Structure Sensitivity of Formic Acid Electrooxidation on Transition Metal Surfaces: A First-Principles Study

Figure 1 shows the free energy diagram at 0.00 V for the three mechanisms on Pt(111) and Pt(100). Similar free energy diagrams are provided at potentials corresponding to the positive onset potentials of the three mechanisms in Supplemental Material (Figure S1 and Figure S2 for Pt(111) and Pt(100), respectively).

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We first focus on Pt(111). Starting from HCOOH(g), the first deprotonation step could either result in formate (HCOO^*) or carboxyl (COOH^*). The carboxyl pathway, with an onset potential of just 0.05 V, is less endergonic than the formate pathway by 0.29 eV. We therefore predict that the reaction flux will initially proceed through forming carboxyl at low potentials. After forming carboxyl, we can deprotonate COOH^* once more to produce CO₂(g), or can produce CO^*+H₂O(g) or CO^*+OH^*. Apart from the last, both first and second options are exergonic, with CO^*+H₂O(g) being more exergonic than CO₂(g) production by 0.91 eV. We note here that a difference of 0.06 eV in calculated energetics corresponds to an order-of-magnitude difference in reaction rates. Hence, Pt will be easily poisoned by CO^* at low potentials, as is well-demonstrated by electrochemical and spectroscopic measurements,^79–81 and rationalized theoretically.^82,83 Our analysis is thermodynamic in nature, and overlooks the existence of kinetic barriers. In a recent study of FA vapor-phase decomposition on Pt(111),⁶⁸ Scaranto and Mavrikakis calculated the decomposition energetics of HCOOH on Pt(111) to COOH^*+H^* or HCOO^*+H^*. They found that carboxyl is more stable than formate by ∼0.30 eV, which agrees with our finding in this work that carboxyl is produced less endergonically than formate. They also found that the activation energy barrier for carboxyl formation is higher than that for formate formation, and yet carboxyl decomposes to CO₂(g) easier than formate does.⁶⁸ Further, previous theoretical studies reported high kinetic barriers for CO^* formation from HCOOH on Pt(111); nevertheless, CO^* formation was exergonic with and without solvation effects^84,85 which is in agreement with our calculated energetics. These calculated high barriers for CO^* formation have motivated the proposition of a concerted path on Pt(111) to simultaneously form CO^* and CO₂(g) from FA dimers.⁸²

To gain a deeper mechanistic insight of FAO on Pt(111), we analyze the three paths shown in Figure 1 for onset potentials and associated PDS. The direct oxidation via formate has the formation of formate as the only endergonic step, with a calculated ΔG of 0.34 eV. Since formate appears in our reaction network in conjunction with a single proton-electron pair, its formation becomes more exergonic by 1 eV for each 1 V of applied potential. We therefore calculate an onset potential of 0.34 V for the formate path on Pt(111), which is close to the value of 0.305 V at which a small band for HCOO^* was detected on time-dependent ATR-SEIRA spectra on Pt.¹⁹ Similarly, the onset potential for the direct oxidation via carboxyl is calculated to be 0.05 V, and is reflecting carboxyl formation. Once carboxyl is formed, CO^* formation is downhill in energy, which results in poisoning the surface until water is activated. Water can be activated to form OH^* at a potential as high as 1.23 V, or to form COOH^* at a slightly lower potential of 1.22 V, a value corresponding to the onset potential of the indirect mechanism. Experimentally, cyclic voltammograms^31,86 show two peaks for FAO on Pt, around 0.6 V and 0.9 V, which were attributed to the direct and indirect paths, respectively. Within the limitations of our analysis (see methods section), these two potentials align reasonably well with our predicted onset for the direct path and the indirect path, respectively; yet other interpretations for these peaks attribute them both to the direct path.^16,23,26 Since the carboxyl path becomes exergonic at very low potentials, direct evidence for it can be compromised by the hydrogen underpotential deposition (H-UPD) region, as well as the formation of CO^* poison.

We now turn our attention to Pt(100). The onset potential for the formate and the indirect mechanism is calculated to be 0.23 V and 0.70 V (corresponding to water activation to OH^*), respectively. The carboxyl path is readily exergonic at 0.00 V, where carboxyl is preferred to its formate isomer by 0.47 eV. Compared to Pt(111), Figure 1 shows that the free-energy surface for FAO on Pt(100) is shifted to more negative (or less positive) free energy, which implies stabilization of the various intermediates on the open facet. Therefore, Pt(100) is predicted to be more readily poisoned at low potentials than Pt(111), which explains the lower current densities obtained experimentally in the forward sweep on Pt(100).⁸⁷ Nevertheless, Pt(100) is more capable of removing CO^*, as evidenced by its lower onset potential for the indirect mechanism. The fundamental reason behind this is that water is more easily activated on Pt(100) than on Pt(111), which is in agreement with results from Koper and coworkers.⁸⁸ We predict that, because of its increased ability to remove CO^*, and due to its stronger adsorption of COOH^* (the more stable product of the first deprotonation step), Pt(100) should be more active for FAO than Pt(111). This structure sensitivity is clearly manifested in higher current density in the backward scan on Pt(100), when compared to that on Pt(111).⁸⁷

Figure 2 shows the free energy diagram at 0.00 V for the three FAO mechanisms on Pd(111) and Pd(100). Similar free energy diagrams are provided at potentials corresponding to the positive onset potentials of the three mechanisms in Supplemental Material (Figure S3 and Figure S4 for Pd(111) and Pd(100), respectively).

