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Thermodynamics of Pore Filling Metal Clusters in Metal Organic Frameworks: Pd in UiO-66 Lasse B. Vilhelmsen, and David S. Sholl J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/jz301806b • Publication Date (Web): 28 Nov 2012 Downloaded from http://pubs.acs.org on November 30, 2012
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Thermodynamics of Pore Filling Metal Clusters in Metal Organic Frameworks: Pd in UiO-66 Lasse B. Vilhelmsen† and David S. Sholl∗,‡ Interdisciplinary Nanoscience Center (iNANO) and Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark, and School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100, USA E-mail:
[email protected] ∗ To
whom correspondence should be addressed Nanoscience Center (iNANO) and Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark ‡ School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100, USA † Interdisciplinary
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Abstract Metal Organic Frameworks (MOFs) have experimentally been demonstrated capable of supporting isolated transition metal clusters, but the stability of these clusters with respect to aggregation is unclear. In this paper we use a genetic algorithm together with density functional theory calculations to predict the structure of Pd clusters in UiO-66. The cluster sizes examined are far larger than in any previous modeling studies of metal clusters in MOFs, and allow us to test the hypothesis that the physically separated cavities in UiO-66 could stabilize isolated Pd clusters. Our calculations show that Pd clusters in UiO-66 are, at best, metastable and will aggregate into connected pore filling structures at equilibrium.
Table of Content Graphics
Dose Pd
Connected vs
Isolated
Keywords Cluster stability, heterogenous catalysis, support structures, density functional theory, genetic algorithm, agglomeration
Subject Category • Surfaces, Interfaces, Porous Materials, and Catalysis
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Metal Organic Frameworks have attracted much attention in fields such as gas separation 1,2 , gas storage 3 , drug delivery 4 , sensing 5 , and catalysis 6–8 . A MOF consists of a mixture of metals and organic linkers which together form a periodic network 9–11 . It is possible to synthesize 1D, 2D, and 3D connected MOFs with diverse chemical functionality and different cage and window size distributions in the size range from a few Å to multiple nm 12–14 . In heterogeneous catalysis it is often desirable to disperse an expensive metal as nm sized clusters onto a support structure. The primary role of the support is often to reduce the mobility of the metal clusters thus increasing the lifetime of the catalyst 15 . The ordered nanoporous structure of MOFs defines a potentially useful support for metal clusters. Since the initial work by Fischer on Pd in MOF-5 16 , subsequent experiments have studied Au, Ag, Pd and Ru in MIL-101 17 , ZIF8 18,19 , and MOF-5 16,20 . Lu et al. have recently emphasized three challenges in the use of MOFs as supports for metal clusters 21 : Inserting the metal into the MOF, controlling the size and shape of clusters in the MOF, and the stability of clusters towards agglomeration. If clusters are thermodynamically metastable with respect to aggregation, then creating well dispersed clusters must rely on kinetic limitations. In some materials that define spatially inhomogeneous environments, metal clusters can be stable against aggregation. 2D examples of this phenomenon include graphene moirés on single crystal metal substrates 22 and metal adatoms on Fe3 O4 surfaces 23 . Our aim in this paper is to determine whether this kind of stability can be achieved in MOFs using a specific example where this concept is plausible, Pd in UiO-66. Our choice of UiO-66 (Zr6 O4 (OH)4 (CO2 )12 secondary building blocks connected by 1,4benzene-dicarboxylate linkers) 24 , is motivated by our recent study of Au and Pd clusters in MOF74 25 . MOF-74 has roughly cylindrical pores, and we have shown that small Au and Pd clusters can diffuse along these pores with moderate activation energies. UiO-66 is a MOF with excellent thermal and chemical stability 24,26 with pores defined by cages separated by relative narrow windows with a diameter of 3.87 Å (calculated using the method of Haldoupis et al. 12 ). These cages have the same connectivity as interstitial sites in fcc solids; the smaller cages (type A) are tetrahedrally
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coordinated with the larger octahedral cages (type B) as shown in Figure 1. A cages connect only to B cages, and vice versa. UiO-66 has two A type cages that differ only by the presence of H atoms bonded to an O atom in each corner. Our calculations indicate that these two cages show negligible differences in metal binding energies, so we neglect this distinction below.
