Butler-Volmer electrochemical kinetic expression

To incorporate the effect of the side reaction into the electrochemical kinetics of the main reactions, a modification to the Butler-Volmer electrochemical kinetic expression is introduced ... 

In this section, we derive a general expression to describe activation polarization losses at a given electrode, known as the Butler-Volmer (BV) kinetic model. The BV model is not the only (or necessarily the most appropriate) model to describe a particular electrochemical reaction process. Nevertheless, it is a classical treatment of electrode kinetics that is widely applied to study and model a majority of the electrode kinetics of fuel cells. The BV model describes an electrochemical process limited by the charge transfer of electrons, which is appropriate for the ORR, and in most cases the HOR with pure hydrogen. The fundamental assumption of the BV kinetic model is that the reaction is rate hmited by a single electron transfer step, which may not actually be true. Some reactions may have two or more intermediate charge transfer reactions that compete in parallel or another intermediate step such as reactant adsorption (Tafel reaction from Chapter 2) may limit the overall reaction rate. Nevertheless, the BV model of an electrochemical reaction is standard fare for a student of electrochemistry and can be used to reasonably fit most fuel cell reaction behavior. 

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.)...

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. 

In real (as opposed to model) electrochemical cells, the net current flowing will often be partly determined by the kinetics of electron transfer between electrode and the electroactive species in solution. This is called heterogeneous kinetics, as it refers to the interface instead of the bulk solution. The current in such cases is obtained from the Butler-Volmer expressions relating current to electrode potential [73,74,83,257,559]. We have at an electrode the process (2.18), with concentrations at the electrode/electrolyte interface cj q and cb,Oj respectively. We take as positive current that going into the electrode, i.e., electrons leaving it, which corresponds to the reaction (2.18) going from left to right, or a reduction. Positive or forward (reduction) current if is then related to the potential E by... 

The reaction occurs at the electrode/electrolyte interface (sol-id/liquid interface at the surface of the particle). This reaction occurs as a source term in the equations for the macro scale. In the model equations, accounts for the electrochemical kinetics, (intercalation reaction from the electrolyte phase into the solid matrix and vice-versa). It is a modified form of the Butler-Volmer kinetics, and is given by the following expression ... 

One can derive the Butler-Volmer kinetic expressions by an alternative method based on electrochemical potentials (8, 10, 12, 19-21). Such an approach can be more convenient for more complicated cases, such as requiring the inclusion of double-layer effects or sequences of reactions in a mechanism. The first edition develops it in detail. ... 

In deriving (6.7.14) and (6.7.17), we assumed that Butler-Volmer kinetics apply, as expressed in the i-E characteristic, (3.3.11). Indeed, this assumption (or the adoption of some other model) is necessary before equations can be derived for most electrochemical approaches. However, with the convolutive technique, this assumption is not essential, for the rate law can be written in the general form (27),... 

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. 

The kinetics of electrochemical O2 reduction on Pt has been studied extensively. °° There is a general consensus that it shows first order kineucs in O2. By following the Butler-Volmer approach, the rate expression for the ORR can be expressed by the relationship between kinetic current, i, and potential, E ... 

The irregular type of codeposition is very often characterized by simultaneous influence of cathodic potential and diffusion phenomena, i.e., it mainly occurs under the activation and/or mixed control of the electrodeposition processes. The rate of electrodeposition in such a case is expressed by the Butler-Volmer equation which is usually used for the kinetics of electrochemical processes [1,5] ... 

Assuming that the applied current density is i = io — c and substituting eqs. (3.36) and (3.37) into this expression yields the Butler-Volmer equation that quantifies the kinetics of the electrochemical corrosion... 

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