ARTICLE pubs.acs.org/JPCC
Theoretical Study of Electrochemical Processes on PtNi Alloys Ivana Matanovic,*,†,‡ Fernando H. Garzon,§ and Neil J. Henson† †
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States R. Boskovíc Institute, Department of Physical Chemistry Bijenicka 54, 10000 Zagreb, Croatia § Materials Physics and Application Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States ‡
ABSTRACT: We have carried out an extensive computational study using periodic density functional theory of the structure, reactivity, and stability of three different PtNi alloys, Pt3Ni, PtNi, and PtNi3, with the aim of determining the effect of the subsurface layer composition on the catalytic activity of the platinum surface. The segregation effect was taken into account by modeling slabs with a platinum surface monolayer supported on a second layer containing 50%, 100%, and 75% of nickel, respectively, with a bulk layer below. Calculated equilibrium adsorption potentials for the oxygen reduction reaction (ORR) intermediates and construction of free energy diagrams for the ORR dissociative mechanism are used to gauge the catalytic activity. The critical question of the stability of these materials in an aqueous environment is also assessed in terms of the relative shifts in electrochemical dissolution energies and by the identification of the most stable state of the surface as a function of pH and potential as illustrated in Pourbaix diagrams. The (111) surface of all three models of PtNi alloys is found to exhibit improved oxygen reduction activity compared with that of pure Pt(111). The ORR overpotential was calculated to decrease in the order Pt (0.55 V) > Pt3Ni (0.24 V) > PtNi3 (0.19 V) > PtNi (0.15 V). We can therefore conclude that the catalytic activity for ORR will increase as Pt < Pt3Ni < PtNi3 < PtNi and find that the largest improvement occurs for a PtNi alloy with 100% nickel in the second layer. We also predict that PtNi is the least susceptible to corrosion at similar pH and cell potentials based on the calculated shifts of the electrochemical dissolution potentials for the PtNi alloys relative to platinum with values of 0.27 V for PtNi3, þ0.13 V for Pt3Ni, and þ0.30 V for PtNi.
’ INTRODUCTION Future energy concerns demand a transition from fossil fuels to new, more environmentally benign, and renewable energy sources. A promising route for accomplishing this goal is to use fuel cells for direct conversion of the chemical energy of fuels to electricity. Namely, compared to heat engines, fuel cells have a potential for highly efficient use of chemical fuels; however, many technical challenges remain before a widespread use can be realized. One of the principal limitations at present is the slow kinetics of the oxygen reduction reaction (ORR) in acidic environments, which is a crucial component in fuel-cell systems. The slow kinetics of the ORR, even on a platinum catalyst, gives rise to a significant cathode overpotential which acts to decrease the fuel cell electrical efficiency. In a hydrogen/oxygen fuel cell, for example, the cathode overpotential is between 500 and 600 meV,1 leading to the efficiency of 4555% compared to the theoretical thermodynamic efficiency of 93% at 25 °C.2,3 Relatively high platinum loadings of the catalyst have been used to support acceptable cell currents, which in turn limits commercialization of fuel cells due to the high price of platinum. The problems in efficient fuel cell utilization have motivated considerable interest in both experimental and theoretical research on different aspects of the ORR with the aim of designing the catalysts with fewer drawbacks and superior performance.4 Theoretical studies of electrochemical processes on the surfaces of transition metals constitute a crucial r 2011 American Chemical Society
part of this research. Computational studies have been used to elucidate the reaction mechanisms on the surfaces57 but also to develop predictive models which connect the activity of the catalyst with some of its intrinsic properties.811 Some of these models have in fact been used successfully as the basis for design of new catalysts.7,12 One of the methods that was demonstrated to improve the catalytic activity is the alloying of platinum with other transition metals.13,14 An enhancement of the ORR activity of Pt3M alloys (M = Ni, Co, Fe, V, Ti) over pure platinum, for example, has been demonstrated on extended polyelectrodes and single crystal electrodes having a platinum monolayer on the surface of an alloy.11,12 This improvement has been explained by the weakening of the interaction of oxygen-containing ORR intermediates with the surface via d-band center shifting.8,9 However, the stability of Pt transition metal alloys in acidic environments and high cathode potentials is poor due to the high enthalpy of oxidation of the transition metal component.1517 Additional studies on the stability and activity of various Pt alloy based catalysts are therefore clearly required. Previous computational work in this area has been concerned with both the structure of Pt Received: December 15, 2010 Revised: April 28, 2011 Published: May 11, 2011 10640
dx.doi.org/10.1021/jp111930w | J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
Table 1. Calculated Lattice Parameters and Heats of Formation of Bulk Pt, Pt3Ni, PtNi, PtNi3, and Nia lattice parameters calculated/Å
Pt
Pt3Ni
a = 3.98/3.99
a = 3.89/3.90
PtNi a = 3.86/3.87
PtNi3
Ni
a = 3.66/3.69
a = 3.52/3.56
a = 3.7547
a = 3.5246 5.46/5.17
c/a = 0.94/0.95 experimental/Å
a = 3.9246
a = 3.8925
a = 3.8248,49
E/(eV/per atom)
6.04/5.26
5.97/5.32
5.85/5.33
5.68/5.28
ΔfH/kcal mol1
1.60/1.95
2.20/2.68
1.66/2.05
ΔfHexp/kcal mol1
1.4650b
2.2150
1.6150b
c/a = 0.94
a
b
Calculated values are obtained with PW91/RPBE functionals. The values are obtained from ref 50 by interpolating the heat formations for available PtNi alloy compositions.
bimetallic alloys1821 and the ORR activity on the surface of the Pt alloyed with Co,10,11,18,2224 Fe,10,11,23,24 Ni,10,11,24 Ti,10,11 and V,11 and on Pt monolayers on the surface of several late transition metals such as Au, Pt, Pd, and Ir.7 This work, however, represents the first systematic and comparative study of the structure, activity, and stability of different PtNi alloys and of the influence of the concentration of alloying component. We have chosen nickel for this purpose because of recent reports which demonstrated that alloying with nickel enhances catalytic activity.12,25,26 The precise role played by the composition and the distribution of the alloying component in the modified reactivity of platinum atoms, however, remains unclear. In this study, we used the combination of density functional theory (DFT) calculations and the approach developed by Nørskov and co-workers for calculating free energies of different intermediates in the ORR mechanism.8,27 The relative stability of alloys is investigated in terms of segregation energies, electrochemical dissolution shifts, and surface Pourbaix diagrams28,29 and additionally by the study of diffusion of Ni and Pt atoms from the inner layers to the surface. Changes in the catalytic activity of the Pt surface induced by the change in alloying component concentration are investigated by calculating equilibrium adsorption potentials for ORR intermediates and by constructing free energy diagrams for the ORR dissociative mechanism.
