A Theoretical Consideration on the Surface Structure and

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A Theoretical Consideration on the Surface Structure and Nanoparticle Size Effects of Pt in Hydrogen Electrocatalysis Fan Yang, Qianfan Zhang, Yuwen Liu, and Shengli Chen* Department of Chemistry, Hubei Electrochemical Power Sources Key Laboratory, Wuhan University, Wuhan 430072, China

bS Supporting Information ABSTRACT: Microkinetic modeling and density functional theory (DFT) calculations are combined to understand the surface structure and nanoparticle size effects of Pt on the kinetics of hydrogen electrode reactions (HERs). The microkinetic modeling leads to a mechanism-free volcano relation between the exchange current density of HERs (j0) and the surface coverage of the reactive H adatoms at the equilibrium potential (θ0), making the activity trend of various catalytic surfaces for HERs predictable with θ0. It is shown that catalytic surfaces with θ0 values closer to 0.5 monolayer will have higher j0. A DFT calculation scheme is developed to determine the nature of the reactive H atoms and the corresponding θ0 values. The calculated results on Pt single crystal electrodes predict that j0 follows a trend that Pt(110) ≈ Pt(100) > Pt(111), whereas for Pt nanoparticles the j0 follows a trend that (100) facets > (111) facets ≈ edge rows, which in turn suggests a decrease of j0 with the decreasing particle size of Pt. It is shown that, although the individual edge atom rows on Pt fcc nanoparticles are similar in structures to the top atom rows on the Pt(110) surface, the catalytic properties of the nanoparticle edges are not simply equivalent to the extended (110) surfaces since some of the reactive sites for a reaction on extended (110) surfaces (e.g., the long-bridge sites) are absent at nanoparticle edges. The results presented here not only throw new insights into the long-standing problem about the Pt surface structure and particle size effects in hydrogen electrocatalysis but also provide a general theoretical scheme to identify the most active catalytic surfaces for HERs. More importantly, we demonstrate that not only the thermodynamic data like the adsorption energy but also a detailed nature of the reactive sites and their coverage are very important for the proper prediction of the activity trend of catalytic surfaces.

1. INTRODUCTION The size- and shape-dependent reactivity of nanoparticle catalysts is among the key problems in current catalysis and electrocatalysis.1,2 Understanding such dependence not only helps catalyst optimization but also can be of fundamental significance in nanoscience for establishing propertystructure relationships. For supported metallic nanoparticle catalysts of few nanometers to a few tens of nanometer sizes used in most of the heterogeneous catalytic systems, the particle-dependent catalytic properties should be mainly originated from the sizeand shape-dependent surface structure of nanoparticles since negligible quantum size effect is expected in this size regime.15 It is known that metallic nanoparticles are enclosed with different facets, whose surface percentages vary with the particle size and shape.5 If the adsorption of key intermediates of a reaction, for example, oxygenated species for oxygen reduction and CO for methanol and CO oxidation, is sensitive to the surface lattice structure of a metal, the specific rate of the reaction is expected to change with the surface structure of the metal and therefore with the size and shape of the metal nanoparticles accordingly. On this basis, the surface structure effects of metallic catalysts for various reactions play a key role in particle-dependent catalytic properties. Hydrogen electrode reactions (HERs), including the cathodic H2 evolution and anodic H2 oxidation, play a key role in hydrogen-based energy conversion technologies such as fuel cells r 2011 American Chemical Society

and water electrolysis. Pt is the most active electrocatalysts for HERs. Although HERs have been over the decades serving as archetype processes in electrochemistry and studied extensively, the surface structure and particle size effects of Pt for HERs have been rarely explored and remain in dispute. It is known that both the H2 evolution and oxidation reactions on various metal surfaces involve the adsorbed H atoms (H adatoms) as the intermediates and that the adsorption of H on Pt strongly depends on the crystallographic orientation of surface atoms.6 We have reason to believe that the kinetics of the HERs vary with the surface structure and nanoparticle size of Pt. Earlier studies using Pt single crystal electrodes failed to show surface structure dependence of the hydrogen evolution reaction kinetics,7 which rendered the researchers to believe that the H adatoms formed in the potential region above the onset for the hydrogen evolution reaction (0.050.07 V vs RHE), the so-called UPD (underpotential deposited) H adatoms, are not the reactive intermediates for hydrogen evolution. Recent studies by Markovic et al.2,8 and Conway et al.,9 however, showed that the kinetics of HERs are sensitive to the crystallographic orientation of surface Pt atoms. These authors pointed out that the failure in identifying the Pt surface structure sensitivity of HERs in earlier literature was mainly due to that the actual specific kinetics were obscured Received: July 22, 2011 Published: August 29, 2011 19311

dx.doi.org/10.1021/jp207015w | J. Phys. Chem. C 2011, 115, 19311–19319

The Journal of Physical Chemistry C by the relatively slow diffusion of H2. As for the nanoparticle size effects of Pt for HERs, so far only a few studies can be found in the literature,2,10 in which the catalytic activity of Pt nanocatalysts for HERs was reported to keep unchanged,10a increase,10b or decrease10c upon reducing the particle sizes. We think that the reported literature results on the Pt nanoparticle size effects for HERs might have also suffered from similar problems of improper kinetics determination due to fast kinetics coupled with slow H2 diffusion. It has been long argued that the kinetics of HERs on Pt surfaces might be too fast to measure with the ordinary steady-state voltammetric methods, for example, the rotating disk electrode (RDE) method.11,12 As well as the inconsistent results in various electrochemical kinetic measurements, our fundamental understanding toward the surface structure and nanoparticle size effects of Pt for HERs has been also hampered by the lack of microscopic detail about the relation between HERs and H adsorption. There are a few important questions remaining to be answered, for instance, whether UPD H adatoms serve as reactive intermediate or spectator in HERs,8,11,13 does their formation extend to the potential region below the onset potential of hydrogen evolution reaction,8 what's the nature of the so-called overpotential deposited (OPD) H adatoms which were considered by some authors as the reactive intermediate for HERs,8,9,13 and so on. Due to the fact that the formation of H adatoms is coupled with other processes, it is generally difficult to gain accurate information on the adsorption of H by using conventional electrochemical methods when the evolution or oxidation of H2 is taking place. Recent in situ infrared (IR) spectroscopic results by some authors14,15 suggested a different type of H adatom from the UPD H develops on Pt as potential goes below 0.1 V, which was attributed to H adatoms formed on atop sites and considered the reactive intermediate of HERs. However, the formation of such atop H adatoms was not observed in other IR16 and SFG17 (sum frequency generation) studies. The hydrogen adsorption and the evolution and oxidation of H2 have been also the subjects of recent first principle theoretical calculations studies.1821 The quantum chemistry simulations in principle can provide direct atomic details for each individual process (or reaction step) in a complicated reaction, whereas experimental measurements generally give overall results associated with several processes or steps. However, the quantum chemistry calculation results strongly depend on the model selected to represent the studying system, especially for catalytic and electrocatalytic systems involving the adsorption of molecules and/or atoms on solid surfaces. Therefore, it is very important that quantum chemistry calculations are combined with or guided by proper theoretical modeling. In a recent paper, Skulason et al.20 performed comprehensive density functional theory (DFT) calculations on the reaction and activation energies of each elementary reaction step in HERs with the effects of overpotential and H coverage being considered. By assuming the Tafel reaction as the rate-determining step, their calculated activation barriers on different Pt facets at the equilibrium potential suggested that the exchange current density for HERs (j0) depends on the surface structures of Pt. Furthermore, the predicted trend in j0 for the three low-index single crystal surfaces was similar to the experiments by Markovic et al.2,8 In this work, we perform a combined theoretical modeling and DFT calculations study on the surface structure and nanoparticle size effects of Pt in HERs. Our aim is not only to show how the surface structures and nanoparticle sizes of Pt may affect the

