Understanding Strain and Ligand Effects in Hydrogen Evolution over

Article pubs.acs.org/JPCC

Understanding Strain and Ligand Effects in Hydrogen Evolution over Pd(111) Surfaces Tuhina Adit Maark and Andrew A. Peterson* School of Engineering, Brown University, Providence, Rhode Island 02912, United States ABSTRACT: Pseudomorphic catalytic systems can exhibit enhanced or inhibited activity relative to the pure surface parent metal, based on a combination of strain and ligand effects. In contrast, mechanically strained and dealloyed systems can exhibit pure strain effects. Density functional calculations for hydrogen adsorption at different coverages between 0.25 and 1 monolayer on biaxially strained Pd(111) are carried out to illustrate its differing catalytic behavior for the hydrogen evolution reaction (HER) in comparison to selected pseudomorphic Pd overlayers (Pd/M). The separation of the ligand and strain effects present in Pd/M pseudomorphs and the consequent modification of the binding strengths caused by them individually are estimated. The strain exhibits a systematic contribution to binding energy changes while the ligand effect can act to either intensify or weaken the strain effect. In certain systems (e.g., Pd/Ir) the ligand effect is more pronounced than the strain effect while in others (e.g., Pd/Au) the strain effect is larger. The individual contributions of strain and ligand effects to shifts in the d-band center are also calculated and found to correlate well with the observed binding energy changes. We suggest that in the absence of a ligand effectas would be expected in mechanically strained Pd (111)H binding is tunable, and a differential free energy of hydrogen adsorption of ∼0 eV (at 0 V vs RHE) is achieved at various combinations of strain and coverage. For pure Pd under compressive strain, this leads to a prediction of a broad region of enhanced activity for the HER which may compare favorably to Pd overlayers supported on more expensive metals such as Pt and PtRu.

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INTRODUCTION The use of strain to affect the activity of heterogeneous catalysts has attracted attention for its ability to tailor the reactivity of catalytic surfaces.1−30 A popular strategy to create such catalytic surfaces is through the formation of a pseudomorphic overlayer in which atoms of the catalytically active element (e.g., Pd) are present in a thin layer on a substrate with a differing lattice constant (e.g., Ir).31 Pd overlayers, supported over transition metals and their alloys, have been widely studied with regard to their reactivities toward H, CO, H2, and CO2 adsorption,32−35 the oxygen reduction reaction,36 acetylene cyclization,37 ethylene hydrogenation and dehydrogenation,38 and formic acid oxidation.39 When the overlayer is thin enough (e.g., up to about five monolayers5), the overlayer adopts the lattice structure of the substrate, inducing either tensile or compressive strain in the surface metal. Electronic structure calculations have shown that the resultant change in the metal− metal bonding distance compared to in bulk shifts the position of the central moment of the d-band (the d-band center, εd).35,40,41 The direction of this shift affects the interaction strength between the metal d states and the molecular orbitals of the adsorbates and therefore the chemisorption energies. Such correlation between the catalytic activity of Pd overlayers and εd has been validated for the electrochemical hydrogen evolution reaction.42 A volcano curve was obtained when experimentally measured exchange-current densities were plotted as a function of the calculated hydrogen adsorption © 2014 American Chemical Society

energies; these hydrogen adsorption energies were then correlated to the shift in the d-band center of the Pd overlayer structures. However, in metal overlayers a portion of the changes in the d-band properties are also due to the interaction of the surface metal atoms with the underlying substrateknown as the ligand effect.7 Kitchin et al.8 examined Pt(111) surfaces modified by subsurface 3d transition metals, wherein the subsurface atoms were strained but not the Pt(111) surface. The weakening of the hydrogen and oxygen adsorption energies was attributed to purely the ligand effect. Via a combined experimental and theoretical study of CO adsorption5 on up to 30 layers of Pt deposited on Ru(0001) it was demonstrated that the ligand effect of the substrate dominates for one to three Pt monolayers while the strain effect remained intact and decreased when the number of Pt layers became ≥5. New experimental techniques are identifying means to induce strain in catalytic materials.17,21,24,27 Strasser et al.21 have demonstrated a high electrocatalytic activity for the oxygen reduction reaction (ORR) of PtCu@Cu nanoparticles by dealloying the Pt−Cu shell. The enhanced activity was attributed to a 4−4.5% compressive strain induced modification of εd which weakened adsorption energies of the reactive Received: December 10, 2013 Revised: January 24, 2014 Published: January 30, 2014 4275