’ COMPUTATIONAL DETAILS All the calculations were performed using the spin-polarized generalized gradient approximation (GGA) to density functional theory (DFT) with the Revised-PerdewBurkeErnzerhof (RPBE)30 and PerdewWang (PW91)3133 exchange-correlation functionals. We also examined the performance of the GGAPBE method (PerdewBurkeErnzerhof functional)34,35 in selected √ cases√for comparison. Metal surfaces were represented by 2 3 2 3 unit cells with a size of 61/2a 61/2a, where a is the lattice parameter determined from bulk calculations. The unit cells consist of three layers of metal atoms and a vacuum region of about six layers (about 13 Å). During the optimization, all the atoms in the unit cell were allowed to relax. The projector augmented wave method36,37 was used as implemented in the Vienna Ab initio Software Package (VASP)3841 with a 4 4 1 k-point MonkhorstPack42 mesh of the first Brillouin zone and a plane-wave basis cutoff energy of 400 eV. MethfesselPaxton smearing43 of order 2 with a value of σ = 0.2 was used to aid convergence. The stability of PtNi alloy surfaces at different pH and potentials U was obtained by the approach developed by Nørskov et al. and described in detail in refs 8 and 27. Pourbaix
diagrams were constructed by following the procedure by Hensen et al.28 The details of the model used for the study of the ORR mechanism and for the construction of phase and Pourbaix diagrams in this paper are given in more detail in the Appendix. Similar approaches were used in some related, previous work.7,44,45
’ RESULTS AND DISCUSSION Bulk Study. The accuracy of our methods was assessed by initial calculations on bulk phases where the calculated structural data can be directly compared with experiment. In this study, we have modeled Pt and Ni bulk46 with the fcc structure, Pt3Ni25 and PtNi347 bulk with the Cu3Au-type (L12)18 structure, and PtNi bulk48,49 with the tetragonal CuAu-type (L10)18 structure. The optimized lattice constants obtained with both the GGA-PW91 and GGA-RPBE method are given in Table 1 and agree within about 1% with the experimental values. We also calculated the heats of formations using the reaction
xPtðsÞ þ ð1 xÞNiðsÞ f Ptx Ni1x ðsÞ
ð1Þ
and compared the results with the experimental values from ref 50. The value obtained with the use of PW91 for the case of PtNi agrees remarkably well with the experimental value, whereas RPBE slightly overestimates the heat of formation for PtNi. Experimental values were not directly available for the remaining two alloys considered in this work. Heats of formation for the PtNi3 and Pt3Ni alloys were therefore derived from available data for other alloy compositions using a cubic spline interpolation, and our calculations were found to agree very well with the values estimated from available experimental information. Surface Stability. The slab models used in this work are shown in Figure 1 and described in Table 2. The Pt-segregated Pt3Ni and PtNi structures were built from the corresponding slabs by exchanging Ni atoms from the first layer with Pt atoms in the second layer. The first layer therefore consists only of Pt atoms, while the second layer contains 50% and 100% Ni atoms, respectively, for the two slabs. The tendency for metal atoms with larger radii and lower surface energies to segregate to the surface has been verified both experimentally12 and theoretically.20,21 As previously shown for both Pt3Ni10,51 and PtNi52,53 alloys, after a final annealling the surface atomic layer is enriched with Pt atoms, a phenomenon which is counterbalanced by the depletion of the Pt atoms in the next two or three atomic layers. The segregation model in which the Ni atoms from the first layer were simply exchanged with the Pt atoms in the second layer represents a simplification over the experimentally found compositional trends. However, in previous computational studies 10641
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
this model was shown to capture important structural and electronic properties for the number of segregated Pt3M alloys.20 To supplement our study of the nickel concentration effect on the ORR, a slab with 75% of Ni in the second layer was built by assembling a layer of Pt atoms on a model consisting of two atom layers of the ordered PtNi3 slab as shown in Table 2. We thus evaluated models of three PtNi alloys with Pt segregation taken into account (Figure 1). All three alloys are found to have negative segregation energies, namely, 0.04 eV for Pt3Ni, 0.07 eV for PtNi, and 0.01 eV for PtNi3 (PW91 functional), which indicates that the Pt atoms are thermodynamically able to segregate to the surface. The segregation energy was defined as the difference in the energy per atom of the slab between the Pt segregated and the bulk structure. The layers for all the surfaces were allowed to relax, and the resulting geometric
parameters are summarized in Table 2. As indicated in Figure 1 due to a specific atom composition in deeper layers, Pt atoms in the skin layer are not equivalent. For instance, there are three types of Pt atoms in the case of Pt3Ni: Pt(1) atop site has 4 Pt and 2 Ni atoms as nearest neighbors in deeper layers (2 Pt and 1 Ni in both the second and the bottom layer). Pt(2) atop site has 3 Ni atoms as nearest neighbors, out of which two are located in the second and one in the bottom layer. Pt(3) atop site, on the other hand, has only one Ni atom as its nearest neighbor, located in the second layer. This is reflected not only by the geometry of the slab and the vertical displacements in the layers but also by the strength of the interaction with the studied adsorbates. Adsorption energies were therefore calculated for each nonequivalent atop (hydroxyl adsorption) or fcc site (oxygen adsorption) to determine the value which limits the specific thermodynamic parameter. The largest difference in the vertical position between different types of Pt skin atoms are listed in Table 2 expressed as Δz1 value. As expected, it is the smallest in the case of the PtNi alloy where the concentration of Ni in the second layer is 100%, while it is largest for the PtNi3 alloy because the concentration of Ni is larger relative to Pt3Ni, both in the second and in the bottom layers. Vertical displacement of the atoms of PtNi3 is 0.11 Å in the first and 0.06 Å in the second layer, respectively. Electrochemical Dissolution and Oxidation Process. The corrosion process of the catalyst surface is of crucial importance when considering its stability in the fuel cell and can be represented by the following reaction MðsÞ f Mnþ ðaqÞ þ ne ðaqÞ
ð2Þ
The energy of this reaction can be estimated by calculating the surface cohesive energy, i.e., the energy required to remove a surface metal atom E ¼ EN1 þ EM EN
Figure 1. Structures of the (a) Pt3Ni(111), (b) PtNi(111), and (c) PtNi3(111) surfaces with a Pt monolayer on the surface. Nonequivalent atop and fcc binding sites are also indicated. Blue, Pt atoms; green, Ni atoms.
ð3Þ
where N refers to the number of metal atoms in the model and M refers to the lone metal atom. To calculate the surface cohesive energy, surface Pt atoms in nonequivalent sites in PtNi alloys have been selected and removed and the resulted structure relaxed. The smallest value of the energy needed to “extract” the Pt atom from the nonequivalent surface sites defines the lower limit to the surface dissolution energy. This dissolution energy is directly related to the surface cohesive energy by the addition of a constant,54 and the shift in the dissolution potential (ΔUcorr) of a Pt skin relative to that of bulk platinum can simply be estimated using the relation ΔG/ne where n is the number of exchanged electrons. Results for the three PtNi alloys are given in Table 3. Both Pt3Ni and PtNi can be seen to have higher
Table 2. Slab Models of PtNi Catalysts Used in the Studya catalyst Ni concentration in the first/second/third layer
Pt 0/0/0
Pt3Ni, seg
PtNi, seg
PtNi3, seg
0/0.5/0.25
0/1.0/0.5
0/0.75/0.75
Ni 1.0/1.0/1.0
d12/Å
2.33
2.24
2.11
2.31
2.01
d23/Å
2.33
2.16
1.96
2.06
2.01
Δz1/Å
0.00
0.08
0.02
0.11
0.0
Δz2/Å
0.00
0.04
0.02
0.07
5.62
5.58
5.45
5.41
E/(eV/per atom)
0.0 5.03
a Average distance between the layers i and j (dij), vertical displacement of the atoms in the layer i (Δzi = zi,max zi,min), and energies per atom calculated for the relaxed (111) surfaces. Pt and Ni values are given for comparison.
