Is Thermodynamics a Good Descriptor for the Activity? Re

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Is Thermodynamics a Good Descriptor for the Activity? Re-Investigation of Sabatier’s Principle by the Free Energy Diagram in Electrocatalysis Kai Steffen Exner ACS Catal., Just Accepted Manuscript • Publication Date (Web): 30 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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Is Thermodynamics a Good Descriptor for the Activity? Re-Investigation of Sabatier’s Principle by the Free Energy Diagram in Electrocatalysis Kai S. Exner1,* 1

Sofia University, Faculty of Chemistry and Pharmacy, Department of Physical Chemistry, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria

* Corresponding author: [email protected] ORCID: 0000-0003-2934-6075

Abstract: The computational hydrogen electrode (CHE) approach has spurred ab initio investigations in the field of electrocatalysis, since the underlying concept enables to quantify free energy changes, ΔG (thermodynamics), for the formation of reaction intermediates on an electrocatalyst surface. The connection between thermodynamics and kinetics (activity) is achieved by Sabatier’s principle: the optimum situation to realize an active electrocatalyst is ascribed to reaction intermediates bound thermoneutral (ΔG = 0 eV) at zero overpotential. In order to validate the linkage between thermodynamics and kinetics at zero overpotential for two-electron processes, free energy diagrams as function of the applied electrode potential are compiled. Herein, the chlorine evolution reaction (CER) over RuO2(110), one of the best understood model systems in electrocatalysis, is used as starting point for this investigation. It turns out that the connection between thermodynamics and kinetics at zero overpotential does not reproduce activity trends correctly if the Tafel slope is overpotential dependent. Therefore, it appears expedient to include the applied overpotential into the thermodynamic framework: for electrocatalysts with a change in the Tafel slope, it is suggested to employ the absolute free energy change for the formation of a reaction intermediate at respective overpotential η, |ΔG(η)|, as thermodynamic descriptor for the kinetics of two-electron processes, which may aid the construction of overpotential-dependent Volcano plots for improved material screening. Keywords: electrocatalysis, free energy diagram, thermodynamics, overpotential, Volcano plot, chlorine evolution, ruthenium dioxide -1ACS Paragon Plus Environment

thermodynamic

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Graphical Abstract:

1 Introduction Chlorine belongs to the most important inorganic basic chemicals according to its vast use as oxidizing agent in chemical industry,1 such as for the synthesis of plastics. Production of chlorine is mainly encountered within chlor-alkali electrolysis, the second largest industrial electrochemical process with a capacity of more than 70 million tons Cl2 per year.2-5 As anode material, dimensionally stable anodes (DSA) consisting of Ti plates coated with rutile TiO2 – RuO2 mixed oxides are employed.6-8 A molar ratio of at least 30% RuO2 is required in order to maintain reasonable high current densities during operating, since RuO2 has been identified as active component of the chlorine evolution reaction (CER): 2 Cl–(aq)  Cl2(g) + 2 e– (U0CER = 1.36 V vs. SHE).9 Consequently, RuO2(110) as most stable surface termination of rutile RuO2 is envisioned as appropriate single-crystalline model system to gain an in-depth understanding of the electrochemical CER.10 Recently, it was demonstrated that the underlying physical-chemical processes in the CER are even simpler than in the hydrogen evolution reaction (HER),11 which so far was considered as a benchmark two-electron process in electrocatalysis.12 Meanwhile, the CER over RuO2(110) is probably the best understood system in the field of electrocatalysis, which is reconciled by the fact that the free energy diagram along the reaction coordinate, computed by ab initio theory,13 was validated by experimental Tafel measurements:14 the free energy landscape can also be compiled by an intimate interplay of an ab initio Pourbaix diagram15,16 with the experimental Tafel plot.17 The construction of the free energy diagram by combining experiments for the kinetics and theory for the thermodynamics is a very powerful tool to gain profound insights into the performance of electrocatalysts for various processes.11 Since the free energy diagram directly specifies the kinetics -2ACS Paragon Plus Environment

