Apparent transfer coefficient

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

Fig. 4 Electrochemical reduction of a sulfonium cation (Scheme 6) showing the transition from the concerted to the stepwise mechanism as driving force increases upon raising the scan rate.33 The apparent transfer coefficient, a, is derived from the peak width according to equation (17).

Another striking example, recently discovered, is the reduction of iodoben-zene in DMF.61 The variation of the apparent transfer coefficient with the scan rate indicates that the mechanism passes from concerted to stepwise as the driving force increases (Fig. 5). As expected, the zone where the concerted mechanism prevails enlarges as one raises the temperature. In contrast, bromobenzene and 1-iodonaphthalene exhibit the characteristics of a stepwise mechanism over the whole range of scan rate. 

Fig. 5 Electrochemical reduction of aryl halides showing the variation of the apparent transfer coefficient with the scan rate. iodobenzene, O bromobenzene, V 1-iodonaphthalene, O 4-methyliodobenzene, at 298 K, iodobenzene at 329 K.

On mercury and gold the Volmer reaction is rate determining Tafel behavior is observed, but the apparent transfer coefficients depend on temperature [1],... 

Consider the reaction with two consecutive electron-transfer steps described by Eq. (11.12). (a) Show that, if j0,2 j0,1, there is an intermediate range of negative overpotentials in which the apparent transfer coefficient is (2 — ai) and the apparent exchange current density 2j0,i (see Fig. 11.1). (b) Derive the form of the Tafel plot for jo,i > jo,2-... 

FIGURE 2.6. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying a MHL kinetic law (Xt — 0.7 eV, koo — 4 x 103 cms-1, implying that kg = 0.69 cms-1) and an irreversible follow-up reaction (from bottom to top, k+ = 103, 105, 107, 109s 1). Temperature, 25°C. a Potential-dependent rate constant derived from convolutive manipulation of the cyclic voltammetric data (see the text), b Variation with potential of the apparent transfer coefficient (see the text) obtained from differentiation of the curves in part a. 

The apparent transfer coefficient, as derived from the peak width and the variation of the peak potential with the scan rate, is small (between 0.2 and 0.3) in all cases. This rules out the occurrence of a stepwise mechanism (46, 47), in which the follow-up, bond-breaking step would have been... 

Fig. 13 Experimental (O) and calculated (solid line) potential dependencies of the apparent transfer coefficient a for the electroreduction of 4-X-PhC03Bu-t in DMF/ 0.1 M TBAP at 25 C.

A consequence of eqn. (108) is that the true transfer coefficient, at, can be calculated from the apparent transfer coefficient with the double layer correction calculated from the diffuse double layer theory [6]... 

Experimental attempts to verify the dependence of the transfer coefficient on the electrode potential have been made with simple outer sphere redox electrode reactions (see refs. 5—19 in ref. 70a). Corrections to experimental values of the apparent transfer coefficient due to double layer effects are performed by the use of eqn. (109), but the value of a calculated from experimental data depends on the assumptions about the location of the centre of charge in the transition state in the Helmholtz layer [70b]. 

Analysis of potentiodynamic curves makes it possible to determine, in addition to the diffusion coefficient, the reaction kinetic characteristics the apparent transfer coefficients of the cathodic reaction (a) and anodic reaction (/() and the rate constant k°. Quantitative determination will be discussed in the next section qualitatively, the more the potential difference AEp for the anodic and cathodic current peaks (at a... 

From the slope of the lines in Fig. 22c, and by using the above-mentioned theory of potentiodynamic curves [90], the apparent transfer coefficients of cathodic reaction a (or anodic reaction / ) can be calculated by the following formulas ... 

The apparent transfer coefficient of the cathodic reaction, ac, is a measure of the sensitivity of the transition state to the drop in electrostatic potential between electrolyte and metal [109,112]. According to Ref. 113, it is ac = 0.75 for the O2 reduction on Pt in aqueous acid electrolytes. In Ref. Ill the value ac = 1.0 was reported instead. Since the cathodic reaction is a complex multistep process, it might follow several reaction pathways, and the competition between them is affected by the operation conditions (rj, p, T). Therefore, different values of ac have been reported in different regimes of operation. Although in the simple reactions the transfer coefficient is a microscopic characteristic of the elementary act [112], for complex multistage reactions in fuel cell electrodes it is rather an empirical parameter of the model. The dependence of effective a for methanol oxidation on the catalyst layer preparation was recently studied [114]. 

It is interesting that, despite the high nonuniformity of currents along a CER (Fig. 36), a plot of In versus 6 often yields a Tafel-like behavior from which an apparent transfer coefficient and rate constant can be extracted (60-62). Thus, potential-current density data are not sufficient to indicate multiple reactions. At long retention times in the reactor, however, an unusual maximum and subsequent decrease of the average current density with potential occurs for series reactions (60). This results from fast depletion of species A and B with potential at long space-times, but it is not related to zero concentrations or mass transport-limited reactions. Such maxima or limiting currents have been observed in the stepwise oxidation of unsaturated... 

One important question in the light of current electron transfer theories [85-87] is that of the transition between stepwise (electron transfer and bond cleavage as separate elementary steps) or concerted (dissociative electron transfer [88]) mechanisms. For the two extremes, one expects largely different activation parameters for the electron transfer at an electrode. In particular, in contrast to the simple Butler-Vohner relationship (Eq. 18) with a constant transfer coefficient, potential dependent a values become evident. The experimentally accessible apparent transfer coefficient... 

A further consequence of these equations is that the Tafel plots may not be linear, or they may be linear with a slope determined by an apparent transfer coefficient In the cathodic limit... 

Figure 6-5 The relationship of the reversibility factor and the apparent transfer coefficient a,pp. The solid point represents the simulation and fitting result, then estimated through Equation (2). (Adapted from Reference 3.)...

In multistep electron transfer reactions, the overall reaction rate may be limited by rates of reactant chemisorption, rates of bond breaking, or rates of molecular rearrangement. These are chemical, rather than potential, dependent factors. If the observed reaction rates are limited by chemical dependent factors, the measured transfer coefficients may be only fitting parameters, or apparent transfer coefficients. In this case, the apparent transfer coefficient will be temperature dependent (25-27). Conversely, for reactions that are limited by potential dependent factors, i.e., the rate of outer-sphere electron transfer, the transfer coefficient should be independent of temperature (25-27). 

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