10642
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
Table 3. Density Functional Theory Calculated Surface Cohesive Energies and the Estimation of the Shift in the Electrochemical Dissolution Potential (ΔUcorr) Compared to Pt(111)a reaction
MN(surface) f MN1 þ M
Pt(111) Pt3Ni(111)
ΔE/eV 5.79
ΔUcorr/V
ΔUcorrb/V
0.00
0.00
þ0.13
þ0.10
þ0.30
þ0.30
site 1
6.11
site 2
6.23
site 3
6.04
PtNi(111)
site 1
6.41
PtNi3(111)
site 2 site 1
6.38 5.69
site 2
5.58
0.11
0.23
5.26
0.27
0.30
Ni(111)
a The values are obtained using RPBE and PW91 (denoted with b) exchange functionals.
surface cohesive energies than platinum, and it can thus be expected that they have a lower thermodynamic predisposition to electrochemical dissolution relative to platinum. A surface platinum atom in site 3 in the Pt3Ni alloy (Figure 1), for example, has an extraction energy of 6.04 eV, which is 0.26 eV higher than that for a surface platinum (111) atom. Hence, the equilibrium potential for electrochemical dissolution can be estimated to be 0.13 eV greater than that of pure platinum. A platinum atom in Site 2 in the PtNi alloy has an extraction energy of 6.38 eV, which is 0.60 eV higher than for the surface platinum (111) atom, and the equilibrium potential for electrochemical dissolution can be estimated to be 0.30 eV higher than that of pure platinum. PtNi3, on the other hand, has a lower surface cohesive energy than platinum and as such a slightly higher thermodynamic predisposition to electrochemical dissolution. This would also imply that PtNi3 is less suitable as a catalyst for ORR than Pt as it would dissolve at lower potentials. We would like to point out, however, that our conclusions are based on considering the perfect surfaces, while dissolution would be expected to be more effective at the defect sites than on the terraces. Consequently, the dissolution potentials would depend not only on the layer composition but also on surface topology, such as coordination number of a specific atom. The other process that can seriously decrease the stability of alloys in acidic environments with high cathode potentials is the oxidation of the alloying component. The oxidation mechanism of the PtNi alloys is a highly complex problem, which was not addressed in detail in this work. We can, however, assume that the diffusion of nickel atoms to the surface is the limiting step for the oxidation process due to the high reactivity of nickel atoms. Our calculations show that the diffusion of both nickel and platinum atoms to the surface is exothermic once a surface vacancy is formed, which indicates that it is energetically more favorable for the vacancy to exist in the subsurface layers. Diffusion of platinum atoms, however, is thermodynamically more favorable in the case of Pt3Ni than for PtNi3. In Pt3Ni, for example, the change in energy induced by the diffusion of a platinum atom from the second layer to the surface vacancy is 0.88 eV, while that for diffusion of a nickel atom is 0.39 eV. On the other hand, the analogous process in the PtNi3 alloy induces the energy change of only 0.14 eV, vs a value of 0.36 eV for the diffusion of a nickel atom. We note, however, that in
our model of PtNi alloy only Ni atoms can move to the surface since the concentration of Ni in the second layer is 100%. Kinetic aspects of the diffusion process were investigated by calculations of the barriers for the diffusion of both nickel and platinum to the surface vacancy using the nudged elastic band method55,56 as implemented in VASP.3841 These barriers were found to be 0.42 and 0.46 eV for the diffusion of a Ni or Pt atom, respectively, in the Pt3Ni alloy. This small difference in the barrier heights for the two types of atoms clearly demonstrates that there is no significant change in the kinetic restraints between the two species. The barriers to diffusion in PtNi3 were determined to be 0.55 eV for nickel and 0.64 eV for platinum. These observations lead to the conclusion that the Pt3Ni alloy will show the lowest tendency for the nickel atoms to move from the inner layers to surface defect sites with both PtNi and PtNi3 alloys being more susceptible to this process. The presence of nickel atoms on the surface would further lead to the process of degradation of PtNi and PtNi3 by dissolution of nickel atoms or poisoning of the surface with nickel oxide. However, the PtNi surface has the highest resistance to the formation of surface defects, and overall, the presence of nickel in the surface layer will be thermodynamically less favorable than in PtNi3. PtNi3 shows the lowest resistance to the electrochemical dissolution of platinum surface layer and the highest thermodynamical tendency for the diffusion of nickel atoms from the inner layers to the surface defects. Thus, from all the compositions studied here, PtNi3 is most likely to be the most susceptible to both electrochemical dissolution and poisoning of the surface by the formation of nickel oxide. Oxygen Reduction Reaction. The oxygen reduction reaction can lead to various surface intermediates, i.e., surface phases which, in a simple dissociative mechanism, transform in these steps 1 O2 ðgÞ þ f O 2
ð4Þ
O þ Hþ ðaqÞ þ e f HO
ð5Þ
OH þ Hþ ðaqÞ þ e f H2 OðlÞ þ
ð6Þ
where * denotes a binding site on a metal surface and X* a chemical species X bound to the surface. Specific models used to study different states of the metal surface are described in the Appendix. Each model includes the water bilayer to account for the water environment in the electrochemical cell, and therefore we will start our discussion of the oxygen reduction process by discussing the structure of water in contact with the metal surface. Structure of the Water in the Wetting Layer. While it has recently become known that the structure of water molecules on a solid surface is more complicated than that given by a simple hexagonal model,57,58 we used the simple bilayer hydrogenbonded structure of water molecules described by Ogasawara et al.59 and Michaelides et al.60 for our study of a water-covered surface of PtNi alloys. To account for both the periodicity of water molecules in these bilayers and for the repeating pattern of PtNi atoms √ √ in PtNi alloys, in our calculations we used the 2 3 2 3 unit cell. The two water bilayers on a Pt(111) surface are shown in Figure 2. In one of the structures the OH bonds which are not coordinated to another water molecule are pointing down toward the metal surface (called “H-down” 10643
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
Figure 2. Models used for the structure of the water bilayer on the Pt(111) surface. (a) H-down structure and (b) H-up structure. The distances of the water molecules from the surface are given for PW91 and RPBE functionals (RPBE values in brackets).
Table 4. Density Functional Theory Calculated Adsorption Energies for H2O in Two Bilayer Structures of Water (Hdown and H-up) on the (111) Surface of Pt and PtNi Alloys at pH = 0 and U = 0 reaction 1:
* þ H2O(g) f H2O* 2/3 coverage
ΔEPW91/eV
ΔERPBE/eV
H-down H-up H-down H-up
Pt(111)
0.53
0.50
0.31
Pt3Ni(111)
0.52
0.51
0.35
0.32 0.34
PtNi(111)
0.51
0.50
0.34
0.32
PtNi3(111)
0.50
0.50
0.27
0.33
bilayer), and in the other structure the same OH bonds point away from the metal (called “H-up” bilayer). The binding energies of water molecules for the two structures are calculated using different exchange-correlation functionals as shown in Table 4. We obtained binding energies of 0.53 eV for the H-down structure and 0.50 eV for the H-up structure on a Pt(111) surface using the PW91 functional. Similar results are given by the PBE functional, namely, 0.51 and 0.48 eV, respectively. The RBPE functional, however, gives much lower binding energies, 0.31 eV for a H-down structure and 0.32 eV for the H-up structure. The weaker interaction between water molecules and the surface is reflected in the larger separation of a water bilayer from the surface calculated with the RPBE functional. Distances of water molecules from the surface calculated using RPBE are found to be 0.2 Å larger on average than those calculated with the PBE and PW91 functionals. The same trend was also observed for the water adsorption energies on the Rh(111) surface, where the interaction of water with the metal surface was studied using the DFT-GGA approach but also by applying the vdW-DF functional.61 The well-known deficiency of the DFT-GGA approach in describing the van der Waals interactions could thereby be studied in detail. The authors of this work concluded that the PBE binding energies agree very well with the vdW-DF results but for the wrong reason. Namely, PBE underestimates the watersurface interaction energy of the physisorbed water molecules, and the good agreement between the vdW-DF and PBE results was attributed to the usual error cancellation rule in local-density approximation (LDA) and PBE.