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specific kinetics of HERs but to understand the atomic nature of the surface structure and nanoparticle size effects. Through thermodynamic and kinetic analysis, we establish a microkinetic model in which j0 is described by a single descriptor, the coverage of the reactive H atoms at the equilibrium potential of HERs (θ0). DFT calculations are used to determine the nature of the reactive sites and the corresponding values of θ0 on different Pt single crystal surfaces, which allow the surface structure and particle size effects of Pt to be predicted.

2. MICROKINETIC MODELING Since the activities of various catalytic surfaces for HERs are generally compared by the exchange current density j0, which represents the equalized rate of the oxidation and evolution of H2 at the equilibrium potential, the modeling in the present paper will be focused on the thermodynamics and kinetics at the equilibrium potential of HERs. 2.1. Thermodynamic Analysis. For HERs, H2 T 2H+ + 2e, the reaction free energy can be expressed by eq 1, in which μ̅ e = eE refers to the free energy of electron in the electrode at potential E, μ̅ H+0 and μ̅ 0H2 refer the standard chemical potentials of the proton in the electrolyte solution and the hydrogen molecule in the gas phase, cH+ and pH2 are the concentration of the proton and the partial pressure of H2, and kB and T have their ordinary meanings. ΔG1 ðEÞ ¼ 2μ̅ e ðEÞ þ 2μ̅ 0Hþ μ̅ 0H2 þ kB T lnðcHþ 2 =pH2 Þ

ð1Þ

For simplicity, we will assume in this paper that the standard conditions for HERs are maintained; that is, pH2 and cH+ are kept at 1 atm and 1 mol 3 L1, respectively. These assumptions only simplify the derivations but will not limit the generality of the conclusions obtained. Since that ΔG1(E0) = 0 at the standard equilibrium potential E0, we can easily find from eq 1 that 1 0 μ ¼ μ̅ 0Hþ þ μ̅ e ðE0 Þ 2 ̅ H2

ð2Þ

It is known that HERs may involve three possible elementary reaction steps,11,22 namely, the Tafel reaction (H2 + 2* T 2*H), the Heyrovsky reaction (H2 + * T *H + H+ + e), and the Volmer reaction (*H T * + H+ + e), where * and *H represent respectively the free site and the H adatoms on the surface. The free energies of these reactions can be respectively expressed by eq 3a to 3c, in which μ̅ 0*H(θ) = ∂GMHn(θ)/∂n refers to the change in the total free energy of the electrode surface with H adatoms of θ coverage, GMHn(θ), upon increasing one H adatom. Here n is the number of H adatoms on the surface and θ = n/N with N being the total number of the metal surface atoms. μ̅ 0*H(θ) can also be understood as the free energy of a H adatom at θ coverage. 0

ΔGTafel ðθÞ ¼ 2μ̅ 0H ðθÞ μ̅ H2 þ 2kB T lnðθ=ð1 θÞÞ ð3aÞ 0

0

ΔGHeyrovsky ðθÞ ¼ μ̅ 0H ðθÞ þ μ̅ Hþ þ μ̅ e ðEÞ μ̅ H 2 þ kB T lnðθ=ð1 θÞÞ 19312

ð3bÞ

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The Journal of Physical Chemistry C ΔGVolmer ðθÞ ¼ μ̅ 0Hþ þ μ̅ e ðEÞ μ̅ 0H ðθÞ kB T lnðθ=ð1 θÞÞ

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ð3cÞ

The HERs may proceed through either the TafelVolmer or the HeyrovskyVolmer combination.14 Regardless of the exact reaction mechanism, the H adatoms serve as the intermediate, which makes the reaction kinetics depending on the binding of electrode surface to H. To establish a measure of this binding, we introduce the H2 dissociation reaction, 1/2H2 + * T *H, whose reaction free energy reads 0

ΔG2 ðθÞ ¼ μ̅ 0H ðθÞ 1=2μ̅ H2 þ kB T lnðθ=ð1 θÞÞ ð4Þ The value of μ̅ 0*H(θ) 1/2μ̅ 0H2 can be considered as the free energy difference between a H adatom at θ coverage and a hydrogen atom in a gaseous H2. We define it as the differential free energy of H adsorption at θ coverage and denote it with ΔGH(θ). Thus, we can have the following expression for reaction free energy of H2 dissociation. ΔG2 ðθÞ ¼ ΔGH ðθÞ þ kB T lnðθ=ð1 θÞÞ

