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Surface Tension Effects on the Reactivity of Metal Nanoparticles Lin Li, Frank Abild-Pedersen, Jeffrey Greeley, and Jens K. Norskov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b01746 • Publication Date (Web): 04 Sep 2015 Downloaded from http://pubs.acs.org on September 9, 2015

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The Journal of Physical Chemistry Letters

Surface Tension Effects on the Reactivity of Metal Nanoparticles Lin Li1, Frank Abild-Pedersen2, Jeff Greeley3, Jens K. Nørskov1,2* 1

SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering,

Stanford University, Stanford, CA 94305, USA 2

SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory,

2575 Sand Hill Road, Menlo Park, California 94025, USA 3

Department of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West

Lafayette, Indianapolis 47907, USA Corresponding Author E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT We present calculated adsorption energies of oxygen on gold and platinum clusters with up to 923 atoms (3 nm diameter) using Density Functional Theory. We find that surface tension of the clusters induces a compression, which weakens the bonding of adsorbates compared to the bonding on extended surfaces. The effect is largest for close packed surfaces and almost nonexistent on the more reactive steps and edges. The effect is largest at low coverage and decreases, even changing sign, at higher coverages where the strain changes from compressive to tensile. Quantum-size-effects also influence adsorption energies but only below a critical size of 1.5 nm for platinum and 2.5 nm for gold. We develop a model to describe the strain-induced size effects on adsorption energies, which is able to describe the influence of surface structure, adsorbate, metal, and coverage.

TOC GRAPHICS

KEYWORDS Heterogeneous catalysis, DFT, Finite-size effects.


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One of the fundamental questions that has been a source of discussion in the field of heterogeneous catalysis for decades is the role of finite size effects.

Catalysts are often

nanoparticles supported on high surface area materials, and a key question is to what extent the surface chemistry is affected by the size of the nanoparticles1–3. This, for instance, determines whether data and understanding from single crystal surface studies are directly relevant to an understanding of high surface area catalysis. Finite size effects can be categorized into two main classes. The first can be characterized as intrinsic effects, relating to finite size effects of isolated nano-particles. The second is related to effects due to the support. In the present letter, we address the intrinsic effects of transition metal nanoparticles using very large-scale electronic structure calculations, allowing us to treat Au and Pt particles up to 3.4 and 3.2 nm in diameter, respectively. In particular, we show that on top of quantum size effects due to changes in electronic structure for particles below ca. 2 nm in diameter, we can quantify an effect that is related to the size dependence of surface relaxations due to surface tension. We show a substantial effect for low coverage adsorption on close packed surfaces. We also show that adsorption at edge sites, which are often responsible for the catalytic activity of nanoparticles, are hardly affected by surface relaxation size effects and that the effect on the facets is strongly dependent on the adsorbate coverage. We develop a model of these effects, addressing the size, adsorbate, coverage, and catalyst dependence. We will concentrate first on Pt and Au cuboctahedral clusters ranging from 13 to 923 atoms. There are experimental data showing strong size effects for these metals. In experiments on platinum, Mayrhofer et al. observed an increase in the binding strength of oxygenated species with decreasing particle size4,5. On < 4 nm platinum clusters, Maillard et al. have measured lower mobility of adsorbed CO with decreasing size, suggesting stronger CO binding on small


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metal clusters compared to the extended crystal surface6. The same trend is observed on gold. Bondzie et al. have shown that heat of adsorption of oxygen is higher on gold clusters compared to bulk surfaces7,8. In addition, Lemire et al. have demonstrated that the adsorption of CO on gold is stronger on small clusters at low temperatures9. Although the adsorption bond of small molecules generally appears to strengthen with decreasing cluster size, one exception to this trend is the adsorption on CO on palladium. Flores-Camacho et al. have observed CO bonding to palladium to weaken with decreasing size10. We first consider quantum size effects due to the fact that the electronic spectrum of small metal particles becomes discrete. This is best captured theoretically by studying the variation in chemical activity as a function of particle size for a fixed structure, that is, no relaxations included in the metal particle11. For simplicity and consistency, we have chosen cuboctahedral particles for the study even though these are not the observed structures under experimental conditions. In other words, using more realistic shapes based on Wulff-construction results in differently shaped cluster facets at different sizes, due to discretization at this length scale. In order not to overlook the importance of cluster shape, we extrapolate the trends found on cuboctahedra to Wulff-shapes. We measure the chemical activity by calculating the adsorption energy of primarily atomic O. In addition, we investigate adsorption of OH and CO for selected situations to show generality. We use the density functional theory (DFT) and the RPBE exchange correlation functional12, and note here that comparisons to detailed experimental data for the O adsorption energy as a function of coverage on Pt(111) surfaces show our method to describe reality well both in terms of the absolute magnitude of the adsorption energy as well as the coverage dependence13–15.


