Electrode activation barriers

According to Eq. (23), the critical pore radius r greatly decreases with increasing electrode potential. It is seen that above a certain critical potential AE b the active barrier as well as the critical pore radius decreases steeply with anodic potential. This critical potential AE is the lowest potential of pore formation and below this potential the passive film is stable against electrocapillary breakdown because of an extremely high activation barrier and the large size of pore nucleus required. 

Figure 16 shows the effect of the potential of passivated electrode and the interfacial tension of film-free metal/electrolyte interface on the activation barrier for film breakdown. From Eq. (22), the minimum potential for film breakdown AE corresponding to A b = is given by... 

Figure 16. Activation barrier A for the formation of a breakthrough pore in a thin surface oxide film on metal as a function of electrode potential at two different surface tensions, om, of the metal/electrolyte interface.7The solid lines indicate the values of A b against Aand the dotted lines correspond to die critical potentials for the pore formation. ACd= 1 F m-2, a = 0.01 J m-2, h = 2 x 10-9 m, a, am = 0.41 J m 2 b, am 0.21 J m 2 (From N. Sato, J. Electmchem. Soc. 129, 255, 1982, Fig. 3. Reproduced by permission of The Electrochemical Society, Inc.)...

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

Figure 18. Dependence of activation barrier A f for the nucleation of a thin oxide film on the metal surface as a function of electrode potential. Ey is the equilibrium potential of anodic oxide formation.7 The solid line represents the value of A against and the dotted line corresponds to the critical potential for the film formation. AE = 0.2 V, Cd= -1Fm-2, am = 0.411 m 2, a -0.01 J m-2,...

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

This result is quite in contrast to the common expectation that the electrode potential changes the activation barrier at the interface which would result in a temperature independent transfer coefficient a. Following Agar s discussion (30), such a behavior indicates a potential dependence of the entropy of activation rather than the enthalpy of activation. Such "anomalous" behavior in which the transfer coefficient depends on the temperature seems to be rather common as recently reviewed by Conway (31). 

The latter discussion confirms the results of the potential dependence of the current in that the activation barrier for the hydrogen evolution reaction is, at least on copper and silver, not affected by the electrode potential. This behavior is, on the other hand, connected with the observation of straight lines in a Tafel plot. It would be premature to come up with a comprehensive model that would explain this behavior more experimental work is necessary to substantiate and quantify the effects for a larger variety of systems and reactions. A few aspects, however, should be pointed out. 

Providing that the interactions between the reactant and the electrode in the electrochemical transition state, and between the two reactants in the homogeneous transition state, are negligible ("weak overlap" limit), the activation barriers for reactions 10 and 11 will be closely related. 

For instance, following the dashed line, if the potential of the electrode is made more positive than E°, we increase the activation barrier for the reduction process by a n F- (E - E01), while the activation barrier... 

Figure 16 The transfer coefficient eras a measure of the symmetry of the activation barrier for a faradaic process. The electrode conditions are those cited in Figure 14...

It is important to note that as early as 1931, the density of electronic states in metals, the distribution of electronic states of ions in solution, and the effect of adsorption of species on metal electrode surfaces on activation barriers were adequately taken into account in the seminal Gurney-Butler nonquadratic quantum mechanical treatments, which provide excellent agreement with the observed current-overpotential dependence. 

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) ... 

Activation polarization is an activated process and possesses an activation barrier, just as described earlier in Figure 3.1. There are two parts to the activation process, either one of which can determine the rate of the reaction at the electrode. 

Changing the electrode potential to E = E2Gibbs energy curve of the charged species B. As a result of this, the forward activation barrier is now reduced by ae(El —E2), and hence the reaction rate increases. 

Figure 6.8. Gibbs energy profiles of a proton discharge process resulting in a metal-hydrogen bond formation. The difference in the Gibbs energy of adsorption of hydrogen between metal 1 to metal 2 lowers the activation barrier for the discharge and makes metal 2 the electrocatalytically more favorable (active) electrode material.

The oxygen/water half-cell reaction has been one of the most challenging electrode systems for decades. Despite enormous research, the detailed reaction mechanism of this complex multi-step process has remained elusive. Also elusive has been an electrode material and surface that significantly reduces the rate-determining kinetic activation barriers, and hence shows improvements in the catalytic activity compared to that of the single-noble-metal electrodes such as Pt or Au. 

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