Beyond the Traditional Volcano Concept: Overpotential-Dependent

Jun 17, 2019 - Beyond the Traditional Volcano Concept: Overpotential-Dependent Volcano Plots Exemplified by the Chlorine Evolution Reaction over ...
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Article Cite This: J. Phys. Chem. C 2019, 123, 16921−16928

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Beyond the Traditional Volcano Concept: Overpotential-Dependent Volcano Plots Exemplified by the Chlorine Evolution Reaction over Transition-Metal Oxides Kai S. Exner*

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Faculty of Chemistry and Pharmacy, Department of Physical Chemistry, Sofia University, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria ABSTRACT: The chlorine evolution reaction (CER) over a single-crystalline RuO2(110) model electrode is one of the best understood model systems in the field of electrocatalysis, which is taken here as a benchmark system to advance the concept of activity-based Volcano plots. Volcano curves can be derived from linear scaling relationships, in which thermodynamic considerations based on Sabatier’s principle and the Brønsted−Evans− Polanyi relation at zero overpotential are assumed to describe activity trends of electrocatalysts within a homologous series of materials. However, the underlying approach does not capture the influence of the applied overpotential on the activity, which is given by the Tafel slope. This may explain, why in certain cases the traditional Volcano analysis at zero overpotential does not reproduce activity trends of highly active catalytic materials with an overpotential-dependent Tafel slope correctly. Herein, a novel approach of overpotential-dependent Volcano plots is presented, which connects thermodynamics with kinetics at the respective target overpotential and includes the experimental Tafel slope into the analysis to describe the activity. This methodology is applied to the CER over transition-metal oxide electrodes, such as RuO2(110) and IrO2(110): while the traditional Volcano analysis at zero overpotential ascertains IrO2(110) to be more active in the CER, the overpotential-dependent Volcano plot reproduces the experimentally observed higher CER activity of RuO2(110) compared to IrO2(110) qualitatively as well as quantitatively. This result puts additional emphasis on the fact that the applied overpotential needs to be accounted for in material screening trend studies.

1. INTRODUCTION Volcano plots, which rely on a combination of Sabatier’s principle1 and the Volcano relationship,2,3 are a valuable tool in the fields of heterogeneous4−6 and homogeneous catalysis7 and electrocatalysis8−12 to comprehend on the activity of electrode materials within a homologous series by simple thermodynamic considerations. Meanwhile, the impact of Volcano curves even goes beyond the catalytic community, since the underlying framework was transferred from catalysis to battery research to analyze the intercalation of lithium ions into nanosized electrodes.13,14 In the field of electrocatalysis, Trasatti was the first to construct a Volcano-shaped curve for the electrocatalytic hydrogen evolution reaction (HER) by plotting the exchange current density (evaluated at zero overpotential) as a function of the energy of hydride formation.15 From this time on, the exchange current density was accepted as a measure of the activity of an electrocatalyst in a Volcano plot, whereas the effect of the applied overpotential on the catalytic activity, given by the Tafel slope, was assumed to be negligible within a class of materials.16 At the beginning of the 21st century, the invention of the computational hydrogen electrode (CHE) approach by Nørskov and co-workers17 spurred the electrocatalytic community, since it became possible to determine binding energies of reaction intermediates adsorbed on an electrocatalyst’s surface in dependence of the respective environmental parameters, that is, the applied electrode © 2019 American Chemical Society

potential and pH. Based on the CHE concept, Nørskov and co-workers deduced the so-called thermodynamic overpotential, ηTD, as a measure of the activity of an electrocatalyst by conjoining Sabatier’s principle1 with the Brønsted−Evans− Polanyi (BEP) relation18 at zero overpotential. In principle, the framework of ηTD continues the traditional Volcano analysis in terms of the exchange current density by ab initio theory, since the thermodynamic overpotential is also evaluated at zero overpotential and hence may scale with the exchange current density.19,20 Therefore, ηTD is most commonly used as activity descriptor in ab initio Volcano plots17,19 that can be easily constructed by the framework of linear scaling relationships.20−25 Even though Schmickler and Trasatti inferred from a comparison of experimental exchange current densities with theoretically calculated ηTD values that the concept of the thermodynamic overpotential is overly simplistic,26,27 the construction of Volcano plots with ηTD as measure for the activity is nowadays state of the art in the field of ab initio electrocatalysis.28 This finding is mainly reconciled by the fact that material screening based on ηTD provides an excellent balance of a reasonable accuracy in conjunction with low computational cost: the evaluation of simple binding energies enables to exclude electrocatalysts at the legs of the Volcano so Received: June 5, 2019 Published: June 17, 2019 16921

