Surface electrode reactions

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]. 

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

Here sur is the surface standard rate constant in units of s. By substitution (2.93) and (2.94) into (2.95), one obtains an integral equation, which is a general solution for a surface electrode reaction ... 

In addition, the split peaks can be used for estimation of electron-transfer coefficient as well as for precise determination of the formal potential of the surface electrode reaction. The potential separation between split peaks is insensitive to the electron-transfer coefficient. However, the relative ratio of the heights of the split peaks depends on the electron-transfer coefficient according to the following function ... 

With respect to the formal potential of the surface electrode reaction, Figs. 2.45c and 2.46 show that the split peaks are symmetrically located around the formal potential, which enables precise determination of this important thermodynamic parameter. 

Numerous experimental systems verified the theory of surface electrode reactions. Reductions of methylene blue [92], azobenzene [79, 82] alizarine red S [93], probucol [94], molybdenum(V)-fulvic acid complex [95], molybdeniun(VI)-1,10 phenanthroline-fulvic acid complex [96], indigo [97], and reduction of vana-dium(V) [98] at a mercury electrode are some of the examples for surface electrode... 

Surface Electrode Reaction Involving Interactions Between Immobilized Species... 

To describe a surface electrode reaction in the presence of uniform interactions, besides (2.88) to (2.92), the following form of the kinetic equation is required ... 

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

Surface Electrode Reactions Coupled with Chemical Reactions... 

The physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

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. 

Here, cp = (E —E ) is a dimensionless potential and rs = 1 cm is an auxiliary constant. Recall that in units of cm s is heterogeneous standard rate constant typical for all electrode processes of dissolved redox couples (Sect. 2.2 to 2.4), whereas the standard rate constant ur in units of s is typical for surface electrode processes (Sect. 2.5). This results from the inherent nature of reaction (2.204) in which the reactant HgL(g) is present only immobilized on the electrode surface, whereas the product is dissolved in the solution. For these reasons the cathodic stripping reaction (2.204) is considered as an intermediate form between the electrode reaction of a dissolved redox couple and the genuine surface electrode reaction [135]. The same holds true for the cathodic stripping reaction of a second order (2.205). Using the standard rate constant in units of cms , the kinetic equation for reaction (2.205) has the following form ... 

For a given adsorption constant, the observed electrochemical reversibility depends on the kinetic parameter defined as (O = Xy, or (o =. This reveals that the inherent properties of reaction (2.208) are very close to surface electrode reactions elaborated in Sect. 2.5. The quasireversible maximum is strongly pronounced, being represented by a sharp parabolic dependence of vs. m. The important feature of the maximum is its sensitivity to the adsorption constant, defined by the following equation ... 

The voltammetric features of a reversible reaction are mainly controlled by the thickness parameter A = The dimensionless net peak current depends sigmoidally on log(A), within the interval —0.2 < log(A) <0.1 the dimensionless net peak current increases linearly with A. For log(A )< —0.5 the diSusion exhibits no effect to the response, and the behavior of the system is similar to the surface electrode reaction (Sect. 2.5.1), whereas for log(A) > 0.2, the thickness of the layer is larger than the diffusion layer and the reaction occurs under semi-infinite diffusion conditions. In Fig. 2.93 is shown the typical voltammetric response of a reversible reaction in a film having a thickness parameter A = 0.632, which corresponds to L = 2 pm, / = 100 Hz, and Z) = 1 x 10 cm s . Both the forward and backward components of the response are bell-shaped curves. On the contrary, for a reversible reaction imder semi-infinite diffusion condition, the current components have the common non-zero hmiting current (see Figs. 2.1 and 2.5). Furthermore, the peak potentials as well as the absolute values of peak currents of both the forward and backward components are virtually identical. The relationship between the real net peak current and the frequency depends on the thickness of the film. For Z, > 10 pm and D= x 10 cm s tlie real net peak current depends linearly on the square-root of the frequency, over the frequency interval from 10 to 1000 Hz, whereas for L <2 pm the dependence deviates from linearity. The peak current ratio of the forward and backward components is sensitive to the frequency. For instance, it varies from 1.19 to 1.45 over the frequency interval 10 < //Hz < 1000, which is valid for Z < 10 pm and Z) = 1 x 10 cm s It is important to emphasize that the frequency has no influence upon the peak potential of all components of the response and their values are virtually identical with the formal potential of the redox system. 

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