Effect of an Electric Field on the Adsorption of Metal Clusters on Boron

Sep 15, 2007 - C. K. Acharya and C. H. Turner* ... of a homogeneous external electric field. Due to ... In systems with a positive electric field, the...
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14804

J. Phys. Chem. C 2007, 111, 14804-14812

Effect of an Electric Field on the Adsorption of Metal Clusters on Boron-Doped Carbon Surfaces C. K. Acharya and C. H. Turner* Department of Chemical and Biological Engineering, The UniVersity of Alabama, Tuscaloosa, Alabama 35487-0203 ReceiVed: May 12, 2007; In Final Form: July 19, 2007

Fuel cell catalysts can lose their activity over a period of time due to the sintering of the nanometer-sized catalyst particles. However, the sintering of metal clusters on carbon supports may be reduced by increasing the interaction between the metal and the support. To manipulate this metal-support interaction, carbonsubstituted boron defects were introduced in a graphite lattice, and the adsorption energies of metal clusters (Pt, PtRu, and Au) on the pristine and on the boron-doped carbon were calculated using first-principles density functional theory. The metal-support interaction was also calculated in the presence of an external electric field. Although the metal-support interaction is slightly weakened in the electric field, the boron-doped carbons are still predicted to maintain a significant stabilizing effect.

1. Introduction Pt, PtRu alloys, and Au nanoparticles supported on carbon are very popular catalysts having a wide range of applications, including fuel cell electrode catalysts.1-8 Depending upon the application, the catalytic activity can be significantly influenced by the size and shape of the nanoparticles.8-15 Unfortunately, catalysts can lose their activity over a period of time due to the sintering of the metal nanoparticles, but the details of the sintering process are still rather ambiguous. The two main mechanisms used to explain the sintering process are coalescence and Ostwald ripening.16 In the coalescence mechanism, the entire cluster migrates on the support to form a larger cluster. In the Ostwald ripening mechanism, the atoms migrate from one cluster to another (normally from a smaller cluster to a larger one), leading to the growth of the larger clusters while simultaneously shrinking the smaller ones. Both mechanisms have been reported to occur in the literature, with the dominant mechanism dependent upon the particular catalyst, the support, and the reaction conditions.17-20 The tendency to coalescence may possibly be reduced by increasing the interaction between the metal and the support, resulting in a decrease in the mobility of the clusters on the surface of the support. To manipulate this metal-support interaction, we previously used first-principles density functional theory (DFT) calculations to explore the effects of substitutional defects in carbon supports on the metal-support binding energies.21 In the calculations, Pt clusters and Au and Ru atoms were adsorbed on various carbon surface models, and the binding energies of these metals were predicted to be as much as 40 kcal/mol higher when adsorbed on boron-doped carbon surfaces (as compared to pristine carbon models). Building on the results from our previous investigation, we are now extending our study to elucidate some of the possible effects that an electrochemical environment would have on the predicted binding energies. Due to the inherent limits of time and length scales accessible with electronic structure methods, we are not able to encompass all details. However, to study * Corresponding author. E-mail: [email protected].

one of the more significant environmental effects, we have performed DFT calculations to predict the interactions of Pt, PtRu, and Au metal clusters with pristine and boron-doped graphitic carbon supports, in a neutral system and in the presence of a homogeneous external electric field. Due to the graphitic nature of the carbon models used in our calculations, the results should be comparable to an experimental sample of highly oriented pyrolytic graphite (HOPG). An external electric field of (0.5 V/Å was applied in a direction normal to the surface, which corresponds to an experimental electrode potential of (1.5 V (with reference to the potential of zero charge and assuming the thickness of the inner layer region between the electrode surface and the outer Helmholtz plane in the electrical double layer to be 3 Å).22-24 The binding energies of the metal clusters on the graphite supports in the presence of the external electric field were calculated and compared with the other systems considered here. In systems with a positive electric field, the direction of the field was directed from the cluster toward the surface. This general route for modifying metal-support interactions seems plausible, since the synthesis of different types of carbon with substitutional dopants like N, B, transition metals like Fe, Co, Ni, Rh, and Ir, and alkali metals like Li and K has been previously reported in the literature.25-30 In addition, we have also been successful in experimentally synthesizing boron-doped carbon samples, and our procedure for doing this will be reported soon. The details of the DFT calculations and the models are given below, followed by the results obtained for these systems. The results are presented in three sections: (1) isolated graphite and metal cluster models; (2) metal clusters adsorbed on different graphite models (neutral systems); and (3) metal clusters adsorbed on different graphite models with an external electric field of (0.5 V/Å. 2. Computational Details The electronic structure calculations were performed using a DFT approach, with Vanderbilt ultrasoft pseudopotentials31 for