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intermediates relative to unstrained Pt and placed their material at the top of the “volcano” plot of activity. Importantly, this approach may have closely approximated a pure strain effect, as the dealloyed Pt shell was estimated to be 0.6−1.0 nm thick, equaling three or more Pt-rich layers versus a monolayer, presumably leading to a negligible ligand effect. Recently, Deng et al.43 have presented an experimental approach by which the effect of strain on reaction rate can be isolated as well as quantified. They performed experimental insitu monitoring of strain-induced reactivity modulation of Au and Pt electrodes for the hydrogen evolution reaction. In this work, the Au or Pt electrocatalyst was sputtered onto a polyimide substrate to which the strain was applied. Techniques such as this, and others in development, have the potential to produce stressed surfaces in which the strain is a “tunable” parameter and the ligand effect is largely absent. In order to understand the optimal use of such systems, a knowledge of the differing magnitudes of the strain and ligand effects individually is paramount. In the present work, we use electronic structure calculations to investigate the effect of mechanically induced strain on hydrogen binding energies over Pd(111) surfaces in comparison to pseudomorphic Pd overlayers (Pd/M). Pd/M systems in which the metal substrate is strained to adopt the Pd lattice constant are employed to clearly understand how distinctly the strain and ligand effects act. Additionally, we lay the groundwork for what can be expected in purely strained materials. Recently, Qi and Li44 have predicted from a meanfield microkinetic model of ORR on Pt(111) and (100) a flattening of the catalytic activity versus adsorption strength volcano plot due to enthalpic effects arising from lateral repulsions between surface adsorbates at high coverage and due to entropic effects from site competition. Therefore, herein, we also examine the effects of coverage and show that a high catalytic hydrogen evolution reaction (HER) activity can be expected at different strains, perhaps widening the volcano peak in mechanically strained Pd systems.

Figure 1. Geometric structures of the 2 × 2 × 4 slabs of (a) pure Pd(111) surface, (b) Pd/M pseudomorphic overlayers, and (c) 1.0 ML H-adsorbed Pd(111) surface.

The choice of number of layers in the slab was based on convergence of adsorption energy of H (ΔEH) on the most favored adsorption site, fcc. The calculated ΔEH is −0.39, −0.44, −0.42, −0.44, and −0.42 eV for number of Pd layers = 3, 4, 5, 6, and 8, respectively, in the model. Increasing hydrogen coverages (θH) of 0.25, 0.5, 0.75, and 1.0 ML are considered. For each coverage adsorption of H atoms is examined at varied combinations of the three adsorption sites, i.e., on-top, fcc, and hcp. Adsorption at bridge side did not yield a minima and was therefore discarded thereafter. The strongest H binding energies for every θH were found when each H atom was adsorbed on a fcc site. Thus, for all further calculations adsorption is taken into account at fcc site only. Figure 1c displays such a H-adsorbed Pd(111) surface for a coverage of 1.0 ML. The pseudomorphic Pd overlayers (Pd/M for M = Rh, Ir, Au, and Pt) were similarly constructed, i.e., (2 × 2 × 4) metal substrate M(111) slabs and a 10 Å vacuum, in which the top layer of M atoms was replaced by Pd atoms to form a monolayer (see Figure 1). The RPBE-calculated lattice constants employed were 3.85 Å for Rh, 3.87 Å for Ir, 4.02 Å for Pt, and 4.20 Å for Au. As in the case of Pd(111) the top two layers were allowed to relax. However, in the calculations pertaining to (a) determination of the individual contributions of strain and ligand effects to the combined ligand + strain effect and (b) finding the extent of ligand effect in PdNlay/Ir systems (for Nlay = 1, 2, and 3), only the top layer in each bare surface was allowed to relax to maintain cohesivity. In order to make a direct comparison with Pd/M pseudomorphs, strained Pd(111) surfaces were generated by applying an in-plane uniform biaxial strain (ex = ey) between ±5% and including the induced out-of-plane relaxation along the [111] direction (ez). ez was determined based on the Poisson ratio for Pd evaluated from the elastic constants c11, c12, and c44 as