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On Pd(111), the direct mechanisms via formate and carboxyl have onset potentials of 0.26 V and 0.22 V, respectively. Compared to Pt(111), on Pd(111) carboxyl is destabilized whereas formate is stabilized, thereby closing the gap between the onset potentials of the two direct mechanisms. Since this gap is only 0.04 V wide, one would expect the reaction flux to proceed through both paths, which is in agreement with recent theoretical findings.^67,89 This is an interesting result because the difference in these onset potentials should influence the selectivity toward full oxidation to CO₂(g) against forming the CO^* poison, which can only be formed from COOH^*. As shown in Figure 2, CO^*+H₂O(g) is the most thermodynamically favored state, and therefore Pd(111) should get poisoned by CO^*, despite the close onset potentials of both direct mechanisms. CO^* remains on the surface until water is activated to OH^* at 1.05 V, a voltage marking the onset potential of the indirect mechanism. Pd anodes have generally offered lower tendency to get poisoned by CO^* than Pt anodes.^34,90,91 In fact, CO^* on Pd was not readily detected using spectroscopic techniques;⁹² it has not been until recently that concrete spectroscopic evidence of CO^* formation over Pd has been obtained by combining surface-enhanced infrared spectroscopy with attenuated total reflection and thin-layer flow cell configurations.⁹³ We attribute less CO^* poisoning of Pd(111) compared to Pt(111) to: 1) the higher contribution of HCOO^* path to the overall activity, and 2) lower onset potential (by 0.18 V) of the indirect mechanism, which would contribute toward cleaning the surface from CO^*.

To explore FAO's structure sensitivity on Pd, we next discuss our results on Pd(100). Onset potentials for formate, carboxyl, and indirect mechanisms (corresponding to water activation to OH^*) are determined to be 0.24 V, 0.01 V, and 0.80 V, respectively. Notice that all these onset potentials are more positive than their counterparts on Pt(100), indicating less energy efficiency (i.e. higher overpotential) for Pd(100). The gap between carboxyl and formate onset potentials is 0.23 V, far larger than it is on Pd(111), thus significantly limiting the contribution of the HCOO^* path toward the reactive flux. Compared to Pd(111), water activation is easier on Pd(100) by 0.25 eV. Accordingly, we predict that Pd(100) would show higher activity than Pd(111), because it is better at reactively removing CO^*. Additionally, CO^* is destabilized by 0.17 eV on the open facet (see free energies in Figures 2), which explains the higher collected current density during the forward scan of Pd(100), as compared to Pd(111).⁹⁴

Before discussing the other metal surfaces, we will comment on some debated aspects of the FAO reaction mechanism on Pt and Pd surfaces.³⁴ There have been contradicting reports about the role of formate, with some suggesting that it is the reactive intermediate,^{13,19–23,27} and others that it is a spectator species.^32,33 Furthermore, carboxyl has been elusive to detect spectroscopically, making it difficult to be identified as an active intermediate.³⁴ Although our computational model is simple with no detailed kinetic barriers in the electrochemical environment, we still can draw some insights from the thermochemistry alone. First, COOH^* is elusive to detect because CO^* is the more thermodynamically-preferred product. As discussed earlier, we consider CO^* poisoning as direct evidence that COOH^* is formed. The high CO^* coverage should destabilize HCOO^* formation and further COOH^* formation, pushing the onset potentials for both direct mechanisms higher than they appear in Figures 1 and 2. Upon further increase of potential to the onset potential of the indirect path, the surface is freed of CO^* and the reaction proceeds downhill to CO₂(g). Since carboxyl is calculated to be more stable than formate on both Pt and Pd (based on calculated free energies), we predict that at high potentials, it would be carboxyl that carries the majority of the reaction flux, while at low potentials CO^* poisons the surface. More informed assessments as to the contribution of various intermediates to the FAO reaction flux should come from detailed microkinetic modeling under relevant electrochemical conditions.

Having discussed the two most experimentally studied monometallic systems, we next discuss trends among the remainder of transition metals studied. To facilitate this discussion, we first investigate – for each fcc metal – the direct oxidation mechanisms, in order to determine the preference of each metal to either carboxyl or formate mediation, which gives insights into the propensity of each surface to accumulate CO^* poison. Following this, we discuss the indirect oxidation mechanism for each metal, in order to understand how different metals would likely oxidize CO^* to CO₂(g). In parallel, we compare close-packed and open facets for each metal to elucidate the extent of FAO structure sensitivity. Since we do not study FAO structure sensitivity on hcp metals, we discuss them all at the end. Metals are arranged according to periodic table group in descending order and, within each group, by decreasing atomic number; an order that generally reflects increasing adsorption strength. Table I lists the free energies of key reaction intermediates relative to HCOOH(g) on all surfaces studied. Figure 3, Figure 4, and Figure 5 show the onset potentials for the direct oxidation via formate, the direct oxidation via carboxyl, and the indirect oxidation mechanism, respectively, on all surfaces studied. Supplemental Material contains the free energy diagrams on all surfaces studied at their calculated positive onset potentials.

