Published: August 29, 2011

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

ARTICLE

pubs.acs.org/JPCC

A Theoretical Consideration on the Surface Structure andNanoparticle Size Effects of Pt in Hydrogen ElectrocatalysisFan 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

1. INTRODUCTION

The size- and shape-dependent reactivity of nanoparticlecatalysts is among the key problems in current catalysis andelectrocatalysis.1,2 Understanding such dependence not onlyhelps catalyst optimization but also can be of fundamentalsignificance in nanoscience for establishing property�structurerelationships. For supported metallic nanoparticle catalysts offew nanometers to a few tens of nanometer sizes used in most ofthe heterogeneous catalytic systems, the particle-dependentcatalytic properties should be mainly originated from the size-and shape-dependent surface structure of nanoparticles sincenegligible quantum size effect is expected in this size regime.1�5

It is known that metallic nanoparticles are enclosed with differentfacets, whose surface percentages vary with the particle size andshape.5 If the adsorption of key intermediates of a reaction, forexample, oxygenated species for oxygen reduction and CO formethanol and CO oxidation, is sensitive to the surface latticestructure of a metal, the specific rate of the reaction is expected tochange with the surface structure of the metal and therefore withthe size and shape of the metal nanoparticles accordingly. Onthis basis, the surface structure effects of metallic catalysts forvarious reactions play a key role in particle-dependent catalyticproperties.

Hydrogen electrode reactions (HERs), including the cath-odic H2 evolution and anodic H2 oxidation, play a key role inhydrogen-based energy conversion technologies such as fuel cells

and water electrolysis. Pt is the most active electrocatalysts forHERs. Although HERs have been over the decades serving asarchetype processes in electrochemistry and studied extensively,the surface structure and particle size effects of Pt for HERs havebeen rarely explored and remain in dispute. It is known that boththe H2 evolution and oxidation reactions on various metal sur-faces involve the adsorbed H atoms (H adatoms) as the inter-mediates and that the adsorption of H on Pt strongly depends onthe crystallographic orientation of surface atoms.6 We havereason to believe that the kinetics of the HERs vary with thesurface structure and nanoparticle size of Pt. Earlier studies usingPt single crystal electrodes failed to show surface structuredependence of the hydrogen evolution reaction kinetics,7 whichrendered the researchers to believe that the H adatoms formed inthe potential region above the onset for the hydrogen evolutionreaction (0.05�0.07 V vs RHE), the so-called UPD (under-potential deposited) H adatoms, are not the reactive intermedi-ates for hydrogen evolution. Recent studies by Markovic et al.2,8

and Conway et al.,9 however, showed that the kinetics of HERsare sensitive to the crystallographic orientation of surface Ptatoms. These authors pointed out that the failure in identifyingthe Pt surface structure sensitivity of HERs in earlier literaturewas mainly due to that the actual specific kinetics were obscured

Received: July 22, 2011

ABSTRACT: Microkinetic modeling and density functional theory (DFT) calculationsare combined to understand the surface structure and nanoparticle size effects of Pt on thekinetics of hydrogen electrode reactions (HERs). The microkinetic modeling leads to amechanism-free volcano relation between the exchange current density of HERs (j0) andthe surface coverage of the reactive H adatoms at the equilibrium potential (θ0), makingthe activity trend of various catalytic surfaces forHERs predictable withθ0. It is shown thatcatalytic surfaces with θ0 values closer to 0.5 monolayer will have higher j0. A DFTcalculation scheme is developed to determine the nature of the reactive H atoms and thecorresponding θ0 values. The calculated results on Pt single crystal electrodes predict thatj0 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 ofPt. It is shown that, although the individual edge atom rows on Pt fcc nanoparticles are similar in structures to the top atom rows onthe Pt(110) surface, the catalytic properties of the nanoparticle edges are not simply equivalent to the extended (110) surfaces sincesome of the reactive sites for a reaction on extended (110) surfaces (e.g., the long-bridge sites) are absent at nanoparticle edges. Theresults presented here not only throw new insights into the long-standing problem about the Pt surface structure and particle sizeeffects in hydrogen electrocatalysis but also provide a general theoretical scheme to identify the most active catalytic surfaces forHERs. More importantly, we demonstrate that not only the thermodynamic data like the adsorption energy but also a detailednature of the reactive sites and their coverage are very important for the proper prediction of the activity trend of catalytic surfaces.

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by the relatively slow diffusion of H2. As for the nanoparticle sizeeffects of Pt forHERs, so far only a few studies can be found in theliterature,2,10 in which the catalytic activity of Pt nanocatalysts forHERs was reported to keep unchanged,10a increase,10b ordecrease10c upon reducing the particle sizes. We think that thereported literature results on the Pt nanoparticle size effects forHERs might have also suffered from similar problems of im-proper kinetics determination due to fast kinetics coupled withslow H2 diffusion. It has been long argued that the kinetics ofHERs on Pt surfaces might be too fast to measure with theordinary steady-state voltammetric methods, for example, therotating disk electrode (RDE) method.11,12

