Topologically Guided, Automated Construction of MetalâOrganic

Article Cite This: Cryst. Growth Des. 2017, 17, 5801-5810

pubs.acs.org/crystal

Topologically Guided, Automated Construction of Metal−Organic Frameworks and Their Evaluation for Energy-Related Applications Yamil J. Colón,†,‡,# Diego A. Gómez-Gualdrón,*,†,§,# and Randall Q. Snurr*,† †

Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States ‡ Institute for Molecular Engineering and Materials Science Division, Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States § Department of Chemical and Biological Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401, United States S Supporting Information *

ABSTRACT: Metal−organic frameworks (MOFs) are promising materials for a range of energy and environmental applications. Here we describe in detail a computational algorithm and code to generate MOFs based on edge-transitive topological nets for subsequent evaluation via molecular simulation. This algorithm has been previously used by us to construct and evaluate 13 512 MOFs of 41 different topologies for cryo-adsorbed hydrogen storage. Grand canonical Monte Carlo simulations are used here to evaluate the 13 512 structures for the storage of gaseous fuels such as hydrogen and methane and nondistillative separation of xenon/krypton mixtures at various operating conditions. MOF performance for both gaseous fuel storage and xenon/krypton separation is influenced by topology. Simulation data suggest that gaseous fuel storage performance is topology-dependent due to MOF properties such as void fraction and surface area combining differently in different topologies, whereas xenon/ krypton separation performance is topology-dependent due to how topology constrains the pore size distribution.

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INTRODUCTION Metal−organic frameworks (MOFs) constitute an exciting class of materials synthesized through solvothermal reaction of organic and inorganic precursors, which leads to the selfassembly of three-dimensional crystalline networks. In MOFs, inorganic clusters (nodes) are connected by organic molecules (linkers). Upon removal of the solvent, the MOF is “activated,” leaving a porous structure with textural and chemical properties potentially useful in applications impacting energy usage such as gaseous fuel storage,1,2 nondistillative separations,3−5 and selective catalysis.6−9 MOFs are attractive in great part due to their tunability, which in principle allows for careful alteration of the MOF structure to optimize properties for a target application.10,11 Modification of the combination of inorganic and organic components used in synthesis can mildly or drastically (as desired) alter the MOF properties as a result of changes in the underlying MOF topology along with the size, shape, and chemistry of the pores.12−16 Researchers around the world have taken advantage of the modular (i.e., building block-based) nature of these materials to synthesize thousands of distinct MOFs.17,18 Given the difficulty in comprehensively evaluating such a large “structure space” experimentally, a large fraction of synthesized MOF structures have been evaluated computationally for select applications.18−26 There is, however, an even larger structure space © 2017 American Chemical Society

of millions of MOFs that are yet to be synthesized, in which better materials could be found. Since the structures of these MOFs are not available from experiment, there is a need for methods to computationally construct large numbers of MOF structures for subsequent evaluation through molecular simulation methods. Wilmer et al.27 computationally constructed over 137 000 MOFs using a “bottom-up” approach where molecular building blocks are sequentially connected until a periodic crystal is formed. These structures have been evaluated in silico for various gas storage27−29 and separation3,4,30 applications, resulting in the establishment of useful structure−property relationships3,4,27 and identification of some promising structures that were then synthesized and tested experimentally.27,30 With the chosen building blocks, this implementation of bottom-up MOF construction, however, only produced MOFs in a limited number of topologies (six) with a strong bias toward pcu MOFs.31 This low number does not capture the topological diversity of MOFs. Therefore, methods to computationally construct these materials while controlling the topology are being developed by several groups.32−36 Received: June 18, 2017 Revised: September 6, 2017 Published: September 11, 2017 5801

DOI: 10.1021/acs.cgd.7b00848 Cryst. Growth Des. 2017, 17, 5801−5810

Crystal Growth & Design

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code: Topologically Based Crystal Constructor (ToBaCCo). Similar to the case of molecular simulation codes, the capabilities of the different construction codes are relatively similar, with algorithmic differences potentially leading to differences in speed and handling of input and output files. We wrote ToBaCCo with the goal of being an accessible code to occasional users and MOF researchers without advanced knowledge in crystallography, graph theory, or computational methods. For instance, with the code, we provide intuitive topological blueprint files in the simplest space group: P1. ToBaCCo also allows the user to simplify the construction of MOFs by splitting or merging building blocks as convenient. For instance, organic linkers can be split into edges and nodes to reduce the number of building blocks required to construct a given number of MOFs. Or MOF components can be merged into “supramolecular” building blocks to enable the use of simpler topological blueprints. Herein, we describe in detail the algorithm and input information for our code. In previous work, ToBaCCo was used to construct a set of 13 512 MOFs in 41 different topologies, which were evaluated for cryo-adsorbed hydrogen storage.56 Some promising structures were identified and subsequently synthesized and experimentally tested. ToBaCCo has also been used to construct models to help elucidate the structure of novel MOFs.57 In addition to describing our code, here we explore, through the screening of the above-mentioned topologically diverse set of MOFs (which are nonfunctionalized), the potential role of topology in MOF performance for the storage of gaseous fuels (hydrogen and methane) and for the nondistillative separation of xenon/krypton mixtures.