It was also shown that the structure of the water bilayer is determined by a delicate balance of Pauli repulsion and long-range vdW attractions in watersurface and waterwater interactions. The binding energies of water on the surfaces of PtNi alloys were found to differ only slightly from those calculated for the Pt(111) surface, and the differences in energy between the H-up and H-down structures are even smaller for the PtNi alloys. Because of these rather subtle differences in the energetics, it is not possible to determine which of the two water bilayer structures is more stable on PtNi alloy surfaces within the accuracy of our computational methods. Moreover, in the case of a H-down bilayer, PBE and PW91 converge to a structure very similar to the one observed on Pt (Figure 2) in which the distance from the surface to the water molecules parallel to the surface (H2Op) is smaller than that of the water molecules with an OH bond pointing down to the surface (H2Ov). However, in the course of optimization with the RPBE functional, H2Op molecules were found to move away from the surface, and the structure converges to an alternative H-down bilayer in which the distances of H2Op molecules from the surface become similar to or larger than that of H2Ov water molecules. Calculation using the PW91 functional on a Pt3Ni surface, for example, results in a minimum H-down structure, in which the PtH2Op distance is 3.04 Å and PtH2Ov is 3.29 Å, while the use of RPBE results in a H-down structure in which these distances are 3.85 and 3.65 Å, respectively. It is apparent from the foregoing discussion that more accurate binding energies and structures of water bilayers on these surfaces require further studies which will correctly account for the vdW interactions. Such calculations, however, are beyond the scope of the present work. Surface Pourbaix Diagrams. To determine the most stable states of Pt and PtNi alloy surfaces, we further considered different structures of oxygen, hydroxyl, and hydrogen on these surfaces which correspond to fundamental steps in the ORR mechanism. The results and relevant equations are given in Table 5. While the same surface structures were previously investigated for Pt,8,27,28 we have repeated these calculations with the same approach as for the PtNi alloys. Results for the absolute values of equilibrium adsorption potentials for oxygen, hydroxyl, and hydrogen are given in Table 5 only for the RPBE functional, while the shifts in the equilibrium adsorption potentials relative to the Pt values are given for both RPBE and PW91 functionals. The most stable state of the surface is determined from the results in Table 5 by use of phase diagrams. Details of this approach are given in the Appendix, and an example of such a phase diagram at pH = 0 is shown in Figure 3. Pt(111) Surface. Our calculations show that at negative and very low potentials (up to 0.14 V) hydrogen is adsorbed at the Pt surface with a 1/3 coverage in agreement with the Pt(111) voltammogram, which shows a broad hydrogen desorption/ adsorption peak between 0.05 and 0.375 V.62 This finding also supports the fact that platinum is a good catalyst for hydrogen oxidation under acidic conditions. A pure Pt surface without adsorbates is the most stable state for potentials between 0.14 and 0.63 V. Water starts to oxidize to O* on a Pt surface at potentials above 0.63 V. The initial oxygen coverage is 1/4 and increases at higher potentials to 1/3 and subsequently to 1/2. The equilibrium potentials for the adsorption of oxygen on Pt(111) with 1/3 and 1/2 coverages are calculated as 0.74 and 0.83 V, but it is only above 1.03 V that a 1/2 coverage becomes the most stable structure. Water activation to form a hydroxyl overlayer with 1/3 coverage is not exergonic on the Pt surface 10644
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
until 0.80 V. The stability regions for hydroxyl and oxygen adsorption are quite close, and they can be considered to be equally stable and coexist in the same potential range around 0.8 V. This observation is also supported by the finding that the local electric field in the double layer induced by the external electric field makes hydroxyl in the water layer more stable and thus lowers the equilibrium potential for the adsorption of hydroxyl
relative to that of oxygen.63 The numbers calculated with the RPBE functional are in excellent agreement with the experimental observations. The reversible potential for hydroxyl adsorption of approximately 0.8 V62 is identical to our calculated value of 0.8 V. Electrochemical quartz crystal nanobalance and in situ X-ray studies have also shown that oxidation of a Pt surface proceeds via formation of a monolayer of chemisorbed oxygen in
Table 5. Density Functional Theory Calculated Adsorption Energies (ΔEw), Free Energies (ΔGw), and Equilibrium Potentials (Uf) for the Adsorption of O, OH, and H on Pt(111) and PtNi Alloys at pH = 0 and U = 0a reaction 2: Pt(111)
Pt3Ni(111)
PtNi(111)
PtNi3(111)
* þ H2O(g) f O* þ H2(g)
ΔEw/eV
ΔGw/eV
Uf/V
ΔUf/V
ΔUfb/V
1/4 coverage
1.21
1.26
0.63
0.00
0.00
1/3 coverage 1/2 coverage
1.42 1.61
1.47 1.66
0.74 0.83
0.00 0.00
0.00 0.00
1/4 coverage
1.55
1.60
0.80
0.17
0.11
1/3 coverage
2.04
2.09
1.04
0.30
0.23
1/2 coverage
2.11
2.16
1.08
0.25
0.20
1/4 coverage
2.12
2.17
1.08
0.45
0.36
1/3 coverage
2.34
2.39
1.20
0.46
0.39
1/2 coverage
2.47
2.51
1.26
0.43
0.35
1/4 coverage 1/3 coverage
1.95 2.43
2.00 2.48
1.00 1.24
0.37 0.50
0.36 0.46
1/2 coverage
2.45
2.50
1.25
0.42
0.42
* þ H2O(g) f OH* þ 1/2H2(g)
ΔEw/eV
ΔGw/eV
Uf/V
ΔUf/V
ΔUfb/V
Pt(111)
1/3 coverage
0.45
0.80
0.80
0.00
0.00
Pt3Ni(111)
1/3 coverage
0.74
1.09
1.09
0.29
0.17
PtNi(111)
1/3 coverage
0.97
1.32
1.32
0.52
0.50
PtNi3(111)
1/3 coverage
1.09
1.44
1.44
0.64
0.58
reaction 4:
* þ 1/2H2(g) f H*
ΔEw/eV
ΔGw/eV
Pt(111)
1/3 coverage
0.38
0.14
0.14
0.00
0.00
Pt3Ni(111)
1/3 coverage
0.16
0.08
0.08
0.22
0.16
PtNi(111)
1/3 coverage
0.01
0.23
0.23
0.37
0.29
PtNi3(111)
1/3 coverage
0.10
0.34
0.34
0.48
0.39
reaction 3:
Uf/V
ΔUf/V
ΔUbf /V
a
The values are given only for the RPBE functional, and the shifts in equilibrium formation potentials (ΔUf) relative to the Pt values are given for both RPBE and PW91 (denoted as b) functionals.
