Effective Reversible Potentials and Onset Potentials for O2

Dec 11, 2012 - Although the route where O2 dissociates was calculated to have higher values for their effective reversible potentials, predicted activ...
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Effective Reversible Potentials and Onset Potentials for O2 Electroreduction on Transition Metal Electrodes: Theoretical Analysis Alfred B. Anderson,*,† Ryosuke Jinnouchi,‡ and Jamal Uddin† †

Chemistry Department, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7078, United States Toyota Central R&D Laboratories, Inc., Nagakute, Aichi 480-1192, Japan

‡

ABSTRACT: Results from a comprehensive approach to predicting and explaining activities of 13 transition metal cathode materials toward oxygen electroreduction are presented. Effective reversible potentials for four-electron reduction were calculated based on exergonic O−O bond scission for OOH and O2 on Pt(111), Pt monolayer skins on Pd(111), Pt3Cu(111), Ir(111), Pt3Ni(111), Pt3Co(111), Au(111), Rh(111), Pt3Fe(111), Ru(0001), Ag(111), Pt3Ti(111), and, finally, on pure Au(111). All values based on the OOH(ads) route were several hundred millivolts less than the 1.23 V standard value for the four-electron reduction. Although the route where O2 dissociates was calculated to have higher values for their effective reversible potentials, predicted activation energies were also high, precluding this possibility in most cases. Comparison of predicted effective reversible potentials, which spanned a range of 0.3 V and measured reduction onset potentials, which according to the literature span a narrower ∼0.1 V range, suggests the possibility that higher activation energies will for some materials reduce the measured onset potentials to values less than the effective reversible potentials. Assignments based on the energy scaling model to the left- or right-hand sides of volcano-shaped activity plots at 900 mV vs O and OH adsorption bond strengths were found to be correct when the former was used. It was found for all 13 materials that the Gibbs adsorption bond strengths of OOH are at least 0.9 eV less than the ideal value of 1.35 eV, and an important goal is to reduce this gap through the discovery of new catalysts. When this is accomplished, it will be possible to construct volcano plots using current densities measured at electrode potentials approaching 1.23 V.

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INTRODUCTION In recent decades there has been a worldwide effort to develop or discover catalysts superior to platinum for the electroreduction of O2 at oxygen cathodes in fuel cell applications. The standard reversible potential for the four-electron reduction of O2(g) to H2O(l) is 1.229 V. In both the early work of Appleby1 with electrode potential 0.8 V on the reversible hydrogen electrode (RHE) scale and more recent work of Zhang et al. at 0.9 V (RHE),2 platinum was found to offer higher potentials and current densities than other metals. Development has involved making incremental improvements in platinum by synthesizing and testing alloys of platinum, generally with a single less noble metal such as iron, chromium, nickel, and others. The early work of Mukerjee et al.3 soon inspired others to study oxygen electroreduction on alloy electrodes.2,4−9 An interesting recent approach has been that of Snyder et al. to explore the benefits new electrolytes may provide to enhancing the reaction rate.10 From these studies it is found that the best standard current onset potential for O2 reduction can be extended to around 1.0 V on the mA/cm2 scale. However, even the best of these catalysts provide useful current densities at overpotentials of around 500 mV, that is, at cell potentials of around 0.7 V. Nevertheless, even this potential is satisfactory in view of the high thermodynamic efficiency electric power production of fuel cells relative to the efficiency of power production using generators driven the pressure− volume work produced by burning fuel in internal combustion © 2012 American Chemical Society

engines. Less costly and, preferably, better, meaning with higher activity and stability, catalysts than alloys of platinum will, if discovered, present a breakthrough for the generation of electrical power from hydrogen. Platinum is a satisfactory hydrogen anode catalyst. A second fuel cell breakthrough would be the discovery of inexpensive and stable catalysts that provide efficient use of hydrocarbon fuels with or as replacement for hydrogen. This topic is not addressed further here. Another important topic not addressed here is the oxygen cathode catalyst support material. This is generally carbon, some forms of which are corroded at high potential, shortening the useful life of the cathode. Other development work for oxygen cathodes has focused on improving carbon in its graphite form to become a catalyst itself and not merely a support for catalysts. Graphite has long been known to catalyze two-electron reduction of O2 to hydrogen peroxide, H2O2 and there has recently been activity to develop doped carbon electrodes for fuel cell applications.11−19 Main group compounds20−23 and CuI have also been studied.24−26 The focus of this paper is platinum alloy catalysts and the determination and understanding of thermodynamic and kinetic barriers that retard their performance. The idea of effective reversible potential, Ueff, recently put forth by Tian and Received: July 25, 2012 Revised: December 3, 2012 Published: December 11, 2012 41