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On Au(111), the onset potentials (Figure 3 and Figure 4) for the formate and carboxyl paths are 0.91 V and 1.07 V, respectively; see Figure S5 for free energy diagrams at the onset potentials. The high onset potentials for either mechanism on Au(111) indicate its poor activity toward FAO. This is in agreement with Capon and Parsons⁹⁰ who observed that FAO on Au anodes only takes place at high overpotentials at which an oxide phase of Au is formed. In turn, this can generally be attributed to the weak interaction of Au surfaces, specifically Au nanoparticles larger than 5 nm,⁹⁵ with adsorbates. As depicted in Figure 3 and Figure 4, for Au(100), we calculate onset potentials of 0.80 V and 1.01 V for the formate and carboxyl paths, respectively; see Figure S6 for free energy diagrams at the onset potentials. Therefore, Au(100) stays largely inactive toward FAO compared to either facet of Pt or Pd. We observe that the formate path is dominant on either Au facet. This comes in agreement with a recent ATR-SEIRAS study of FAO on Au, in which Cuesta et al.²⁹ determined formate as the reactive intermediate. They, however, argue based on electro-kinetic data, that formate oxidation to CO₂ is the rate determining step, similarly to what we suggested previously for FA vapor-phase decomposition on Au.⁹⁶ A more rigorous scheme for calculating barriers of electrochemical steps, as well as microkinetic modeling, will be needed to extract definitive conclusions on the mechanism on a given surface. Our calculations of the thermochemistry suggest that formate deprotonation is exergonic, and that the main challenge for the weak-adsorbing Au catalysts is to form formate in the first place. It is due to this challenge that the (100) facet shows lower onset potentials – for either direct mechanism – than the (111) facet. This is the case because the PDS for both mechanisms on either Au facets results in the formation of an adsorbed species, a step that is less endergonic on the open facet. Accordingly, FAO shows structure sensitivity on Au, as the dominant path (formate) is calculated to have a lower onset potential on the (100) facet than the (111) facet by ∼0.10 V. Yet, both Au facets would appear largely inactive compared to Pt or Pd.

We do not consider the indirect mechanism to be relevant on either facet of Au for the following reasons: 1) HCOO^* is more easily formed than COOH^*, the CO^* precursor, and 2) the formation of CO^* from COOH^* is endergonic at the onset potential of the carboxyl path; see Table I, Figure S5, and Figure S6. We conclude that both facets of Au will be free of CO^* poisoning. In this respect, it is worth mentioning that Cuesta et al.²⁹ could not detect any CO^* on an Au anode, as expected from our theoretical results.

Compared to Au, the onset potential for the formate path imparts higher activity to Ag, especially for the open facet. The onset potential for the formate path is 0.37 V on Ag(111), and 0.29 V on Ag(100); see Figure 3, Figure S7, and Figure S8 for free energy diagrams at the onset potential. Compared to the corresponding Au facets, both facets of Ag: 1) destabilize COOH^*, 2) stabilize HCOO^*, and, thus, 3) have much stronger preference to HCOO^* than to COOH^*. This stronger preference to formate on Ag, relative to Au, reflects the stronger binding of adsorbates binding through O (HCOO^*, OH^*, and O^*), compared to those binding through C (COOH^*, CO^*, and C^*) on Ag.^41,48,49,51 This trend suggests that the carboxyl path may not contribute to any observed current on Ag anodes, as indicated by the large gap in calculated onset potentials for the formate and carboxyl paths. Similar to what we found on Au, the Ag(100) facet shows lower onset potentials toward the formation of adsorbed species, indicating strong structure sensitivity for FAO on Ag. Owing to the high onset potentials for the carboxyl mechanism (1.29 V on Ag(111) and 1.14 V on Ag(100); see Figure 4, Figure S7, and Figure S8), we predict that Ag surfaces, like Au surfaces, would be free of CO^* poison, especially because forming CO^* from COOH^* is endergonic at the onset potential of the carboxyl mechanism; see Table I, Figure S7, and Figure S8. Consequently, the indirect mechanism on Ag surfaces appears to be less relevant and is not discussed further. Despite being CO^* free while retaining reasonable onset potentials for the formate mechanism, Ag is likely to experience dissolution and/or oxidation in acidic media,⁹⁷ which would tend to diminish Ag's relevance for practical application in FAO.

While the formate mechanism proceeds downhill on both facets of Cu at 0.00 V (Figure 3), the carboxyl mechanism is characterized by high onset potentials: 0.79 V and 0.63 V on the (111) and (100) facets, respectively. The high onset potentials originate from the difficulty of activating FA to COOH^* (Figure 4), hence the lower onset potential on Cu(100), which stabilizes COOH^* with respect to Cu(111). At the high onset potentials of the carboxyl mechanism on either facet, CO₂(g), not CO^*, becomes the more thermodynamically-favorable product of the COOH^* decomposition; see Figure S9 and Figure S10. As a result, CO^* is not predicted to poison Cu catalysts. Like Ag, the tolerance toward CO^* poisoning of Cu does not originate from its weak binding and inability to activate FA, but rather from its strong preference to forming HCOO^*. This comes in agreement with a recent study of FA vapor-phase decomposition on Cu catalysts, where HCOO^* was found to be the dominant reactive intermediate.⁹⁸ Owing to the stronger stabilization of HCOO^* on the (100) facet, Cu(100) should show higher activity than Cu(111). However, Cu, like Ag, exhibits poor oxidation resistance⁹⁹ and will likely dissolve in electrochemical environments, thus limiting its practical use in monometallic anodes of DFAFCs.

