In Silico Design of Three-Dimensional Porous Covalent Organic

Article pubs.acs.org/JPCC

In Silico Design of Three-Dimensional Porous Covalent Organic Frameworks via Known Synthesis Routes and Commercially Available Species Richard L. Martin,† Cory M. Simon,§ Bharat Medasani,† David K. Britt,‡ Berend Smit,§,∥ and Maciej Haranczyk*,† †

Computational Research Division and ‡Materials Science Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F-1650, Berkeley, California 94720-8139, United States § Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States ∥ Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: Covalent organic frameworks (COFs) are a class of advanced nanoporous polymeric materials which combine the crystallinity of metal−organic frameworks (MOFs) with the stability and potentially low-cost organic chemistry of porous polymer networks (PPNs). Like other advanced porous materials, COFs can potentially be designed to meet the needs of a variety of applications, from energy, to security, to human health. In this work, we construct in silico a database of hypothetical three-dimensional, crystalline COFs. In constructing this library we generate novel COFs using only established synthetic routes, previously utilized tetrahedral building units, and commercially available bridging “linker” molecules. This ensures that there are no known chemical barriers to synthesizing all materials in our database. We relaxed all materials in our database through semiempirical electronic structure calculations. In addition, for those structures that allow interpenetration, we designed interpenetrated versions of the basic structure. Then, we characterized the porosity of each of these structures. The final set of 4147 structures (based on 620 unique noninterpenetrated structures) and their computed properties are publicly available and can be screened to identify promising materials for a wide variety of applications. Here, we assess the suitability of our COFs for vehicular methane storage by performing molecular simulations to predict the equilibrium methane uptake.

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INTRODUCTION Porous materials have generated a great deal of research interest in recent years. In particular, so-called advanced porous materials (APMs)1 such as metal−organic frameworks (MOFs),2 covalent organic frameworks (COFs),3,4 porous polymer networks (PPNs, or porous aromatic frameworks, PAFs),5,6 and zeolitic imidazolate frameworks (ZIFs)7 have been investigated for diverse applications such as drug delivery,8 catalysis,9 sensing,10,11 gas storage,12,13 and gas separations,14 including CO2 capture15 and hydrocarbon and other liquid separations.16,17 Much of the interest in these new classes of material arises from the utilization of reticular chemistry18 in their design, facilitating modular assembly of materials with predictable topology and atomic-scale control over their internal surface chemistry. Accordingly, advanced porous materials are highly versatile and can potentially be customdesigned to meet the specific technological and economic requirements of many diverse applications from energy to security to human health technologies. COFs, comprising covalently bonded organic components, are of great interest because they are lightweight, highly thermally stable, crystalline and exhibit permanent porosity.3 COFs can be broadly classified as either two- or threedimensional structures (2D or 3D); while 2D COFs comprise © 2014 American Chemical Society

closely stacked layers resulting in dense structures and onedimensional channel systems, 3D COFs are typically highly porous, exhibiting low densities and higher surface areas. One can use the principles of reticular chemistry to design COFs based on specific underlying topologies, or nets (layers for 2D systems).19−21 Because of the lower density of 3D COFs as well as potentially low synthesis cost and significant stability, they are considered to be promising candidate materials for a variety of gas storage and separation applications. To date, 3D COFs have been realized via the use of tetrahedrally coordinated building blocks (it has been theorized that the combination of tetragonal and trigonal building blocks may also lead to 3D COFs22), which may further be bridged by components with linear, trigonal, or other coordination geometries.3 Databases of computationally predicted porous material structures including zeolites,23,24 MOFs,25,26 ZIFs,27,28 and PPNs29 have recently been generated. Computational design of both 2D and 3D COFs has also been explored.30,22 Notably, and in contrast to the vast number of 3D MOFs, relatively few 3D COFs have been synthesized or designed computationally.3 Received: July 17, 2014 Revised: September 12, 2014 Published: September 18, 2014 23790

dx.doi.org/10.1021/jp507152j | J. Phys. Chem. C 2014, 118, 23790−23802

The Journal of Physical Chemistry C

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Figure 1. Tetrahedral building blocks utilized in 3D COF design. Left: TAM. Right: TBPM (X = C) and TBPS (X = Si).

coordination chemistry, leading to a potentially vast space of possible materials. Each structure designed herein is thus built from two building blocks: the specified tetrahedral component and one of the possible linker components. We explore both two-coordinated (linear) and three-coordinated (trigonal) linkers with the appropriate chemical functional groups, all of which were identified with SMARTS textual filters39 and the Open Babel software package40 and downloaded from the eMolecules31 database of commercially available chemical species. We also explored the space of possible trigonal building blocks formed by two singly coordinated silanetriol compounds (the three pairs of −OH groups face each other to form the trigonal geometry). We list the quantities of building blocks of each type in Table 1. We note that the number of