As well as the inconsistent results in various electrochemicalkinetic measurements, our fundamental understanding towardthe surface structure and nanoparticle size effects of Pt for HERshas been also hampered by the lack of microscopic detail aboutthe relation between HERs and H adsorption. There are a fewimportant questions remaining to be answered, for instance,whether UPD H adatoms serve as reactive intermediate orspectator in HERs,8,11,13 does their formation extend to thepotential region below the onset potential of hydrogen evolutionreaction,8 what's the nature of the so-called overpotential depos-ited (OPD) H adatoms which were considered by some authorsas the reactive intermediate for HERs,8,9,13 and so on. Due to thefact that the formation of H adatoms is coupled with otherprocesses, it is generally difficult to gain accurate information onthe adsorption of H by using conventional electrochemicalmethods when the evolution or oxidation of H2 is taking place.Recent in situ infrared (IR) spectroscopic results by someauthors14,15 suggested a different type of H adatom from theUPD H develops on Pt as potential goes below 0.1 V, which wasattributed to H adatoms formed on atop sites and considered thereactive intermediate of HERs. However, the formation of suchatop H adatoms was not observed in other IR16 and SFG17 (sumfrequency generation) studies.

The hydrogen adsorption and the evolution and oxidation ofH2 have been also the subjects of recent first principle theoreticalcalculations studies.18�21 The quantum chemistry simulations inprinciple can provide direct atomic details for each individualprocess (or reaction step) in a complicated reaction, whereasexperimental measurements generally give overall results asso-ciated with several processes or steps. However, the quantumchemistry calculation results strongly depend on the modelselected to represent the studying system, especially for catalyticand electrocatalytic systems involving the adsorption of mol-ecules and/or atoms on solid surfaces. Therefore, it is veryimportant that quantum chemistry calculations are combinedwith or guided by proper theoretical modeling. In a recent paper,Sk�ulason et al.20 performed comprehensive density functionaltheory (DFT) calculations on the reaction and activation en-ergies of each elementary reaction step in HERs with the effectsof overpotential and H coverage being considered. By assumingthe Tafel reaction as the rate-determining step, their calculatedactivation barriers on different Pt facets at the equilibriumpotential suggested that the exchange current density for HERs(j0) depends on the surface structures of Pt. Furthermore, thepredicted trend in j0 for the three low-index single crystal surfaceswas similar to the experiments by Markovic et al.2,8

In this work, we perform a combined theoretical modeling andDFT calculations study on the surface structure and nanoparticlesize effects of Pt in HERs. Our aim is not only to show how thesurface structures and nanoparticle sizes of Pt may affect the

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

2. MICROKINETIC MODELING

Since the activities of various catalytic surfaces for HERs aregenerally compared by the exchange current density j0, whichrepresents the equalized rate of the oxidation and evolution of H2

at the equilibrium potential, the modeling in the present paperwill be focused on the thermodynamics and kinetics at theequilibrium potential of HERs.2.1. Thermodynamic Analysis. For HERs, H2T 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 atpotential E, μ̅H+

0 and μ̅H2

0 refer the standard chemical potentialsof the proton in the electrolyte solution and the hydrogenmolecule in the gas phase, cH+ and pH2

are the concentration ofthe proton and the partial pressure of H2, and kB and T have theirordinary meanings.

ΔG1ðEÞ ¼ 2μ̅ e� ðEÞ þ 2μ̅ 0Hþ � μ̅ 0

H2

þ kBT lnðcHþ 2=pH2Þ ð1Þ

For simplicity, we will assume in this paper that the standardconditions for HERs are maintained; that is, pH2

and cH+ are keptat 1 atm and 1 mol 3 L

�1, respectively. These assumptions onlysimplify the derivations but will not limit the generality of theconclusions obtained. Since that ΔG1(E

0) = 0 at the standardequilibrium potential E0, we can easily find from eq 1 that

12μ̅ 0

H2¼ μ̅ 0

Hþ þ μ̅ e�ðE0Þ ð2Þ

It is known that HERs may involve three possible elementaryreaction steps,11,22 namely, the Tafel reaction (H2 + 2*T 2*H),the Heyrovsky reaction (H2 + * T *H + H+ + e�), and theVolmer reaction (*HT * + H+ + e�), where * and *H representrespectively the free site and the H adatoms on the surface. Thefree energies of these reactions can be respectively expressed byeq 3a to 3c, in which μ̅ *H

0 (θ) = ∂GMHn(θ)/∂n refers to the change

in the total free energy of the electrode surface with H adatoms ofθ coverage, GMHn

(θ), upon increasing one H adatom. Here n isthe number of H adatoms on the surface and θ = n/N with Nbeing the total number of the metal surface atoms. μ̅ *H

0 (θ) canalso be understood as the free energy of a H adatom at θcoverage.

