Size-Dependence of the Adsorption Energy of CO on Pt Nanoparticles

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Size-Dependence of the Adsorption Energyof CO on Pt Nanoparticles: Tracing Two Intersecting Trends by DFT Calculations Svetlana S. Laletina, Mikhail Mamatkulov, Elena A. Shor, Vasily V Kaichev, Alexander Genest, Ilya V. Yudanov, and Notker Roesch J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05580 • Publication Date (Web): 25 Jul 2017 Downloaded from http://pubs.acs.org on August 1, 2017

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The Journal of Physical Chemistry

Size-Dependence of the Adsorption Energy of CO on Pt Nanoparticles: Tracing Two Intersecting Trends by DFT Calculations Svetlana S. Laletina,† Mikhail Mamatkulov, ‡ Elena A. Shor, † Vasily V. Kaichev, ‡ Alexander Genest, ơ Ilya V. Yudanov,*, †,‡ Notker Rösch*,ơ,§ †

Institute of Chemistry and Chemical Technology of the Siberian Branch of Russian

Academy of Sciences (SB RAS), Federal Research Center “Krasnoyarsk Scientific Center SB RAS”, 660036 Krasnoyarsk, Russia, ‡ Boreskov Institute of Catalysis SB RAS, 630090 Novosibirsk, Russia, ơ Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, Connexis #16-16, Singapore 138632, Singapore § Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany AUTHOR INFORMATION: * (I.Y.) E-mail: [email protected]. * (N.R.) E-mail: [email protected]. ABSTRACT With density functional calculations, we studied the size dependence of adsorption properties of metal nanoparticles (NPs) on the example of CO as a probe on Ptn clusters with n = 38–260 atoms. For the largest NPs considered, the calculated adsorption energies lie below the corresponding value for an (ideal) infinite surface Pt(111). For clusters of 38–116 atoms, we calculated a sharp increase of the adsorption energy with decreasing cluster size. These opposite trends meet in an intermediate size range, for clusters of about 200 atoms, yielding the lowest adsorption energies. These computational results suggest that a nano-sized transition to a pronounced higher adsorption activity occurs for Pt NPs at notably larger nuclearities than for Pd NPs. We analyze the results by invoking the concept of generalized coordination numbers, adapted to the second-order level.

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1. INTRODUCTION The functionality of metal nanoparticles (NP) in modern materials including catalysts is intimately linked to their structure in terms of size and shape.1 Therefore, a detailed understanding if and how the reactivity of such NPs scales with size is crucial for the rational design of new nano-sized catalysts with enhanced catalytic properties.1 A key question is at what size nano-effects become substantial for obtaining a quantitatively and/or qualitatively new chemistry in comparison to extended surfaces. Density functional (DF) calculations proved to be a valuable tool for studying size-dependent properties of transition metal NPs in the context of catalytic applications.2-6 Today there is considerable evidence that sites on regular facets of metal NPs with more than 102-103 atoms offer very similar adsorption properties as analogous sites on extended single-crystal surfaces.3-7 The first experimental evidence for a peculiar size dependence of CO adsorption energy on metal NPs, namely a notable increase in the adsorption strength for particles of intermediate size, was found early on in scattering experiments8 where the rate of CO desorption from supported Pd clusters of different sizes was measured at varying temperatures. More recent experiments, employing an advanced microcalorimetry set-up,9 were unable to confirm the high adsorption activity for particle diameters of 3–4 nm,8 as decreasing CO adsorption energies were obtained for Pd NPs down to 1.8 nm.9 Subsequently, a detailed DF study6 on Pd model clusters corroborated that CO binding energies exhibit a non-monotonic dependence on the particle size, hence confirming the peculiar trend obtained in early experiments,8 yet for much smaller particle sizes below 1 nm. For large particles, the energy of CO adsorption at three-fold hollow sites slowly decreases with cluster size from the asymptotic value for an (ideal) infinite surface Pd(111) due to surface stress (surface tension in continuum model approximation).10,11 On the other hand, for clusters of less than 30 Pd atoms, the adsorption energy grows quickly with decreasing cluster size, yielding values well above the asymptotic value of an ideal surface.6 These opposite trends meet in an intermediate size range, for clusters of 30–50 atoms which exhibit the smallest adsorption energies of CO on Pd NPs.6 The significantly enhanced activity of metal particles of ~1 nm and below arises due a drastic modification of the electronic structure by a large fraction of low-coordinated centers.6 Previous theoretical studies of CO adsorption at Pt NPs demonstrated an increase of the CO binding energy with decreasing nuclearities for particle sizes of less than 100 atoms.4,12 For