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Anderson, causes thermodynamic barriers.27 The Ueff potential is equal to the standard reversible potential for the four-electron reduction of O2 minus the sum of energies for exergonic intermediate steps ΔGexer that take place during the course of the reaction but do not involve electron transfer, divided by 4e where e is the electron charge: Ueff = 1.229 V − ΔGexer(4e)−1

simplifying approximations that the O2(g) and H2O(l) adsorption Gibbs bond strengths are zero, it follows that the adsorption Gibbs bond strengths for OOH(aq), OH(aq), and O(aq) to the catalyst surface are respectively 1.35, 1.49, and 2.49 eV. Because of the new reversible potential assigned above to eq 4, the last value is 0.11 eV greater than that reported previously in refs 27 and 28. Since Gibbs energy is a state function, these adsorption bond strengths also apply if the reaction mechanism first has O2 dissociating on the catalyst surface, followed by reduction of both O(ads) to OH(ads) and reduction of OH(ads) to H2O(l). Electrocatalysts are sometimes compared by making measurements of current densities for O2 reduction over them at a chosen potential. When these current densities are graphed as functions of the adsorption bond strengths of O, OH, or OOH to the catalyst surfaces, volcano-shaped plots often appear.1−3 Note that most discussions of volcano plots have been based on bond strengths represented as internal energies, E, not Gibbs energies, G. Appleby explained the behavior by noting that for a group of catalysts ordered so that adsorption bond strength for the first adsorbed intermediate, OOH, increased it was expected that the adsorption bond strength of the last adsorbed intermediate, OH, also increased.1 This means that as the first step increased its rate the last step would decrease its rate. The material with the maximum rate for the overall reaction would have the most favorable balance of these bond strengths. This is an application of the Sabatier principle. It has been assumed that the OOH, OH, and O adsorption bond strengths all move is the same direction from one material to another, that is, they scale with one another, and theoretical works by Rossmeisl et al.,33 Koper,29 and Man et al.34 have supported the existence of the scaling relationship. Therefore, all else being equal, for a given mechanism involving these intermediates, there is an optimal OH adsorption bond strength that will result in the highest current density at the chosen potential. According to a recent review by Zhang, the maximum reduction onset potential over catalysts consisting of alloys of platinum is about 1.0 V.35 This limit has been suggested to be caused wholly by the dissociation of OOH(ads) being 0.9 eV, or more, exergonic, which according to Tian and Anderson leads to an effective reversible potential for the four-electron reduction around 0.9 V.27,28 A recent preliminary calculation reported by Anderson indicated that on Pt(111) the OOH(ads) Gibbs adsorption bond strength significantly less than the ideal value of 1.35 eV and calculations have shown that O and OH Gibbs adsorption bond strengths are too high by about 0.7 and 0.8 eV, respectively.36 Then, for this mechanism, the scaling relationship may hold for OOH and OH Gibbs adsorption bond strengths, but to push the effective reversible in the positive direction toward 1.23 V while the OH adsorption Gibbs bond decreases toward 1.49 eV and the O adsorption Gibbs bond strength decreases toward 2.49 eV, the adsorption Gibbs bond strength of OOH must increase toward 1.35 eV. As long as this is the case, the peaks in volcano plots cannot approach 1.23 V. Koper29 and Stephenson et al.30 also noticed that the scaling relationship observed for platinum and platinum alloys prevented approaching the desired 1.23 V potential, but these workers did not recognize that if OOH(ads) dissociation is exergonic, the reversible fourelectron reduction potential will be lowered to Ueff as given in eq 1.

(1)

Contributions to ΔGexer include reactant adsorption energies and dissociation of adsorbed intermediates. The basis for eq 1 lies in elementary thermodynamics. At constant pressure and temperature, the maximum nonexpansion work a reacting system can do is the Gibbs reaction energy, we,max = ΔreactG. The prime example of this sort of work is electrical work from a fuel cell: ΔreactG° = −nFU°, where ΔreactG° is the standard reaction Gibbs energy, n is the number of electrons transferred in the reaction, F is the Faraday constant, and U° is the standard reversible potential. If some of ΔreactG° is spent in ways other than allowing electrons to do electrical work, we can say that the maximum nonexpansion electrical work, we,max′, the system can produce is we,max′ = ΔreactG° − ΔexergonicG = −nFUeff, from which eq 1 follows. Endergonic steps such as product desorption and adsorbed intermediate bond breaking will contribute to the kinetics. On Pt(111) electrode surfaces the intermediate reaction OOH(ads) → O(ads) + OH(ads)

(2)

was calculated to be about 1.2 eV exergonic for a variety of plausible surface conditions. When the O2(gas) adsorption energy and H2O(ads) desorption energy were ignored, both giving relatively small contributions for the conditions studied, the predicted reversible potential was 0.93 V, which is about the potential at which current is observed to begin go flow at the milliampere scale on platinum electrode surfaces. Using the reversible potentials for the following bulk solution reactions O2 (g) + H+(aq) + e− = OOH(aq),

