Beyond the Rate-Determining Step in the Oxygen Evolution Reaction

Research Article Cite This: ACS Catal. 2019, 9, 6755−6765

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Beyond the Rate-Determining Step in the Oxygen Evolution Reaction over a Single-Crystalline IrO2(110) Model Electrode: Kinetic Scaling Relations Kai S. Exner*,† and Herbert Over*,‡ †

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Faculty of Chemistry and Pharmacy, Department of Physical Chemistry, Sofia University, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria ‡ Physical Chemistry Department, Justus-Liebig-University Giessen, Heinrich-Buff-Ring 17, 35392 Giessen, Germany S Supporting Information *

ABSTRACT: Electrochemical water splitting is a key technology for moving toward a promising energy scenario based on renewable (regenerative) energy resources in that wind and solar energy can be stored and buffered in chemical bonds, such as in H2. The efficiency of water electrolysis is, however, limited by the sluggish oxygen evolution reaction (OER) at the anode, for which IrO2-based electrodes are considered to be the best compromise of a stable and reasonably active OER electrocatalyst in acidic medium. To improve existing OER electrocatalysts and to advance a rational search of promising alternative electrode materials, it is imperative to identify the ratedetermining step (rds). We apply here the concept of the free energy diagram along the reaction coordinate to identify the rate-determining step (rds) in the oxygen evolution reaction (OER) over an IrO2(110) model anode in both acidic and basic media. The free energy diagram as a function of the applied electrode potential is constructed from experimental Tafel plots and ab initio Pourbaix diagrams. Quite in contrast to common perception, the rds for the OER over IrO2(110) at high overpotentials is identified with the decomposition of the OOH adsorbate via a decoupled electron−proton transfer to form gaseous O2. Combining linear scaling relationships with the free energy diagram approach leads to the introduction of kinetic scaling relations, which allow us to predict the rate-determining step (rds) of the OER over general transition metal oxide electrocatalysts in the high-overpotential regime by a single descriptor, namely, the free formation energy of oxygen with respect to the OH adsorbate (ΔG2) on the anode surface. On the basis of kinetic scaling relations we suggest that further improvement of the catalytic OER performance may require a decoupling of the electron−proton transfer in the rds. KEYWORDS: electrocatalysis, oxygen evolution reaction (OER), IrO2, transition metal oxides, linear scaling relationships, free energy diagram, kinetic scaling relations

1. INTRODUCTION Renewable energy1−3 needs to be stored to match demand,4,5 for instance, by electrochemical water splitting to produce the energy vector H2. So far only proton-exchange membrane (PEM) electrolyzers in acidic conditions have been able to cope with the intermittent energy supply delivered by solar and wind energy.6 The sluggish oxygen evolution reaction (OER) at the anode limits the efficiency of this process with the most active electrocatalyst in acidic milieu being RuO2. Unfortunately, RuO2 faces severe stability problems7−11 so that IrO2based electrodes are considered as the “gold standard” of a stable and reasonably active OER electrocatalyst.12−14 The widely accepted reaction mechanism for the OER in acidic media consists of four proton-coupled electron transfers,15−19 in which the OH, O, and OOH adsorbate need to be stabilized on the electrocatalyst surface. Several ab initio thermodynamics studies for the OER over IrO2(110) have © XXXX American Chemical Society

been devoted to investigate the adsorption energies of these reaction intermediates.20−23 For both RuO2(110) and IrO2(110), the OOH intermediate has been identified spectroscopically,24−26 thus corroborating a mechanistic description via the OOH intermediate. The formation of the OOH adsorbate is widely accepted to govern the performance of transition metal oxides in the OER,14,27−29 which has been proven by a first-principles kinetics study30 for the case of RuO2(110) and which is compatible with model experiments.31 In addition to experimental OER studies over polycrystalline IrO 2 32−35 and hydrous IrO 2 , 36,37 there are also two experimental studies reported on single-crystalline IrO2(110) Received: April 17, 2019 Revised: June 13, 2019 Published: June 17, 2019 6755

DOI: 10.1021/acscatal.9b01564 ACS Catal. 2019, 9, 6755−6765

Research Article

ACS Catalysis model catalysts13,38 that provide kinetic data in the form of Tafel plots both for alkaline and for acidic conditions. Surprisingly, a (tight) link between these model experiments and corresponding theoretical data is missing. Recently the authors31,39 developed a universal approach to derive (the essential part of) the free energy diagram along the reaction coordinate of an electrocatalytic reaction by analyzing experimental Tafel plots to quantify the free energies of the transition states, while free energies of the reaction intermediates are taken from ab initio thermodynamics calculations (surface Pourbaix diagrams). This approach was applied to several important electrocatalytic reactions,31 including chlorine and oxygen evolution over RuO2(110) and the hydrogen evolution reaction (HER) over Pt(111). For the case of the CER (chlorine evolution reaction) over RuO2(110), the derived free energy diagram turned out to be in quantitative agreement with kinetics from first-principles.40 Here, we apply the free energy diagram approach to resolve the reaction mechanism of the OER over an IrO2(110) model anode in both acidic and alkaline environments. We analyze the experimental Tafel plots from Kuo et al.38 and construct an ab initio Pourbaix diagram based on the ab initio thermodynamics data from the literature20−23,28 to merge this information into the free energy diagram as a function of the applied electrode potential. It turns out that the ratedetermining step (rds) for the OER over IrO2(110) is not reconciled with the formation of the OOH adsorbate but instead with the decomposition of the OOH adsorbate into O2. Combining the concept of linear scaling relationships based on ab initio thermodynamics18 with the approach of the free energy diagram allows us to predict the kinetic bottleneck (rds) of the OER over general transition metal oxide electrocatalysts in the high-overpotential regime. We discuss the decoupling of the electron−proton transfer within the rds in acidic medium as a promising strategy to improve catalytic OER activity.

