Barrierless and Activationless Processes

Let us now consider, using a phenomenological approach, two limiting cases, namely, highly exothermic and highly endothermic reactions. We shall proceed from the well-known dependence of the activation energy of an electrode reaction on overpotential, which has already been discussed above  

Experiments show that the transfer coefficient a is constant in a certain range of potentials. In many cases it has a value close to 

The activation energy of a forward process decreases with an increase in the overpotential on the other hand, for the reverse reaction it increases  

It follows from thermodynamics that for the same potential a + 6 = 

Let us consider a discharge reaction, for example, a cathodic reaction. Since its activation energy at a given potential is finite and since it decreases with increasing overpotential, it evidently 

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Subsequently, Marcus extended his theory to electrochemical electron transfer reactions/ " However, the role played by the electron energy spectrum in the electrode in these works was not elaborated. All the calculations were performed for a simplified model, where the potential energy surfaces for different electronic states were replaced by two potential energy surfaces (one for the initial state and one for the final state). Further calculations have shown that such considerations do not enable us to explain the fact that the transfer coefficient, a, for electrochemical reactions takes values in the interval from 0 to 1. In particular, it does not enable us to explain the existence of barrierless and activationless process (see Chapter 3 by Krishtalik in this volume). 

The quantum mechanical theory leads to a number of conclusions in respect to the kinetics of electrochemical reactions, in particular to the hydrogen evolution reaction. These conclusions are, to a certain degree, opposite to those of the classical approach. Thus, the consistent incorporation of the electronic energy spectrum in the electrode in the theory leads to the conclusion that barrierless and activationless transitions should be observed under certain conditions. In the theories which consider transitions to only one electronic energy level (the Fermi level), the transition probability should increase, reach a maximum, and then decrease with decrease of the reaction free energy. Experiment shows the existence of the barrierless and activationless processes. 

Initially, in the theory of barrierless and activationless processes, it was postulated that the activation energy varies monotonically with the potential after has decreased all the way to zero, its increase was considered impossible. Corroboration of this monotony principle can be found when the energy spectrum of electrons in a metal is taken into account. 

The deduction as to the preferential participation of electrons from the Fermi level (or, to be more precise, from a band several kT wide near this level, as was first shown by Gerischer ) holds true only in the case of an ordinary discharge, but is quite different with respect to barrierless and activationless processes. 

Consider now some specific features of the kinetics of barrierless and activationless processes. At a constant potential and for invariant double-layer structure, the discharge rate varies directly with the discharging particle concentration. This, of course, applies to any discharge process, be it an ordinary, barrierless or activationless one. If, however, we make a comparison at a constant overpotential, rather than at a constant potential, the relations... 

Fig. 7.5. Potential energy curves for barrierless and activationless processes. The horizontal lines show the energy levels of the reagents before they approach the optimal distance for the reaction.

In view of the possible existence of three types of electrode processes, namely, barrierless, ordinary and activationless, the polarization curve can be as shown schematically in Figure 6. The possibility of experimentally examining a selected portion of the curve depends on the kinetic characteristics of the process, in particular, its energetics. 

We can thus expect in principle that every electrode (and not only an electrode) process can be realized in three forms barrierless, ordinary, and activationless. If we ignore the complications associated with the influence of other stages of the reaction, the... 

Some authors[86,87] consider that the concept of barrierless processes was introduced by Despic and Bockris[84]. As a matter of fact, however, in this paper, which appeared somewhat later than our publication[85], the authors discuss only a tendency to an activationless process and not the reverse case of a barrierless process. 

For highly exothermic reactions, -AI > Es> and a = 0 (activationless process), while for highly endothermic reactions, AI > Es> and a = 1 (barrierless process). As we have mentioned in Chapter 1, these extreme cases follow from the general phenomenological theory of an elementary act. A gradual transition from one extreme value of a to another is natural The specific form of the dependence described by Equation (3.9) follows from the parabolic shape of the potential curves, i.e. from the harmonic oscillator approximation. 

So far, Temkin s interpretation cannot be substantiated strictly. However, it seems quite probable that relation (4.6) is valid, since in the limiting cases of barrierless (a = 1) and activationless (6=1) processes. Equation (1.6) turns into expressions having clear physical meaning. Indeed, for a barrierless and an activationless process the activated state coincides with the final and the initial state respectively, and the same holds for their entropies this is precisely the result obtained from Equation (4.6). 