Topology-based design has been central to the development of new MOFs in the lab.14,15,37 Often, when a MOF in a synthetically attractive topology is realized, the MOF structure is modified using isoreticular expansion,11 linker functionalization,10,38 and metal substitution39 as strategies to obtain analogous MOF structures with tuned properties. This has led experiments to focus on certain topologies more intensively than others. For instance, the (3,24)-connected rht topology pioneered by Nouar et al.40,41 forbids catenation, so it has been exploited to attain very high gravimetric surface areas via isoreticular expansion. Thus, a number of rht MOFs have been synthesized and tested for methane and hydrogen storage, which are applications that can benefit from large surface areas.42,43 In another instance, the 12-connected fcu topology pioneered by Cavka et al.,44 which is based on Zr6O8 nodes that typically confer MOFs with high hydrothermal stability, has been widely investigated (especially the flagship UiO-66 material). Looking to exploit the stability of Zr6O8 but with different MOF pore properties, other authors explored other Zr6O8-compatible topologies such as the (4,12)-connected ftw topology developed by Morris et al.45 (recently exploited by Wang et al.46 and Liu et al.47 to obtain water-stable ultrahigh surface area MOFs) and the (4,8)-connected flu topology introduced by Zhang et al.48 MOF topology could also impact MOF performance more directly. A computational study on Zr-MOFs of four topologies by Gomez-Gualdron et al.49 showed ftw MOFs to outperform scu and csq MOFs for volumetric methane storage, despite these three topologies featuring the same kind of linkers. Another computational study by Bao et al.25 on ditopic linkerbased MOFs of nine topologies showed different correlations between methane adsorption and MOF surface area depending on the topology. Such differences could be due to topologydependent property-property relationships. Martin and Haranczyk50 computationally investigated pseudo-MOFs based on “abstract” linkers and found a topology-dependent relationship between gravimetric and volumetric surface areas. Most recently, experiments by Deria et al.51 on the catalytic activity of three Zr-MOFs of ftw, scu, and csq topologies showed topology-dependent performance for acyl transfer reactions. Experimental efforts to develop new MOFs topologies continue to date.37,52,53 However, experimental exploration of new topologies can be slow due to the need to identify optimal synthesis conditions (i.e., precursors, modulators, concentrations, temperature) for every new MOF. Computational efforts can economize experimental efforts by identifying the most promising MOFs or MOF topological “families” on which to focus. To this end, comprehensive sets of diverse topological MOF families could be studied computationally much more easily than experimentally to elucidate the potential role of topology in MOF performance for target applications. To control topology during computational MOF construction, a top-down or reverse topological approach35 can be used. Contrary to the bottom-up approach,27 the top-down approach introduces some representation of MOF topology as an input and uses it as a guide to map building blocks onto it. Different algorithmic variations of the top-down approach to construct MOFs have been proposed and used by Lewis et al.,54 Rodriguez-Albelo et al.,55 Schmid et al.,35 Martin and Haranczyk,34 Addicoat et al.,33 and Boyd and Woo,32 and implemented in their respective codes. Here, we present our own top-down algorithmic approach and associated in-house

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MOF CONSTRUCTION ALGORITHM Our top-down MOF construction algorithm is written in Python and uses topological blueprints and molecular building blocks as input. With the goal of facilitating the use of ToBaCCo by third parties, we aimed to set up the code so the input files (vide inf ra) and overall use of the code are as intuitive as possible for the occasional user. The code and all pertinent files can be found at https://github.com/tobaccomofs/tobacco. Topological Blueprints. ToBaCCo reads information about the topological blueprintwhich corresponds to a periodic, abstract netthat guides the placement of MOF building blocks from a template file. The template file contains information about the net (or topological blueprint): unit cell parameters, positions of the net nodes and edges, and coordination and symmetry of the nodes. The unit cell is described by the a, b, and c crystallographic vectors, and the positions of the net nodes and edges are provided in fractional coordinates. Information on the coordination and symmetry of the nodes is also provided and used by ToBaCCo to identify building blocks compatible with the blueprint. Some wellknown MOFs and their underlying nets are presented in Figure 1. Net nodes can be thought of intuitively as points where, as one “traces” the net, one sees a change in direction. Net edges are the straight lines that connect nodes,14 and edge positions are the midpoints of these lines. The provided version of the code can construct MOFs based on edge-transitive nets, i.e., those where all edges are of the same “kind.” This means that edge-transitive nets are those nets where all edge positions can be reproduced by symmetry operations on any given edge. In 5802