10.1021/jp073643a CCC: $37.00 © 2007 American Chemical Society Published on Web 09/15/2007

Metal Clusters on Boron-Doped Carbon Surfaces

J. Phys. Chem. C, Vol. 111, No. 40, 2007 14805

Figure 1. Graphite models used for the adsorption of the metal clusters. The gray and green atoms are carbon and boron, respectively.

the inert core electrons and a plane-wave basis set for the valance orbitals, as developed in the Vienna Atomic Simulation Package (VASP).32-35 A generalized gradient approximation (GGA), with the exchange-correlation functional of Perdew and Wang (PW91)36 was used for structure relaxations. A hexagonal supercell of 12.35 × 12.35 × 27.16 Å with periodic boundary conditions was used for graphite, and the plane-wave basis set had a kinetic energy cutoff of 400 eV. To avoid unphysical interactions among repeating slabs in the direction normal to the surface (z-dimension), sufficient surrounding vacuum was included. The integration of the Brillouin zone was performed using a 5 × 5 × 1 Monkhorst-Pack grid37 with Γ included and first-order Methfessel-Paxton smearing38 with 0.2 eV. A single layer of graphite with 50 carbon atoms was used to model the carbon support. This has been reported in the literature as a reasonable model for the carbon support,39,40 since dispersion interactions dominate between the subsequent graphite layers. The metal clusters were adsorbed on relaxed graphite unit cell models and were further relaxed until the absolute forces on each atom was less than 0.05 eV/Å and the total energy was converged to 1 meV/atom. The projector augmented wave41,42 (PAW) pseudopotential was also tested on some of the systems, and this method predicted roughly 0.4 kcal/atom higher binding energies of the metal clusters on both pristine and boron-doped graphite models when compared to the Vanderbilt ultrasoft pseudopotentials. The metal clusters considered here were Pt6, Pt2Ru4, and Au6. For Pt6, an initial fcc configuration was used (with the bulk parameters), and this cluster was adsorbed on graphite with the four atoms in one layer interfacing with the surface. To study the oxygen adsorption on Pt, Janin et al.43 have also used the same model for the Pt6 cluster. In the Pt2Ru4 cluster, the four Pt atoms interfacing with the graphite were replaced with Ru. This model of the PtRu alloy cluster was chosen because Nuzzo et al.40,44-48 have found that PtRu clusters are seen experimentally in an fcc geometry with the Pt segregating to the ambient surface when supported on a carbon surface. Triangular planar fcc Au6 clusters with D3h symmetry were adsorbed on graphite, since this structure has been reported by Olson et al.49 as the most stable geometry. It should be emphasized that there are

other stable isolated metal clusters which could give different results when compared to the metal cluster models considered here; however, the relative energies (or at least the energy trends) of the metal clusters on the different graphite models should be the same, irrespective of what metal cluster model is chosen. The graphite models considered here were C50 (pristine), C42B8 in a BC5 configuration (one boron in each ring), C46B4 with the four boron atoms located in the center of the graphite unit cell and each boron atom was bonded to carbon atoms (without any boron-boron bonds), which will be denoted as B-C hereafter, and C46B4 with the four boron atoms located in the center of the graphite unit cell and each boron atom bonded to other boron atoms, which will be called the B-B graphite model. These four models, representative of several possible (stable) dopant configurations, are illustrated in Figure 1. Non-spin-polarized calculations were performed on all the systems considered here. Spin-polarized calculations were performed on some of the systems, which included pristine and boron-doped carbon systems. The difference in energies between the spin-polarized and non-spin-polarized calculations was less than 2 kcal/mol on both pristine and boron-doped graphite systems. Also, the shift in the energies calculated by the two methods on the pristine and boron-doped graphite systems was consistent. Therefore, from these test calculations, the relative energies between the different systems considered here are not expected to be significantly affected by our approach. For the Bader charge analyses,50,51 the PAW method with hard pseudopotentials only for carbon and boron was used. Single-point energy calculations with a kinetic energy cutoff of 700 eV for the plane-wave basis set (to accommodate the hard pseudopotentials) were performed on the geometryoptimized structures. Hard pseudopotentials, which are required for an accurate Bader charge analysis, were not available for boron and carbon in the Vanderbilt ultrasoft pseudopotential library. The density of states (DOS) were calculated by taking the charge density of a geometry-optimized system and performing a static calculation on it with a 7 × 7 × 3 MonkhorstPack grid and a first-order Methfessel-Paxton smearing with 0.2 eV. Also, in the presence of external electric field, the monopole/dipole and quadrupole corrections were performed.