In this work, we present a database of 4147 3D COFs designed in silico, based on 620 unique noninterpenetrated structures. To maximize the synthetic feasibility of the materials in our database, we utilize only (a) established3 3D COF synthetic routes and tetrahedral building units and (b) commercially available bridging “linker” molecules with linear and trigonal coordination geometries and the appropriate functional groups from the eMolecules database.31 In total, 620 model structures were assembled using our recently developed topology-based modeling algorithm,32 which is available within our open source porous materials design and analysis suite, Zeo++.33 All structure models were relaxed using semiempirical electronic structure calculations, which were validated using density functional theory34,35 (DFT) and experimental data. Where the topology and porosity of materials enabled interpenetration, interpenetrated versions were generated, up to the maximum possible number of nets for each structure. The final set of 4147 structures36 was characterized by their geometric properties calculated using Zeo ++. All COFs were computationally screened for applicability as adsorbents for vehicular natural gas fuel tanks by simulating equilibrium methane uptake via the grand-canonical Monte Carlo algorithm.37 All structures and characterizing data are available online for the benefit of the materials community; this database of COFs can for instance be screened to identify promising candidate materials for applications other than methane storage.

Table 1. Quantities of Commercially Available Bridging Linkers of Each Type Identified within the eMolecules Online Database31 onecoordinateda aldehydes dialcohols acetonide-protected catechols silanetriols

twocoordinateda

threecoordinateda

283 (282) 53 (53) 112 (106)

7 (5) 9 (1) 2 (0)

6 (2)

a

The quantities successfully utilized in COF model assembly are provided in parentheses.

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METHODS Our construction and characterization of a database of 3D COF materials comprises six steps, detailed below. Selection of Building Blocks. All 3D COFs achieved to date are based on tetrahedral building blocks;3 in this work we aim to enumerate alternative materials based on the same tetrahedral components, namely tetra(4-anilyl)methane (TAM), tetra(4-dihydroxyborylphenyl)methane (TBPM), and tetra(4-dihydroxyborylphenyl)silane (TBPS) (Figure 1). Selfcondensation of TBPM and TBPS results in COF-102 and COF-103, respectively,38 which exhibit the ctn topology; the ctn net comprises tetrahedral and trigonal vertices, and in this case, the trigonal vertex arises from the boroxine linkage formed where three TBPM/TBPS meet. Each of these tetrahedral components can also be cocondensed with bridging linker molecules of the appropriate

commercially available two-coordinated linkers of each type (i.e., molecules exhibiting two instances of the required functional group) is significantly greater than the quantity of three-coordinated linkers. We thereby explore four established synthetic routes,3 each based on one tetrahedral building block and one class of linker molecule. The four synthetic routes are as follows (illustrated in Figure 2): 1. TAM combined with an aldehyde, resulting in imine linkages 2. Either tetraboronic acid (TBPM/TBPS) combined with a dialcohol, resulting in boronate ester linkages 3. Either tetraboronic acid (TBPM/TBPS) combined with an acetonide-protected catechol (APC), resulting in boronate ester linkages 23791



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Figure 2. Four synthesis routes utilized in 3D COF design. 1: TAM combined with an aldehyde results in an imine linkage. 2: TBPM or TBPS combined with a dialcohol results in a boronate ester linkage. 3: TBPM or TBPS combined with an acetonide-protected catechol results in a boronate ester linkage. 4: TBPM or TBPS combined with two silanetriols results in a borosilicate linkage. Reaction byproducts and proper stoichiometry are not shown.

the preference for one net over another in each case are not fully understood, and so we explore both possibilities in the generation of our COF database. Schematic illustrations of the considered nets are available at the RCSR.46 The topologybased structure assembly tool32 within Zeo++33 was utilized to computationally construct large numbers of materials based on each of these topologies in a high-throughput manner. When only the chemical building blocks are provided, this tool can rapidly assemble a crystal structure model exhibiting any of these topologies (a process typically requiring only a fraction of a second per model). The combination of tetrahedral and linear or trigonal building blocks, according to the synthetic routes described above, results in a total of 620 models. This set comprises 600 dia net structures arising from the combination of 282 aldehydes with TAM, and 53 dialcohols and 106 acetonideprotected catechols with either TBPM or TBPS, as well as 11 ctn and 9 bor net structures arising from the combination of five aldehydes with TAM, the single valid dialcohol with either TBPM or TBPS, and two silanetriols with TBPM or TBPS (both silanetriols form materials exhibiting the ctn net, but only the smaller of the two allows formation of the bor net) (Table 1). The preference for dia net structures in this data set is due to two factors. First, as mentioned above, there are significantly more commercially available molecules exhibiting two instances of the required functional group, compared to the quantity exhibiting three. Similarly, silanetriol chemistry is sufficiently uncommon in commercial chemicals to account for the few molecules with this functional group. Second, while a two-