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template file to denote a given “kind” of symmetry. For instance, “4” for tetrahedral symmetry (Td) and “5” for square symmetry (D4). ToBaCCo does not associate symmetry operations with this integer code, but it uses the code to identify compatible building blocks (as explained in the next subsection), which it will map onto the nodes. Building Blocks. ToBaCCo reads the geometry information on molecular building blocks from crystallographic information files (CIFs). One can think of building blocks as molecular units that when properly connected form a MOF. Computationally, there are different ways that a MOF can be dissected into building blocks. Two ways to dissect IRMOF-1 are shown in Figure 3. One option would be based on the

Figure 1. MOF structures (top) and their corresponding underlying nets (bottom). For top row, C = gray, H = white, O = red, Zn = blue, Zr = cyan, and Cu = orange. For bottom row, red and green = nodes, blue = edges.

the template file, however, all edge positions are provided explicitly. Edge-transitive nets can have up to two kinds of nodes, under the condition that if “x” and “y” are the kinds of these nodes, then the only kind of edge in the net is the one that connects “x” with “y.” For both kinds of nodes, all node positions can be reproduced by symmetry operations on any given node of the same kind. In the template file, however, all node positions are provided explicitly. Notice that the same symmetry operations are applied to the nodes and edges, and these symmetry operations denote the space group of the net. Since the template files explicitly write all positions of edges and nodes, ToBaCCo does not perform symmetry operations and in practice treats the nets as P1 (the lowest symmetry space group). An excellent source to get the information for nets is the Reticular Chemistry Structure Resource (RCSR) database.58 The template files for 41 edge-transitive nets used as topological blueprints to construct 13 512 MOFs are provided in the GitHub repository (vide supra). Each template file also includes information about the number, coordination, and symmetry of each kind of node. The coordination of a node is the number of edges connected to it, whereas the symmetry describes the spatial arrangement of edges around the node. Nodes can have the same coordination but different symmetry as illustrated in Figure 2. The RCSR database provides the point group describing the symmetry of each kind of node in a net. For simplicity, however, an integer code is used in the

Figure 3. Possible decompositions of IRMOF-1 into building blocks. (a) Assembled IRMOF-1. (b) IRMOF-1 decomposed into building blocks consistent with chemical synthesis. (c) IRMOF-1 decomposed into building blocks that facilitate computational construction. Inorganic and organic building blocks in (b) and (c) enclosed in boxed area. (d) Connection of building blocks in (b) require four connection points per coordination. (e) Connection of building blocks in (c) only require two points per coordination. C = gray, O = red, H = white, Zn = blue, connection points = yellow.

molecules used in the MOF synthesis, for example, considering carboxylate oxygens as part of the organic building block as shown in Figure 3b. The way presented in Figure 3c is, however, more convenient because it results in building blocks with simpler connections. The connection points, which coincide with building block atoms, are tagged in the CIF. Connecting the building blocks, then, amounts to making a single bond per connection (Figure 3e). This building block decomposition also makes sense from a topological net perspective, since there is only one connection between nodes and edges. In Figure 3, the Zn4O-based cluster is a “nodular” building block and the phenyl is a “connecting” building block. ToBaCCo places connecting and nodular building blocks onto net edges and compatible nodes (same symmetry), respectively. ToBaCCo determines the nodular building block symmetry from the CIF name, which must start as “sym_n” where n is an integer equivalent to those used in the template file to describe the symmetry of the net nodes. Inspecting HKUST-1 and its underlying net in Figure 1, it is clear that multitopic organic linkers can also occupy net nodes. In these cases, one can think of the linker central group as occupying a net node and the linker arms as occupying net edges. Accordingly, for use with ToBaCCo, multitopic organic linker molecules can be dissected into connecting and nodular (organic) building blocks. This is