U ° = −0.125 V (3)

+

−

O(aq) + H (aq) + e = OH(aq),

OH(aq) + H+(aq) + e− = H 2O(l),

U ° = 2.23 V

(4)

U ° = 2.72 V (5)

and ΔG° = (4)1.229 eV for the four-electron reduction, it is found that the dissociation Gibbs energy for OOH(aq) forming O(aq) + OH(aq) is 2.63 eV. This value is 0.11 eV greater than used previously in this lab because for eq 4 the assumed value the solvation Gibbs energy of O, of 0.00 eV, is now replaced by the calculated value 0.11 eV. As is well-known, for the reaction over an ideal catalyst, the standard reversible potential for each intermediate electron transfer step will be the same as the standard reversible potential for the overall reaction, 1.229 V.28−30 This is because the activation energies for the electron−proton transfer steps during reduction reactions increase as the electrode potential increases. The activation energies at the reversible potentials have been found theoretically to be of the order 0.1−0.2 eV according to a local reaction center electron tunneling model28 and also adiabatic electron transfer models. 31,32 Ideal adsorption Gibbs bond strengths can be calculated by balancing the adsorption energies of the oxygen-containing molecules on the two sides of the equal signs in eqs 3 and 4 to make the reversible potential for each reaction 1.23 V. Making use of the 42

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at a very low surface coverage condition and at potentials of zero charge. For O2 the Gibbs adsorption bond strength, DGO2, was calculated as the negative of the Gibbs energy difference between O2(ads) and O2(g):

It is illustrative of the significance of the optimal adsorption Gibbs energies to mention that if the OOH, OH, and O adsorption Gibbs bond strengths had the values, for example, 0.00 eV for OOH, 1.73 eV for O, and 0.90 eV for OH, Ueff would be 1.23 V and the reversible potentials for O2, O, and OH reduction would be −0.12, 1.40, and 1.82 V, respectively. This would result in a high activation energy for OOH formation, but for O and OH reductions the barriers would be low. If the respective adsorption bond strengths were 2.00, 2.5, and 2.13 eV, the respective reversible potentials would be 1.86, 1.88, and 0.54 V, resulting in high activation energy for OH reduction and low barriers for O reduction and OOH formation. There will be less electrical work available if the potential is set to values less than 1.23 V. Given that the metal and metal alloy systems generally fall on a volcano plot when enough data are available to define one, we have undertaken a study of 13 different (111) metal surfaces to calculate OOH and OH adsorption Gibbs and internal bond strengths. Our goal is to learn whether the OOH adsorption bond strengths are always too small and if the OH and O adsorption bond strengths are always too large and to find out how much less than 1.23 V the effective reversible potentials, based on the exergonicity of OOH(ads) dissociation, eq 3, are for the systems. We extend the perspective by including predictions of effective reversible potentials based on the exergonicity and activation energies for O2(g) dissociative adsorption. For the present paper we have calculated the adsorption Gibbs bond strengths of OOH, OH, and O on Pt(111), Pt monolayer skins on Pd(111), Pt3Cu(111), Ir(111), Pt3Ni(111), Pt3Co(111), Au(111), Rh(111), Pt3Fe(111), Ru(0001), Ag(111), Pt3Ti(111), and, finally, on pure Au(111).

DGO2 (g) = G(O2 , g) − G(O2 , ads)

(6)

In ref 41, gas phase Gibbs adsorption bond strengths, DG(ads,gas), were calculated for all adsorbates using six atomic layer slabs of pure Pt(111), Pt alloys, and Pt core−shells with a 2 × 2 periodic structure, which corresponds to the surface coverage of 1/4 ML, as shown in Figure 1. The Gibbs

Figure 1. Six-layer slab model used for calculation of adsorption energies of molecules to form 1/4 ML coverage at the solid−gas interface.

adsorption bond strengths for the molecules in the gas phase changed only a few meV when the surface coverage was decreased from 1/4 ML. Hence, 1/4 ML Gibbs adsorption bond strengths are very close to the limit of low coverage for the gas interface. The standard states for the OOH, OH, O, and H2O molecules in eqs 3−5 are all aqueous, and the Gibbs adsorption bond strengths, DG, were calculated as the negative of the Gibbs energy differences between the solvated bulk solution phase molecules and the solvated adsorbed molecules. For example, for O