ð5Þ

The value of ΔGH(θ) would vary from one surface to another and can serve as an indicator of the binding of a surface to H. Here, we have avoided using the term of standard free energy of H adsorption or standard chemical potential of H adatoms since that defining the standard state for an adsorbed species is somewhat a complicated issue. For instance, the standard state for H adatoms was defined as the half monolayer coverage by Parsons in deriving the j0 expressions for HERs,23 while it was defined as zero coverage by other researchers.24,25 In addition, adsorption isotherms have to be included in the free energy expressions for adsorption processes when the standard state is employed, which would bring about not only additional parameters but sometimes uncertainties (Section 2.3). According to the above free energy expressions, we can also have relations that ΔGTafel(θ) = 2ΔG2(θ), ΔGHeyrovsky(θ) = 1/ 2ΔG1(E) + ΔG2(θ), and ΔGVolmer(θ) = 1/2ΔG1(E) ΔG2(θ). It can be easily proven that all of the elementary reactions would be in equilibrium at the equilibrium potential of HERs (θ = θ0, E = E0), that is, ΔGTafel(θ0) = ΔGHeyrovsky(θ0) = ΔGVolmer(θ0) = 0, and we then have ΔG2(θ0) = 0. This says that the H coverage at which ΔG2(θ) equals zero for a catalytic surface is right that at which HERs reach equilibrium at this surface. In another word, we can determine θ0 values from the coverage-dependent free energy values of the gas-phase dissociation reaction according to eq 5. It has been shown through DFT calculations18 and surface science studies24 that the solvent and electric field have negligible effects on the adsorption of H, which justifies the strategy of using the thermodynamic data obtained from the gas-phase dissociation reaction to describe the H adsorption at electrode surfaces in electrochemical environments. 2.2. Kinetic Analysis. Depending on the reaction mechanism, the exchange current density of HERs should satisfy eq 6a (TafelVolmer mechanism) or eq 6b (HeyrovskyVolmer 0 mechanism), in which k+0 x and kx (x = Volmer or Heyrovsky) refer to the rate constants of the forward (+) and backward () processes of the corresponding reaction steps at equilibrium potential. 0 0 0 j0 ¼ Fkþ0 Volmer θ ¼ FkVolmer ð1 θ Þ

ð6aÞ

Figure 1. Schematic illustration of the free energy variation in HERs at the equilibrium potential for surfaces with zero and nonzero differential adsorption free energy ΔGH(θ0). 0 0 þ0 j0 ¼ Fðkþ0 Heyrovsky ð1 θ Þ þ kVolmer θ Þ 0 0 0 ¼ Fðk0 Heyrovsky θ þ kVolmer ð1 θ ÞÞ

ð6bÞ

and k0 are to the transition-state theory, x ¼ 0 (θ ) corresponding activation free energy, ΔG+06 x 0

According related to the ¼ (θ ), by the following equations. and ΔG06 x

k+0 x

þ06¼ 0 kþ0 x ¼ ðkB T=hÞexpð ΔGx ðθ Þ=kB TÞ

ð7aÞ

06¼ 0 k0 x ¼ ðkB T=hÞexpð ΔGx ðθ Þ=kB TÞ

ð7bÞ

The activation free energies in the Volmer and Heyrovsky reactions depend on not only the electrode potential, but also the binding of H adatoms on the electrode surface which can be described in terms of ΔGH(θ) defined earlier. Therefore, ¼ 0 ¼ 0 (θ ) and ΔG06 (θ ) are not necessarily equal to each ΔG+06 x x other. In general, only the simple outer-sphere electrochemical electron-transfer reactions have equalized forward and backward rate constants (and therefore activation energies) at the standard equilibrium potentials.26 According to the free energy expressions of eqs 2 to 5, we can easily find that μ̅ 0*H(θ0) = 1/ 2μ̅ 0H2 = μ̅ H+0 + μ̅ e (E0) as θ0 = 0.5, that is, ΔGH(θ0) = 0. This means that all of the possible elementary reaction steps in HERs, that is, the transformation between a H2 molecule and two H adatoms (Tafel reaction), the transformation between “H+ + e” and a H adatom (Volmer reaction), and the transformation between a H2 molecule and a H adatom plus “H+ + e” (Heyrovsky reaction), will be in thermodynamic neutral conditions at E0 if θ0 = 0.5. In this case, the forward and backward processes of these reactions would have equalized activation energies (therefore rate constants). The free energy curves in Figure 1 provide a schematic illustration showing how ¼ 0 ¼ 0 (θ ) and ΔG06 (θ ). The solid ΔGH(θ0) affects ΔG+06 x x and dashed curves represent respectively those for θ0 = 0.5 (ΔGH(θ0) = 0) and θ0 6¼ 0.5. 6 0.5 (ΔGH(θ0) ¼ 6 0), the elementary reactions will have As θ0 ¼ different forward and backward activation energies. In fact, the equalized forward and backward rate constants for the elementary reaction steps at E = E0 and θ0 = 0.5 can also be proven from the reaction kinetics (e.g., eq 5a) when considering that the elementary reactions will be in equilibrium as E = E0. We may denote such equalized activation free energy and rate constant as ΔG06x¼ and k0x, respectively. They are related to each other by eq 8. k0x ¼ ðkB T=hÞexpð ΔG06x ¼ðθ0 Þ=kB TÞ

ð8Þ 27,28

On the basis of the BrønstedEvansPolanyi (BEP) principle, the forward and backward activation free energies for a surface 19313


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Figure 2. Theoretical plots of j0 (in logarithm form) as functions of (a) ΔGH(θ0) and (b) θ0 predicted by eqs 9 and 10.

with θ0 would deviate from ΔGx6¼0 by a fraction of ΔGH(θ0), ¼ 0 (θ ) = ΔG6x¼0 + αxΔGH(θ0) in which αx for example, ΔG+06 x is a constant usually called symmetric factor (the detailed expressions for various reactions are given by eqs s1s4 in the Supporting Information). Accordingly, the rate constants of each elementary reaction for any surfaces can be expressed in terms of k0x , ΔGH(θ0), and αx, for example, k+0 Heyrovsky = k0Heyrovsky exp(αHeyrovskyΔGH(θ0)/kBT) (see eqs s5s8). Combining these relations with eqs 67 and assuming that all of the elementary reactions have the same symmetric factor α, we can have the following general relations for j0, in which k0 equals to k0Volmer or (k0Volmer + k0Heyrovsky) depending on the reaction mechanism (Supporting Information). We may consider k0 as the standard rate constant of HERs. j0 ¼ Fk0 ðθ0 Þα ð1 θ0 Þð1 αÞ

ð9Þ

j0 ¼ Fk0 expð αΔGH ðθ0 Þ=kB TÞ=ð1 þ expð ΔGH ðθ0 Þ=kB TÞÞ

ð10Þ Thus, we have established one-to-one relations between j0 and θ0 and between j0 and ΔGH(θ0). Since these relations have been derived through relatively rigorous thermodynamic and kinetic analysis without specifying the reaction mechanism and the rate-determining step, they should apply to HERs regardless of the reaction mechanism. At surfaces where θ0 = 0.5 (ΔGH(θ0) = 0), the value of j0 equals to 0.5Fk0. For convenience, we will use a dimensionless exchange current density in the following by normalizing j0 with the product of 0.5Fk0, such that the only parameter left in the j0∼θ0 and j0∼ΔGH(θ0) relations is the symmetric factor α. The j0 value for θ0 = 0.5 will then become 1. We may further assume that α = 0.5. It has been well-known that the symmetric factors for interfacial charge transfer processes are approximately equal to 0.5 as far as the potential is not far away from the standard equilibrium potential.26 In addition, a α value other than 0.5 will result in an asymmetric j0∼ΔGH(θ0) plot, which is inconsistent to the reported volcano plots for the experimental values of j0 (see discussions in the next section).19,29 2.3. Volcano Plots of j0. In Figure 2, the logarithm of the dimensionless j0 is plotted against ΔGH(θ0) and θ0, respectively, according to eqs 9 and 10. It can be seen that the plots of log j0 are shaped very differently with ΔGH(θ0) and θ0, although eq 9 and eq 10 are equivalent. As shown in Figure 2a, over a range of a few decades j0 shows a nearly linear variation in its logarithm when it

