Tafel equation reactions

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). 

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... 

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... 

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

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). 

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)... 

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... 

These reaction currents given by Eqns. 7-32 and 7-33 are formally in agreement with the Tafel equation of Eqn. 7-19 obtained by experimental observations. Note that the rate equations in Eqns. 7-32 and 7-33 apply to the forward reaction only and disregard the backward reaction rate. 

The transfer currents of redox electrons and redox holes represented by Eqns. 8-63 and 8-64 are formally in agreement with the Tafel equation given by Eqn. 7-32. However, the Tafel constant (the transfer coefficient) a equals one or zero at semiconductor electrodes in contrast with metal electrodes at which a is close to 0.5. From Eqns. 8-64 and 8-65 for reaction currents, the Tafel constants is obtained as defined in Eqns. 8-66 and 8-67 ... 

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 ... 

Activation Polarization Activation polarization is present when the rate of an electrochemical reaction at an electrode surface is controlled by sluggish electrode kinetics. In other words, activation polarization is directly related to the rates of electrochemical reactions. There is a close similarity between electrochemical and chemical reactions in that both involve an activation barrier that must be overcome by the reacting species. In the case of an electrochemical reaction with riact> 50-100 mV, rjact is described by the general form of the Tafel equation (see Section 2.2.4) ... 

St.eadyr .t te Measurements. In order to obtain a more quantitative understanding of the process resulting in the inhibition of the 0 reduction reaction, Tafel measurements were made. The mass transport corrected Tafel equation [35] ... 

Butler in 1924 developed the idea that the Nemst equilibrium potential for an electrochemical process is the potential at which the forward and back reactions proceed at the same rate [37]. Following this, Bowden and Rideal [38] introduced the term jo as the value of the forward and back current density at the reversible Nemst potential and wrote the Tafel equation in the form of Equation 1.6. 

Linear kinetic behaviour according to the Tafel equation indicates a linear free energy relationship between activation energy and driving force for the reaction and the value of a is defined by Equation 1.11. Methods based on polarography or linear sweep voltammetr) are available for the determination of a in the electron... 

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. 

The Butler-Volmer (BV) approximation is the simplest approach to model and capture the essential features of the empirical Tafel equation. It considers an electrochemical half-cell reaction as an activated process, with the forward and backward reaction rates following an Arrhenius type law according to... 

In chemical reaction kinetics, the basic measurement is that of rate (v) per unit area as a function of temperature, with application of the classical Arrhenius equation, v = Ae E/RT Electrochemical reactions also vaiy with temperature (see Section 7.5.14). However, the basic measurement for electrochemical kinetics is the rate as a function of potential36 at constant temperature, with application of the corresponding Tafel equation, v = A e ar F/RT. 

Another point to be considered is what parameters are really important for the evaluation of the electrocatalytic activity. It is well known that, apart from mass transfer and ohmic loss problems, the overpotential can be related to the reaction rate by the (Tafel) equation ... 

The detrimental consequence of liquid water on the CL voltage loss primarily comes from the impeded oxygen transport and reduced electrochemically active area as explained above which can be described by the electrochemical kinetics in terms of the reaction current density,/, through the Tafel equation.27... 

If the reaction proceeds via an electron transfer from the plane RP (see Fig. 11.2), one could see a factor (/) in the Tafel equation, so that ... 

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