Electrode kinetics, Butler-Volmer

Electrode kinetics electrode, kinetics, Butler-Volmer equation, -> charge transfer kinetics, - Marcus... 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Like all cathodes, early electrochemical kinetic studies of LSM focused heavily on steady-state d.c. characteristics, attempting to extract mechanistic information from the Tand F02 dependence of linear and Tafel parameters.As recently as 1997, some workers have continued to support a view that LSM is limited entirely by electrochemical kinetics at the LSM/electrolyte Interface based on this type of analysis. However, as we have seen for other materials (including Pt), the fact that an electrode obeys Butler—Volmer kinetics means little in terms of identifying rate-limiting phenomena or in determining how close the reaction occurs to the TPB. To understand LSM at a nonempirical level, we must examine other techniques and results. 

The kinetics of charge transfer between metallic electrodes and conducting polymer films have proved to be difficult to investigate, and little reliable data exist. Charge-transfer limitations have been claimed in cyclic voltammetry, and Butler-Volmer kinetics have been used in a number of... 

Experimental studies of electrode kinetics resulted in the formnlation of the basic empirical relationship, the Volmer-Butler equation, (6.10) or (6.13), describing the dependence of the electric current on the electrode potential. This eqnation involves the potential E, the rate constants, and the concentrations. 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

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)]. 

When Afh -a oo, a Nernstian response is obtained. The half-wave potential is equal to the standard potential. Conversely, when Afh —> 0, the electrode electron transfer is irreversible. In the case of a Butler-Volmer kinetic law, the half-wave potential is expressed as... 

Analysis of the cyclic voltammetric responses is also possible if a kinetic law different from Butler-Volmers governs the electrode electron transfer. Derivation of the kinetic law from the cyclic voltammetric responses may benefit from a convolution approach similar to that described in the preceding section. 

Here kf and kb are the adsorption and desorption constants when 9 —> 0. The derivation of the equation above is similar to establishment of the Butler-Volmer kinetic law for electrochemical electron transfer reactions, where the symmetry factor, a, is regarded as independent from the electrode potential. Similarly, in the present case, the symmetry factor, a, is assumed to be independent of the coverage, 9. 

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

When the electrode reaction (2.30) is quasireversible, (2.37) and (2.38) are combined with the Butler-Volmer kinetic equation (2.42) [60] ... 

Considering kinetically controlled process at the electrode surface without lateral interactions between immobilized species, the following form of the Butler-Volmer equation holds ... 

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

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. 

The Butler-Volmer equation has yielded much that is essentia] to the first appreciation of electrode kinetics. It has not, however, been mined out. One has to dig deeper, and after electron transfer at one interface has been understood in a more general way, electrochemical systems or cells with two electrode/electrolyte interfaces must be tackled. It is the theoretical descriptions of these systems that provide the basis... 

A discussion of the effects of the structure of the interface on electrode kinetic rates is the right moment to introduce a seminal figure in electrochemistry, a person who played a part later than—but hardly less than—that of Butler and of Volmer and Erdey-Gmz, in establishing the basis of the modem subject. It was A. N. Frumkin who first introduced interfacial structure considerations into electrode kinetics, in 1932. However, to leave a mention of Frumkin at that would sadly underdescribe a great leader whose influence in creating physical electrochemistry was outstanding.16... 

The introduction of 0 in the equations for current density need by no means refer only to the adsorbed intermediates in the electrode reaction. What of other entities that may he adsorbed on the surface For example, suppose one adds to the solution an oiganic substance (e.g., aniline) and this becomes adsorbed on the electrode surface. Then, the 0 for the adsorbed organic substance must also be allowed for in the electrode kinetic equations. So, in Eq. (7.149), the value of 0 would really have to become a 0, where the summation is over all the entities that remain upon the surface and block off sites for the discharging entities. Many practical aspects of electrodics arise from this aspect of the Butler-Volmer equation. For example, the action of organic corrosion inhibitors partly arises in this way (adsorption and blocking of the surface of the electrode and hence reduction of the rate of the corrosion reaction per apparent unit area).67... 

---