Simple Surface Electrode Reaction

The simplest form of a surface electrode reaction is given by the following Eq. [76-83]  

For the sake of simplicity, the charges of the species are omitted. The subscript (ads) implies immobilization of the species on the electrode surface by adsorption, although the adsorption is not the only means of immobilization. The redox species are attributed with their surface concentration r, which is a function of time. At the begiiming of the experiment, only the R form is present at the electrode surface. 

In the conrse of the voltammetric experiment, the total mass of the electroactive material is preserved, which is mathematically expressed by the condition  

The derivation of the latter equation with respect to t, yields  

The solntions of the above differential eqnations can be readily obtained by integration over the time of the voltammetric experiment, yielding the following solutions  

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The values of (ft>int)max are identical with cobax for the simple surface electrode reaction given in Table 2.3. 

In the last two decades, significant attention has been paid to the study of surface electrode reactions with SWV and various methodologies have been developed for thermodynamic and kinetic characterization of these reactions. In the following chapter, several types of surface electrode processes are addressed, including simple quasireversible surface electrode reaction [76-84], surface reactions involving lateral interactions between immobilized species [85], surface reactions coupled with chemical reactions [86-89], as well as two-step surface reactions [90,91]. 

Similar to the pure surface electrode reaction, the response of reaction (2.146) is characterized by splitting of the net peak under appropriate conditions. The splitting occurs for an electrochemically quasireversible reaction and vanishes for the pure reversible reaction. Typical regions where the splitting emerges are 3 < m < 10 and 0.1 < r < 10 for a = 0.5 and i sw = 50 mV. Contrary to the surface electrode reaction where the ratio of the split peak currents is solely sensitive to a, in the present system this ratio depends additionally on r. For instance, if a = 0.5 and r = 1 the ratio is = 1 for r = 10, > 1 and r = 0.1, < 1. Finally it is worth mentioning when experimentally possible, the electrode mechanism represented by (2.145) to (2.147) has to be simplified to a simple surface reaction (Sect. 2.5.1) in order to avoid the complexity arising from the effect of diffusion mass transport. 

The effect of the volume and the surface catalytic reaction is sketched in Figs. 2.80 and 2.81, respectively. Obviously, the voltammetric behavior of the mechanism (2.188) is substantially different compared to the simple catalytic reaction described in Sect. 2.4.4. In the current mechanism, the effect of the volume catalytic reaction is remarkably different to the surface catalytic reaction, revealing that SWV can discriminate between the volume and the surface follow-up chemical reactions. The extremely high maxima shown in Fig. 2.81 correspond to the exhaustive reuse of the electroactive material adsorbed on the electrode surface, as a consequence of the synchronization of the surface catalytic reaction rate, adsorption equilibria, mass transfer rate of the electroactive species, and duration of the SW potential pulses. These results clearly reveal how powerful square-wave voltammetry is for analytical purposes when a moderate adsorption is combined with a catalytic regeneration of the electroactive material. This is also illustrated by a comparative analysis of the mechanism (2.188) with the simple surface catalytic reaction (Sect. 2.5.3) and the simple catalytic reaction of a dissolved redox couple (Sect. 2.4.4), given in Fig. 2.82. 

The theory of electrode impedance in the case of a faradaic process proceeding at the surface has been thoroughly formulated and many special cases have been solved [1,2, 14, 15]. The formulation is based on Pick s laws with appropriate boundary conditions which take into account the periodic time-dependence of the perturbation voltage. Since the mathematics involved are rather complicated, they will be omitted here. Instead, a general solution will be given [16] for a simple, slow electrode reaction of the first order and the plane diffusion... 

The degree of adsorption can be controlled to some extent by addition of an organic solvent to the aqueous electrolyte, e.g., acetonitrile [128,130] because an increasingly hydrophobic solvent mixture will shift the adsorption equilibrium to the solution side. In a pure aqueous medium of a low pH, the electrode mechanism follows a simple surface EQ reaction, as explained in the Sect. 2.5.3. However, in an acidic aqueous medium containing 50% (v/v) acetonitrile, the mechanism transforms into one of the adsorption coupled ECi reaction mechanisms (2.177) or (2.178). In such medium, the response increases in proportion to the rate of the follow-up chemical reactions, as evidenced by voltammograms depicted in Fig. 2.83. In Fig. 2.85,... 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

To illustrate the influence exerted by the energy of adsorption of an intermediate on the rate of an electrocatalytic reaction, consider a very simple two-step reaction of the type A —> X —> B where X, the intermediate, is reversibly adsorbed on the electrode (with a degree of surface coverage 9x). For the sake of simplicity, the electrode surface will be assumed to be homogeneous (i.e., conditions of Langmuir adsorption hold), while the system lacks adsorbed species other than X. The rate, of the adsorption step (the first step) is then proportional to the bulk concentration of the starting material, c, and to the free surface part (1 - 9x) (the part not taken up by species X), while the rate of further transformation of intermediate X, which is tied to its desorption, will be proportional to the surface fraction, 9x, taken up by it ... 

The principle of this method is quite simple The electrode is kept at the equilibrium potential at times t < 0 at t = 0 a potential step of magnitude r) is applied with the aid of a potentiostat (a device that keeps the potential constant at a preset value), and the current transient is recorded. Since the surface concentrations of the reactants change as the reaction proceeds, the current varies with time, and will generally decrease. Transport to and from the electrode is by diffusion. In the case of a simple redox reaction obeying the Butler-Volmer law, the diffusion equation can be solved explicitly, and the transient of the current density j(t) is (see Fig. 13.1) ... 

Consider a very simple electrode reaction consisting of a fast one-electron transfer from an electrode to molecules attached to the electrode surface,... 

In addition to the development of new methods, new applications of molecular dynamics computer simulation are also needed in order to make comparisons with experimental results. In particular, more complicated chemical reactions, beyond the relatively simple electron transfer reaction, could be studied. Examples include the study of chemical adsorption, hydrogen evolution reactions, and chemical modification of the electrode surface. All of the above directions and opportunities promise to keep this area of research very active ... 

The enhancement of SWV net peak current caused by the reactant adsorption on the working electrode surface was utilized for detection of chloride, bromide and iodide induced adsorption of bismuth(III), cadmium(II) and lead(II) ions on mercury electrodes [236-243]. An example is shown in Fig. 3.13. The SWV net peak currents of lead(II) ions in bromide media are enhanced in the range of bromide concentrations in which the nentral complex PbBr2 is formed in the solntion [239]. If the simple electrode reaction is electrochemically reversible, the net peak cnnent is independent of the composition of supporting electrolyte. So, its enhancement is an indication that one of the complex species is adsorbed at the electrode snrface. 

If not all electrode reactions, then electrocatalytic If one has a redox reaction, an electrode reaction in which nothing happens except that the ion concerned gives up (Fe2+ —> Fe3+ + e) or receives (Fe3+ + e — Fe2) an electron, there is no catalysis. Such redox reactions do not involve adsoibed reaction intermediates. Hence, there is no chemical bonding with the electrode surface and no dependence on its nature. However, simple redox reactions are not used much outside the research laboratory and the truth is that most electrode reactions do involve intermediates adsorbed onto the electrode and therefore exhibit a rate that is substrate dependent. 

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