Tafel regime by determining the apparent transfer coefficient ß from the Tafel slope b according to eq 2: b=

k T ln(10) dη 59 mV/dec 59 mV/dec = B = = d log j (γ + rrdsαrds)e γ + rrdsαrds ß (2)

At room temperature kBT ln(10)/e amounts to about 59 mV. The denominator ß = (γ + rrdsαrds) consists of the number of electrons γ transferred before the rate-determining TS, while rrds distinguishes whether the rate-determining TS corresponds to a chemical (rrds = 0) or an electrochemical (rrds = 1) reaction step. In the case that the rate-determining TS is of electrochemical nature, αrds denotes the underlying transfer coefficient. In general, experimental Tafel plots exhibit one or even more linear Tafel regions. A change in the Tafel slope indicates a variation of the number of transferred electrons to pass over the rate-determining TS counting from the AS that can be rationalized in different ways. Either the rate-determining reaction step has changed as encountered with the CER over RuO 2 (110), 39 or the AS has varied, which requires renumbering of the electron transfers, or both the AS as well as the rate-determining TS have changed as reported for the OER over RuO2(110).31 To retrieve the essential part of the free energy surface from experimental Tafel plots, the linear Tafel lines in each linear Tafel regime are extrapolated to zero overpotential, which allows quantifying the exchange current density j0 and thereby the TS free energy G#rds of the corresponding rate-determining TS (cf. eq 1). In addition to the TS free energies, the corresponding positions in the reaction mechanism (by counting the number of electrons starting from the AS as given by the apparent transfer coefficient ß) can be determined for all elementary reaction steps that leave a fingerprint in the experimental Tafel plot. Ab initio theory in the form of Pourbaix diagrams20,41−43 is needed to complement the free energy surface with the energetics of the RIs and to determine the active starting surface (AS) of the electrocatalyst.44 The number of electrons transferred (derived from the Tafel slope), the TS free energy of the rate-determining reaction step (derived from the exchange current density), the starting surface of the electrocatalytic cycle (from the ab initio Pourbaix diagram), and the free energies of the reaction intermediates (from ab initio thermodynamics calculations) merge into the free energy diagram along the reaction coordinate at zero overpotential (cf. Figure 1) that can be adopted to any overpotential η due to the knowledge of the transfer coefficients of the relevant TS. Our free energy diagram approach is superficially reminiscent of the conventional Tafel analysis45−47 where the value of the Tafel slope is correlated to the rate-determining reaction step. However, we need to emphasize that our approach goes far beyond a traditional Tafel analysis and extends the conventional concept in four crucial points:31

2. METHODOLOGICAL ASPECTS The construction of the free energy diagram along the reaction coordinate is based on the combination of experimental Tafel plots and ab initio Pourbaix diagrams.31 As the reaction intermediates (RIs) preceding the transition state (TS) with the highest free energy (G#rds) are in quasiequilibrium with the reactants and the active surface (AS) of the electrocatalyst, the exchange current density j0 is given by31,39 kT # j0 = B ze Γcat exp( −Grds /kBT ) (1) h In eq 1, e, kB, T, h, and z denote the elementary charge, Boltzmann’s constant, the absolute temperature in K, Planck’s constant, and the number of electrons transferred in the overall reaction (OER: z = 4), respectively, while G#rds represents the free energy of the rate-determining TS, and Γact denotes the number of electrocatalyst’s active sites per surface area with a reactant molecule or ion in the double layer.31 The ratedetermining TS corresponds to the highest transition state free energy in the free energy diagram relative to the free energy of the thermodynamically most stable surface state (active surface: AS), which is provided by the surface Pourbaix diagram.20,41−43 The evaluation of experimental Tafel plots over singlecrystalline model electrodes allows monitoring the transition from the AS to the TS with highest free energy in each linear

(a) We focus on the free energy diagram along the reaction coordinate. (b) We derive the free energies of the rate-determining transition states from the experimental exchange current density. (c) The ab initio Pourbaix diagram defines the starting surface (AS) of the electrocatalytic cycle from which the number of electrons transferred is counted. A change in 6756


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Figure 2. (a) Pourbaix diagram of a single-crystalline IrO2(110) electrode at T = 298.15 K. The active surface of the IrO2(110) electrocatalyst is hydroxylated in the overpotential range 0 V ≤ ηOER ≤ 0.21 V but transforms to an oxygen-terminated phase for 0.21 V ≤ ηOER ≤ 0.30 V. For even higher overpotentials ηOER ≥ 0.30 V, the thermodynamically most stable surface changes in that now the OOHot adsorbate is stabilized. (b) Cut through stick and ball representations along the [001] direction of the three different adsorbate structures, Ircus−OHot, Ircus−Oot, and Ircus−OOHot, as observed in the Pourbaix diagram. Red balls, Ircus; green balls, oxygen; gray balls, hydrogen. Figure 1. Schematic representation how the free energy diagram along the reaction coordinate at zero overpotential is derived on the basis of the combination of the experimental Tafel plot for the kinetics (yellow background) with the ab initio Pourbaix diagram for the thermodynamics (gray background). RI and AS correspond to the reaction intermediate and the active surface, respectively, while P denotes the product.

