The Electrode Kinetics

At the illuminated electrode, as discussed above, we need the A,B couple to be reversible so that B is easily converted to A, but we also require that, as far as pos- sible, the conversion of Y to Z is blocked. The electrode will then be close to the standard electrode notential of the A, B couple little B reaches 

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Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

The principle of electrochemical noise experiments is to monitor, without perturbation, the spontaneous fluctuations of potential or current which occur at the electrode surface. The stochastic processes which give rise to the noise signals are related to the electrode kinetics which govern the corrosion rate of the system. Much can be learned about the corrosion of the coated substrate from these experiments. The technique of these measurements is discussed elsewhere (A). 

Table 1. The reasons for the apparent breakdown of the original principle have included chemical interaction between one couple and an intermediate species of the other, changes produced in the structure of the electrode surface and, most common of all, adsorption on the surface of a component of one couple that affected the electrode kinetics of the other. The underlying problem in these cases has been the untenable premise that each couple acts quite independently of the other and is not affected by the other s presence. However, as many of these studies have shown, the premise of additivity still applies whenever the interactions have been allowed for by carrying out the electrochemical experiments in an appropriate fashion. The validity of adding or superimposing electrochemical curves can therefore be considerably extended by restating the principle as follows ...

Thus, worldwide efforts have focused on the elucidation of the reaction mechanism. For this purpose, knowledge about the following items is vital (1) identification of reaction products and the electrode kinetics of the reactions involved, (2) identification of adsorbed intermediate species and their distribution on the electrode surface, and (3) dependence of the electrode kinetics of the intermediate steps in the overall and parasitic reactions on the structure and composition of the electrocatalyst. It is only after a better knowledge of the reaction mechanisms is obtained that it will be possible to propose modifications of the composition and/or structure of the electrocatalyst in order to significantly increase the rate of the reaction. 

The electrocatalytic oxidation of methanol has been thoroughly investigated during the past three decades (see reviews in Refs. 21-27), particularly in regard to the possible development of DMFCs. The oxidation of methanol, the electrocatalytic reaction, consists of several steps, which also include adsorbed species. The determination of the mechanism of this reaction needs two kinds of information (1) the electrode kinetics of the formation of partially oxidized and completely oxidized products (main and side products) and (2) the nature and the distribution of intermediates adsorbed at the electrode surface. 

Parthasarathy A, Srinivasan S, Appleby AJ, et al. 1992a. Temperature dependence of the electrode kinetics of oxygen reduction at the platinum/Nafion interface—A microelectrode investigation. J Electrochem Soc 139 2530-2537. 

A number of metal porphyrins have been examined as electrocatalysts for H20 reduction to H2. Cobalt complexes of water soluble masri-tetrakis(7V-methylpyridinium-4-yl)porphyrin chloride, meso-tetrakis(4-pyridyl)porphyrin, and mam-tetrakis(A,A,A-trimethylamlinium-4-yl)porphyrin chloride have been shown to catalyze H2 production via controlled potential electrolysis at relatively low overpotential (—0.95 V vs. SCE at Hg pool in 0.1 M in fluoroacetic acid), with nearly 100% current efficiency.12 Since the electrode kinetics appeared to be dominated by porphyrin adsorption at the electrode surface, H2-evolution catalysts have been examined at Co-porphyrin films on electrode surfaces.13,14 These catalytic systems appeared to be limited by slow electron transfer or poor stability.13 However, CoTPP incorporated into a Nafion membrane coated on a Pt electrode shows high activity for H2 production, and the catalysis takes place at the theoretical potential of H+/H2.14... 

V, where the plateau is reached and a quantitative determination can be done. The column effluent is pumped through the detector, and if this contains compounds that can be oxidized at the set potential the current through the electrode increases. The current is equivalent to the amount of compounds, but not necessarily the same for all kinds of compounds. This depends on the number of electrons that are involved in the electrode reaction, on the electrode kinetics, and on the thickness of the diffusion layer, d. This is expressed in Fick s first law ... 

This result represents the first use of FTIR measurements to obtain information about the hydrogen evolution reaction on iron. It also represents one of the first uses of FTIR to study the mechanism of the electrode kinetic reaction (14). 

Agar had suggested in 1947 that there might be a temperature dependence of p, the electrode kinetic parameter, and Conway took this up in 1982 and showed experimentally that in certain reactions this was the case. 

Compared to Pick s first law for ideal systems (which real systems only approach at the high dilution), two extra terms are introduced (i) the transference number of the electrons and (ii) the Wagner factor. Their part in the electrode kinetics will be discussed in more detail. 

Although the diffusion of the counterion is faster in polypyrrole than in polyacetylene, its value is still low enough to influence the rate of the electrochemical charge and discharge processes of lithium/polymer batteries. Indeed the current output of these batteries is generally confined to a few mA cm . Possibly, improvements in the electrode kinetics, and thus in the battery rates, may be obtained by the replacement of standard ... 

In general, the electrochemical performance of carbon materials is basically determined by the electronic properties, and given its interfacial character, by the surface structure and surface chemistry (i.e. surface terminal functional groups or adsorption processes) [1,2]. Such features will affect the electrode kinetics, potential limits, background currents and the interaction with molecules in solution [2]. From the point of view of electroanalysis, the remarkable benefits of CNT-modified electrodes have been widely praised, including low detection limits, increased sensitivity, decreased overpotentials and resistance to surface fouling [5, 9, 11, 17]. 