Figure 1: The two cage types of UiO-66. Each corner unit contains 32 O atoms encapsulating 6 Zr atoms. To the left the A type cage is shown and to the right the B cage. The semi-transparent yellow spheres show the cavity diameter of each cage. The coloring is: C: Gray, H: White, O: Red. Characterizing metal clusters comprised of more than a few atoms solely with density functional theory (DFT) is challenging because of the many structural isomers these clusters can adopt. To meet this challenge, we performed DFT calculations in conjunction with a genetic algorithm (GA) used to generate candidate structures 27 . Our earlier work on MOF-74 showed the applicability of this approach to MOFs 25 . In the following we apply this method to clusters with >30 atoms, far larger than in our earlier work. We do not know of other examples that systematically examine large sets of cluster isomers at this level of theory on 2D surfaces or in 3D porous materials. The real-space DFT code GPAW 28,29 was used for all energy and force calculations with the generalized gradient approximation PBE 30 employed for the exchange and correlation effects. A grid spacing of h = 0.19 Å was used and only the Γ-point was sampled. The unit cell of UiO66 is taken from Cavka et al. 24 and the unit cell parameters were optimized using GPAW. The optimized unit cell parameters are a = b = c = 14.90 Å, α = β = γ = 60.0 ◦ , in good agreement with experiment. All calculations used a cell containing one unit cell. The only change made to the GA compared to Refs. 25,27 is in how the starting populations have been made. To make it possible to randomly generate closely packed starting populations a Monte Carlo technique with 4
insertions, deletions and displacements has been used. Atoms are not allowed to move outside the volume defining the given cage and as in Ref. 25 atoms are not allowed to overlap. As in Ref. 25 we use a two-step optimization technique where structures are first relaxed with the use of a LCAO basis and subsequently relaxed using the real-space grid basis (GB) if the structure is different than previously encountered structures. It is reasonable to expect that small Pd clusters will preferentially adsorb in the smaller A cage as it exposes the carbon atoms of the organic linkers whereas the larger B cage has H atoms pointing directly toward the center of the cage. To test this expectation, the GA was used to analyze the structure of Pd8 clusters in each cage. The GA was run separately for each cage with the starting population for each run confined to the largest cavity diameter (LCD) 12 of the cage (the yellow spheres seen in Figure 1). The LCD for the A (B) cage is 7.48 Å (8.59 Å) respectively. The GA was used to test 180 (116) Pd8 candidates in the A (B) cage respectively. Figure 2 shows the preferred structure in each cage as identified by the GA. The cluster in the B cage is 2.1 eV higher in energy and there is, as expected, a clear bias towards the A cage for small clusters. The adsorption energy (see definition in the Supporting Information (SI) Eq. S1) for Pd8 in the A cage of UiO-66 is 1.27 eV more favorable than for Pd8 in MOF-74 as computed with equivalent methods 27 . This increased binding is related to the number of aromatic rings to which the cluster can coordinate; in UiO-66 (MOF-74) the Pd8 cluster coordinates to five (three) different rings.
Figure 2: The most stable structure found for Pd8 adsorbed in the two cage types. Pd is colored dark blue.