DOI: 10.1021/acs.jpcc.9b05364 J. Phys. Chem. C 2019, 123, 16921−16928

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The Journal of Physical Chemistry C that the search for improved electrode materials can be focused on promising candidates at the top or close to the apex of the Volcano curve.29 However, recently, critical remarks concerning the reliability of the conventional Volcano concept have increased: several researchers reported independently that ηTD does not reproduce activity trends of electrocatalysts correctly,30−34 where in particular the trends of highly active catalytic materials are affected.30,31 Such highly active electrocatalysts reveal a switch in the Tafel slope (small Tafel slope in the lowoverpotential regime and an increased Tafel slope in the highoverpotential regime), which is traced to the fact that a smaller Tafel slope is accompanied by a larger apparent transfer coefficient.2,35 Hence, the transition state (TS) free energy of the rate-determining TS is most efficiently stabilized before the change in the Tafel slope takes place, which improves the catalytic activity with increasing overpotential.36 Actually, an overpotential-dependent Tafel slope can even alter activity trends within a homologous series of materials.37 The effect of the Tafel slope on the activity, however, cannot be captured by the application of ηTD as activity descriptor in Volcano plots: the thermodynamic overpotential, ηTD = ΔGmax(η = 0 V)/e, corresponds to the highest free-energy change at zero overpotential, ΔGmax(η = 0 V), among the set of reaction intermediates divided by the elementary charge. Hence, the traditional Volcano analysis refers to the (standard) equilibrium potential of the underlying electrocatalytic reaction, which corresponds to zero overpotential.8−12 The concept of overpotential-dependent Volcano plots relies on the idea to account for a change in the Tafel slope with increasing overpotential. This is only possible, if the respective Tafel slopes of single-crystalline model systems are known. Here, the chlorine evolution reaction (CER) over RuO2(110) can be seen as a benchmark system in the field of electrocatalysis,36 since complete information on the thermodynamics (active surface and reaction intermediates)38−41 and the kinetics (transition-state free energies and Tafel slope)42−46 are available. Recently, Suntivich and co-workers have investigated the CER over IrO2(110) and demonstrated that RuO2(110) is by about 2 orders of magnitude more active than IrO2(110).46 Herein, the reason for the higher activity of RuO2(110) in the CER is elucidated by connecting the experimental Tafel slope with a recently proposed thermodynamic descriptor for the activity, |ΔG(η)|,37 which is capable of comprehending on a change in the Tafel slope with increasing overpotential. This procedure enables to assess activity trends not only qualitatively, but also quantitatively for a specific situation. The constructed overpotential-dependent Volcano curve may provide a guide to the hand, where promising electrode materials in the same class of materials can be found, assuming that the Tafel kinetics in this homologous series remains unaltered. The present work introduces an alternative material screening approach compared to the framework of ηTD and continues recent research activities of various groups to develop material screening approaches beyond the traditional Volcano analysis.31,47,48

(OER) takes place, which constitutes a detrimental side reaction and reduces CER selectivity.49−53 The encountered selectivity problem is solved by acidifying the electrolyte solution, since for most electrode materials the OER is efficiently suppressed in an acidic environment (pH < 1), where only the CER is operative.53 The most prominent CER electrocatalyst is RuO2 with the (110) facet as most stable surface termination54 because RuO2 has been identified as active component35 in dimensionally stable anodes (DSA)55−57 that are employed at anode side in the industrial chlor-alkali process.58−60 The surface chemistry of RuO2(110) under CER conditions and the reaction mechanism have been intensively studied by theoretical38−41 and experimental42−46 investigations: under CER conditions, that is, ηCER = U − UCER0 > 0 V, the RuO2(110) surface is fully oxygen-covered, i.e., all onefold coordinatively unsaturated Ru surface atoms (Rucus) are capped by on-top oxygen (Oot) and the neighboring Ru2f atoms are bridged by undercoordinated surface oxygen (Obr); a ball-and-stick model of the fully oxygen-covered RuO2(110)-Oot surface is shown in Figure 1a.

