Tafel equations

Equations 6.11 and 6.12 have been extensively used to experimentally define both and p. Let us take the natural logarithm of Equations 6.11 and 6.12  

Julius Tafel (1862-1918) was a Swiss physical chemist, who made a number of contributions, including an experimentally discovered relationship between the rate of an electrochemical reaction and the applied potential. This relation is known as the Tafel equation. 

Inzelt, and F. Scholz, Electrochemical Dictionary, Springer, Berlin, Germany, 2008. 

FIGURE 6.7 An example of the Tafel plot. The current density and the exchange current density are A cm .  

In the kinetic region, when the activation overpotential AE and current density (j) are plotted in the form of AE versus logj, a straight line exits. This was found in 1905 and is called the Tafel plot  

Based on the thermodynamics, the Tafel plot was later found to be a simplified Buttler-Volmer equation when AE is larger than about 116 mV/n, (Bard and Faulkner 1980), where n, is the number of electrons involved in the rate-determining step (not necessarily equal to the number of electrons involved in one reactant molecule) and it is 1 for the ORR. For the ORR, the OCV is already more than 180 mV lower than the thermodynamic voltage the activation overpotential AE, will be even higher when there is a current flow. So, the activation overpotential AE, for the ORR should follow the Tafel relationship. Based on the thermodynamics, the Tafel relationship is 

The charge transfer coefficient represents what a portion of the input electrical energy is used to change the electrochemical reaction rate. When the linear plot of AE versus log) is extrapolated to AE = 0, the intercept at the logj axis is logj° then j° can be obtain. The slope of the plot is 2.3RT/(an,F), from which a can be obtained. For the HOR on Pt, a is around 0.5. For the ORR on Pt, a is normally between 0.1 and 0.7, depending on the reaction environment for general purposes, 0.5 can be used for estimation. 

The Tafel plot is valid only when AE is large enough (e.g., 116 mV/n ). If AEa is very small leading to AE ART/OrF) far smaller than 1 

Due to the extremely small j° for the ORR, the Tafel plot is valid whenever there is a current flowing through the cell. Since there is one electron involved in the rate-determining step for the ORR, i.e., n = 1, the Tafel slope at 298 K is around 118 mV per decade [(1000 x 2.3 x 8.31 x 298)7(0.5 x 1 x 96,485)]. 

The behavior of electrode systems, in absence of reactant transport limitations, typically displays an exponential relationship between the current and the overpotential, r. This is represented by the Tafel equation  

Where b is referred to as the Tafel slope and can be determined from the plot of overpotential as a function of log(i). Using the exchange current density, the Tafel equation for the cathodic reaction in the fuel cell is provided by 

For an electrochemical half-cell reaction, the overall relationship describing the complete current-potential characteristic is given by the Butler-Volmer equation  

It is important to understand that the forward and backward reactions can be driven to large values, even with a small at significant deviations from E°. This is important for the cathode reaction in the fuel cell, which has sluggish kinetics that must be overcome by large overpotentials on the cathode. 

For very small overpotentials, the exponential function can be represented by a linear equation, and the ratio of overpotential to current is referred to as 

The activation polarization takes place from kinetics impediments of the charge-transfer reaction occurring at the electrode/electrolyte interface this form of kinetics is better understood applying the transition state theory. 

JA and IA are the anodic current density and the anodic current, respectively Jc and Ic are the cathodic current density and the cathodic current, respectively S is the electrode surface area 

If the transition state theory is applied, the reaction takes a course comprising an activated complex, where the rate-limiting step is the dissociation of the activated complex [6,10,66,123,124], Applying Equation 8.52 for a first-order reaction, the net current flow is given by the Butler-Volmer equation 

When the overpotential is high and positive, corresponding to the anode during electrolysis 

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The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

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

Overvoltage. Overvoltage (ti. ) arises from kinetic limitations or from the inherent rate (be it slow or fast) of the electrode reaction on a given substrate. The magnitude of this value can be generally expressed in the form of the Tafel equation... 

The activation overpotential, and hence the activation energy, varies exponentially with the rate of charge transfer per unit area of electrode surface, as defined by the well-known Tafel equation... 

In order to evaluate from the Tafel equation it must be expressed in terms of E. By definition... 

Initially, the curve conforms to the Tafel equation and curve AB which is referred to as the active region, corresponds with the reaction Fe- Fe (aq). At B there is a departure from linearity that b omes more pronounced ns the potential is increased, and at a potential C the current decreases to a very small value. The current density and potential at which the transition occurs are referred to as the critical current density, and the passivation potential Fpp, respectively. In this connection it should be noted that whereas is determined from the active to passive transition, the Flade potential Ef is determined from the passive to active transition... 

This is commonly known as the high field equation. It is of similar form to the Tafel equation for activation controlled electrochemical reactions with... 