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THEORETICAL APPROACH Density functional theory (DFT)37,38 calculations were carried out by using a computational code “Interface” which was introduced by Jinnouchi and Anderson39,40 and was recently parallelized by Jinnouchi et al.41 Full details are in refs 39−41, so only a general physical and conceptual introduction is given here. The surfaces were modeled by extended slabs with vacuum on one face and adsorbed molecules on the other, and two-dimensional periodic boundary conditions were used. The basis sets consisted of pseudoatomic orbitals. Triple-zeta plus polarization (TZP) basis sets were used for H and O, and a double-ζ plus polarization (DZP) basis set was used for Pt. Troullier−Martins type scalar relativistic norm-conserving pseudopotentials42 were used for describing all the effective core potentials. The RPBE functional43 was used because it has been confirmed in ref 40 to be more accurate in giving Pt−O and O(ads) bond strengths on Pt than PBE44 and PW-91 functionals,45 both of which yield values too high for these bond strengths. Some hydrogen-bonded water molecules participating with the solvation of the adsorbed molecules were added to the translational cells. The electrolyte was modeled using dielectric medium theory with a modified Poisson−Boltzmann treatment of ion distribution densities. To obtain the Gibbs free energies, thermal components were added to the energies from the DFT calculations to take into account zero-point vibrational energies and thermal motions of the atoms and molecules. Standard pressures of 1.0 bar and standard concentrations of 1.0 M were assumed, and concentration effects were calculated assuming unit activity coefficients. The temperature was 298.15 K. The calculations were performed to obtain the Gibbs adsorption bond strengths

DGO = G(O, aq) − G(O, ads, solvated)

(7)

For these calculations, a four atomic layer slab of pure Pt(111) with 3 × 2√3 periodic structure was used. For the calculation of G(O,ads,solvated), the coverage of O(ads) was set at 1/12 ML, and the coverage of explicit water molecules was set at 2/3 ML, as shown in Figure 2, and half the water molecules are nearly parallel to the surface and half have OH bonds pointed toward the surface. This represents a low-coverage limit for O and provides adsorption bond lengths in the presence of electrolyte in this limit for comparison with the ideal values. When two and three monolayers are present, the perpendicular OH bonds point away from the surface instead (not shown) since Pt is hydrophobic.40 When O is on the surface, each atom passivates three Pt atoms (1/4 of the total surface atoms) and the water layer is repelled, and no hydrogen bonds to O(ads) are evident in Figure 2. For the calculations of G(OH,ads,solvated) and G(OOH,ads,solvated), the coverage of OH(ads) or OOH(ads) was set at 1/12 ML, and the coverage of explicit water molecules was set at 7/12 ML, as shown in Figure 3, and similarly to the model for the calculation of G(OH,ads,solvated), half the water molecules are parallel to the surface and half have OH bonds pointed toward the surface. When OH and OOH are on the surface, hydrogen bonding draws some of the 43

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otherwise, there will be reaction bottlenecks. This makes the low-coverage model the proper one to use when seeking the ideal catalyst.

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RESULTS AND DISCUSSION Adsorption Energy Trends and Volcano Plots. We first ordered the 13 metals according to decreasing OH adsorption bond strength, beginning with the one to which OH bonded most strongly, Pt(111), and ending with Au(111). These adsorption energies are plotted in the left-hand panel in Figure 4. Adsorption bond strengths for OOH, O, O2, and H2O are included in the figure, and the adsorption Gibbs bond strengths for O(aq) and OH(aq) are in columns 1 and 2 in Table 1. Two types of adsorption bond strengths are shown for each molecule. The red points, DG, represent the Gibbs energies required to remove molecule from the surface of the electrochemical interface and place it in bulk solution. The black points, De, represent the internal energies required to remove a molecule from the surface in vacuum and place it in vacuum, and they are from the bottoms of the Born− Oppenheimer potentials, without zero-point energy contributions. The two types of energy track each other closely across the series. Years ago the simplest internal energy calculations for electron transfer reactions using a vacuum model produced reversible potentials which were equal to experimental values plus a constant; this is reviewed in ref 28. Reference 28 also explains why the tracking behavior holds for electron transfer reactions between molecules adsorbed on electrode surfaces. The essential idea is that part of the relatively weak stabilizing solvation shells in bulk solution are replaced by strong bonds to the surfaces. For OH, the Gibbs and internal adsorption bond strengths on the various surfaces differ by a few hundredths of an electronvolt from one another, and for the other molecules the differences are around 0.4 eV, but they track each other almost exactly, as has been established recently by several groups.29,33,34 All values of DG are at the potential of zero charge, meaning no electron density was added to or subtracted from the surface when the Gibbs energies were calculated for the electrochemical interface. When evaluated at the reversible potentials, the DG may vary by as much as 0.1 V for O(ads) and OH(ads).28 These small variations depend on the surface coverage of water molecules, and given their weak adsorption, the water coverage is probably fluxional, but the variations give an idea as to the range in uncertainty in DG due to lack of knowledge about the structure of the electrochemical interface. As discussed in ref 28, the hydrogen-bonding interaction of OH(ads) with two coadsorbed water molecule is 0.3 eV, and as more water molecules are added, H2O to H2O hydrogen bonding begins to play a role in the total energy. For example, in the present calculations, when seven H2O(ads) per OH(ads) H2O molecules with the structure with in Figure 3 were used, the calculated stabilization relative to isolated adsorbed H2O in the dielectric continuum was 0.426 eV. At lower water coverage, 3, 2, and 1 H2O per unit cell respective OH stabilizations were 0.254, 0.335 (close to ref 28 with its different structure model), and 0.244 eV, corresponding to a single hydrogen bond. However, with a bilayer of 15 H2O and a trilayer of 23 H2O, the respective stabilizations are 0.602 and 0.439 eV. As is evident in ref 28 and the present calculations, coadsorbed water molecules do not form hydrogen bonds with O(ads). We note that different calculations have yielded different orders. The trend reported by the Mavrikakis group46 is only