Figure 3. Theoretical j0∼θ0 volcano plot near the maximum of j0. The marked data points indicate the j0 values corresponding to the DFTdetermined θ0 for various single crystal surfaces and nanoparticle edges of Pt.

is plotted against ΔGH(θ0 ), forming a pyramid-shaped volcano curve. When plotting log j0 against θ0, a bell-shaped curve is obtained (Figure 2b), with little variation occurring in a broad region of θ0 between 0.01 and 0.99, but a few decades variation in the very narrow θ0 regions of below 0.01 and above 0.99. On the basis of the two plots, we think that ΔGH(θ0) would be an appropriate descriptor to predict the trends in j0 for different metals with vast-scale variation of hydrogen binding ability. Using θ0 to describe such large variations of j0 will be problematic since a very small uncertainty in θ0 could result in decades of deviation in j0. For catalytic surfaces located near the maximum of the j0 curves, however, θ0 can be a very useful descriptor. This is more clearly illustrated in Figure 3, which gives the plot of j0 against θ0 spanning from 0.01 to 0.99. It can be seen that the value of j0 shows only a few times decrease from the maximum in this ca. 99% of entire coverage spectrum (the corresponding ΔGH(θ0) change is within (0.1 eV). Thus, the j0 values for various catalytic surfaces near the maximum of volcano plot can be easily distinguished by their θ0 values. This would be very useful in comparing the activity trends of catalytic surfaces near the volcano apex, for example, Pt-based catalysts. We will use Figure 3 to distinguish the activities of various Pt single crystal electrode surfaces and Pt nanoparticle sites for HERs in the following. It should be pointed out that the volcano plots of j0 for HERs with the metalhydrogen interaction have been known for more than 50 years.19,23,25,29,30 As will be discussed in the following, however, most of the so far reported ones are not straightforward in dealing with HERs at surfaces located near the apex of the plots. In the most representative and generally quoted fundamental treatments by Parsons,23 the volcano relation of j0 was expressed in terms of the so-called standard free energy of adsorption (ΔG0). In addition to the arbitrariness in defining the standard state of adsorption as stated earlier, the use of ΔG0 may cause complexity and uncertainties since an adsorption isotherm has to be assumed. In reality, the adsorption isotherm could change from one surface to another or even with coverage on the same surface. As will be shown later on, this indeed occurs for H adsorption on various Pt surfaces. By assuming Langmuir adsorption of H, Parsons derived a relation between j0 and ΔG0 which results in a pyramid-like volcano plot of log j0 with symmetric ascending and descending legs and a maximum at zero ΔG0. In the case of Temkin 19314


The Journal of Physical Chemistry C adsorption, however, he arrived in a relation in which j0 surprisingly appears to be independent of ΔG0. Considering that Temkin adsorption may only occur at middle coverage values, the author proposed that the actual j0∼ΔG0 plot would be that the top of the pyramidal volcano curve is replaced by a horizontal region. To the best of our knowledge, such a horizontal region has not been shown in any forms of volcano plots reported on the experimental values of j0 for HERs. Instead, an approximately symmetric volcano plot of pyramid shape between the experimental j0 and various metalhydrogen bond energies has been reported, with Pt located near the apex.29 Recently, Nørskov and his co-workers19,20 revisited this topic by plotting the experimental values of log j0 reported in the literature with their DFT-calculated adsorption free energy of H on the (111) surface of various transition metals, which also produced a symmetric pyramid-like volcano plot with Pt being near the maximum. In addition, the authors showed that using the adsorption free energy values at different H coverage (e.g., 0.25 or 1 monolayers (ML)) would not change the trend of the volcano plot. They have also introduced model relations between j0 and the adsorption free energy of H, in which the ascending and descending branches of the volcano plot were described with different relations by distinguishing between the cases of exoenergetic and endoenergetic adsorption, respectively. Although the model is somewhat oversimplified,30 it showed reasonable fit to the observed plots of the experimental j0 with the DFTcalculated H adsorption free energy for various transition metals. It is surprising that the trend in j0 for different metals seems to be describable with arbitrarily chosen thermodynamic quantities related to the metalhydrogen interaction, for example, the metalhydrogen bond energy29 or the H adsorption free energy at an arbitrary coverage.19,20 In another word, the reported volcano plots or relations seem to tell that H coverage effect is unimportant in predicting the j0 trend. For instance, the experimental value of j0 can be reasonably described by the model relation based on simple Langmuir adsorption, whereas the model based on more realistic adsorption isotherms gives unrealistic predictions. By carefully inspecting Parsons' derivation, we found that his “horizontal region” prediction was due to some simplifications made on the Temkin adsorption isotherm. For instance, he simply omitted the important item of kBT ln((1 θ)/θ). It has been argued by Schmickler and Trasatti30 that various thermodynamic quantities associated with metalhydrogen interaction roughly scale with each other. If so, plotting j0 against different quantities would only result in a shift of the volcano curve along the abscissa without changing the qualitative trend. Such an argument might apply when metals with largely different binding abilities to H are considered. As will be shown at a later point, however, the use of adsorption data at arbitrary coverage could lead to wrong prediction in HER activity order for various Pt single crystal surfaces. For catalytic surfaces located near the top of the volcano plot, for example, Pt based catalyst surfaces, the H adsorption data at the equilibrium potential are not necessarily scaled with those at low coverage since the adsorption site may change. In this case, one needs to relate j0 strictly with the H adsorption properties of the catalytic surfaces at the equilibrium potential of HERs. Actually, if ΔG0 in Parsons' derivation had been considered as the differential free energy of H adsorption as defined in present study, he would have been able to arrive in eq 10 given above without assuming any adsorption isotherms.