consequence that transitions with an equal number of protons and electrons transferred become lines with zero slope in the Pourbaix diagram (cf. Figure 2a). In the potential range of oxygen electrocatalysis on IrO2(110), the active (starting) electrode surface changes twice, which has profound implications on the interpretation of experimental Tafel plots: While for ηOER ≤ 0.21 V = ΔG1TD/e the reaction mechanism starts from a hydroxylated surface (OHot), the oxygen-terminated surface (Oot) is the starting point of the OER in the overpotential area of 0.21 V ≤ ηOER ≤ 0.30 V. Finally, for ηOER ≥ 0.30 V = (ΔG1TD + ΔG2TD)/e the IrO2(110) surface stabilizes the OOHot adsorbate from which the OER commences. Kuo et al. prepared epitaxially grown single-crystalline IrO2(110) films on TiO2(110) single-crystal substrates and performed Tafel experiments in the potential range of the OER in both acidic (pH = 1) and alkaline (pH = 12.9) environments.38 Detailed information concerning the analysis of the experimental plots in alkaline medium can be found in the SI, Section S2, while a detailed discussion of an acidic electrolyte is provided in Section 3.1.1. These IrO2(110) films are very stable under OER conditions and are not prone to dissolve14,48 or to form other compounds such as Iroxohydroxides. In the following the experimental Tafel plots of the OER are combined with the ab initio Pourbaix diagram (cf. Figure 2) to derive the free energy landscape coordinate, which is discussed in Sections 3.1.1 or 3.1.2 for an acidic or alkaline electrolyte, respectively. 3.1.1. OER over IrO2(110) in Acidic Medium. The Tafel plot in the acidic environment (pH = 1)38 is depicted in Figure 3. The Tafel plot reveals two linear Tafel regions. The Tafel slope of the first region is 49 mV/dec (0.35 V ≤ ηOER ≤ 0.39 V) and translates to an apparent transfer coefficient of ß = 1.20; i.e., one electron is transferred (γ = 1) before the rate-determining electrochemical (rrds = 1) reaction step (rds) so that the transfer coefficient of the rds amounts to α = 0.20. Similarly, the significantly higher Tafel slope of 78 mV/dec (ηOER ≥ 0.43 V) leads to an apparent transfer coefficient of ß = 0.76; i.e., the first electrochemical (rrds = 1) reaction step in the electrocatalytic cycle of OER is rate-determining, and no electron is transferred before the rds (γ = 0). Consequently, the transfer

the AS (depending on the applied overpotential) requires a renumbering of the electron transfers within the reaction mechanism. (d) The free energies of the reaction intermediates are taken from the ab initio Pourbaix diagram or, if the free energies of certain adsorbate structures cannot be extracted from the Pourbaix diagram, from further ab initio thermodynamics calculations. Only taking these four aspects into account ensures identifying the rate-determining reaction step based on the constructed free energy diagram depending on the applied electrode potential. In principle the free energy surface can also be determined by ab initio theory only. However, this approach is computationally demanding and at the moment not reliable enough due to the underlying approximations.31 Therefore, the present approach combines the best features of both worlds: we combine high quality model experiments for the kinetics with ab initio theory for the thermodynamics to finally derive the free energy diagram along the reaction coordinate of an electrocatalytic reaction.

3. RESULTS 3.1. OER over IrO2(110). Ab initio thermodynamics calculations for an IrO2(110) model electrode in an aqueous electrochemical environment were performed by Hansen et al.,20 Gauthier et al.,21 Briquet et al.,22 Sumaria et al.,23 and Ping et al.28 The calculated free energies of the relevant adsorbates within the catalytic OER cycle, namely, OHot, Oot, as well as OOHot, are compiled in the form of a surface Pourbaix diagram, depicted in Figure 2; further information is provided in the Supporting Information (SI, Section S1). Note that the electrode potential is referenced against the reversible hydrogen electrode (RHE) and not against the SHE with the 6757


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the (essential part of) free energy diagram along the reaction coordinate at ηOER = 0 V, summarized in Figure 4.

Figure 3. Tafel plot of the electrochemical measurements at pH = 1 in the overpotential regime of 0.35 V ≤ ηOER ≤ 0.47 V. Data taken from ref 38.

coefficient of the rds is α = 0.76. From the extrapolation of the two linear Tafel lines (cf. Figure 3) to zero overpotential we obtain log j0 = −12.3 (49 mV/dec) and log j0 = −9.3 (78 mV/ dec). These values translate to G# = 1.29 eV and G# = 1.11 eV, respectively, by considering a density of active surface sites of Γact = 7 × 1014 cm−2.28 The free energy diagram for the OER over IrO2(110) in acidic media is constructed by combining the free energies derived from the experimental Tafel plot (cf. Figure 3) with those from the ab initio Pourbaix diagram (cf. Figure 2). For 0.35 V ≤ ηOER ≤ 0.39 V, oxygen electrocatalysis over the active IrO2(110)−OOHot surface (cf. Pourbaix diagram in Figure 2) proceeds via the following reaction scheme:

Figure 4. Essential part of the free energy diagram for the OER over IrO2(110) in acidic media (pH = 1) at zero overpotential. It turns out that the formation of OHot is rate-determining (solid blue thick line).

For 0.30 > ηOER > 0.21 V = ΔG1TD/e, the active surface switches from the OHot to the Oot-terminated IrO2(110) surface, and hence, the electron transfers need to be renumbered (cf. Figure 5a). At ηOER > 0.30 V = (ΔG1TD +

Ircus−OOHot + 2H 2O F Ircus + O2 + 1e− + 1H+ + 2H 2O rds

→Ircus−OHot + O2 + 2e− + 2H+ + 1H 2O FIrcus−Oot + O2 + 3e− + 3H+ + 1H 2O FIrcus−OOHot + O2 + 4e− + 4H+

Since the active surface remains unaltered in the overpotential regime of ηOER > 0.40 V, the change in the Tafel slope is traced to a switch of the rds: Ircus−OOHot + 2H 2O rds

→ Ircus + O2 + 1e− + 1H+ + 2H 2O FIrcus−OHot + O2 + 2e− + 2H+ + 1H 2O FIrcus−Oot + O2 + 3e− + 3H+ + 1H 2O FIrcus−OOHot + O2 + 4e− + 4H+