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Figure 1. Calculated O adsorption energies on clusters and strain-free surface slabs. In panel a) and b) O was adsorbed on the most FCC-like site on each cluster. In panel c), O was adsorbed on the central edge site on each cluster. Solid circles represent calculations that involved geometry optimization for the clusters. The horizontal lines represent the adsorption energies of the corresponding relaxed surface slab. Hollow hexagons represent the difference in calculations between fixed clusters and fixed slabs, referenced to the energies on relaxed surface slabs. In panel a), the data for fixed clusters were take from works of Kleis et al16. The calculated adsorption energy of O on the FCC sites of free-standing Au and Pt clusters are shown in Figure 1a and 1b, whereas the same results for adsorption at an edge site for the Pt clusters are included in Figure 1c. Also included in the Figure is the adsorption energy of O on the same adsorption site on an extended surface – FCC(111) for the close packed facet and the


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stepped FCC(211) surface to model the edge sites. In the case of unrelaxed clusters, it can be seen that the extended surface model limits are reached at 147 and 561 atoms for Pt and Au, respectively. Additional phenomena exist at this size regime. For example, electron spill-out effects were reported to decrease the screening efficiency at the cluster surface16. As a result, adsorbates become more sensitive to the environment near the adsorption site. However, the scope of our study is limited to effects of cluster compression. Next, we include relaxation in the particle before and after adsorption in the calculations. These data are also included in Figure 1. On both metals, the adsorption energies at the facets on clusters appear to converge to a value that is ~ 0.3 eV weaker than on (111) surface. This weakening in the adsorption energy is clearly an effect of geometry relaxation, since the same clusters in fixed geometries converged to the extended surface limit 11,17. For the edge sites on Pt clusters, on the other hand, there is no offset from the extended surface (211) limit, and within the accuracy of the calculations we see no finite size effects at such sites above ca. 2 nm. It has been suggested that the surface strain that results for the surface tension of finite size particles should result in changes in adsorption properties18,19. Small metal clusters are known to contract20–23, and according to the d-band model of adsorption, this contraction should lead to a weakening in adsorption energies on late transition metals24, thus accounting qualitatively for the results we observe in Figure 1. In the following, we propose a model that quantitatively explains the origin of this offset between adsorption on relaxed Pt clusters and the surface limit. We start by comparing the adsorption energies calculated on the Pt561 cluster with those on a Pt surface with an applied strain (-3%) that matches what was found on the cluster surface. At this size, quantum-size effects were shown to be minimal; and by mimicking the strain found on the cluster surface, one could differentiate whether this relaxation-based finite-size effect is long-


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ranged or local to the adsorption site. In Figure 2a, we applied this approach to the binding of oxygen on the same Pt FCC and edge sites from Figure 1. To show generality, we have also calculated the adsorption of CO and OH on both Pt561 and strained Pt(111). It is clear that the model captures both the surface structure and adsorbate dependence quite well. This agreement suggests that, when the clusters are sufficiently large to avoid quantum-size effects, strain alone quantitatively accounts for the difference between adsorption on clusters and on continuous surfaces.

Figure 2. Panel a) shows the surface strain effects on Pt561 cluster versus the strain effects estimated from the continuum model. For each point, the x-value is the difference between adsorption energies calculated using the surface slab and those on freestanding clusters. Each yvalue is the change in adsorption energy on surface slabs, due to the same lateral strain as the Pt561 cluster compression. The red line is the parity line comparing the results from these two methods, and the black line represents results from a traditional surface science model. Panel b) and c) illustrates the impact of surface strain on the adsorption energies on Pt(111), and Pt(211) facets, respectively. DFT calculations were performed on slabs with -3%, 0%, and +3% strain. Adsorption energies are referenced to that of the same adsorbate on the strain-free slab. Now we extend this method of predicting the impact of surface compression beyond a single particle size. Given the locality of strain effects, one could separately describe the particle size


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dependent surface strain, and the strain dependence of the adsorption energy on an extended surface: Δ ≈

Δ

(1)