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3. DFT CALCULATIONS 3.1. Determining the Reactive H Adatoms and Their θ0 from DFT Calculations. As pointed out in the modeling section,

the value of θ0 can be determined by finding the coverage of H atom at which ΔG2(θ) = 0. Following Nørskov et al.,18,19 ΔG2(θ) can be calculated according to eq 11, in which ΔEH(θ), ΔSH(θ), and ΔZPEH represent the energy, entropy, and zeropoint energy contributions to ΔGH(θ), respectively. ΔG2 ðθÞ ¼ ΔEH ðθÞ TΔSH ðθÞ þ ΔZPEH þ kB T lnðθ=ð1 θÞÞ

ð11Þ The differential adsorption energy of H2, ΔEH(θ), can be expressed by eq 12, where E(θ)MHn is the total energy of the surface of θ coverage. 1 ΔEH ðθÞ ¼ ∂EðθÞMHn =∂n EH2 2 1 ¼ ∂ EðθÞMHn =N θEH2 =∂θ 2

ð12Þ

Considering that the entropies of the adsorbed atoms are small when compared with the entropies of gaseous molecules and that the zero-point energy of the adsorbed H atom changes little from one metal surface to another, the contributions from the entropy and zero-point energy changes together to ΔGH(θ) have been estimated to be approximately 0.24 eV for standard temperature by Nørskov et al.18,19 Therefore, eq 11 can be converted to the form of eq 13. 1 ΔG2 ðθÞ ¼ ∂ EðθÞMHn =N θEH2 =∂θ þ 0:24 2 ð13Þ þ kB T lnðθ=ð1 θÞÞ The values of E(θ)MHn and EH2 are directly accessible to DFT calculations. By using Pt slabs of different sizes, we can obtain a series of E(θ)MHn values. The values of ΔEH(θ) at various θ can be obtained according to eq 12 by differentiating the plots of (E(θ)MHn/N 1/2θEH2) against θ. We use the spin-polarized DFT method under the generalized gradient approximation (GGA) of PerdewBurkeErnzerhof (PBE), as implemented with plane-wave self-consistent field (PWSCF) code contained in the Quantum ESPRESSO distribution,31 to perform the calculations. The details are given in the Supporting Information. The calculated ΔEH(θ) values at various possible surface sites and their coverage dependence (Figure s1 of the Supporting Information) suggest that, up to a coverage near 1 monolayer (ML, one adsorbed atom per surface Pt atom), the H atom prefers to be adsorbed at the 3-fold face-centered cubic (fcc) hollow sites on Pt(111), the 2-fold bridge sites on Pt(100), and the short-bridge sites between two adjacent Pt atoms in the top atom rows on Pt(110), respectively. After the first preferred sites are occupied, H atoms will adsorb at the atop sites on Pt(111) and the long-bridge sites between the adjacent top atom rows on Pt(110). Since each surface atom on the Pt(100) surface possesses two bridge sites, a total H coverage of 2 ML will be reached if all of the bridge sites are occupied. As θ is below 1 ML, H atoms prefer to occupy the bridge sites associated with different surface atoms so that they may stay away from each other to minimize the repulsion interaction. We may consider thus-adsorbed atoms as the first type of bridge H atoms on Pt(100) surface. As θ is above 1 ML, the additional H atoms have 19315



Figure 4. Plots of the DFT-calculated reaction free energy of H2 dissociation as a function of H coverage for Pt(111), Pt(110), and Pt(100) surfaces and the nanoparticle edge (insert).

to occupy the second bridge sites associated with some of the surface atoms. The repulsion between such pair-adsorbed H atoms results in a substantial positive change in the ΔEH(θ) (Figure s1 of the Supporting Information). We may consider these pair-adsorbed H atoms as the second type of bridge H atoms on the Pt(100) surface. It is known that the Pt(110) surface may possess a missing row structure under electrochemical conditions.32 We therefore have also performed calculations on the missing row Pt(110) surface. It is found that H atoms first prefer to adsorb at the short-bridge sites on the outermost atom rows, which can lead to a total H coverage of 1/3 ML. Following the outermost short-bridge sites, H atoms may adsorb on either the (111) microfacet sites and the valley sites, on which we found that the H adsorption energies are very close. So, we think there is no obvious adsorption preference of H on the (111) microfacets sites and the valley sites The site preferences of H adsorption on various Pt single crystal surfaces inferred from the present calculations agree with the recent calculations by Skulason et al.20 As shown in Figure s1 of the Supporting Information, ΔEH(θ) exhibits reasonable linear dependence on θ for the same type of adsorption sites on various Pt single crystal surfaces, suggesting that H adsorption on Pt approximately follows the Termkin adsorption isotherms. It is also seen that the slopes of the ΔEH(θ)∼θ plots vary from one surface to another and from one type of sites to another. Therefore, it is not a simple issue to model HERs in terms of the adsorption isotherm together with the standard adsorption energy. Fitting the calculated ΔEH(θ)∼θ data to linear lines enables us to obtain ΔEH(θ) values at any θ, from which the plots of ΔG2(θ) as a function of θ for various surfaces can be established according to eq 13. The thusobtained ΔG2(θ)∼θ plots for Pt (111), Pt(100), and Pt(110) surfaces are given in Figure 4. A detailed discussion on these curves and their implication on the kinetics of HERs will be given elsewhere. Our analysis will be focused on H adsorption at the equilibrium potential of HERs since we are interested in the trend in j0 for different surfaces. It can be seen that the coverage of H at which the value of ΔG2(θ) reaches zero varies with the crystallographic orientation of Pt surface atoms. On the Pt(111) surface, the zero value of ΔG2(θ) occurs at the H coverage of ca. 0.95 ML on the firstpreferred adsorption sites (fcc hollow sites). Experimentally, it has been known that the H coverage on Pt(111) reaches a value of about 2/3 ML at potential before the onset for hydrogen

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Figure 5. Calculated ΔGH(θ)∼θ plot for H adsorption on the Pt(110) surface with a missing row structure.