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(activity) of the underlying surface reaction, it becomes feasible to investigate thoroughly, whether the application of thermodynamics as measure for the electrocatalytic activity is justified. This presumption is commonly used in Volcano plots that aim to predict improved catalytic materials.18-24 Most theoretical studies in the literature apply the framework of Nørskov and co-workers, who invented the concept of the so-called thermodynamic overpotential, ηTD, as thermodynamic descriptor for the activity in Volcano plots.25 In the associated approach, the free energy change for the formation of a reaction intermediate at zero overpotential, ΔGTD, is connected to the activity of an electrocatalyst via Sabatier’s principle26 and the Brønstedt-Evans Polanyi (BEP) relation.27 The latter one stipulates that a change in the transition state free energy (kinetics) follows an alternation in the free energy change (thermodynamics), which warrants the link between thermodynamics and kinetics in order to comprehend on the activity of electrocatalysts within a class of materials.28-31 The reason, why the connection between thermodynamics and kinetics is established at zero overpotential might be traced to the investigations of Trasatti in the past century, who was the first to construct a Volcano-shaped curve for the electrocatalytic HER by plotting the exchange current density (evaluated at zero overpotential) as function of the energy of hydride formation.32 This formalism was adopted by theoreticians, in that ηTD (evaluated at zero overpotential) serves as measure for the exchange current density in ab initio Volcano plots.33 Despite of the fact that Schmickler and Trasatti came to the conclusion that the concept of assessing exchange current densities in terms of ηTD is overly simplistic,34,35 exactly this simplicity of the approach of Nørskov and co-workers has made it extremely popular in the electrochemical community. Yet, recently critical remarks concerning the reliability of Volcano curves increased, indicating that in certain cases the thermodynamic framework of ηTD fails in describing activity trends of electrocatalysts correctly.36-40 The framework of ηTD has been extensively used in the past fifteen years to comprehend on the activity of various electrocatalytic processes; however, only little progress has been made to revise the use of ηTD as thermodynamic descriptor for the activity in Volcano plots.38 In this article, the link between thermodynamics and kinetics at zero overpotential based on Sabatier’s principle26 and the BEP relation27 is discussed for a two-electron process, such as the CER or the HER. Since the CER over RuO2(110) can be seen as a benchmark two-electron process in electrocatalysis,11 the free energy diagram for this reaction is used as starting point: two further free energy diagrams are derived based on the free energy landscape of the CER and translated to various -3ACS Paragon Plus Environment

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overpotentials in order to comprehend on the application of ηTD as thermodynamic measure for the activity. It turns out that ηTD is not capable of reproducing activity trends if the experimental Tafel plot reveals a switch in the Tafel slope with increasing overpotential, a well-known characteristic of highly active electrocatalysts especially. In case of a potential-dependent Tafel slope, it is suggested to include the applied overpotential explicitly into the analysis, when connecting thermodynamics with kinetics via Sabatier’s principle26 and the BEP relation.27

2 Free Energy Diagram of the CER over RuO2(110): Connection to Volcano Curves In the literature, essentially three reaction mechanisms are discussed for the electrocatalytic CER, namely

Volmer–Tafel,

Volmer–Heyrovsky,

and

the

Krishtalik

mechanism.41

Several

experimental and theoretical studies confirmed the Volmer-Heyrovsky pathway42,43 as mechanistic description of the CER over a single-crystalline RuO2(110) electrode.11,13,14,43-46 In the following, the free energy diagram for the CER over RuO2(110) is derived. Under CER conditions, i.e., at ηCER = U – U0CER > 0 V, all unsaturated ruthenium surface atoms (Rucus) are capped by on-top oxygen (Oot).47,48 Consequently, a chloride anion is adsorbed and discharged on the active Rucus–Oot site under the formation of Rucus–OClot precursor structure in the Volmer step: Rucus–Oot + Cl–  Rucus–OClot + e–

(Volmer step)

(1)

Subsequently, the chlorine atom in the Rucus–OClot precursor state directly recombines with another chloride anion from the electrolyte solution in the Heyrovsky step, resulting into the formation of gaseous chlorine: Rucus–OClot + Cl–  Rucus–Oot + Cl2 + e–

(Heyrovsky step)

(2)

Ab initio theory computed the transition state (TS) free energies for the Volmer step, G1#, and the Heyrovsky step, G2#, to G1# = 0.68 eV and G2# = 0.79 eV at zero overpotential.13 These values were counterchecked by highly accurate TS free energies extracted from experimental Tafel plots:17 the analysis reveals G1# = 0.77 eV and G2# = 0.89 eV at ηCER = 0 V.17 The free energy change for the formation of the Rucus–OClot precursor was calculated to ΔGTD = 0.13 eV48 or ΔGTD = 0.34 eV13 at ηCER = 0 V. The first model includes the surrounding aqueous electrolyte solution into the evaluation of the free energy by additional cluster calculations based on the self-consistent reaction field (SCRF) approach.49-51 In contrast, the second model realizes solvation by explicit -4ACS Paragon Plus Environment

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water molecules on top of the investigated surface slab.52 While the application of explicit water molecules for the solvent is indispensable for a proper treatment of the kinetics in ab initio studies,13 the SCRF approach appears more reliable in predicting thermodynamics, as the utilization of explicit water molecules requires to average all (possible) water configurations. Consequently, the free energy change at zero overpotential (ΔGTD = 0.13 eV) calculated by the SCRF approach is taken for the thermodynamics and combined with the experimental values for the TS free energies (G1# = 0.77 eV and G2# = 0.89 eV at ηCER = 0 V). These values directly merge into the free energy diagram along the reaction coordinate, which is shown in Figure 1. The evaluation of thermodynamics or kinetics is much easier in theoretical or experimental studies, respectively, which makes the combination of experiments for the kinetics with theory for the thermodynamics in terms of the free energy diagram such an efficient approach.11

Figure 1: Free energy diagram for the CER over RuO2(110) at zero overpotential according to the Volmer-Heyrovsky mechanism. While the kinetic information (blue) is taken from Tafel plot experiments, ab initio theory complements the free energy landscape with the thermodynamic information (red).