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large cluster sizes a decrease in CO adsorption energy was determined compared to the Pt(111) surface.13 Hence one may expect a similar behavior as in Pd where two intersecting trends will lead to cluster sizes exhibiting minimum CO adsorption energies. Despite recent progress in theoretical studies on the reactivity of Pt nanoclusters4,5,12-19 addressing the issue of sizesensitivity, there is still a need for characterizing the size range where the transition to higher activity is taking place. There is experimental evidence for strong size effects in the activity for Pt NPs where an increase in the binding strength of oxygenated species was observed for decreasing particle size.20,21 A lower mobility of adsorbed CO with decreasing nuclearity was measured for Pt NPs with diameters below 4 nm, suggesting stronger CO binding compared to the extended (ideal) crystal surface.22 In the present work, using an extended series of Pt NP models, we explore the size region where the transition to higher CO adsorption energies occurs as the nuclearity of the NPs is reduced. We selected closely related on-top adsorption sites and we will focus the discussion on the highest calculated binding energy values. The analysis of trends also includes an extension of the recently introduced generalized coordination numbers CN

18,19

of the adsorption sites to

reflect the effects of one more shell of neighboring atoms, which notably improves the scaling. In contrast to previous studies, we also report an in-depth comparison of size-dependent trends of Pt NPs to those determined for Pd,6 focusing on the remarkable differences of these two elements of group 10. 2. COMPUTATIONAL DETAILS The DF calculations were carried out with the plane-wave Vienna ab initio Simulation Package (VASP),23,24 using the generalized gradient approximation (GGA) in the form of the PW91 exchange-correlation functional.25 The effect of the core electrons on the valence density was taken into account by means of the projector augmented wave (PAW) method.26,27 A kinetic energy cutoff of 400 eV was used, ensuring convergence of the energies to less than 10-6 eV. Partial occupancies of the one-electron levels were allowed by a Gaussian broadening of 0.1 eV.28 Extrapolation to zero broadening leads to a total energy change of less than 0.02 eV per atom. The integration in the reciprocal space was carried out using the k-point sampling scheme of Monkhorst and Pack.29 Γ-centered 4×4×1 and 1×1×1 k-point meshes were utilized for slab and NPs calculations, respectively. All calculations were done in non-spin-polarized


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fashion. Geometry optimizations were carried out using a conjugate-gradient algorithm until forces acting on each atom became smaller than 0.01 eV/Å. The Pt(111) surface was modeled using a five-layer periodic slab (3×3 unit cell consisting of 45 atoms) with the thickness of about 0.9 nm, separated by a vacuum spacing of 1.8 nm from the next cell. In these calculations, the “bottom” three layers of the slab (27 atoms) were constrained to their DFoptimized bulk positions whereas the two “top” layers (18 atoms) were fully relaxed. CO adsorbate molecules were placed at the relaxed side of the slab with a low coverage of 1/9 ML. The clusters extend up to 1.6 nm (Pt260) along the principle axes. Therefore, they were modeled by a three-dimensional periodic arrangement with a large cubic cell of 3.4×3.4×3.4 nm3 to minimize lateral interactions. The structures of the free Pt NPs and clusters with adsorbates were fully optimized, without any symmetry constraints. However, bare NPs exhibit Oh symmetry. We calculated the surface relaxation, i.e. the change in energy of the bare cluster caused by the relaxation of metal atoms induced by the adsorption by a single CO ligand. These relaxation energies range from 13 kJ mol-1 for a t site on the Pt(111) slab to 36 kJ mol-1 for t1 on Pt79. These results may be seen as a hint why high coverages of CO lead to a surface reconstruction.30 Adsorption energies, Eads, were determined from the total energies Etot(CO) of a CO molecule in the gas phase, Etot(substrate) of the relaxed Pt substrate, and Etot(CO/substrate) of the adsorption complex: Eads = Etot(CO/substrate) – Etot(CO) – Etot(substrate)

(3)

With this definition, a negative Eads value corresponds to a stable adsorption complex on the surface. The value Etot(CO) was obtained by placing a free molecule CO at the center of a 2.0×2.1×2.2 nm3 unit cell; the Brillouin zone was sampled at the Γ-point only. 3. RESULTS AND DISCUSSION As in a previous study on Pd NPs,6 we focused on model clusters with fcc-like atomic packing of truncated octahedral shape, exhibiting facets of (111) and (100) orientation to minimize the surface energy. The Ptn model clusters studied, with n ranging from 38 to 260, are depicted in Fig. 1. In experiments addressing the scaling of CO adsorption energies with particle size, clusters have to be supported, mostly on an oxide. Therefore, such studies admit only limited access to the goal of our computational work, namely the genuine properties of