2. RESULTS AND DISCUSSION 2.1. Chorine Evolution Reaction (CER). The CER is a fast two-electron process, in which two chloride anions are discharged under the formation of gaseous chlorine: 2Cl(aq)− → Cl2(g) + 2e−, UCER0 = 1.36 V vs SHE. In the same potential window of the CER, the competing oxygen evolution reaction

The reaction mechanism of the CER over RuO2(110) is ascribed to the pathway of Volmer−Heyrovsky:61,62 in the Volmer step, a chloride anion from the electrolyte solution is adsorbed on the active Rucus−Oot site, thereby forming a Rucus−OClot precursor species. Thereafter, the chlorine atom in the Rucus−OClot precursor state directly recombines with

Figure 1. (a) Ball-and-stick model of the fully oxygen-covered RuO2(110)-Oot surface, i.e., all undercoordinated Rucus sites are capped by on-top oxygen (Oot), in which Rucus-Oot surface complexes are reconciled as active site for chlorine formation. Color code: the red balls indicate onefold coordinatively unsaturated ruthenium atoms (Rucus), while the green balls and blue balls denote oxygen atoms and coordinatively saturated Ru atoms (Ru2f), respectively. (b) Reaction mechanism of the CER over the active Rucus-Oot site corresponding to the description of Volmer−Heyrovsky: while for ηCER < 0.10 V the Heyrovsky step (solid thick blue line) with an apparent transfer coefficient of β = 1.5 governs the kinetics, the Volmer step (dashed thick violet line), comprising β = 0.5, limits the activity for ηCER > 0.10 V.

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catalysts binds all reaction intermediates thermoneutral at zero overpotential, the framework of |ΔGOCl(ηCER)| = 0 suggests that the decisive reaction intermediate, here OClot, needs to be stabilized on the electrocatalyst’s surface at target overpotential ηCER.37 The stabilization of OClot at target overpotential ηCER ensures that the free energy of OClot becomes smaller than that of the precursor Oot for η > ηCER, which results in a switch of active surface from Oot to OClot for η > ηCER. The alternation of the active surface configuration is accompanied by a change in the Tafel slope, which increases from 40 mV/dec (η < ηCER) to 120 mV/dec (η > ηCER) due to a renumbering of the electron transfers in the free-energy diagram.30,36 The smaller Tafel slope of 40 mV/dec in the low-overpotential regime (η < ηCER) causes the applied overpotential to most efficiently decrease the free energy of the rate-determining TS, which results in an improved electrocatalytic activity in the overpotential regime of the Tafel slope change, that is, at η = ηCER.37 The requirement |ΔGOCl(ηCER)| = 0 shows that any applied overpotential ηCER reveals its own specific oxygen binding strength, ΔEO, for which the underlying electrocatalytic reaction, here the CER, is catalyzed with optimum capability. This methodology is applied in the CER overpotential range of ηCER > 0.03 V, where a linear ηCER vs log j relation according to the Tafel kinetics64−66 is obtained. The rate of an electrocatalytic reaction is governed by the TS with highest free energy,2,36,67 denoted as Grds#, which corresponds either to the Volmer or to the Heyrovsky step (cf. Figure 1b). The experimental measurements of Suntivich and co-workers indicate that both RuO2(110) and IrO2(110) reveal a switch in the Tafel slope at about ηCER = 0.10 V,46 which coincides with the data of Over and co-workers for RuO2(110).44,45 Consequently, the free energy of the rate-determining transition state Grds# is lowered by 1.5·e·ηCER (β = 1.5) or 0.5·e·ηCER (β = 0.5) for ηCER < 0.10 V or ηCER > 0.10 V, respectively (cf. Figure 1b). The link of thermodynamics with kinetics at target overpotential ηCER by determining ΔEO as a function of ηCER in conjunction with the decrease of Grds#(ηCER) with increasing overpotential according to the apparent transfer coefficient β derived from the Tafel slope enables to compile an overpotential-dependent Volcano plot, which is shown in Figure 2. While the slope of each Volcano in Figure 2 is given by the prefactor of ΔEO in the linear scaling function (cf. eq 4), the activity in terms of the rate-determining transition-state free energy, Grds#(ηCER), is indicated with respect to its value at ηCER = 0 V. The overpotential-dependent Volcano plot in Figure 2 reveals that an increase in the applied overpotential shifts the optimum performance of transition-metal oxides in the CER to weaker oxygen binding: while for small overpotentials, that is, ηCER = 0.03 V, the optimum oxygen binding energy amounts to ΔEO = 1.45 eV, quite in contrast, ΔEO = 1.75 eV is obtained at ηCER = 0.15 V. This finding differs from a conventional Volcano plot with ηTD as activity descriptor, where it is assumed that the ΔEO value, determined at ηCER = 0 V, governs the performance in the complete overpotential window.17,28 The optimum oxygen binding energy corresponding to the conventional Volcano plot amounts to ΔEO = 1.38 eV, that is, the oxygen binding energy where the reaction intermediate is bound thermoneutral at zero overpotential, equivalent to ηTD = 0 V. This value is compared in the further course to the overpotential-dependent Volcano curve when

