Butler-Volmer electrochemical kinetic

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 ... 

Chang et al. [2, 3] provided an extended model with Butler-Volmer electrochemical reaction kinetics and the capabihty of predicting complete polarization curves. The results obtained for Y-shaped [2] andF-shaped [3] formic acid/dissolved oxygen-based cells were in good agreement with previous experimental studies [4, 5] and confirmed the cathodic activity and mass transport limitation of these cells. Consequently, the predicted cell performance was essentially independent of anodic fonnic add concentration. The numerical results also recommended high aspect... 

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. 

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

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... 

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... 

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. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

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. 

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. 

Like all cathodes, early electrochemical kinetic studies of LSM focused heavily on steady-state d.c. characteristics, attempting to extract mechanistic information from the Tand F02 dependence of linear and Tafel parameters.As recently as 1997, some workers have continued to support a view that LSM is limited entirely by electrochemical kinetics at the LSM/electrolyte Interface based on this type of analysis. However, as we have seen for other materials (including Pt), the fact that an electrode obeys Butler—Volmer kinetics means little in terms of identifying rate-limiting phenomena or in determining how close the reaction occurs to the TPB. To understand LSM at a nonempirical level, we must examine other techniques and results. 

Equation (25) is general in that it does not depend on the electrochemical method employed to obtain the i-E data. Moreover, unlike conventional electrochemical methods such as cyclic or linear scan voltammetry, all of the experimental i-E data are used in kinetic analysis (as opposed to using limited information such as the peak potentials and half-widths when using cyclic voltammetry). Finally, and of particular importance, the convolution analysis has the great advantage that the heterogeneous ET kinetics can be analyzed without the need of defining a priori the ET rate law. By contrast, in conventional voltammetric analyses, a specific ET rate law (as a rule, the Butler-Volmer rate law) must be used to extract the relevant kinetic information. 

The Butler-Volmer equation has yielded much that is essentia] to the first appreciation of electrode kinetics. It has not, however, been mined out. One has to dig deeper, and after electron transfer at one interface has been understood in a more general way, electrochemical systems or cells with two electrode/electrolyte interfaces must be tackled. It is the theoretical descriptions of these systems that provide the basis... 

Since the electrochemical reactions are supposed to take place at the electrodeelectrolyte interface, then the Butler-Volmer equation, regulating the electrochemical kinetics, sets the boundary condition, whilst j (production rate) in Equation (3.37) is replaced with J (current density produced), as explained in detail in Section 3.7.2. 

In the numerical model calibration phase, the unknown parameters are those contained in Fick s law and in the Butler-Volmer equation, i.e. the diffusion coefficients representing the porous micro-structural characteristics (e and r), and the electrochemical kinetics parameter (A and Ea). It should be noted that the calibration pro-... 

As another example of solving the nonlinear model by ADM, we assume that at high overpotentials the electrochemical kinetics can be represented by the following high field Butler-Volmer approximation, the current density in Eq. (227) is rewritten as ... 

If the adsorbate itself does not react electrochemically, but inhibits the electron transfer of a faradaic reaction that proceeds via Butler-Volmer kinetics on the free surface, the temporal evolution of DL reads... 

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... 

This process of electrochemically deconstructing the corrosion reaction provides a convenient experimental methodology for investigating active corrosion conditions and is illustrated schematically in Fig. 8. Each half-reaction should obey Butler-Volmer kinetics, in which the current increases exponentially [posi-... 

Butler, John Alfred Valentine — (Feb. 14,1899, Winch-combe, Gloucestershire, England - July 16,1977). Butler greatly contributed to theoretical electrochemistry, particularly, to connection of electrochemical kinetics and thermodynamics [i,ii]. The famous Butler-Volmer equation (1924) showing the exponential relation between current and potential was named after him (and... 

Volmer turned his attention to processes at - nonpo-larizable electrodes [iv], and in 1930 followed the famous publication (together with - Erdey-Gruz) on the theory of hydrogen - overpotential [v], which today forms the background of phenomenological kinetics of electrochemistry, and which resulted in the famous - Butler-Volmer equation that describes the dependence of the electrochemical rate constant on applied overpotential. His major work, Kinetics of Phase Formation , was published in 1939 [v]. See also the Volmer reaction (- hydrogen), and the Volmer biography with selected papers [vi]. 

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