Here, ∆E(s) represents the change in adsorption energy due to surface strain (s), s(d) represents surface strain on a particle with size (d), and ∆E(d) represents the effect of strain on adsorption energy at particle size (d). For example, combining the strain dependence of adsorption on Pt(111) and Pt(211) with the strain found on Pt561 would yield the results shown on Figure 2a. How adsorption energy changes with respect to strain depends strongly on the adsorbate and the adsorption site, as shown in Figures 2b and c. A comparison of data for FCC (111) and (211) surfaces (close-packed and stepped adsorption sites) shows that the strain effect is much smaller at the steps than on the terraces. The reason is that at the steps, the metal atoms can respond to strain by relaxing parallel to the surface, in and out of the step, and therefore need not get closer to the metal neighbors, which is the effect that leads to d-band shifts and changed reactivity. This explains immediately why the step data in Figure 1c are much less size-dependent than the data for the close-packed surfaces. In the following we shall discuss two approaches to describe strain on a particle as a function of size. First, the classical continuum approach for cluster strain developed after the liquid-drop model proposed by Perdew et al25. The analytical result using this model is shown in Figure 3a (solid black line) and predicts increasing compressive strain for particles smaller than 5nm and convergence to the bulk limit for particles larger than 10nm. In the continuum model, the surface strain is given by the inter-planar distance between opposing (111) facets and it is seen to agree very well with calculated data for clusters up to 3 nm (black triangles) and reported experimental values26 (black circles). In Figure 3b the blue triangles show the calculated intra-planar


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contraction parallel to the (111) surface. Such contractions within the (111) plane introduce a driving force to bend that plane away from the cluster, thus lessening the inter-planar compression. In the second approach, we explicitly account for the contraction within the (111) layer and this results in a convergence towards the bulk limit for cuboctahedral particle structures that is much slower (blue dashed line) than for the continuum model. This approach is described in more detail in the supporting information.

Figure 3. Panel a) shows the continuum model for the inter-planar compression of Pt clusters with size. The triangles are calculated and circles are experimental values. Panel b) shows the intra-planar surface strain. The blue line represents strain on cuboctahedra and red for Wulffshaped clusters. In reality, particle structures are defined by the facet surface energies through a Wulffconstruction scheme and this gives rise to geometries with larger (111) facets than found on


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cuboctahedral particles. Hence, there is a greater number of terrace atoms compared to the edge and corner atoms at a given size on the Wulff-constructed particles. Including this effect, the surface strain is found to converge faster than on cuboctahedral particles, as illustrated in Figure 3b (red dashed line).

Figure 4. Surface stress at the listed coverage, for each (111) slab at its DFT-optimized bulk lattice constant. Panel a) shows the coverage effects of CO on surface stress, and b) shows coverage effects of O. A positive value indicates a favoring towards surface contraction, and negative suggests expansion. Surface stress at the bulk lattice constant was calculated based on the total energies of systems with -3%, 0% and +3% lateral strain. The model described above extends beyond adsorption on clean surfaces. Assuming strain is proportional to stress, one can make a similar strain-continuum model as a function of coverage, based on the strain model for the bare cluster, the stress of the clean surface, and the surface stress at the corresponding coverage. Figure 4a and b show the surface stress on various metal (111) facets under difference surface coverage of CO and O for four different metals. There appears to be a common trend that the surface stress on the clean metal surface is relieved by adsorbates. Above certain coverage, the metal (111) surface prefers lateral expansion, which implies metal clusters would expand relative to the bulk lattice constant at sufficiently high


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coverage. This type of adsorbate-induced expansion is also observed experimentally27,28. This strain-free crossover occurs at different coverage for each combination of metal and adsorbate. For example, on platinum surfaces, there is diminished surface strain around 1/3 coverage for oxygen, but 1/2 coverage for CO. At this coverage, the stress-free cluster geometry is expected to have similar surface metal-metal distance as that of the strain-free slab; therefore, the effects of strain on adsorption energies that we have described above will be eliminated at these coverages. The results presented here suggest the following picture of finite size effects on freestanding metal clusters. Quantum size effects are important for the smallest clusters. For Au that exhibits pronounced shell effects in the s-electron system there are substantial variations up to ca. 2.5nm whereas for Pt, with a large number of d states at the Fermi level, the purely electronic structure effect is small after ca. 1.5 nm. The main result of the present study is the understanding of an additional finite size effect due to surface relaxation. We show that this effect can be quantified as being due to a combination of a size-dependent surface strain of small particles and an intrinsic strain-dependence of the adsorption energy. The latter is strongly dependent on the adsorption site and on coverage. The strongest fine-size effects, however, are related to the fact that the relative number of edge and corner sites increases strongly with decreasing particle size. Except for particles below 1nm the difference between adsorption on low coordinated and planar surface sites is considerably larger that any of the other effects considered here, as shown in Figure 1. An interesting exception is the case of adsorption of CO on palladium, where the binding energies are very similar between edge and FCC sites29. Here the effect of strain could become evident even for the lowest coverages. For the many reactions/catalysts where the active site is at steps or edges30, the strain-induced effects on surface reactivity will be of minor importance. The same is true for reactions on close-