Figure 3. Phase diagram showing the calculated free energy for different surface structures for water at pH = 0 in contact with Pt(111), Pt3Ni(111)seg, H* and PtNi(111)seg. The figure is based on the free energy values in Table 1. The violet line is related to H*: ΔGH* W (U) = ΔGW (0) þ 0.33U; the blue line to OH* OH* O* H* OH*: ΔGW (U) = ΔGW (0) 0.33U, the red line to O* with a 1/3 coverage: ΔGW (U) = ΔGW (0) 0.66U; and the magenta line to O* with a 1/2 O* coverage: (ΔGO* W (U) = ΔGW (0) U. 10645
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C the 0.851.15 V range.64,65 It is only in the higher potential range (1.151.4 V) that the experiments show evidence for the formation of metal oxide by a mechanism of site exchange of O and Pt, further formation of PtO, and surface diffusion of PtO to energetically favorable sites.15,64,65 (111) Surface of PtNi Alloys. The trend in the equilibrium adsorption potentials of oxygen with an increase in coverage is observed to be the same for all three alloys as for Pt. At higher coverages, the oxygen-covered surface is less stable, and the water oxidation to form the O* with a higher coverage becomes exergonic at more positive potentials. The oxygen equilibrium adsorption potential for the Pt3Ni alloy at 1/4 coverage shifts to higher values for þ0.17 V relative to Pt as calculated using the RPBE functional. The shift is somewhat larger for higher coverages, namely, þ0.30 V for 1/3 coverage and þ0.25 V for 1/2 coverage. The hydroxyl adsorption potential on Pt3Ni is also found to be higher that that of Pt with a shift þ0.29 V for the RPBE functional. Adsorption of hydrogen on the Pt3Ni surface, on the other hand, becomes exergonic at more negative potentials then on the Pt surface with a shift of 0.22 V. The calculated shifts can be compared with the experimentally determined voltammograms of Pt3Ni(111) and Pt(111).12 Careful inspection of both voltammograms revealed a dramatic negative shift (∼0.15 V) in the formation of adsorbed hydrogen and a positive shift (∼0.1 V) in the formation of a hydroxyl layer on the Pt3Ni(111) surface relative to Pt(111).12 Compared to the values calculated using the RPBE functional, we can conclude that the agreement is reasonable in the case of hydrogen adsorption; however, the calculated shift is overestimated for hydroxyl adsorption. Both the positive shifts in the equilibrium adsorption potentials of oxygen and hydroxyl and the negative shift in equilibrium adsorption potential of hydrogen become larger as the concentration of nickel in the second layer changes from 50% in Pt3Ni to 75% in PtNi3 and 100% in PtNi alloy. This is clearly seen from Table 5 and Figure 3. The shifts in equilibrium adsorption potentials of oxygen and hydroxyl are more pronounced when the nickel concentration is changed from 50% to 75%, but the shift is not as significant when the nickel concentration is raised from 75% to 100%. The same trend was observed for PtCo alloy surfaces with a Pt skin, where the shift of the reversible potentials for adsorption of hydroxyl and water do not significantly change above a cobalt concentration of 75%.18 The strength of the interactions of oxygen and hydroxyl with the metal surface can be correlated with the shift in the position of the d-band induced by the change in the concentration of nickel in the alloy. An important surface parameter which governs the reactivity of the surface was indeed previously identified to be the position of the d-band relative to the Fermi level.10,66 Namely, the strength of the oxygenmetal bond depends on the strength of the coupling between the oxygen 2p states and the metal d states which leads to the formation of bonding and antibonding states. The shift and thus the degree of filling of the antibonding states is determined by the position of the d-band. The d-band centers of PtNi alloys are calculated as the average for the Pt atoms in the skin and are found to be 2.01 eV for Pt, 2.17 eV for Pt3Ni, 2.31 eV for PtNi, and 2.56 eV for PtNi3. The downward shift of d states relative to the Fermi level results in a downward shift of the antibonding states, which leads to increased filling and thus a weaker oxygenmetal interaction, and correlates well with the upward shift in the oxygen equilibrium adsorption potentials given in Table 5.
ARTICLE
Figure 4. Calculated surface Pourbaix diagrams for (a) Pt3Ni(111) and (b) PtNi(111) compared to a bulk Pt Pourbaix diagram15,67 (black dashed lines). The gray region denotes the UpH region where the PtxNi1x surface is stable without adsorbates, and the violet region corresponds to a region where different adsorbates on the surface exist. The red lines denote the beginning of the area where water is oxidized to O* (1/3 coverage), and the blue lines denote the area where 1/3 hydroxyl in a hexagonal layer of water is starting to be stable on a Pt(111) surface (dashed lines) and on a PtxNi1x surface (solid lines). The brown region shows the estimated change in the corrosion region relative to Pt(111). With black solid lines, we also indicated the potentials of the reversible hydrogen and oxygen electrodes to mark the stability range of water.
On the basis of the results discussed above, we constructed the Pourbaix diagrams for the surface of PtNi alloys. In Figure 4, Pourbaix diagrams for the surface of Pt3Ni and PtNi alloys are shown; the diagrams for PtNi3 and PtNi are similar. Although the change in the reversible potential for forming O* and OH* on PtNi alloys relative to Pt has been previously discussed, our diagrams depict the manner in which the reversible adsorption potentials change with varying pH. Nernst-like behavior was assumed. Also, a comparison with the Pourbaix diagram of bulk platinum is given.15,67 So far, we discussed only the results obtained using the RPBE functional. The comparison between the results obtained with the RPBE functional on one hand and PW91 and PBE functionals on the other hand deserves some additional attention. Equilibrium potentials for oxygen and hydrogen adsorption obtained using PW91 and PBE functionals on Pt(111) are found to be very similar to those calculated with the RPBE functional. DFT calculations with a PW91 functional, for example, predict that the Pt surface with an oxygen coverage of 1/4 will become 10646
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
Figure 5. Interaction energy of a H2Op monomer with the Pt(111) surface as a function of vertical OPt distance for the H2Op water (black RPBE, red PW91 energy profile).
stable at potentials above 0.66 V. Furthermore, the equilibrium potentials for the adsorption of oxygen on Pt(111) with 1/3 and 1/2 coverages are found to be 0.75 and 0.83 V and the equilibrium potentials for the adsorption of hydrogen 0.22 V. The equilibrium potential for the adsorption of hydroxyl, however, is significantly lower with the PW91 and PBE functionals, namely, 0.50 and 0.53 V, respectively, compared to 0.8 V for RPBE and experiment. There are two reasons for this disagreement. First, PW91 and PBE predict the hydroxyl layer to be more stable than does RPBE, which results in lower equilibrium potentials for the adsorption of hydroxyl calculated with these two functionals. The adsorption energy of hydroxyl without the presence of water given as E(OH*) E(*) E(OH) is 3.0 eV for PW91 and 2.14 eV for RPBE. Second, the nature of the specific model used to calculate the energy of adsorption of hydroxyl in the half dissociated water layer (OH* model explained in detail in the Appendix) requires that adsorption values calculated with PW91 and PBE functionals be corrected by a term which takes into account the dependence of the adsorption energy of water on the distance of H2Op molecules from the surface. Namely, the change in free energy for reaction 3 in Table 5 was calculated as the difference in energy for the reaction in which the hydroxyl forms embedded in the hexagonal hydrogen bonded network of water, i.e. þ 2H2 O f OH, H2 O þ 1=2H2
ð7Þ
