Kinetics Butler-Volmer model

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]. 

The two models most commonly applied to the heterogeneous electron transfer kinetics are the Butler-Volmer model, which is primarily a macroscopic approach... 

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]. 

There are two approaches to modeling the SOFC electrochemistry at the mesoscale an elementary kinetics-based model and a modified Butler-Volmer model. In the elementary kinetics-based model, the electrochemical reactions of the SOFC are modeled exactly, whereas in the modified Butler-Volmer model, the phenomenological Butler-Volmer equation is solved based on the local Faradaic current density. 

Steady-State value in the bulk solution, A mass transport rate for a redox mediator increases from D/a in the bulk solution to D/(i with the narrow tip-substrate gap (D is the diffusion coefficient of the redox mediator) to render the tip current more sensitive to the kinetics of the tip reaction. When the tip reaction is quasireversible and also follows the classical Butler-Volmer model... 

Simplified Butler-Volmer Equation 1 Facile Kinetics—LinearizedButler-Volmer Model... 

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

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. 

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 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. 

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

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