Fundamental Equations of Electrode Kinetics

Butler-Volmer equation — The Butler-Volmer or -> Erdey-Gruz-Volmer or Butler-Erdey-Gruz-Volmer equation is the fundamental equation of -> electrode kinetics that describes the exponential relationship between the -> current density and the -> electrode potential. Based on this model the -> equilibrium electrode potential (or the reversible electrode potential) can also be interpreted. 

Tills must be regarded as the fundamental equation of electrode kinetics, and it shows the way in which current density varies with exchange current density, overpotential, and the transfer coefficients. In the laboratory it is, however, more common to use one of the three limiting forms of Equation (1.31). The first two apply at high overpotentials. At high positive overpotentials / > /, and the second term may be ignored the anodic current density if then given by... 

Equation (13.5-21) is a fundamental equation of electrode kinetics. It indicates that... 

Note that Equation 6.6 is one of the most important equations in electrochanical science and engineering and is the fundamental equation of electrode kinetics that describes the exponential relationship between the current density and the electrode overpotential. One of the key assumptions in deriving Equation 6.6 is that the electro-chemically active solution at the electrode is extensively stirred and the current is kept... 

For many years the Tafel equation was viewed as an empirical equation. A theoretical interpretation was proposed only after Eyring, Polanyi and Horiuti developed the transition-state theory for chemical kinetics, in the early 1930s. Since the Tafel equation is one of the most important fundamental equations of electrode kinetics, we shall derive it first for a single-step process and then extend the treatment for multiple consecutive steps. Before we do that, however, we shall review very briefly the derivation of the equations of the transition-state theory of chemical kinetics. 

In the case of energy producing power sources, the equifibrium shifts to one side, resulting in the flow of net current and the subsequent loss of equifibrium at the electrode. A system of this nature is said to be polarized. The net current that flows through the polarized system at any given overpotential is <=(electroactive species in the bulk and at the electrode interface are equal which reduces Eq.(3.23) to the Butler-Volmer equation (3.28), which is a fundamental equation in electrode kinetics. 

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. 

Srinivasan S, Hurwitz HD, Bockris JMO. Fundamental equations of electrochemical kinetics at porous gas-diffusion electrodes. J ChemPhys 1967 46(8) 3108-22. 

This equation (Tafel equation) is of fundamental importance in studies of electrode kinetics. It is actually an approximation of the - Butler-Volmer equation at... 

The net rate of electrochemical current generation in an electrode section is given by the Butler-Volmer equation, a fundamental relation in electrode kinetics [109],... 

We know that thermodynamics is a very powerful tool for the study of systems at equilibrium, but electrode processes are systems not at equilibrium when at equilibrium there is no net flow of current and no net reaction. Therefore electrode reactions should be studied using the concepts and formalities of kinetics. Indeed, the same period that saw the flourishing of solution electrochemistry, also saw the formulation of the fundamental theoretical concepts of electrode kinetics the work of Tafel on the relationship of current and potential was published in 1905 those of Butler and Volmer and Erdey Gruz, which formulated the basic equation for electrode kinetics, were published in 1924 and 1930 respectively. Frumkin in 1933 showed the correlation between the structure of the double layer and the kinetics of the electrode process. The first quantum mechanical approach to electrode kinetics was published by Gurney in 1931. 

In studies of electrode kinetics it should be borne in mind that the fundamental equations used are derived with the tacit assumption of uniformity of current distribution. Hence, the analysis of the current-potential relationship is valid only when this assumption applies to a very good approximation. 

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... 

As noted above, often the kinetic equations are written as a function of i0 rather than k°. One of the advantages of using i0 is that the faradaic current can be described as a function of the difference between the potential applied to the electrode, E, and the equilibrium potential, Eeq, rather than with respect to the formal electrode potential, E01, (which, as previously mentioned, is a particular case of equilibrium potential [COx(0,f) = CRed(0,t)], and at times may be unknown). In fact, dividing the fundamental expression of i by that of i0 one obtains ... 

To discuss the enthalpy of activation in electrode kinetics, we make use of the fundamental rate equation... 

In 1940, Frumkin explored the relationships among the double-layer structure on mercury electrodes, the capacitance measured by use of a Wheatstone bridge, and the surface tension, following the theoretical underpinnings of the Lippmann equation. Grahame ° expanded this treatment of the mercury electrode, providing a fundamental understanding of the structure of the electrical double layer. Dolin and Ershler applied the concept of an equivalent circuit to electrochemical kinetics for which the circuit elements were independent of frequency. Randles developed an equivalent circuit for an ideally polarized mercury electrode that accounted for the kinetics of adsorption reactions. ... 

It is fair to say that the effect of ultrasound upon the fundamental electron transfer processes at an electrode have been less widely studied than the effects upon mass transport phenomena. Electrode kinetics is defined by the Butler—Volmer equation, which by a series of practical assumptions reduces to the Tafel equation [44],... 

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... 

RDE is a commonly used technique for investigating the ORR in terms of both the electron transfer process on electrode surface and diffusion—convection kinetics near the electrode. To make appropriate usage in the ORR study, fundamental understanding of both the electron transfer process on electrode surface and diffusion—convection kinetics near the electrode is necessary. In this chapter, two kinds of RDE are presented, one is the smooth electrode surface, and the other is the catalyst layer-coated electrode. Based on the electrochemical reaction 0 + ne R), the RDE theory, particularly those of the diffusion—convection kinetics, and its coupling with the electron-transfer process are presented. The famous Koutecky—Levich equation and its... 

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 deriving the latter expression we assumed that R R- Equation 196 is very fundamental, and it provides a relationship between the macroscopic rate constant k and the macroscopic processes of substrate electrode kinetics and spherical diffusion at the catalytic particle. On the rhs of Eqn. 196 the first term describes the effect of heterogeneous kinetics of the substrate at the particle surface. This rate constant k is a strong function of electrode potential. The second term describes the spherical diffusion of substrate to the catalytic particle. When ks DsIR the mass transport of S to the particle surface is rate-determining. Alternatively when k E DsiR then the electron transfer process at the particle surface is rate-determining. 

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