The (total) TS free energies of both transition states at zero overpotential are calculated to be G#1 = 1.11 eV + 0.51 eV = 1.62 eV (O2 formation); G#2 = 1.29 eV + 0.51 eV = 1.80 eV (formation of OHot) by combining the calculated transition state free energies derived from the experimental Tafel plot (cf. Figure 3) with the free formation energies of the active Oot surface (ΔG1TD = 0.21 eV) as well as the active OOHot surface (ΔG2TD = 0.09 eV) taken from the Pourbaix diagram in Figure 2. The free energy penalty of 0.51 eV actually corresponds to the free energy difference of the OOHot phase with respect to the OHot surface at zero overpotential. The transition state free energies G#1 and G#2 in conjunction with the calculated transfer coefficients of α1 = 0.76 (O2 formation) and α2 = 0.20 (formation of OHot) derived from the Tafel slopes merge into

Figure 5. Essential part of the free energy diagram for the OER over IrO2(110) in acidic media (pH = 1) at (a) 0.30 > ηOER > 0.21 V and (b) ηOER > 0.30 V. Changes in the active surface that require a renumbering of the corresponding electron transfers are indicated in turquoise. In both cases, the formation of OHot is rate-determining (solid blue thick line). 6758


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ACS Catalysis ΔG2TD)/e, a second switch of the starting surface is encountered, namely, from the Oot to the OOHot-terminated surface that again requires a renumbering of the electron transfers (cf. Figure 5b). Figure 6 displays the free energy diagram at an applied overpotential of ηOER = 0.41 V and confirms that at this

electrochemical reaction is rate-determining with a transfer coefficient of α = 0.63. From the Pourbaix diagram in Figure 2, oxygen evolution proceeds from the active IrO2(110)−OOHot surface at ηOER ≥ 0.34 V via the following reaction scheme: Ircus−OOHot + 4OH− rds

→ Ircus + O2 + 1e− + 3OH− + 1H 2O FIrcus−OHot + O2 + 2e− + 2OH− + 2H 2O FIrcus−Oot + O2 + 3e− + 1OH− + 3H 2O FIrcus−OOHot + O2 + 4e− + 4H 2O

In the SI, Section S2, free energy diagrams for different OER overpotentials are depicted and discussed (cf. SI, Figures S3− S5). To compare the OER kinetics in the high-overpotential regime (ηOER > 0.40 V) in alkaline media to that in acidic media, the free energy diagram is also depicted at ηOER = 0.47 V in Figure 8. The decomposition OOHot + OH− → *ot + O2 + 1 e− + 1H2O turns out to be rate-determining with a TS free energy of 0.81 eV (cf. Section S2 of the SI). Figure 6. Essential part of the free energy diagram for the OER over IrO2(110) in acidic media (pH = 1) at ηOER = 0.41. The TS free energies of O2 formation and OHot are identical so that the experimental Tafel plot reveals a bending area in this overpotential regime.

threshold overpotential the TS free energies of OHot and O2 formation are identical, thereby defining the bending region of the experimental Tafel plot (cf. Figure 3).31 The free energy diagram depicted in Figure 7 indicates that O2 formation constitutes the rate-determining reaction step at

Figure 8. Essential part of the free energy diagram for the OER over IrO2(110) in alkaline media (pH = 12.9) at ηOER = 0.47 V. The formation of molecular oxygen O2 from the OOHot adsorbate (solid violet thick line) constitutes the kinetically limiting reaction step with a TS free energy of 0.81 eV. The dotted violet line indicates the kinetics of O2 formation at ηOER = 0.47 V in acidic environment (cf. Figure 7), which reveals a smaller TS free energy of 0.75 eV.

The comparison of the free energy diagram for the OER over IrO2(110) in the alkaline environment at ηOER = 0.47 V with that in acidic medium (cf. Figure 7) reveals that the TS free energy of the rate-limiting O2 formation is 60 meV smaller in acidic solution (pH = 1) than in alkaline environment (pH = 12.9), which explains the 10 times higher current density in acidic media compared to alkaline medium (cf. Tafel plots in Figure 3 and Figure S2). 3.2. Scaling Relations Meet the Free Energy Diagram: Kinetic Scaling Relations. It is a universal feature of electrocatalytic reactions that the first elementary electrochemical reaction step becomes rate-determining in the highoverpotential regime,31,39 since the first transition state in the electrocatalytic cycle exhibits the smallest apparent transfer coefficient (cf. Section 2) and hence is least affected by an increase in overpotential. The first elementary electrochemical reaction step being the rds is reconciled with a Tafel slope larger than 59 mV/dec. For both, the OER over IrO2(110) (cf.

Figure 7. Essential part of the free energy diagram for the OER over IrO2(110) in acidic media (pH = 1) at ηOER = 0.47. The formation of O2 is identified as the rate-determining reaction step (solid violet thick line).