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free metal particles. One may expect that the effect of a weakly interacting support on CO adsorption energies will be rather minor as soon as the NPs consist of several shells. In particular, DF calculations on Pd clusters10,31 with the same structure as shown in Fig. 1 made it possible to rationalize the experimental trends in size-dependence of CO adsorption heats on model catalytic particles grown on thin oxide films which are assumed to have the shape of truncated (half)octhadera and are terminated mainly by (111) facets with a small fraction of (001) facets.8,32 We examined the adsorption properties of Pt clusters by depositing CO molecules at on-top sites of closed-packed nanofacets of (111) orientation, Fig. 1. Here, it is appropriate to mention the so-called “CO puzzle”, namely that most common approximations to the exchange-correlation term lead to a severe over-binding of CO on a Pt(111) surface and at the same time to a wrong preference for hollow adsorption sites over the experimentally found top site.33-40 Recently the use of hybrid DF methods, random-phase approximation (RPA) as well as the DFT+Umol approach with an explicit Hubbard-type on-site correction U was examined for Pt clusters and particles.2,12,14 However, for the purpose of the present (model) study, focused exclusively on the scaling of the strength at on-top sites, we chose to stay within the conventional semi-local GGA approach. Other adsorption sites on facets12 as well as adsorption on cluster edges, which are present at higher fraction on smaller clusters (e.g., 49% of the surface atoms of Pt201 are located at edges), also contribute to the activity. However, to maintain comparability with the previous study on Pd NPs,6 we focus here just on the one type of adsorption sites at the ideal Pt(111) surface to examine how their properties change with particle size. Fig. 2a shows the calculated CO adsorption energies, Eads, as function of n-1/3 (a quantity that scales as the inverse of the effective cluster diameter D, i.e., n–1/3 ~ 1/D). Obviously the CO adsorption interaction becomes stronger with shrinking cluster size from the largest clusters Ptn considered, n = 260 and 201, to smaller nuclearities n. For comparison with the NP results, Eads calculated on the periodic Pt(111) is also shown in Fig. 2a at n-1/3 = 0. The Eads values of the largest clusters considered, Pt201 and Pt260, are slightly lower than the adsorption strength on the periodic slab model. Thus, qualitatively the size-dependency of Eads follows the same trends as previously established for Pd NPs.6,10,11 For comparison, the data of the previous computational study on Pd NPs are shown in Fig. 2b. The first trend, strongly increasing with decreasing particle size, prevails for small particles; see the solid (red) line in Fig. 2a. It reflects the decreasing average coordination number of ACS Paragon Plus Environment

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metal atoms with decreasing cluster size, which results in an upward shift of the metal d-band, inducing a stronger interaction with the adsorbate.6 An analytical expression for this trend has previously been suggested:6 Eads ( n) = Emin /(1 − c1n −1/ 3 )

(1)

This expression is based on a perturbation theory argument that invokes orbital interactions between CO and a transition metal cluster in the spirit of the Blyholder model.41,42 Similarly to the case of Pd clusters,6 the parameters of Eq. (1), Emin = -116.3 kJ mol–1 and c1 = 1.43, were obtained numerically by fitting the calculated Eads values for Ptn NPs. Note that the parameter c1 is essentially that previously determined for Pd NPs, 1.45.6 According to the theoretical model developed previously for large Pd particles, Eads of CO on closed-packed Pt(111) facets correlates linearly with n-1/3, i.e., the quantity decreases weakly with decreasing cluster size:6,11 Eads ( n) = E∞ (1 − c2 n −1/ 3 )

(2)