4. Either tetraboronic acid (TBPM/TBPS) combined with two (identical) silanetriols, resulting in borosilicate linkages Given this set of tetrahedral building blocks, bridging linkers, and synthetic routes for combining them, the next step is to assemble the corresponding models. Assembly of Initial Structure Models. Depending on the coordination geometry of the building blocks, various crystalline materials with distinct topologies can form. Approximately 2100 candidate topologies (nets and layers) are available online via the Reticular Chemistry Structural Resource (RCSR).21 However, high-symmetry nets with one kind of edge or one kind of vertex are generally the most likely to form in experiment.41−43 One can exploit this known bias to prioritize the exploration of such nets in the computational prediction of new materials: utilizing the most prevalent net(s) as templates for material design will result in predicted structures that are similar to those either previously achieved or likely to be achievable. In this work, structures based on the co-condensation of tetrahedral and linear building blocks are modeled with the dia net, known to be by far the most common topology for such materials,41 and exemplified by COF-300.44 Materials based on tetrahedral and trigonal building blocks are modeled with both the ctn and bor topologies. The use of both nets is motivated by the occurrence of each for distinct COF materials based on co-condensation of tetrahedral and trigonal components. For instance, COF-10538 and COF-20245 form the ctn net, while COF-10838 exhibits bor; at present, the factors which lead to 23792



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property and can achieve interpenetrated models. We note that by subsuming vertices of the bor and tbo nets, the self-dual pcu net can be achieved (indeed, the RCSR explicitly includes a database entry for the bor-c net). In previous work,66 we observed that interpenetrated models of PPNs with the greatest predicted energetic stability were those with the minimal accessible surface area, i.e., that the close geometric arrangement of independent frameworks is the most energetically favorable because it maximizes van der Waals interactions between framework atoms. This led to a hypothesis that feasible interpenetrated modes can be rapidly identified by finding the arrangement of nets that minimizes the surface area. Indeed, using this close-packing approach with two nets enabled the successful reproduction of the experimental methane adsorption performance of a dia net porous polymer network, PPN-3,6 whereas a “crystalline” interpenetration approach (i.e., using the dia-c2 net) could not.66 Therefore, we have identified candidate interpenetrated modes for the 3D COF structure models designed herein by searching for the lowest surface area arrangements via a 0.25 Å resolution scan, displacing one net from another by increments of this distance in each of the crystal axes. When the lowest surface area arrangement and corresponding displacement were identified, successively greater levels of interpenetration were achieved by the iterative addition of further nets with the same displacement, as far as possible (within a hard sphere approximation of framework atoms). The greatest extent of interpenetration achieved was a 14-net structure model; in all cases, lower than maximum levels of interpenetration were also preserved in the database. While the above interpenetration protocol led to a model that could successfully reproduce the experimental methane adsorption data for a PPN material,66 COFs are, in contrast to PPNs, crystalline. Therefore, the crystalline interpenetration approach may be also relevant to COFs (experimental data is inconclusive: while the five-net COF-300 exhibits the dia-c5 net, it simultaneously exhibits a close-packed arrangement of nets44). To give further insights into which mode of interpenetration may be relevant to COF structures, we have estimated the energetics of both forms. Here, we relaxed structures using the PM6-DH2 semiempirical method, which contains empirical corrections for van der Waals and hydrogen bond interactions between interpenetrating frameworks, and compared the resulting heat of formation. Our results suggest that the low surface area, lower-symmetry isomer is more stable, just as in the case of PPN materials. Nevertheless, we note that future synthetic work, including structure determination of new interpenetrated COFs, is required to determine which mode of framework interpenetration is preferred under given circumstances, in particular the effects of solvent used in synthesis and trapped within the structure. Therefore, we also generated crystalline interpenetrated forms of all structures where possible, i.e., dia-cn and bor-cn structure models (where n is the number of nets). Geometric Analysis. All structures were characterized in terms of their methane-accessible pore space using the materials analysis algorithms within the open source tool Zeo ++.33 Methane was modeled as a hard sphere with radius of 1.625 Å, and hard sphere radii for framework atoms were taken from the Cambridge Crystallographic Data Centre.67 For accurate calculation of restricting pore apertures and other geometric properties in these polydisperse systems (i.e., multiple atomic radii), the high-accuracy setting in Zeo++