Figure 2. Four-layer slab model used for calculation of adsorption energies. Top panels show water molecules without adsorbates. Bottom panel shows water molecules with 1/12 ML of O atoms to form the model of the liquid electrolyte−solid interface.

Figure 3. Four-layer slab models used for calculation of adsorption energies of OH and OOH molecules to form 1/12 ML coverage at the liquid electrolyte−solid interface. Top panels show water molecules without adsorbates.

water molecule closer to the surface, as shown in Figure 3. The calculated solvation Gibbs energies relative to the molecules being adsorbed at the vacuum interface are −0.005 eV for O(ads), −0.544 eV for OH(ads), and −0.287 eV for OOH(ads). Hence, the solvation stabilizes OH(ads) the most. Changes in surface coverage models will change the adsorption bond strengths by small amounts, putting them closer to or further from the ideal values. It was found in ref 41 that when coverage effects on the energetics were included, the optimal point of the volcano plot was unchanged. However, during reaction conditions, the ideal catalyst will experience only low concentrations of short-lived adsorbed intermediates; 44

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Figure 4. Left panel plots adsorption bond strengths in order of decreasing OH values and right panel graphs them in order of decreasing O values.

Table 1. O(aq) Adsorption Gibbs Energies, DGO (eV), OH(aq) Adsorption Gibbs Energies, DGOH (eV), OOH(aq) Adsorption Gibbs Energies, DGOOH, O2(g) Adsorption Gibbs Energies, DGO2, H2O(l) Adsorption Gibbs Energies, DGH2O, Effective Reversible Potentials for OOH(ads) Dissociation Pathway, Ueff(OOH) (V), Effective Reversible Potentials for O2 Dissociation Pathway, Ueff(O2) (V), and Activation Gibbs Energy for O2 Dissociative Adsorption in the Low-Coverage Limit, Da0 (eV), for the 13 Metal Surfaces in the Order of decreasing DGO, As Shown in Figure 4 metal

DGO

DGOH

DGOOH

DGO2

DGH2O

Ueff(OOH)

Ueff(O2)

Da0

Au(111)@Pt Ag(111)@Pt Pt(111) Pd(111)@Pt Pt3Cu(111) Pt3Ni(111) Pt3Co(111) Pt3Fe(111) Ir(111)@Pt Rh(111)@Pt Pt3Ti(111) Ru(0001)@Pt Au(111)

3.31 3.31 3.10 3.03 2.89 2.85 2.68 2.67 2.65 2.56 2.50 2.40 2.00

1.76 1.56 1.84 1.82 1.79 1.77 1.77 1.63 1.77 1.66 1.38 1.61 1.23

0.40 0.25 0.47 0.45 0.42 0.42 0.37 0.29 0.37 0.29 0.26 0.24 −0.21

−0.35

−0.19 −0.23 −0.22 −0.23 −0.23 −0.23 −0.26 −0.21 −0.23 −0.25 −0.19 −0.25 −0.31

0.77 0.78 0.82 0.84 0.88 0.89 0.92 0.94 0.93 0.96 1.04 1.00 1.08

0.85 0.85 0.96 1.00 1.06 1.08 1.16 1.17 1.18

0.45 0.45 0.54 0.58 0.79 0.96 1.10 1.08 1.12 1.24 1.26 1.43

−0.22 −0.21 −0.48 −0.48 −0.54 −0.59 −0.41 −0.46

(111), and Ir(111)@Pt and these should lie on the left-hand side of the volcano peak. Furthermore, all of the others should lie on the right-hand side. However, according to this criterion, Ir(111)@Pt and Au(111)@Pt are on the wrong sides. We decided to try an ordering based on DGO. In the right-hand panel in Figure 4, the order is based on descending from the highest DGO for Au(111)@Pt to the lowest, Au(111). Based on these bond strengths, the assignments to the left-hand and right-hand sides of the volcano centered on Pt3Ni(111) are correct. This might appear to suggest that a balance of OOH and OH adsorption energies is not responsible for the volcano plots but rather a balance of OOH and O adsorption energies is instead. However, the story is more complicated. The right-hand panel in Figure 4 shows the differences between DGO and DGOH becoming smaller across the series. Then according to energy conservation, the reversible potential for the reduction of O(ads) to OH(ads)