Here, E∞ represents the single-crystal limit of Eads, -164.6 kJ mol-1, as calculated for a periodic slab model of Pt(111), shown at n-1/3 = 0 in Fig. 2a. The parameter c2 in Eq. (2) was determined as suggested previously6,11 by combining two linear relationships: (i) the well-known decrease of the average nearest-neighbor distance d ~ n-1/3 in metal NPs due to surface stress, induced by surface atoms with unsaturated coordination;43 and (ii) a linear response of Eads to a small variation of d according to quantum chemical calculations on infinite metal surfaces44 as well as on NPs.4 Further details for determining the parameter c2 are given as Supporting Information (SI). The resulting trend according to Eq. (2) is shown in Fig. 2 as the dashed (blue) line. Such a trend to weaker adsorption of CO on NPs compared to a single-crystal surface, was previously demonstrated for Pd NPs, both computationally and experimentally.6,9 A direct microcalorimetric measurement of the heat of CO adsorption on Pd nanoclusters of welldefined structure showed that the initial heat of adsorption decreases from 126 kJ mol–1 to 106 kJ mol–1 for Pd particles ranging from ~5000 atoms (D ≈ 8 nm) to ~100 atoms (D ≈ 1.8 nm), respectively. The energies measured on Pd NPs were always smaller than the corresponding


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value for the Pd(111) surface.9 To the best of our knowledge, no experiments of similar accuracy are available yet for Pt NPs. For large Pt NPs, the calculated CO adsorption energy values scatter somewhat, mainly due to variations in the adsorption site. In an earlier study on Pt NPs, the authors reported the evolution of adsorption energies for CO at a specific site on similar clusters of growing size.4 In the present work, we studied the strongest adsorption site of 2 binding sites for varying cluster topologies, which may lead to a variation of up to 16 kJ mol-1, which rationalizes the scattering of values for large clusters for different studies, as different adsorption sites have been chosen. Besides lattice strain which is taken into account by Eq. (2),4,6,11 other factors leading to weaker adsorption of CO on the facets of finite clusters compared to the infinite close-packed surface have previously been discussed: (i) an electrostatic effect due to a negative potential over facets of the clusters created by a local excess of electron density;13 (ii) a change in the van-der-Waals attraction of sites on NPs compared to sites on single crystal surfaces.9,32 The adsorption energy, Eads(Pt) = -165 kJ mol-1, on an ideal Pt(111) slab notably overestimates (by absolute value) the experimental result for a Pt(111) single crystal, -132 kJ mol-1.40 For the DF study of CO adsorption on Pd clusters, an extrapolated single-crystal limit of the CO binding energy has been reported, Eads(Pd) = -183 kJ mol-1,6 while the experimental value is -143 kJ mol-1.40 Thus, both for Pt (present work) and Pd (all-electron scalar relativistic study using a localized basis set)6 computational results overestimate the binding on an ideal (111) surface in a comparable fashion, by 25 % and 28 %, respectively, despite of notable methodological differences between two studies. Assuming a similar overestimation of CO binding on NPs, the trends for the two metals (Fig. 2) can be compared, with due caution even by absolute values. Both trends for Eads, defined by Eqs. (1) and (2) as functions of n-1/3, imply a scalability of the properties with changing cluster size. However, in the case of Pd the ascending trend (1) involves only clusters of a few dozens of metal atoms (less than 50, Fig. 2b) where strong quantum-size effects are expected.45 Indeed, Eads values deviate notably from the trend (1), Fig. 2b, and, therefore, the scaling trend (1) is only approximate in the case of Pd, being applied in the non-scalable size regime.46 In the non-scalable regime particles are small enough for quantum effects to alter properties with the smallest change in size, i.e., “every atom counts”,46 in contrast to the regime of larger particles where scaling relationships can be applied to quantify how properties depend on particle size and approach the bulk limit.2 For Pt, in contrast ACS Paragon Plus Environment