In material screening, the free energy change at zero overpotential for the formation of the reaction intermediate (RI), i.e., ΔGTD = 0.13 eV in Figure 1, is translated to ηTD = ΔGTD(η = 0 V)/e = 0.13 V. In Volcano plots, ηTD is applied as activity parameter on the y-axis: it is assumed that an electrocatalyst with ηTD < 0.13 V reveals a higher activity than the electrocatalyst in Figure 1 and vice versa. However, the neglection of TS free energies in the underlying approach may lead to -5ACS Paragon Plus Environment

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erroneous conclusions, which was thoroughly analyzed by Koper at the example of the HER.29 Koper demonstrated that the potential-dependent reaction step, associated with ηTD, is not necessarily related to the rate-determining reaction step in the free energy profile at zero overpotential. In this case the thermodynamic analysis may lead to wrongful predictions. The present contribution extends Koper’s in-depth analysis of two-electron processes by the thermodynamic framework of ηTD, in that the effect of the applied electrode potential which hitherto has been neglected and largely overlooked in trend studies on the activity of electrocatalysts is quantified. For this purpose, two further free energy profiles besides Figure 1 are derived and transmitted to various overpotentials. 3 Free Energy Diagrams as Function of the Applied Overpotential The free energy diagram at zero overpotential can be translated to any arbitrary overpotential as soon as the transfer coefficients of the TSs are known, which can be easily derived from the experimental Tafel slope.11,17 For the CER over RuO2(110), the transfer coefficients amount to α1 = 0.69 and α2 = 0.64 for the Volmer and the Heyrovsky step, respectively.26 In order to generalize and simplify the analysis, it is assumed that the transfer coefficients α1 and α2 are equal to 0.5 both. The chemical nature of the Rucus–Oot complex (active surface configuration at η = 0 V) and the Rucus–OClot precursor (RI) are abbreviated as A and B, respectively. The resulting free energy profile, referring to electrocatalyst I (cf. Figure 2a), at η = 0 V is transmitted to η1 = 0.1 V, η2 = 0.13 V and η3 = 0.25 V in Figure 2b–d. Please note that electrocatalyst I stabilizes RI B at η2 = 0.13 V. Hence, the active starting surface switches from A to B at η2 = 0.13 V, which requires a renumbering of the electron transfers in the reaction mechanism.11 Microkinetics of electrocatalytic reactions is simplified according to quasi-equilibrium of the RIs preceding the TS with highest free energy (G#rds) and the reactants.53 Based on the work of Parsons, the rate-determining reaction step (rds) is given by the transition from the active surface configuration to the TS with highest free energy.11,54,55 This transition is defined by a TS free energy (with the active surface configuration as reference) rather than by a free energy barrier to the previous RI, since the discussion of free energy barriers ultimately requires the inclusion of surface coverages into the analysis.11 The active surface configuration is assumed to correspond to the RI with lowest free energy among the set of RIs in the electrocatalytic cycle, which can be determined by an ab initio Pourbaix diagram.36 The outlined framework indicates that the activity -6ACS Paragon Plus Environment

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of an electrocatalyst can be directly deduced from the free energy diagram by extracting the TS with highest free energy (G#rds) as function of the applied overpotential. Table 1 summarizes the activity (G#rds) of electrocatalyst I, corresponding to the free energy diagrams in Figure 2, in dependence of the applied overpotential.

Figure 2: Free energy diagram of electrocatalyst I consisting of surface configurations A and B, in which the educt (E) is transformed to the product (P) by a two-electron process, at a) η = 0 V, b) η1 = 0.1 V, c) η2 = 0.13 V and d) η3 = 0.25 V. The value of the highest TS free energy (G#rds), which governs the kinetics, is marked in violet colour. Turquoise color indicates a switch of the active surface, which requires a renumbering of the electron transfers. Brown arrows in a) indicate the transfer coefficients that quantify the impact of the applied overpotential on the free energies of the RIs and the TSs for η > 0 V. Table 1: Transition state free energy G#rds (activity) in dependence of the applied overpotential for electrocatalyst I.

G#

rds

/ eV

η=0V 0.89

η = 0.1 V 0.74

η = 0.25 V 0.635

According to the thermodynamic framework of ηTD, an ideal catalyst binds the RI thermoneutral at zero overpotential, i.e., ΔGTD = 0 eV and hence ηTD = 0 V. In material screening an electrocatalyst comprising ηTD = 0 V corresponds to the apex of the Volcano plot. Here, it is assumed that such a catalyst exhibits highest activity. Starting from the free energy diagram in Figure 2a the free energy -7ACS Paragon Plus Environment

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profile of an ideal catalyst, denoted as electrocatalyst II, is constructed, in which as constraint the sum of the TS free energies should be preserved. In order to reach maximum activity the TS free energies G1# and G2# should be as small as possible at η = 0 V. This finding results into G#rds = G1# = G2# = 0.83 eV. Figure 3a plots the free energy diagram of the associated electrocatalyst II at zero overpotential, which is translated to η1 = 0.1 V and η3 = 0.25 V in Figure 3b–c. Since RI B is already stabilized at η = 0 V, the electron transfers need to be renumbered for η > 0 V, in which the electrocatalytic reaction commences from B as starting surface. Table 2 compiles the TS free energy of the rds for electrocatalyst II as function of the applied overpotential.