ΔGTafelðθÞ ¼ 2μ̅ 0�HðθÞ � μ̅

0H2

þ 2kBT lnðθ=ð1� θÞÞð3aÞ

ΔGHeyrovskyðθÞ ¼ μ̅ 0�HðθÞ þ μ̅

0

Hþ þ μ̅ e�ðEÞ � μ̅0

H2

þ kBT lnðθ=ð1� θÞÞ ð3bÞ

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ΔGVolmerðθÞ ¼ μ̅ 0Hþ þ μ̅ e� ðEÞ � μ̅ 0

�HðθÞ� kBT lnðθ=ð1� θÞÞ ð3cÞ

The HERs may proceed through either the Tafel�Volmer orthe Heyrovsky�Volmer combination.14 Regardless of the exactreaction mechanism, the H adatoms serve as the intermediate,which makes the reaction kinetics depending on the binding ofelectrode surface to H. To establish a measure of this binding, weintroduce the H2 dissociation reaction, 1/2H2 + *T *H, whosereaction free energy reads

ΔG2ðθÞ ¼ μ̅ 0�HðθÞ � 1=2μ̅

0H2

þ kBT lnðθ=ð1� θÞÞð4Þ

The value of μ̅ *H0 (θ) � 1/2μ̅H2

0 can be considered as the freeenergy difference between a H adatom at θ coverage and ahydrogen atom in a gaseous H2. We define it as the differentialfree energy of H adsorption at θ coverage and denote it withΔGH(θ). Thus, we can have the following expression for reactionfree energy of H2 dissociation.

ΔG2ðθÞ ¼ ΔGHðθÞ þ kBT lnðθ=ð1� θÞÞ ð5ÞThe value of ΔGH(θ) would vary from one surface to anotherand can serve as an indicator of the binding of a surface to H.Here, we have avoided using the term of standard free energy ofH adsorption or standard chemical potential of H adatoms sincethat defining the standard state for an adsorbed species issomewhat a complicated issue. For instance, the standard statefor H adatoms was defined as the half monolayer coverage byParsons in deriving the j0 expressions for HERs,23 while it wasdefined as zero coverage by other researchers.24,25 In addition,adsorption isotherms have to be included in the free energyexpressions for adsorption processes when the standard state isemployed, which would bring about not only additional para-meters 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), andΔGVolmer(θ) = 1/2ΔG1(E)�ΔG2(θ).It can be easily proven that all of the elementary reactions wouldbe in equilibrium at the equilibrium potential of HERs (θ = θ0,E =E0), that is,ΔGTafel(θ

0) =ΔGHeyrovsky(θ0) =ΔGVolmer(θ

0) = 0,and we then have ΔG2(θ

0) = 0. This says that the H coverage atwhich ΔG2(θ) equals zero for a catalytic surface is right that atwhich HERs reach equilibrium at this surface. In another word,we can determine θ0 values from the coverage-dependent freeenergy values of the gas-phase dissociation reaction according toeq 5. It has been shown through DFT calculations18 and surfacescience studies24 that the solvent and electric field have negligibleeffects on the adsorption of H, which justifies the strategy ofusing the thermodynamic data obtained from the gas-phasedissociation reaction to describe the H adsorption at electrodesurfaces in electrochemical environments.2.2. Kinetic Analysis.Depending on the reaction mechanism,

the exchange current density of HERs should satisfy eq 6a(Tafel�Volmer mechanism) or eq 6b (Heyrovsky�Volmermechanism), in which kx

+0 and kx�0 (x = Volmer or Heyrovsky)

refer to the rate constants of the forward (+) and backward (�)processes of the corresponding reaction steps at equilibriumpotential.

j0 ¼ Fkþ0Volmerθ

0 ¼ Fk�0Volmerð1� θ0Þ ð6aÞ

j0 ¼ Fðkþ0Heyrovskyð1� θ0Þ þ kþ0

Volmerθ0Þ

¼ Fðk�0Heyrovskyθ

0 þ k�0Volmerð1� θ0ÞÞ ð6bÞ

According to the transition-state theory, kx+0 and kx

�0 arerelated to the corresponding activation free energy, ΔGx

+0 6¼(θ0)and ΔGx

�0 6¼(θ0), by the following equations.

kþ0x ¼ ðkBT=hÞexpð �ΔGþ0 6¼

x ðθ0Þ=kBTÞ ð7aÞ

k�0x ¼ ðkBT=hÞexpð �ΔG�0 6¼

x ðθ0Þ=kBTÞ ð7bÞThe activation free energies in the Volmer and Heyrovsky

reactions depend on not only the electrode potential, but alsothe binding of H adatoms on the electrode surface which can bedescribed in terms of ΔGH(θ) defined earlier. Therefore,ΔGx

+0 6¼(θ0) and ΔGx�0 6¼(θ0) are not necessarily equal to each

other. In general, only the simple outer-sphere electrochemicalelectron-transfer reactions have equalized forward and back-ward rate constants (and therefore activation energies) at thestandard equilibrium potentials.26 According to the free energyexpressions of eqs 2 to 5, we can easily find that μ̅ *H

0 (θ0) = 1/2μ̅H2

0 = μ̅H+0 + μ̅ e� (E

0) as θ0 = 0.5, that is, ΔGH(θ0) = 0. This

means that all of the possible elementary reaction steps inHERs, that is, the transformation between a H2 molecule andtwo H adatoms (Tafel reaction), the transformation between“H+ + e�” and a H adatom (Volmer reaction), and thetransformation between a H2 molecule and a H adatom plus“H+ + e�” (Heyrovsky reaction), will be in thermodynamicneutral conditions at E0 if θ0 = 0.5. In this case, the forward andbackward processes of these reactions would have equalizedactivation energies (therefore rate constants). The free energycurves in Figure 1 provide a schematic illustration showing howΔGH(θ