connected molecule must exhibit only (approximately) linear coordination in order to form the dia net, a three-connected molecule must exhibit (approximately) regular triangular coordination geometry to form either the ctn or bor net, which is intuitively a less common occurrence. Accordingly, only 6 out of 18 three-connected molecules lead to valid frameworks (similarly, only 2 out of 6 silanetriols), compared to 441 out of 448 two-connected molecules (Table 1). Structural Relaxation. The initial COF crystal structure models were assembled using the structure building component of our Zeo++ code,32,33 which, for the purposes of highthroughput predictive modeling, assumes that the molecular building blocks are rigid entities. To refine the model from this simplifying assumption, we have relaxed all generated structures prior to computing geometric properties and simulating methane adsorption. All structures were relaxed using the PM6 semiempirical electronic structure method,47,49 within MOPAC2012,48,49 permitting all atomic positions and unit cell parameters to relax, and utilizing periodic boundary conditions. We recently utilized this structural relaxation protocol for another class of nonmetallic porous materials, PPNs, in both the generation of a database of approximately 18 000 computationally predicted PPNs29 and the validation of the method’s performance versus DFT.50 The 620 PM6-relaxed COF structures were then analyzed for their potential to interpenetrate, as discussed in the next section. Our DFT relaxation process involved performing full geometry optimization, including the lattice vectors. The lattice vectors and atomic positions are relaxed either until the residual force on each atom is smaller than 0.1 eV/Å or for a minimum of 200 ionic steps. The structures are relaxed in two stages to minimize the Pulay stress. The DFT calculations are performed using the Vienna ab initio simulation package (VASP)51 with the Perdew−Burke−Ernzerhof (PBE)52 exchange-correlation functional, projector augmented wave (PAW)53,54 potentials, and a 400 eV kinetic energy cutoff for plane wave basis set. For k-point sampling, a 2 × 2 × 2 Monkhorst−Pack grid is used.55 Interpenetration. Interpenetration56 (interweaving or catenation57) is a phenomenon in which two or more independent structural frameworks interlock.58 Interpenetration increases material density and reduces accessible pore volume and surface area; hence, interpenetration is typically considered to be a negative outcome of material synthesis.59,60 However, the reduced pore sizes which occur in interpenetrated materials may improve adsorption performance by providing more van der Waals interactions with the adsorbate in the pores.61,62 Therefore, prediction of interpenetrated modes is an important component of in silico materials design. Of the three nets explored in this work, we note that only the dia net is selfdual; hence, the other nets in this study are mathematically precluded from self-interpenetration. Importantly, however, the inability of a net to self-interpenetrate does not preclude a material exhibiting that net to self-interpenetrate. This phenomenon is exemplified by the interpenetrated MOFs PCN-663 and TCM-8,64 which, like the MOF HKUST-1,65 exhibit the nonself-dual tbo net. However, these structures also exhibit sufficient porosity, due to the large trigonal organic linkers, for the smaller octahedral cages of one net to lie within the larger cuboctahedral cages of the other (and necessarily, vice versa). With this example in mind, we also attempt interpenetration for the ctn and bor net COF structure models. However, apart from the dia net, only the bor net exhibits this 23793



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“nan” indicates that no simulation was completed (10 of the 160).

was utilized (large framework atoms were replaced by clusters of identical smaller atoms).68 Accessible internal surface areas and pore volumes were computed using the Monte Carlo sampling routines. The attractive methane-framework interaction range was approximated as 3.75−4.6 Å for calculation of the van der Waals void fraction descriptor.69 Molecular Simulations of Methane Adsorption. To demonstrate an application of our database, we screened the database to identify promising methane storage materials. We predicted the equilibrium methane uptake in COFs using classical grand-canonical Monte Carlo simulations. We modeled the interactions of a methane molecule with the framework atoms of the COFs and other methane molecules as pairwise and with Lennard-Jones potentials with parameters from the Dreiding70 and TraPPE71 force fields, respectively (a force field comprises the model and parameters used to describe the energetic interactions of a methane molecule with the atoms of the crystal as well as with other methane molecules). The TraPPE force field recapitulates the vapor− liquid equilibrium curve of bulk methane; the Dreiding force field was developed to reproduce crystal structures of organic compounds. This model is standard for studying methane adsorption isotherms in metal−organic frameworks and COFs.13 We then used Lorentz−Berthelot mixing rules to obtain methane-framework atom parameters. We validated our utilization of Lennard-Jones parameters from the Dreiding force field by comparing simulated isotherms using Dreiding,70 OPLS,72 and UFF73 to experimentally measured methane uptake data for COF-102 and COF-103 (Figure 4). We found that both Dreiding and OPLS recapitulate the experimentally measured methane adsorption isotherm when scaled to account for differing theoretical and measured pore volume but that UFF overestimated the uptake significantly (data not shown); we therefore chose the Dreiding force field to be consistent with our simulated methane isotherms in PPNs.29 To compute the methane adsorption isotherms, we performed grand-canonical Monte Carlo simulations.37 The pressure of bulk methane is related to chemical potential using the Peng−Robinson equation of state. Lennard-Jones potentials are truncated beyond a cutoff radius of 12.5 Å, allowing us to implement periodic boundary conditions to mimic a crystal of infinite extent. Structures are taken as rigid throughout the simulation. For helium void fraction calculations in COF-102 and COF103, we perform Widom insertions according to the method of Talu and Myers;74 we take helium parameters given in Talu and Myers and use the Dreiding force field for the framework atoms, applying Lorentz−Berthelot mixing rules for crossinteractions as above. As 160 of the COF structures have prohibitively large unit cells, these COFs are excluded from the methane storage analysis because of the large computational cost of simulation; as each of these excluded COFs have very large pores (>20 Å diameter), they are very unlikely to be promising candidates for vehicular methane storage (Figure 5). We performed additional simulations on these 160 highly porous structures with fewer Monte Carlo cycles in order to obtain an estimate for the equilibrium methane uptake; of these, 10 COFs remained prohibitively expensive to simulate. All adsorption data is available in the Supporting Information; an asterisk by the name of a structure indicates that it was simulated with fewer cycles (160 COFs), while an equilibrium methane uptake of

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RESULTS Validation of Structure Relaxation. To investigate the performance of the PM6-based relaxation protocol in the

Table 2. Geometric Properties of Two Selected COF Models, Relaxed Using Either the PM6 or DFT Approach TAM_with_aldehyde_dia_004

3

density (g/cm ) included sphere diameter (Å) free sphere diameter (Å) accessible surface area (m2/g) accessible volume (cm3/g)

TBPM_with_dialcohol_bor_001

DFTrelaxed

PM6-relaxeda

DFTrelaxed

PM6-relaxeda

0.16 20.22

0.14 (−9.38) 21.39 (5.78)

0.19 23.51

0.18 (−3.66) 24.70 (5.02)

16.52

18.59 (12.55)

15.81

16.76 (6.04)

7361.58

7542.08 (2.45)

6240.34

6309.85 (1.11)

4.70

5.32 (13.09)

3.88

4.08 (5.13)

a

PM6 relaxed results as percentage deviations from DFT are provided in parentheses.