slightly different from that reported here, and the trend from the Balbuena group47 is very different. The causes of these differences are not known. The small differences between some of the adsorption energies mean the ordering based on these differences is uncertain. The scaling of our calculated DGOOH and DeOOH adsorption bond strength values with those for DGOH and DeOH in the left-hand panel of Figure 4 is not perfect. The OOH adsorption bond strengths and especially the O adsorption bond strengths deviate from the uniform trend in OH adsorption bond strengths that was set up. Let us relate this to the volcano plot based on compiled experimental current densities at 0.9 V as collected by Rossmeisl and Norskov.48 The low activity over gold observed by Appleby1 was not included in these references, but our calculated data are added to the figures. Of these systems, experimental data are lacking only for Ag(111)@Pt [this notation means one monolayer of Pt atoms is on the Au(111) surface], but it should behave similarly to Au(111)@Pt. The highest activity is for Pt3Ni. It might be expected that all catalysts to which the OH adsorption is stronger than on Pt3Ni would be less active than Pt3Ni. This means that Pt(111), Pd(111)@Pt, Pt3Cu-

O(ads) + H+(aq) + e− = OH(ads)

(8)

is increasing across the series, and the activation energy for the reaction is therefore decreasing. For further discussion of the 45

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increase in the value of DGO − DGOH going up the series in Table 1 is in support. Effective Reversible Potentials and Volcano Plots. In past work, effective reversible potentials based on OOH(ads) dissociation, eq 2, now termed Ueff(OOH) instead of simply Ueff, were calculated by using the assumption that the small calculated values for adsorption Gibbs bond strengths for O2(g) and H2O(l) could be replaced by zero, a reduction in parameters without introducing much error. Figure 4 shows that these adsorption bond strengths are in fact small, several tenths of an electronvolt negative, with O2(ads) being less stable than H2O(ads). For several surfaces there was no local minimum point corresponding to O2(ads), and so there are no entries in the figures for them. The energies indicate that when O2 approaches the surface, the H2O(ads) will be displaced. Also, in ref 40, it was found with potential-dependent interface calculations that in the water dielectric medium model O2(ads) + H2O(l) would be thermodynamically more stable than O2(g) + H2O(ads) at potentials greater than 0.5 V. Thus, as previously assumed, the process of O2 adsorption in the presence of liquid water is not exergonic, but there may be small activation energies for O2 to reach the surfaces. This leaves the exergonic O−O bond-breaking step, whether in OOH(ads) or O2(ads), responsible for the effective reversible potential being less than the 1.23 V standard value for the fourelectron reduction. In the following, the effective reversible potential based on O2 dissociation in eq 8 will be symbolized by Ueff(O2). Calculated values for the Gibbs energies of the reaction of eq 2 have been used in eq 1 to make predictions of Ueff(OOH) for the 13 metal surfaces based on the exergonicity of O−OH(ads) bond scission, eq 2. We point out that the exogernicity calculated here is purely theoretical, meaning we did not modify the experimental value of 2.63 eV found above using eqs 3−5 for OOH(aq) dissociation by using the calculated adsorption energies of OOH(aq), O(aq), and OH(aq), but instead used the calculated dissociation energy of 2.85 eV. For the reaction on Pt(111), Ueff(OOH) is calculated to be 0.82 V, which is slightly different from the value 0.93 V previously reported.27 This is because the model used here is in the low-coverage limit whereas in the previous work about 1/6 ML OH(ads) was present, and this weakens the stabilities of the O(ads) and OH(ads) dissociation products, which, when formed, increase the coverage of strongly adsorbed O and OH to 1/2 ML. As shown also in the mean-field study of ref 41, at this coverage repulsion interactions become the order of magnitude of 0.1 eV. There are also differences in the amounts of explicit water molecules used in the translational cell models. Predicted Ueff(OOH) values for the 13 surfaces based on eq 2 are in column 6 of Table 1, where it is seen that as DGO decreases, Ueff(OOH) generally increases, and the trend provides no insight into understanding the volcano plot and its peak at Pt3Ni. This is understood as follows. Two have slightly lower Ueff(OOH) values than the trend, Ir(111)@Pt and Ru(0001)@Pt, and this is related to DGOH being higher than their trend line for these two surfaces. Pt3Ni(111), the most active surface, according to the volcano plots, has its Ueff(OOH) in the middle of the range of 0.77 V for Au(111)@ Pt and 1.08 V for Au(111). Entries to the left of Pt3Ni(111), with lower Ueff(OOH), seem to be following the expectation that increasing values mean higher activity,27,41 but to the right increasing values lead to lower activity. Might this be caused by increasing activation energies for O−OH(ads) dissociation (eq

effect of shifting the reversible potential on activation energy at a given potential, see ref 36, particularly Figure 2. The OH(ads) adsorption bond strengths are slowly changing across the series with Pt3Ti(111) and Au(111) adsorbing OH more weakly than the other surfaces. This means that, except for the last two surfaces, reversible potentials for OH(ads) + H+(aq) + e− = H 2O(l)