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TABLE 1: Properties of the Graphite Models and the Metal Clustersa bond length (Å)

a

system

C-C

C50 C42B8 B-C B-B Pt6 Pt2Ru4 Au6

1.42 1.39-1.47 1.39-1.46 1.39-1.46

C-B 1.51-1.53 1.48-1.51 1.45-1.58

B-B

M-M

fermi energy (eV)

work function (eV)

2.51-2.71 2.23-2.69 2.64-2.80

-3.31 -4.55 -4.11 -4.01 -3.88 -3.75 -5.68

4.34 5.51 5.10 5.03 4.17 3.99 5.96

1.47-1.61

C-C, C-B, B-B, and M-M represent the bond lengths between carbon-carbon, carbon-boron, boron-boron, and metal-metal, respectively.

3. Results and Discussion 3.1. Isolated Graphite and Metal Clusters. The graphite models shown in Figure 1 remained planar when their geometries were relaxed, and the bond lengths in the different graphite models (after relaxation) are all given in Table 1. The changes in the bond lengths due to the boron substitution in the graphite lattice reported here are close to those calculated by others in the literature.26,52 Also, the Fermi energy and the work function given in Table 1 are close to the values calculated by Ooi et al.53 for pristine graphite. It is known that when two different systems are brought into contact, the electrons from the system of lower work function will flow into the other system until an interface potential develops that opposes further electron flow.54 Therefore, the work functions reported here should help identify the direction and the extent of charge transfer between metal clusters and graphite surfaces. The Fermi energies of the borondoped graphite models compared to pristine graphite increased in magnitude, which resulted in an increase in the work function. In our calculations, the work function was obtained by calculating the difference between the vacuum and the Fermi level, and the vacuum level did not change significantly with the graphite models. The vacuum level was obtained from the planar-averaged potential of the system, which can be generated with VASP. The projected density of states (PDOS) of the C50 and C42B8 graphite are given in Figure 2, with the Fermi level adjusted to zero. The PDOS of the other boron-doped graphite models are shown in the Supporting Information (Figure S1).

The s orbital contribution is seen at the lower energy levels, while the contribution to the lower portion (more negative) of the p orbital mainly comes from the px and py orbitals (their contribution is not seen above the Fermi level). The contribution to the upper portion of the p orbital is mainly due to the pz orbital, and its contribution is seen both below and above the Fermi level. In the boron-doped samples, there are more states at the Fermi level, which is due to the vacancies at the top of the valance π band, created by the electron-deficient boron atoms in the carbon lattice. The increased density of states at the Fermi level increase the tunneling current, which should lead to brighter spots at the boron locations in a scanning tunneling microscopy (STM) image. Due to the delocalized nature of the boron defect in the graphite lattice, the neighboring carbon atoms should also look brighter, which is evident from the computed constant height STM mode images of the different graphite models shown in Figure 3. These images are consistent with the images obtained experimentally by Endo et al.26 A greater number of states at the Fermi level in the boron-doped carbon should result in better electrical conductivity when compared to the pristine carbon. The metal clusters were relaxed before they were adsorbed on the graphite models and the details of their geometry and energies are given in Table 1. The work function of the Pt6 and the Pt2Ru4 metal cluster was lower than that of the graphite models, which should result in an electron transfer from the metal cluster to the graphite surface. Furthermore, the transfer to the boron-doped graphite should be greater when compared to the pristine graphite, since the work function of the borondoped graphite is greater than the pristine graphite. The Au6 cluster had a work function greater than that of the graphite models which would favor an electron transfer from the graphite models to the gold cluster or a very low electron transfer from the gold cluster to the graphite models. 3.2. Metal Clusters on Graphite (Neutral Systems). The metal clusters were adsorbed on the graphite models (as shown in Figure 4), and the adsorption energy, or the binding energy (BE) per metal atom (M) on a graphite sheet, was calculated by the expression

BE/M )

Figure 2. Projected density of states of the different graphite models. The Fermi level is adjusted to zero.