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COMPUTATIONAL METHODS All calculations have been performed using the open-source plane-wave density functional theory code DACAPO with atomistic manipulations managed in the Atomic Simulation Environment (ASE).45,46 Vanderbilt ultrasoft pseudopotentials47 were implemented, and the exchange-correlation energy and potential were described using the revised Perdew−Burke− Ernzerhof (RPBE) functional.48 For all surface calculations a 4 × 4 × 1 Monkhorst−Pack k-point mesh was used along with plane wave and density cutoff energies of 340.15 and 500.00 eV, respectively. To obtain the d-band center and width, density of states was calculated (DOS) for a Pd atom belonging to the top layer of the slab at a higher accuracy with 6 × 6 × 2 k-points using a cutoff radius of 1.0 Å. The d-band center was derived as the average energy of the d-band: εd = ∫ ρE dE/∫ ρ dE. As shown in Figure 1, the Pd(111) surface was modeled as a 2 × 2 (atoms) periodic slab four layers thick and with 10 Å of vacuum between slabs. Of the four layers, the top two were allowed to relax and the bottom two were fixed at their bulk DFT (RPBE)-calculated lattice constant of 4.016 Å. H adsorption was allowed on only one of the two exposed surfaces, and a dipole correction was implemented at the farthest point in the vacuum to account for this nonsymmetry.

ez /ex = −2(c11 + 2c12 − 2c44)/(c11 + 2c12 + 4c44)

(1)

Accordingly, at each strain the interlayer distance between the lower two layers of the slab was fixed. The elastic constants were separately computed for bulk Pd using the RPBE functional, plane-wave cutoff 650 eV, density cutoff 800 eV, and 8 × 8 × 8 k-points. The bulk DFT (RPBE)-calculated lattice constant of PdH is 4.189 Å. For a biaxial strain (ex = ey) along the (001) crystal axis the induced out-of-plane relaxation along the z-axis (ez) in both strained bulk Pd and PdH was also determined from the elastic constants c11 and c12 as ez /e x = −2c12/c11 4276

(2)

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KINETIC MODEL The overall hydrogen evolution reaction is H + + e− →

1 H2 2

(3)

We start by considering the Volmer−Tafel mechanism for HER over Pd metal: H+ + e− + ∗ → H∗

(4)

2H∗ → H 2 + ∗

(5)

where ∗ is an available adsorption site and H∗ represents an H atom adsorbed on the surface. Based on a simple kinetic model introduced by Nørskov et al.,49 when reaction 3 is in equilibrium the exchange currents of the forward and backward reactions are equal, such that i0 = i+,eq = |i−,eq| = −er0

(6)

The rate r0 can be obtained from the rates of either eqs 4 and 5. Based on the former r1 = k1(1 − θH)c H+

(7)

where k1 is the rate constant, cH+ is concentration of protons, and θH = exp(−ΔGH/kT)/(1 + exp(−ΔGH/kT)). In the case of ΔGH < 0, k1 is independent of ΔGH and can be written as k1 = k0. Then the hydrogen evolution exchangecurrent density in eq 6 becomes i0 = −ek 0[1/(1 + exp(−ΔG H /kT )]

(8)

where e is the charge on an electron and k is the Boltzmann constant. But for ΔGH > 0, k1 will be associated with k0 by a factor that exhibits its dependence on ΔGH so that i0 = −ek 0[exp(−ΔG H /kT )/(1 + exp(−ΔG H /kT )] −1

(9)

−1

From refs 42 and 49 k0 is taken as 200 s site , and the average total site density for the metals is 1.5 × 1015 cm−2. Equations 7 and 8 show that the volcano peak occurs when ΔGH ∼ 0. In the above equations we have calculated free energies of H adsorption for different coverages (θH = 0.25, 0.5, 0.75, and 1.0 ML) ΔGH(θH) based on the computational hydrogen electrode model50 as ΔG H(θH) = ΔE H(θH) + ΔEZPE − T ΔSH + ΔG U

Figure 2. Free energy diagram for hydrogen evolution (at U = 0 V RHE) over (a) −2.5% strained, (b) −3.5% strained, and (c) −5% strained Pd(111) at θH = 0.25, 0.5, 0.75, and 1.0 ML.