Figure 3: Free energy diagram of electrocatalyst II consisting of surface configurations A and B, in which the educt (E) is transformed to the product (P) by a two-electron process, at a) η = 0 V, b) η1 = 0.1 V and c) η3 = 0.25 V. The value of the highest TS free energy (G#rds), which governs the kinetics, is marked in violet colour. Turquoise color indicates a switch of the active surface, which requires a renumbering of the electron transfers. Table 2: Transition state free energy G#rds (activity) in dependence of the applied overpotential for electrocatalyst II.

G#rds / eV

η=0V 0.83

η = 0.1 V 0.78

η = 0.25 V 0.705

Finally, a third free energy profile, corresponding to electrocatalyst III, is compiled, which from a thermodynamic and kinetic point of view should be less favorable than electrocatalyst I (cf. -8ACS Paragon Plus Environment

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Figure 2a). Therefore, the free energy change (ΔGTD = 0.13 eV) for the formation of RI B is raised by 0.10 eV to ΔGTD = 0.23 eV (i.e., ηTD = 0.23 V) at zero overpotential. Thus, the difference between the TS free energies G1# and G2# is increased by 0.10 eV correspondingly, i.e., G2# and G1# amount to 0.94 eV and 0.72 eV, respectively. The resulting free energy diagram of electrocatalyst III, depicted in Figure 4a, is translated to η1 = 0.1 V, η2 = 0.23 V and η3 = 0.25 V in Figure 4b–d. RI B is stabilized at η2 = 0.23 V so that a renumbering of the electron transfers is accounted for applied overpotentials exceeding 0.23 V. Table 3 summarizes the activity (G#rds) of electrocatalyst III as function of the applied overpotential.

Figure 4: Free energy diagram of electrocatalyst III consisting of surface configurations A and B, in which the educt (E) is transformed to the product (P) by a two-electron process, at a) η = 0 V, b) η1 = 0.1 V, c) η2 = 0.23 V and d) η3 = 0.25 V. The value of the highest TS free energy (G#rds), which governs the kinetics, is marked in violet colour. Turquoise color indicates a switch of the active surface, which requires a renumbering of the electron transfers. Table 3: Transition state free energy G#rds (activity) in dependence of the applied overpotential for electrocatalyst III.

G#

rds

/ eV

η=0V 0.94

η = 0.1 V 0.79

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η = 0.25 V 0.585

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4 Discussion The TS free energies corresponding to the rds (G#rds) and the values of the thermodynamic overpotential ηTD are compiled for the three free energy diagrams (cf. Figure 2–4) at various overpotentials in Table 4. According to Sabatier’s principle and the BEP relation, electrocatalyst II referring to an ideal catalyst (ηTD = 0 V) should reveal highest activity compared to the two other electrocatalysts. This finding is met at η = 0 V, as electrocatalyst II reveals the lowest TS free energy of all free energy profiles. However, a comparison of the TS free energies as function of the applied overpotential indicates that at η = 0.1 V or η = 0.25 V electrocatalyst I or III exhibits superior performance than electrocatalyst II according to the smallest G#rds-value. These activity trends cannot be reproduced by the thermodynamic overpotential, which displays electrocatalyst II as most active catalytic material independent of the applied overpotential. Here, a further discussion is required in order to understand why an ideal electrocatalyst referring to thermodynamics (ΔGTD = 0 eV) at zero overpotential does not show optimum performance at η >> 0 V. Table 4: Thermodynamic overpotential ηTD for electrocatalysts I – III as function of the activity (G#rds) at various overpotentials. The most active electrocatalyst, corresponding to the lowest G#rds-value, is marked in bold font at each overpotential.

ηTD / V Electrocatalyst I Electrocatalyst II Electrocatalyst III

0.13 0.00 0.23

G#rds / eV (@η = 0 V) 0.89 0.83 0.94

G#rds / eV (@η = 0.1 V) 0.74 0.78 0.79

G#rds / eV (@η = 0.25 V) 0.635 0.705 0.585

4.1 Converting the Free Energy Diagram into a Tafel Plot In Figure 5a, the TS free energies corresponding to the rds (G#rds), as extracted from the free energy diagrams in Figure 2–4, are plotted as function of the applied overpotential for the three electrocatalysts. The G#rds vs. η plot can be directly translated to a Tafel plot: please note that the Tafel approximation of the generalized Butler-Volmer equation is only valid in the overpotential range above 30 mV.11,55-57 Consequently the Tafel plot is depicted for applied overpotentials η > 0.03 V as inset in Figure 5a.