0) affects ΔGx+0 6¼(θ0) and ΔGx

�0 6¼(θ0). The solidand dashed curves represent respectively those for θ0 = 0.5(ΔGH(θ

0) = 0) and θ0 6¼ 0.5.As θ0 6¼ 0.5 (ΔGH(θ

0) 6¼ 0), the elementary reactions will havedifferent forward and backward activation energies. In fact, theequalized forward and backward rate constants for the elementaryreaction steps at E = E0 and θ0 = 0.5 can also be proven from thereaction kinetics (e.g., eq 5a) when considering that the elemen-tary reactions will be in equilibrium asE = E0.Wemay denote suchequalized activation free energy and rate constant asΔGx

06¼ and kx0,

respectively. They are related to each other by eq 8.

k0x ¼ ðkBT=hÞexpð �ΔG0 6¼x ðθ0Þ=kBTÞ ð8Þ

Onthebasis of theBrønsted�Evans�Polanyi (BEP) principle,27,28

the forward and backward activation free energies for a surface

Figure 1. Schematic illustration of the free energy variation in HERs atthe equilibrium potential for surfaces with zero and nonzero differentialadsorption free energy ΔGH(θ

0).

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The Journal of Physical Chemistry C ARTICLE

with θ0 would deviate from ΔGx6¼0 by a fraction of ΔGH(θ

0),for example, ΔGx

+0 6¼(θ0) = ΔGx6¼0 + αxΔGH(θ

0) in which αx

is a constant usually called symmetric factor (the detailed ex-pressions for various reactions are given by eqs s1�s4 in theSupporting Information). Accordingly, the rate constants ofeach elementary reaction for any surfaces can be expressedin terms of kx

0, ΔGH(θ0), and αx, for example, kHeyrovsky

+0 =kHeyrovsky0 exp(�αHeyrovskyΔGH(θ

0)/kBT) (see eqs s5�s8).Combining these relations with eqs 6�7 and assuming that allof the elementary reactions have the same symmetric factor α,we can have the following general relations for j0, in which k0

equals to kVolmer0 or (kVolmer

0 + kHeyrovsky0 ) depending on the

reaction mechanism (Supporting Information). We may con-sider k0 as the standard rate constant of HERs.

j0 ¼ Fk0ðθ0Þαð1� θ0Þð1 � αÞ ð9Þ

j0 ¼ Fk0 expð � αΔGHðθ0Þ=kBTÞ=ð1 þ expð �ΔGHðθ0Þ=kBTÞÞð10Þ

Thus, we have established one-to-one relations between j0

and θ0 and between j0 andΔGH(θ0). Since these relations have

been derived through relatively rigorous thermodynamic andkinetic analysis without specifying the reaction mechanism andthe rate-determining step, they should apply to HERs regard-less of the reaction mechanism. At surfaces where θ0 = 0.5(ΔGH(θ

0) = 0), the value of j0 equals to 0.5Fk0. For conven-ience, we will use a dimensionless exchange current density inthe following by normalizing j0 with the product of 0.5Fk0, suchthat the only parameter left in the j0∼θ0 and j0∼ΔGH(θ

0)relations is the symmetric factor α. The j0 value for θ0 = 0.5 willthen become 1. We may further assume that α = 0.5. It has beenwell-known that the symmetric factors for interfacial chargetransfer processes are approximately equal to 0.5 as far as thepotential is not far away from the standard equilibrium poten-tial.26 In addition, a α value other than 0.5 will result in anasymmetric j0∼ΔGH(θ

0) plot, which is inconsistent to thereported volcano plots for the experimental values of j0 (seediscussions in the next section).19,29

2.3. Volcano Plots of j0. In Figure 2, the logarithm of thedimensionless j0 is plotted againstΔGH(θ

0) and θ0, respectively,according to eqs 9 and 10. It can be seen that the plots of log j0 areshaped very differently withΔGH(θ

0) and θ0, although eq 9 andeq 10 are equivalent. As shown in Figure 2a, over a range of a fewdecades j0 shows a nearly linear variation in its logarithm when it

is plotted against ΔGH(θ0), forming a pyramid-shaped volca-

no curve. When plotting log j0 against θ0, a bell-shaped curveis obtained (Figure 2b), with little variation occurring in abroad region of θ0 between 0.01 and 0.99, but a few decadesvariation in the very narrow θ0 regions of below 0.01 andabove 0.99.On the basis of the two plots, we think thatΔGH(θ

0) would bean appropriate descriptor to predict the trends in j0 for differentmetals with vast-scale variation of hydrogen binding ability.Using θ0 to describe such large variations of j0 will be problematicsince a very small uncertainty in θ0 could result in decades ofdeviation in j0. For catalytic surfaces located near the maximumof the j0 curves, however, θ0 can be a very useful descriptor. Thisis 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 thevalue of j0 shows only a few times decrease from the maximum inthis ca. 99% of entire coverage spectrum (the correspondingΔGH(θ