(10)

computational hydrogen electrode model.50 Under the lowcoverage limit of 0.25 ML, it is evident from Figure 2 that at each strain the first step of H∗ formation is downhill, but the H2 evolution step is uphill in free energy. Overall increasing θH shifts the position of H∗ state upward such that step 1 of the mechanism becomes uphill for −3.5% strained Pd(111) at θH = 1.0 ML and for −5% strained Pd(111) at θH = 0.75 and 1.0 ML. In comparison for −2.5, −3.5, and −5.0% strained Pd(111) ΔGH ∼ 0 eV occurs at θH = 1.0, 0.75, and 0.5 ML, respectively and these states will be the first to get activated. This suggests the existence of such high hydrogen coverage states at these strains. Variation of Differential Free Energy of H Adsorption with Strain. Figure 3 displays the results of our calculations for the variation of ΔGH of Pd(111) surface with uniform in-plane biaxial strain at increasing coverages. It can be seen that irrespective of coverage, compression weakens hydrogen adsorption strength and expansion makes it stronger. But for θH = 0.25 ML ΔGH is < 0 at all strains and H adsorption is

where the electrical potential is introduced as ΔGU = −eU. A pH correction is unnecessary as the reversible hydrogen electrode (RHE) is used. The free energy diagrams are constructed for U = 0 and using ΔEZPE − TΔSH = 0.24 eV at 298 K, as taken from ref 49 in eq 10. ΔEH is the differential adsorption energy for hydrogen obtained as total energy differences: ΔE H(θH) = E[nH∗] − E[(n − 1)H∗] −

1 E[H 2] 2

(11)

where n = 1, 2, 3, and 4 H atoms for θH = 0.25, 0.5, 0.75, and 1.0 ML, respectively, and each H atom is adsorbed on a fcc site.

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RESULTS AND DISCUSSION Free Energy Profiles under Strain. Calculated free energy diagrams for hydrogen evolution (at a potential of U = 0 V RHE) over selected compressed Pd(111) surfaces at these four θH are illustrated in Figure 2, with free energies based on the 4277

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the same strain as their Pd/M counterparts, in which only strain effect is present, and (iii) hypothetical Pd/M overlayers where the metal substrate is at the lattice constant of Pd, in which only the ligand effect is active while the strain effect on Pd is absent. These are referred to as “Ligand + Strain”, “Strain”, and “Ligand”, respectively. Hydrogen adsorption at a coverage of 0.25 ML only was considered. The corresponding ΔGH values relative to that of unstrained Pd(111) are plotted in Figure 4. It

Figure 3. Differential free energy of hydrogen adsorption on Pd(111) at various coverages and pseudomorphic Pd overlayers (Pd/M) at 0.25 ML hydrogen coverage as a function of biaxial strain. θH = 0.25, 0.5, 0.75 and 1.0 ML are represented as 1/4, 2/4, 3/4 and 4/4, respectively. Pd/M systems are plotted at strains based on the mismatch between RPBE lattice constants of Pd and the metal substrates, except for PtRu alloy for which PW91 value is used from ref 51 and its corresponding data point is taken from ref 42. The dashed arrows show the deviation between ΔGH of pseudomorphic Pd overlayers and strained Pd(111) at the same strain and hydrogen coverage (0.25 ML).

