Kinetics Tafel

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

This limit is called linear kinetics. On the other hand, if the surface overpotential is large, one of the exponential terms is negligible. This limit is called Tafel kinetics. The relationship was found empirically. In the anodic Tafel region... 

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. 

Since the ORR is a first-order reaction following Tafel kinetics, the solution of the mass conservation equation (eq 23) in a spherical agglomerate yields an analytic expression for the effectiveness factor... 

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Perry et al. [24] and Jaouen et al. [25] have provided useful diagnostic criteria. They concluded that cathodes controlled by either Tafel kinetics and oxygen diffusion in the agglomerate regions, or by Tafel kinetics and proton transport in the catalyst layer could result in double Tafel slopes. If the cathode was controlled by Tafel kinetics, oxygen diffusion, and proton transport all together, quadruple Tafel slopes would appear. 

Figure 4.33a shows an oveipotential that is controlled only by Tafel kinetics. Under Tafel kinetics, the reaction is reaction rate... 

While an ovapotential may be applied electrically, we are interested in the overpotential that is reached via chemical equilibrium with a second reaction. As mentioned previously, the oxidation of a metal requires a corresponding reduction reaction. As shown in Figure 4.34, both copper oxidation, and the corresponding reduction reaction may be plotted on the same scale to determine the chemical equilibrium between the two reactions. The intersection of the two curves in Figure 4.34 gives the mixed potential and the corrosion current. The intersection point depends upon several factors including (the reversible potential of the cathodic reaction), cu2+/cu> Tafel slopes and of each reaction, and whether the reactions are controlled by Tafel kinetics or concentration polarization. In addition, other reduction and oxidation reactions may occur simultaneously which will influence the mixed potential. 

Reactions (4.23) and (4.37) are controlled by Tafel kinetics (i.e., diffusion of the reactants or products does not limit the reaction rate) ... 

At the high current densities suggested by Figure 4.44b, titanium dissolution and copper oxidation may be controlled by concentration polarization rather than Tafel kinetics. Under concentration polarization, the current does not increase proportional to... 

Reference [23] describes a treatment of the secondary current distribution on the pattern scale in a case with two adjacent zones with different active-area densities. The development shows that, in the Tafel kinetic regime, the current distribution should depend on the geometry, the Wagner number, and the ratio of the two active-area densities. The Wagner number is based on the length scale of the pattern nonuniformity (for example, the distance from the center of zone (1) to the center of zone (2)) and based on the superficial current density. There is a primary current distribution in the case of Woj = 0, in which /gyp is uniform and i/ is inversely proportional to a. This represents the most extreme case of nonuniformity that pattern effects can produce. Fortunately, differences in active-area densities on patterned workpieces often exist across relatively short distances, and Wa is higher than 1. However, if there is a wide variation of the active-area density from place to place, the pattern-driven nonuniformity can still be severe, even across short distances. 

At the cathode surface, the active current density is related to the surface overpotential t/s by the Tafel kinetic expression. 

Estimate the maximum amplitude one should use for a potential perturbation for a system imder Tafel kinetics with ... 

The assumption of linear kinetics applies for f << tQ. Under assumption of Tafel kinetics, the current density at the electrode surface could be expressed as... 

For Tafel kinetics, valid for I io, the parameter J was defined to be a function of radial position on the electrode surface as... 

The local charge-transfer resistance for Tafel kinetics can be expressed in terms of parameters used in equation (13.49) as... 

For linear kinetics, Rt is independent of radial position, but, under Tafel kinetics, as shown in equation (13.52), Rt depends on radial position. From a mathematical perspective, the principal difference between the linear and Tafel cases is that and Rt are held constant for linear polarization whereas, for the Tafel kinetics. 

While the calculations presented here were performed in terms of solution of Laplace s equation for a disk geometry, the nature of the electrode-electrolyte interface can be imderstood in the context of the schematic representation given in Figure 13.5. Under linear kinetics, both Co and Rt can be considered to be independent of radial position, whereas, for Tafel kinetics, 1/Rf varies with radial position in accordance with the current distribution presented in Figure 5.10. The calculated results for global impedance, local impedance, local interfacial impedance, and both local and global Ohmic impedances are presented in this section. 

Figure 13.6 Calculated representation of the impedance response for a disk electrode under assumption of Tafel kinetics with / as a parameter. The value / = 0 corresponds to an ideally capacitive blocking electrode a) real part and b) imaginary part.

Figure 13.8 Calculated representation of the local impedance response for a disk electrode as a function of dimensionless frequency K under assumptions of Tafel kinetics with 7 = 1. (Taken from Huang et al. and reproduced with permission of The Electrochemical Society.)...

The calculated local impedance is presented in Figure 13.8 for Tafel kinetics with 7 = 1 and with radial position as a parameter. The impedance is largest at the center of the disk and smallest at the periphery, reflecting the greater accessibility of the periphery of the disk electrode. Similar results were also obtained for J = 0.1, but the differences between radial positions were much less sigiuficant. Inductive loops are observed at high frequencies, and these are seen in both Tafel and linear calculations for J = 0.1 and J = 1.0. ... 

The local Ohmic impedance Zg accounts for the difference between the loccil interfacial and the local impedances. The calculated local Ohmic impedance for Tafel kinetics with 7 = 1.0 is presented in Figure 13.9 in Nyquist format with normalized radial position as a pcirameter. The results obtained here for the local Ohmic impedance are very similar to those reported for the ideally polarized electrode and for the blocking electrode with local CPE behavior. ° ° At the periphery of the electrode, two time constants (inductive and capacitive loops) are seen, whereais at the electrode center only an inductive loop is evident. These loops are distributed around the asymptotic real value of 1/4. 

It is not possible to resolve this transcendental equation for the explicit rjo(jo) dependence. However, two limiting cases can be conveniently studied in the limit jo [Pg.486]

Fig. 12 Log-log plot of normalized current density versus exponent of normalized voltage losses incurred by the cathode catalyst layer (Uc = rjo), in the limit of fast oxygen diffusion (Sect. 8.2.3.4.3). This representation reveals the transition from the simple Tafel kinetics at jo

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