Tafel equation cathodic reaction

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. 

Equation (6.13), in fact, reflects the physical nature of the electrode process, consisting of the anode (the first term) and cathode (the second term) reactions. At equilibrium potential, E = Eq, the rates of both reactions are equal and the net current is zero, although both anode and cathode currents are nonzero and are equal to the exchange current f. With the variation of the electrode potential, the rate of one of these reactions increases, whereas that of the other decreases. At sufficiently large electrode polarization (i.e., deviation of the electrode potential from Eg), one of these processes dominates (depending on the sign of E - Eg) and the dependence of the net current on the potential is approximately exponential (Tafel equation). 

In the range of potential away from the equilibrium potential, the backward reaction current can be disregarded, and the anodic and the cathodic reaction currents are expressed, respectively, by the Tafel equations described in Eqn. 9-11 ... 

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

We recall that the Tafel equation was originally observed for the hydrogen evolution reaction on mercury. We should therefore have an equation similar to Eq. 41E to describe the current-potential relationship. For a single cathodic step we wrote ... 

The most reliable data are from studies of hydrogen evolution on mercury cathodes in acid solutions. This reaction has been studied most extensively over the years. The use of a renewable surface (a dropping mercury electrode, in which a new surface is formed every few seconds), our ability to purify the electrode by distillation, the long range of overpotentials over which the Tafel equation is applicable and the relatively simple mechanism of the reaction in this system all combine to give high credence to the conclusion that p = 0.5. This value has been used in almost all mechanistic studies in electrode kinetics and has led to consistent interpretations of the experimental behavior. It... 

The kinetics of this reaction on stainless steel cathode in a wide range of current densities up to very high i can be described by the Tafel equation Ec = —1.25 — 0.14 log i [27], where Ec (in volts) is referred to a standard hydrogen electrode (SHE), i is expressed in amperes per square centimeter. 

Tafel plots of E vs. log /, such as those shown in Figure 26.31, are often used to determine the rate of a corrosion process. For a corroding metal (anode) that is driven by a single kinetically controlled reduction reaction (such as hydrogen evolution from an acid-containing solution), one can write the following Tafel equations for cathodic proton reduction and anodic metal dissolution ... 

The net (or experimental) anodic and cathodic polarization curves in Fig. 6.2 also can be expressed with Ecorr and Icorr as parameters. This form is used in establishing expressions that provide the basis of one of the experimental techniques for determination of Icorr. At the specific condition that E = Ecorr and Iex = 0, Iox M = Ired x = Icorr therefore, the Tafel expressions for the currents of the individual anodic and cathodic reactions can be equated, or... 

Tafel Curve Modeling (Ref 4, 5). Equation 6.5 provides the form of the experimental polarization curve when the anodic and cathodic reactions follow Tafel behavior. The equation accounts for the curvature near Ecorr and Icorr, which is observed experimentally. Physically, the curvature is a consequence of both the anodic and cathodic reactions having measurable effects on Iex at potentials near Ecorr. Tafel-curve modeling uses experimental data taken within approximately 25 mV of Ecorr where the corrosion process is less disturbed by induced corro-... 

It is assumed that a single cathodic deposition reaction occurs and that the current density normal to the cathode surface is described by the concentration dependent Tafel equation,... 

Equation (122) was empirically proposed in 1905 by Tafel (3). The same form of equation holds for an anodic reaction at overpotentials high enough for the rate of the cathodic reaction to be neglected in comparison with the forward anodic current density. 

Kaesche and Hackerman (13) have investigated the inhibition of several aliphatic and aromatic amines on pure iron corroding in IN hydrochloric acid. These authors observed in thirteen out of fourteen cases that the inhibition was both anodic and cathodic, albeit predominantly anodic. The exception was methylamine which acted only cathodically. In the case of the corrosion inhibition on pure iron by B-naphthoquinoline in sodium sulfate/sulfuric acid solution (13). one observes a simple parallel shift of the anodic and cathodic Tafel lines towards smaller values of current density. Here the effect is almost symetrical, indicating that this inhibitor acts to the same extent upon anodic and cathodic reaction rates. Therefore, the effect of B-naphthoquinoline can be explained on the basis that its adsorption blocks a fraction 0 of the metal surface for all electrode reactions. If equation 9 describes the external polarization behavior in terms of a function of the partial current potential relationship for the anodic and cathodic reactions in the usual terms ... 

Equation (41) is identical in form to Eqs. (18 and 24). The curve is centered around Ecorr rather than and the current density at zero overpotential is icorr instead of io- This expression, along with the theory for mixed potentials, was derived by Wagner and Traud, and therefore will be referred to as the Wagner-Traud equation. As described in the Chapter 7.3.1.2 on experimental techniques, the Wagner-Traud equation is used in software analysis packages that accompany modem computer-controlled potentiostats. A nonlinear least squares fit of this equation to the experimental data provides values of corr. corr. ha. and he vvith the assumption that perfect Tafel behavior is observed for both the anodic and cathodic reactions, and that the extrapolations of the Tafel portions of the curves both intersect at the corrosion potential. 

It should be noted that the Stern-Geary equation is dominated by the smaller of the Tafel slopes. Often in corrosion, the cathodic reaction is diffusion limited oxygen reduction, so be = 00. In that case, the corrosion rate is given by ... 

Comparison of the anodic and cathodic Tafel constants shows that when a = 0.5, a = — a -, b = — b. Tables 3.2 and 3.3 list values of the Tafel constants for cathodic hydrogen evolution at T= 20 it 2 ° C on different metals and the effect of electrode materials and solution composition on oxygen overpotential [21]. The Tafel equation has been confirmed for numerous cathodic and anodic reactions, and its use is illustrated in the examples and case studies that follow. 

Solution pH, velocity, and oxidizer concentration change the properties of the anodic curve of the active-passive metal. For example, the equilibrium potential of the cathodic reaction shifts according to the Nemst equation in the noble direction by increasing the oxidizer concentration. Mixed potential theory, in this case, may predict the intersection of the cathodic and anodic Tafel fines and corrosion rate or extent of passivation of the metal. 

Calculation of exchange current density for cathodic reaction using the Tafel equation ... 

Since the surface of the metal is equipotential, the hydrogen reduction on the metal has the same overpotential. Thus, the Tafel equations for the cathodic reaction for each of the metals in the aUoy are ... 

Figures 14.6 and 14.7 depict the polarization curves of iron in weak HCI solutions, when the cathodic reaction is the hydrogen evolution reaction and when the cathodic process is the reduction of oxygen, respectively. In the former case, both the anodic and the cathodic processes are charge-transfer controlled, represented by the Tafel equation as ...

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