evolution reaction (0.050.07 V).8b It can be found from Figure 4 that the value of ΔG2(θ) for Pt(111) at θ = 2/3 ML is around 0.07 eV. If assuming that the Volmer reaction is reversible in HERs, one can prove that ΔG2(θ) = eE.18 Therefore, we can also infer from the present DFT calculation results that the H coverage reaches about 2/3 ML on Pt(111) at E ≈ 0.07 V, agreeing with the experimental observations. Considering the contribution of the configurational entropy to the change in the free energy of H adsorption, that is, the kBT ln(θ/(1 θ)) in eq 13, a zero value of ΔG2(θ) can also occur for H adsorption on the atop sites of Pt(111) surface at very low coverage. On the basis of the fitted ΔEH(θ)∼θ relation for atop H adatoms, the coverage at the equilibrium potential is estimated being less than 0.01 ML. Therefore, we think that the H adatoms on Pt(111) surface at the equilibrium potential are predominantly those adsorbed on 3-fold fcc sites. The so-called OPD (atop-adsorbed) H adatoms may form mainly at potentials more negative than the equilibrium potential. On the basis of the difference in the adsorption energies and the dipole matrix elements, Skulason et al.18b have also drawn a conclusion that the coverage of the atop-adsorbed H atoms is extremely low on Pt(111) at the equilibrium potential. On Pt(100) surface, the zero value of ΔG2(θ) is found to occur when ca. 0.26 ML of the second type of the bridge sites have been occupied by H atoms (the green plot in Figure 4). This means that the total coverage of H atom on Pt(100) is about 1.26 ML at the equilibrium potential. The recent experimental study by Strmcnik et al.8b also suggested that the H coverage on Pt(100) exceeds one monolayer at the equilibrium potential. If we consider the H atoms adsorbed on the first half of bridge sites the UPD H, those pair-adsorbed bridge H atoms may be considered as the so-called OPD H on Pt(100) surface. On Pt(110) surface, ΔG2(θ) reaches zero as ca. 0.2 ML of the second preferred sites, that is, the long-bridge sites, have been occupied. This says that Pt(110) surface can also bind more than 1 ML of H atoms at the equilibrium potential of HERs. Figure 5 gives the calculated ΔG2(θ)∼θ data for H adsorption on Pt(110) surface with a missing row structure. Since the free energies of H adsorption on the (111) microfacets and the valleys are close to each other, H atoms may adsorb simultaneously on these two types of sites after the short-bridge sites on the outermost atom rows have been occupied. The values of ΔG2(θ) can reach zero when either about 80% of the (111) microfacets sites or about 70% of the valley sites are occupied by H atoms. This suggests that there are three types of H adatoms on the 19316


The Journal of Physical Chemistry C missing row Pt(110) surface at the equilibrium potential. About 80% of the (111) microfacet sites and 70% of the valley sites correspond respectively to 0.55 and 0.23 ML of Pt atoms on the missing row Pt(110) surface. Thus, the total H coverage at the equilibrium potential will be about 0.33 + 0.55 + 0.23 = 1.21 ML, which is similar to that on the normal Pt(110) surface. In recent in situ infrared (IR) spectroscopic studies on polycrystalline Pt film electrodes, Kunimatsu et al.15 observed a new IR absorption band around 2090 cm1 in addition to that associated with the UPD H adatoms as the potential goes below 0.1 V. The authors assigned this additional band to the vibration absorption of the so-called OPD H adatoms on Pt surfaces. The polycrystalline electrode surface may consist of different Pt facets. The present calculation results suggest that there are indeed more than one type of H adatoms formed on various Pt single crystal electrode surfaces as the potential is below 0.1 V. This somewhat agrees with the in situ IR results by Kunimatsu et al.15 However, the OPD H adatoms are not necessarily the atop H adatoms. As indicated by the present DFT-calculated results, the second preferred sites for H adsorption on Pt(100) and Pt(110) surfaces are not atop sites. In addition, the UPD H adatoms are not necessarily all adsorbed on hollow sites. The first preferred H adsorption sites on Pt(100) and Pt(110) are the bridge sites. The present calculations also suggest that the reactive intermediates for HERs are not necessarily the OPD H adatoms. The nature of the reactive H atoms depends on the potentials. According to the kinetic model derived earlier (eq 9), we know that the reactivity of a certain type of H adatoms at the equilibrium potential, that is, their contribution to j0, depends on their coverage at the equilibrium potential. It can be found from the theoretical volcano plot in Figure 3 that those with θ0 close to 0 (e.g., atop H adatoms on Pt(111) surface) or 1 ML (e.g., the first half bridge H adatoms on Pt(100) surface and the short-bridge H adatoms on the outermost atom rows on Pt(110) surface) would make a negligible contribution to j0. Therefore, we may conclude that the reactive intermediates of HERs at the equilibrium potential are respectively the fcc H adatoms on Pt(111) surface, the pair-adsorbed bridge H adatoms on Pt(100) surface, and the long-bridge (or the (111) microfacet and valley) H adatoms on Pt(110) surfaces. On this basis, the UPD H adatoms serve as the reactive intermediates on the Pt(111) surface. 3.2. Surface Structure Effects of Pt. On the basis of the calculated θ0 values, the dimensionless values of j0 can be estimated to be about 0.9, 0.82, and 0.43, respectively, for Pt(100), Pt(110), and Pt(111) surfaces (see the marked points in Figure 3). As for the missing row Pt(110) surface, H adatoms on both the (111) microfacet sites and the valley sites can serve as the reactive intermediates for HERs at the equilibrium potential. Their θ0 values are 0.8 and 0.7 ML, respectively. The dimensionless values of j0 corresponding to these θ0 values should be ca. 0.8 and 0.9 (Figure 3). Since that the fractions of the (111) microfacet sites and the valley sites are about 2/3 and 1/3, respectively, the j0 value for the missing row Pt(110) surface would be 2/3 0.8 + 1/3 0.9 ≈ 0.83, which is close to that estimated for the unreconstructured Pt(110) surface. Considering the accuracy of DFT calculations, we may infer from the above analysis and estimation that the values of j0 on Pt(110) and Pt(100) electrode surfaces should be similar to each other, whereas they are nearly two times higher than that on Pt(111) surface. Such a prediction agrees reasonably with the recent

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Figure 6. Number ratios of the edge and (100) facet atoms to the (111) facet atoms and the (100) facet atoms to the edge and (111) facet atoms.