another chloride anion from the electrolyte solution in the Heyrovsky step, resulting in the formation of gaseous chlorine Rucus−Oot + Cl− → Rucus−OClot + e− (Volmer step) (1)

Rucus−OClot + Cl− → Rucus−Oot + Cl 2 + e− (Heyrovsky step)

(2)

The rate-determining reaction step (rds) of the CER over RuO2(110) strongly depends on the applied overpotential; while for small overpotentials, that is, ηCER < 0.10 V, the Heyrovsky step (cf. eq 2) limits the activity, a switch in the rds is observed for ηCER > 0.10 V, where the Volmer step (cf. eq 1) governs the kinetics (cf. Figure 1b).30,36 The alternation of the rds at ηCER > 0.10 V causes a change in the Tafel slope from 36 to 86 mV/dec, thereby reducing the apparent transfer coefficient. To generalize the analysis, the traditional Tafel slope values of 40 and 120 mV/dec are taken, which correspond to apparent transfer coefficients (β) of 1.5 and 0.5. Since β directly specifies the number of electrons transferred to pass over the rate-determining transition state, the experimental Tafel slope reveals a direct link to the freeenergy diagram along the reaction coordinate, which is depicted in Figure 1b.36 It shall be stressed that the outcome of Figure 1b is independent of using the precise (36 and 86 mV/dec) or the generalized Tafel slope values (40 and 120 mV/dec). The threshold potential for the switch in the Tafel slope has also been scrutinized by temperature-dependent experiments, where an overpotential value of ηCER = 0.10 V was determined, which coincides with the discussion of the transfer coefficients in Figure 1b.44 A general presumption in material screening is that the reaction mechanism remains unchanged within a homologous series of materials.63 Therefore, it is expected that the CER over general transition-metal oxide electrodes proceeds via the Volmer−Heyrovsky mechanism, in which either the Volmer or the Heyrovsky step is rate-limiting. This hypothesis is actually fulfilled for the CER over IrO2(110), as demonstrated by Viswanathan and co-workers in a recent contribution.41 By the construction of a surface Pourbaix diagram, the authors identified an OClot precursor state as a crucial reaction intermediate in the CER, which coincides with the case of RuO2(110).39,40 2.2. Overpotential-Dependent Volcano Plot for the Chlorine Evolution Reaction over Transition-Metal Oxides. The analysis of Viswanathan and co-workers was extended to general transition-metal oxides, including RuO2(110) and IrO2(110), for which the authors determined a linear scaling relationship of the free energy of the precursor species OClot as a function of the energy of the active site Oot ΔGOCl = 0.4·ΔEO + 0.81 eV

