Volmer-Butler kinetics

The kinetics of charge transfer between metallic electrodes and conducting polymer films have proved to be difficult to investigate, and little reliable data exist. Charge-transfer limitations have been claimed in cyclic voltammetry, and Butler-Volmer kinetics have been used in a number of... 

Butler-Volmer kinetics and mechanism of electron transfer, 587... 

Electron transfer mechanism Butler-Volmer kinetics and, 587 in electronically conducting polymers, 568... 

The dimensionless time (t), potential ( ), and current (i/0 are all as defined in equations (1.4). The exact characteristics of the voltammograms depend on the rate law. In the case of Butler-Volmer kinetics,... 

When Afh -a oo, a Nernstian response is obtained. The half-wave potential is equal to the standard potential. Conversely, when Afh —> 0, the electrode electron transfer is irreversible. In the case of a Butler-Volmer kinetic law, the half-wave potential is expressed as... 

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. 

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

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... 

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. 

This is the simplest case which involves that partial current I in Eq. (4-4) identifies itself with the overall faradaic current /F. The faradaic current is ruled out by a Butler-Volmer kinetics ... 

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. 

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

Comparison Between Marcus-Hush and Butler-Volmer Kinetics. 167... 

Up to now, the treatment of non-reversible electrode process has focused on the usual Butler-Volmer kinetics for which the rate constants take the form (see Sect. 1.7.1) ... 

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. 

Fig. 6.18 Dimensionless current-time (a) and charge-time (b) curves corresponding to the application of a constant potential Ei — /ic° = —0.2 V to an electro-active monolayer calculated from Eqs. (6.116) and (6.115) assuming a Butler-Volmer kinetics with a = 0.5. The values of (k°-r) are 0.05 (black), 0.1 (red), 0.25 (green), 0.5 (blue),...

In this case, the Nernstian condition given in Eq. (H.5) must be replaced by the following relationship [in which a Butler-Volmer kinetics formalism has been assumed see Eq. (1.101)] ... 

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... 

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-... 

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 ... 

Cyclic voltammetric, chronoamperometric and AC impedance spectroscopic (ACTS) methods have typically been used to determine the electron-transfer rates in SAMs. Laviron developed a simple method for determining electron-transfer rate constants by cyclic voltammetry [92], The method allows the determination of from the dependence of the cathodic/anodic peak separation, /SEp, upon sweep rate, but it is inherently inaccurate because it is based on Butler-Volmer kinetics [78, 93, 94]. 

This rather complicated equation is based on the Butler-Volmer kinetic expression,... 

With one exception, that of 1-fluoro-l-methyl-2,2-diphenylcyclopropane 160, which exhibited no reduction before confomitant reduction of either the solvent or the supporting electrolyte, a single irreversible cathodic wave was always observed. The values of the transfer coefficients were derived from the cyclic voltammetric peaks widths, assuming that the Butler-Volmer kinetics apply a= 1.85(rf/F)(Ep 2 — p) [132g,h]. Of interest was... 

The average values of y. were determined from the cyclic voltammatric peak widths, assuming the Butler-Volmer Kinetics apply a = 1.85 (rt F) (Epj — p). 

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