Table 3. PM6 Relaxed Results As Average Deviations from DFT, Calculated over Seven COF Materials overestimation (%) density (g/cm3) included sphere diameter (Å) free sphere diameter (Å) accessible surface area (m2/g) accessible volume (cm3/g)

−5.75 4.48 5.21 2.06 8.87

specific case of COF materials, we performed two validations: (a) comparing PM6-relaxed structures to DFT-relaxed structures and (b) comparing the experimental COF structure to our predicted COF structure and its PM6-relaxed counterpart. In each test, we compare the geometric properties of the various structural models. First, we compared the results of relaxing seven diverse computationally designed COF materials using PM6 versus using DFT (described above). Here, the PM6 method is assumed to be accurate if it can closely reproduce the results of DFT relaxation (i.e., a higher level of theory, and typically greater than 2 orders of magnitude higher computational cost). We find that PM6 provides good agreement with DFT (Table 2), with an average deviation of less than 10% from the DFTrelaxed structure properties (Table 3). PM6 typically leads to slightly higher pore volumes and hence lower density, larger pore diameter, and higher gravimetric surface area models. These observations are consistent with those previously generated for PPN materials, which are also entirely nonmetallic structures.50 Second, we compared the geometric porosity properties of the experimental crystal structure of COF-102 to our computationally predicted (unrelaxed) model of COF-102, as well as to the PM6-relaxed versions thereof. We find that applying PM6 to the experimental structure results in no more than 3% deviation in the structural properties (Table 4), suggesting that this method does not significantly perturb the morphology of crystallographically determined structures. The unrelaxed, computationally predicted model exhibits between 4 23794



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Table 4. Geometric Properties of the Experimental Structure of COF-102, a PM6-Relaxed Version of the Experimental Structure, a Computationally Predicted (Unrelaxed) Model of COF-102, and a PM6-Relaxed Version Thereof 3

density (g/cm ) included sphere diameter (Å) free sphere diameter (Å) accessible surface area (m2/g) accessible volume (cm3/g) a

experiment

PM6-relaxed experimenta

model (unrelaxed)a

PM6-relaxed modela

0.42 9.04 7.99 5189.68 1.00

0.43 (1.71) 8.94 (−1.11) 7.93 (−0.73) 5124.67 (−1.25) 0.97 (−3.00)

0.40 (−5.44) 9.56 (5.79) 7.67 (−4.06) 5730.52 (10.42) 1.07 (6.75)

0.43 (2.40) 8.52 (−5.73) 7.84 (−1.93) 5425.27 (4.54) 0.93 (−6.67)

Results as percentage deviations from experiment are provided in parentheses.

reducing the deviation, with the final properties between 1.9 and 6.7% of those of the experimental structure. We assume that the good performance of the PM6 relaxation method for COF-102 is transferrable to other materials in our database as they all share similar chemistry (being composed entirely of light, nonmetallic elements). Comparison of Geometric Properties. The 4147 3D COF materials in this database exhibit a wide range of structural properties (Table 5). Of particular note are the very large pore diameters in the dia net structures. The minimum pore size is bounded by the use of large tetrahedral building blocks and can become very large with the use of long linear linkers, leading to materials with high gravimetric and correspondingly low volumetric surface areas. The latter structures with large pores will tend to exist in their interpenetrated forms unless this issue is addressed during synthesis. The ctn and bor topologies on the other hand offer more modest variation of the pore size, 10−19 Å and 12−26 Å,

Table 5. Geometric Properties of Non-Interpenetrated 3D COF Structure Models in This Work included sphere diameter (Å)

accessible surface area (m2/g)

accessible surface area (m2/cm3)

net

min

max

min

max

min

max

dia ctn bor

14.7 10.3 12.0

88.1 19.2 26.0

4594.5 4328.4 5100.6

9861.0 7456.4 7420.2

149.1 1177.1 1078.5

2045.0 2416.6 2090.0

and 10.5% deviation from experiment. These larger deviations are not surprising considering that the structure models are designed assuming rigid chemical building blocks; however, we note that an approximately 10% deviation is consistent with previous comparisons between models generated with this technique and experimental structures.32 Finally, applying PM6 to the computationally predicted model serves to improve the structure with respect to the experimental one, in all cases

Figure 3. Distributions of geometric properties of databases of computationally predicted MOFs, PPNs, zeolites, and COFs. Top left: largest included sphere. Top right: geometric void fraction. Bottom left: crystal density. Bottom right: accessible surface area. 23795



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Figure 4. Comparison of simulated and experimental methane adsorption isotherms in COF-102 and COF-103 at 298 K. Simulated uptake matches the experimental data scaled by the ratio of calculated to experimentally measured pore volume.