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Having established that adsorption in the A cage is preferred for small clusters we now move on to an investigation of larger clusters. To compare the energy of differently sized clusters a common reference point is needed. We take as reference the energy of a Pd atom in vacuum, EPd1 , and define EPd (N) =
Etot (N) − EMOF − N · EPd1 N
(1)
where Etot (N) is the total energy of the MOF with PdN adsorbed and EMOF is the energy of the MOF without metal adsorbed. Figure 3 shows the lowest energy structures of Pd28 and Pd32 in the A cage from our GADFT calculations (images for N = 12, 16, 20, 24 are shown in the SI Figure S1). The distribution of EPd (N) for each cluster size is plotted in Figure 4 and the most stable ones in Figure 5. The number of local minima computed, Ntested , and EPd (N) is listed in Table 1. Figure 5 shows that the clusters become more stable as the cage is filled. With 28 Pd atoms, however, the cluster forms a high symmetry structure that exactly fills the cage and there is an energy cost associated with adding more atoms to the cage.
Pd28
Pd32
Figure 3: The most stable structures of Pd28 and Pd32 as identified with the GA. The energetics and number of tested structures are shown in Table 1. The higher stability of Pd28 compared to Pd32 can be explained by two mechanisms. The first relates to the deformation of the UiO-66 framework, and the second to the Pd coordination. The deformation energy per Pd atom (defined in Ref. 25 and restated in the SI Eq. S2) for the Pd28 and Pd32 clusters are Ed (28)/28 = 0.200 eV and Ed (32)/32 = 0.219 eV respectively (see Table Table 1). The difference in deformation energies per Pd atom, 0.019 eV, accounts for more than 6
Table 1: Energetics for the structures marked in Figure 5. EPd (N)
Ed (N)
Ntested (LCAO) Ntested (GB)
Pd8 Pd12 Pd16 Pd20 Pd24 Pd28 Pd32
-2.57 eV -2.71 eV -2.81 eV -2.86 eV -2.88 eV -2.91 eV -2.87 eV
1.67 eV 2.68 eV 2.66 eV 3.09 eV 3.76 eV 5.61 eV 7.02 eV
280 200 165 186 514 577 560
159 109 86 110 112 132 206
Pd28 +Pd12 Pd28 +Pd16
-2.91 eV -2.96 eV
5.72 eV 371 5.99 eV 541
135 134
Footnote: Energy per Pd, EPd (N), framework deformation energies, Ed (N), and the number of tested candidates with the GA, Ntested , for the structures shown in Figure 2, Figure 3 and Figure 6 and in the SI Figure S1. LCAO and GB refer to the basis set used for the DFT calculations.
−2.0
N = 8B N =8
N = 12 N = 16
N = 20 N = 24
N = 28 N = 32
100 150 Configuration Number
200
EPd(N ) / eV
−2.2 −2.4 −2.6 −2.8 −3.0 0
50
Figure 4: Distribution of EPd for each localized cluster size considered. For Pd8 both the A and B cage was tested. The B cage is indicated with a B.
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−2.5
Pd Cluster Localized in Cage A Pd Cluster Extending to Cage B
EPd (N ) / eV
−2.6 −2.7 −2.8 −2.9 −3.0
8
12
16
20 24 28 32 36 Number of Pd Atoms
40
44
Figure 5: Energy per Pd atom for increasingly large Pd clusters in UiO-66. The structures are shown in Figure 2, Figure 3 and Figure 6 and in the SI Figure S1. half of the difference in Pd stability (EPd (32) − EPd (28) = 0.035 eV). The second contribution to the lower stability of Pd32 compared to Pd28 is related to the coordination and symmetry of the adsorbed clusters. The Pd28 cluster has four fold symmetry with three Pd atoms exposed in each window (see SI Figure S2). The 12 exposed Pd atoms all coordinate to five Pd atoms, with further 12 seven fold coordinated atoms behind them and a core of four twelve fold coordinated atoms in the center. The structure of Pd32 is the same as Pd28 , but with the additional atoms added in two of the windows. These four additional Pd atoms only coordinate to four Pd atoms each, reducing the lowest coordination of atoms in the cluster. The four added Pd atoms thus both increase the deformation of the UiO-66 framework and the internal coordination of the cluster. Having established that Pd28 is the largest cluster that can be confined to the A cage, we now consider clusters extending out of this cage. It is advantageous to exploit the periodicity of the UiO-66 structure to simulate a high Pd loading. A computational cell containing one unit cell of UiO-66 has two A cages and one B cage. That means that four of the eight windows into the B cage are from the same A cage. Keeping one A cage in the cell filled with Pd28 allows us to investigate the energetics of connecting a network of A cages through B cages.