(E(graphite + Mn) - E(graphite) - E(Mn)) n

(1)

where Mn represents the metal cluster containing n atoms, E(graphite + Mn) is the total energy of the system containing Mn ) Pt6, Pt2Ru4, and Au6 adsorbed on graphite, and E(graphite) and E(Mn) are the energies of the isolated groups. A negative value of binding energy corresponds to a stable adsorption of a metal cluster on graphite, with stronger adsorption indicated by more negative values.

Metal Clusters on Boron-Doped Carbon Surfaces

Figure 3. Computed constant height STM images of the different graphite models.

Figure 4. Geometry-optimized metal clusters on the graphite surfaces. The gray, green, blue, red, and yellow atoms are carbon, boron, platinum, ruthenium, and gold, respectively.

Table 2 gives the binding energies of the different model systems, the range of bond lengths connecting carbon-carbon (C-C), carbon-boron (C-B), and boron-boron (B-B) in the different graphite models, the minimum distance between the metal clusters and the graphite in the direction normal to the surface (Dmin), the maximum displacement of an atom in the graphite surface from planarity after the adsorption of the metal

J. Phys. Chem. C, Vol. 111, No. 40, 2007 14807 cluster (∆Dmax), and the Bader charge on the metal clusters. This table shows that all of the binding energies of the metal clusters are greater on the boron-doped graphite when compared to the pristine graphite, and this is consistent with our previous investigation.21 The order of the adsorption strengths of the metal clusters on the graphite models were Pt2Ru4 > Pt6 > Au6, and this order did not change even when compared with additional calculations of single atom adsorption (Ru1, Pt1, and Au1). Wang et al.40 reported the binding energies of Pt37 and Pt6Ru31 clusters adsorbed on pristine graphite to be -1.44 to -1.68 and -3.90 to -5.23 kcal/atom, respectively, which is comparable to the values of -2.33 and -9.87 kcal/atom reported here for the Pt6 and Pt2Ru4 clusters, respectively. The deviation in values observed between our calculations and those of Wang et al. can be partly attributed to the much different cluster sizes (a 37 atom cluster versus a 6 atom cluster used here). Also, Wang et al. used somewhat different computational parameters, such as the local density approximation, PAW pseudopotentials, a kinetic energy cutoff of 250 eV, and a k-point mesh of 2 × 2 × 1. In our work, the difference in binding energies of the metal clusters on the three different boron-doped graphite models was not very significant (with the exception of the Au6 cluster on the B-B graphite model), and the binding energies of the Pt6 cluster adsorbed on the boron-doped graphite models are comparable to the energies reported earlier.21 The range of bond lengths reported in Table 2 include all the bond lengths that were seen in the metal clusters and the graphite models before adsorption. The structure of the Pt6 and the Pt2Ru4 cluster after adsorption resembled an fcc structure. Some of the bonds that existed before the adsorption were not seen after the adsorption because of the displacement of some of the atoms, but their values are nevertheless included in the table. The Au6 cluster remained planar, even after adsorption on the pristine graphite model, but when adsorbed on the borondoped graphite models, the planar Au6 cluster assumed a 3-D structure. This reconfiguration could have significant impacts on catalytic activity, since many reactions are sensitive to catalyst structure, and our results suggest that the boron-doped carbon supports may affect the adsorbed structure of this metal. The minimum distance between the metal clusters and the boron-doped graphite surface was lower than that of the pristine graphite surface due to the higher binding energies of the metal clusters on the boron-doped graphite models. The order of the minimum distance between the metal cluster and the graphite models was Pt2Ru4 < Pt6 < Au6, which can be correlated to the relative binding energies of each metal cluster. The greatest maximum displacement of an atom in the graphite sheet from planarity was seen in the B-B graphite models, and this was because of the weak boron-boron bond strength when compared to the carbon-carbon or carbon-boron bond strength. The atoms in the B-C graphite models had a greater displacement than the C42B8 graphite models, and this was likely because the defect was localized in the B-C model as opposed to a homogeneous distribution of boron atoms in the C42B8 model. In the calculations, electron density was transferred from the Pt6 and the Pt2Ru4 clusters to the graphite models as predicted from a Bader charge analysis, and this behavior is attributed to the fact that the graphite models had work functions greater than either of the metal clusters. The positive charge on the two metal clusters was greater when adsorbed on the borondoped graphite models since the work functions between the metal cluster and the surface had a greater gap, as compared to the work functions between the metal cluster and the pristine graphite. The work function gaps between the Pt2Ru4 cluster