(3)

The linear scaling function in eq 3, which corresponds to zero electrode potential, U = 0 V vs. SHE, can be translated to an arbitrary CER overpotential, η CER , by combining the mechanistic description in eq 1 with the CHE method ΔGOCl(ηCER ) = 0.4·EO − 0.55 eV − e·ηCER

(4)

The recently presented framework of |ΔG(η)| shows that optimum performance is ascribed to the precondition |ΔGOCl(ηCER)| = 0.37 While the conventional analysis based on the thermodynamic overpotential, ηTD,17 states that an ideal 16923

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Figure 2. Overpotential-dependent Volcano plot for the CER over general transition-metal oxide electrodes. For each specified applied overpotential ηCER, thermodynamics according to the underlying framework of |ΔGOCl(ηCER)| = 0 is linked to the kinetics in terms of the transition-state free energy Grds#(ηCER), which governs the activity of an electrocatalyst. Herein, Grds#(ηCER) is indicated with respect to the corresponding value at zero overpotential, that is, Grds#(ηCER = 0 V). The decline of the rate-determining transition-state free energy with increasing overpotential is given by the apparent transfer coefficient β that can be deduced from the experimental Tafel slope. If the applied overpotential ηCER is enhanced, the apex (indicated by a circle) of each Volcano, corresponding to optimum performance in the CER at respective overpotential ηCER, is shifted toward weaker oxygen binding, i.e., larger values of ΔEO.

Figure 3. Overpotential-dependent Volcano plot for the CER over general transition-metal oxide electrodes. The center of the oxygen binding energy for RuO2(110) (yellow background) is localized at larger ΔEO values than that of IrO2(110) (pink background). This may explain the higher activity of RuO2(110) compared to IrO2(110) in the CER at typical overpotentials of chlor-alkali electrolysis (ηCER = 0.10 V), which is also reflected by experimental studies.46

contrast, the weaker oxygen binding of RuO2(110) compared to IrO2(110) results in a higher CER activity at ηCER > 0.05 V, where the Heyrovsky step (β = 1.5) governs the activity (cf. Figure 1b). This can be quantified by calculating Grds#(ηCER) = −1.5·e·ηCER vs Grds#(ηCER = 0 V): in the case of IrO2(110), the center of the oxygen binding energy (ΔEO = 1.39 eV) translates to ηCER = 0.01 V, which is reconciled with Grds#(ηCER) = −0.015 eV vs Grds#(ηCER = 0 V). In analogy, the center of the oxygen binding energy for RuO2(110), that is, ΔEO = 1.53 eV, converts to ηCER = 0.06 V, which yields Grds#(ηCER) = −0.09 eV vs Grds#(ηCER = 0 V). A difference of 75 meV in the transition-state free energy causes a higher CER activity of about 1.3 orders of magnitude in an experimental Tafel plot,36 when evaluating log10[exp(0.075 eV/kBT)], where kB and T denote Boltzmann constant and the absolute temperature (T = 298.15 K), respectively. The underlying calculation assumes that the density of active surface sites of IrO2(110) and RuO2(110) is comparable and does not affect the outcome;36 this precondition is actually fulfilled.41 The higher CER activity of RuO2(110) fairly agrees with the experimental results of Suntivich and co-workers, who reported that RuO2(110) is by about 2 orders of magnitude more active than IrO2(110) in the CER by comparing the current densities of the experimentally measured Tafel plots.46 Actually, also a difference of 2 orders of magnitude in CER activity can be reproduced when considering the oxygen binding energies’ error bars of both electrode materials: in the case of IrO2(110), ΔEO = 1.38 eV translates to ηCER = 0 V, which provides Grds#(ηCER) = Grds#(ηCER = 0 V). In analogy, ΔEO = 1.57 eV for RuO2(110) converts to ηCER = 0.08 V. This yields Grds#(ηCER) = −0.12 eV vs Grds#(ηCER = 0 V). A difference of 120 meV in the transition-state free energy indicates that RuO2(110) is 2 orders of magnitude more active than IrO2(110) in the CER due to log10[exp(0.12 eV/kBT)] ≈ 2. When comparing the overpotential-dependent Volcano plot to the conventional Volcano analysis with ηTD as descriptor, it turns out that the conventional Volcano plot suggests IrO2(110) to be more active than RuO2(110) in the CER: the oxygen binding energy of IrO2(110), that is, ΔEO = (1.39 ± 0.10) eV, is located directly at the apex of the conventional Volcano corresponding to ΔEO = 1.38 eV. Quite in contrast, the oxygen binding energy of RuO2(110), that is, ΔEO = (1.53