This energy difference ΔE(OH*, H2O*) has to be corrected for the binding relative to water by subtracting the adsorption energy of water (ΔE(H2O*) from reaction 1 in Table 4). However, the adsorption energy of water for the PW91 functional depends strongly on the distance of H2Op water molecules from the surface as can be seen from Figure 5. Since the H2Op distance from the surface is 2.21 Å in a layer in which the H2Op is hydrogen bonded to a hexagonal network with adsorbed hydroxyl, as compared with 2.90 Å in a hexagonal water bilayer, ΔE(OH*, H2O*) has to be corrected for the water adsorption energy ΔE(H2O*) at d = 2.21 Å which is around 0.2 eV lower than the adsorption energy at d = 2.90 Å. With the addition of this estimated correction term, the calculated reversible potentials for hydroxyl adsorption for the PW91 and RPBE functionals become more positive. The adsorption energy of the H2Op for the RPBE functional is much less dependent on the PtOH2 distance as a result of an underestimation of the nonlocal correlation, i.e., the
vdW interaction term. The correction term for the same model in this case is thus negligible, and the RPBE gives the “correct” reversible potential for hydroxyl adsorption The RPBE functional, as discussed previously, reproduces the correct absolute value of the formation potential for adsorbed oxygen, hydrogen, and hydroxyl, while both PW91 and PBE underestimate the formation potential of hydroxyl on Pt(111). Yet, we can conclude from a comparison of the calculated values for Pt3Ni with the experimentally determined voltammogram that the RPBE functional overestimates shifts in the equilibrium adsorption potentials of oxygen and hydroxyl on Pt3Ni relative to Pt, while the PW91 functional gives better agreement with experiment. For instance, the RPBE predicts a shift of þ0.30 V for the hydroxyl adsorption potential on Pt3Ni relative to Pt, while the PW91 and PBE predict a shift of þ0.17 V. The value of þ0.17 V is in much better agreement with the experimental value of ∼0.10 V. The same is true for the oxygen adsorption on Pt3Ni for all coverages. The RPBE functional systematically predicts larger shifts than the PW91 functional for the oxygen adsorption potential on Pt3Ni relative to Pt. Thus, one could easily assume that the shifts predicted by the RPBE functional for the oxygen and hydroxyl adsorption potentials are overestimated on PtNi and PtNi3 also. However, as overestimates are systematic, they do not effect the conclusions made previously about the relative stability of different states of PtNi surfaces. ORR Overpotentials. With the aid of adsorption energies provided in Table 5, we can calculate the free energy changes for reactions which result in the formation of water from oxygen adsorbed on the surface of a catalyst by a dissociative mechanism. We used the following relations ΔG1 ðUÞ ¼ ΔGOþHþ e f HO ¼ ΔGþH2 O f HO þ 1=2H2 ΔGþH2 O f O þ H2 þ eU ð8Þ ΔG2 ðUÞ ¼ ΔGHOþHþ e f H2 O þ ¼ ΔGþH2 O f HO þ 1=2H2 þ eU
ð9Þ
Moreover, the free energy diagrams for the ORR mechanism on PtNi alloys can be obtained from the calculated free energy changes. The diagrams for Pt, Pt3Ni, and PtNi at zero volts, at the maximum cell potential (1.23 V) and a cell potential of 0.80 V, are shown in Figure 6. All the steps in ORR are exergonic at U = 0 V on all four surfaces studied. If the cell potential is changed to 1.23 V, the last two steps, i.e., the formation of adsorbed hydroxyl from adsorbed oxygen and the formation of water from adsorbed hydroxyl, become endergonic in all three cases. The largest change in energy for the ORR steps can be considered as a lower limit to the activation energy for the rate-limiting step and thereby define the potential at which one of the steps in the ORR becomes uphill and inhibits the ORR reaction. This can be used to estimate the overpotential for ORR on the surface of a catalyst. For Pt(111), we obtain values for the free energy change of the reactions eq 8 and eq 9 of ΔG1 = 0.68 eV and ΔG2 = 0.80 eV with the RPBE functional. The cell potential at which water starts to dissociate spontaneously to form adsorbed hydroxyl is therefore 0.80 V, at which point the proton/electron transfer to adsorbed hydroxyl to form adsorbed oxygen is already downhill for 0.13 eV (Figure 6). The proton/electron transfer to adsorbed oxygen to form hydroxyl becomes endergonic at a somewhat lower potential of 0.68 V, so we can estimate the 10647
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
Figure 6. Free energy diagrams for oxygen reduction over Pt(111), Pt3Ni(111), and PtNi(111) based on the adsorption energies in Table 5. The results are shown for 1/3 coverage of oxygen and hydroxyl at (a) zero and maximum cell potentials (U = 1.23 V) and (b) zero and a cell potential of U = 0.8 V.
calculated overpotential on a pure Pt surface to be between 0.55 and 0.43 V in agreement with experiment.62,68 All the steps in the ORR mechanism on Pt3Ni, PtNi, and PtNi3 at the cell potential of 0.8 V are, however, still exergonic. It is only at potentials larger than 0.99 V that the hydrogen/electron transfer to adsorbed oxygen to form hydroxyl becomes uphill on Pt3Ni. In addition, at potentials larger than 1.09 V water dissociation is spontaneous and slows down the ORR reaction. Thus, the overpotential on Pt3Ni can be estimated to be 0.24 V, which is about 0.25 V less than that on the pure Pt. This confirms previous findings that the (111) surface of Pt3Ni shows improved oxygen reduction activity over the Pt slab.12 However, the calculated overpotential is overestimated by approximately 0.15 V. The calculated decrease in the overpotential calculated for PtNi and PtNi3 relative to Pt is even larger. The potential at which one of the steps in the ORR mechanism turns uphill shifts to even more positive values of potentials, i.e., to 1.08 V on the PtNi surface and to 1.04 V on the PtNi3 surface. We can thus conclude that the largest change in the ORR overpotential is brought by alloying Pt with 25% Ni. A further increase in the nickel concentration to 50% is found to decrease the Pt3Ni ORR overpotential by some 30%, so that we can conclude that the PtNi alloy has the lowest value of the overpotential for ORR of all the compositions investigated by us. As PtNi with 100% nickel in the second layer showed the largest shift in the ORR overpotential relative to platinum, we further investigated the influence of the nickel atom distribution in the inner layers on the ORR activity of the PtNi alloy. The model of the PtNi alloy used throughout the study is in accordance with low-energy electron diffraction data on bimetallic Pt50Ni50 alloys that show the concentration of nickel in the second layer to be around 90%.52,53 However, if we assume a PtNi alloy in which the concentration of nickel in the second layer is decreased to 50%, we find that the overpotential of such an alloy is increased to 0.21 V. Namely, the equilibrium adsorption potentials for hydroxyl and oxygen are found to be 1.18 and 1.10 V with this hypothetical model of PtNi alloy, the values being intermediate to the values calculated for the Pt3Ni with 50% nickel and for the PtNi alloy with 100% of nickel in the second layer, respectively. This clearly shows that the distribution of alloying atoms in the layer directly below the surface has an important effect on the properties of a particular alloy. The results obtained in our study can be compared to the most recent measurements of ORR activity on PtNi alloys over a
wide range of compositions,69 which have demonstrated that Pt3Ni7 has a superior catalytic activity compared with that of other compositions. Although this precise composition was not studied here, our results show that the alloys with higher nickel composition can have improved catalytic activity over both platinum and the PtNi alloys with lower nickel composition. Previous investigations by Toda et al.70 on PtNi alloys over a 0100% compositional range, on the other hand, show the PtNi alloy's kinetic activity peak at ∼30% of nickel concentration and essentially no activity at 70% and above. Our study of stability of PtNi alloys also showed that the alloys with high nickel concentration (around 75% of nickel) have lower dissolution potentials than platinum, making these alloys less suitable as catalysts due to the larger susceptibility to both electrochemical dissolution and the poisoning of the surface with nickel oxide.