experimental results obtained from low-temperature RDE measurements by Markovic and his co-workers,8a who showed that the values of j0 for HERs follow the order of Pt(111), Pt(100) < Pt(110). It is worth noticing that, if we simply consider the ΔGH(θ) at a θ value for the first preferred sites of various surfaces, one could draw a conclusion according to the previously reported volcano relations or plots19,23,29 that the Pt(111) surface has much higher j0 than the other two low index crystal surfaces of Pt since the ΔGH(θ) values for Pt(111) surface are closer to zero. The previous volcano relations omitted or improperly treated the coverage effect on the adsorption energy and did not realize the possible changes in the reactive sites and the adsorption isotherm from one surface to another. 3.3. Nanoparticle Size Effects of Pt. It is known that the fcc Pt nanocrystallites most preferably have a cuboctahedral shape (Figure s2a of the Supporting Information),5,33 which are enclosed with (111) and (100) facets and edge atom rows that are thought to be similar to the topmost rows on (110) surface.2,3,5 As the particle diameters are smaller than 8 nm, the fraction of the edge atoms increases pronouncedly with the decreasing particle size (Figure s2b of the Supporting Information). If simply considering that the edge atom rows on fcc Pt nanoparticles are similar in structure to the top atom rows on Pt(110) surface, one may at first glance think that j0 would increase with the decreasing Pt particle sizes based on the Pt surface structure dependence of j0 estimated above since the atom number ratio of the (100) facet and edge atoms to the less active (111) facets increases with decreasing particle size (Figure 6). Such a positive size effect in turn suggests that Pt catalysts on the anode of fuel cells should be made as small as possible until the occurrence of the quantum size effect, which simultaneously increase the surface area per mass of Pt and the activity per surface area. However, this will be found to be not true when further considering the reactive site difference on various single crystal surfaces of Pt. As indicated in the above DFT calculations, the reactive sites of HERs on the extended Pt(110) surface at the equilibrium potential would the longbridge sites between the nearest neighbor atom rows or the (111) microfacet sites and the valley sites if the Pt(110) surface has a missing row structure. These sites are absent for nanoparticle edges. Thus, H adatoms would be adsorbed on atop sites on nanoparticle edge atom rows after the short bridge sites are nearly completely occupied. As shown in the inset of Figure 4, the 19317


The Journal of Physical Chemistry C zero value of ΔG2(θ) occurs at a coverage of ca. 0.05 ML for such top H adatoms. On this basis, we may conclude that the values of j0 for different surface atoms on Pt nanoparticles follow the order that (100) facet > (111) facet ≈ edge (Figure 3). As shown in Figure 6, the atom number ratio of the (100) facets to (111) facets plus edges decreases with decreasing particle size, and a negative particle size effect of Pt on j0 thus would be expected; that is, j0 decreases with the decreasing size of the Pt nanoparticle catalyst.

4. SUMMARY This work has presented a theoretical scheme to understand the surface structure and particle size effects of Pt in hydrogen electrocatalysis. Through rigorous thermodynamic and kinetic analysis, we have established a volcano relation between the exchange current density (j0) of HERs and the surface coverage of reactive H atoms at the equilibrium potential (θ0), which allows distinguishing the activity of catalytic surfaces located near the apex of the volcano plots for HERs more accurately than the so-far reported ones. It is demonstrated that the nature and the coverage of the reactive H adatoms at a catalytic surface at the equilibrium potential of HERs can be deduced from the DFTcalculated adsorption isotherm. The main results and conclusions are detailed as follows. (i) According to the theoretically derived volcano relation, catalytic surfaces with θ0 values closer to 0.5 ML would have higher value of j0. (ii) According to the DFT calculated adsorption isotherms, the reactive H atoms at the equilibrium potential of HERs are those adsorbed at the 3-fold fcc sites on Pt(111) surface, those pair-adsorbed at the bridge sites on Pt(100) surface, and those adsorbed at the long-bridge sites on Pt(110) surfaces (or those adsorbed at the (111) microfacet and valley sites on the missing row Pt(110) surface). The calculated θ0 values for these H adatoms suggest that j0 for HERs on Pt (110) and Pt(100) surfaces are similar to each other, which are nearly two times higher than that on Pt(111) surfaces. (iii) Although the individual edge atom rows on fcc metal nanoparticles are similar in structures to the top atom rows on the corresponding (110) surfaces, the catalytic properties of the nanoparticle edges are not simply equivalent to the extended (110) surfaces due to that some adsorption sites for reactive intermediates could be absent at nanoparticle edges, for example, the long-bridge sites on Pt(110) surface for HERs. (iv) The reactive sites on the edge of Pt nanoparticles for HERs are found to be the top sites. The calculated θ0 value suggests that the activity of the Pt nanoparticle edges for HERs is similar to the (111) facets but much lower than the (100) facets. According to the particle size dependent surface atom distributions, a negative particle size effect of Pt would be expected for HERs; that is, j0 decreases with the decreasing particle size. This work should represent a major step forward in understanding the origin of the surface structure and particle size effects of Pt in HERs, which has been a long-standing problem in electrochemistry and fuel cells. The methodology and results presented in this work may be of general significance in correlating the catalyst performance with their morphologies and sizes. It

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has been also demonstrated that not only the thermodynamic adsorption energy but also a detailed nature of the reactive sites are very important for the proper prediction of activity trends in catalytic and electrocatalytic reactions.

’ ASSOCIATED CONTENT

bS

Supporting Information. Derivation of the volcano relations, DFT calculation details, and supporting figures. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Email: [email protected].

’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (NSFC No. 21073137), the Fundamental Research Funds for the Central Universities, and the State Education Ministry of China under the program for New Century Excellent Talents in Universities of China (NCET-060612). ’ REFERENCES (1) (a) Van Santen, R. A. Acc. Chem. Res. 2009, 42, 57. (b) den Breejen, J. P.; Radstake, P. B.; Bezemer, G. L.; Bitter, J. H.; Froseth, V.; Holmen, A.; de Jong, K. P. J. Am. Chem. Soc. 2009, 131, 7197. (2) (a) Maillard, F. Fuel Cell Catalysis; Koper, M. T. M., Ed.; John Wiley & Sons, Inc.: New York, 2009; pp 507568. (b) Markovic, N. M.; Radmilovic, V.; Ross, P. N. Catalysis and Electrocatalysis at Nanoparticle Surfaces; Wieckowski, A., Ed.; Marcel Dekker: New York, 2003; Chapter 9. (3) (a) Kinoshita, K. J. Electrochem. Soc. 1990, 137, 845. (b) Mayrhofer, K. J. J.; Blizanac, B. B.; Arenz, M.; Stamenkovic, V. R.; Ross, P. N.; Markovic, N. M. J. Phys. Chem. B 2005, 109, 14433. (4) Arenz, M.; Mayrhofer, K. J. J.; Stamenkovic, V. R.; Blizanac, B. B.; Tada, T.; Markovic, N. M.; Ross, P. N. J. Am. Chem. Soc. 2005, 127, 6819. (5) Henry, C. R. Surf. Sci. Rep. 1998, 31, 231–325. (6) (a) Clavilier, J.; Rodes, A.; El Achi, K.; Zamakhchari, M. A. J. Chim. Phys. 1991, 88, 1291 and references therein. (b) Morin, S.; Dumont, H.; Conway, B. E. J. Electroanal. Chem. 1996, 412, 39. (7) (a) Kita, H.; Ye, S.; Gao, Y. J. Electroanal. Chem. 1992, 334, 351. (b) Kita, H. J. Mol. Catal. 2003, 199, 161. (c) Seto, K.; Ianelli, A.; Love, B.; Lipkowski, J. J. Electroanal. Chem. 1987, 226, 351. (d) Gomez, R.; Fernandez-Vega, A.; Feliu, J. M.; Aldaz, A. J. Phys. Chem. 1993, 97, 4769. (8) (a) Markovic, N. M.; Grgur, B. N.; Ross, P. N. J. Phys. Chem. B 1997, 101, 5405. (b) Strmcnik, D.; Tripkovic, D.; Van der Vliet, D.; Stamenkovic, V. R.; Markovic, N. M. Electrochem. Commun. 2008, 10, 1602. (9) Barber, J.; Morin, S.; Conway, B. E. J. Electroanal. Chem. 1998, 446, 125. (10) (a) Babic, B. M.; Vracar, L. M.; Radmilovic, V.; Krstajic, N. V. Electrochim. Acta 2006, 51, 3820. (b) Takasu, Y.; Fujii, Y.; Yasuda, K.; Iwanaga, Y.; Matsuda, Y. Electrochim. Acta 1989, 34, 453. (c) Vogel, W.; Lundquist, J.; Ross, P.; Stonehart, P. Electrochim. Acta 1975, 20, 79. (11) Chen, S. L.; Kucernak, A. J. Phys. Chem. B 2004, 108, 13984. (12) (a) Harrison, J. A.; Khan, Z. A. J. Electroanal. Chem. 1971, 30, 327. (b) Bagotzky, V. S.; Osetrova, N. V. J. Electroanal. Chem. 1973, 43, 233. (c) Gasteiger, H. A.; Panels, J. E.; Yan, S. G. J. Power Sources 2004, 127, 162. (d) Vetter, K. J. Electrochemical Kinetics; Bruckenstein, S., Howard, B., Eds.; Academic Press: New York, 1967; pp 516614. 19318