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TABLE 2: Metal Clusters Adsorbed on the Different Graphite Modelsa system

BE/M (kcal/mol)

C-C

Pt6/C50 Pt6/C42B8 Pt6/B-C Pt6/B-B Pt2Ru4/C50 Pt2Ru4/C42B8 Pt2Ru4/B-C Pt2Ru4/B-B Au6/C50 Au6/C42B8 Au6/B-C Au6/B-B

-2.33 -19.16 -20.54 -19.68 -9.87 -27.30 -31.35 -30.07 -0.33 -2.80 -5.52 -11.53

1.40-1.44 1.40-1.49 1.40-1.47 1.40-1.49 1.41-1.46 1.41-1.49 1.41-1.47 1.41-1.48 1.42 1.39-1.46 1.41-1.46 1.41-1.46

bond length (Å) C-B B-B 1.51-1.55 1.49-1.52 1.48-1.53

1.59-1.70

1.51-1.55 1.50-1.53 1.50-1.55

1.59-1.66

1.51-1.54 1.50-1.54 1.51-1.54

1.66-1.79

M-M

Dmin (Å)

∆Dmax (Å)

charge on M (Bader)

2.56-2.78 2.56-2.95 2.58-2.82 2.57-2.95 2.22-3.47 2.24-3.30 2.20-3.53 2.21-3.54 2.64-2.81 2.66-2.85 2.62-2.89 2.61-3.03

2.19 1.70 1.97 1.84 2.20 1.59 1.51 1.13 3.35 2.15 2.39 2.52

0.21 0.27 0.12 0.38 0.19 0.44 0.66 1.05 0.23 0.22 0.48 1.09

0.13 0.60 0.26 0.02 0.82 1.29 1.14 1.00 0.02 0.31 0.06 -0.19

a BE/M is the binding energy per metal atom of the cluster on a graphite surface. C-C, C-B, B-B, and M-M represent the bond lengths between carbon-carbon, carbon-boron, boron-boron, and metal-metal, respectively. The minimum distance between the metal clusters and the graphite in the direction normal to the surface is given by Dmin, while the maximum displacement of an atom in the graphite surface from planarity after the adsorption of the metal cluster is given by ∆Dmax.

Figure 5. Projected density of states of the Pt6 cluster adsorbed on the different graphite models. The total DOS of the Pt6 cluster and the graphite models, the contribution of the p orbital of the graphite model, and the d orbital of the Pt6 cluster to the total DOS are given in each panel. The Fermi energy is adjusted to zero.

and the graphite models were greater than that between the Pt6 cluster and the graphite models, which lead to higher binding energies of the Pt2Ru4 clusters when compared to the Pt6 cluster on the graphite models. The graphite surface buckled slightly away from the Pt6 and Pt2Ru4 clusters upon their adsorption, which could be due to the electron transfer from the cluster to the graphite surface. In contrast, the Au6 cluster has a work function greater than the graphite models, and this should favor electron transfer from the graphite models to the cluster,55 thus limiting the electron transfer and the binding energies. The Au6 cluster adsorbed on the B-B graphite model had a negative Bader charge, but it adopted a positive charge when adsorbed on the other graphite models. In the B-B graphite model all the boron atoms are clumped together, reducing the delocalizing

nature of the boron defect in graphite and facilitating an easier donation of electrons to the Au6 cluster. The positive charges on the Au6 clusters adsorbed on the other graphite models were very small, except the Au6 on C42B8 graphite. The boron-doped graphite surfaces buckled slightly toward the Au6 cluster, which could be due to the electron transfer from the graphite surface to the cluster. The projected density of states of the Pt6 clusters adsorbed on the graphite models was generated, and the PDOS of Pt6 on the C50 and C42B8 graphite are shown in Figure 5. The PDOS of the Pt6 on other boron-doped graphite models are shown in the Supporting Information (Figure S2). At the lower energy levels, the s orbital in graphite mainly contributed to the total DOS, whereas the p orbital mainly contributed to the total DOS

