Butler-Volmer kinetic model

Fig. 1.14 Variation of the reduction and oxidation rate constants with the applied potential according to the Butler-Volmer kinetic model...

Example 4.4 Selection of Proper Butler-Volmer Kinetic Model Solve for the most... 

The model was developed with the following hypothesis (Scheme in Fig. 6-11) At the metal polymer-interface (y = 0), we assume a Butler-Volmer kinetics for the polymer confined redox couple P/Q. 

In Fig. 3.14a, the dimensionless limiting current 7j ne(t)/7j ne(tp) (where lp is the total duration of the potential step) at a planar electrode is plotted versus 1 / ft under the Butler-Volmer (solid line) and Marcus-Hush (dashed lines) treatments for a fully irreversible process with k° = 10 4 cm s 1, where the differences between both models are more apparent according to the above discussion. Regarding the BV model, a unique curve is predicted independently of the electrode kinetics with a slope unity and a null intercept. With respect to the MH model, for typical values of the reorganization energy (X = 0.5 — 1 eV, A 20 — 40 [4]), the variation of the limiting current with time compares well with that predicted by Butler-Volmer kinetics. On the other hand, for small X values (A < 20) and short times, differences between the BV and MH results are observed such that the current expected with the MH model is smaller. In addition, a nonlinear dependence of 7 1 e(fp) with 1 / /l i s predicted, and any attempt at linearization would result in poor correlation coefficient and a slope smaller than unity and non-null intercept. 

Although such terms as Butler-Volmer equation or Butler-Volmer expression or Butler-Volmer kinetics or Butler-Volmer model are widely used in the literature, see e.g., Refs, [ii-xii], its definition is ambiguous and even the name is questionable in the light of the historical facts [viii, xiii, xiv]. 

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 ... 

Kawamoto (2) developed a two-dimensional model that is based on a double iterative boundary element method. The numerical method calculates the secondary current distribution and the current distribution within anisotropic resistive electrodes. However, the model assumes only the initial current distribution and does not take into account the effect of the growing deposit. Matlosz et al. (3) developed a theoretical model that predicts the current distribution in the presence of Butler-Volmer kinetics, the current distribution within a resistive electrode and the effect of the growing metal. Vallotton et al. (4) compared their numerical simulations with experimental data taken during lead electrodeposition on a Ni-P substrate and found limitations to the applicability of the model that were attributed to mass transfer effects. 

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),... 

Based on Newman s well-known modelling approach [8 10] the impedance of a commercial cell is described. This approach combines concentrated solution theory, porous electrode theory and Butler-Volmer kinetics to form a set of coupled partial differential equations. 

Fermeglia et al. [15] 2D cross flow Dynamic Reduced momen- tum balance Cell WGS (equil.) Overall Butler—Volmer kinetics Unclear Overdeter- mined electrode model... 

Heidebrecht et al. [16-18] 2D cross flow with HR Dynamic Cell/stack SMR (rate) WGS (rate) Lumped model with Butler-Volmer kinetics and mass transport I given 250 kW stack, 342 cells at 0.79 m Includes HR Coupling A/C via burner Cathode gas recycle Transport limitation in HR... 

A model of the SOFC anode developed by the Imperial College group (Aguiar et ah, 2004) includes Butler-Volmer kinetics and transport losses on both sides of the cell. The results (Aguiar et ah, 2004) show that for a cell temperature 800 - - 273 K, the diffusion of reactants to the catalyst sites has a minor effect on cell performance. 

Hin presented a combined continuum and KMC method for simulating the kinetics of Li intercalation and structural changes, as well as the morphological evolution of the Li-rich/Li-poor phase boundary in Li FeP04 electrode particles. The KMC model was coupled with a finite difference continuum model to treat the Li-ion diffusion flux within the electrolyte. Also, the local particle adsorption was coupled to concentration fields by Butler-Volmer kinetics. The KMC-simulated galvanostatic discharge process was performed at room temperature, and a comparison of the computational and experimental results is shown in Figure 3. 

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

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]. 

In the theoretical modeling, the kinetics of anion transfer is assumed to obey the Butler-Volmer equation [29] ... 

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 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-... 

The analysis of the kinetics of the charge transfer is presented in Sect. 1.7 for the Butler-Volmer and Marcus-Hush formalisms, and in the latter, the extension to the Marcus-Hush-Chidsey model and a discussion on the adiabatic character of the charge transfer process are also included. The presence of mass transport and its influence on the current-potential response are discussed in Sect. 1.8. 

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