless, voltammetric methods can also be exploited for kinetic studies on chemical reactions occurring independently of the electrode process in the bulk of the solution. For this purpose all voltammetric techniques can be used for which the dependence of voltammetric response on the concentration of one or more reactants is defined in a simple way. Various amperometric sensors are mostly applied, working at the potentials of limiting current. The response need not be a diffusion-controlled current. Kinetic currents within the diffusion-controlled zone can also be taken into account. 

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