(9)

are only slowly increasing. However, the activation energy for eq 8 is rapidly decreasing and, at 0.9 V, may drop below that for eq 9, perhaps around Pt(111). Then both eq 8 and eq 9 should have relatively low activation energies for entries on the righthand side of the volcano curve, and either O adsorption or OH adsorption energies could be mentioned for scaling with the OOH adsorption energy. Supporting this suggestion, it was found in the mean-field study of Jinnouchi et al.41 that metals to the right of Pt3Ni had their activity controlled by the first reaction step, OOH(ads) formation by O2 (g) + H+ + e− = OOH(ads)

(10)

or O(ads) formation by O2 (g) → 2O(ads)

(11)

Consequently, for metals to the right of Pt3Ni the activation energies of eq 8 and eq 9 did not control the reaction rate. For metals to the left of Pt3Ni, they found O(ads) or OH(ads) removal controlled the activity. Whether eq 11 is thermodynamically allowed on a surface depends on the O2(g) bond strength and on DGO for the surface. The calculated Gibbs energy for O2 dissociation at 1.0 bar pressure is 5.10 eV, which overestimates the empirical value of 4.80 eV. Using the calculated gas phase dissociation energy and the DGO values in Table 1, dissociation on the surfaces is thermodynamically not expected to take place on Au(111) and Ru(0001)@Pt and perhaps not on Pt3Ti(111). At least four additional surfaces are only slightly favored for this reaction, and the remaining ones are strongly favored. The activation Gibbs energies for eq 8 have been calculated to be high in the low-coverage limit, ranging from 0.449 eV for Au(111)@Pt and Ag(111)@Pt to 1.431 eV for Ru(0001)@Pt.41 Furthermore, at operating potentials, the combined O(ads) + OH(ads) coverage on Pt(111) has been predicted to be around 0.2 ML,41 and the presence of these strongly bound molecules would tend to make activation energies become even greater, reducing the probability of O2 dissociation. This suggests to us that eq 11 does not contribute significantly to the formation of O(ads) for entries below possibly the Pt(111) entry in Table 1, which leaves OOH(ads) formation, eq 10, as the probable “adsorption step” in applying the Sabatier principle for them. There are two choices for the rate-limiting step, called the desorption step by Appleby: after OOH(ads) dissociation, O(ads) reduction to OH(ads) or OH(ads) reduction to H2O(l). On the basis of the potential dependencies of calculated activation energies that were obtained using resonant electron tunneling theory and a local reaction center model, it has been suggested that OH(ads) reduction has the lower activation energy on platinum surfaces in acid electrolytes.49 The greater success of basing the left-hand and right-hand entries in the volcano plot in the adsorption Gibbs energy bond strengths for O rather than OH provides support for O(ads) reduction being the controlling “desorption step”, and the expected increase in activation energy for eq 8 due to the 46

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be the most active, according to the volcano plot of current densities vs oxygen atom adsorption bond strengths for several metal electrodes.1 However, dissociation of the O−O bond may not have participated in the reduction. Blizanac et al. recently measured an onset potential of about 0.55 V on Au(111) and a polarization curve with a shallow slope in acid electrolyte; it was concluded that reduction was entirely twoelectron, forming hydrogen peroxide.50 The weak activity measured by Appleby at the higher potential may have been caused by impurities but might have been the result of following the OOH(ads) formation mechanism, which is also the first step in hydrogen peroxide generation. Once OOH(ads) forms, if it cannot dissociate, it will be reduced to hydrogen peroxide which bonds weakly to the surface and desorbs into solution. Zhang et al. measured the onset potential for O2(g) reduction on Ru(0001)@Pt is about 0.87 V, and the current density increases slowly as the electrode potential was decreased, as shown in a polarization curve.2 This suggests that the kinetics are slower than for other catalysts below 0.87 V: could there be an O2 dissociation component to the reduction in this case? Because of the high Da0, the mechanism probably is by OOH(ads) dissociation, and some surface structure property must have caused the polarization curve to have its shape. Pt3Ti is calculated to have a high Ueff(OOH), 1.04 V, but the polarization curve measured by Yoo et al. had a slope similar to platinum and the onset potential about 0.93 V, similar to platinum.51 As shown in ref 2, the observed onset potentials for Rh(111)@Pt and Ir(111)@Pt are about 0.9 V, compared with the respective predictions of 0.96 and 0.93 V, and the polarization curves are slightly less steep than for platinum. The predicted Ueff may be larger than the observed onset potentials because of high activation energies for some reaction steps reducing the onset potentials, but the agreement is good. It is necessary to recognize that there is about 0.1 V uncertainty in the calculated Ueff, and therefore it is probably not possible to derive accurate ordering of the observed onset potentials from these values for Ueff.