strong. At −5.0% strain the exchange-current density i0 is calculated to be only 3.02 mA cm−2. Increasing the coverage weakens the H binding at each strain, in some cases causing ΔGH to even become positive. Data for pseudomorphic Pd overlayers at θH = 0.25 ML are also plotted in Figure 3 at strains based on the mismatch between lattice constants of Pd and the metal substrate. For Pd/Au the ΔGH value is similar to that of an equally expanded Pd(111) for the same coverage. But the ΔGH of all other Pd/M systems are much greater than that of a similarly strained Pd(111) as is evident from the dashed arrows in the figure. It can thereby be inferred that in these Pd overlayers the H binding is significantly weaker than the strained Pd(111) counterparts. Pd/Pt is an interesting case as it corresponds to an expansion of 0.1% but unlike Pd/Au (4.6% expansion) has a weaker hydrogen adsorption strength than the unstrained Pd(111) at θH = 0.25 ML. This clearly indicates that the ligand effect plays a strong role in affecting the ΔGH of Pd pseudomorphs. Separating Strain and Ligand Effects. Kitchin and coworkers7 have previously explained the ligand and strain effects by incorporating suitable terms into the interatomic matrix element (V) which describes the bonding between the metal of interest and its environment. It is predicted that for a smaller V, the d band is narrower, and the d band is shifted up in energy relative to the bulk. For a larger V, it is the opposite and d band is shifted down in energy. Pašti et al.52 in their DFT (GGAPBE) study of hydrogen adsorption on Pd and Pt overlayers have attempted to separate the ligand and strain effects. For the former they inserted a monolayer of the metal substrate under the first surface layer of Pd and Pt in the pure slabs, forming subsurface alloys. For the latter they have used double monolayers of Pd and Pt on the M(111) substrates. Furthermore, they considered hydrogen adsorption on both sides of the slab. Herein we employ a different approach to directly quantify the large ligand effect by examining three types of systems: (i) real Pd/M overlayers where Pd adopts the lattice constant of M and the ligand and strain effects act simultaneously, (ii) pure Pd(111) surfaces biaxially strained at

Figure 4. (a) Relative differential free energies of hydrogen adsorption at θH = 0.25 ML and (b) relative d-band centers of pure Pd (111) biaxially strained at the same strain as the corresponding true Pd/M system and hypothetical Pd/M systems in which the metal substrate has the lattice constant of Pd. These are represented Strain, Ligand, and Strain + Ligand, respectively, in the figures. The free energies and d-band centers are plotted relative to the corresponding value of unstrained Pd (111).

is easily noticeable that the combined heights of the Strain and Ligand bars agree reasonably with the height of the corresponding Strain + Ligand bar, showcasing that individual ligand and strain effects on hydrogen binding are approximately additive to the full effects in the true pseudomorphic Pd overlayers. Depending upon the type of strain applied (expansive or compressive), the H binding is strengthened or weakened relative to the unstrained Pd(111). But irrespective of the ligand, ΔGH is always shifted up by the ligand effect in these metal pairs. In the case of Pd/Au the strain effect is the dominant effect and overall hydrogen adsorption is strengthened. The opposite of this occurs in Pd/Pt due to their similar lattice constants: the ligand effect is dominant, and ΔGH is positive. In Pd/Rh and Pd/Ir both the strain and ligand effects shift up ΔGH, and the prominence of the ligand effect leads to a greater weakening of H binding than expected from a pure strain effect. It is noticeable from Figure 4a that the ligand and strain effects are additive, but not exactly quantitatively. This is understandable because in the hypothetical Pd/M pseudomorphs even though the Pd layer experiences only ligand effect, the M atoms in the substrate themselves are strained to have 4278

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Figure 5. (a) Variation of differential free energy of hydrogen adsorption of strained Pd(111) and pseudomorphic Pd overlayers (Pd/M) as a function of the shifting d-band center (εd). (b) Hydrogen evolution exchange-current density i0 (on a logarithmic scale) as a function of biaxial strain at various coverages. θH = 0.25, 0.5, 0.75, and 1.0 ML are represented as 1/4, 2/4, 3/4, and 4/4, respectively. We have elected to remove the data point for d-band center of Pd/PtRu from (a) from ref 42 due to its outlier nature, and we do not wish to overstate what may be study-to-study variations. In (b) the data point for Pd/PtRu is taken from ref 42, and values for pseudomorphic Pd overlayers are plotted at strains based on the mismatch between RPBE lattice constants of Pd and the metal substrates, except for PtRu alloy for which PW91 value is used from ref 51.