Figure 2. Examples of nodes with the same coordination but different symmetry. (a) Square planar (left) and tetrahedral (right) 4coordinated nodes. (b) Octahedral (left) and triangular prism (right) 6-coordinated nodes. Red = node, blue = edges. Green lines outline the polyhedron representing the node coordination and symmetry. 5803



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Figure 4. Scaling factor calculation. The total distance from nodular building block to nodular building block, a + x + b + x + c (right), is divided by the node to node distance, dNN (left), in the template to obtain the scaling factor, S.

vectors that point from the building block centroid to the connecting points. Then, ToBaCCo uses the positions of the n edges associated with the node to create n unit vectors that point from the node to the edgesn is the coordination of the nodes. Using quaternion-based rotation,59 ToBaCCo finds the rotation that maximizes the matching between the node and building block vectors. The whole building block is then rotated per that rotation. For the rotation and matching maximization, the transformations.py routine by Gohlke60 is used. Note that the node vectors are not necessarily listed in the same order as building block vectors; e.g., the first listed node vector is not necessarily supposed to match with the first listed building block vector. When this occurs, it prevents the matching criterion to be met. Thus, brute force shuffling of vectors until the criterion can be met is done for n ≤ 8. For n = 10, 12, and 24, ToBaCCo currently takes advantage of special symmetries of the used building blocks to assist the matching (see Supporting Information), but more generalized procedures applicable to all n > 8 cases are desirable. Connectivity Information. ToBaCCo does not check for atom overlap. The reason is that atoms that may originally appear too close (when this occurs, it often corresponds to long functional groups) could find reasonable positions once the structures created by ToBaCCo are optimized with some molecular mechanics code. To this end, the connectivity information is inherited from the building blocks (detailed in standard form in the building block CIF) and replicated in the constructed MOF. This prevents incorrectly establishing a connection between atoms that are too close but should not be connected, as would occur if a postconstruction distance-based connectivity determination routine were used. The only connections that ToBaCCo establishes postconstruction are the connections between building block connecting points, which are simply established using the vectors of the building blocks. The position and bonds (including type of bond information) for all atoms in the constructed MOFs are detailed in the final MOF CIF, which then can be used as input for structure optimization. The name of the CIF contains information about the topology and building blocks used in the MOF construction. Running through a Library of Nets and Building Blocks. When presented with a library of nets (topological blueprints) and nodular and connecting building blocks, the workflow of ToBaCCo can be summarized as in Figure 5. The code iterates through different nets. For each net, it iterates through the nodular building blocks and selects those that are compatible. For each compatible set of nodular building blocks, it iterates through all connecting building blocks. For a given selection of connecting and compatible nodular building blocks,

the approach we used, as it reduces the number of building blocks needed as input to construct MOFs with different multitopic linkers. Building block CIFs used in the automated MOF construction are provided in the GitHub repository (vide supra). When ToBaCCo determines that a set of building blocks is compatible with a given net, it then proceeds to resize the net so the building blocks to be placed approximately fit onto the net. Since ToBaCCo is currently set to work only with edgetransitive nets, only a single scaling factor is needed to resize the net because edge-transitive nets expand and contract isotropically. ToBaCCo sets the scaling factor to get the distance between connecting points (of separate building blocks) that are intended to connect to be around 1.5 Å (a distance within the range of typical covalent bonds). Figure 4 illustrates how ToBaCCo calculates the scaling factors using the construction of IRMOF-1 as example. First, the node to edge distance, dNE, is read from the net template file. The node to node distance, dNN, is calculated as twice this distance. The scaling factor, S, is equal to (a + x + b + x + c)/dNN, where a and c are the average distance between the centroid of the nodular building blocks (to be mapped onto the net) and their corresponding connecting points (which are tagged in the CIFs), b is the distance between the connecting points of the connecting building block, and x is equal to 1.5 Å. Evidently, for IRMOF-1, a and c are the same, as only one kind of nodular building block is used to construct the structure. Once the net is properly resized, ToBaCCo proceeds to place the building blocks onto the net. Building Block Placement. To place the building blocks onto the net, ToBaCCo initially focuses on the building block centroids. For instance, for the initial placement of a nodular building block, ToBaCCo determines the building block centroid coordinates from the CIF and the target node coordinates from the template file (fractional coordinates are read from these files, but ToBaCCo converts them into Cartesian coordinates). The difference vector between the node and building block centroid coordinates determines the translation vector applied to all building block atoms. The result is that the building block is “centered” onto the node. This procedure is repeated with all nodes and edges and the respectively matching nodular and connecting building blocks. Once a nodular or connecting building block is centered onto a node or edge, respectively, the building block is rotated around its centroid so the building block is correctly oriented. To do this, ToBaCCo focuses on the building block centroid and connecting points. For instance, to properly orient a given nodular building block on its corresponding node, ToBaCCo uses the positions of the n connecting points to create n unit 5804