Metal Clusters on Boron-Doped Carbon Surfaces

J. Phys. Chem. C, Vol. 111, No. 40, 2007 14809

Figure 6. Projected density of states of the Pt2Ru4 cluster adsorbed on the different graphite models. The data presented here are similar to those of Figure 5.

at the higher energy levels. The pz orbital contributed to the majority of the states in the p orbital at the Fermi level. The contribution from the s and p orbitals of the Pt6 cluster was very low, and the total DOS was somewhat similar to the d orbital PDOS. The overlap of the number of states between the Pt6 and the boron-doped graphite models was greater than the Pt6 and the pristine graphite model, which is consistent with the relative binding energies calculated in these systems. Due to the lowering of the Fermi level in the boron-doped graphite, the interaction between the p orbital of the graphite and the d orbital of the Pt6 cluster was greater than the pristine carbon, leading to the stabilization of the cluster on the boron-doped graphite. The PDOS of the Pt2Ru4 cluster adsorbed on the C50 and C42B8 graphite is shown in Figure 6. The contributions from the s and p orbitals in the Pt2Ru4 cluster were very low, and the total DOS was similar to the d orbital PDOS. The metal cluster had higher binding energies on the boron-doped graphite when compared to the pristine graphite since the overlap of the number of states between the Pt2Ru4 and the boron-doped graphite models was greater than that with the pristine graphite model. The contribution from the dxz, dyz, and dz2 orbitals to the d orbital at the Fermi level was greater for the Pt2Ru4 clusters adsorbed on graphite when compared to the Pt6 clusters adsorbed on the graphite models, which could explain the higher binding energies observed for the Pt2Ru4 when compared to the Pt6 clusters on graphite. The PDOS of the Au6 cluster adsorbed on the C50 and C42B8 graphite is shown in Figure 7. The majority of the contribution to the total DOS comes from the p orbital of graphite and the d orbital of the Au6 cluster. The number of states at the Fermi level was low, resulting in lower binding energies for the Au6 cluster when compared to the Pt6 and Pt2Ru4 clusters on graphite. The overlap of the number of states between the Au6 and the

boron-doped graphite models was greater than on the pristine graphite model, resulting in a stronger binding energy. In the energy range from -1.2 to 0 eV, the number of states in the graphite models was greater than that of the Au6 cluster (the DOS was very small when adsorbed on pristine graphite in that energy range), which was contrary to what was seen with the Pt6 and Pt2Ru4 clusters adsorbed on the graphite models. This is due to the fact that the Fermi energy of the Au6 cluster is higher than the graphite models, favoring the flow of electrons from the graphite surface to the metal cluster. In addition, the adsorption energies of a Pt atom on different adsorption sites in the pristine and boron-doped graphite (ontop site, 2-fold bridge site, and 6-fold hollow site) have been calculated (data not shown) by placing the Pt atom on top of these sites and performing geometry optimization, and the potential energy well for the migration of a Pt atom from one site to another on the boron-doped graphite was predicted to be four times deeper than on the pristine graphite. This suggests that the boron-doped surfaces should help mitigate the diffusion of the metal particles. We are in the process of exhaustively scanning the potential energy surface of C18 and C16B2 graphite models for the adsorption of Pt and Ru atoms, the results of which will be reported in the future. 3.3. Metal Clusters on Graphite (External Electric Field). The binding energies of the metal clusters on the graphite surfaces in the presence of an external electric field of (0.5 V/Å in a direction normal to the surface were calculated by two different methods. In the first method (eq 2), the binding energies were obtained by

E(graphite + metal)F - E(graphite)F - E(metal)F)0

(2)

where F is the electric field. This method was used under the assumption that in an electrochemical experiment (under ideal

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Figure 7. Projected density of states of the Au6 cluster adsorbed on the different graphite models. The data presented here are similar to those of Figure 5.