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(13) (a) Jerkiewicz, G.; Conway, B. E. Solid State Ionics 2002, 150, 93. (b) Tilak, B. V.; Conway, B. E. Electrochim. Acta 2002, 47, 3571. (14) (a) Nichols, R. J.; Bewick, A. J. Electroanal. Chem. 1988, 243, 445. (b) Nichols, R. J. Adsorption of Molecules at Metal Electrodes; Lipkowski, J., Ross, P. N., Eds.; VCH: New York, 1992; p 347. (15) (a) Kunimatsu, K.; Uchida, H.; Osawa, M.; Watanabe, M. J. Electroanal. Chem. 2006, 587, 299. (b) Kunimatsu, K.; Senzaki, T.; Tsushima, M.; Osawa, M. Chem. Phys. Lett. 2005, 401, 451. (16) (a) Nanbu, N.; Kitamura, F.; Ohsaka, T.; Tokuda, K. J. Electroanal. Chem. 2000, 485, 128. (b) Ogasawara, H.; Ito, M. Chem. Phys. Lett. 1994, 221, 213. (17) Tadjeddine, A.; Peremans, A. Surf. Sci. 1996, 368, 377. (18) (a) Karlberg, G. S.; Jaramillo, T. F.; Skulason, E.; Rossmeisl, J.; Bligaard, T.; Nørskov, J. K. Phys. Rev. Lett. 2007, 99, 126101. (b) Skulason, E.; Kalberg, G. S.; Rossmeisl, J.; Bligaard, T.; Greeley, J.; Jonsson, H.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2007, 9, 3241. (19) Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U. J. Electrochem. Soc. 2005, 152, J23. (20) Skulason, E.; Tripkovic, V.; Bjrketun, M. E.; Gudmundsdttir, S.; Karlberg, G.; Rossmeisl, J.; Bligaard, T.; Jnsson, H.; Nørskov, J. K. J. Phys. Chem. C 2010, 114, 18182. (21) Santana, J. A.; Mateo, J. J.; Ishikawa, Y. J. Phys. Chem. C 2010, 114, 4995. (22) (a) Wang, X. J.; Springer, T. E.; Adzic, R. R. J. Electrochem. Soc. 2006, 153, A1732. (b) Shuldiner, S. J. Electrochem. Soc. 1960, 107, 452. (c) Conway, B. E.; Tilak, B. V. Electrochim. Acta 2002, 47, 3571. (23) Parsons, R. Trans. Faraday Soc. 1958, 54, 1053. (24) Ross, P. N. Surf. Sci. 1981, 102, 463. (25) Frumkin, A. N.; Dolin, P. I.; Ershler, B. V. Acta Physicochim. U.R. S.S. 1940, 13, 779. (c) Bockris, J. O'M.; Conway, B. E. J. Chem. Phys. 1957, 26, 532. (26) Bard, A. J.; Faulkner, L. R. Electrochemical methods: fundamentals and applications, 2nd ed.; John Wiley & Sons: New York, 2001. (27) (a) van Santen, R. A.; Neurock, M.; Shetty, S. G. Chem. Rev. 2010, 110, 2005. (b) Eyring, H.; Polanyi, M. Z. Phys. Chem. B 1931, 12, 279. (c) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11. (d) van Santen, R. A.; Niemantsverdriet, J. W. Chemical Kinetics and Catalysis; Plenum Press: New York, 1995. (28) (a) Hammer, B.; Nørskov, J. Adv. Catal. 2000, 45, 71. (b) Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Bahn, S.; Hansen, L. B.; Bollinger, M.; Bengaard, H.; Hammer, B.; Sljivancanin, Z.; Mavrikakis, M.; Xu, Y.; Dahl, S.; Jacobsen, C. J. H. J. Catal. 2002, 209, 275. (29) (a) Trasatti, S. J. Electroanal. Chem. 1972, 39, 163. (b) Krishtalik, L. Adv. Electrochem. Electrochem. Eng. 1970, 7, 283. (c) Trasatti, S. Handbook of Fuel Cells—Fundamentals, Technology and Applications; Vielstich, W., Lamm, A., Gasteiger, H. A., Eds.; John Wiley & Sons, Ltd.: Chichester, 2003; Vol. 2, Part 2, pp 8892. (30) Schmickler, W.; Trasatti, S. J. Electrochem. Soc. 2006, 153, L31. (31) Giannozzi, P.; Baronial, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. J. Phys.: Condens. Matter 2009, 21, 395502. (32) Markovic, N. M.; Ross, P. N. Surf. Sci. Rep. 2002, 45, 117. (33) Hardeveld, R. V.; Montfoort, A. V. Surf. Sci. 1966, 4, 396.

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A Theoretical Consideration on the Surface Structure and

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