of Ir from one to three. Convergence of ΔGH with that of the unstrained pure Pd(111) would be an indicator of where the ligand effect ceases to exist. At θH of 0.25 ML the ΔGH when Nlay = 1, 2, and 3 was calculated to be −0.007, −0.153, and −0.204 eV, respectively. The last value for Nlay = 3 agrees excellently with ΔGH (−0.203 eV) of the unstrained pure Pd(111). One can thereby infer that the extent of ligand effect in Pd/M overlayers on HER may be reduced by adsorbing 2.0 ML of Pd or fully negated by employing ≥3.0 ML of Pd on the metal substrate. This is in agreement with earlier reports of Pt deposited on Ru, showing the vanishing of substrate effect for three Pt monolayers with regard to its activity toward CO adsorption5 and ORR.26 HER Activity under Mechanical Strain. Figure 5a depicts the variation of the differential free energy for hydrogen adsorption of the strained Pd(111) and pseudomorphic Pd overlayers with the d-band center. For both systems, in agreement with the d-band theory as εd shifts up in energy on expansion, the H binding strengthens, and when εd moves down in energy on compression, ΔGH weakens. It is noticeable that the ΔGH variation of the mechanically strained Pd(111) with εd at each hydrogen coverage is smooth and monotonic, showcasing the (apparent) ease of stress control of the hydrogen evolution reaction. It can be observed from Figure 3 that ΔGH of Pd(111) at (a) 1.0 ML and −2.5% strain, (b) 0.75 ML and −3.5% strain, and (c) 0.5 ML and −5.0% strain is calculated to be ∼0 eV. A direct consequence of this is the prediction of a peak in the hydrogen evolution exchange-current density, shown in Figure 5b, at these strains and coverages similar to the case of pseudomorphic Pd overlayers at Pd/PtRu at θH = 0.5 ML. Clearly, this predicts that the HER will be enhanced under compressive strain but also predicts a broad range of strains at which HER will have similar high activity. In our computations we have examined four discrete hydrogen coverages leading to a jaggedness in the region of peak activity. However, during experiments the coverage effects may be more complex than in the simple 2 × 2 atom unit cell. So we expect that experimentally the changes in strain will lead to smoother variations in coverage than from computations. Thus, an experimental HER activity plot for Pd as a function of compressive strain with a broadened volcano peak will likely be

the same positions as the unstrained Pd atoms. For M = Pt the strain felt by it is small (−0.1%), the hypothetical Pd/Pt is more representative of the actual ligand effect in the true Pd/Pt, and the two effects add up to give the full ligand plus strain effect. But when M = Rh, Ir, or Au, the strain felt is quite significant: 4.3, 3.2, and −4.4%, respectively, and some differences in additivity of strain and ligand effects are observed. To assess the electronic origin of these phenomena in terms of the d-band model,40 the varying behaviors of the strain (S), ligand (L), and ligand + strain (L + S) effects were also analyzed in terms of the shifts in d-band center relative to that of the unstrained Pd(111). Figure 4b shows that on expansion (compression) εd shifts up (down), and except for Pd/Au, L effects shift the εd down. The modification of εd due to combined individual L and S effects approximately equal the shift due to the L + S effect in Pd/M systems. With the exclusion of Pd/Au where S effect dominates, clearly, without inclusion of L effects εd’s of biaxially strained Pd and Pd overlayers would be different from each other. The ligand-induced effect on εd can be understood as follows. As mentioned earlier according to Kitchin et al.,7 the d-band width is known to be directly related to the interatomic matrix element (V). In the hypothetical Pd/M pseudomorphs V is reflective of the interaction between d-bands of Pd and M substrate. The closer the d-band centers of the two metals, the stronger will be their interaction. As in Pd/M the M is strained to have the same lattice constants as Pd (aPd), in order to obtain the appropriate εd’s, we perform density of states calculations for pure M(111) surfaces constructing using aPd. The εd’s thereby calculated are −3.31, −1.70, −1.29, and −1.09 eV for Au, Pt, Ir, and Rh, respectively. As d-band center of Pd is −1.33 eV, this suggests the following the order of strength of Pd−M interaction and consequently of V and the d-band width: Pd−Ir > Pd−Rh > Pd−Pt > Pd−Au. The more wide the d-band, the more downshifted will the εd be in energy and greater will be the weakening of H adsorption energy. This explains the exhibited trend in Figure 4 of the relative changes in d-band center and ΔGH: Pd−Ir > Pd−Rh > Pd−Pt > Pd− Au. To determine how far the ligand effect on HER is felt, we further investigated the hypothetical Pd/Ir pseudomorph by progressively increasing the number of Pd layers (Nlay) on top 4279

