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 example treated above is of appreciable relevance for several parts of this chapter, as will be seen later. The potential dependence of c 0 and Cr can be derived explicitly if it is known how kf depends on E. As an illustration in Fig. 2(a), c 0 vs. E curves are given assuming the commonly accepted Butler—Volmer model... 

The Buder-Volmer equation can be applied to many, but not all, systems. Moreover, many of the systems that do not follow the Buder-Volmer model are of great practical importance, eg, in the corrosion of passivating metals (see Corrosion and corrosion control). 

In the phenomenological Butler-Volmer model (BV) [28, 29], the effect of the applied potential E on the energy of the transition state is assumed to be between that of the oxidized and reduced states, although no molecular description of the activation process is proposed. Accordingly, the activation energies for the reduction and oxidation reactions can be written as ... 

In this section, both approaches will be compared in chronoamperometry under limiting current conditions at spherical electrodes and microelectrodes. As is well known, for spherical electrodes and taking into account the Butler-Volmer model, the value of the diffusion-controlled reduction current at large overpotentials, e B is given by the following expression (see Eq. (2.147) of Sect. 2.5.2) ... 

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]. 

More interesting is the mobile equivalent of the LcUigmuir equation. For this case the Volmer model applies. We already derived (see 11.1.5.22 and 23)... 

The presence of at least two fluorophores, and possibly a third, associated with metal ion binding in fulvic acid strongly suggests the need for multiple binding site models. Existing linear and nonlinear models will be reviewed for both fluorescence quenching and enhancement. A new modified 1 1 Stem - Volmer model will be introduced as well as two site and multiple site models. Application of the models to Cu binding by fulvic acid and certain well defined model systems are discussed. 

Derivation of the Modified Stern-Volmer Model for Metal Complexation. The... 

In equation 11, v=[ML]/Cl, and all other symbols used are the same as defined previously for nonlinear and modified Stem-Volmer models. Theoretically, a plot of v versus v/[L] should yield a straight line with K as the y intercept and -K as the slope. Algebraic manipulation of Cl and mass balance relationships (equations 4 and 5) and substitution into equation 11, yields equation 12. 

Modeling of Multisite Fluorescence Quenching. A traditional multisite fluorescence quenching model using a Stem-Volmer approach has been developed and applied to quenching curves involving residual protein fluorescence (32). More recently, however, the multiple site model has been used to describe structural characteristics in diverse polymer environments (33-3f). The multisite Stem-Volmer model shown in equation 13 may be used to define multiple fluorescent binding sites present under one emission peak... 

Quantitative data are available by fitting the data to the fractional quenching model (15). The Stern-Volmer model is modified by assuming that only a fraction f of the fluorophores can be quenched. The remaining (1-f ) are protected ... 

Stern-Volmer Model. When the chromophores are sufficiently mobile as in fluid solution, the bimolecular quenching process of A by a quenching molecule, B, including the triplet energy transfer and some collisional quenching, will result in the single exponential... 

As the dynamic quenching for a phosphorophore gives single exponential decay in nonviscous solution (Stern-Volmer model), it is necessary to consider why the dynamic quenching in polymer solids especially below T results in a non-exponential decay profile. Kinetics for Non-exponential Decay Due to Dynamic Quenching (6,29)... 

The parameters F, and K are the same as in Tables 5.2 through 5.4. Setting Q = 0 (assuming equilibrium surface-subsurface), from each expression in Table 5.5 we deduce the respective equilibrium adsorption isotherm in Table 5.2. In addition, for P = 0 the expressions for Q related to the Frumkin and van der Waals model reduce, respectively, to the expressions for Q in the Langmuir and Volmer models. For Fj F both the Frumkin and Langmuir expressions in Table 5.5 reduce to the Henry expression. 

The linear Tafel plots and a values close to 0.5 indicate that conventional ET theory, e.g., Buttler-Volmer model, is applicable to heterogeneous reactions at the ITIES. ... 

IMPLICATIONS OF THE BUTLER-VOLMER MODEL FOR THE ONE-STEP, ONE-ELECTRON PROCESS... 

Implications of the Butler-Volmer Model for the One-Step, One-Electron Process 99... 

---