0) change is within (0.1 eV). Thus, the j0 values forvarious catalytic surfaces near the maximum of volcano plot canbe easily distinguished by their θ0 values. This would be veryuseful in comparing the activity trends of catalytic surfaces nearthe volcano apex, for example, Pt-based catalysts. We will useFigure 3 to distinguish the activities of various Pt single crystalelectrode surfaces and Pt nanoparticle sites for HERs in thefollowing.It should be pointed out that the volcano plots of j0 for HERs

with the metal�hydrogen interaction have been known for morethan 50 years.19,23,25,29,30 As will be discussed in the following,however, most of the so far reported ones are not straightforwardin dealing with HERs at surfaces located near the apex of theplots. In the most representative and generally quoted funda-mental treatments by Parsons,23 the volcano relation of j0 wasexpressed in terms of the so-called standard free energy ofadsorption (ΔG0). In addition to the arbitrariness in defining thestandard state of adsorption as stated earlier, the use ofΔG0 maycause complexity and uncertainties since an adsorption isothermhas to be assumed. In reality, the adsorption isotherm couldchange from one surface to another or even with coverage on thesame surface. As will be shown later on, this indeed occurs for Hadsorption on various Pt surfaces.By assuming Langmuir adsorption of H, Parsons derived a

relation between j0 and ΔG0 which results in a pyramid-likevolcano plot of log j0 with symmetric ascending and descendinglegs and a maximum at zero ΔG0. In the case of Temkin

Figure 2. Theoretical plots of j0 (in logarithm form) as functions of (a)ΔGH(θ

0) and (b) θ0 predicted by eqs 9 and 10.

Figure 3. Theoretical j0∼θ0 volcano plot near the maximum of j0. Themarked data points indicate the j0 values corresponding to the DFT-determined θ0 for various single crystal surfaces and nanoparticleedges of Pt.

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adsorption, however, he arrived in a relation in which j0 surpris-ingly appears to be independent of ΔG0. Considering thatTemkin adsorption may only occur at middle coverage values,the author proposed that the actual j0∼ΔG0 plot would be thatthe top of the pyramidal volcano curve is replaced by a horizontalregion. To the best of our knowledge, such a horizontal regionhas not been shown in any forms of volcano plots reported on theexperimental values of j0 for HERs. Instead, an approximatelysymmetric volcano plot of pyramid shape between the experi-mental j0 and various metal�hydrogen bond energies has beenreported, with Pt located near the apex.29

Recently, Nørskov and his co-workers19,20 revisited this topicby plotting the experimental values of log j0 reported in theliterature with their DFT-calculated adsorption free energy of Hon the (111) surface of various transition metals, which alsoproduced a symmetric pyramid-like volcano plot with Pt beingnear the maximum. In addition, the authors showed that usingthe adsorption free energy values at different H coverage (e.g.,0.25 or 1 monolayers (ML)) would not change the trend of thevolcano plot. They have also introducedmodel relations betweenj0 and the adsorption free energy of H, in which the ascendingand descending branches of the volcano plot were describedwith different relations by distinguishing between the casesof exoenergetic and endoenergetic adsorption, respectively. Al-though themodel is somewhat oversimplified,30 it showed reasonablefit to the observed plots of the experimental j0 with the DFT-calculated 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 thermodynamicquantities related to the metal�hydrogen interaction, forexample, the metal�hydrogen bond energy29 or the H ad-sorption free energy at an arbitrary coverage.19,20 In anotherword, the reported volcano plots or relations seem to tell thatH coverage effect is unimportant in predicting the j0 trend. Forinstance, the experimental value of j0 can be reasonablydescribed by the model relation based on simple Langmuir adsorp-tion, whereas themodel based onmore realistic adsorption isothermsgives unrealistic predictions. By carefully inspecting Parsons' deriva-tion,we found that his “horizontal region”predictionwas due to somesimplifications made on the Temkin adsorption isotherm. Forinstance, 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 metal�hydrogeninteraction roughly scale with each other. If so, plotting j0

against different quantities would only result in a shift of thevolcano curve along the abscissa without changing the qualita-tive trend. Such an argument might apply when metals withlargely different binding abilities to H are considered. As will beshown at a later point, however, the use of adsorption data atarbitrary coverage could lead to wrong prediction in HERactivity order for various Pt single crystal surfaces. For catalyticsurfaces located near the top of the volcano plot, for example, Ptbased catalyst surfaces, the H adsorption data at the equilibriumpotential are not necessarily scaled with those at low coveragesince the adsorption site may change. In this case, one needs torelate j0 strictly with the H adsorption properties of the catalyticsurfaces at the equilibrium potential of HERs. Actually, if ΔG0

in Parsons' derivation had been considered as the differentialfree energy of H adsorption as defined in present study, hewould have been able to arrive in eq 10 given above withoutassuming any adsorption isotherms.

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 Hatom 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 zero-point energy contributions to ΔGH(θ), respectively.