’ CONCLUSIONS We have presented the most complete and thorough theoretical study to date of the electrochemical processes on PtNi alloys with the aim of determining the effect of the alloying atom distribution in the subsurface layers on the catalytic activity of the platinum. We find that the PtNi alloys investigated by us have improved oxygen reduction activity over pure Pt. It is to be expected that the overpotential on PtNi surfaces studied in this work decreases as the nickel concentration in the second layer is changed from 50% in Pt3Ni to 75% in PtNi3 and further to 100% in PtNi. We can thus expect that the catalytic activity for the ORR will increase in the order Pt < Pt3Ni < PtNi3 < PtNi. Analysis of the density of states shows that the improved catalytic activity of PtNi alloys is the result of a modification of the electronic structure of the platinum atoms on the surface induced by a specific distribution of nickel atoms in the layers directly below. Namely, we have found a perfect correlation between the position of the d-band center of surface platinum atoms with the adsorption energies for oxygen and hydroxyl. We also find that the decrease in adsorption energies, and thus the increase in the equilibrium adsorption potentials, correlates with the decrease in the overpotential for oxygen reduction. Our DFT calculations, however, overestimate the increase in the ORR intermediates equilibrium adsorption potentials for the PtNi alloys relative to that of platinum. Finally, we wish to emphasize the importance of the effect of alloying on the dissolution potentials and thus the 10648
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C
ARTICLE
stability of the surface. Namely, our studies did not find any correlation between the energy of the surface and the surface cohesive energy, i.e., dissolution potentials. Since corrosion can result in a severe decrease of the performance of the catalyst, investigations of both the corrosion process and the oxygen reduction mechanism should be treated with equal importance when screening materials as prospective catalysts.
’ APPENDIX Methodology. Four different surface states are studied in this work: [H2O*] To model a water-covered metal surface we used two different bilayers of water molecules described √ √by Ogasawara et al.59 and Michaelides et al.60 with a 2 3 2 3 periodicity. The two bilayers are shown in Figure 2. In one of the structures the OH bonds that are not coordinated to another water molecule are pointing down toward the metal surface (Hdown bilayer), and in the other structure the same OH bonds point away from metal (H-up bilayer). [O*] To model an oxygen-covered metal surface, a water bilayer (H-down) was added on top of the O which is adsorbed on the metal surface on fcc sites with coverages of 1/4, 1/3, and 1/2. [OH*] To model a hydroxide-covered metal surface, water molecules with OH bonds pointing away or toward the metal surface in a water bilayer were substituted with HO*. OH* is thus embedded in the hexagonal hydrogen-bonded network with water. The total coverage of hydroxyl and water molecules is 2/3, and the coverage of hydroxyl is 1/3. The water to hydroxyl ratio of 1:1 is found to be the most stable in both theoretical44,71 and experimental72 studies of a waterhydroxyl layer structure on the metal surfaces and as such was not varied. [H*] To model a hydrogen-covered metal surface, a water bilayer (H-up) was added on top of the H which is adsorbed on the metal surface with a 1/3 coverage. To calculate the stability of metal surfaces at different pH and potentials U we used the approach developed by Nørskov et al. and described in detail in refs 8 and 27. It is assumed that the studied surfaces are in equilibrium with protons and liquid water at 300 K. By the use of the hydrogen electrode, the chemical potential for (Hþ þ e) is related to that of 1/2H2(g), and the free energy difference for the AH* f A* þ Hþ(aq) þ e reaction is, under standard conditions, calculated as the free energy change for the AH* f A* þ 1/2 H2 reaction
ΔGw ðU ¼ 0, pH ¼ 0Þ ¼ ΔEw þ ΔZPE þ TΔS
ð10Þ
where ΔEw is a change in the electronic energy of the reaction in the presence of water which is, as explained previously, taken explicitly into calculations by modeling the solvated adsorbates. ΔZPE is the change in the zero-point energy of the adsorbates and is also obtained from electronic structure calculations. The change in the entropy term ΔS is calculated from thermodynamical tables73 as a loss of entropy upon binding the adsorbates on the surface. At finite pH and potential, the free energy change of the reaction becomes ΔGw ðU, pHÞ ¼ ΔGw ðU ¼ 0, pH ¼ 0Þ neU kB T ln 10 log
with n, and U is the electrode potential. In the case of chemical reactions eqs 46, this reduces to ΔGw ðU, pHÞ ¼ ΔGw ðU ¼ 0, pH ¼ 0Þ neU kB T ln 10 pH
ð12Þ The effect of the local electric field generated in the electrochemical double layer, μE, where μ is the dipole moment of the adsorbate and E is the electric field, was not taken into account as it is shown in previous studies that the effect on the adsorption energy of O* and OH* is very small.27,63 Pourbaix Diagrams. The above reactions were also used for the construction of Pourbaix diagrams for the PtNi alloys. At pH = 0, the equilibrium potential for the adsorption of different adsorbates is determined by using a Gibbs relation between the reaction energy and the electrochemical potential Uf ¼ ΔGðpH ¼ 0Þ=ne
ð13Þ
as a potential at which the Gibbs free energy becomes negative (ΔGW(Uf) e 0). The most stable surface structure is however determined from eq 12 as the structure with the lowest free energy at a given set of conditions.28 Following the procedure we first identified the most stable structures at pH = 0 by constructing the phase diagrams using ΔGw ðU, pHÞper surface atom ¼ ðΔGw ðU ¼ 0, pH ¼ 0ÞÞper adsorbate neUÞ
nadsorbates nsurface atoms
ð14Þ
The lowest line in the phase diagram determines the surface with the lowest free energy at a given potential and pH. The pH dependence of a formation potential for the most stable structure in the Pourbaix diagram is then governed only by a kBT ln 10 pH/ e term, which means that the potentials for the formation of O* or OH* are represented on the Pourbaix diagram as a line with a slope of 0.59 mV/pH at 298 K (Nernst behavior).