Figure 5. Evaluation of the COF database for vehicular methane storage. Top left: distribution of simulated deliverable capacities of our COF database for the two operating pressure ranges considered. Vertical lines indicate free-space tank (no material) performance. Top right: performance arc, color-coded by void fraction; black square is the deliverable capacity of a free-space tank. Bottom figures: relationships between 65 to 5.8 bar deliverable capacity and various geometric properties. Horizontal lines indicate free-space tank performance to show limiting behavior. Colored points are the four COFs with the highest deliverable capacities. Red, TBPM_with_dialcohol_bor_001_02-net_max-sym (181.67 v STP/v); blue, TBPM_with_dialcohol_dia_005_04-net_max-sym (180.89 v STP/v); magenta, TBPS_with_dialcohol_bor_001_02-net_max-sym (178.28 v STP/ v); cyan, TAM_with_aldehyde_dia_004_03-net_max-sym (178.16 v STP/v).

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It is instructive to compare the porosity properties of our COF database with databases of other material classes. Figure 3 provides histograms comparing the geometric properties of various classes of porous material; all materials shown are computationally predicted. COFs, designed in this work, can be seen to exhibit large pores (i.e., large included sphere diameters, Figure 3 upper left) and correspondingly high void fractions (upper right) and low crystal densities (lower left) compared to MOFs25 and zeolites.23,24 A consistent ranking of the modes of the included sphere, void fraction, and density distributions for the material classes (zeolites, MOFs, COFs, and then PPNs29) can be observed. While a large included sphere typically leads to a large void fraction, the comparison with crystal density explicitly takes account of the mass of the material atoms; here, we find that the materials with the largest pores and highest void fractions are also those exhibiting entirely nonmetallic (lighter) elements. A distinct ranking is observed with respect to volumetric surface area (lower right), for which zeolites exhibit the lowest surface area per volume, followed by PPNs, COFs, and finally MOFs. We note that volumetric surface area can be maximized in organic or inorganic−organic structures by, for instance, lateral branching on organic linkers,75 which increases surface area without increasing the void fraction; the comparatively simple inorganic chemistry of zeolites prevents such a design strategy and hence leads them to perform poorly

Table 6. Top COF Candidates for Vehicular Methane Storage: Names of Structures (Including Building Blocks, Topology, Building Block ID, Number of Nets, and Mode of Interpenetration) and Corresponding 65 to 5.8 bar Deliverable Capacity of Methane structure name TAM_with_aldehyde_dia_004_03net_max-sym TBPS_with_dialcohol_bor_001_02net_max-sym TBPM_with_dialcohol_dia_005_04net_max-sym TBPM_with_dialcohol_bor_001_02net_max-sym

deliverable capacity 65 to 5.8 bar (v STP/v) 178.16 178.28 180.89 181.67

respectively. Simultaneously, and in contrast to the dia network, they offer smaller gravimetric surface area and correspondingly higher volumetric surface area. As of 2012,4 the largest reported pore size among experimentally synthesized 3D COFs is COF-10838 with 31 Å; the smallest pore size reported is COF-30044 with 8 Å. Comparing this pore size range of synthesized 3D COFs with that of our COF database in Figure 3, less than 10% of our COF database has pores larger than those of COF-108.

Figure 6. Top COF candidates for vehicular methane storage. Shown are potential energy contours at −10 kJ/mol (light blue) and −12 kJ/mol (dark blue), in increasing order of 65 to 5.8 bar deliverable capacity. Top left: TAM_with_aldehyde_dia_004_03-net_max-sym (178.16 v STP/v). Top right: TBPS_with_dialcohol_bor_001_02-net_max-sym (178.28 v STP/v). Bottom left: TBPM_with_dialcohol_dia_005_04-net_max-sym (180.89 v STP/v). Bottom right: TBPM_with_dialcohol_bor_001_02-net_max-sym (181.67 v STP/v). 23797



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Figure 7. Building blocks in top COF candidates for vehicular methane storage. Numbers indicate the synthesis routes utilized for each material (referencing Figure 2) using the building blocks shown. From top to bottom, in increasing order of 65 to 5.8 bar deliverable capacity: TAM_with_aldehyde_dia_004_03-net_max-sym (178.16 v STP/v), TBPS_with_dialcohol_bor_001_02-net_max-sym (178.28 v STP/v), TBPM_with_dialcohol_dia_005_04-net_max-sym (180.89 v STP/v), TBPM_with_dialcohol_bor_001_02-net_max-sym (181.67 v STP/v).

