Tafel law

COads + OHads recombination occurs in an electrochemical step and follows a Tafel law with a 0.5, and is particle-size-dependent when the size decreases to 1.8 nm, feox falls by about an order of magnitude. 

However, the form of (9.38) is not that of the first (cathodic) term in the familiar Butler-Volmer equation (7.24), which itself does indeed give the experimentally required Tafel law at 1) > RT/F. 

The growth of the components ip and i is restricted by the corresponding limiting currents (see Fig. 6b). Thus, for semiconductors of, say, n-type, the dependence of the hole current ip on

cathodic polarization, and must be restricted by the limiting current ipm of minority carriers under anodic polarization. 

Once one plots the geometry of the transition state with two geometrical coordinates, then in order to locate the transition state one needs to consider two properties of the transition state. One of these, cr, describes the symmetry of the transition state. We choose the symbol a since it is conventionally used in electron transfers (Tafel Law) and in proton transfers (Bronsted Law). Low values of a mean that the transition state is reactant-like, and values of cr approaching unity means that the transition state is product-like. The value of a is of course connected with the Hammond postulate for the symmetry of the transition state. It is helpful now to replace the geometric co-ordinates used hitherto in Figs. 1-4 with bond-order co-ordinates, tj, that measure the degree of nucleophilic participation. These new co-ordinates are defined in (12) and (13), where CP refers to the appropriate caged pair. The relation between bond... 

These last two expressions are forms of the Tafel law. They are an example of a linear free energy relationship (linear relation between a kinetic and a thermodynamic parameter) the parameters in this case being the flux (or the current) and the potential. 

The Tafel law can be corrected for transport effects, enlarging the region of the voltammetric curve that can be utilized in Tafel plots. 

For an irreversible reaction and for overpotentials corresponding to the exponential region, the Tafel law is... 

Na(Hg). The dependence of the rate of reaction for acetylene reduction by the Zn amalgam on the induced potential is shown in Figure 7. It is apparent that the dependence follows the Tafel law nv = A + ctE (here v is the rate and E is the induced potential). 

Example 8.1 Guideline for Linearity We wish to establish a guideline for the perturbation amplitude needed to maintain linearity under potentiostatic regulation. An electrochemical system that follows a Tafel law is polarized at a potential V. If a large potential sinusoidal modulation is superimposed, write the current response in the form of a Taylor series and calculate the complete expression of the dc current. By considering only the first three terms of the Taylor series, write the expression cf the current under the form of the first three harmonics. 

Dimensionless Form of Basic Equations At rjo > 3b the rate of current generation is well approximated using the Tafel law given by Eq. (46). It is convenient to rewrite the basic set of equations in an entirely dimensionless form [17],... 

Sufficiently far from equilibrium, which is the only interesting regime for current generation, the Tafel law (129), (130) with effective parameters is used in the simulations. Measurements performed on model electrocatalysts suggest different values for these parameters depending on the particular catalysts used or just their different structure. The mesoscopic effects in electrocatalysis are the hot topic nowadays [127, 187-189] and they are probable candidates for one of the reasons of this variance. The main cause of this variance may be associated with the complicated interplay between adsorption and reaction stages, and a modeler interested in fuel... 

We see that this simple model well describes the characteristic S-shaped profiles of local polarization curves far from the channel inlet, detected in experiments [197, 200]. Physically, these maxima result from the effect of oxygen starvation . Qualitatively, Eq. (154) shows that local current is a product of two factors. The preexponential factor a describes the growth of local current with the increase in rj due to exponential dependence of the rate constant of ORR on rj (Tafel law). The second (exponential) term in Eq. (154) describes oxygen consumption upstream from the given point z. 

Note that lezyl should not be too small—the Tafel law holds only beyond a bias that satisfies kz > k[jT. When rj —> 0 the net current which results from the balance between the direct and reverse reactions, must vanish like rj. This imphes that the Tafel behavior is always preceded by a low bias Ohmic regime. 

Among the factors that may determine the geometric shape of an experimental polarization curve and the region where the validity of the Tafel law begins to be evident, are the quantities a and fi. The influence these parameters exert on the graphic shape of a polarization curve is discussed in some studies [37, 38]. 

Examination of this relation shows that the difference between the actual trend of the polarization curve and the one conforming to the Tafel law increases with increasing the ohmic drop contribution. It also shows that, in the case of an experimental curve, the parameters to be determined are generally and R,. 

The importance of the relation (23) lies in the fact that it can be used for the evaluation of the solution resistance R , adopting the numerical technique of successive approximations and assuming that the electrochemical behaviour of the system under examination is described by the Tafel law. 

At the level of single agglomerates, cf. Figure 2.1b, complex distributions of reactants, reaction rates, and electrode potential emerge, mainly caused by electrostatic effects. These effects lead to a modified Tafel law equal in form... 

In the case a = 1, Equation reduces to the original Tafel law with to the uniform reaction rate distribution. 

A modified Tafel law can be written for the current-voltage performance... 

Fuc accounts for the deviations form the generic Tafel characteristics. These deviations are mainly affected by L and a. For a close to 1, catalyst utilization becomes uniform, Fuc 1 and the unmodified Tafel law is recovered,... 

At the agglomerate level, discussed in Section 2.5, electrostatic effects determine the radial distributions of proton concentrations and electrode potential. Using these distributions in the Tafel law gives the resulting distribution of the electrochemical rate. It depends on the transfer coefficient a, how uniformly catalyst particles are utilized in the wetted pores of agglomerates. Uniform utilization and, thus, effectiveness factors close to 1 are obtained for a 1. 

One of the first analytical models of CCL was developed by Springer and Gottesfeld [6], based on Pick s equation for oxygen transport and Tafel law for the rate of ORR. A similar approach was then used by Perry, Newman and Cairns [5] and by Eikerling and Komyshev [7]. 

For the rate of ORR, we employ the Tafel law with a first-order dependence on oxygen concentration ... 

The overpotential terms of Equations (17.5) and (17.6) are the driving forces of the electrochemical reaction. The most commonly used kinetic expression in electrochemistry is undoubtedly the Tafel law, which predicts an exponential increase of the current density of the desired reaction, Ia, with the electrode overpotential. For the anodic reaction of Equation (17.1) ... 

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