TABLE 3: Metal Clusters Adsorbed on the Different Graphite Models with a +0.5 V/Å External Electric Fielda system Pt6/C50 Pt6/C42B8 Pt6/B-C Pt6/B-B Pt2Ru4/C50 Pt2Ru4/C42B8 Pt2Ru4/B-C Pt2Ru4/B-B Au6/C42B8 Au6/B-C Au6/B-B a

BE/M (kcal/mol) eq 2 eq 3 -2.89 -18.41 -20.30 -19.47 -10.25 -26.19 -30.70 -29.41 -1.99 -5.33 -13.34

-1.99 -17.52 -19.41 -18.57 -8.69 -24.65 -29.13 -27.85 -0.14 -3.49 -11.49

C-C 1.40-1.44 1.40-1.49 1.40-1.47 1.40-1.49 1.41-1.46 1.41-1.49 1.41-1.47 1.41-1.48 1.39-1.46 1.41-1.46 1.41-1.47

bond length (Å) C-B B-B 1.51-1.55 1.49-1.52 1.48-1.53 1.51-1.55 1.50-1.53 1.50-1.55 1.51-1.54 1.50-1.54 1.51-1.54

1.59-1.71

1.58-1.66 1.66-1.79

M-M

Dmin (Å)

∆Dmax (Å)

charge on M (Bader)

2.56-2.78 2.57-2.96 2.58-2.83 2.58-2.95 2.22-3.47 2.24-3.32 2.21-3.53 2.22-3.55 2.65-2.85 2.62-2.89 2.61-3.03

2.19 1.69 1.98 1.84 2.20 1.58 1.51 1.13 2.17 2.39 2.48

0.20 0.28 0.12 0.38 0.19 0.46 0.66 1.05 0.22 0.47 1.09

-0.12 0.31 -0.04 -0.27 0.55 1.00 0.86 0.72 0.01 -0.19 -0.54

The symbols shown here correspond to those of Table 2.

conditions) an isolated cluster will not experience an electric field.56-58 In the second method (eq 3), the effect of the electric field on the isolated cluster was considered and the binding energies were calculated by

E(graphite + metal)F - E(graphite)F - E(metal)F (3) The binding energies, range of bond lengths, Dmin, ∆Dmax, and Bader charges in a positive and negative electric field are given in Table 3 and Table 4, respectively. The binding energies calculated by eq 3 gave weaker (less negative) values than eq 2 because the energy of the isolated metal cluster increased in magnitude in the electric field due to the induced dipole moment. The dipole moments of all of the isolated boron-doped graphite were greater than the pristine graphite in the positive electric field, and vice versa in the negative electric field. The binding energies of the Pt6 and Pt2Ru4 on pristine graphite, and Au6 on B-B graphite in the positive electric field were greater than the corresponding neutral systems without the electric field when

calculated by eq 2. Furthermore, the binding energy of the Pt6 cluster adsorbed on the B-C graphite surface in the presence of the negative electric field calculated by eq 2 and eq 3 was stronger than that of the corresponding neutral system without the electric field. There was a significant structural change upon adsorption of the Pt6 cluster on the B-C graphite (shown in Figure 8), and this is also evident from the bond lengths (Dmin and ∆Dmax) given in Table 4. The Au6 cluster did not prefer to adsorb on the pristine graphite sheet. The binding energies of all of the Au6 clusters were weaker than those of the corresponding neutral systems (in the absence of an external electric field) when calculated by eq 3. Although, the values of the binding energies of the metal clusters on the carbon supports were slightly dependent upon the method of calculation, both approaches predicted only a small change in the metal cluster binding energies on graphite surfaces when compared to the binding energies of the metal clusters in systems without an electric field. Therefore, the

Metal Clusters on Boron-Doped Carbon Surfaces

J. Phys. Chem. C, Vol. 111, No. 40, 2007 14811

TABLE 4: Metal Clusters Adsorbed on the Different Graphite Models with a -0.5 V/Å External Electric Fielda BE/M (kcal/mol)

bond length (Å)

system

eq 2

eq 3

C-C

Pt6/C50 Pt6/C42B8 Pt6/B-C Pt6/B-B Pt2Ru4/C50 Pt2Ru4/C42B8 Pt2Ru4/B-C Pt2Ru4/B-B Au6/C42B8 Au6/B-C Au6/B-B

-1.05 -18.51 -23.35 -18.79 -9.04 -27.05 -30.82 -29.70 -2.66 -4.96 -11.52

-0.29 -17.76 -22.59 -18.03 -8.01 -26.03 -29.79 -28.67 -0.82 -3.11 -9.68

1.40-1.44 1.40-1.48 1.41-1.46 1.40-1.49 1.41-1.46 1.41-1.49 1.41-1.47 1.41-1.48 1.40-1.46 1.40-1.46 1.40-1.46

a

C-B 1.51-1.55 1.50-1.54 1.48-1.53 1.51-1.55 1.50-1.53 1.50-1.55 1.51-1.54 1.50-1.54 1.51-1.54

B-B

1.59-1.70

1.59-1.66 1.66-1.82

M-M

Dmin (Å)