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Figure 6 shows the structure of the most stable Pd12 and Pd16 clusters in the B cage when one of the A cages in the cell is filled with Pd28 . In these calculations, sampling using the GA was only applied to atoms in the B cage, although all Pd atoms and the MOF framework were optimized to find local energy minima. The energetics of these added clusters are shown in Figure 5 for 28+12 = 40 and 28+16 = 44 atoms respectively. An illustration emphasizing the extended nature of these clusters is shown in the SI Figure S3.
Figure 6: Pd12 (left) and Pd16 (right) adsorbed in the B type cage together with Pd28 adsorbed in the A type cage. The truncated Pd28 cluster in the A type cage is marked with bright semi transparent spheres. Figure 5 shows that the energy of having isolated Pd28 clusters in the A cage is comparable to the energy of connecting these clusters through Pd12 in the B type one. A Pd16 cluster in the B cage, however, is sufficient to connect the four windows in a way that lowers EPd (N) compared to the isolated clusters. The structure of the added Pd16 cluster is, just as Pd28 in the A cage, in a four fold symmetric geometry. Three Pd atoms coordinate to each exposed window of the Pd28 cluster and the remaining four Pd atoms are in a nine fold coordinated geometry. The coordination of the previously five fold coordinated Pd atoms at the windows increase to seven fold coordinated atoms and there is thus only 7, 9 and 12 fold coordinated Pd atoms in the framework. An interesting feature of this stucture is that the 16 Pd in the B cage interact only weakly with the framework. The adsorption energy of these 16 atoms alone is 6.21 eV less favorable than Pd16 in the A cage. The previous calculations show that even though UiO-66 has relatively narrow windows separating its cages, it cannot thermodynamically limit the growth of Pd clusters across cage boundaries. We began this work with the hypothesis that the spatially inhomogeneous pores in UiO-66
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might make disperse metal clusters thermodynamically stable. Our calculations show this is not the case for Pd, and it seems likely that the same conclusion applies to other metals in this MOF. Our results, however, suggest a way to select MOFs that can potentially yield stable disperse clusters. The discussion above highlighted the ability of multiple Pd atoms to coordinate across the windows connecting A and B cages in UiO-66. The diameter of this window is, as mentioned, 3.87 Å, which is clearly large enough to accommodate multiple metal atoms. There are many MOFs, however, with window dimensions smaller than this 12,31 . MOFs with cages separated by windows 1-2 metal atoms in diameter may therefore be good candidates for stabilizing well dispersed metal clusters. Finally, we comment on the desirable metal loading in any MOF that does allow dispersed clusters to exist. Our calculations support the intuitive idea that clusters will typically grow to fill individual cages in MOFs. Therefore it would be vital for catalytic uses to use a loading below that which would prevent percolating networks of unfilled cages existing in the MOF to allow access of reactants and products to metal clusters. This means that only MOFs with 2D or 3D cage topologies could be considered for these purposes. Acknowledgements: DSS received partial support from the National Science Foundation (Grant number 0966582) and the Center for Atomic Level Catalyst Design, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001058 (Center for Atomic Level Catalyst Design). LBV received support from the Lundbeck Foundation. All calculations were carried out with support from the Danish Center for Scientific Computing (DCSC). Supporting Information Available: The supporting information contains definitions of adsorption and deformation energies, a figure of Pd12 , Pd16 , Pd20 and Pd24 in the A type cavity, a figure of Pd28 and Pd32 in the A-type cavity coloured by the atoms coordination, and finally a figure of how the spanning Pd cluster connects throughout the framework. This information is available free of charge via the Internet at http://pubs.acs.org/.
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