Screening for Methane Storage Materials. Because of their potential low cost and stability,3 an exciting potential application of COFs is to use them as adsorbents for vehicular fuel tanks to enable natural gas-fueled vehicles.1 Natural gas, which is mostly methane, is economically77 and possibly environmentally favorable78,79 compared to petrol, but suffers from a low volumetric energy density.1 The two densification strategies in the market today, liquefied natural gas (LNG) and

in this measure. Furthermore, a recent comparison of crystal nets in terms of achievable surface area76 demonstrated that the pcu net can achieve high volumetric surface area more easily than the dia net; this explains the high volumetric surface area of the MOF data set, which is largely pcu net structures, as compared to the PPN data set and the majority of the COF data set, which are dia net structures. 23798



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5 (see bottom figures). For simplicity, we consider only the 65−5.8 bar operation. The first plot shows that the highest deliverable capacities appear in a range of pore sizes from 8.5 to 13 Å. A spherical shell model29 can be used to illustrate that pore size controls the proximity of framework atoms to the adsorbed methane molecule and free volume for methane to occupy, leading to this characteristic trend. As larger pores lead to higher void fractions, the deliverable capacity correlation with void fraction resembles that with the largest included sphere. As structures with large pores tend to have low crystal densities, the relationship between crystal density and deliverable capacity also mimics that with the largest included sphere. Intuitively, the deliverable capacities of our COF materials increase with surface area, as more regions of space inside the pores are available for van der Waals interactions to recruit guest molecules. For each plot, we indicate the deliverable capacity of an empty tank as a horizontal line to show that materials with low crystal density, high void fraction, small surface area, and a large included sphere approach an empty tank limit. Materials with extremely high densities have deliverable capacities less than an empty tank because the atoms of the material occupy too much space, leaving little room for methane to reside. We also investigated the influence of interpenetration on the deliverable capacity. The distribution of the number of interpenetrated nets in our COF structures is shown in Figure S1 of the Supporting Information. The color-coding of each bin indicates the average deliverable capacity of a structure with that number of nets. The highest average deliverable capacity occurs in structures with 2−3 interpenetrated nets; interpenetrated nets can benefit structures that have large pores by yielding smaller pores closer to the optimal pore size and by increasing the surface area of material with which methane can interact. However, interpenetrated nets also densify the material, leaving less free volume for methane to reside, which is sometimes detrimental to the deliverable capacity as Figure 5 (bottom figures) shows. Thus, in color-coding the structure−property relationships in Figure 5 by the number of interpenetrated nets (Figure S2 of the Supporting Information), we do not observe any clear relationships between the number of interpenetrated nets and performance. As interpenetration can improve or degrade the deliverable capacity of a given material depending on the starting point, the deliverable capacity trends in Figure S1 of the Supporting Information are an artifact of the distribution of pore sizes and linker sizes utilized in the construction of our database and not a general property of interpenetration. The crystal structures of the top four COF candidates for vehicular methane storage, with deliverable capacities between 178.16 and 181.67 v STP/v (listed in Table 6) with the 65 to 5.8 bar operating pressures, are shown in Figure 6. To visualize the regions that are most favorable for methane adsorption, we show the potential energy contours at −10 and −12 kJ/mol in blue. Synthesis routes and building blocks utilized for these top materials are illustrated in Figure 7. We note that each of the materials with the highest deliverable capacity is modeled using the maximum-symmetry placement of interpenetrating nets; the best materials under the close-packed nets model are illustrated in Figure S4 of the Supporting Information, while the best noninterpenetrated materials are illustrated in Figure S5 of the Supporting Information. Figure 5 displays each of the top materials in a different color to visualize the combination of geometric properties exhibited by these structures. The variance

compressed natural gas (CNG), suffer from the required costly infrastructure and heavy, bulky, nonconformable fuel tanks. Here, we screen our COF database for promising candidates for vehicular natural gas storage at ambient temperature and relatively low pressures (35−65 bar) using molecular simulations. To assess the reliability of our prediction of equilibrium methane uptake in the COF crystal structures using grandcanonical Monte Carlo simulations, we compare our simulated isotherms to available experimental methane adsorption isotherms in the literature for COF-102 and COF-103.80 We took the COF-102 and COF-103 crystal structures from the Yaghi group38 and relaxed them using PM6 (resulting densities, 428 and 388 kg/m3, respectively). Figure 4 shows a comparison between the simulated and experimental methane adsorption isotherms at 298 K (Figure S3 of the Supporting Information shows 273 K data) using the Dreiding force field.70 The simulated methane uptake is considerably higher than the raw experimental methane uptake data. However, the measured helium pore volume of COF-102 and COF-103 of 1.55 and 1.54 cm3/g, respectively, is significantly less than that given by our calculated helium void fraction from Widom insertions74 at 298 K (0.81 and 0.82), 1.88 cm3/g and 2.12 cm3/g, respectively. This suggests that the COF-102 and COF-103 structures were partially collapsed, slightly amorphous, or contained remaining oligomers in the pores, reducing the measured methane uptake from the full crystalline capacity. Thus, we rescaled the experimental isotherms by the ratio of the calculated to experimentally measured pore volumes. The simulated isotherms match the scaled isotherms very well, giving us confidence that the Dreiding force field yields a reasonable prediction of methane uptake in COFs. Using the Dreiding force field, we computed equilibrium methane uptake in every structure in our COF database at 298 K and 1, 5.8, 35, and 65 bar of pressure. The Advanced Research Projects Agency-Energy (ARPA-E) subsidiary of the United States Department of Energy set storage targets for delivering methane to the engine with an adsorbed natural gas fuel tank using a pressure swing from 35 to 1 bar or 65 to 5.8 bar, motivating our choice of pressures. The deliverable capacity is defined as the methane stored per volume at the tank charging pressure of 65 bar (or 35) minus that at 5.8 bar (1 bar); this metric reflects that a material must not only store a large amount of methane when the tank is full but also release the methane to feed the engine.62 The distribution of deliverable capacities with the two sets of operating pressures is shown in Figure 5 (top left). The vertical lines indicate the deliverable capacity of a free-space tank (no material) to show the gain in volumetric energy density stored in the tank, directly related to the deliverable capacity, by using COF adsorbents. For both pressure ranges, we find COFs with relatively high deliverable capacities, the highest being 181.67 v STP/v for 65−5.8 bar operation. Generally, we find more high-performance COFs in the 65−5.8 bar operating range. Figure 5 (top right) shows a characteristic performance arc relating the two deliverable capacity metrics as found in our study of PPN materials.29 As our dia net COFs have relatively large pores, we observe a high density of COF structures in the approach to empty tank performance, shown as a black square in Figure 5 (top right). The color-coding according to void fraction shows that highly porous materials approximate an empty tank. Several interesting correlations between methane deliverable capacity and geometric structural characteristics arise in Figure 23799