∆Dmax (Å)

charge on M (Bader)

2.55-2.81 2.55-2.95 2.51-3.56 2.57-2.94 2.22-3.46 2.23-3.30 2.20-3.52 2.20-3.54 2.66-2.97 2.62-2.86 2.61-3.05

2.20 1.69 1.38 1.83 2.20 1.59 1.51 1.14 2.12 2.40 2.55

0.21 0.27 0.67 0.38 0.19 0.44 0.66 1.05 0.25 0.48 1.14

0.40 0.89 0.77 0.31 1.11 1.55 1.41 1.26 0.69 0.32 0.14

The symbols shown here correspond to those of Table 2.

Figure 8. Geometry-optimized Pt6/B-C systems with and without the external electric field. The gray, green, and blue atoms are carbon, boron, and platinum, respectively.

binding energies of the metal clusters on the boron-doped graphite were still significantly higher than the binding energies of the metal clusters on pristine graphite. The range of bond lengths, Dmin, and ∆Dmax, in the presence and absence of the external electric field were similar. In the presence of the positive electric field, the Bader charges on the metal clusters were either more negative (or less positive) when compared to the corresponding metal clusters without the electric field, due to the direction of the field, which opposes the flow of electrons from the cluster to the support. The opposite effect was seen in the presence of the negative electric field, in which case the field assists the flow of electrons from the metal clusters to the graphite supports. 4. Conclusions Our DFT calculations show that the metal clusters considered here (Pt6, Pt2Ru4, and Au6) are strongly adsorbed on borondoped carbon surfaces. However, the differences among the binding energies of the metal clusters on the three different boron-doped graphite configurations (BC5, B-C, and B-B) were not substantial. The magnitude of the adsorption energies

of the metal clusters on the graphite surfaces were Pt2Ru4 > Pt6 > Au6, regardless of the particular graphite model (pristine or doped). This ranking was also consistent with our calculations of single-atom adsorption. By analyzing the density of states in each of our systems, we suggest that the stabilization of the metal clusters on the boron-doped graphite is due to the significant overlap of the p-states of the graphite and the d-states of the metal clusters. The binding energies are also consistent with the work function gaps between the cluster and the support in each of our systems. While our investigation was limited to boron dopants, there could also be other dopants or co-dopants in graphite (such as nitrogen) that exhibit similar or better characteristics, and we are currently exploring these other possibilities. In the presence of an external electric field, the binding energies of the metal clusters on the graphite surfaces were typically slightly lower than the binding energies of the metal clusters on surfaces without an electric field. This resulted in the metal clusters still being significantly stable on boron-doped graphite surfaces when compared to the pristine graphite. In conclusion, although thermal sintering would be minimal at typical fuel cell operating conditions, the catalysts used in electrochemical systems may experience increased sintering due to the voltage and the surrounding charged species, since the adsorption on the surface may be weakened. Also, since the shape of the metal clusters (especially Au6) and the charge distribution on the clusters changed when adsorbed on borondoped graphite, any reactions that are effected by the structure or the local electrostatics could be different. While the borondoped surfaces may help mitigate sintering, the stabilizing effect may wane as the particles increase in size, closer to the dimensions of actual fuel cell catalysts. Unfortunately, larger system studies quickly become impractical due to the poor computational scaling of first-principles DFT methods. Therefore, we are currently using experimental routes to verify our DFT predictions. Acknowledgment. Funding for this work was provided by DOE EPSCoR, Grant No. DE-FG02-01ER45867. Supercomputer resources were provided by the Alabama Supercomputer Center, NCSA TeraGrid, and the Pacific Northwest National Laboratory EMSL facility. Supporting Information Available: Figures of (a) the projected density of states of the boron-doped graphite models, (b) projected density of states of the Pt6 cluster adsorbed on the boron-doped graphite models, (c) projected density of states of the Pt2Ru4 cluster adsorbed on the different boron-doped graphite models, and (d) projected density of states of the Au6

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