We first consider the formate path. Table I indicates higher stability of HCOO^* relative to COOH^*, on both facets of Ni, with HCOO^* being more stable on Ni(100) compared to Ni(111). Interestingly, this higher stability of formate on the open facet does not correspond to lower onset potential for the formate path (see Figure 3, Figure S11, and Figure S12); while the formate path proceeds downhill on Ni(111) at 0.00 V, it is not activated on Ni(100) until 0.13 V. The fundamental reason behind this result is the different PDS for the formate path on the two facets. While Ni(111) adsorbs and dissociates HCOO^* spontaneously, Ni(100) adsorbs HCOO^* strong enough that its dissociation to CO₂(g) is the most endergonic step of the formate path. On the other hand, the carboxyl path has the formation of COOH^* as the PDS for both Ni facets (see Figure 4, Figure S11, and Figure S12), therefore showing a higher onset potential (0.26 V) for Ni(111), while proceeding spontaneously on Ni(100). Hence, while we predict that formate is the active intermediate of FAO over Ni(111), we predict that it will result in HCOO^* spectators on Ni(100), poisoning the surface at low potentials. Given that COOH^* is not spontaneously formed on Ni(111) at 0.00 V, we predict a narrow operating window via the formate path at potentials below 0.26 V, beyond which COOH^* is formed and, in turn, CO^* poisons the surface.

Ni also shows interesting features for the indirect mechanism; see Figure 5, Figure S11, and Figure S12. Water activation (H₂O(g)→OH^*) is endergonic on both facets of Ni, although less so on the open facet which stabilizes OH^*. However, water activation is not the PDS on either facet; rather CO^*+OH^*→CO₂(g) is. While water activation needs 0.36 V on Ni(111), the PDS needs up to 0.64 V to be activated, thus setting the onset potential of the indirect mechanism. Similarly, the onset potential of the indirect mechanism on Ni(100) is 0.87 V, while water activation to produce OH^* needs only 0.11 V. The higher onset potential of the indirect mechanism on Ni(100) again points out to the stronger stabilization of both CO^* and OH^* on the open facet relative to the close-packed facet.

The discussion above reveals that FAO is structure sensitive on Ni catalysts. Not only do onset potentials change, but also the PDS of the formate mechanism depends on the Ni facet. We predict that Ni(111) will be active predominantly via the formate path at low potentials, where carboxyl formation is uphill. At moderate potentials, carboxyl would be formed, resulting in CO^* which can be removed at 0.64 V. On the other hand, Ni(100) would have to free the surface from accumulating HCOO^* and CO^*, with the latter not leaving the surface until 0.87 V. Therefore, Ni(111) is predicted to be less-poisoned and more active than Ni(100).

As shown in Figure 3, Figure 4, and Figure S13, both direct mechanisms proceed spontaneously to CO₂(g) at 0.00 V on Ir(111). This is not the case on Ir(100); see Figure 3, Figure 4, and Figure S14, where the deprotonation of HCOO^* or COOH^* to CO₂(g) requires 0.02 V and 0.17 V, thereby setting the onset potentials of the formate and carboxyl paths, respectively. For the indirect mechanism on Ir(111), FAO needs to overcome an onset potential of 0.86 V to activate water to OH^* in order to oxidize the readily-formed CO^*. Ir(100), however, activates water at a much milder potential of 0.32 V (see Figure 5, Figure S13, and Figure S14), but needs 0.85 V to oxidize CO^* with the formed OH^*. We conclude that FAO is structure-sensitive on Ir, showing different PDS (for the indirect mechanism) and different onset potentials on each facet. Ir(100), which stabilizes all reaction intermediates relative to Ir(111), is predicted to be more poisoned, as corroborated by the lower current in the forward potential scan on Ir(100).¹⁰⁰

The FAO reaction mechanism on Rh(111) is very similar to that on Ir(111); both direct mechanisms proceed spontaneously at 0.00 V. Unlike Ir(100), which stabilizes HCOO^* and COOH^* enough to show positive onset potentials for their activation, Rh(100) retains their spontaneous dissociation to CO₂(g) despite stabilizing them relative to Rh(111), as shown in Figure 3, Figure 4, Figure S15, and Figure S16. For the indirect mechanism, the PDS is different on the two facets; see Figure 5, Figure S15, and Figure S16. While Rh(111) requires 0.68 V to activate water to OH^* (followed by the spontaneous removal of CO^* with the formed OH^*), OH^* formation proceeds much easier on Rh(100) at 0.39 V. However, the strongly bound CO^* and OH^* are not removed from the Rh(100) surface until 0.64 V. Accordingly, both surfaces will suffer from CO^* poisoning, which agrees with cyclic voltammograms on both surfaces at low potentials,¹⁰¹ as well as spectroscopic evidence for CO^* on Rh electrodes.¹⁰²