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molecules were modeled with a single LJ site according to the TraPPE model.67 LJ parameters for the xenon68 and krypton69 atoms were taken from the literature. LJ parameters for the MOF atoms were assigned according to the Universal Force Field.62 A cutoff of 12.8 Å was used for all LJ interactions, and Ewald summations were used to calculate the Coulomb interactions. Lorentz−Berthelot mixing rules were used to determine LJ parameters for cross-term interactions. For each MOF, a supercell composed of the necessary number of unit cells to avoid adsorbate molecules interacting with their periodic images was used. MOF atoms were held fixed during simulations. Calculation of Other Properties. Surface areas of MOF structures were calculated by rolling a nitrogen probe over the framework atoms.70 Void fractions for the structures were calculated using Widom insertions of He.71 Heats of adsorption were calculated from fluctuation theory during the GCMC simulations.72 The above were performed using the RASPA code.63 The pore limiting diameter (PLD) and largest cavity diameter (LCD) for each MOF were calculated using Zeo++.73 Calculations with Zeo++ used the high accuracy flag and considered framework atoms to have the same diameters as the σ LJ parameters listed in Table S1.

Figure 5. ToBaCCo workflow when running through a library of nets and building blocks.

ToBaCCo scales the net and then proceeds to map the building blocks onto the current net per the procedures detailed above and finally establishes the missing connectivity information (that is not inherited from the building blocks). It is worth pointing out that we found thousands of structures only containing carbon-based nodes when ToBaCCo was run with our library of building blocks. Those structures (easily identified from their CIF names) were discarded, resulting in the 13 512 MOFs we focused on in our previous work56 and here.

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RESULTS AND DISCUSSION Dependence of Property−Property Relationships on Topology. Before examining how MOF performance is correlated with material properties, in this subsection, we examine how different MOF properties are correlated with each other. The evaluated structures present void fractions between 0 and 1, volumetric surface areas between 0 and 2800 m2/cm3, gravimetric surface areas between 0 and 10 000 m2/g, and pore sizes between 0 and 70 Å. Our goal was to look for any topological dependence of the way MOF properties relate to each other, as this may be reflected in a topology-dependent performance for the applications we are considering in this work. Figure 6 plots the relation between volumetric surface area and void fraction, with eight topologies highlighted to illustrate

MOLECULAR SIMULATION METHODS

MOF Structure Optimization. The structures constructed by ToBaCCo are stored as CIFs, making software like Materials Studio61 well suited for visualization and geometry optimization. Each constructed MOF structure was optimized using the Forcite module in Materials Studio.61 The MOFs were optimized in two-steps: (i) optimization while fixing the unit cell lattice parameters to help release significant bond strain that may have been introduced during the generation process while minimizing undue structural deformation and (ii) reoptimization allowing the unit cell lattice parameters to relax. Nonbonded and bonded interactions were described by the universal force field (UFF).62 UFF does not treat correctly the 5-coordinated environment of Cu in Cu-paddlewheels, leading to distortions of the paddlewheel. Thus, axial oxygen atoms were coordinated to Cupaddlewheels to make Cu 6-coordinated to prevent twisting during the optimization (Figure S6). Once the optimization was finished, the axial atoms were removed. Adsorption Simulations. Grand canonical Monte Carlo (GCMC) simulations were performed to simulate adsorption of hydrogen, methane, and 20/80 xenon/krypton mixtures in 13 512 MOFs using the RASPA code.63 Hydrogen adsorption simulations were done at 100 bar for temperatures of 130, 200, and 243 K. Methane adsorption simulations were done at 6, 65, and 100 bar for a temperature of 298 K. Xenon/krypton simulations were done at 1 and 5 bar for a temperature of 298 K. A total of 1000 and 2000 cycles were used for equilibration and ensemble averaging, respectively, for the hydrogen and methane simulations, and 5000 equilibration and 5000 ensemble averaging cycles were used for the xenon/krypton simulations. In each cycle, N Monte Carlo moves are performed, where N is the larger between the number of adsorbate molecules in the unit cell and 20. Monte Carlo moves were identity change (only for xenon/krypton simulations), translation, rotation (only for H2), insertion, deletion, and random reinsertion. Nonbonded interactions were described with a Lennard−Jones (LJ) plus Coulomb potential. Hydrogen molecules were modeled according to LJ parameters from the Michels−Degraaff−Tenseldam model64 and partial charges from the Darkrim−Levesque model.65 MOF-hydrogen electrostatic interactions were neglected, because they have a negligible effect on predicted MOF hydrogen storage capacity.29,66 Methane