ΔG2ðθÞ ¼ ΔEHðθÞ � TΔSHðθÞ þ ΔZPEH þ kBT lnðθ=ð1� θÞÞð11Þ

The differential adsorption energy of H2, ΔEH(θ), can be ex-pressed by eq 12, where E(θ)MHn

is the total energy of the surfaceof θ coverage.

ΔEHðθÞ ¼ ∂EðθÞMHn=∂n� 1

2EH2

¼ ∂ EðθÞMHn=N � 1

2θEH2

� �=∂θ ð12Þ

Considering that the entropies of the adsorbed atoms are smallwhen compared with the entropies of gaseous molecules and thatthe zero-point energy of the adsorbed H atom changes little fromone metal surface to another, the contributions from the entropyand zero-point energy changes together to ΔGH(θ) have beenestimated to be approximately 0.24 eV for standard temperatureby Nørskov et al.18,19 Therefore, eq 11 can be converted to theform of eq 13.

ΔG2ðθÞ ¼ ∂ EðθÞMHn=N � 1

2θEH2

� �=∂θ þ 0:24

þ kBT lnðθ=ð1� θÞÞ ð13ÞThe values of E(θ)MHn

and EH2are directly accessible to DFT

calculations. By using Pt slabs of different sizes, we can obtain aseries of E(θ)MHn

values. The values of ΔEH(θ) at various θ canbe 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 Perdew�Burke�Ernzerhof (PBE), as implementedwith plane-wave self-consistent field (PWSCF) code containedin the Quantum ESPRESSO distribution,31 to perform the cal-culations. The details are given in the Supporting Information.The calculatedΔEH(θ) values at various possible surface sites

and their coverage dependence (Figure s1 of the SupportingInformation) suggest that, up to a coverage near 1 monolayer(ML, one adsorbed atom per surface Pt atom), the H atomprefers to be adsorbed at the 3-fold face-centered cubic (fcc)hollow sites on Pt(111), the 2-fold bridge sites on Pt(100), andthe short-bridge sites between two adjacent Pt atoms in the topatom rows on Pt(110), respectively. After the first preferred sitesare occupied, H atoms will adsorb at the atop sites on Pt(111)and the long-bridge sites between the adjacent top atom rows onPt(110). Since each surface atom on the Pt(100) surfacepossesses two bridge sites, a total H coverage of 2 ML will bereached if all of the bridge sites are occupied. As θ is below 1ML,H atoms prefer to occupy the bridge sites associated withdifferent surface atoms so that they may stay away from eachother to minimize the repulsion interaction. We may considerthus-adsorbed atoms as the first type of bridge H atoms onPt(100) surface. As θ is above 1ML, the additional H atoms have

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to occupy the second bridge sites associated with some of thesurface atoms. The repulsion between such pair-adsorbed Hatoms results in a substantial positive change in the ΔEH(θ)(Figure s1 of the Supporting Information). We may considerthese pair-adsorbed H atoms as the second type of bridge Hatoms 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 havealso performed calculations on the missing row Pt(110) surface.It is found that H atoms first prefer to adsorb at the short-bridgesites on the outermost atom rows, which can lead to a total Hcoverage of 1/3 ML. Following the outermost short-bridge sites,H atoms may adsorb on either the (111) microfacet sites and thevalley sites, on which we found that the H adsorption energiesare very close. So, we think there is no obvious adsorption pre-ference of H on the (111) microfacets sites and the valley sitesThe site preferences of H adsorption on various Pt single crystalsurfaces inferred from the present calculations agree with therecent calculations by Sk�ulason et al.20

As shown in Figure s1 of the Supporting Information,ΔEH(θ)exhibits reasonable linear dependence on θ for the same type ofadsorption sites on various Pt single crystal surfaces, suggestingthat H adsorption on Pt approximately follows the Termkinadsorption isotherms. It is also seen that the slopes of theΔEH(θ)∼θ plots vary from one surface to another and fromone type of sites to another. Therefore, it is not a simple issue tomodel HERs in terms of the adsorption isotherm together withthe standard adsorption energy. Fitting the calculated ΔEH-(θ)∼θ data to linear lines enables us to obtain ΔEH(θ) valuesat any θ, from which the plots of ΔG2(θ) as a function of θ forvarious surfaces can be established according to eq 13. The thus-obtained ΔG2(θ)∼θ plots for Pt (111), Pt(100), and Pt(110)surfaces are given in Figure 4. A detailed discussion on thesecurves and their implication on the kinetics of HERs will be givenelsewhere. Our analysis will be focused on H adsorption at theequilibrium potential of HERs since we are interested in thetrend 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 orientationof Pt surface atoms. On the Pt(111) surface, the zero value ofΔG2(θ) occurs at the H coverage of ca. 0.95 ML on the first-preferred adsorption sites (fcc hollow sites). Experimentally, ithas been known that the H coverage on Pt(111) reaches a valueof about 2/3 ML at potential before the onset for hydrogen

evolution reaction (0.05�0.07 V).8b It can be found fromFigure 4 that the value of ΔG2(θ) for Pt(111) at θ = 2/3 MLis around �0.07 eV. If assuming that the Volmer reaction isreversible in HERs, one can prove that ΔG2(θ) = �eE.18