Another possible method of determining AG involves a bipartition of the energy (overpotential) difference between the points corresponding to a transition from a barrierless to an ordinary process and from an ordinary to an activationless process (see Figure 7.5). 

Finally, we note here that the representation of the potential dependence of P in the diagram in Despic and Bockris s paper (their Fig. 14) implies ultimately that activationless discharge will set in, as treated by Krishtalik. Then, of course, the process becomes entirely diffusion limited. Correspondingly, barrierless discharge would arise at the other extreme. 

The first barrierless electrochemical processes were predicted and investigated experimentally by Krishtalik " for the hydrogen evolution reaction at metals with high overpotential. The theory of barrierless transitions (and therefore also of the activationless transitions for the reverse process) for the hydrogen evolution reaction at metals was given by Dogonadze et al. 

These, and a number of other experimental facts, give evidence that the physical assumptions on which the theory is based are, in general, correct. In a number of cases, there is also quantitative agreement between theory and experiment. The main difficulty of the theory which is not yet overcome consists in the quantitative description of the transition regions between the normal region of the process, and the activationless and barrierless ones.t It is hoped that this problem will be also solved by further experimental and theoretical investigations. 

In other barrierless reactions, particularly chlorine evolution on graphite, no limiting current in the backward process was observed, the reason being that, in these cases, the slow step of the forward reaction was the transfer of the first electron, followed by that of the second, e.g., in an electrochemical desorption step. In the backward process, the slow activationless step is, in this case, preceded by the transfer of a single electron. The relationship between the rate of this process and the potential masks the limiting current phenomenon. 

It is not always, of course, that a barrierless (j3 = 1) or activationless (/3 = 0) process produces slopes corresponding, respectively, to 60 mV and 00. As can be seen, for example, from Eq. (52), under conditions where a preceding equilibrium step is involved, these values of jS may result in slopes corresponding to 0.030 and 0.060 V, respectively. Conversely, it is equally possible that in certain cases, such slopes which are sometimes interpreted as indicative of a slow chemical step, correspond, in fact, to the limiting cases of the electrochemical reaction per 5e, considered above. 

Fig. 1.6. Potential energy curves for ordinary, activationless, and barrierless processes. The initial state for the ordinary discharge is shown by curves 1 and 2, while curves 3 and 4 show the activationless and barrierless discharge respectively. Curve 5 corresponds to the final state.

In Chapter 2, we proved the existence of the barrierless discharge of hydronium ions. The adsorbed hydrogen atom in this process is removed by activationless electrochemical desorption. In principle, activationless desorption may involve various proton donors, both H30 ions and water molecules. As was shown in section 2.1, in experiments on barrierless discharge a hydronium ion is the proton donor in a desorption reaction. Later, we shall show that this fact makes the bond stretching model improbable. 

The most typical case, although not the only possible one, corresponds to a = aq = ur. Here, the coordinate of the optimal point lies between the initial and the final equilibrium coordinates. However, for highly exothermic and highly endothermic processes (but still before a transition to the activationless or barrierless... 

Since the reaction reverse to a barrierless process is activationless it would seem that all the particles formed, for example, during a barrierless discharge should be rapidly ionized and so return to the initial state. Thus, the total current is equal to zero, and the barrierless process cannot be observed experimentally. 

On the basis of similar arguments, we should expect a limiting current for the barrierless electrochemical desorption if we consider the electrochemical adsorption mechanism. In this case we can ignore the rate of reduction of the adsorbed atoms (a process opposite to the discharge of chloride ions) at potentials that are not too cathodic, and electrochemical desorption should be activationless. 

It can be seen easily that these equations yield the correct values for the orders of anodic and cathodic currents with respect to Cl , CI2, and H (taking into account the above remarks concerning the additional effects of surface dissociation). As mentioned above, the anodic slope of 30 mV for the Tafel line coincides with the experimental value for 3 = 1, i.e. for a barrierless discharge. The condition 3=1 means that a = 0, i.e. the cathodic process is activationless and a limiting current must be observed. This conclusion completely agrees with experiment. As far as we know, this is the first direct observation of the limiting current of an activationless electrode process... 

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