To summarize, one can say that the electrochemical performance of CNT electrodes is correlated to the DOS of the CNT electrode with energies close to the redox formal potential of the solution species. The electron transfer and adsorption reactivity of CNT electrodes is remarkably dependent on the density of edge sites/defects that are the more reactive sites for that process, increasing considerably the electron-transfer rate. Additionally, surface oxygen functionalities can exert a big influence on the electrode kinetics. However, not all redox systems respond in the same way to the surface characteristics or can have electrocatalytical activity. This is very dependent on their own redox mechanism. Moreover, the high surface area and the nanometer size are the key factors in the electrochemical performance of the carbon nanotubes. 

If the reaction (1.1) is controlled by the electrode kinetics, i.e., when the electrode reaction is not electrochemically reversible, the response depends on the dimensionless kinetic parameter k = and the transfer coefficient a [15-17],... 

In this case, besides the thermodynamic and kinetic parameters of the preceding chemical reaction, the response depends on the kinetics of the electrode reaction represented by the electrode kinetic parameter k = (see Sect. 2.1.2) [60], Figure 2.29 shows the variation of A Fp with e for various k. It is obvious that there is... 

The variation of the peak current with the electrode kinetic parameter k and chemical kinetic parameter e is shown in Fig. 2.31. When the quasireversible electrode reaction is fast (curves 1 and 2 in Fig. 2.31) the dependence is similar as for the reversible case and characterized by a pronounced minimum If the electrode reaction is rather slow (curves 3-5), the dependence A fJ, vs. log( ) transforms into a sigmoidal curve. Although the backward chemical reaction is sufficiently fast to re-supply the electroactive material on the time scale of the reverse (reduction) potential pulses, the reuse of the electroactive form is prevented due to the very low kinetics of the electrode reaction. This situation corresponds to the lower plateau of curves 3-5 in Fig. 2.31. 

Fig. 2.41 Theoretical net voltammograms simulated for different values of to. The electrode kinetic parameter increases from left to right from log (to) = —1.7 to 2.2 with an increment of 0.1. Other conditions of the simulations are a = 0.5, wE-w = 50 mV, A = 5 mV...

Fignre 2.41 indicates that the net peak current is a parabolic function of the electrode kinetic parameter. This is illnstrated in Fig. 2.43. With respect to the electrochemical reversibility of the electrode reaction, approximately three distinct regions can be identified. The reaction is totally irreversible for log(ca) < — 2 and reversible for log(ft)) > 2. Within this interval, the reaction is qnasireversible. The parabolic dependence of the net peak cnrrent on the logarithm of the kinetic parameter asso-... 

Table 2.5 Critical values of the SW amplitude and corresponding potential separations of the split peaks for various values of the electrode kinetic parameter. Conditions of the simulations are the same as for Fig. 2.41...

Here, m = is the electrode kinetic parameter typical for surface electrode processes (see Sect. 2.5.1) and 7= rg is dimensionless diffusion parameter. The latter parameter represents the inflnence of the mass transfer of electroactive species. 

The second-order reaction with adsorption of the ligand (2.210) signifies the most complex cathodic stripping mechanism, which combines the voltammetric features of the reactions (2.205) and (2.208) [137]. For the electrochemically reversible case, the effect of the ligand concentration and its adsorption strength is identical as for reaction (2.205) and (2.208), respectively. A representative theoretical voltammo-gram of a quasireversible electrode reaction is shown in Fig. 2.86d. The dimensionless response is controlled by the electrode kinetic parameter m, the adsorption... 

A quasireversible electrode reaction is controlled by the film thickness parameter A, and additionally by the electrode kinetic parameter k. The definition and physical meaning of the latter parameter is the same as for quasireversible reaction under semi-infinite diffusion conditions (Sect. 2.1.2). Like for a reversible reaction, the dimensionless net peak current depends sigmoidally on the logarithm of the thickness parameter. The typical region of restricted diffusion depends slightly on K. For instance, for log( If) = -0.6, the reaction is under restricted diffusion condition within the interval log(A) < 0.2, whereas for log(if) = 0.6, the corresponding interval is log(A) <0.4. 

Figure 2.96 shows the splitting of the net peak under increasing of the dimensionless electrode kinetic parameter for a given film thickness. The potential separation between split peaks increases in proportion to the electrode kinetic parameter and the amplitude of the potential modulation. The dependence of the peak potential separation on the amplitude is separately illustrated in Fig. 2.97. The analysis of the splitting by varying the amplitude is particularly appeahng, since this instrumental parameter affects solely the split peak without altering the film thickness parameter. Table 2.7 lists the critical intervals of the film thickness and the electrode kinetic parameters attributed with the splitting.

The results reviewed above suggest that gas-phase diffusion can contribute significantly to polarization as O2 concentrations as high as a few percent and are not necessarily identifiable as a separate feature in the impedance. Workers studying the P02 -dependence of the electrode kinetics are therefore urged to eliminate as much external mass-transfer resistance in their experiments as possible and verify experimentally (using variations in balance gas or total pressure) that gas-phase effects are not obscuring their results. 

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