Therefore, we can also infer from the present DFT calculationresults that the H coverage reaches about 2/3 ML on Pt(111) atE ≈ 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 kBTln(θ/(1� θ)) in eq 13, a zero value ofΔG2(θ) can also occur forH adsorption on the atop sites of Pt(111) surface at very lowcoverage. On the basis of the fitted ΔEH(θ)∼θ relation for atopH adatoms, the coverage at the equilibrium potential is estimatedbeing less than 0.01 ML. Therefore, we think that the H adatomson Pt(111) surface at the equilibrium potential are predomi-nantly those adsorbed on 3-fold fcc sites. The so-called OPD(atop-adsorbed) H adatoms may form mainly at potentials morenegative than the equilibrium potential. On the basis of the dif-ference in the adsorption energies and the dipole matrix ele-ments, Sk�ulason et al.18b have also drawn a conclusion that thecoverage of the atop-adsorbed H atoms is extremely low onPt(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 siteshave been occupied byH atoms (the green plot in Figure 4). Thismeans that the total coverage of H atom on Pt(100) is about 1.26ML at the equilibrium potential. The recent experimental studyby Strmcnik et al.8b also suggested that the H coverage onPt(100) exceeds one monolayer at the equilibrium potential. Ifwe consider the H atoms adsorbed on the first half of bridge sitesthe UPD H, those pair-adsorbed bridge H atoms may beconsidered 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 beenoccupied. This says that Pt(110) surface can also bind more than1 ML of H atoms at the equilibrium potential of HERs. Figure 5gives the calculated ΔG2(θ)∼θ data for H adsorption onPt(110) surface with a missing row structure. Since the freeenergies ofH adsorption on the (111)microfacets and the valleysare close to each other, H atoms may adsorb simultaneously onthese two types of sites after the short-bridge sites on theoutermost atom rows have been occupied. The values ofΔG2(θ)can reach zero when either about 80% of the (111) microfacetssites or about 70% of the valley sites are occupied by H atoms.This suggests that there are three types of H adatoms on the

Figure 4. Plots of the DFT-calculated reaction free energy of H2

dissociation as a function of H coverage for Pt(111), Pt(110), andPt(100) surfaces and the nanoparticle edge (insert).

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

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missing row Pt(110) surface at the equilibrium potential. About80% of the (111) microfacet sites and 70% of the valley sitescorrespond respectively to 0.55 and 0.23 ML of Pt atoms on themissing row Pt(110) surface. Thus, the total H coverage at theequilibrium 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 anew IR absorption band around 2090 cm�1 in addition to thatassociated with the UPD H adatoms as the potential goes below0.1 V. The authors assigned this additional band to the vibrationabsorption of the so-called OPD H adatoms on Pt surfaces. Thepolycrystalline electrode surface may consist of different Ptfacets. The present calculation results suggest that there areindeed more than one type of H adatoms formed on various Ptsingle crystal electrode surfaces as the potential is below 0.1 V.This somewhat agrees with the in situ IR results by Kunimatsuet al.15 However, the OPD H adatoms are not necessarily theatop H adatoms. As indicated by the present DFT-calculatedresults, the second preferred sites for H adsorption on Pt(100)and Pt(110) surfaces are not atop sites. In addition, the UPD Hadatoms are not necessarily all adsorbed on hollow sites. The firstpreferred H adsorption sites on Pt(100) and Pt(110) are thebridge sites.The present calculations also suggest that the reactive inter-

mediates 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 knowthat the reactivity of a certain type of H adatoms at theequilibrium potential, that is, their contribution to j0, dependson their coverage at the equilibrium potential. It can be foundfrom 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 theshort-bridge H adatoms on the outermost atom rows onPt(110) surface) would make a negligible contribution to j0.Therefore, we may conclude that the reactive intermediates ofHERs at the equilibrium potential are respectively the fcc Hadatoms on Pt(111) surface, the pair-adsorbed bridge Hadatoms 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 reactiveintermediates 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 beestimated to be about 0.9, 0.82, and 0.43, respectively, forPt(100), Pt(110), and Pt(111) surfaces (see the marked pointsin Figure 3). As for the missing row Pt(110) surface, H adatomson both the (111)microfacet sites and the valley sites can serve asthe reactive intermediates for HERs at the equilibrium potential.Their θ0 values are 0.8 and 0.7 ML, respectively. The dimension-less values of j0 corresponding to these θ0 values should be ca. 0.8and 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) surfacewould be 2/3 � 0.8 + 1/3 � 0.9 ≈ 0.83, which is close to thatestimated for the unreconstructured Pt(110) surface. Consider-ing the accuracy of DFT calculations, we may infer from theabove analysis and estimation that the values of j0 on Pt(110) andPt(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

experimental results obtained from low-temperature RDE mea-surements by Markovic and his co-workers,8a who showed thatthe values of j0 for HERs follow the order of Pt(111), Pt(100) <Pt(110).It is worth noticing that, if we simply consider theΔGH(θ) at a