discussing the CER activity trends of IrO2(110) and RuO2(110). The apex of a Volcano plot is generally a subject of large error bars.50 In principle, a Volcano plot consists of two different error components that affect the analysis as well as the underlying conclusions: (a) the error of the linear scaling relation, which alters the position of the Volcano; (b) the error of the electrode material’s position in the Volcano, which is given in this specific case by the oxygen binding energy (ΔEO) of RuO2(110) and IrO2(110). While the Volcano curve is relatively robust independent of the chosen GGA functional in the DFT calculations, the main error source constitutes an inaccurate determination of the electrode material’s position in the Volcano.29 Consequently, the error related to the position of RuO2(110) and IrO2(110) in the Volcano curve (cf. Figure 2) is discussed hereafter, whereas the Volcano itself is assumed to be robust. The affiliated oxygen binding energies for IrO2(110) and RuO2(110) including their error bars from the study of Viswanathan and co-workers,41 that is, ΔEO = (1.39 ± 0.10) eV and ΔEO = (1.53 ± 0.10) eV, respectively, are indicated in Figure 3. Figure 3 reveals that for ΔEO < 1.43 eV, IrO2(110) may show a superior performance to RuO2(110) (pink background), whereas the opposite case is encountered for ΔEO > 1.49 eV (yellow background). For 1.43 eV < ΔEO < 1.49 eV, either IrO2(110) or RuO2(110) is the better electrocatalyst (light brown background), since in this area the error bars of both oxygen binding energies overlap. The affiliated oxygen binding energy regimes of IrO2(110) and RuO2(110) can be translated to CER overpotentials via the framework of |ΔGOCl(ηCER)| = 0, which amount to ηCER < 0.02 V (ΔEO < 1.43 eV) and ηCER > 0.05 V (ΔEO > 1.49 eV), respectively. Consequently, IrO2(110) is assumed to show a better performance than RuO2(110) in the backward reaction, that is, the chlorine reduction reaction (CRR), which in the presence of gaseous chlorine is operative at ηCER < 0 V. In 16924

