Tafel slopes equations

The plot of overpotential versus current density in log scale gives the parameters a, b, and io (h is called the Tafel slope). Equation 3.28, which is only valid for i > io, suggests that the exchange current density io can be also regarded as the current density value at which the overpotential begins to exert its function to make possible the electrochemical reaction, becoming different from zero. 

If the cell current is high, the polarization curves of CLs are similar, when either feed or ion transport is insufficient. In both the cases, the curve exhibits doubling of the Tafel slope (Equations 4.88 and 4.134). This makes it difficult to distinguish the physical origin of this doubling, by measuring the polarization curve only. 

If the oxygen reduction is the counter reaction of metal dissolution, its kinetics is often determined by diffusion due to the small solubility of O2 gas and long diffusion distances especially in unstirred solution. In this case, the cathodic reaction gets potential independent at negative potentials with a diffusion-limited cathodic current density Ido2 the vicinity of the rest potential (Figure 1.42). In this situation, the corrosion current density ic is equal to the limiting cathodic current density ip,02/ and Equation 1.159 simplifies to Equation 1.164, which becomes Equation 1.165 for n -> 0 (E —> Er). Hence ic can be calculated from Rp and the anodic Tafel slope (Equation 1.166). 

Tafel equation Tafel kinetics Tafel slope Taffy process Taft s SV function Tagamet [51481-61-9] d-Tagatose... 

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... 

Fig. 19.10 Plots of the right-hand side of equation 19.16 w. AE = E combinations of Tafel slopes, (a) constant at 120 mV, varied, and (b) b ...

Figure 19.10a shows a theoretical plot of the right-hand side of equation 19.16 vs. AE in which the cathodic Tafel slope has been assumed to be constant at 120 mV and the anodic Tafel slope to have the arbitrary slopes of 40, 60 and 120 mV. It can be seen that linearity over a range of positive and negative potentials AE is achieved only when b = and that linearity is confined to AE 0 when b and b differ. 

Determine from this plot the Tafel slopes 6, and 6 by curve fitting using the theoretical curves calculated for various values of 6 and 6,.. Calculate from equation 19.14 using the Rp, value evaluated in Step 1 and the Tafel slopes determined in Step 3. 

Attention should be drawn to the signs in equations 20.66 and 20.67 and it should be noted that the Tafel slope b is always positive for an anodic process and negative for a cathodic process and that the constant a is of opposite sign to the slope. 

These are the coefficients that determine the Tafel slope of the log / against q curve of a multistep reaction, and they are of fundamental importance in providing information on the mechanism of the reaction. Equations 20.86 and 20.87 are of the same form as equations 20.59 and 20.58 that were derived for a simple one-step reaction involving a symmetrical energy barrier, and under these circumstances equations 20.90 and 20.91 simplify to... 

From the magnitude of the Tafel slope 3tj/3 log / ( 0-12V), the magnitude of dr)/d In ( 0-24 V) and the linearity of the J vs. /i curves for pure iron in H2SO4 and NaOH at various temperatures in the range 18-80°C, Bockris, et al. concluded that the mechanism conformed to the reaction sequence shown in equation 20.107. 

Figure 11 exemplifies experimentally observed dependences of the current density on the imposed voltage at a constant oxide thickness. It is seen that they fit both equations fairly well. Tafel slopes [Eq. (44)] are in the range of 0.4 V cm-1 dec-1. All other... 

Tafel s equation (eqn (30)) is accurate at large overpotentials, but fails as q approaches zero. The Tafel plot is obtained by plotting rj vs. log i, with b referred to as the Tafel slope. The Tafel slope is a function of the transfer coefficients and temperature, where... 

In this notation, anodic current is positive, while cathodic current is negative. As the later section on oxygen reduction will show, the Tafel slope can change with overpotential. This is because the Butler-Volmer law only applies to outer-sphere reactions. Although it can describe electrode reactions, the equation does not account for repulsive interactions of the adsorbates or changes in the reaction mechanism as potential is changed. 

The equations used in these models are primarily those described above. Mainly, the diffusion equation with reaction is used (e.g., eq 56). For the flooded-agglomerate models, diffusion across the electrolyte film is included, along with the use of equilibrium for the dissolved gas concentration in the electrolyte. These models were able to match the experimental findings such as the doubling of the Tafel slope due to mass-transport limitations. The equations are amenable to analytic solution mainly because of the assumption of first-order reaction with Tafel kinetics, which means that eq 13 and not eq 15 must be used for the kinetic expression. The different equations and limiting cases are described in the literature models as well as elsewhere. 

The use of the impedance technique in the study of polymer coated steel, has been thoroughly described elsewhere. The present paper compares this technique with that of harmonic analysis, originally proposed by Meszaros ). The authors have presented preliminary data using the latter technique(3) wherein the early stages of polymer breakdown have been studied. The current paper extends this work to polymers which have been immersed for a considerable period of time. The harmonic method gives information not available from the impedance technique in the Tafel slopes and the corrosion current are directly measurable. A brief summary of the harmonic method and the equations used are given below. 

Equation (7.17) is the Tafel equation and expresses the way in which the applied potential difference operates to enhance the reaction rate [22]. Since the unit of q is volts, the units of a and b are also volts a is called the Tafel intercept, that is, the overpotential at 7 = 1 (which depends on the units of 7, A or mA or pA) b is known as the Tafel slope, that is, the variation of q per decade of current. 

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. 

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 ... 

This is the steady-state current which is theoretically predicted if stage 1 is the rate-determining step in the sub-stages sequence represented in Equations 4.8 1.12. An important parameter to compare both in theory and experimentally is the Tafel slope or the transfer coefficient which results from it. Therefore, Equation 4.30 has to be written in a form that contains only one exponential term. Since the considered I-E curve is an oxidation wave, the effect of the reduction (second term in the right-hand part of Equation 4.30) will be negligible with potentials that are situated sufficiently far away from the equilibrium potential, and for the anodic current the following applies ... 

Equation 4.45 cannot explain the experimentally observed influence of the pH and predicts a Tafel slope of 1 and an influence of the oxygen concentration, which was not experimentally observed. The rate equation for a rate-determining fourth stage of the reaction sequence was calculated with Equations 4.41,4.32,4.21,4.22 and 4.24, and, under the additional condition k 3 k4 and/or k 2 k4, the following applies ... 

When comparing the experimental Tafel slopes and the dependency of the current of hydroxide ions and hydrogen peroxide concentration to what Equation 4.47 theoretically predicts, mechanism 2 with stage 5 as RDS can be considered as a correct sub-mechanism and this over the entire potential area. The predicted reaction orders amount to 3/2 and -1/2 for hydrogen peroxide and OH , respectively. In section4.9, it is verified whether a combination of mechanism 1, where stage 4 or 5 is the RDS, with mechanism 2, where stage 5 is the RDS, corresponds to the experimental data. 

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