As the corrosion rate, inclusive of local-cell corrosion, of a metal is related to electrode potential, usually by means of the Tafel equation and, of course, Faraday s second law of electrolysis, a necessary precursor to corrosion rate calculation is the assessment of electrode potential distribution on each metal in a system. In the absence of significant concentration variations in the electrolyte, a condition certainly satisfied in most practical sea-water systems, the exact prediction of electrode potential distribution at a given time involves the solution of the Laplace equation for the electrostatic potential (P) in the electrolyte at the position given by the three spatial coordinates (x, y, z). 

Referring to Fig. 11.5b, the initial rise in current corresponds to simple metal dissolution, expressed quantitatively through the Tafel equation relating potential and current logarithmically, and for multi-grained metals... 

Tafel equation, 14 Tafel plot, 15 Tetrathiafulvalene, 179 Thallium, 85... 

Conway, B. E. The Temperature and Potential Dependence of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation 16... 

It follows when Eqs. (6.5) and (6.12) are compared that the value of the empirical constant a in the Tafel equation is given by... 

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. 

It can be seen from Fig. 15.2 that in semilogarithmic plots of AE vs. log/, the polarization characteristics are linear [i.e., obey the Tafel equation (6.3)]. Slopes b practically coincide for most metals and have values of 0.11 to 0.13 V. However, the absolute values of polarization recorded for a given current density (CD) vary within... 

The shape of polarization curves for metals with low polarizability depends primarily on concentration polarization. In the case of highly polarizable metals, where activation polarization can be measured sufficiently accurately, the polarization curve can usually be described by an equation of the type (6.3) (i.e., by a Tafel equation). For metals forming polyvalent ions, slope b in this equation often has values between 30 and 60 mV. 

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). 

Whereas is relatively easy to determine from the calculated binding energies, it is not easy to measure experimentally, since the measured potentials are always related to a specific current. Therefore, in order to compare directly with experiment, we have to calculate polarization curves, i.e., the current. The link between Gqrr and the current is the Tafel equation. 

Applying the Tafel equation with Uq, we obtain the polarization curves for Pt and PtsNi (Fig. 3.10). The experimental polarization curves fall off at the transport limiting current since the model only deals with the surface catalysis, this part of the polarization curve is not included in the theoretical curves. Looking at the low current limit, the model actually predicts the relative activity semiquantitatively. We call it semiquantitative since the absolute value for the prefactor on Pt is really a fitting parameter. 

Plotting the overpotential against the decadic logarithm of the absolute value of the current density yields the Tafel plot (see Fig. 5.3). Both branches of the resultant curve approach the asymptotes for r RT/F. When this condition is fulfilled, either the first or second exponential term on the right-hand side of Eq. (5.2.28) can be neglected. The electrode reaction then becomes irreversible (cf. page 257) and the polarization curve is given by the Tafel equation... 

The above-described theory, which has been extended for the transfer of protons from an oxonium ion to the electrode (see page 353) and some more complicated reactions was applied in only a limited number of cases to interpretation of the experimental data nonetheless, it still represents a basic contribution to the understanding of electrode reactions. More frequently, the empirical values n, k° and a (Eq. 5.2.24) are the final result of the investigation, and still more often only fcconv and cm (cf. Eq. 5.2.49) or the corresponding constant of the Tafel equation (5.2.32) and the reaction order of the electrode reaction with respect to the electroactive substance (Eq. 5.2.4) are determined. 

This is the Tafel equation (5.2.32) or (5.2.36) for the rate of an irreversible electrode reaction in the absence of transport processes. Clearly, transport to and from the electrode has no effect on the rate of the overall process and on the current density. Under these conditions, the current density is termed the kinetic current density as it is controlled by the kinetics of the electrode process alone. 

Table 5.5 Constants a and b of the Tafel equation and the probable mechanism of the hydrogen evolution reaction at various electrodes with H30+ as electroactive species (aH3o+ ) (According to L. I. Krishtalik)... 

The anodic evolution of oxygen takes place at platinum and other noble metal electrodes at high overpotentials. The polarization curve obeys the Tafel equation in the potential range from 1.2 to 2.0 V with a b value between 0.10 and 0.13. Under these conditions, the rate-controlling process is probably the oxidation of hydroxide ions or water molecules on the surface of the electrode covered with surface oxide ... 

In addition to hydrocarbons, other products have also been found, especially in the reactions of the higher fatty acids. In steady state, the current density obeys the Tafel equation with a high value of constant b 0.5. At a constant potential the current usually does not depend very much on the sort of acid. The fact that the evolution of oxygen ceases in the... 

In Moscow Power Engineering Institute (TU) portable air aluminum batteries with saline electrolyte were developed [7, 18, and 20], In our devices, the air electrodes consist of two layers. Diffusion layer contains PTFE, carbon black and metal screen active layer consists of activated carbon and PTFE. At 293 K and the range of current density 2-25 mA/ cm2 dependence of cathode potential E (in H-scale) upon current density J (Figure 2) may by written by the Tafel equation (12). 

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