Electrode kinetics, Butler-Volmer metals

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... 

In this chapter we derive the Butler-Volmer equation for the current-potential relationship, describe techniques for the study of electrode processes, discuss the influence of mass transport on electrode kinetics, and present atomistic aspects of electrodeposition of metals. 

In contrast to the sitnation for a metal electrode, the rate constant for ET or HT at a doped semicondnctor electrode is therefore independent of U. The rate (cnrrent) increases exponentially with overpotential because the concentration of charge carriers at the electrode surface does. In the absence of current-limiting slow steps such as diffusion, the current at a semiconductor electrode is therefore predicted to obey Butler-Volmer kinetics (up to the limit where the Boltzmann approximation to the Fermi probabihty function is vahd). 

A theoretical current-potential curve (/7/q vs. fj) is given in Fig. 7.3 for r] = 0.5. It should be emphasized here that Eq. (7.11) is only valid in this simple form if the current is really kinetically controlled, i.e. if diffusion of the redox species toward the electrode surface is sufficiently fast. According to the Butler-Volmer equation (Eq. 7.11) the current increases exponentially with potential in both directions. In this aspect charge transfer processes at metal electrodes differ completely from those at semiconductors. When the overpotential is sufficiently large, erj/kT 1. one of the exponential terms in Eq. (7.11) can be neglected compared to the other. In this case we have either... 

Kawamoto (2) developed a two-dimensional model that is based on a double iterative boundary element method. The numerical method calculates the secondary current distribution and the current distribution within anisotropic resistive electrodes. However, the model assumes only the initial current distribution and does not take into account the effect of the growing deposit. Matlosz et al. (3) developed a theoretical model that predicts the current distribution in the presence of Butler-Volmer kinetics, the current distribution within a resistive electrode and the effect of the growing metal. Vallotton et al. (4) compared their numerical simulations with experimental data taken during lead electrodeposition on a Ni-P substrate and found limitations to the applicability of the model that were attributed to mass transfer effects. 

It is obvious that this reaction can only lead to metal dissolution, if the metal electrode potential is negative from the hydrogen electrode potential. This is the reason for the classification of metals into noble metals (the equilibrium potential is more positive than the standard hydrogen potential) and non-noble metals (the equilibrium potential is more negative than the standard hydrogen potential). The kinetic of the total process can be described by the Butler-Volmer equation for the two partial reactions. 

We see that, unlike the former reactions which dealt with processes whose rate limited the rate of the overall electrode reaction, this section did not deal with processes limited by the rate of adsorption. We studied here the influence of adsorption on reactions where kinetics are given by the Butler-Volmer equation. We saw that if the reactant or the product is adsorbed on the electrode, and this adsorption depends on the potential—then the expected behaviour of a simple electron-transfer overpotential is not observed. There is another class of electrode reaction which does not behave simply, because their rate depends on the availability of suitable sites on the electrode surface. These are the electrocrystallization reactions, in particular, metal deposition reactions. 

In many technical applications of electrodics, practice has preceded theory by many decades. For example, electrodeposition of metals was practised in the last century, many years before the work of Tafel or Butler and Volmer, who laid the foundation of electrode kinetics. Indeed this field has only recently become the subject of intensive basic research. On the other hand, the application of electrodics to analytical chemistry follows the theoretical studies very closely, mainly due to the fact that the same instruments are used for basic research and analytical research and application with very little engineering being involved. In the field of fuel cells, the theoretical knowledge exceeds the practical since the problems in this area are largely non-electrochemical. 

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