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packed surfaces at medium coverages. At higher coverages, we identify a new size-dependent contribution to the adsorbate-adsorbate interactions, which is worth a systematic study by itself. We conclude on this basis that for a number of situations, data from studies of extended surfaces have direct quantitative relevance to understanding reactions on small particles. There are, however, exceptions: reactions taking place a low coverage on the most close-packed facets. Even here we do, however, expect that trends from one catalyst to the next will be well described by results from more extended surfaces. The present results are for un-supported clusters. To describe heterogeneous catalysis one would need to include the effect of the support on strain. Most likely the interaction with the support will constrain the active nano-particles and reduce the effect of strain, but this is an area where more quantitative studies are needed. Finally, to obtain a complete picture of strain effects one would need to include finite-temperature effects. Generally, relaxation effects are lifted by anharmonic (thermal expansion) effects at higher temperature31, and this will likely reduce the finite size effects discussed here. 22,28,32,33


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The systems investigates are platinum and gold cuboctahedron clusters ranging from 13 to 923 atoms, as well as platinum, gold, palladium and copper surface slabs. Adsorption energies on clusters were calculated at the local coverage limit of one adsorbate per cluster. For oxygen adsorption on the FCC site, the low coverage limit of 1/16 ML coverage was calculated on a sixlayer 4x4 (111) surface computation cell. Calculations probing the effects of surface strain and surface stress are carried out on six-layer 2x2 (111) facets and six-layer 2x3 (211) facets. Surface slabs of platinum, gold, palladium, and copper were constructed using the lattice constants 3.999 Å, 4.219 Å, 4.034 Å, and 3.721 Å, respectively. In all surface slab calculations, the top two layers of the metal were allowed to relax, 10 Å of vacuum was added in the z-direction, and periodic boundaries were applied in the x and y-direction. For each slab calculation, the Brillouin zone was sampled using the Monkhorst-Pack scheme, with 4x4x1 k-points, and the Fermitemperature was set to 0.1 eV. For the cluster calculations, atoms are kept at least 7 Å away from each boundary, periodic boundaries were not applied, and Fermi-temperature was set to 0.01 eV. The total energies in this study were calculated using the density functional theory (DFT) code, GPAW.34,35 This is code implements the projector augmented wave (PAW) method36 on a realspace grid. A grid spacing of 0.14 Å was used for each energy calculation. The exchange and correlation energies were described using the RPBE functional.12 The structures were relaxed using a BFGS type optimizer, until the forces acting on all atoms were less than 0.05 eV/Å. Calculations of clusters above 147 atoms were carried out on the BlueGene/P and BlueGene/Q supercomputers at Argonne National Laboratory, utilizing up to 131,072 CPU cores. The strainbased continuum model for adsorption energy was developed by combining how cluster strain changes with size with how adsorption energy changes with strain. The liquid-drop continuum


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model developed for cluster strain, shown on figure 2a, was fitted based on the Wigner-Seitz radii of Pt atoms within DFT optimized cluster geometries. Wigner-Seitz radius was calculated based on the edge length of the clusters and the equation for volume of a cuboctahedron. How adsorption energy changes with surface strain was investigated using the 2x2 (111) and 3x2 (211) facets is mentioned above. For (111) facets, -3%, 0%, and +3% lateral strain were introduced. For (211) facets, -3%, 0%, and +3% strain were introduced in the direction along the edge. Surface stress shown on Figure 4 is calculated as the following:

Stress =

1 d [E (s)] A ds tot s=0

(2)

Where Etot(s) is the total energy of the surface slab at the specified strain (s), and A is the surface (twice of cross-sectional) area of the strain-free slab.


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Corresponding Author *Email: [email protected] Notes The authors declare no competing financial interests.


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The authors thank Dr. Ask. H. Larsen for discussions. L.L, F.A-P, and J.K.N. acknowledge support from the DOE Office of Basic Energy Science to the SUNCAT Center for Interface Science and Catalysis. J.G. acknowledges support through a DOE Early Career Award from the Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences Division. The authors acknowledge the use of computational resources through an Innovative and Novel Computational Impact on Theory and Experiment (INCITE) grant at the Argonne Leadership Computing Facility.

Supporting Information Available: Details regarding the calculation of surface strain. This material is available free of charge via the Internet at http://pubs.acs.org


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Surface Tension Effects on the Reactivity of Metal Nanoparticles - The

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