Butler-Volmer equation reduction

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... 

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. 

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.)...

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... 

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-... 

Many of the electrode theories have assumed that the anodic reaction is rate-limiting and that the cathodic reduction of silver ions from silver halide is not rate-limiting and might not present any limitations to the process of development. Hamano et al. [112] contend that there are instances where the cathodic process does influence development. They use the Butler-Volmer equation as the basis for their development rate model and derive Eq. (83),... 

The transition state approach leads in a natural way to the Butler-Volmer equation, but is relatively weak in its predictive properties regarding the exchange current, ( 0, which is proportional to the frequency factor kr(., i and to exp(—AG J). The latter is quite closely related to the enthalpy and standard entropy of formation of the adsorbed reduction product or intermediate, and this is one main reason for the very intense modern efforts to develop predictive theoretical tools for the ab initio computation of adsorption energies at... 

The wave shapes observed for electrochemically irreversible or quasi-reversible voltammograms are governed by the Tick s law of diffusion (Eq. II. 1.6) and the Butler-Volmer expression (Eq. II. 1.16). By rewriting the Butler-Volmer equation for the case of a reduction A h- n e" B (Eq. n.1.19), it can be shown that, for the limit of extremely fast electron transfer kinetics, kg oo, theNemst law (Eq. n.1.7) is obtained as anticipated. 

In the electrochemical mechanism of corrosion, the metal dissolution—which involves the loss of electrons vis- -vis oxidation—must be accompanied by a cathodic reaction that consumes electrons, which is typically oxygen or proton or water reduction. According to the Butler-Volmer equation, the current density for the anodic reaction varies according to... 

The oxygen reduction reaction is considered as very slow in this case Jo -> 0 and J7c, °o and the Butler-Volmer equation becomes ... 

Equations (4.91) to (4.93) can be applied to any cathodic partial reaction for which the charge-transfer step obeys the Butler-Volmer equation. In corrosion, oxygen reduction is often under mixed control. Figure 4.25 shows the cathodic polarization curve for oxygen reduction, measured on a platinum electrode [6]. The shape of the curve suggests a relatively low value for the ratio I o/ltil-... 

In equilibrium, the standard reduction and oxidation processes occur at equal rates and the exchange currents produced by the two reactions balance each other. The current density, i A/cm2, is given by Butler-Volmer equation [3] ... 

When the system is no longer at equihbrium, the reaction is favored in the direction of oxidation at the anode (production of electrons) and in the direction of reduction at the cathode (consumption of electrons). We can write a Butler-Volmer equation at each electrode ... 

For a polarized electrode under steady-state current flow, the generalized reaction given by eq. (1.2) can be used to derive the Butler-Volmer equation, which involves energy barriers known as activation eneigies. Only the activation energy change is used for the forward (AG/) (reduction) and reverse (AGr) (oxidation) reactions. For example, the hydrogen reaction, 2e = H2 at... 

The oxygen reduction reaction is notoriously sluggish. The faradaic current density for this reaction is given by the cathodic branch of the Butler-Volmer equation ... 

For small overvoltages, the oxygen reduction will follow the Butler- Volmer equation... 

For metals at elevated temperatures, especially liquid metals, the exchange current density as defined by the Butler-Volmer equation is extremely large. Therefore, it is believed that no or very little Zr " or Zr + ion forms at the anode. When the potential difference is not too high, the other metals in the alloy are not oxidised, because they are more noble than zirconium. Similarly, reduction of the alkali or alkali-earth chlorides in the salt does not occur either, because they are less noble than zirconium. 

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... 

The activation overpotential described in the Butler-Volmer equation can be thought of as a reduction in the voltage of a fuel cell from its theoretical thermodynamic voltage that must be incurred in order to operate at a useful current... 

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