ηOER = 0.47 V due to its higher TS free energy (G# = 0.75 eV) compared to the formation of OHot (G# = 0.72 eV). 3.1.2. OER over IrO2(110) in Alkaline Medium. The analysis of the experimental OER data on IrO2(110) in alkaline medium (pH = 12.9)38 is illustrated in the SI, Section S2. The procedure is analogous to that presented in the previous Section 3.1.1 for an acidic electrolyte solution. The experimental Tafel plot (cf. Figure S7) reveals only one linear Tafel regime with a slope of 94 mV/dec in the overpotential regime of ηOER ≥ 0.34 V. It turns out that the first elementary 6759


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ACS Catalysis Section 3.1) and the OER over RuO2(110),31,39 the Tafel slope exceeds 59 mV/dec for ηOER > 0.40 V. The formation of molecular oxygen as rate-determining reaction step in the OER over IrO2(110) in the highoverpotential regime is a paradigm shift in oxygen electrocatalysis. Hitherto researchers have proposed the formation of the OOH adsorbate to be rate-limiting,28,38,49 although the formation of OOH has been proven to be rate-determining only for the OER over a single-crystalline RuO2(110) electrode in the high-overpotential regime.30,31,39 To rationalize the different OER behavior on IrO2(110) and RuO2(110), we combine the free energy diagram approach with the concept of linear scaling relationships in an acidic electrolyte.17,18,50,51 The free energy changes ΔGj (j = 1, 2, 3, 4) of the four protoncoupled electron transfers of the OER are given by eqs 3−6: H 2O(l) + * → *−OH + (H+ + e−)

ΔG1

(3)

*−OH → *−O + (H+ + e−) *−O + H 2O(l) → *−OOH + (H+ + e−)

ΔG2 ΔG3

(4) (5)

*−OOH → * + O2(g) + (H+ + e−)

ΔG4

(6)

Figure 9. Linear scaling relationships in conjunction with the free energy diagram allow the determination of the active surface as well as the rds for the OER over transition metal oxide surfaces for ηOER > 0.40 V. The uncertainties of the linear scaling are indicated by dotted lines.18 The area, in which either the formation of OOH or the formation of molecular oxygen is rate-determining, is marked in gray.

Figure 9 suggests how to improve the performance of transition metal oxide OER electrocatalysts. For electrocatalysts on the right side of Figure 9, it is beneficial to further stabilize the TS of O2 formation, which can be realized by lowering the ΔG2 value according to the Brønsted−Evans Polanyi (BEP) relation.52 Quite in contrast, electrocatalysts on the left side of Figure 9 need to stabilize the TS of OOH formation for achieving improved activity. Following the BEP relation, this can be realized by increasing the ΔG2 value. Therefore, transition oxides with ΔG2 values in the gray region of Figure 9 may exhibit superior activity; further details can be found in the SI, Section S3.

Here, the star (*) denotes the catalytically active site. The scaling relations of Man et al.18 indicate that the sum of the free energy changes for the formation of the O (ΔG2) and the OOH (ΔG3) adsorbate amounts to 3.2 eV for the class of transition metal oxides. This relationship is used to identify the thermodynamically most stable surface (AS) in the highoverpotential regime, that is, ηOER = 0.40 V, where the first reaction step is reconciled as the rds. The AS serves as the starting point in the electrocatalytic OER cycle (cf. Sections 3.1.1 and 3.1.2). It turns out that the free formation energy of oxygen with respect to the OH adsorbate (ΔG2) determines the surface configuration of transition metal oxide OER electrocatalysts: For ΔG2 < 1.37 eV the electrocatalyst’s surface is O-covered, and the electrocatalytic OER cycle starts with the elementary reaction step of OOH formation (cf. eq 5), while for ΔG2 > 1.77 eV, the OOH adsorbate is stabilized on the electrocatalyst’s surface, and consequently the formation of molecular oxygen constitutes the first elementary electrochemical reaction step (cf. eq 6). For 1.37 eV < ΔG2 < 1.77 eV, the active surface under reaction conditions cannot be determined solely based on the value of ΔG2. Instead, all four free energy changes according to eqs 3−6 need to be considered for the determination of the energetically most stable surface under reaction conditions, which is either the O-covered or the OOH-covered phase. This uncertainty is due to the quoted standard deviation of ±0.2 eV in the work of Man et al.18 Combining the ab initio thermodynamics approach in terms of linear scaling relationships with our free energy diagram approach allows an a priori determination of the active surface (AS) under reaction conditions and the rds for the OER in the high-overpotential regime (ηOER > 0.40 V). For ΔG2 < 1.37 eV the formation of the OOH adsorbate starting from an oxygenterminated surface constitutes the rds. For ΔG2 > 1.77 eV the electrocatalyst stabilizes the OOH-terminated surface, and the formation of molecular oxygen is kinetically limiting. While the first case (formation of OOH as the rds) is encountered with the OER over RuO2(110), the second case (decomposition of OOH as the rds) applies to the OER over IrO2(110). Figure 9 summarizes the discussion.

4. DISCUSSION 4.1. Validation of ab Initio Kinetics with the Free Energy Diagram as the Benchmark. For the OER over IrO2(110), Ping et al. investigated the kinetics of oxygen evolution in an acidic environment (pH = 0) by calculating transition states for selected reaction steps.28 The authors concluded that the formation of OOHot via a chemical reaction step without charge transfer should constitute the ratedetermining reaction step. On the basis of microkinetic modeling, the authors calculated a Tafel plot, in which two linear Tafel regimes are observed: The Tafel slope is 47 mV/ dec for small overpotentials (0.10 V ≤ ηOER ≤ 0.30 V) and 240 mV/dec for high overpotentials (ηOER ≥ 0.35 V). The change in the Tafel slope was ascribed to a switch of active surface under OER conditions, which is reconciled with the ab initio Pourbaix diagram (cf. Figure 2). However, the theoretical Tafel slopes conflict with experimental Tafel measurements of Kuo et al.38 and Stoerzinger et al.13 (cf. SI, Section S2) and are not consistent with the constructed free energy diagram along the reaction coordinate based on the experimental data (cf. Figure 4). Considering the proposed rate-determining formation of the OOHot adsorbate via a chemical reaction step, the authors overlooked that the OOHot adsorbate is already stabilized on the IrO2(110) surface in the high-overpotential range (ηOER > 0.30 V, cf. Figure 2). Hence, the OER starts from the OOHotterminated surface with the formation of molecular oxygen as the initial step of the electrocatalytic cycle. Additionally, the value of the experimental Tafel slope clearly indicates that the 6760


