Electrode kinetics Tafel reaction

The usual Tafel evaluation yielded a transfer coefficient a = 0.52 and a rate constant k of 4x 10 cm s at the standard potential of the MV /MV couple. This k value corresponds to a moderately fast electrochemical reaction. In this electrode-kinetic treatment the changes in the rate of electron transfer with pH were attributed only to the changes in the overpotential. A more exact treatment should also take into account the electrostatic effect on the rate of reaction which also changes with pH. 

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) ... 

The great importance of the Tafel relation—because it is too widely observed to be applicable in electrode kinetics—does not seem to have been appreciated during the time (about 1960-1980) in which Gaussian concepts were frequently used to present a quantal approach to electrode kinetics. Supporting a theoretical view that does not yield what is in effect the first law of electrode kinetics is similar to supporting a theory of gas reactions that does not lead to the exponential dependence of rate on temperature. It represents a remarkable historical aberration in the field. Thus the... 

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. 

These contributions were taken explicitly to a quantum mechanical level by Levich during the 1960s and then by Schmickler, who finally published an elegant summary of quantum electrode kinetics in 1996. Schmickler stressed the quantum mechanical formulation made by Levich, Dogonadze, and Kuznetsov. However, his summary of the quantum mechanical formulation of electrode reactions still possesses the Achilles heel of earlier formulations it is restricted to nonbond-breaking, seldom-occurring outer-sphere reactions and involves the harmonic approximation for the energy variation, which is the main reason of such theories cannot replicate Tafel s law (Khan and Sidik, 1997). 

An aim of the model is to determine the influence of the various mass transport parameters and show how they influence the polarization behavior of three-dimensional electrodes. In the model we have adopted relatively simple electrode kinetics, i.e., Tafel type, The approach can also be applied to more complicated electrode kinetics which exhibit non-linear dependency of reaction rate (current density) on reactant concentration. 

An example of the size of the impurity effects that may arise is shown in Fig. 1, which gives the electrode kinetics for the ferro-ferricyanide reaction on three different zinc oxide single crystals of varying conductivity. Each of the crystals was in excess of 99.999% pure. As can be seen, each crystal gives a linear Tafel plot under cathodic bias. However, the exchange currents, i.e, the extrapolations back to the reversible potential (+. 19 volts), differ by a factor of about 1000 and... 

Equipped with the assumption of quasi-equilibrium, we can now proceed to calculate the Tafel slopes and some other kinetic parameters for a few very simple hypothetical cases, to show how such calculations are made. In Section 15 we shall discuss the kinetics of several reactions that either have been important in the development of the theory of electrode kinetics or are of current practical importance. 

The Tafel slope for this mechanism is 2.3RT/PF, and this is one of the few cases offering good evidence that P = a, namely, that the experimentally measured transfer coefficient is equal to the symmetry factor. A plot of log i versus E for the hydrogen evolution reaction (h.e.r.), obtained on a dropping mercury electrode in a dilute acid solution is shown in Fig. 4F. The accuracy shown here is not common in electrode kinetics measurements, even when a DME is employed. On solid electrodes, one must accept an even lower level of accuracy and reproducibility. The best values of the symmetry factor obtained in this kind of experiment are close to, but not exactly equal to, 0.500. It should be noted, however, that the Tafel line is very straight that is, P is strictly independent of potential over 0.6-0.7 V, corresponding to five to six orders of magnitude of current density. 

The most reliable data are from studies of hydrogen evolution on mercury cathodes in acid solutions. This reaction has been studied most extensively over the years. The use of a renewable surface (a dropping mercury electrode, in which a new surface is formed every few seconds), our ability to purify the electrode by distillation, the long range of overpotentials over which the Tafel equation is applicable and the relatively simple mechanism of the reaction in this system all combine to give high credence to the conclusion that p = 0.5. This value has been used in almost all mechanistic studies in electrode kinetics and has led to consistent interpretations of the experimental behavior. It... 

It is thus seen that interpretation of Tafel slopes requires information on adsorption behavior as /(F), complementary to that as /(C,). The derivative dln6/d nC, required for interpretation of reaction order, R = dlni/dlnC, must also be taken at a controlled potential that is, d n6/d nC,)y/, the isotherm derivative in the reaction-order expression (Section X), must also be evaluated at constant overpotential, r , or electrode potential, V, in the case of electrocatalytic reactions, especially those involving small organic molecules or Cl. Unfortunately, in many experimental works on electrode kinetics, except those on pH effects, these important details involving the adsorption behavior of reactant and/or intermediate(s) have been neglected, with adverse consequences for mechanism determination. 

Extensive work on reaction orders in electrode kinetics, and their interpretation, have been made by Vetter (140), Yokoyama and Enyo for the Clj evolution and other reactions (141, 142, 144), and by Conway and Salomon for the HER (143). In the extensive treatment of the kinetics of O2 evolution by Bockris (145), reaction orders were derived for various possible reaction mechanisms and provide, among other factors, diagnostic criteria for the mechanisms in relation to the experimentally determined behavior, for example, pH effects in the kinetics and Tafel slope values (145). 