Figure 6. Volumetric surface area vs void fraction for 13 512 MOFs with some topologies highlighted. dia = blue, rht = yellow, spn = red, fcu = green, srs = orange, soc = turquoise, ith = gray, crs = dark green, all others = purple.

how different topologies occupy different regions of the plot even though a given region can be occupied by several topologies. The highlighted topologies show that for void fractions above 0.80 to 0.85 (which is accomplished by increasing the length of the connecting building blocks), there is a steep decrease in volumetric surface area. Topologies such as spn and crs, which tend to present large pores even with the shortest connecting building blocks, do not reach high volumetric surface areas. Topologies such as fcu, which tend to 5805



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Figure 7. (a) Volumetric and (b) gravimetric surface area vs node to node distance, dNN, with some topologies highlighted. dia = blue, rht = yellow, spn = red, fcu = green, srs = orange, soc = turquoise, ith = gray, crs = dark green, all others = purple.

Figure 8. Volumetric vs gravimetric hydrogen (top) and methane (bottom) uptake with some topologies highlighted. (a) Hydrogen at 77 K and 100 bar, (b) hydrogen at 130 K and 100 bar, (c) methane at 298 K and 65 bar, (d) methane at 298 K and 100 bar. dia = blue, rht = yellow, spn = red, fcu = green, srs = orange, soc = turquoise, ith = gray, crs = dark green, all others = purple.

distance, dNN, highlighting the same topologies as in Figure 6. dNN depends on the size of both the nodular and connecting building blocks. Note that the rht topology is offset to the right despite using the same connecting building blocks as the other topologies, because one of its nodular building blocks is a 24connected supramolecular cage with a radius around 12 Å. Figure 7a shows that the volumetric surface areas of different topologies reach their maxima with different optimal dNN. Related to Figure 6, the optimal dNN values occur when the resulting structure of a given topology has a void fraction close to 0.8. Figure 7b, on the other hand, shows that the gravimetric surface areas continue to increase with dNN. The rht topology

present small pores, can combine high volumetric surface areas with high void fractions, but only with relatively long connecting building blocks, which may pose a challenge for activation. On the other hand, the well-known rht topology can achieve simultaneous high surface area and high void fraction (which is desirable for gas storage) with moderately long linkers that can facilitate MOF activation and experimental testing. This indicates that some topologies exhibit property combinations that some others do not. Looking more directly at MOF property dependence on linker length, in Figure 7 we plot how volumetric (left) and gravimetric (right) surface area vary with the node to node 5806



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the corresponding standard deviation, σ(dij)avg, were calculated. (dij)avg provides a measure of the absolute scatter among topologies, which decreases as the temperature increases. This is not surprising, because as the temperature increases the hydrogen uptake is significantly lower for each MOF. Attempting to quantify the relative scatter of topologies, we scaled the distance between topologies by dividing dij by the distance of the centroid of all data to the origin to obtain sij. (sij)avg indicates that the relative scatter of topologies generally increases with temperature. A visual representation of the scatter analysis can be found in Figure S67. The same type of analysis can be performed for methane; the values are reported in Table 2. The increase in pressure from 65

reaches gravimetric surface areas near 7000 m2/g with the longest connecting building blocks used here. Note that some of the MOFs with the highest gravimetric surface areas in the literature have been synthesized in the rht topology, including NU-110.74 Other topologies such as dia show potential for reaching higher surface areas with shorter connecting building blocks, which may facilitate activation. However, dia MOFs may undergo catenation, and we did not include any structures with catenation in this study. Additional property−property plots can be found in Figures S7−S26; the data clearly show that MOF properties can be correlated differently depending on the topology. So now we proceed to look at the role of topology on performance in different applications. Dependence of Gas Storage on Topology. In previous work,56 we calculated hydrogen adsorption at 77 K and 100 bar for the 13 512 constructed MOFs. Here, we add predicted hydrogen uptakes at higher temperatures. Figure 8a, Figure 8b, and Figure S30 show the topology-dependent trade-off between volumetric and gravimetric hydrogen uptakes at 77, 130, 200, and 243 K. The topology dependence remains qualitatively similar as the temperature varies, in that topologies that perform better at low temperature also perform better at high temperature. Figure 8c,d shows the corresponding topologydependence for methane adsorption at 35 and 65 bar, respectively, and 298 K (the same topologies are highlighted in all cases). Note that the “regions” occupied by each topology are similar in all cases. For instance, the rht topology always has MOFs with high volumetric gas adsorption (relative to the highest values for a given operating condition), but spn and crs topologies only have MOFs with low volumetric adsorption. Previously,56 we noted that the topology-dependent volumetric vs gravimetric hydrogen adsorption trade-off at cryogenic conditions correlates with the topology-dependent volumetric vs gravimetric surface area trade-off. Since a similar trade-off in hydrogen adsorption is observed at higher temperatures, it suggests that volumetric and gravimetric surface areas continue to strongly influence hydrogen adsorption even as temperature increases. A similar argument can be made for methane adsorption with varying pressure. The volumetric hydrogen adsorption maximum becomes sharper at higher temperatures, while the maximum volumetric methane adsorption peak becomes sharper at lower pressures. Table 1 quantifies the scatter among topologies at each temperature as a measure of topological dependence for the