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interactions with the electrode the interaction with the solvent dominates, and hence, decoupled electron−proton transfer processes become energetically preferred. On the left side of Figure 9, i.e., ΔG2 < 1.37 eV, the electrocatalysts bind the O adsorbate (key intermediate) strongly, and hence, the formation of OOH as the rds in the high-overpotential regime should proceed by a coupled electron−proton transfer in the high-overpotential regime (ηOER > 0.40 V). On the right side of Figure 9, i.e., ΔG2 > 1.77 eV, the OOH adsorbate is identified as the key intermediate, which is also bound strongly to the electrocatalyst’s surface (i.e., ΔG3 is small, cf. Figure 9; further information is given in the SI, Section S4). Hence, the rate-determining step of O2 formation should proceed again via a concerted electron− proton transfer. However, in the threshold region of 1.37 eV < ΔG2 < 1.77 eV, either the O or the OOH adsorbate is stabilized as the key intermediate, but neither is strongly bound to the electrocatalyst surface. Accordingly, the interaction of the key intermediate with the surrounding solvent may dominate so that the rate-determining OOH formation or OOH decomposition may take place by a decoupled electron−proton transfer (cf. Figure 9). If the elementary step of OOH formation, i.e., *−O + H2O(l) → *−OOH + H+ + e−, is ratelimiting in the threshold region of 1.37 eV < ΔG2 < 1.77 eV, then the electron transfer precedes the proton transfer; i.e., a cation is formed as intermediate.

rate-determining reaction step cannot be of a purely chemical nature. Another important issue is that the calculated TS free energies are largely underestimated in the theoretical study. At ηOER = 0.30 V, Ping et al. calculate a TS free energy of 0.58 eV for the chemical formation of the OOHot adsorbate, while the free energy diagram along the reaction coordinate (cf. Figure 5b) reveals a TS free energy of 0.93 eV for the ratedetermining formation of the OHot phase. The difference of 0.35 eV in the TS free energies leads to an overestimation of the current densities in the theoretical study by six orders of magnitude. The constructed free energy diagram for the OER over IrO2(110) based on the experimental Tafel plot (cf. Figure 4) may serve as a benchmark for future kinetics investigations from first-principles, thereby allowing to assess and advance theoretical ab initio electrochemistry. 4.2. Comparison of the Free Energy Diagram with Experimental Data. In a recent communication, Saveleva et al.53 studied the OER over electrochemically and thermally synthesized IrO2 electrodes in the acidic environment by a combination of X-ray photoelectron and absorption spectroscopy under operando conditions to gain molecular insights into the mechanistic processes. The authors concluded that the formation of molecular oxygen occurs through a chemical step from an electrophilic O(−I) species, which itself is formed in an electrochemical step. This result can directly be linked to the free energy diagram (cf. Figure 7), in which the OOHotterminated surface defines the starting point of the electrocatalytic cycle. In the Ircus−OOHot precursor structure, the oxidation state of both oxygen atoms is −I due to the single oxygen−oxygen bond, thereby corroborating the OOH adsorbate as the reaction intermediate within oxygen electrocatalysis. The OOH species is formed by an electrochemical reaction step (Ircus−O + H2O(l) → Ircus−OOH + H+ + e−) as proposed by Saveleva et al.53 The discussion of the OER reaction mechanism in eqs 3−6 is based on the assumption of coupled electron−proton transfer processes so that in turn the constructed free energy diagram in Figure 7 indicates electrochemical reaction steps only. For the OER over IrO2(110), the formation of molecular oxygen via Ircus−OOH → Ircus + O2(g) + H+ + e− is identified as the rds in the high-overpotential regime (ηOER > 0.40 V). A chemical reaction step as part of the reaction mechanism can be envisioned in two different scenarios. First, the rds for the OER over IrO2(110) can be decomposed into the sequence of an electrochemical (Ircus−OOH → Ircus−OO + H+ + e−) followed by a chemical (Ircus−OO → * + O2) step, or second, a chemical reaction step can also be reconciled with decoupled electron−proton transfer within the reaction mechanism for the OER. However, the proposed chemical process cannot be rate-determining for the OER over IrO2(110), since a chemical reaction step as the rds conflicts with the experimentally measured Tafel slope in the high-overpotential regime.13,38 4.3. Implications of Concerted or Decoupled Electron−Proton Transfer Processes. For an in-depth analysis of decoupled or concerted electron−proton transfer processes, it is important to recall the discussion of Koper, who analyzed the potential energy surface for different scenarios.54,55 Koper concluded that, in case of strong interactions of the key intermediate with the electrode surface, concerted electron− proton transfer reactions are favored, whereas in cases of weak

*−O + H 2O → *−O−O+H 2 + e− → *−O−OH + H+ + e−

Note that the formation of an anion by a preceding proton transfer is chemically not sensible, as this situation conflicts with the octet rule. Quite in contrast, if the decomposition of OOH according to *−OOH → * + O2(g) + H+ + e− constitutes the kinetic bottleneck for 1.37 eV < ΔG2 < 1.77 eV, the proton transfer precedes the electron transfer; i.e., an anion is formed as intermediate. *−O−OH → *−O−O− + H+ → * + O2 + H+ + e−