Contrary to common belief, the Tafel equation as represented by Eqs. (1) or (4), with b given by Eq. (5), virtually never represents the electrode-kinetic behavior of electrochemical processes (except probably simple ionic redox reactions that have minimal chemical coupling of one kind or another, p. 125) in particular with reference... 

A final and very important general phenomenological conclusion is that the conventional form of the Tafel equation with slope b = RT/aF with a constant is rarely observed at least for those cases where adequate and reliable 7-dependence studies of the electrode kinetics have been made (cf. Yeager ). Simple ionic redox reactions seem, however, to be an exception. ... 

Chapter 2, by B. E. Conway, deals with a curious fundamental but hitherto little-examined problem in electrode kinetics the real form of the Tafel equation with regard to the temperature dependence of the Tafel-slope parameter 6, conventionally written as fe = RT/ aF where a is a transfer coefficient. He shows, extending his 1970 paper and earlier works of others, that this form of the relation for b rarely represents the experimental behavior for a variety of reactions over any appreciable temperature range. Rather, b is of the form RT/(aH + ctsT)F or RT/a F + X, where and as are enthalpy and entropy components of the transfer coefficient (or symmetry factor for a one-step electron transfer reaction), and X is a temperature-independent parameter, the apparent limiting... 

When the electrode kinetics are very sluggish (k is very small), the anodic and cathodic terms of (5.1.3) are never simultaneously significant. That is, when an appreciable net cathodic current is flowing, the second term in (5.1.3) has a negligibly small effect, and vice versa. To observe the net current, the forward process must be so strongly activated (by application of an overpotential) that the back reaction is virtually totally inhibited. In such cases, observations are always made in the Tafel region, hence one of the terms in... 

Equation (117.IV) is the usual form of the Tafel relation, which has been experimentally observed in many electrode reactions and,therefore, is considered a fundamental law of electrode kinetics /158,159/. The conditions of its validity in a more or less extended AcporAp -range are expressed by the inequalities (112,IV) or (116. IV), respectively, provided the reaction occurs in the temperature range T >T /2 that 3e is independent of electrode potential. It should be emphasized that the above justification of Tafel equation results from a general analysis based on the collision theory of reaction kinetics, without any reference to the particular mechanism of electrode reactions. 

Electrode kinetics is the study of reaction rates at the interface between an electrode and a liquid. The science of electrode kinetics has made possible many advances in the understanding of corrosion and the practical measurement of corrosion rates. The interpretation of corrosion processes by superimposing electrochemical partial processes was developed by Wagner and Traud [1]. Important concepts of electrode kinetics that wifi be introduced in this chapter are the corrosion potential (also called the mixed potential and the rest potential), corrosion current density, exchange current density, and Tafel slope. The treatment of electrode kinetics in this book is, of necessity, elementary and directed toward application of corrosion science. For more detailed discussion of electrode kinetics, the reader should refer to specialized texts Usted at the end of the chapter. 

From the above discussion, it is clear that various kinetic criteria (reaction orders, Tafel slopes, and log/-AGads plots on different electrode materials, where appropriate) can be used to determine the reaction mechanism and the coverage conditions. For reactions involving protons, the separation factors (H-T or H-D) can also be used as another criterion, since the barrier heights vary characteristically with mechanism because of the relatively large zero point energy difference between the isotopes and their different quantum mechanical tunneling properties. This is evaluated in Refs. 50 and 51, and may be used to confirm other evidence. 

In electrode kinetics, as empirically represented by Tafel s equation, a basic feature is the potential-dependence of the reaction rate (current-density). This effect arises in Gurney s representation in a fundamental and general way as the electric potential V, of the electrode metal is changed by AV relative to that of the solution (in practice, measured relative to the potential of a reference electrode at open-circuit), the effective value of the electron work function 4> of the metal is changed according to... 

In the past, the majority of the basic laws and concepts in electrode kinetics were developed and verified by Tafel [11], Volmer [12], and Frumkin [13] using the hydrogen electrode. Two important reaction mechanisms are well recognized and experimentally validated. The first is the Volmer-Tafel mechanism, shown in Equations 3.11-3.13. The other, which is more important for the hydrogen electrode, is the Hyrovsky-Volmer mechanism, expressed in Equations 3.14-3.17. 

This result was also seen from Example 5.3. For large q, the forward reaction dominates and thus the reaction process is completely irreversible. Though the Tafel equation predicts the forward reaction for large q, it does not account the mass transfer limited current at high q. If electrode kinetics are fairly fast, then mass transfer limited currents are easily reached at high q. For such cases, the Tafel equation does not apply well. On the other hand, when the electrode kinetics is slow, then the significant overpotential is required and the Tafel relationship holds good. 

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