2) or O2 dissociation (eq 11)? We think that is a possibility, as explained next. Values for Ueff(O2) were calculated based on O2 dissociation, eq 11, are in column 7 of Table 1. The adsorption bond strength for O2 at the aqueous electrochemical interface was taken to be zero. Gibbs activation energies for O2(g) dissociative adsorption, Da0, in the limit of low coverage of O(ads) and OH(ads), taken from ref 41, are included in Table 1 in the eighth column. Under fuel cell operating conditions, O−O bond breaking activation energies will increase because the ∼0.2 ML coverage of OH(ads) and O(ads) will weaken the adsorption bond strengths of the dissociation products. Gibbs activation energies for the OOH(ads) dissociation reaction were not calculated, but they will show the same trend, as may be seen in internal activation energy calculations for Pt(111) and Pt layers on Au(111), Pd(111), and Ir(111) in the work of Nilekar and Mavrikakis.46 Table 1 shows that Ueff(O2) have higher values for these surfaces than Ueff(OOH), and for the last four entries, Rh(111)@Pt, Pt3Ti, Ru(0001)@Pt, and Au(111) the values calculated for DGO are so small that Ueff(O2) is 1.23 V for them because the dissociations will not be exergonic. However, the activation energies for reaction by eq 8 are prohibitively high for these four surfaces, around 1.2−1.4 eV, and they remain high going up the column, decreasing to 0.96 eV over Pt3Ni(111), to 0.54 eV over Pt(111), to 0.45 eV over Au(111)@Pt at the top of the column. This suggests that the O2 dissociation pathway will be inactive for most of these surfaces. In Jinnouchi et al.’s mean-field study of O2 reduction over Pt(111), it was predicted that the fraction of current density due to the OOH and subsequent dissociation formation was 4/5 at 0.9 V, with 1/5 of the current density due to the O2 dissociation path. At potentials approaching 0.6 V, and below the OOH forming pathway became exclusive,41 and this was attributed to the activation Gibbs energy for OOH(ads) formation decreasing while the activation Gibbs energy for O2 dissociation remained constant. On the basis of this and the data in Table 1, we expect that for Au(111)@Pt and Ag(111)@ Pt the O2 dissociation will play a role greater than on Pt(111), and going down the column in Table 1, the participation of this pathway will quickly approach zero. In mean-field model study of Jinnouchi et al.,41 a volcano plot was generated using the internal energies of O2 dissociative chemisorption, which is proportional to the negative of the Pt− O adsorption bond strengths. It was found that maximum activity would be had for Pt3Ni(111), which was near the volcano peak, and for the metals with higher adsorption bond strengths than Pt3Ni(111) the activity decreased monotonically, in agreement with the experimental literature. For the metals with decreasing adsorption bond strengths, the predicted activities were less, in agreement with experiment, but the monotonic ordering was lost. The low activities on the surfaces where adsorption was strong were proposed to be caused by the relatively high activation energies causing O(ads) or OH(ads) reduction to be the slow step in the four-electron reduction. The low activities for the surfaces with weak adsorption were proposed to be caused by the relatively high activation energies for OOH(ads) formation, an electron transfer reaction, or the dissociative chemisorption of O2(g). For the reasons presented in the previous section, we believe OOH(ads) formation dominates in the cases of weak adsorption. Appleby found a gold electrode in acid to be, by orders of magnitude, the least active at 800 mV (RHE) and platinum to

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CONCLUSIONS

We have shown that although effective reversible potentials, Ueff(O2), based on O2 dissociation on the 13 metal surfaces studied here are higher than the effective reversible potentials Ueff(OOH) based on OOH(ads) dissociation to O(ads) + OH(ads), the inability of O2 to dissociate on some surfaces negates the advantage. We conclude that in general |Ueff − U| is the minimum absolute overpotential for an electrochemical process, and kinetics can in some cases dominate the observed onset potential. We found that the scaling of O and OOH adsorption bond strengths correlates with the assignments of materials to the left- and right-hand sides of the empirical volcano plot for these materials, but the ordering in the righthand side was not reproduced. For all materials in this study the OOH adsorption bond strength was calculated to be several hundred meV less than the ideal value, and an important goal is to reduce this gap through the discovery of new catalysts. When this is accomplished, it will be possible to construct volcano plots using current densities measured at electrode potentials approaching 1.23 V. 47

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AUTHOR INFORMATION

Corresponding Author

*Ph 216-368-5044; Fax 216-368-3006; e-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant CHE-0809209.

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