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Figure 5: a) Transition state free energy corresponding to the rds (G#rds) as function of the applied overpotential η for the respective electrocatalysts I, II and III in blue, violet and green color, respectively. The most active electrocatalyst is indicated in the associated overpotential window. Inset with frame: Simulated Tafel plot for the three electrocatalysts at η > 0.03 V, including the values of the Tafel slope. b) Absolute free energy change for the formation of the RI B in dependence of the applied overpotential, |ΔG(η)|, as function of the applied overpotential η for electrocatalysts I, II and III in blue, violet and green color, respectively. The thermodynamically favoured electrocatalyst according to |ΔG(η)| is indicated in the associated overpotential window.

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In order to transmit the free energy diagram into a Tafel plot, the slope (dG#rds/dη) of each electrocatalyst in Figure 5a is converted to the Tafel slope, b, according to equation (3): 𝑏=

𝑑𝜂 𝑑log 𝑗

=

―𝑒 ∙ 59 mV/dec.

(3)

𝑑𝐺# rds 𝑑𝜂

( )

The exchange current density j0 of the respective electrocatalyst is connected with the TS free energy at η = 0 V:11 𝑗0 =

𝑘B𝑇𝑧𝑒𝛤act ℎ

∙ exp

(

― 𝐺#rds(𝜂 = 0 V) 𝑘B𝑇

)

(4)

In equation (4), e, kB. T, h and z denote the elementary charge, Boltzmann’s constant, the absolute temperature in K (T = 298.15 K), Planck’s constant and the number of electrons transferred in the overall reaction (z = 2), respectively, while the number of active sites per surface area, Γact, is assumed to be 1015 cm-2. Table 5 compiles the values of the exchange current density and the Tafel slope for the three electrocatalysts.

Table 5: Thermodynamic overpotential ηTD for electrocatalysts I – III in dependence of the exchange current density j0 and the Tafel slope b according to equations (4) and (3), respectively.

Electrocatalyst I Electrocatalyst II Electrocatalyst III

ηTD / V 0.13

j0 / μA⋅cm-2 1.85

0.00 0.23

1.91 0.25

Tafel slope b η < 0.13 V: 40 mV/dec. η > 0.13 V: 118 mV/dec. 118 mV/dec. η < 0.23 V: 40 mV/dec. η > 0.23 V: 118 mV/dec.

It turns out that electrocatalyst II reveals a constantly decreasing slope of (dG#rds/dη) = –0.5⋅e in the whole overpotential range, which according to equation (3) translates to a Tafel slope of 118 mV/dec. This finding is reconciled with the fact that the first elementary reaction step in the free energy diagram is rate determining (cf. Figure 3), which remains unaltered by an increase in overpotential. Quite in contrast for electrocatalyst I the second elementary reaction step governs the kinetics for small overpotentials (cf. Figure 2a–b). Hence, the slope (dG#rds/dη) amounts to –1.5⋅e for η < 0.13 V, which corresponds to a Tafel slope of 40 mV/dec. Even though electrocatalyst I reveals a smaller exchange current density than electrocatalyst II (cf. Table 5), electrocatalyst I is able to stabilize the rate-determining TS better than electrocatalyst II with - 12 ACS Paragon Plus Environment

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increasing overpotential according to the smaller Tafel slope. Consequently, at η > 0.06 V electrocatalyst I reveals a higher activity compared to electrocatalyst II due to the smaller TS free energy (cf. Figure 5a). At η > 0.13 V the slope (dG#rds/dη) of electrocatalyst I changes from –1.5⋅e to –0.5⋅e, since the rate-determining TS switches from the second to the first elementary reaction step (cf. Figure 2c). This is accompanied with an increase in the Tafel slope from 40 mV/dec. to 118 mV/dec. (cf. Table 5). Therefore, electrocatalyst I reduces the free energy of the rate-determining TS in the same degree as electrocatalyst II and correspondingly electrocatalyst I remains more active than electrocatalyst II for applied overpotentials exceeding 0.13 V (cf. Tafel plot in Figure 5a). A similar finding is observed for electrocatalyst III, which at η = 0 V is the least active catalyst due to the smallest exchange current density (cf. Table 5). The slope (dG#rds/dη) of electrocatalyst III amounts to –1.5⋅e (equal to 40 mV/dec. in the Tafel plot) and –0.5⋅e (equal to 118 mV/dec. in the Tafel plot) for 0 V < η < 0.23 V and 0.23 V < η < 0.25 V, respectively. Therefore, in the overpotential window of 0.13 V < η < 0.23 V, where the Tafel slope of the hitherto most active electrocatalyst I is already increased to 118 mV/dec., electrocatalyst III stabilizes the ratedetermining TS more efficiently than electrocatalyst I if the applied overpotential is enhanced (cf. Figure 5a). Consequently, electrocatalyst III reveals higher activity than electrocatalyst I at η > 0.18 V. In summary, each electrocatalyst reveals its own overpotential window of superior activity: Electrocatalyst II, I and III are most active for 0 V < η < 0.06 V, 0.06 V < η < 0.18 V and η > 0.18 V, respectively. This finding demonstrates that the evaluation of the exchange current density at η = 0 V (cf. Table 5) is not sufficient in order to comprehend on the activity of the underlying electrocatalyst. These activity trends can only be explained, if the Tafel slope, i.e., the increase in activity as result of an enhanced driving force, is taken into account. This aspect is not backed up by the concept of the thermodynamic overpotential as discussed in the following. 4.2 Evaluation of the Thermodynamic Overpotential as Measure for the Activity By comparing the framework of the thermodynamic overpotential, ηTD, with the modeled Tafel plot (cf. Table 5) it turns out that ηTD is able to reproduce activity trends around zero overpotential correctly: electrocatalyst II with the smallest ηTD-value exhibits the highest activity for η < 0.06 V - 13 ACS Paragon Plus Environment