Table 2. Quantification of Scatter of Topologies in Volumetric vs. Gravimetric Methane Adsorption Plots at 298 Ka

(dij)avg

σ(dij)avg

(sij)avg

σ(sij)avg

77 130 200 243

6.9 5.6 3.3 2.7

4.1 3.7 2.4 2.1

0.48 0.47 0.50 0.53

0.34 0.33 0.39 0.42

(dij)avg

σ (dij)avg

(sij)avg

σ(sij)avg

65 100

200.7 304.8

144.3 228.2

0.47 0.49

0.31 0.34

a

dij and sij are the absolute and scaled distances between the centroids of topologies i and j.

to 100 bar leads to an increase in methane loadings, so the scatter of topologies, as given by (dij)avg, increases with pressure. The relative scatter of topologies as given by (sij)avg increases slightly with pressure as well. Notice that, as in other studies,27,29,75 volumetric hydrogen loadings (at all temperatures) present a volcano type relationship with void fractions, where the volumetric loading maximum is located at void fractions around 0.8 (Figure S27). This shape reflects the volcano type relationship between volumetric surface areas and void fractions (Figure 6), where volumetric surface area also exhibits a maximum at void fractions around 0.8. The volumetric surface maximum is different among topologies, so those with higher volumetric surface area obtain the highest adsorption loadings. These adsorption loadings are ∼57 g/L, ∼39 g/L, ∼22 g/L, and ∼17 g/L for temperatures of 77, 130, 200, and 243 K. The heat of adsorption linked to these loadings changes from ∼4 kJ/mol to ∼8 kJ/mol as the temperature increases from 77 to 243 K (see ref 56 and Figure S29). Similar to hydrogen, methane also presents a volcano type relationship between adsorption loading and void fraction, with the maximum volumetric methane loadings appearing at void fractions around 0.8 for 100 bar and 298 K (Figure S47). This is consistent with previous studies of methane adsorption in MOFs at 35 and 65 bar.24 Although methane−MOF interactions are stronger than hydrogen−MOF interactions, volumetric surface area seems to play a fundamental role in both. For instance, in Figure S49, which plots the relationship between methane adsorption loadings at 100 bar and methane heats of adsorption at 6 bar (a lower pressure at which heats of adsorption better reflect methane-MOF interactions), numerous MOFs present optimal heats of adsorption (12−20 kJ/mol), but those with higher volumetric surface areas have higher methane loadings. Dependence of Xenon/Krypton Separations on Topology. Extraction of xenon from xenon/krypton mixtures in low energy-intensity separation processes such as pressureswing adsorption requires high adsorption selectivity for xenon by an adsorbent material. The selectivity of xenon over krypton, αXe/Kr, is defined as

Table 1. Quantification of Scatter of Topologies in Volumetric vs. Gravimetric Hydrogen Adsorption Plots at 100 bara T (K)

P (bar)

a dij and sij are the absolute and scaled distances between the centroids of topologies i and j.

trade-off between volumetric and gravimetric hydrogen adsorption. To obtain the data in Table 1, from Figure 8a, Figure 8b, and Figure S30, we calculated the centroid ci for each topology i. The absolute distance between topology i and j is then dij = |ci − cj|. After calculating dij for all possible topology pairings, the average distance between topologies, (dij)avg, and 5807



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Figure 9. Xe/Kr selectivity at 298 K vs largest cavity diameter (LCD) with some highlighted topologies. (a) Adsorption at 1 bar. (b) Adsorption at 5 bar. dia = blue, rht = yellow, spn = red, fcu = green, srs = orange, soc = turquoise, ith = gray, crs = dark green, all others = purple. Three data points (corresponding to flu and ith topologies) with selectivity close to or greater than 100 were omitted for clarity.