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descriptor |ΔG(η)| that the author introduced in a recent contribution: |ΔG(η)| is able to account for a change in the Tafel slope with increasing overpotential due to a switch in the active surface configuration, whereas an alternation of the ratedetermining reaction step (rds) is not captured in the underlying approach.37 This finding, however, does not affect the location of the electrode material in the overpotentialdependent Volcano (x-axis) and hence may not influence the qualitative analysis, in which the performance of the electrocatalyst in dependence of the applied overpotential is assessed. Quite in contrast, for electrocatalysts with a change in the rds, the quantitative assessment of activity trends within a homologous series of materials could become erroneous, since a switch of the rds reduces the apparent transfer coefficient, which has direct implications on the TS free energy in dependence of the applied overpotential, Grds#(η) (cf. Section 2.1). In the case of the CER over RuO2(110) and IrO2(110), the discussed shortcoming does not affect the outcome of the analysis, since the observed activity trends coincide quantitatively with the model experiments of Suntivich and co-workers.46 Another subtlety is related to the material screening approach discussed in Section 2.3: by using the constructed overpotential-dependent Volcano curve of the CER over RuO2(110) and IrO2(110) for material screening investigations of general transition-metal oxides, it is tacitly assumed that the Tafel kinetics of all other electrode materials in the same class of materials remains unchanged, i.e., the switch in the Tafel slope occurs at the same threshold overpotential for all electrocatalysts. This presumption might be fulfilled for certain electrode materials, but is not necessarily met for all transition-metal oxides. The qualitative analysis, i.e., at which applied overpotential the decisive reaction intermediate is stabilized by a certain transition-metal oxide, is not affected by this subtlety, since the location of the electrode material in the overpotential-dependent Volcano (x-axis) is given by the linear scaling function determined from ab initio theory. However, a different kinetics in terms of the Tafel slope directly affects Grds#(η) on the y-axis so that in the worst case activity trends are assessed erroneous: a possible scenario is that overmuch electrode materials fall into the auspicious oxygen binding energy range for the CER over transition-metal oxides, ΔEO = (1.50−1.85) eV (cf. Section 2.3), whereas only a few of these materials are practically relevant for chlorine electrocatalysis, since the irrelevant catalysts reveal an unfavorable Tafel behavior (such as only one linear Tafel regime).37 Another potential option is that particular active electrode materials do not fall into the proposed oxygen binding energy regime, as the reaction mechanism fundamentally differs.41 In this regard, it should be emphasized that the purpose of material screening is to identify certain promising electrode materials, on which the further search of improved materials can be focused.28,29 Actually, this criterion is still met by the construction of overpotential-dependent Volcano plots, in that potentially active electrocatalysts are suggested based on a combination of experimental Tafel plots and linear scaling relationships, where compared to the conventional Volcano approach, the effect of the applied overpotential on activity trends is accounted for.

± 0.10), is situated beneath the Volcano’s apex, which is reconciled with smaller activity. This outcome is in contrast to experiments46 as well as to the overpotential-dependent Volcano plot (cf. Figure 3). Therefore, it can be concluded that a consideration of the applied overpotential is indispensable when assessing activity trends of electrocatalysts in a homologous series of materials with a change in the Tafel slope.37 The oxygen binding energy of RuO2(110), ΔEO = (1.53 ± 0.10) eV, can be converted into an overpotential operating window by the framework of |ΔGOCl(ηCER)| = 0, which is given by ηCER = (0.06 ± 0.04) eV (cf. Figure 3). This indicates that the center of optimum performance for RuO2(110) is situated at slightly lower overpotentials compared to the chlor-alkali process, where typical overpotentials of at least ηCER = 0.10 V are applied.54,59 However, DSA in industrial electrolysis consists of a mixture of RuO2 and TiO2. Since the vicinity of TiO2 lowers the oxygen binding strength of RuO2,50 the DSA composition might be located at somewhat larger ΔEO values compared to RuO2(110), which explains the excellent performance of DSA on a molecular level under the respective operating conditions of industrial electrolysis. 2.3. Generalization of the Presented Approach: Overpotential-Dependent Volcano Plots for Material Screening Purposes. In general, the outlined methodology of overpotential-dependent Volcano plots enables to elucidate activity trends of electrocatalysts in dependence of the applied overpotential qualitatively as well as quantitatively (cf. Section 2.2). As precondition, both experimental and theoretical data need to be available for the investigated set of electrode materials. If for the evaluated set of electrocatalysts the respective activity trends are resolved and well understood, the constructed overpotential-dependent Volcano curve can be used as a guideline to screen improved electrode materials in the same class of materials by the application of simple ab initio thermodynamics calculations.68−71 This aspect is illustrated at the example of the CER over RuO2(110) and IrO2(110) and continues the above discussion. The overpotential-dependent Volcano in Figure 3 exhibits the (optimum) oxygen binding energy as a function of the applied overpotential by relying on the framework of |ΔGOCl(ηCER)| = 0.37 Since typical overpotentials in the CER amount to at least ηCER = 0.10 V,54,59 an overpotential regime of ηCER = (0.10−0.15) V as operating CER window is assumed, which translates to an oxygen binding energy range of ΔEO = (1.60−1.75) eV (cf. Figure 3). Assuming an error of ±0.10 eV for the location of the electrode material in the overpotentialdependent Volcano,41 the related oxygen binding energy regime of ΔEO = (1.50−1.85) eV appears to be auspicious for chorine electrocatalysis over transition-metal oxides. Material screening may now be conducted by density functional theory (DFT) calculations to evaluate the largest possible set of electrocatalysts within the class of transition-metal oxides: electrode materials that fall within the specified range of ΔEO = (1.50−1.85) eV are identified as promising CER electrocatalysts. The suitability of the recognized electrode materials in the affiliated ΔEO regime needs to be counterchecked thereafter by recording an experimental Tafel plot, in that the measured current density is compared to a suitable reference system, in this specific case, the CER over RuO2(110).44−46 2.4. Shortcomings and Subtleties of OverpotentialDependent Volcano Plots. The construction of overpotential-dependent Volcano plots relies on the activity