θ value for the first preferred sites of various surfaces, one coulddraw a conclusion according to the previously reported volcanorelations or plots19,23,29 that the Pt(111) surface has much higherj0 than the other two low index crystal surfaces of Pt since theΔGH(θ) values for Pt(111) surface are closer to zero. The pre-vious volcano relations omitted or improperly treated the cover-age effect on the adsorption energy and did not realize thepossible changes in the reactive sites and the adsorption isothermfrom 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 areenclosed with (111) and (100) facets and edge atom rows thatare thought to be similar to the topmost rows on (110)surface.2,3,5 As the particle diameters are smaller than 8 nm, thefraction of the edge atoms increases pronouncedly with thedecreasing particle size (Figure s2b of the Supporting In-formation). If simply considering that the edge atom rows onfcc Pt nanoparticles are similar in structure to the top atom rowson Pt(110) surface, one may at first glance think that j0 wouldincrease with the decreasing Pt particle sizes based on the Ptsurface structure dependence of j0 estimated above since theatom number ratio of the (100) facet and edge atoms to the lessactive (111) facets increases with decreasing particle size(Figure 6). Such a positive size effect in turn suggests that Ptcatalysts on the anode of fuel cells should be made as small aspossible until the occurrence of the quantum size effect, whichsimultaneously increase the surface area per mass of Pt and theactivity per surface area. However, this will be found to be nottrue when further considering the reactive site difference onvarious single crystal surfaces of Pt. As indicated in the aboveDFT calculations, the reactive sites of HERs on the extendedPt(110) surface at the equilibrium potential would the long-bridge sites between the nearest neighbor atom rows or the (111)microfacet sites and the valley sites if the Pt(110) surface has amissing row structure. These sites are absent for nanoparticleedges. Thus, H adatoms would be adsorbed on atop sites onnanoparticle edge atom rows after the short bridge sites arenearly completely occupied. As shown in the inset of Figure 4, the

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.

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zero value ofΔG2(θ) occurs at a coverage of ca. 0.05ML for suchtop H adatoms. On this basis, we may conclude that the values ofj0 for different surface atoms on Pt nanoparticles follow the orderthat (100) facet > (111) facet ≈ edge (Figure 3). As shown inFigure 6, the atom number ratio of the (100) facets to (111)facets plus edges decreases with decreasing particle size, and anegative particle size effect of Pt on j0 thus would be expected;that is, j0 decreases with the decreasing size of the Pt nanoparticlecatalyst.

4. SUMMARY

This work has presented a theoretical scheme to understandthe surface structure and particle size effects of Pt in hydrogenelectrocatalysis. Through rigorous thermodynamic and kineticanalysis, we have established a volcano relation between theexchange current density (j0) of HERs and the surface coverageof reactive H atoms at the equilibrium potential (θ0), whichallows distinguishing the activity of catalytic surfaces located nearthe apex of the volcano plots for HERs more accurately than theso-far reported ones. It is demonstrated that the nature and thecoverage of the reactive H adatoms at a catalytic surface at theequilibrium potential of HERs can be deduced from the DFT-calculated adsorption isotherm. The main results and conclu-sions are detailed as follows.(i) According to the theoretically derived volcano relation,

catalytic surfaces with θ0 values closer to 0.5 ML wouldhave higher value of j0.

(ii) According to the DFT calculated adsorption isotherms,the reactive H atoms at the equilibrium potential of HERsare 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 onPt(110) surfaces (or those adsorbed at the (111) micro-facet and valley sites on the missing row Pt(110) surface).The calculated θ0 values for these H adatoms suggest thatj0 for HERs on Pt (110) and Pt(100) surfaces are similarto each other, which are nearly two times higher than thaton Pt(111) surfaces.

(iii) Although the individual edge atom rows on fcc metalnanoparticles are similar in structures to the top atomrows on the corresponding (110) surfaces, the cata-lytic properties of the nanoparticle edges are notsimply equivalent to the extended (110) surfacesdue to that some adsorption sites for reactive inter-mediates could be absent at nanoparticle edges, forexample, the long-bridge sites on Pt(110) surfacefor HERs.

(iv) The reactive sites on the edge of Pt nanoparticles forHERs are found to be the top sites. The calculated θ0

value suggests that the activity of the Pt nanoparticleedges for HERs is similar to the (111) facets but muchlower than the (100) facets. According to the particle sizedependent surface atom distributions, a negative particlesize 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 under-

standing the origin of the surface structure and particle sizeeffects of Pt in HERs, which has been a long-standing problem inelectrochemistry and fuel cells. The methodology and resultspresented in this work may be of general significance in correlat-ing the catalyst performance with their morphologies and sizes. It

has been also demonstrated that not only the thermodynamicadsorption energy but also a detailed nature of the reactive sitesare very important for the proper prediction of activity trends incatalytic and electrocatalytic reactions.

’ASSOCIATED CONTENT

bS Supporting Information. Derivation of the volcano rela-tions, DFT calculation details, and supporting figures. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

’AUTHOR INFORMATION

Corresponding Author*Email: slchen@whu.edu.cn.

’ACKNOWLEDGMENT

This work is supported by the National Natural ScienceFoundation of China (NSFC No. 21073137), the FundamentalResearch Funds for the Central Universities, and the StateEducation Ministry of China under the program for NewCentury Excellent Talents in Universities of China (NCET-06-0612).

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