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to Pd, the transition from the descending trend (2) to the ascending trend (1) (with decreasing nuclearity) occurs at cluster sizes of about 200 atoms which commonly is assigned to the scalable size regime.46 Note that the increase in the adsorption interaction for Pt clusters corresponding to trend (1), based, however, on fewer models (Pt79, Pt116, Pt231), was obtained also by all-electron scalar-relativistic DF calculations,12 thus providing evidence for the stability of these results with respect methodological differences. These observations imply important consequences for the design of nanosized catalysts, e.g., the preparation of size-selected Pt particles.47 Whereas for Pd clusters, exhibiting the highest activity in the non-scalable size regime, a clear selectivity in size and shape is required for obtaining a highly active catalyst. Highly active samples of Pt NPs can be obtained already for sizes of about 100 atoms. We expect a further increase of activity for Pt particles smaller than Pt38. However, a detailed study of CO adsorption on Pt clusters in the non-scalable size range is outside the scope of the present work. These findings also have some consequences for the computational models of NPs. Often a single cluster model is used to study the properties of NPs in general, e.g., a truncated octahedron of 79 or 116 atoms (Fig. 1).48-50 In the case of Pd, these models lie in the size range described by the weak trend (2) and adsorption sites on close-packed facets of Pd79 or Pd116 feature properties that resemble those of an infinite Pd surface model, although the adsorption on the cluster is slightly weaker. In contrast, the clusters Pt79 and Pt116 fall in the size range featuring trend (1). Compared to Pt(111), adsorbates bind considerably stronger on these clusters, even on their closed-packed facets. In the present study, all on-top sites of Pt NPs probed by CO adsorption are located on closepacked (111) facets of NPs (Fig. 1), coordinated by nine Pt neighbors as on the ideal Pt(111) surface. However, in nanoclusters, in contrast to Pt(111), even adsorption sites on facets often exhibit already the second coordination shell with a lower coordination number. To quantify this distinction with a bond competition argument in mind, the concept of a generalized coordination number, CN , of the adsorption site has recently been suggested.18,19 Thereby, each metal atom in the first coordination sphere of the adsorption site is assumed to contribute to the bond saturation of the adsorption site only according to the completion of its coordination sphere, i.e., by the fraction determined as the number of its neighbors divided by the maximum coordination number (12 for fcc-type metals). 18


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Table 1 lists the CO adsorption energies Eads for all sites on Pt NPs determined in the present study, together with the corresponding generalized coordination numbers, CN (Table 1). The highest absolute value of Eads was calculated for top site t of Pt38, characterized by the lowest value CN = 6. The lowest absolute Eads value is obtained for the site t1 in the center of the (111) facet of the cluster Pt201 which is the only site in the present study that fully mimics Pt atoms of the ideal Pt(111) surface regarding the first two coordination shells, with CN = 7.5 (Figs. 1, Table 1). Fig. 3a obviously displays a notable correlation between Eads and CN values. Thus, the increase of the binding energy displayed by trend (1) in Fig. 2 is closely associated with the presence of low-coordinated edge atoms in the vicinity of the adsorption sites. Note that there still are effects which cannot be rationalized just by changes in CN , a quantity that reflects only two coordination spheres of the adsorption site. For instance, the sites t of Pt79 and Pt116 and site t2 of Pt260 are characterized by the same value CN = 6.67. However, Eads in this series decreases with higher nuclearities in accordance with trend (1) as discussed above. To take into account an extended coordination environment of an adsorption site i, we introduce here a modified (second-order) generalized coordination number CN

(2)

(i ) as the

average over CN ( j ) of the nearest-neighbors of site i, the total number of which equals the conventional coordination number of atom i, cn(i) : CN

(2)

cn ( i )

(i ) =

∑ CN ( j ) / cn(i )

(3)

j =1

By this definition the new descriptor accounts for three coordination spheres of the adsorption site. The values CN

(2)

differ from CN in a subtle way. Yet, the two types of sites with the

same value CN = 6.67 exhibit different values of CN

(2)

which overall show an improved

correlation with the adsorption energies Eads (Fig. 3b). The adsorption sites t1 on Pt201 and t on Pt(111) ( CN = 7.5 for both sites) are also well-resolved by the descriptor CN Note that for the ideal (111) surface, CN

(2)

(2)

.

= 8.75 is much closer than CN = 7.5 to the

common value CN = 9. However, the t site of Pt(111) exhibits a stronger adsorption despite of its higher CN

(2)

value. Also other sites of Pt201 and Pt260, despite a lower effective coordination,

exhibit weaker or similar adsorption energies as determined for Pt(111). Here, one has to refer


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to the trend described by Eq. (2) (Fig. 2) to rationalize the difference in Eads of t sites on Ptn with n about 200 and site t on Pt(111). The qualitative switch of trends, shown in Fig. 2, is also visible in Fig. 3, rationalized by the compressive lattice strain in nanoparticles. This is not surprising because both Eq. (1)6 and the CN approach18 reflect correlations of the d-band energies of the metal substrate with the

coordination numbers. The result for the Pt(111) slab does not comply with the trend Eads( CN

(2)

) due to the compressive lattice strain which affects the properties of nanoparticles

(Eq. 2).6,11 Therefore, we separated the cluster and the slab results, to obtain a perfect linear correlation Eads ~ CN

(2)

, with the regression coefficient R2 = 0.98 (solid line in Fig. 3b,), a

notably improved result compared to the correlation, R2 = 0.76, of all data, including that for Pt(111) (dashed, Fig. 3b). In summary, the combination of Eqs. (1) and (2) with descriptors CN and CN

