Butler-Volmer reaction kinetics

These models combine Butler-Volmer reaction kinetics with mass transport kinetics in a simple approach [16, 45]. The mass transport between the gas phase in... 

We assume, in the first place, that the charge transfer at the metal-solution interface represents the rate-limiting step and, secondly, that the kinetics of the two partial reactions are independent of one another. The partial current density of each reaction then obeys the Butler-Volmer reaction. 

The oxidation reactions in equation (7.110) and equation (7.112) follow a Butler-Volmer-type kinetics ... 

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 ... 

Ramadass et al. [20] developed a capacity-fade model and represented the loss of active Hthium during charge-discharge cycling as due to a continuous SEI film formation over the surface of the negative electrode. No transport limitation for the solvent in the SEI was considered. A Butler-Volmer type kinetics was used to describe the side reaction kinetics. Briefly, for the negative electrode, an additional component, due to the side reaction for the SEI formation, was added to the anode transfer current density, ja. namely ja = Ja,electrode + Ja.side reaction. The contribution to the electrode overpotential is reflected by an additional ohmic drop due to the film formation, that is, [20] ... 

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. 

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 voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

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... 

It is difficult to measure kinetic currents at high overpotentials, since then the reaction is fast and usually transport controlled (see Chapter 13). At small overpotentials only Butler-Volmer behavior is observed, and the deviations predicted by theory were doubted for some time. But they have now been observed beyond doubt, and we will review some relevant experimental results in Chapter 8. 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

FIGURE 2.5. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying the Butler-Volmer law (with a = 0.5) and an irreversible follow-up reaction, a Variation of the peak potential with the scan rate, b Variation of the peak width with scan rate. Dots represent examples of experimental data points obtained over a six-order-of-magnitude variation of the scan rate. 

As compared to the Nemstian case, the plateau is the same but the wave is shifted toward more negative potentials, the more so the slower the electrode electron transfer. An illustration is given in Figure 4.13 for a value of the kinetic parameter where the catalytic plateau is under mixed kinetic control, in between catalytic reaction and substrate diffusion control. For the kjet(E) function, rather than the classical Butler-Volmer law [equation (1.26)], we have chosen the nonlinear MHL law [equation (1.37)]. 

Here kf and kb are the adsorption and desorption constants when 9 —> 0. The derivation of the equation above is similar to establishment of the Butler-Volmer kinetic law for electrochemical electron transfer reactions, where the symmetry factor, a, is regarded as independent from the electrode potential. Similarly, in the present case, the symmetry factor, a, is assumed to be independent of the coverage, 9. 

If the electrode reaction (1.1) is kinetically controlled, (1.8) mnst be snbstituted by the Butler-Volmer equation ... 

When the electrode reaction (2.30) is quasireversible, (2.37) and (2.38) are combined with the Butler-Volmer kinetic equation (2.42) [60] ... 

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

These kinetic expressions represent the hydrogen oxidation reaction (HOR) in the anode catalyst layer and oxygen reduction reaction (ORR) in the cathode catalyst layer, respectively. These are simplified from the general Butler-Volmer kinetics, eq 5. The HOR... 

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.)...

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