The formation of a cation by a preceding electron transfer is chemically not meaningful when looking at the oxidation states of the involved oxygen atoms. In both cases, an experimental Tafel slope exceeding 59 mV/dec indicates the electron transfer to be rate-determining, while, for a chemical reaction step (proton transfer) as the rds, the Tafel slope would tend to infinity. The discussion of decoupled electron−proton transfers can now be applied to the OER over IrO2(110). From experiments, the value of ΔG2 is known to be (1.56 ± 0.03) eV,38 which is located in the threshold regime of the kinetic scaling relations (cf. Figure 9). This finding agrees fairly well with the theoretical value of ΔG2 from ab initio thermodynamics calculations, which amounts to (1.44 ± 0.05) eV (cf. SI, Section S1). Consequently, in the high-overpotential regime (ηOER > 0.40 V) the proton transfer may precede the electron transfer in the rate-determining decomposition of OOHot according to Ircus−OOHot → Ircus−OOot− + H+ → Ircus + O2 + H+ + e−, which is consistent with the proposed anion redox mechanism of Saveleva et al.53 Since the Tafel slope for the OER over IrO2(110) is 78 mV/dec in the high-overpotential regime, the release of O2 from the OOot− anion precursor is reconciled with the rds. This is summarized in the free energy diagram of Figure 10. 6761


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For the concept of kinetic scaling relations only the knowledge of the free formation energy of oxygen with respect to the OH adsorbate, ΔG2, is required. ΔG2 is accessible to simple ab initio thermodynamics calculations or, as reported by Kuo et al.,49 can also be determined from experiments applying cyclic voltammetry. This correlation promotes computational researchers in materials screening to investigate directly how the transition state of the rate-determining reaction step of the OER can be stabilized to increase the catalytic activity. The concept of kinetic scaling relations is not limited to the OER on transition metal oxide surfaces but rather can be applied to any other multielectron electrocatalytic key reactions over singlecrystalline model electrodes to gain molecular insights into the kinetics and to simplify the kinetic description. 4.5. Robustness of the Kinetic Scaling Relations Approach. The concept of kinetic scaling relations describes the OER kinetics over general transition metal oxides in the high-overpotential regime, that is, ηOER > 0.40 V, where the first reaction step is rate-determining as reflected by a Tafel slope of larger than 59 mV/dec (cf. Section 3.2). Various sources of uncertainties could affect the present analysis:

Figure 10. Essential part of the free energy diagram for the OER over IrO2(110) in acidic media (pH = 1) at ηOER > 0.40, in which the formation of O2 is identified as the rate-determining reaction step. The OOH decomposition proceeds by a decoupled electron−proton transfer, in which the proton transfer (dashed violet line) precedes the rate-determining electron transfer (solid violet line). The formation of an anionic Ircus−OOot− intermediate is consistent with the proposed anion redox mechanism of Saveleva et al.53

We may recall that the rate-determining transition state of OOH decomposition is stabilized by 0.06 eV in acidic medium compared to alkaline medium (cf. Section 3.1.2). This finding may be rationalized by the possibility of decoupled electron− proton transfer in acidic medium that cannot take place in alkaline solution, where hydroxide anions serve as nucleophile. For the case of RuO2(110), the value of ΔG2 is (1.36 ± 0.07) eV.49 Consequently, RuO2(110) also falls also into the threshold regime of a decoupled electron−proton transfer (cf. Figure 9), which may explain the high OER activity of RuO2(110). Altogether, we come to the conclusion that a decoupling of the electron−proton transfer in the ratedetermining OOH formation or OOH decomposition may enhance the activity of transition metal oxide electrocatalysts in acidic medium. 4.4. Decoupled Electron−Proton Transfer Processes: Kinetic Scaling Relations vs Volcano Plots. The concept of kinetic scaling relations presented in Section 3.2 directly provides the kinetic bottleneck (rds) in the high-overpotential regime of the OER and in addition inspires the discussion of concerted or decoupled electron−proton transfer steps. Thus far, linear scaling relationships have been used to construct Volcano plots, in which researchers discussed the “activity” in terms of the thermodynamic overpotential56 as a function of a thermodynamic binding energy (descriptor), such as the free formation energy of oxygen or the free formation energy of oxygen with respect to the OH adsorbate (ΔG2).17,18,20,22,27,43,52,54,57−63 While the construction of a Volcano plot for the OER requires at least two linear scaling functions,17,18 kinetic scaling relations can already be deduced from a single linear scaling relationship; most importantly, kinetic scaling relations allow for kinetic insights into the reaction within a class of materials in contrast to the conventional Volcano concept. The combination of linear scaling relationships17,18 with the free energy diagram approach31 appears to be a valuable extension of thermodynamically based material screening methods, which in certain cases fail to describe the activity of electrocatalysts44,64,65 or are not able to predict the activity trends of highly active catalysts correctly.48,66 The proposed concept of kinetic scaling relations may resolve these discrepancies with the electron−proton transfer to be decoupled for such highly active electrode materials (cf. Figure 9).

(a) The active surface configuration (AS) needs to be determined accurately in the overpotential regime of ηOER > 0.40 V so that conclusions made on the ratedetermining reaction step are unambiguous. (b) The linear scaling relations exhibit error bars due to a linear regression of the DFT-calculated free energies. In addition, the position of the respective electrode material in the linear scaling plot is subject of imprecision. (c) The calculated transition state free energies G#rds within the free energy diagram approach depend on the density of active surface sites Γact (cf. eq 1). For source (a), in the case of the OER over IrO2(110), the active surface state (AS) is identified with the Ircus−OOHot surface termination, which is stabilized at applied overpotential ηOER > 0.30 V (cf. Pourbaix diagram in Figure 2). Two alternative scenarios are conceivable: DFT underestimates or overestimates the free energy for the formation of the Ircus− OOHot surface species. If the actual overpotential value, at which the OOHot adsorbate is stabilized, is smaller than ηOER = 0.30 V then the analysis is not affected. If the threshold overpotential for OOHot stabilization is larger than ηOER = 0.30 V the conclusion may alter. Assume that the switch from the O-covered to the OOH-covered surface takes place at ηOER = 0.41 V; then, the experimentally observed change in Tafel slope from 78 to 49 mV/dec (cf. Figure 3) would be traced to a switch of the active surface configuration from Ircus−Oot to Ircus−OOHot,31,39 while the rds (decomposition of the OOHot adsorbate) remains unchanged. However, this scenario appears to be very unlikely: on one hand, the experimentally observed transfer coefficients in both Tafel regimes are sufficiently different (α = 0.76 or α = 0.20), whereas the transfer coefficient of the same rds should hardly be affected by a change in the active surface configuration. On the other hand, a switch in the Tafel slope is not observed in the corresponding measurements in alkaline media at the same electrode potential on the RHE scale so that the formation of the active Ircus− OOHot surface state at ηOER = 0.41 V can be ruled out. Alternatively, the formation of the OOH-covered surface might occur in an overpotential regime that is not addressed in the experiments (0.35 V ≤ ηOER ≤ 0.47 V), that is, ηOER > 0.47 V. 6762


