Electron-transfer number overall

The overall permeation rate of a material is determined by both ambipolar conductivity in the bulk and interfacial exchange kinetics. For -> solid electrolytes where the electron - transference numbers are low (see -> electrolytic domain), the ambipolar diffusion and permeability are often limited by electronic transport. 

For the example considered, the overall electron-transfer number in Eq. (16) is n = 2. 

As shown, this overall electrochemical reaction has a thermodynamic cell voltage ( °eu) of 1.229 V at reversible conditions. Accordingly, the standard free enei change of the overall reaction (AG°g[[ = —nFEggy, where n is the electron transfer number of the overall reaction (here n = 2), and F is the Faraday s constant, 96,745 C mol ). If the AG°g j is negative, the corresponding cell reaction should have spontaneity in standard conditions. 

Therefore, using RDE measurements, the kinetic parameters of electron-transfer kinetics such as the electron-transfer number (n) and coefficient (a) and the exchange current density (f) can be estimated. At the same time, the reactant transport parameters such as the overall electron-transfer number n for the complex reaction), reactant diffusion coefficient, the kinetic viscosity can also be estimated. 

Due to the production of H2O2 or HO2 through a 2-electron-transfer pathway, the overall electron-transfer number of the ORR process is always less than 4. This electron-transfer number is normally called the apparent number of electrons transferred per O2 molecule. Actually, this apparent number of electron transfer can be measured by the RRDE technique, from which the percentage of H2O2 formation in the ORR can also be calculated. Generally to say, the apparent number of electron transfer and the percentage of peroxide produced in the ORR process are two important pieces of information in evaluating the ORR catalyst s catalytic activity. 

As discussed in Chapter 5 for RDE technique, this apparent electron-transfer number of ORR or the overall ORR electron-transfer number can be obtained using the slope of the... 

Table 7.6. ORR Kinetic Current Densities and Overall Electron Transfer Numbers. Obtained Based on tbe Data in Figure 7.19, Collected on a Co-N/C Coated Glassy Carbon Electrode Rotating at Various Rotation Rates. Electrolyte 02-Saturated 0.5 M H2SO4 Solution Co Loading in the Coating Layer ...

To obtain the overall ORR electron-transfer numbers, the RRDE measurements were also carried out in this work. The obtained overall electron numbers and the percentages of H2O2 production are shown as a function of electrode potential in Figure 7.20(A) and (B), respectively. It can be seen that the ORR electron-transfer number varies in the range of 3.6—3.8,... 

From Figure 7.22, it can be seen that the overall ORR electron-transfer numbers catalyzed by Ti407 in these KOH solutions are in... 

Figure 7.22 (A) Plots of overall electron-transfer number and (B) percentage H2O2 produced as a function of electrode potential at three different concentrations of 02-saturated KOH solution. Calculations based on current-potential data collected at rotation rate of 1600 rpm. Reprinted with permission from Ref. 66.

Chapter 7 reviews the applications of RDE and RRDE techniques in ORR research and its associated catalyst evaluation. Some typical examples for RDE and RRDE analysis in obtaining the ORR kinetic information such as the overall electron transfer number, electron transfer coefficiency, and exchange current density are also given in this chapter. It demonstrates that both RDE and RRDE methods are a powerful tool in ORR study, and using RDE and RRDE methods, ORR has been successfully studied on Pt electrode, carbon electrode, monolayer metal catalyst, Pt-based catalyst, and nonnoble metal-based catalysts. 

In this mechanism. Reaction (12.1) is the chemical reaction to form the adduct, which has a reaction rate constant of 1.0 x 10 cms, as determined by the RDE measurements in this work. Reaction (12.11) is the ORR RDS on the Ti407 electrode surface, whose rate constants are given in Table 12.1. Reaction (12.III) represents the reactions for peroxide formation. After HO2 formation, HO2 can react in one of two ways further 2-electron reduction to OH through Reaction (12.1V), or chemical desorption through Reaction (12.V) to form a free peroxide ion, which then enters into the bulk solution and can be detected by the ring electrode of the RRDE. The ORR on the Ti407 electrode has a mixed 2- and 4-electron transfer pathway and gives an overall electron transfer number of <4. The relative portion of Reaction (12.IV) can be expressed as x, and the portion of Reaction (12.V) can be expressed as (1-x). When x= 1, the mechanism will follow a totally 4-electron transfer pathway, and when x = 0, the mechanism will be a totally 2-electron pathway. If the x value is >0 and < 1, the ORR will have a mixed 2- and 4-electron transfer pathway. Note that this ORR mechanism is only hypothetical, to facilitate further discussion. More evidence is needed to validate the mechanism. 

The key to balancing complicated redox equations is to balance electrons as well as atoms. Because electrons do not appear in chemical formulas or balanced net reactions, however, the number of electrons transferred in a redox reaction often is not obvious. To balance complicated redox reactions, therefore, we need a procedure that shows the electrons involved in the oxidation and the reduction. One such procedure separates redox reactions into two parts, an oxidation and a reduction. Each part is a half-reaction that describes half of the overall redox process. 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

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 case of an irreversible reaction, therefore, two parameters are now defined with respect to the number of electrons transferred in the reaction n now refers to the electrons transferred overall, while na indicates the number of electrons participating in the rds. Thus, for example, we can rewrite equations (2,144) and (2.146) as ... 

As a 3-step mechanism, the electron-transfer paradigm provides a pair of discrete intermediates [D, A] and D+, A for the prior organization and the activation, respectively, of the donor and the acceptor. The quantitative evaluation of these intermediates would allow the overall second-order reaction (k2) to be determined. Although the presence of [D, A] does not necessarily imply its transformation to D+, A-, a large number and variety of donor/ acceptor couples showing transient charge-transfer absorptions associated with [D, A] have now been identified. In each case, the product can be predicted from the expected behavior of the individual ion radicals D+ and A-. Consider for example, the labile 1 1 benzene complex with bromine that has been isolated at low temperatures and characterized crystallographically (Chart 9).256... 

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