Amorphous PAF-1: Guiding the Rational Design of Ultraporous

Aug 5, 2014 - A number of topological structures for PAF-1 are compared with an amorphous structure for PAF-1, reproducing the ultrahigh surface area ...
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Amorphous PAF-1: Guiding the Rational Design of Ultraporous Materials Jens M. H. Thomas† and Abbie Trewin*,‡ †

Institute of Integrative Biology, University of Liverpool, Liverpool L69 7ZB, United Kingdom Department of Chemistry, Lancaster University, Bailrigg, Lancaster LA1 4YB, United Kingdom

‡

S Supporting Information *

ABSTRACT: A number of topological structures for PAF-1 are compared with an amorphous structure for PAF-1, reproducing the ultrahigh surface area and pore volume observed experimentally. We compare the porosity properties of these structures and discuss potential structural strategies for increasing porosity and gas uptake properties. The PAF-1 network formation mechanism is simulated through use of an automated generation process, revealing the importance of the solvent in the resulting network structure and porosity properties. This opens up new rational design strategies and considerations for developing the next generation of porous framework materials.

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INTRODUCTION The high surface area and pore volume of microporous materials has led to their widespread use in applications such as gas adsorption, heterogeneous catalysis, and chemical separations.1−5 There is a pressing need for the discovery of materials with ultrahigh porosity to attain the advanced functionality demanded by these increasingly important applications. It is widely believed that ultrahigh porosity can only be achieved for framework materials with a high degree of crystallinity, including metal−organic frameworks (MOFs)6−8 and covalent organic frameworks (COFs),9−13 the obvious example being the highest reported surface area for any material (over 7000 m2 g−1) for MOF NU-110.14 Design strategies for future framework materials with increasingly high porosity include increasing the strut length of the crystalline framework and hence increasing the interspatial void. However, this strategy often results in framework interpenetration and ironically a reduction in the porosity. Increasingly, the stability and the ability to further functionalize a framework is of greater importance for the materials’ applications. In this sense, the physical and chemical stability and the potential for vast synthetic diversity of amorphous materials, including microporous organic polymers (MOPs), hyper-cross-linked polymers (HCPs),15 conjugated microporous polymers (CMPs),16,17 polymers of intrinsic microporosity (PIMs),18 and covalent triazine-based frameworks (CTFs)19 have many advantages over other classes of porous materials. However, these materials have typically not yet attained the ultrahigh porosity of their crystalline counterparts. PAFs, a MOP first described in 2010 by Ben et al. and shown in Figure 1a,20−22 offer an intriguing middle ground. A BET surface area of over 5600 m2 g−1 was reported with pore volume ranging 0.89−1.44 cm3 g−1 for PAF-123 and with exceptional physical and chemical stability. A number of recent © XXXX American Chemical Society

reports demonstrate the synthetic diversity and scope for postsynthetic modification.21,24−30 However, the structural model of these framework materials has not yet been conclusively determined. A crystalline diamondoid structure was presented that can account for the surface area and gas uptake properties observed but does not explain the lack of long-range order evident in the powder X-ray diffraction (PXRD) pattern. Here, we explore a number of potential alternative crystalline and amorphous topologies. We show that of these, only the amorphous PAF-1 structure is able to fully rationalize the properties of the PAF-1 material. Furthermore, we are able to rationalize the synthetic route to the amorphous structure. We are able to suggest some broad design strategies that increase the pore volume and hence the gas uptake capacity of the material. This implies that there are new directions in the design strategy of functional materials with high porosity available to be exploited.

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STRUCTURE IDENTIFICATION Topologically, PAF-1 is similar to the 4-connected nets that underlie the structures of silica, aluminosilicate zeolites, and simple tetrahedral solids (e.g., carbon diamond and zinc oxide wurtzite structures). For silicate structures, these tetrahedral SiO4 units are termed T-sites; here we use the same term for the PAF-1 tetrahedral unit, tetraphenylmethane (Figure 1a,b, bottom left). Where silicate T-sites are connected by four oxygen atoms to four other tetrahedral silicon sites, for PAF-1 a biphenyl group connects the tetrahedral carbon atoms. Such a topological mapping between nets and structures has successfully been exploited in structure prediction for a range Received: March 7, 2014 Revised: July 30, 2014