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(cf. Figure 5a). This finding is explained by the fact that the linkage between ηTD and the activity via Sabatier’s principle and the BEP relation is established at η = 0 V. However, ηTD fails in describing activity trends if the applied overpotential is sufficiently large, since electrocatalyst I or III reveals superior activity compared to electrocatalyst II for η > 0.06 V. In principle, the thermodynamic overpotential would reproduce the activity trends of the three electrocatalysts correctly, as soon as electrocatalysts I and III reveal the same Tafel slope of 118 mV/dec. as electrocatalysts II in the whole overpotential regime: in that case the activity depends only on the exchange current density. Basically, the (tacit) assumptions, on which material screening in terms of ηTD is founded, are: a) It is assumed that the thermodynamic overpotential reproduces the exchange current density, since the linkage between thermodynamics and kinetics is established at η = 0 V; b) It is supposed that the exchange current density reproduces the kinetics in the complete overpotential range, i.e., the Tafel slope does not change within a homologous series of materials or does not alter activity trends. While the first aspect was already criticized by Schmickler and Trasatti shortly after introducing the framework of ηTD in Volcano plots by Nørskov and co-workers,34,35 the second point is outlined in the present contribution at the example of electrocatalysts I, II and III (cf. Figure 5). It turns out that presumption b) is violated for highly active electrocatalysts: most active materials reveal two linear Tafel regions (cf. electrocatalysts I and III in the Tafel plot of Figure 5a),9,12,32 in which in the first linear Tafel region a small Tafel slope is observed, i.e., the applied overpotentials reveals maximum impact on the TS free energy of the rds and hence the activity. In the second linear Tafel regime, the Tafel slope increases, since the rate-determining TS corresponds to the first TS in the free energy landscape. This discussion directly highlights that the assumption of ηTD = 0 V as apex in Volcano plots is in somehow contradictory: in case of electrocatalyst II, corresponding to an ideal catalyst, the first TS is rate determining in the complete overpotential range due to the change in active surface configuration at η = 0 V (cf. Figure 3). Thus, electrocatalyst II reveals only one linear Tafel regime with a large Tafel slope of 118 mV/dec. (cf. Figure 5a), i.e., electrocatalyst II does not correspond to an active electrocatalyst, if the applied overpotential is sufficiently large. In the literature, it has been reported that the framework of ηTD especially fails in case of highly active electrocatalysts,36-40 which, according to the discussion above, reveal an overpotentialdependent Tafel slope. This finding initiates to revise the concept of ηTD by including the applied - 14 ACS Paragon Plus Environment

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overpotential into the link between thermodynamics and kinetics for such active electrocatalysts, which is illustrated in the following.

4.3 |ΔG(η)| as Thermodynamic Descriptor for Two-Electron Processes I would like to emphasize that the application of ηTD as measure for the kinetics according to Sabatier’s principle and the BEP relation is not incorrect, if the overpotential range around η = 0 V (cf. Table 5) is viewed. However, even most two-electron processes are driven at overpotentials of η = 0.10 V or higher,10-12 i.e., far from equilibrium. In order to comprehend on activity trends in such overpotential regimes for electrocatalysts with a switch in the Tafel slope, it appears straightforward to revise the concept of the ηTD by including the applied overpotential explicitly into the analysis: it is suggested to introduce |ΔG(η)|, which evaluates the free energy change for the formation of the RI not at zero overpotential, but rather at target overpotential η. The novel thermodynamic measure |ΔG(η)| may be helpful to distinguish activity trends of highly active electrocatalysts that cannot be reproduced by the framework of ηTD. In Figure 5b, |ΔG(η)| is plotted as function of the applied overpotential. It turns out that electrocatalyst II reveals the smallest |ΔG(η)|-value for η < 0.07 V. While electrocatalyst II has stabilized RI B already at η = 0 V on the electrocatalyst’s surface (cf. Figure 3a), electrocatalyst I stabilizes the RI at η = 0.13 V (cf. Figure 2c). Therefore, the (|ΔG(η)|/dη)-slope for electrocatalyst II or I is increasing or decreasing for η < 0.13 V, respectively (cf. Figure 5b). Consequently, electrocatalyst I reveals a smaller |ΔG(η)|-value compared to electrocatalyst II for η > 0.07 V, which goes hand in hand with the enhanced activity of electrocatalyst I (cf. Figure 5a). A similar finding is observed for electrocatalyst III compared to electrocatalyst I, since for η > 0.18 V electrocatalyst III exhibits the smallest |ΔG(η)|-value (cf. Figure 5b), which is accompanied with highest activity among the set of electrocatalysts discussed (cf. Figure 5a). Interestingly, the |ΔG(η)|-curve for each electrocatalyst forms its own (upside-down) Volcano with optimum performance according to Sabatier’s principle at |ΔG(η)| = 0 (cf. Figure 5b). The corresponding η-values for |ΔG(η)| = 0 (η = 0 V, η = 0.13 V and η = 0.23 V for electrocatalyst II, I, III, respectively) coincide with the thermodynamic overpotential ηTD (cf. Table 4). This indicates that in case of highly active electrocatalysts ηTD can be used to determine the overpotential regime of the respective electrocatalyst, where the performance of the catalytic - 15 ACS Paragon Plus Environment