Before discussing our results on the hcp metals, we conclude this section on the fcc metals by comparing Ni, Ir, and Rh to Pt and Pd. For the more stable close-packed facet, Ni, Ir, and Rh all show lower onset potentials for the indirect mechanism than Pt or Pd. However, Ni is known to leach in acidic media typical of DFAFCs.¹⁰³ Hence, the advantage of high activity of Ni(111) is offset by its low stability. Additionally, Ir and Rh are shown to be poor FAO catalysts due to a limited double layer region,⁹⁰ the effect of which is largely neglected in our model. Moreover, Ir and Rh are known for their strong binding of adsorbates, as well as their propensity to form oxides at low potentials.¹⁰⁰ Our results confirm that OH^* and HCOO^* bind more strongly on either facet of these two metals relative to Pt and Pd. Additionally, CO^* is adsorbed strongly on either facet of Ir and Rh. In fact, because Ir and Rh do show some activity toward FAO while being extensively covered by CO^*, it has been suggested¹⁰⁴ that CO^* should not be thought of as a poison, but rather a reaction intermediate that tangibly contributes to collected currents. This is inferred from slow ¹³CO/¹²CO isotopic exchange at low potentials, but fast ¹³CO/¹²CO isotopic exchange at potentials beyond that of FAO onset.¹⁰⁴ Further, the open facets of Pt or Pd are more energy-efficient than the open facets of Ni and Ir, which tend to get more easily poisoned by reaction intermediates than Pt or Pd do. This leaves Pt and Pd as the only monometallic catalysts among those studied here so far, which strike a compromise between activity and stability.³⁴

We studied the (0001) facet of these four hcp metals. Co(0001) prefers HCOO^* to COOH^* by 0.51 eV, rendering the formate path as the dominant path at low applied bias; the onset potential for the formate path (corresponding to decomposing HCOO^* to CO₂(g)) is only 0.02 V (see Figure 3 and Figure S17). At 0.23 V, the carboxyl path is activated, spontaneously poisoning the surface with CO^* (see Figure 4). Hence, similar to Ni(111), we predict a narrow operating window for Co(0001) between 0.02 V and 0.23 V. Water is easily activated at 0.15 V, leaving CO^* oxidation with OH^* to be the PDS of the indirect mechanism with an onset potential of 0.67 V (see Figure 5 and Figure S17).

As shown in Figure 3, all remaining three hcp(0001) surfaces are characterized by too strong binding of HCOO^* such that CO₂(g) formation is potential-determining for the formate mechanism. The onset potential for the formate mechanism is 0.38 V for Os (Figure S18), 0.31 V for Ru (Figure S19), and 0.41 V for Re (Figure S20). By contrast, COOH^* is less stable than HCOO^* on all these surfaces, yielding a spontaneous deprotonation of COOH^* to CO₂(g) on Ru and Re (see Figure 4, Figure S19, and Figure S20), and a slightly endergonic COOH^* deprotonation to CO₂(g) (by 0.05 V) for Os (see Figure 4 and Figure S18). As we move from Os, to Ru, to Re, CO^* binding weakens, while OH^* binding gets stronger.^41,48,51 The net effect is increased poisoning by oxygenated species – most likely atomic O^{*41,105–107} – as we move from Os, to Ru, to Re, again indicating the propensity of these surfaces to form oxides. The weakening trend of CO^* binding is also reflected in weaker COOH^* binding, and thus the observed declining onset potential for the COOH^* path (corresponding to COOH^* deprotonation to CO₂(g)) as we move from Os (0.05 V), to Ru and Re (spontaneous). Nevertheless, it is still exergonic to form COOH^* followed by CO^*, which is likely to poison the surface, together with O^*/OH^*. The PDS of the indirect mechanism on all three surfaces, as shown in Figure 5, is CO^*+OH^*→CO₂(g), with onset potentials of 0.83 V on Os (Figure S18), 0.81 V on Ru (Figure S19), and 0.95 V on Re (Figure S20).

To conclude the discussion of FAO on hcp metals, we note that Os, Ru, and Re tend to get more poisoned by reaction intermediates due to the strong stabilization of various adsorbates on their surfaces. Although Co shows moderate binding characteristics (it binds the weakest among the hcp metals), much like Ni, it too suffers from poor corrosion resistance in acidic media.¹⁰⁸

We conclude our discussion of onset potentials by recognizing the Sabatier principle, which states that an optimal catalyst would bind adsorbates not too strongly and not too weakly. In a descending order of periodic table grouping, Au and Ag bind adsorbates too weakly, rendering them poor catalysts for FAO because of their inability to activate HCOOH(g). On the other hand, surfaces that bind adsorbates too strongly are likely to get poisoned by reaction intermediates, or develop oxide phases, also rendering them largely inactive toward FAO. With Ni and Co being largely unstable under acidic media, Pt and Pd are the only monometallic catalysts that strike the delicate balance between activity and stability.

Figure 6 summarizes the onset potentials (Figures 3–5) of all three mechanisms on all surfaces studied. An interesting general trend is observed; the open facets of the noble metals (Au, Ag, Cu), and of Pt and Pd have lower overpotentials, thereby offering higher energy-efficiency, than their close-packed facets, while the opposite is true for the more reactive metals: Ni, Ir, and Rh (see Figure 6). Further, Au, Ag, and Pt(111) require unpractically high overpotentials to activate water for the indirect mechanism. These trends are attributed to the fact that the close-packed facets of the less reactive metals (Au, Ag, Cu, Pt, and Pd) bind adsorbates too weakly, while the open facets of the more reactive metals (Ni, Ir, and Rh) bind adsorbates too strongly. Accordingly, the PDS on close-packed surfaces of the less reactive metals have their PDS yielding adsorbed species, whereas open facets of the more reactive metals have their PDS yielding gas-phase species from adsorbed intermediates.