3. CONCLUSIONS In this communication, the concept of overpotential-dependent Volcano plots based on a recently suggested thermodynamic activity descriptor |ΔG(η)|37 is presented. The frame16925

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work of overpotential-dependent Volcano curves enables to screen activity trends of electrode materials within a homologous series of materials by explicitly including the applied overpotential into the analysis. The presented methodology revises the conventional Volcano approach of Nørskov and co-workers in terms of ηTD as a measure of the activity, in that thermodynamics and kinetics are not linked at zero overpotential, but rather at target overpotential η. This procedure ensures that the effect of the applied overpotential η on the activity, given by the Tafel slope, is captured in the underlying approach. The constructed overpotential-dependent Volcano plot for the CER over transition-metal oxides enables to explain the experimentally observed higher activity of RuO2(110) compared to IrO2(110) on a molecular level: due to weaker oxygen binding, RuO2(110) is by about 2 orders of magnitude more active than IrO2(110) in the CER. The outlined concept of overpotential-dependent Volcano plots might become a valuable tool to explain and quantify activity trends of electrocatalytic materials, for which both experimental and theoretical data in the form of Tafel plots and ab initio thermodynamics calculations are available. The knowledge gained from the evaluated specific situation can be used for material screening purposes thereafter by relying on the (tacit) assumption that the Tafel kinetics remains unchanged in the investigated class of materials. This might enable to predict promising electrode materials for two-electron processes with applications in energy and environmental science, including electrolysers and fuel cells, where the hydrogen evolution or reduction reaction is operative at cathode or anode side, respectively.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kai S. Exner: 0000-0003-2934-6075 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author gratefully acknowledges funding from the Alexander von Humboldt Foundation and the International Society of Electrochemistry (ISE) for an ISE Travel Award for Young Electrochemists.

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REFERENCES

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4. METHODS AND MATERIALS The free-energy diagram along the reaction coordinate in Figure 1b is constructed based on experimental Tafel measurements for the kinetics and DFT calculations for the thermodynamics. The Tafel plot was measured by chronoamperometric pulse experiments, which is described in ref 44 in detail. The underlying DFT calculations of the author were performed using PBE+D3 as exchange correlation functional. Solvation is considered by adding explicit water molecules on top of the RuO2(110) surface slab. Complete computational details are given in ref 40. The construction of the free energy diagram along the reaction coordinate by combining experiments with ab initio theory is described in ref 36. The linear scaling function for the OClot precursor in dependence of the active Oot site is taken from the study of Viswanathan and co-workers in ref 41, who scaled the calculated (free) energies of the two decisive CER intermediates for the class of transition-metal oxides based on the CHE approach of Nørskov and co-workers (ref 17). In the underlying DFT calculations, the Bayesian error estimation functional with van der Waals correlation (BEEF-vdW) was applied, which has built-in error estimation capabilities to quantify the confidence in theoretical calculations. The construction of the overpotential-dependent Volcano plot in Figures 2 and 3 is based on the framework of the thermodynamic descriptor |ΔG(η)|, which enables to link thermodynamics with kinetics via Sabatier’s principle and the BEP relation at target overpotential η. The underlying approach of the author is described in ref 37. 16926

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