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material might be superior compared to other electrocatalyst with sufficient dissimilar ηTD-values. Comparing the observed Volcano relations of the |ΔG(η)|-curves (cf. Figure 5b) with the simulated Tafel plot in Figure 5a, it turns out that electrocatalyst I and electrocatalyst III reveal a switch of the Tafel slope, when the |ΔG(η)|-Volcano indicates optimum performance (|ΔG(η)| = 0). This finding is not surprising, since a switch of active surface (corresponding to |ΔG(η)| = 0) requires a renumbering of the electron transfers in the reaction mechanism, which results in an altered Tafel slope.11 In return, this correlation can also be used for experimental investigations in that the experimental Tafel plot is recorded for the respective electrode material. When the Tafel plot reveals a non-linear η vs. log j relation, e.g., when the Tafel slope switches from 40 mV/dec. to 118 mV/dec., this may indicate that for the respective overpotential value the condition |ΔG(η)| = 0 is fulfilled. This correlation might allow to validate theoretically determined |ΔG(η)|-values for two-electron processes. It should be emphasized that the switch of the Tafel slope does not occur at a single electrode potential, but rather a gradual alteration of the Tafel slope is observed.9,56 For the CER over RuO2(110), the change in the Tafel slope was quantified in the overpotential range of 0.10 V < η < 0.15 V.11,17 Consequently, the error bars in the experimental measurements for the determination of ΔG(η) may not exceed 0.05 eV. Another error source might be related to the determination of the reversible equilibrium potential, whose determination is required to translate the applied electrode potential into an applied overpotential. However, this error is considered to be small and in a first approximation negligible, since the experimentally determined reversible equilibrium potential can be counterchecked by the Nernst equation.14 4.4 Shortcomings and Subtleties of the Presented Approach The application of |ΔG(η)| as measure for the activity in Volcano plots is restricted to a twoelectron process, where the Tafel plot reveals a switch in the Tafel slope with increasing overpotential. It shall be stressed that there are counterexamples, where the usage of |ΔG(η)| fails in describing activity trends. Assuming that the values of the TS free energies G1# and G2# in the free energy profiles of Figures 2-4 are switched, then in all three energy landscapes the first elementary reaction step is rate determining. Since in that case the Tafel slope does not have an influence on the activity order (the Tafel slope amounts to 120 mV/dec. for all three electrocatalysts at η > 0.03 V), the activity ranking is given by the sequence electrocatalyst II > I - 16 ACS Paragon Plus Environment

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> III in the complete overpotential range. The framework of ηTD directly reproduces this order, since in this simple case the evaluation of the exchange current density is sufficient in order to comprehend on activity trends (cf. Table 5). Quite in contrast, here the evaluation of |ΔG(η)| as measure for the activity leads to erroneous conclusions, since the precondition of a change in the Tafel slope is not fulfilled. Another limitation of the model discussed displays the assumption that the sum of the TS free energies G1# and G2# in the free energy diagrams (cf. Figure 2-4) is constant. Material screening comprises the presumption that the reaction mechanism remains unchanged within a class of materials. This educated guess can only be fulfilled, if the energetics of electrocatalysts in a homologous series of materials is sufficiently similar, which manifests the underlying hypothesis. The evaluation of ΔG(η) by experiments also need to be treated with some caution: a change in the Tafel slope is either traced to a switch of the active surface configuration (corresponding to |ΔG(η)| = 0) or to a change in the rate-determining reaction step.11 When the latter is the reason for the alternation of the Tafel slope, the determination of ΔG(η) might be erroneous. However, even if the switch in the Tafel slope is not necessarily associated with the condition |ΔG(η)| = 0, it might be the case that the overpotential value relating to the change in the Tafel slope is a good measure for the activity of electrocatalyst within a class of materials: the larger the overpotential, where the switch in the Tafel slope occurs, the higher the activity of the electrocatalyst, since the electrocatalyst can stabilize the rate-determining TS most efficiently over a preferably wide overpotential range (cf. electrocatalyst III in Figure 4). It is strongly encouraged to explore this hypothesis, in which material screening is based on a combination of experimental Tafel measurements and DFT calculations. 4.5 Discussion of Many-Electron Transfer Processes The suggestion of |ΔG(η)| as replacement for ηTD as thermodynamic descriptor for the activity in Volcano plots is related to a two-electron process, such as the HER or the CER (cf. Figure 1). For many-electron processes, such as the OER or ORR,58-61 Over and the author specified the highest free energy among all reaction intermediates, Gmax, as a more robust parameter compared to the thermodynamic overpotential for the kinetics.36 However, for a two-electron process with one RI (cf. free energy diagrams in Figure 2-4), Gmax corresponds to ΔGTD (and thus to ηTD). This finding underlines, why the determination of a novel descriptor for a two-electron process is - 17 ACS Paragon Plus Environment