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In this section, we formulate the insights gained above into phase diagrams (or volcanoes) at 0.0 V and 0.6 V (a value chosen high enough to show the effect of applied bias, but low enough to avoid the potential region of oxide formation (∼0.80 V) on Pt^13,16 and Pd),²⁷ see Figure 7, showing the activity and rate determining steps on a continuous spectrum, which may enable strategies for improved catalyst design. We start by developing linear scaling relations (see Supplemental Material, Figures S21 and S22) between the free energies (relative to CO₂(g), H₂O(g), and H₂(g)) of COOH^* and HCOO^* and those of CO^* and OH^*, respectively. This allows us to map out the complete energetics of the reaction network using only values for the free energies of CO^* and OH^*. Such scaling relations have been shown to exist¹⁰⁹ among carbon-containing species and among oxygen-containing species, and have been used extensively in the literature.^42,48–52 Consequently, the free energy change of all elementary steps could be readily calculated at a given pair of the free energies of CO^* and OH^*, rendering these two as reactivity descriptors for FAO. The overall phase space is divided into regions defined by rate determining steps, as estimated from scaling relations. We note that the free energies of CO^* and OH^* correlate poorly to each other, leading to the need for these two distinct descriptors. It is relevant to note that these two descriptors have also been found to dictate the energetics of the electrooxidation of methanol,^48–50 dimethyl ether,^51,52,55 and ethanol and ethylene glycol,⁵⁷ thus establishing the free energies of CO^* and OH^* as near-universal descriptors for the activities of metallic surfaces toward the electrooxidation of small oxygenate molecules.

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In what follows, we analyze the various regions in these phase diagrams, starting with the low applied voltage (0.0V) cases first (Figures 7a and 7c). The top right corners of the phase diagrams represent regions where the binding of both CO^* and OH^* is weak, while bottom left corners represent strong binding of both species. In the top right side of the volcano, the high values of the descriptors (G_CO^* and G_OH^*) indicate weak enough binding of COOH^* and HCOO^*, so that CO^* formation is not feasible, leaving the direct oxidation via carboxyl or formate paths to dominate reactivity. Following their weak binding, COOH^* or HCOO^* are readily oxidized to CO₂(g), leaving the first deprotonation step of FA as rate determining. It is important to note that HCOO^* is more stable than COOH^* for the close-packed facets (Figure 7a) in the top right corner of the phase space, while the opposite is true for the open facets, giving rise to the region HCOOH(g)→COOH^* in Figure 7c. As we descend vertically from this region along stronger binding of OH^* (Figures 7c), the binding of HCOO^* gets stronger until it becomes more stable than COOH^*. Accordingly, the mechanism changes into the direct oxidation via formate. At intermediate binding of OH^* (see Figures 7a and 7c), HCOO^* is bound weakly enough to readily decompose to CO₂(g), rendering HCOO^* formation the rate determining step. As the binding of OH^* moves to less positive values, the binding of HCOO^* gets stronger such that its deprotonation to CO₂(g) – rather than its formation from FA – becomes rate determining.

A similar path can be taken, starting from the top right corners and moving left along stronger binding of CO^* (or interchangeably COOH^*). As we move left, COOH^* formation no longer becomes unfavorable (as in Figure 7a) or limiting (as in Figures 7c). At such values of G_CO^*, it is downhill to form CO^*, thus signaling a change to the indirect mechanism of FAO. In the top left corner, OH^* binding is much weaker than that of CO^*, leaving CO^* removal to depend on COOH^*, which is stable enough following its linear correlation to CO^*. As a result, the rate determining step in the top left corner is the back-formation of COOH^* from CO^*.

Moving along a vertical line from the top left corner to stronger binding of OH^* makes water activation (to OH^*) more feasible than the formation of COOH^* from CO^*. Therefore, water activation to OH^* becomes rate determining at intermediate binding of OH^*. As we transition to the left bottom corner, the binding of OH^* becomes even stronger, such that its formation from water is no longer difficult. Together with the strongly-bound CO^*, the rate determining step becomes the removal of these two strongly bound species.

