Volcano Activity Relationships for Proton-Coupled Electron Transfer Reactions in Electrocatalysis
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This paper studies simple kinetic models for proton-coupled electron transfer reactions, and demonstrates that for reactions in which proton and electron do not transfer simultaneously, pH dependence of the overall reaction rate is expected. In particular, if the current is evaluated on the reversible hydrogen scale, this may lead to volcano-type activity relations as a function of pH. In case that an acid–base equilibrium is part of the mechanism, the optimal pH occurs close to the pKa of this equilibrium.
KeywordsElectrocatalysis Proton-coupled electron transfer Volcano plot pH dependence
Electrocatalysis may be broadly defined as the catalysis of redox reactions . A more specific definition of electrocatalysis highlights the role of “the electrode material on the rate and the mechanism of electrode reactions” . The catalyst’s role is to offer alternative pathways for the overall reaction by stabilizing catalytic intermediates through a specific chemical interaction between the intermediates and the catalyst. As a result, the Sabatier principle  also applies to electrocatalysis. Volcano activity plots, which depict the activity towards a certain reaction versus the energy of stabilization of the key catalytic intermediate (or any other related system parameter), have become highly popular in the heterogeneous electrocatalysis community as a means to organize activity data and to design new catalysts [4, 5, 6, 7, 8], though the concept is less widespread in the molecular electrocatalysis community.
Examples include the hydrogen evolution reaction, hydrogen oxidation reaction, oxygen reduction reaction, oxygen evolution reaction, reduction of CO2, oxidation of organic molecules, dinitrogen reduction, ammonia oxidation, and many more . Typically these reactions take place in an aqueous electrolyte, but some of the reactions are also routinely studied in non-aqueous solvents employing suitable proton donors.
Acidity is one of the electrolyte properties that can impact significantly on the rate of an electrode reaction and the performance of an electrochemical device. While this observation is generally acknowledged in the electrochemistry literature, explanations vary and are often very specific to the system under consideration . In this paper, I will show that pH dependence follows naturally from the general theory of PCET reactions, and may lead to volcano-type activity plots. Thermodynamic arguments for this statement were given in a previous paper . Here, I will consider simple kinetic models, and I will emphasize the idea to view the electrochemical system as a whole, that is: to include the fact that the pH dependence of the reaction under consideration must be compared to the pH dependence of the second (counter or reference) electrode to understand the “final” impact of pH on device performance. While this is somehow natural to people working in the field of fuel cells and water electrolysis, this idea is not generally included in the PCET theory. This difference in viewpoint, though conceptually rather trivial, is often at the basis of the confusion that arises when the heterogeneous electrocatalysis community and the PCET community argue about pH dependence.
2 Model: Results and Discussion
Detailed expressions exist for the rates and the energies of activation of the various pathways shown in Fig. 1 [10, 13, 15, 16]. In general, CPET takes place if the free energies of the off-diagonal states AH+ and A− are high. If the free energies of either AH+ or A− are comparable to AH, the activation energies for the sequential ET and PT steps are generally lower than that for the concerted step, and the reaction typically follows a sequential pathway (“decoupled proton-electron transfer”) .
In the remainder of this section, I will consider simple kinetic models for two typical situations of PCET: the situation in which proton transfer (or deprotonation) precedes ET, and the situation in which ET (or reduction) precedes proton transfer. All equations to be derived below are steady-state expressions in which the eventual effect of slow diffusion of reactants is not accounted for.
Since typically α ≈ 0.5, this equation reduces to pH = pKa. This implies that in a device with the above “slow” oxidation reaction at the anode, and a fast reversible H+/e− CPET reaction at the other electrode, the current output maximizes at pH = pKa. The reason for the increasingly lower reaction rate for pH > pKa is the fact that at this pH the concentration of A− has saturated (and it is therefore no longer pH dependent) but the rate of ET of reaction 3 is evaluated at increasingly higher overpotential because of the pH dependent reference potential. This pH-dependent volcano-type activity plot has been observed experimentally for the electrocatalytic oxidation of formic acid on platinum and gold electrodes [17, 20], but also for the homogeneously catalyzed oxidation of formic acid by a molecular iridium-ruthenium complex .
It is important to emphasize that there is no fundamental difference between Fig. 2a and b; they are different ways of plotting the same result. Using the RHE reference, one “corrects” for the expected pH dependence of concerted proton–electron transfer, i.e. the 60 mV/pH shift observed on the SHE scale. In the heterogeneous electrocatalysis community, CPET is often considered the norm and therefore it is logical to consider pH dependence on the RHE scale, since the RHE scale incorporates this intrinsic pH dependence of CPET processes. A half cell reaction showing pH dependence on the RHE scale hence implies the existence of decoupled proton-electron transfer pathways. On the other hand, in the molecular electrocatalysis literature, CPET pathways are considered more exceptional, and decoupled pathways are the norm. Hence, there is no tradition to employ a pH corrected reference electrode such as the RHE. In addition, in non-aqueous solvents, as often employed in molecular electrocatalyis studies, there exists no obvious practical alternative for the RHE in aqueous electrolytes.
Depending on the rate of reaction 2b (with corresponding rate constant k 1b ), i.e. in which water is the proton donor, the rate at high pH will settle onto a constant value, as illustrated by the dotted line. On the RHE scale, the reaction rate increases with increasing pH, as the ET reaction is probed at increasingly lower overpotential. The saturation is again due to the lower availability of protons, which exactly counteracts this effect, at least in the model. In reality, water will likely act as proton donor at such high pH, and no such saturation is expected, as illustrated by the dotted line. The observation that the rate of oxygen reduction increases with pH agrees well with experiments on gold electrodes: the oxygen reduction proceeds much closer to the equilibrium potential of the overall oxygen reduction to water (i.e. 1.23 V vs RHE) in alkaline media than in an acidic media . The fact that the mechanism for the oxygen reduction reaction on gold proceeds through a superoxide anion intermediate is therefore the reason why gold is such a good electrode material for oxygen reduction in alkaline media [10, 23].
Since the acid–base reaction is considered out-of-equilibrium, its pKa plays no role in the maximum activity, at least not in this simple kinetic model. The pH of maximum activity now depends on the relative rates of formation and protonation of the A− intermediate (Eq. 14). The reason for the maximum lies in the fact in this version of the model, there is saturation in the concentration of the intermediate. When this saturation is reached, higher values of the pH slow down the overall reaction rate on the RHE scale. Whether the maximum actually develops depends on the rate of reaction 2b, as can be seen from Fig. 4b. If this reaction is fast, this alternative protonation pathway will dominate and the rate will become constant at high pH due to the pH independent rate of this reaction.
This paper has considered pH dependent reactivity maps for electrochemical PCET reactions in which sequential proton-electron transfer takes place. The simple kinetic modeling theory presented here builds on previous Hamiltonian modeling  and thermodynamic considerations . The modeling confirms the role of pH in optimizing the reactivity of electrocatalytic reactions, leading to volcano-type activity relations if acid–base equilibria are involved in the reaction mechanism. The importance of considering the potential reference scale (i.e. SHE and RHE) has also been illustrated, which should be helpful in avoiding future confusion about the interpretation of “pH dependence” of PCET reactions.
I would like to acknowledge the Université de Paris-Denis Diderot for a visiting professorship and Professors Cyrille Costentin, Marc Robert, and Jean-Michel Savéant at the Laboratoire d’Electrochimie Moleculaire of the Université de Paris-Denis Diderot for very helpful discussions.
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