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required, since the framework of Gmax leads to the same erroneous conclusion as the application of ηTD for a two-electron process if the Tafel plot reveals a change in the Tafel slope. So far it remains elusive, whether the inclusion of the applied overpotential into the thermodynamic descriptor Gmax, i.e., |Gmax(η)|, improves the thermodynamic analysis of manyelectron processes, such as the OER and ORR. This aspect is not in the scope of the present study, but will be tackled in a subsequent contribution. 4.6 Outlook to Overpotential-Dependent Volcano Plots In conclusion, the proposed thermodynamic quantity |ΔG(η)| is able to reproduce activity trends of electrocatalysts with an overpotential-dependent Tafel slope (cf. Figure 5) in contrast to the thermodynamic overpotential (cf. Table 4). In principle, material screening in terms of |ΔG(η)| requires to combine theoretical DFT calculations with experimental Tafel measurements in order to scrutinize, whether the Tafel slope is overpotential dependent. However, for most two-electron processes the experimental Tafel plot reveals a switch in the Tafel slope, such as encountered with the CER over RuO2(110) or the HER over Pt(111).9,11,41 Therefore, material screening based on the framework of |ΔG(η)| may rely on the (tacit) assumption that the precondition of an overpotential dependent Tafel slope is actually fulfilled for most two-electron processes. As main result of the presented investigations relating to a two-electron process I would like to point out that the usage of ηTD as descriptor for the activity in Volcano curves might be contradictory and misleading. The present contribution highlights that for the application of Sabatier’s principle thermodynamics as measure for the activity should not be evaluated at zero overpotential but rather at target overpotential. This knowledge should be transmitted to the construction of Volcano plots in material screening, where the (free) binding energy of oxygen is frequently applied as descriptor of the underlying electrocatalytic process on the x-axis.18-24 Each Volcano curve needs to be related to a certain, previously defined overpotential, at which the activity of electrocatalysts within a class of materials is assessed based on the thermodynamic framework of |ΔG(η)|. While the thermodynamic overpotential might be replaced by |ΔG(η)| as measure for the activity on the y-axis, the (free) binding energy of oxygen on the x-axis can be related to the target overpotential within the CHE concept of Nørskov and co-workers.25 This procedure might allow to include the applied overpotential into linear scaling relationships, hence leading to overpotential-dependent Volcano plots for improved material screening. The - 18 ACS Paragon Plus Environment

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development of novel approaches beyond the traditional Volcano approach in terms of ηTD is currently contemporary, which is also reflected by the introduction of activity-stability Volcano plots,62 where besides the activity the stability is employed as second performance parameter.63 5 Conclusions In this manuscript, the link between thermodynamics and kinetics for a two-electron process is discussed by evaluating free energy diagrams as function of the applied overpotential. The free energy profile of the CER over RuO2(110), a benchmark system in the field of electrocatalysis,11 is used as starting point and compared to two further derived free energy landscapes. The presented model comprises the assumption that the sum of the TS free energies is constant, which is related to the similar energetics of electrocatalysts within a homologous series of materials. Each electrocatalyst exhibits superior electrocatalytic activity in its own specific overpotential range depending on the TS free energy at η = 0 V in conjunction with the affiliated Tafel slope. The thermodynamic overpotential, ηTD, which is most commonly applied as measure for the activity in Volcano curves, is evaluated at zero overpotential so that thermodynamics is linked to kinetics at η = 0 V. Correspondingly, within the underlying concept the influence of the applied overpotential on the activity, which is given by the Tafel slope, is neglected. This finding explains why ηTD does not always reproduce activity trends correctly: especially the activity ranking of highly active electrocatalysts, which exhibit a switch in the Tafel slope, cannot be deduced by the framework of ηTD. Therefore, an advanced thermodynamic quantity |ΔG(η)|, i.e., the absolute free energy change for the formation of the RI at respective overpotential η, is suggested to connect thermodynamics with the activity for a two-electron process. |ΔG(η)| reproduces the activity trends of the compiled free energy diagrams properly and enables to specify the overpotential window of optimum performance for the respective electrocatalyst according to Sabatier’s principle. These novel insights may be employed in order to revise the construction of Volcano plots in material screening by linking thermodynamics with kinetics not at zero overpotential, but rather at the respective target overpotential depending on the underlying electrocatalytic process. Acknowledgement: The author 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. - 19 ACS Paragon Plus Environment

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