Before we describe the higher applied voltage cases, it is instructive to compare the low bias phase diagrams (0.0 V) for close-packed and open facets (Figures 7a and 7c). Starting with similarities, a shallow peak exists at the boundaries of the two rate determining steps of the direct oxidation via formate mechanism (the light cyan region), at an intermediate binding of OH^* (or interchangeably, HCOO^*). Once CO^* binding becomes strong enough to make COOH^* favorable to HCOO^*, the mechanism shifts into the indirect oxidation pathway, which is inactive because a catalytic surface would be poisoned by CO^* at low potentials, since all steps that might remove CO^* are more endergonic or less exergonic than those involved in the direct oxidation via formate mechanism. This is manifested in the apparent discontinuity in the phase diagrams, where the peak in the formate mechanism abruptly ends when the indirect mechanism is invoked. Although both facets are qualitatively similar, there are some subtle differences, brought about mainly by the quantitatively distinct linear scaling relations used for the two types of facets. Firstly, the border between CO^*→COOH^* and H₂O(g)→OH^* regions is shifted downward for the open facets, again due to the stabilization of COOH^* on the open facets, which allows the region of CO^*→COOH^* to expand at the expense of that of H₂O(g)→OH^*. Generally, open facets stabilize COOH^* more than HCOO^*, when compared to close-packed facets. In fact, our linear scaling relations predict that HCOO^* would rather be marginally destabilized on the open facets relative to the close-packed facets, in the free energy sense. We remind here of the approximate nature of the linear scaling relations, especially that the scaling relations of the close-packed facets show mean absolute errors greater than 0.10 eV (Figure S21). As a consequence, the formate mechanism retreats on the open facets (Figure 7c), and gives way to larger regions for the indirect mechanism.

We now turn our attention to the phase diagrams developed for higher applied voltage: 0.6 V (Figures 7b and 7d). As the potential is increased to higher positive bias, all faradaic steps become more exergonic, and the more negative region (blue color) of ΔG_RDS becomes accessible. The formate regions retreat for both facets compared to low bias (e.g.: for 0.0 V), since at high bias COOH^* is formed at moderate G_CO^*, giving rise to the carboxyl and indirect mechanisms. The high bias cases show similar regions as do the low bias cases, with the notable exception of the region HCOOH(g)→COOH^*, which emerges at the stronger binding end of G_OH^* at high bias. In this region, CO^* is not stabilized enough to make CO^*+OH^*→CO₂(g) rate-determining, nor is OH^* destabilized enough to make its formation rate-determining. The emergence of this new region at high bias gives rise to a shallow peak, which is less active than the horizontal peak at the interface between the two steps of the direct formate path.

It is instructive to characterize the regions of higher activity, or the tip of the volcano. At low potentials, we notice a definite active region at the interface between the two regions of the formate path. However, the carboxyl region does not show such a peak, since any surfaces that form carboxyl at the low potential would likely be inactive due to CO^* poisoning. When the problem of CO^* poisoning is alleviated at high potentials however, one notices two active peaks; one in each of the formate or carboxyl regions, with the peak in the latter region being less active. We note that the region of maximum activity, or interchangeably, more negative ΔG_RDS, takes place at intermediate binding of CO^* or OH^*. This is in accord with the Sabatier principle, stating that an active catalyst should bind adsorbates neither too weakly nor too strongly. Relative to the optimal values of the two descriptors, more positive free energies of G_CO^* or G_OH^* indicate weaker binding to the surface, and thus less activity in initiating the reaction. On the other hand, more negative values of the descriptors indicate much stronger binding of reaction intermediates, which poisons the catalyst and inhibits the catalytic cycle. We also note that the less active peak takes place at stronger binding of CO^* as compared to the more active peak, indicating the higher activity of surfaces that bind CO^* less strongly.

Before attempting to utilize the volcano plots of Figure 7 for designing improved FAO catalysts, we wish to emphasize two important aspects of the catalyst design problem, which are not accounted for in these phase diagrams: (i) catalyst stability and metal dissolution potential, which could be determined in suitable durability tests; and (ii) metal oxide formation. Both are challenges that many metals are faced with under typical DFAFCs operational conditions.¹¹⁰

We start by noting that all close-packed and open facets of the metals studied have been placed in the four panels of Figure 7, based on their DFT-calculated G_CO^* and G_OH^*. The linear scaling relations used for preparing the volcano plots in Figure 7 introduce some error due to their approximate nature (Figure S21 and Figure S22). The scatter in these linear scaling relations is partially attributed to the different preferred adsorption sites of the correlated species on the different surfaces.¹⁰⁹ We provide specific geometric information on preferred adsorption configurations in Figures S23–S27, and in Tables S1-S4. As a result, true areas of higher activity and true regions defining the rate-determining steps (RDS) may differ from what is shown in Figure 7. Nevertheless, Figure 7 is still useful in informing strategies for catalyst design.

Pt(111) is the non-group-11 metal with the weakest CO^* binding among the close-packed facets, while this is the case for Pd(100) among the open facets. Although these two surfaces bind CO^* relatively weakly, they also bind OH^* weakly, resulting in their inefficiency at activating water. The latter is reflected in the high onset potential calculated for that step (Figure 5). This points to a key challenge for DFAFC anode catalysts allowing the carboxyl pathway: for them to be better than Pt or Pd in FAO, they should be able to activate water easier than Pt or Pd, a condition analogous to what has been suggested for methanol electrooxidation.^48,49 At the same time, they should be able to efficiently remove OH^*. Our results suggest that the hcp metals, as well as Ni(100), Ir(100), and Rh(100) all bind OH^* and CO^* too strongly, as demonstrated by their PDS for the indirect mechanism; see Figure 5. We also note that improved catalysts allowing the COOH^* path should also exhibit weaker binding of CO^* (together with stronger binding of OH^* to promote water activation), more so for the open facets which have their optimal G_CO^* less negative (i.e. at weaker binding) than their close-packed counterparts.

