Butler-Volmer equation current-potential relationship

We have considered above the Butler-Volmer equation for the relationship between current density and potential under the situation when transport of ions in solution makes little or no difference to the rate of an electrode reaction. In order to considered the situation in which transport does control the flow we shall adopt a correspondingly simple counterassumption electron transfer at the interface no longer has control of the electrode reaction. 

The two-step charge transfer [cf. Eqs. (7) and (8)] with formation of a significant amount of monovalent aluminum ion is indicated by experimental evidence. As early as 1857, Wholer and Buff discovered that aluminum dissolves with a current efficiency larger than 100% if calculated on the basis of three electrons per atom.22 The anomalous overall valency (between 1 and 3) is likely to result from some monovalent ions going away from the M/O interface, before they are further oxidized electrochemically, and reacting chemically with water further away in the oxide or at the O/S interface.23,24 If such a mechanism was operative with activation-controlled kinetics,25 the current-potential relationship should be given by the Butler-Volmer equation... 

This current-potential relationship, also known as the Butler-Volmer equation, governs all the (fast and single step) heterogeneous electron transfers. 

RELATIONSHIP BETWEEN CURRENT AND POTENTIAL BUTLER-VOLMER EQUATION... 

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. 

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. 

Corrosion current density — Anodic metal dissolution is compensated electronically by a cathodic process, like cathodic hydrogen evolution or oxygen reduction. These processes follow the exponential current density-potential relationship of the - Butler-Volmer equation in case of their charge transfer control or they may be transport controlled (- diffusion or - migration). At the -> rest potential Er both - current densities have the same value with opposite sign and compensate each other with a zero current density in the outer electronic circuit. In this case the rest potential is a -> mixed potential. This metal dissolution is related to the corro-... 

The Butler-Volmer equations simplify in the case where one of the exponential terms dominate, which will happen if the loss potential in question is large. In this case the electrode potential is linearly related to the logarithm of the corresponding current, and if the losses occur equally at both electrodes, then the total potential becomes linearly related to log(f). This is called the Tafel relation, and the slope of the line is called the "Tafel slope". The following sections will give many examples of potential-current relationships, and except for the interval of smallest currents, the Tafel approximation is often a valid one. 

E and the reversible equilibrium potential of the electrochemical reaction Thus the driving force for the electrochemical reaction is not the absolute potential it is the activation overpotential riaof This relationship between the current density and activation overpotential has been further developed and resulted in the Butler-Volmer equation ... 

For a system in which the rate of reaction is limited by activation overvoltage, the relationship between the rate of reaction, or current density i, and the driving force for the reaction, or potential E, is given by the Butler-Volmer equation ... 

Current-potential relationship, shown in Fig. 5.1, describes a redox system that departs shghtly (10-20 mV) from its equihbrium state. As shown in the figure, the relationship between the current and the apphed potential is nearly linear when measured close to the equihbrium potential. In this case, the overpotential in Butler-Volmer equation (3.28) is small and is equal to the inequahty ... 

In previous chapters only the linearized form of the current-potential relation has been used. The other terms of the Taylor series expansion were dropped. However, in reality, current-potential relationships show a considerable amount of curvature. The Taylor series expansion of the Butler-Volmer equation predicts that... 

If the electrocrystalli2ation is controlled by the formation of two or three-dimensional isolated nuclei, the current-potential relationship has a stronger overpotential dependence than predicted by the Butler-Volmer equation [58],... 

This section describes the electrode reactions that are limited by the rate of charge transfer at the electrode-electrolyte interface. In this case, the Butler-Volmer equation (B V equation) provides a functional relationship between the potential and the current... 

Electrode Kinetic and Mass Transfer for Fuel Cell Reactions For the reaction occurring inside a porous three-dimensional catalyst layer, a thin-film flooded agglomerate model has been developed [149, 150] to describe the potential-current behavior as a function of reaction kinetics and reactant diffusion. For simplicity, if the kinetic parameters, such as flie exchange current density and diffusion limiting current density, can be defined as apparent parameters, the corresponding Butler-Volmer and mass diffusion relationships can be obtained [134]. For an H2/air (O2) fuel cell, considering bofli the electrode kinetic and the mass transfer, the i-rj relationships of the fuel cell electrode reactions within flie catalyst layer can be expressed as Equations 1.130 and 1.131, respectively, based on Equation 1.122. The i-rj relationship of the catalyzed cathode reaction wifliin the catalyst layer is... 

For an electrochemical half-cell reaction, the overall relationship describing the complete current-potential characteristic is given by the Butler-Volmer equation ... 

This is the usual form of the Butler-Volmer equation, which describes the relationship between current density and potential for a simple electrode reaction controlled by charge transfer. 

The Butler-Volmer equation written in the form (44) is frequently used in corrosion. It describes the relationship between current density and potential of an electrode reaction under charge transfer control in terms of three easily measurable quantities P, and P, . For large anodic overvoltages (tl/p 1) Eq. (44)... 

If charge transfer is rate limiting, the Butler-Volmer equation (35) described the current-potential relationship of each partial reaction. With the overvoltage of the metal dissolution reaction, r j = - reduction reaction, rjg... 

Tibor Erdey-Gruz (1902-1976) was a Hungarian physical chanist, who is most known for his work on transport processes in electrolyte solutions. He woiked with Max Volmer in the development of the relationship between current and electrode potential and is known as the Erdey-Gruz-Volmer equation, which was, in fact, a prototype of the Butler-Volmer equation. 

Current Potential Relationship—Butler-Volmer Equation... 

Butler-Volmer equation for relationship between electrical current and potential,... 

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