(2)

[Eq. (3)]

helps to rationalize and predict the relative adsorption strength of a variety of adsorption sites on nanoclusters of different size. Moreover, the extension of the generalized CN approach to higher order, as suggested in the present work, allows one to distinguish properly the sites characterized by the same value of the descriptor CN , thus improving the correlation with Eads. 4. CONCLUSIONS The theoretical model involving Eqs. (1) and (2) to describe the strength of adsorption sites of metal NPs, with sizes ranging from several dozens of atoms up to the single-crystal limit, was previously developed from general principles and applied to the case of CO adsorption on Pd NPs.6 In the present work we demonstrated that this relatively simple model also describes the adsorption of CO on Pt NPs. When one goes from a single-crystal surface to nanosized particles, a transition occurs from trend (2), which describes the weakening of the adsorption strength mainly due to the lattice contraction, to trend (1), which describes a drastic strengthening of adsorption interaction due to an upward shift of the d-band of the transition metal. In the case of Pt NPs this transition between the two trends is found at nuclearities of about 200 atoms, hence for considerably larger nuclearities than about 30 atoms, previously determined for Pd NPs.6 The activity trends of the sites of NPs with different environment are better reflected by the generalized descriptors CN and the newly introduced second-order CN

(2)

, accounting for the second and third coordination sphere, respectively. ACS Paragon Plus Environment

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ACKNOWLEDGMENTS This work was supported by Russian Academy of Sciences and Russian Federal Agency for Scientific Organizations (project 0303-2016-0001). S.L. thanks for a grant 15-33-50437 from Russian Foundation of Basic Research supporting her research stay at BIC and grant 16-33-00578 supporting her work at ICCT. The use of generous computing resources at the Siberian Supercomputing Center in Novosibirsk is acknowledged.

Supporting Information. Details regarding the influence of the slab structure on adsorption energies, the parameterization of Eq. (2) for Pt NPs, and Cartesian coordinates for all calculated systems. This material is available free of charge via the Internet at http://pubs.acs.org.


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Table 1. Calculated adsorption energies, Eads (kJ mol–1), of CO adsorbed on Pt clusters and a Pt(111) slab model as well as generalized coordination numbers CN of the adsorption sites.

Cluster Pt38 Pt79 Pt116 Pt201 Pt260 Pt(111)

Site a

CN

t t t t1 t2 t1 t2 t

6.00 6.67 6.67 7.50 6.92 7.16 6.67 7.50

b

CN

(2) c

5.67 6.85 6.99 8.36 7.49 7.88 7.12 8.75

Eads -196.8 -180.4 -170.8 -148.6 -164.0 -156.3 -167.9 -164.6

a

For the designations of the sites, see Fig. 1.

b

Generalized coordination number according to Ref. 18 of the surface Pt atoms probed by CO

adsorption. c

Modified second-order generalized coordination numbers according to Eq. (3).


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Figure 1. Pt nanoclusters with indicated on-top sites on (111) facets, probed by CO adsorption. The bare clusters are described by Oh symmetry. Only a single CO molecule was deposited on each cluster when calculating the adsorption energy.


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Figure 2. Calculated energies of CO adsorption, Eads (open circles, kJ mol–1), on Ptn (a) and Pdn (b) clusters as a function of n–1/3. The short-range trend according to Eq. (1) is shown by the solid (red) line. The long-range trend, Eq. (2), up to the limit of CO adsorption on an (infinite) single-crystal (111) surface (filled circle) is shown by the dashed (blue) line. The data for Pd are taken from a previous study,6 the results for Pt are calculated in the present work.


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Figure 3. Calculated energies of CO adsorption, Eads (kJ mol–1), on-top of 9-coordinated sites of Ptn clusters (open diamonds) with n ranging from 38 to 260 (see Fig. 1) and Pt(111) (filled diamond) as a function of (a) the generalized coordination number, CN , which accounts for the average coordination of the atoms adjacent to the adsorption site, Ref. 17; (b) the secondorder generalized coordination number, CN

(2)

, according to Eq. (3). Cluster nuclearities are

given near the data points. The trend lines are obtained by least-squares fits either of all data (dashed lines, regression coefficients R2 = 0.79 (a) and 0.76 (b)) or only the data for the clusters (solid line, R2 = 0.98), excluding Pt(111).


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TOC graphics


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Size-Dependence of the Adsorption Energy of CO on Pt Nanoparticles

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