αXe/Kr =

x Xe/x Kr yXe /yKr

Table 3. Quantification of Scatter of Topologies in Xe/Kr Selectivity vs. MOF Largest Cavity Diameter Plots at 298 Ka

where xi and yi are the adsorbed and gas phase mole fractions of species i, respectively. The selectivities at 1 and 5 bar are plotted in Figure 9 versus the largest cavity diameter (LCD) of these MOFs. Our focus on LCD is based on studies by Sikora et al.3 and Simon et al.5 that identified pore size as a variable having a strong impact on selectivity for this system. In agreement with previous studies,3,5 MOFs with LCD values in the 4−6 Å range presented high selectivity. As LCD increases beyond 6 Å, the selectivity slowly decreases. In Figure 9, we highlight the same topologies we highlighted for methane- and hydrogen-related plots, which also reveals a topology dependence for the selectivity αXe/Kr. For selectivity, however, the topology-dependence originates from the connection between topology and pore polydispersity. The spn topology illustrates this well. MOFs with this (3,6)connected topology have a small pore and a large pore, which are dramatically different in diameter but roughly maintain the same proportionality with different connecting building blocks. From Figure 9, it can be inferred that with the shortest of connecting building blocks, the spn topology still has pores of at least ca. 20 Å. Therefore, independently of the size of the small pores, the selectivity is not very high. On the other hand, when the connecting building blocks are long and the LCD is even larger, the spn topology still has some dramatically smaller pores that do not let the selectivity decay as fast as in other MOFs. A similar situation occurs with the rht topology, for which the 24-connected supramolecular cage does not change in size irrespective the size of the connecting building blocks. The spn topology, however, appears to the right of the rht topology in Figure 9, because the same connecting building blocks make larger pores in the former. Since the same mechanism dominates selectivity at both 1 and 5 bar, a similar topology-dependence for the selectivity-pore size relationship is observed at both 1 and 5 bar. To further illustrate the topological dependence and to quantify the scatter of the topologies, the same scatter analysis was performed as for hydrogen and methane storage. Table 3 reports the results. As the pressure increases, the selectivity values decrease, lowering the absolute values of the topology scattering slightly. However, on a relative scale, the scattering values increase with increasing pressure.

P (bar)

(dij)avg

σ (dij)avg

(sij)avg

σ (sij)avg

1 5

11.29 11.19

7.99 8.03

3.41 3.69

2.5 2.7

a dij and sij are the absolute and scaled distances between the centroids of topologies i and j..

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CONCLUSIONS A total of 13 512 MOF structures of 41 different edge-transitive topologies were generated using the ToBaCCo code. This code relies on a reverse topological approach which uses the topology as a template on which to map building blocks. ToBaCCo works in P1 symmetry to produce simulation-ready MOF structures and takes advantage of deconstructing organic linkers into nodular and connecting building blocks to reduce the number of required building blocks to produce a given number of MOFs. Further, the code allows the use of supramolecular building blocks to allow the use of simpler topological blueprints to construct otherwise more topologically complex MOF structures. We demonstrated the utility of the code in facilitating the study of topology influence on hydrogen storage, methane storage, and Xe/Kr separation. This study reveals, through large-scale high-throughput screening, the existence of a topological dependence for gas storage and separations in MOFs. For gas storage, the topological dependence is related to the combination of MOF textural properties that each topology can achieve. For separations, the topological dependence is due to how topology affects pore polydispersity. Given the role of topology on MOF performance, this work encourages continuing the extension of MOF construction approaches toward the use of the 2000+ topological nets known to date.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b00848. Topologies and building blocks used, additional ToBaCCo details, simulation details, additional results for physical properties, hydrogen storage, methane storage, and Xe/Kr separation, and tabulated adsorption results (PDF) 5808



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Article

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AUTHOR INFORMATION

Corresponding Authors

*(D.A.G.-G.) E-mail: [email protected]. *(R.Q.S.) E-mail: [email protected]. ORCID

Randall Q. Snurr: 0000-0003-2925-9246 Author Contributions #

These authors contributed equally.

Notes

The authors declare the following competing financial interest(s): R.Q.S. has a financial interest in the startup company NuMat Technologies, which is seeking to commercialize metal-organic frameworks.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (NSF) Grant DMR-1334928. Simulations were made possible by the high-performance computing system, QUEST, at Northwestern University and the NERSC computing resources of the U.S. Department of Energy (DOE).

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