Kinetically Controlled Electrode Reaction

In this case, SN is dependent on the axial coordinate the tubular electrode is not uniformly accessible. This complicates the mathematical description of partially kinetically controlled reactions at the TE. However, for total kinetic control (irreversible reaction at the foot of the wave), the flux is uniform as radial convection is uniformly zero along the tube. 

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... 

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... 

When concentration changes affect the operation of an electrode while activation polarization is not present (Section 6.3), the electrode is said to operate in the diffusion mode (nnder diffusion control), and the cnrrent is called a diffusion current i. When activation polarization is operative while marked concentration changes are absent (Section 6.2), the electrode is said to operate in the kinetic mode (under kinetic control), and the current is called a reaction or kinetic current i,. When both types of polarization are operative (Section 6.4), the electrode is said to operate in the mixed mode (nnder mixed control). 

It follows from the figures and also from an analysis of Eq. (6.40) that in the particular case being discussed, electrode operation is almost purely diffusion controlled at all potentials when flij>5. By convention, reactions of this type are called reversible (reactions thermodynamically in equilibrium). When this ratio is decreased, a region of mixed control arises at low current densities. When the ratio falls below 0.05, we are in a region of almost purely kinetic control. In the case of reactions for which the ratio has values of less than 0.02, the kinetic region is not restricted to low values of polarization but extends partly to high values of polarization. By convention, such reactions are called irreversible. We must remember... 

Measurements must be made under kinetic control or at least under mixed control of electrode operation if we want to determine the kinetic parameters of electrochemical reactions. When the measurements are made under purely kinetic control (i.e., when the kinetic currents 4 are measured directly), the accuracy with which the kinetic parameters can be determined will depend only on the accuracy with which... 

As compared to the Nemstian case, the plateau is the same but the wave is shifted toward more negative potentials, the more so the slower the electrode electron transfer. An illustration is given in Figure 4.13 for a value of the kinetic parameter where the catalytic plateau is under mixed kinetic control, in between catalytic reaction and substrate diffusion control. For the kjet(E) function, rather than the classical Butler-Volmer law [equation (1.26)], we have chosen the nonlinear MHL law [equation (1.37)]. 

Activation Polarization Activation polarization is present when the rate of an electrochemical reaction at an electrode surface is controlled by sluggish electrode kinetics. In other words, activation polarization is directly related to the rates of electrochemical reactions. There is a close similarity between electrochemical and chemical reactions in that both involve an activation barrier that must be overcome by the reacting species. In the case of an electrochemical reaction with riact> 50-100 mV, rjact is described by the general form of the Tafel equation (see Section 2.2.4) ... 

If the electrode reaction (1.1) is kinetically controlled, (1.8) mnst be snbstituted by the Butler-Volmer equation ... 

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],... 

If the electrode reaction (1.1) is kinetically controlled, the response depends on both the parameter p and the kinetic parameter k [26,27]. If the electrode size is constant and the frequency is varied, both parameters p and k ate changed. Also, if a certain reaction is measured at constant frequency, with a range of microelectrodes having various diameters, the apparent reversibility of the reaction decreases with the decreasing diameter because of radial diffusion. So, the relationship between... 

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. 

Of great interest in lots of domains, oxygen has been studied by voltammetry under very different experimental conditions. As its reaction is under kinetic control, the electrode reaction is influenced by various factors, in particular by the nature of the electrode and of the solution. The metal, through its chemical properties and surface states, which influence the adsorption-desorption of electroactive species or... 

The voltammetric data and other relevant kinetic and thermodynamic information are summarized in Table 2. While for X = H the initial ET controls the electrode rate, as indicated by the rather large p shift and peak width, the electrode process is, at low scan rates, under mixed ET-bond cleavage kinetic control (see Section 2) for X = Ph, and CN. Although the voltammetric reduction of these ethers is irreversible, in the case of the COMe derivative, some reversibility starts to show up at 500 Vs in fact, this reduction features a classical case of Nernstian ET followed by a first-order reaction. The reduction of the nitro derivative is reversible even at very low scan rate although, on a much longer timescale, this radical anion also decays. 

The voltammetric reduction of a series of dialkyl and arylalkyl disulfides has recently been studied in detail, in DMF/0.1 M TBAP at the glassy carbon electrode The ET kinetics was analyzed after addition of 1 equivalent of acetic acid to avoid father-son reactions, such as self-protonation or nucleophilic attack on the starting disulfide by the most reactive RS anion. Father-son reactions have the consequence of lowering the electron consumption from the expected two-electron stoichiometry. Addition of a suitable acid results in the protonation of active nucleophiles or bases. The peak potentials for the irreversible voltammetric reduction of disulfides are strongly dependent on the nature of the groups bonded to the sulfur atoms. Table 11 summarizes some relevant electrochemical data. These results indicate that the initial ET controls the electrode kinetics. In addition, the decrease of the normalized peak current and the corresponding increase of the peak width when v increases, point to a potential dependence of a, as discussed thoroughly in Section 2. 

Temperature control in electrode kinetics, 1121 Terraces, electrodepositon, 1307, 1336 Thermal desorption spectroscopy (TDS), 787 Thermal reactions in semiconductors, definition, 1088... 

This is the famous Butler-Volmer (B-V) equation, the central equation of phenomenological electrode kinetics, valid under conditions where there is a plentiful supply of reactant (e.g., the Ag+ ions) by easy diffusion to and from electrodes in the solution, so that the rate of the reaction is indeed controlled by the electric charge transfer at the interface, and not by transport of ions to the electrode or away from it. 

Tafel s law is the primary law of electrode kinetics, in the sense that Arrhenius law is the basic law of thermal reaction. It applies universally to all processes that are controlled in rate by the interfacial transfer of electrons or by a rate-determining surface reaction that may be coupled to the interfacial electron [Fig. 9.25(a)]. Redox reactions without surface intermediates demonstrate Tafel s law well [Fig. 9.25(b)]. 

Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

The cathodic pinacolisation of 2- and 4-acetylpyridine, which had been investigated by one of the present authors (231-233), offered the chance for a complete kinetic analysis as the respective current voltage curves are of reversible character. They allow for evaluation of the kinetics of consecutive reactions, and one can show that at low pH reaction, Eq. (45c) is only possible if strong surfactants are absent. Such surfactants, by occupying the electrode surface, displace ketyl radicals, RiR2(OH)C , from the electrode surface because the latter are relatively weakly adsorbed and cannot compete with strong surfactants in adsorption. Ketyl radicals dissolved in aqueous or organic solvents of low pH are protonated in a fast almost diffusion-controlled reaction. After protonation they are further immediately reduced to form the monomeric carbinol instead of the hydrodimer—the pinacol ... 

In electrode kinetics, however, the charge transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes so separation of /eapp and kd can be achieved. Experiments under high mass transport rate at electrodes are the analogous to relaxation methods such as the stop flow method for the study of reactions in solution. 

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