Tafel slope doubling

The factor 2 on the right-hand side manifests the effect of Tafel slope doubling. As discussed above, at high currents, owing to poor ionic conductivity of the CL, ions do not penetrate deep into the catalyst layer and the electrochemical conversion runs at the electrolyte (membrane) interface. This regime of conversion requires a much higher polarization voltage. Note that the transport terms in Eqs. (23.35) and (23.37) coincide. 

This figure shows the physical origin of the Tafel slope doubling in the high-current regime (see the next page). Poor proton transport induces a... 

The factor on the right side of Eq. (2.59) is 2b instead of b. Equation (2.59) exhibits the effect of apparent Tafel slope doubling discussed above. 

In dimensional form, Equation 4.87 explicitly exhibits the Tafel slope doubling ... 

The factor 2 exhibits the Tafel slope doubling at high currents resulting from insufficient rate of proton transport in the CCL. In dimensional form. Equation 4.133 reads... 

Figure 4.16b shows the physical origin of the effect of Tafel slope doubling. Low ap forces the electrochemical conversion to occur close to the membrane, where the expenditure for the ionic transport is lower. The nonuniform electrochemical conversion appears to be expensive in terms of rjo. 

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. 

It is known that double-layer effects are the most pronounced in the reaction of multivalent ions in a dilute solution. According to the calculation of Grahame, d°HP A3 potential region far from the pzc. Evaluate the cathodic and anodic Tafel slope values for the reaction... 

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. 

For redox processes, there is some evidence of Tafel slope curvature for certain processes under certain circumstances.228,229 These may be a partial result of double layer effects.196 In other cases experimental Tafel plots which are close to linear appear.177 230 The controversial question of P possibly varying with temperature231 232 will not be discussed here, although double layer effects196 may often be responsible. 

A relatively constant Tafel slope for reactions not involving adsorption, and those involving adsorption with complete charge transfer across the double layer, distorted by second order effects, may also be explained in terms of a non-Franck-Condon process. Since adsorbed intermediates in charge transfer processes also show adsorption energies depending on potential in the same way as the potential energy barrier maxima, these should also follow the same phenomena. 

Tafel slopes for the anodic and the cathodic process double-layer capacitance ( lF/cm ) capacitance of the Helmholtz double layer capacitance of the diffuse double layer double-layer capacitance at 0 = 0 double-layer capacitance at 0 = 1 adsorption pseudocapacitance (llF/cm ) adsorption pseudocapacitance derived from the Langmuir isotherm... 

High r factors are, however, not without some other complications since they imply porosity of materials. Porosity can lead to the following difficulties (a) impediment to disengagement of evolved gases or of diffusion of elec-trochemically consumable gases (as in fuel-cell electrodes 7i2) (b) expulsion of electrolyte from pores on gas evolution and (c) internal current distribution effects associated with pore resistance or interparticle resistance effects that can lead to anomalously high Tafel slopes (132, 477) and (d) difficulties in the use of impedance measurements for characterizing adsorption and the double-layer capacitance behavior of such materials. On the other hand, it is possible that finely porous materials, such as Raney nickels, can develop special catalytic properties associated with small atomic metal cluster structures, as known from the unusual catalytic activities of such synthetically produced polyatomic metal clusters (133). 

Deviation of 60 mV/decade can be seen in Table 5.3 under different conditions. In addition to the potential distribution in the two double layers, there are two other possible causes for the deviations. The first is possible potential drops in other parts of the electrical circuit, e.g., in the electrolyte and semiconductor. The second possibility is the change of effective surface area due to the formation of a porous silicon layer during the course of i-V curve measurement. In addition, if the reaction is controlled by a process involving the Helmholtz layer, the apparent Tafel slope may be smaller than the 60 mV/decade as would be expected from the formula, B = kTI23anq, because the effective dissolution valence n is not a constant with respect to potential but varies from 2 to 3 in the exponential region. 

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

The Double Tafel Slope as a Signature of Transport Limitations The kind of transport limitations that prevail depend on the structure of the catalyst layer. If it has insufficient porosity, but a continuous... 

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