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We introduce a powerful combination of the free energy diagram in terms of the active surface and the rate-determining reaction step (rds) with linear scaling relationships of the adsorbates OH, O, and OOH relevant to oxygen electrocatalysis18 that may aid material screening. This concept of kinetic scaling relations is able to predict the rds of the OER, namely, either decomposition or formation of the OOH adsorbate, over general transition metal oxides in the highoverpotential regime by the free formation energy of oxygen with respect to the OH adsorbate (ΔG2). This approach goes beyond the concept of volcano curves, which cannot reproduce the activity trends of highly active electrocatalysts correctly.49,64−66 The concept of kinetic scaling relations allows an in-depth discussion of concerted or decoupled electron−proton transfer of the rate-determining OOH formation or decomposition. We suggest that a decoupling of the electron−proton transfer in the rds via the formation of a cation or an anion intermediate state for the formation or the decomposition of OOH, respectively, may enhance the OER activity of transition metal oxide electrocatalysts in acidic media.

In this case, the O-terminated surface would be present in the experimental overpotential range, and the formation rather than the decomposition of the OOH adsorbate would be reconciled with the rds. Correspondingly, the equilibrium potential for the formation of the OOH adsorbate would appear at U0RHE > 1.80 V on the RHE scale. Actually, there is one ab initio study that reported an equilibrium potential for the Oot → OOHot transition of 1.82 V versus RHE (cf. SI, Section S1). However, Hansen et al. neglected the surrounding aqueous electrolyte solution in their calculations,20 which according to Gauthier et al. has major implications on the stabilization of the OOHot adsorbate on the IrO2(110) surface: the solvent stabilizes the OOH adsorbate by about 0.3 eV.21 Therefore, we infer that a threshold overpotential of ηOER > 0.47 V for the formation of the Ircus−OOHot active state is improbable, consistent with DFT calculations of Briquet et al.,22 Sumaria et al.,23 and Ping et al.28 Altogether, the above discussion emphasizes that the formation of the active Ircus− OOHot surface configuration proceeds in an overpotential window of ηOER < 0.35 V. For source (b), a linear scaling relation or a Volcano plot is affected by the error bars of the linear scaling relationship due to the linear regression and the error of the electrode material’s position in the linear scaling given by ΔG2. The error bars of the linear regression have been addressed in Figure 9. These uncertainties are rather small compared to the electrode material’s position in the linear scaling, as the linear scaling function is relatively robust and independent of the chosen GGA functional in the underlying DFT calculations.57 Therefore, the main error source is the electrode material’s position in the linear scaling plot (ΔG2).57 Both experimental (ΔG2 = (1.56 eV ± 0.03) eV)49 and theoretical (ΔG2 = (1.44 eV ± 0.05) eV) data suggest that IrO2(110) is in the threshold regime of a decoupled electron−proton transfer (1.37 eV < ΔG2 < 1.77 eV). However, the discussion of concerted or decoupled electron−proton transfer steps should be treated with some caution, since already a variation of a few 100 mV in the free energy change ΔG2 could lead to erroneous conclusions concerning the rds and/or a decoupled or a concerted electron−proton transfer. For source (c), the quantitative analysis of the free energy diagram (cf. Figure 4) in terms of the TS free energies depends on the density of active surface sites Γact (cf. eq 1). If we assume that the actual density of active surface sites differs from our proposed value by one order of magnitude, the corresponding TS free energies are affected by less than 0.06 eV. This uncertainty in the TS free energies is much smaller compared to the error bars of current state-of-the-art ab initio kinetic models.31,57

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.9b01564.

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Ab initio Pourbaix diagram, free energy diagram, kinetic scaling relations, and a discussion of concerted or decoupled electron−proton transfers based on the kinetic scaling relations (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Herbert Over: 0000-0001-7689-7385 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS K.S.E. gratefully acknowledges funding from the Alexander von Humboldt Foundation and thanks the International Society of Electrochemistry (ISE) for an ISE Travel Award for Young Electrochemists. H.O. is thankful for financial support from the BMBF (project: 05K2016- HEXCHEM) and the DFG (SPP2080: Ov21-16).

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5. CONCLUSIONS With the combination of experimental Tafel plots38 and ab initio Pourbaix diagrams20−23,28 the essential part of the free energy diagram along the reaction coordinate can be constructed,31,39 which in turn may serve as the benchmark for future ab initio kinetic studies. This approach was successfully applied to the OER over a single-crystalline IrO2(110) electrode surface to identify the kinetic bottleneck in the reaction mechanism. It turns out that the decomposition of the OOH adsorbate into molecular oxygen constitutes the rate-determining reaction step in the high-overpotential regime (ηOER > 0.40 V).

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Beyond the Rate-Determining Step in the Oxygen Evolution Reaction

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