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT I.M. thanks the LANL LDRD program for a postdoctoral fellowship and the U.S. Department of Energy, Energy Efficiency and Renewable Energy for financial support. I.M. also wants to thank the support of MZOS project 098-0352851-2921. The authors thank Christopher Taylor, Peter J. Feibelman, and Juergen Eckert for useful discussions. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. This paper has been designated LA-UR 10-08136. ’ REFERENCES
Y
ðaK ÞνK
ð11Þ
K
where v is a stoichiometric number for the chemical species K with activity a. The number of the electrons in the electrode is denoted
(1) Gasteiger, H. A.; Panels, J. E.; Yan, S. G. J. Power Sources 2004, 127, 162–171. (2) Lutz, A. E.; Larson, R. S.; Keller, J. O. Int. J. Hydrogen Energy 2002, 27, 1103–1111. (3) Kartha, S.; Grimes, P. Phys. Today 1994, 47, 54–61. (4) Gewirth, A. A.; Thorum, M. S. Inorg. Chem. 2010, 49, 3557–3566. 10649
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
The Journal of Physical Chemistry C (5) Gokhale, A. A.; Dumesic, J. A.; Mavrikakis, M. J. Am. Chem. Soc. 2008, 130, 1402. (6) Kandoi, S.; Gokhale, A. A.; Grabow, L. C.; Dumesic, J. A.; Mavrikakis, M. Catal. Lett. 2004, 93, 93. (7) Nilekar, A. U.; Mavrikakis, M. Surf. Sci. 2008, 602, L89–L94. (8) Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jonsson, H. J. Phys. Chem. B 2004, 108, 17886–17892. (9) Kitchin, J. R.; Nørskov, J. K.; Barteau, M. A.; Chen, J. G. J. Chem. Phys. 2004, 120, 10240–10246. (10) Stamenkovic, V. R.; Mun, B. S.; Mayrhofer, K. J. J.; Ross, P. N.; Markovic, N. M.; Rossmeisl, J.; Greeley, J.; Nørskov, J. K. Angew. Chem., Int. Ed. 2006, 45, 2897–2901. (11) Stamenkovic, V. R.; Mun, B. S.; Arenz, M.; Mayrhofer, K. J.; Lucas, C. A.; Wang, G.; Ross, P. N.; Markovic, N. M. Nat. Mater. 2007, 6, 241–247. (12) Stamenkovic, V. R.; Fowler, B.; Mun, B. S.; Wang, G.; Ross, P. N.; Lucas, C. A.; Markovic, N. M. Science 2007, 315, 493. (13) Antolini, E. Mater. Chem. Phys. 2003, 78, 563–573. (14) Gasteiger, H. A.; Kocha, S. S.; Sompalli, B.; Wagner, F. T. Appl. Catal., B 2005, 56, 9–35. (15) Borup, R.; Chem. Rev. 2007, 107, 3904–3951. (16) Kocha, S.; Wagner, F.; Gasteiger, H. ECS Meeting Abstr. 2006, 503, 199–199. (17) Colon-Mercado, H. R.; Popov, B. N. J. Power Sources 2006, 155, 253–263. (18) Roques, J.; Anderson, A. B. Surf. Sci. 2005, 581, 105–117. (19) Hand, B. C.; der Ven, A. V.; Ceder, G.; Hwang, B.-J. Phys. Rev. B 2005, 72, 205409:1–9. (20) Ma, Y.; Balbuena, P. B. Surf. Sci. 2008, 602, 107–113. (21) Ma, Y.; Balbuena, P. B. Surf. Sci. 2009, 603, 349–353. (22) Roques, J.; Anderson, A. B.; Murthi, V. S.; Mukerjee, S. J. Electrochem. Soc. 2005, 152, E193–E199. (23) Xu, Y.; Ruban, A. V.; Mavrikakis, M. J. Am. Chem. Soc. 2004, 126, 4717–1725. (24) Anderson, A. B.; Roques, J.; Mukerjee, S.; Murthi, V. S.; Markovic, N. M.; Stamenkovic, V. J. Phys. Chem. B 2005, 109, 1198–1203. (25) Wu, H.; Wexler, D.; Wang, G. J. Alloys Compd. 2009, 488, 195–198. (26) Yang, H.; Zhang, J.; Kumar, S.; Zhang, H.; Yang, R.; Fang, J.; Zou, S. Electrochem. Commun. 2009, 11, 2278–2281. (27) Rossmeisl, J.; Nørskov, J. K.; Taylor, C. D.; Janik, M. J.; Neurock, M. J. Phys. Chem. B 2006, 110, 21833–21839. (28) Hansen, H. A.; Rossmeisl, J.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2008, 10, 3722. (29) Tang, L.; Han, B.; Persson, K.; Friesen, C.; He, T.; Sieradziki, K.; Ceder, G. J. Am. Chem. Soc. 2010, 132, 596–600. (30) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. Rev. B 1999, 59, 7413. (31) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244. (32) Perdew, J.; Chevary, J.; Vosko, S.; Jackson, K.; Pederson, M.; Singh, D.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671. (33) Perdew, J.; Chevary, J.; Vosko, S.; Jackson, K.; Pederson, M.; Singh, D.; Fiolhais, C. Phys. Rev. B 1993, 48, 4978. (34) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (35) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (36) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. (37) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (38) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (39) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251. (40) Kresse, G.; Furthm€uller, J. Comput. Mater. Sci. 1996, 6, 15. (41) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169. (42) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188. (43) Methfessel, M.; Paxton, A. T. Phys. Rev. B 1989, 40, 3616. (44) Rossmeisl, J.; Karlberg, G. S.; Jaramillo, T.; Nørskov, J. K. Faraday Discuss. 2008, 140, 337–346.
ARTICLE
(45) Ramirez-Caballero, G. E.; Hirunsit, P.; Balbuena, P. B. J. Chem. Phys. 2010, 133, 134705. (46) Swanson, H. E.; Tatge, E. Natl. Bur. Stand. (U.S.), Circ. 1953, 539, 1–95. (47) Kussmann, A.; von Steinwehr, H. E. Z. Metallkd. 1949, 40, 263–266. (48) Esch, U.; Schneider, A. Z. Elektrochem. Angew. Phys. Chem. 1944, 50, 268–274. (49) Leroux, C.; Cadeville, M.; Pierron-Bohnes, V.; Inden, G.; Hinz, F. J. Phys. F 1988, 18, 2033–2051. (50) Walker, R. A.; Darby, J. B. Acta Metall. 1970, 18, 1261. (51) Stamenkovic, V. R.; Mun, B. S.; Mayrhofer, K. J. J.; Ross, P. N.; Markovic, N. M. J. Am. Chem. Soc. 2006, 128, 8813. (52) Gauthier, Y.; Joly, Y.; Baudoing, R.; Rundgren, J. Phys. Rev. B 1985, 31, 6216–6218. (53) Gauthier, Y. Surf. Rev. Lett. 1996, 3, 1663. (54) Taylor, C. D.; Neurock, M.; Scully, J. R. J. Electrochem. Soc. 2008, 155, C407–C414. (55) Mills, G.; Jonsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305–337. (56) Jonsson, H.; Mills, G.; Jacobsen, K. W. Nudged elastic band method for finding minimum energy paths of transition in Clasical and quantum dynamics in condensed phase simulations; World Scientific: River Edge, NJ, 1998; pp 385404. (57) Feibelman, P. J. Phys. Today 2010, 63, 34–39. (58) Nie, S.; Feibelman, P. J.; Bartelt, N. C.; Th€urmer, K. Phys. Rev. Lett. 2010, 105, 026102(4). (59) Ogasawara, H.; Brena, B.; Nordlund, D.; Nyberg, M.; Pelmenschikov, A.; Pettersson, L. G. M.; Nilsson, A. Phys. Rev. Lett. 2002, 89, 276102. (60) Michaelides, A.; Alavi, A.; King, D. A. Phys. Rev. B 2004, 69, 113404. (61) Hamada, I.; Lee, K.; Morikawa, Y. Phys. Rev. B 1999, 81, 115452. (62) Markovic, N. M.; Ross, P. N. Surf. Sci. Rep. 2002, 45, 117–229. (63) Karlberg, G. S.; Rossmeisl, J.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2007, 9, 5158–5161. (64) Jerkiewitz, G.; Vatankhah, G.; Lessard, J.; Soriaga, M. P.; Park, Y.-S. Electrochim. Acta 2004, 49, 1451–1459. (65) Nagy, Z.; You, H. Electrochim. Acta 2002, 47, 3037–3055. (66) Hammer, B.; Nørskov, J. K. Surf. Sci. 1995, 343, 211–220. (67) Pourbaix, M. Atlas of electrochemical equilibria in aqueous solutions; Oxford: Pergamon, 1996. (68) Hoogers, G.; Thompsett, D. CATTECH 1999, 3, 106. (69) Debe, M. K.; Steinbach, A. J.; Vernstrom, G. D.; Hendricks, S. M.; Kurkowski, M. J.; Atanasoski, R. T.; Kadera, P.; Stevens, D. A.; Sanderson, R. J.; Marvel, E.; Dahn, J. R. ECS Trans. 2010, 33, 143–152. (70) Toda, T.; Igarashi, H.; Uchida, H.; Watanabe, M. J. Electrochem. Soc. 1999, 146, 3750–3756. (71) Karlberg, G. S.; Wahnstr€om, G. J. Chem. Phys. 2005, 122, 194705. (72) Clay, C.; Haq, S.; Hodgson, A. Phys. Rev. Lett. 2004, 92, 046102. (73) Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, U.K., 1994; pp C9C14.
10650
dx.doi.org/10.1021/jp111930w |J. Phys. Chem. C 2011, 115, 10640–10650