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The Journal of Physical Chemistry C much smoother than the strongly jagged one illustrated in Figure 5b. It is known that even under low hydrogen pressures and room temperatures Pd metals can absorb hydrogen to form Pd hydride, which can in turn affect its activity. Though an indepth study of this topic is outside the scope of this work, we have evaluated formation energies (ΔEf) for bulk PdH from Pd and H2 at biaxial compressive strains along the crystal axes. At 0%, −1.5%, −2.5%, −3.5%, and −5.0% strain ΔEf(PdH) is −0.034, −0.033, −0.031, −0.029, and −0.024 eV, respectively. In a previously reported study,53 free energies for 1 ML hydrogen absorption in Pd(111) and Pdn/Au(111) (n = 2−4) have been calculated from DFT. Values of −0.029 and −0.050 eV were obtained for octahedral and tetrahedral absorption, respectively, in Pd(111). In comparison, the absorption energies for Pdn/Au(111) overlayers were much more favorable (−0.192 to −0.256 eV) as in these systems the lattice of Pd was expanded. From the above discussion it can be inferred that increasing compressive strain will cause hydrogen absorption in Pd(111) to become more difficult. Further, Johansson et al.54 have considered H adsorption on Pd(111) and Pd hydride surfaces for different H coverages. Using DFT calculations, they showed that at θH = 1.0 ML, which is representative of experimental conditions, differential adsorption energy of Pd hydride differed by a small amount of 12.3 kJ/mol H2 or 0.064 eV/H atom only from that of Pd(111). This suggests that in the eventuality of formation of Pd hydride ΔGH ∼ 0.0 eV may be achieved at lower compressive strains and may thereby aid hydrogen evolution activity. It will be interesting to see whether this is borne out experimentally.

ACKNOWLEDGMENTS

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REFERENCES

This material is based upon work supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under the Multi University Research Initiative MURI Grant W911NF11-1-0353 at Brown University. The authors thank our collaborators on the program, especially Bill Curtin, Michael Francis, and Pradeep Guduru, for fruitful discussions. Electronic structure calculations were carried out at the Brown University Center for Computation and Visualization (CCV).

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CONCLUSIONS In conclusion, our study has shown that there is a linear relation between biaxial strain and differential free energies of hydrogen adsorption (ΔGH) of Pd(111). Individual strain and ligand effects were illustrated to add up to the combined strain and ligand effects in pseudomorphic Pd overlayers. The relatively weaker effect of compression than pseudomorphic Pd overlayers can lead to demonstration of ΔGH ∼ 0 eV at different combinations of strains and hydrogen coverages. The results presented above predict the existence of high hydrogen coverage states at compressive strains and achievement of a maximum in the exchange-current density for hydrogen evolution for those cases. The variation in ΔGH was attributed to the change in position of d-band center (εd) of Pd(111) with strain. Furthermore, the systematic shifts in the εd’s of Pd(111) on compression/expansion and the resulting smooth variance of hydrogen adsorption strengths suggest use of mechanical strain for the more systematic “tunable” enhancement and controllability of the catalytic activity of Pd(111). This implies that the more abundantly available55 Pd under compression is predicted to exhibit similar activity to Pt or Pd/PtRu systems which require the more expensive and limited in supply Pt.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel 401 863-9045 (A.A.P.). Notes

The authors declare no competing financial interest. 4280

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