Electron transfer, Tafel slopes

This follows theTafei relationship w h a Tafel slope Of,2/3 RT/F = 0- 4 V. hce direct transfer of two electrons aS shown in equation 1.92 is highly unlikely, it Would, appear that the mechanism might involve a twO Step prOr cess in which one Step is rale determining, say... 

Thus, in the region of very high anodic or cathodic polarization, the RDS is always the first step in the reaction path. The transfer coefficient of the full reaction which is equal to that of this step is always smaller than unity (for a one-electron RDS), while slope i in the Tafel equation is always larger than 0.06 V. When the potential is outside the region of low polarization, a section will appear in the polarization curve at intermediate values of anodic or cathodic polarization where the transfer coefficient is larger than unity and b is smaller than 0.06 V. This indicates that in this region the step that is second in the reaction path is rate determining. 

Influence of surface oxidation, 12-28 Potential energy surface, 66-73 Reaction order, 21 -22 Tafel slope, 18-20, 276-277, 297 Oxygen tolerance, 618-620 Outer sphere electron transfer, 33-38... 

It follows that the Tafel slope of an electrode reaction is connected in its physical meaning to the reaction order of transferring electrons or ions from the electrode (metal electrode). 

Figure 11-7 shows the polarization curve of an iron electrode in an acidic solution in which the anodic reaction is the anodic transfer of iron ions for metal dissolution (Tafel slope 40 mV/decade) the cathodic reaction is the cathodic transfer of electrons for reduction of hydrogen ions (Tafel slope 120 mV /decade) across the interface of iron electrode. 

In this case, the formation of a surface oxide (Oads) occurs electrochemically with two successive electron transfers. Therefore, if step (7.28) is rate determining, the mechanism is EE with a predicted Tafel slope of 40 mV at low OHads coverage. 

With an n-type Si electrode, the reduction current density increases exponentially with decreasing potential, the apparent Tafel slope was found equal to 140-160 mV/decade. This is much higher than the 60mV/decade required for the processes that are limited by the supply of electrons from the semiconductor whose space charge is under the accumulation regime. In other words, the HER at the Si surface is a slow electron transfer, that is, a relatively large overpotential is required to... 

In this equation, SLm represents the Tafel slope for the mixture of X plus Y, and Slx,Siy represents the Tafel slopes for the individual components. This equation enables a determination of / from Tafel representations, providing that the quotients between the individual electrochemical rate constants, kx and ky, and the electron transfer coefficients, ocxnax,ocYnaY, are known. 

This reaction was believed to account for the experimentally observed low Tafel slope of about —60 mV per decade of current (unit mV/dec) compared to the normal -20 mV/dec (see definition of Tafel slope in Section 2.3) which is typically indicative of a one-electron transfer process. 

The actual current passed / = 2F/4Jt,[H + ]exp[ — J pAE] since two electrons are transferred for every occurrence of reaction I. Equation (1.64) constitutes the fundamental kinetic equation for the hydrogen evolution reaction (her) under the conditions that the first reaction is rate limiting and that the reverse reaction can be neglected. From this equation, we can calculate the two main observables that can be measured in any electrochemical reaction. The first is the Tafel slope, defined for historical reasons as ... 

A second related issue is the asymmetry in the E-i response near Ecelectron transfer reaction that is different from the metal oxidation reaction. Therefore there is no fundamental reason why pa and pc should be equal, and they should be expected to differ. The extent of their difference defines the degree of asymmetry. Asymmetry matters because the extent of the region where Eq. (2) is a good approximation of Eq. (1) then differs for anodic and cathodic polarization (29). The errors in assuming 10 mV linearity using both the tangent to the E-i data at Econ and for +10 or -10 mV potentiostatic polarizations have been defined for different Tafel slopes (30). 

Electrochemical kinetic measurements show that many reactions have a rather constant Tafel slope over a wide overpotential range. This is true for both redox79 and combined electron- and atom-transfer reactions, particularly proton transfer.3,80 None of the approaches discussed above account for the experimental facts. References 41-50, 55-59, and 67 all... 

Given that electrochemical rate constants are usually extremely sensitive to the electrode potential, there has been longstanding interest in examining the nature of the rate-potential dependence. Broadly speaking, these examinations are of two types. Firstly, for multistep (especially multielectron) processes, the slope of the log kob-E plots (so-called "Tafel slopes ) can yield information on the reaction mechanism. Such treatments, although beyond the scope of the present discussion, are detailed elsewhere [13, 72]. Secondly, for single-electron processes, the functional form of log k-E plots has come under detailed scrutiny in connection with the prediction of electron-transfer models that the activation free energy should depend non-linearly upon the overpotential (Sect. 3.2). 

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