Figure 7 suggests that the activity of Pt or Pd could be improved by alloying with metals characterized by stronger binding of OH^*, e.g.: Ir, Ni, Co, Ru. Following a simple interpolation logic,¹¹¹ one might expect such alloys to exhibit G_OH^* intermediate between those of the two alloying elements. Alternatively, two alloyed elements could infer synergistic effects on each other, rendering the descriptors' values for the alloy beyond the range limited by the individual's values for the same descriptors. Cai and coworkers³⁴ have recently reviewed improved Pd and Pt alloy catalysts for FAO. Figure 7 suggests that both facets of Cu and Ag lie in a region of low FAO overpotential, but both metals suffer from low stability in the acidic environment of FAO. One possible strategy for identifying improved FAO electrocatalysts would be to alloy these metals with other more stable metals (e.g.: Pd or Pt), so that their stability is enhanced while maintaining local ensembles of active sites rich in Cu/Ag. Indeed, higher activities and better stabilities were reported for PtCu,¹¹² PdCu,¹¹³ PtAg,¹¹⁴ and PdAg¹¹⁵ alloys, compared to the corresponding monometallic Pt or Pd catalysts.

Enhanced activity has also been reported for PdCo,^116,117 PdIr,¹¹⁸ PdNi,^119,120 and PtPd.^121,122 In addition, three-dimensional PtCo nanowire assemblies¹²³ have shown improved performance for methanol electrooxidation. Since we have identified similar requirements for improved catalysis for methanol electrooxidation and FAO (i.e. the requirement to oxidize accumulating CO^*), we expect catalysts showing improved behavior for one to also improve the other reaction. This has also been suggested for the bifunctional PtRu alloy,¹²⁴ as well as PdRu.¹²⁵ Enhanced activity has largely been attributed to improved CO^* tolerance and/or easier water activation. The improved CO^* tolerance can also be a result of ensemble effects, which discourage the dehydration pathway due to the lack of favorable geometrical arrangements of Pt atoms toward CO^* formation. This has been reported for PtPd^122,126 and PtAu^127–131 alloys. More successful examples of Pd-based alloys have also been recently reviewed,^132,133 while Demirci reviews the theoretical tools for screening bimetallic anode catalysts for electrochemical oxidation of liquid fuels, including FA.¹³⁴ Skillful inorganic synthesis plays a major role in realizing the predicted improved active sites by tuning their morphology and composition.^135,136 Accordingly, there have been some excellent recent reviews of this research area.^135,137,138

On the other hand, not all alloying attempts have been successful in improving activity. For instance, Pd₉₀Ir₁₀ and Pd₉₀Pt₁₀ alloys¹³⁹ were found to be more poisoned by CO^* than Pd. A later study identified Pd₇₉Ir₂₁ as more active and CO^* tolerant than Pd,¹¹⁸ whereas a previous study has identified a Pd₉₀Pt₁₀ alloy as most active among a series of Pd_xPt_1-x compared to Pd.¹²² These studies speak to the importance of tuning atomic ratios as well as shapes of bimetallic alloys toward improving electrocatalyst activity and stability.

In addition to bulk alloys, near-surface alloys (NSAs) have gained popularity due to their unique properties and controllable syntheses. Defined as alloys in which the solute element exists near the surface at concentrations different from those in the bulk,¹⁴⁰ the solute could form an overlayer structure, or shell in nanoparticles, on top of the host/core metal. Reactivity of the overlayer/shell metal is modulated by the core metal through strain and ligand effects.^141,142 In the context of FAO, Kibler et al.¹⁴³ have pseudomorphically deposited a monolayer of Pd atop a number of (111) single crystals of transition metals, as well as a PtRu bulk alloy. While some systems exhibited inferior activities compared to pristine Pd, the monolayers on Pt and Au exhibited higher current density than that of pure Pd(111). The Pd monolayer on the PtRu alloy far exceeded the activity of all systems studied.

In addition to electronic and geometrical modification of the overlayer metal, its deposition only in the near surface increases its dispersion and improves its utilization efficiency.³⁵ The synthesis of these overlayer structures with a controlled number of layers has been well-established,^144,145 and have been found to be more stable than pristine metals in electrochemical environments.¹⁴⁶ Accordingly, Pt and Pd overlayers on transition metals could be a promising class of catalysts for FAO. We are currently exploring reactivity trends for FAO on Pt and Pd monolayers on transition metals.

Finally, we briefly discuss the implications of the FAO mechanism on the challenges facing the design of DFAFCs anode electrocatalysts. The reaction mechanism recognizes COOH^* as the only precursor to CO^* poison formation. On all surfaces studied, forming CO^* is guaranteed if COOH^* is more stable than HCOO^*, or if COOH^* formation is downhill in free energy. This establishes an important strategy of CO^* tolerant anode electrocatalysts for DFAFCs: they need to stabilize HCOO^*, and destabilize COOH^*. On a related topic, Yoo et al.⁶⁰ have recently identified HCOO^*, not COOH^*, to be the desired intermediate for selective CO₂ electroreduction to HCOOH; this reaction is the reverse of FAO. This leaves HCOO^* as a common desirable intermediate for HCOOH electrochemistry. To explore the feasibility of attaining such a constraint, we plot in Figure 8 the free energy of COOH^* versus that of HCOO^*, for all surfaces studied. A poor correlation between these two quantities is found, indicating the possibility of designing transition metal catalysts that selectively stabilize HCOO^*.

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