The Journal of Physical Chemistry C in pore size, void fraction, and surface area of the top materials illustrates that there is not a unique, simple geometrical recipe for constructing an optimal material. We note that the COF predicted to exhibit the highest 65 to 5.8 bar deliverable capacity, TBPM_with_dialcohol_bor_001_02-net_max-sym (181.67 v STP/v), exhibits the same underlying net as COF-108,38 which comprises the same building blocks and exhibits the same bor topology; our material, however, exhibits two-net maximum-symmetry interpenetration. The non-interpenetrated version of this material, which is equivalent to COF-108, is also present within our database as TBPM_with_dialcohol_bor_001, exhibiting a 65 to 5.8 bar deliverable capacity of 123.78 v STP/v. Similarly, the COF predicted to exhibit the third highest 65 to 5.8 bar deliverable capacity, TBPS_with_dialcohol_bor_001_02-net_max-sym (178.28 v STP/v), also utilizes the same building blocks as COF-105,38 however with the bor rather than the ctn net, and again, with two-net maximum-symmetry interpenetration. Again, the non-interpenetrated, ctn-net version of this material, equivalent to COF-105, is present within our database as TBPS_with_dialcohol_ctn_001, exhibiting a 65 to 5.8 bar deliverable capacity of 126.00 v STP/v. The structural similarity between these COFs with high predicted methane storage performance and existing COF materials suggests that improved materials may be achievable with greater control over synthesis.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Article

S Supporting Information *

Supplemental figures illustrating structure−property relationships, comparison of experiment to simulation at 273 K, and synthesis routes and building blocks utilized for the top materials modeled using close-packed or no interpenetration. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Tel.: (+1) 510 486 7749. Fax: (+1) 510 486 5812. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This worked was supported by (a) CAMERA: The Center for Applied Mathematics for Energy Research Applications at Lawrence Berkeley National Laboratory supported by the U.S. Department of Energy under Contract DE-AC02-05CH11231 (to R.L.M. and D.K.B. for structure enumeration) and (b) the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences under Award DE-FG02-12ER16362 (to C.M.S., B.S., and M.H. for structure characterization and molecular simulations). Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract DE-AC0205CH11231.This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

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CONCLUSIONS We developed a database of hypothetical three-dimensional, crystalline COF materials. We restricted our structure enumeration to established synthetic routes and compatible substrates. The latter involve previously utilized tetrahedral building units and commercially available bridging “linker” molecules. Our crystal structure enumeration effort was therefore aimed at synthesizable COF materials. Future synthetic work is needed to confirm this assumption as well as to understand the overall synthesizability of COF materials. Structure models were constructed according to dia, ctn, or bor topology using the structure modeling algorithms within our Zeo++ software tool. Each of the 620 structure models was relaxed using the semiempirical PM6 electronic structure method. Moreover, interpenetrated versions of structures were also assembled where possible, leading to the final set of 4147 structures. The resulting COF database was characterized in terms of pore geometry and compared with other families of predicted porous materials. We found that the distribution of geometric properties in our COF database differs from that of predicted MOF, PPN, and zeolite material databases. Moreover, we demonstrated an application of our database in screening for vehicular methane storage materials. We predicted the deliverable capacity of each COF in our database. An adsorbed natural gas fuel tank with the best material in our data set is predicted to have a deliverable capacity of 181.67 v STP/v with 65 to 5.8 bar operating pressures, almost three times that of an empty tank. For comparison, the current record high deliverable capacity (65 to 5.8 bar) is held by the metal−organic frameworks MOF-5 and HKUST-1, with deliverable capacities of ∼185 v STP/v.81,82 In addition to identifying the top COF candidates, we unearthed interesting relationships between geometric characteristics of the structures and the deliverable capacity.

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