Butler Volmer equation

Equations such as V-96 are known as Butler-Volmer equations [150]. At equilibrium, there will be equal and opposite currents in both directions, =... 

As tire reaction leading to tire complex involves electron transfer it is clear that tire activation energy AG" for complex fonnation can be lowered or raised by an applied potential (A). Of course, botlr tire forward (oxidation) and well as tire reverse (reduction) reaction are influenced by A4>. If one expresses tire reaction rate as a current flow (/ ), tire above equation C2.8.11 can be expressed in tenns of tire Butler-Volmer equation (for a more detailed... 

The exchange current density for common redox couples (at room temperature) can range from 10-6 pAcm-2 to A cm"2. Equation (1-24) can be written in terms of the exchange current to give the Butler-Volmer equation ... 

Background current, 21, 65 Background subtraction, 40, 106 Bacteria electrode, 182 Band microelectrodes, 130, 135 Beryllium, 82 Bienzyme electrodes, 175 Biocatalytic devices, 172 Biological recognition, 171 Biosensors, 50, 171 Bipotentiostat, 106 Blood electrolyte, 165 Boltzmann equation, 19 Brain analysis, 40, 116 Butler-Volmer equation, 14... 

This is the relaxation time of the polymer oxidation under electro-chemically stimulated conformational relaxation control. So features concerning both electrochemistry and polymer science are integrated in a single equation defining a temporal magnitude for electrochemical oxidation as a function of the energetic terms acting on this oxidation. A theoretical development similar to the one performed for the Butler-Volmer equation yields... 

The activation overpotential Tiac,w is due to slow charge transfer reactions at the electrode-electrolyte interface and is related to current via the Butler-Volmer equation (4.7). A slow chemical reaction (e.g. adsorption, desorption, spillover) preceding or following the charge-transfer step can also contribute to the development of activation overpotential. 

I. Development of a simple, Butler-Volmer equation-based kinetic model for MiXi (CdTe) electrodeposition. J Electrochem Soc 132 2904-2909... 

No steady-state theory for kinetically controlled heterogeneous IT has been developed for micropipettes. However, for a thin-wall pipette (e.g., RG < 2) the micro-ITIES is essentially uniformly accessible. When CT occurs via a one-step first-order heterogeneous reaction governed by Butler-Volmer equation, the steady-state voltammetric response can be calculated as [8a]... 

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 is the most commonly employed form of the Butler -Volmer equation as it does not involve the unmeasurable surface concentration terms. It must be remembered, however, that equation (1.35) is only applicable under the conditions where [0]0 [O ] and [R]0 =t- [R ]- We must now examine this equation in some detail, as its form dictates the nature of a number of electrochemical techniques for exploring reaction mechanisms. 

The Butler-Volmer equation can be employed only when O and R are chemically stable on the timescale of the experiment. Within this requirement, we can envisage two limiting cases ... 

In practice, the Butler- Volmer equation is only obeyed in any case for potentials close to Et, or, more generally, for small currents, not through any neglect of factors such as anharmonicity but rather because the rate of transport of the ions to the electrode becomes rate-limiting, a problem we turn to next. 

The values of the parameters derived from the best fit can be related to the fundamental physical constants, such as the electrochemical rate constants, by explicit calculation. From the Butler- Volmer equation,... 

Providing that the potential is sufficiently negative, the kinetics of the reduction reaction in equation (2.125) can usually be rendered fast enough to tip the system into the diffusion-controlled regime, as was shown in the discussion of the Butler-Volmer equation in chapter 1. 

Thus, cyclic or linear sweep voltammetry can be used to indicate whether a reaction occurs, at what potential and may indicate, for reversible processes, the number of electrons taking part overall. In addition, for an irreversible reaction, the kinetic parameters na and (i can be obtained. However, LSV and CV are dynamic techniques and cannot give any information about the kinetics of a typical static electrochemical reaction at a given potential. This is possible in chronoamperometry and chronocoulometry over short periods by applying the Butler Volmer equations, i.e. while the reaction is still under diffusion control. However, after a very short time such factors as thermal... 

Figure 5.2 Current-potential curves according to the Butler-Volmer equation.

For small overpotentials, in the range Fr RT, the Butler-Volmer equation can be linearized by expanding the exponentials ... 

Inner-sphere electron-transfer reactions are not expected to obey the Butler-Volmer equation. In these reactions the breaking or formation of a bond, or an adsorption step, may be rate determining. When the reactant is adsorbed on the metal surface, the electrostatic potential that it experiences must change appreciably when the electrode potential is varied. 

On application of an overpotential rj, the Gibbs energy of the electron-transfer step changes by eo[r) — Afa rj), where Afa(rj) is the corresponding change in the potential fa at the reaction site. Consequently, rj must be replaced by [rj — Afa r )] in the Butler-Volmer equation (5.13). 

---