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Figure 1. (a) Left: the monomeric building unit of PAF-1, right: the node-strut topology. (b) Topological mapping of PAF structures from other 4connected net systems. On the left, the conversion of an underlying T-site to a PAF tetraphenylmethane site is shown. On the right, the 4-connected nets for diamond, quartz, and amorphous silica are shown (top) along with the topologically equivalent PAF structures (bottom).

procedure is described in full in section S1, Supporting Information). Results. Figure 2a−c shows a plot of the relative energy per T-site, surface area, and pore volume versus density for the structures explored, respectively. An additional fully labeled plot for energy versus density is shown in Figure S1, Supporting Information. Table S1 and section S3, Supporting Information, show the full list of structures, their relative energies per T-site, and images of their structure. Concentrating first on the noninterpenetrated structures, there is a general trend that with increasing density, the relative energy decreases, with the dia topology lying lowest in energy. In general, interpenetrating structures are lower in energy than those without network interpenetration. The dia and interpenetrated dia topology series (dia-c, dia-c3, dia-c6, and dia-c4, where N of dia-cN indicates the number of increasing interpenetrating nets) have low relative energy. The relative energy decreases considerably from dia to dia-c (by 50 kJ mol−1 per T-site), presumably through the gain of favorable dispersive interactions between the two networks. The relative energy continues to decrease slightly through further interpenetration in the dia-c3 structure (by 7 kJ mol−1 per T-site). Further interpenetration to form dia-c4 then causes an increase in energy (by 51 kJ mol−1 per Tsite). We assume this results from there being no further space for additional networks without introducing strain into the structures. The dia-c3 structure is the lowest energy structure for all those investigated here and thus the thermodynamically favored structure, with dia being the most energetically favorable of the noninterpenetrating structures. Reaction mechanisms under thermodynamic control, such as those with reversible reactions, should result in the formation of the lowest energy structure, as the breaking and making of bonds allows self-healing and energetically unfavorable structural imperfections to be removed over time. By contrast,

of materials, including bulk oxides, sulfides and nitrides, inorganic microprous materials, and MOFs.31−36 In the specific case of PAF-1, we previously showed that an amorphous PAF-1 structure generated through topological mapping from an amorphous silica structure provided an alternative to the proposed diamondoid structure for PAF-1.37 This amorphous PAF-1 structure rationalized the surface area, lack of end groups, and the lack of experimental evidence for long-range order. Computational Method. In this study, we compare these amorphous and dia PAF-1 structures with 31 other topological structures for networks. These were selected from three different databases that collate both experimentally realized and hypothetical crystal structures: the Zeolite Atlas of the International Zeolite Association38−40 (topologies of experimentally synthesized microporous (alumino) silicates and related materials, with a three capital letter code, e.g., SOD for each structure), Treacy’s database of hypothetical zeolite structures40−42 (hypothetical siliceous zeolite topologies enumerated through a graph search, with a xx_y_zzzzz code, where xx is the space group in which the topology was found and y the number of symmetry unique tetrahedral atoms), and the Reticular Chemistry Structure Resource Database43−46 (topologies of both hypothetical nets and experimentally known minerals, with three lowercase letter codes, e.g., dia for diamond). A PERL script was written to automate the isomorphic substitution of PAF nodes for the other tetrahedral nodes. The structures were initially optimized using PCFF47 in Accelrys’ Materials Studio 5.048 using the Forcite module. The resultant structure was then optimized using the TINKER molecular modeling package49 with the MM350 force field, which was recently extended by Schmid et al. for COFs51 and followed by Monte Carlo (MC) conformational searches (this B

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Materials Studio 5.0 software48 with a probe radius of 1.82 Å, the kinetic radius of N2 and a grid spacing of 0.25 Å.54,55 As the degree of interpenetration increases through dia to dia-c4, the surface area of the structures decreases from 5422 m2 g−1 for dia to 2283 m2 g−1 for dia-c, until finally the dia-c3 and dia-c4 structures have effectively zero surface area, as the network interpenetration efficiently fills all void space. A similar decrease with increasing interpenetration is also observed for the models’ calculated pore volumes. These observations effectively rule out a fully interpenetrated experimental structure, as they are at odds with the experimentally observed high surface area of PAF-1. This is also consistent with the expectation discussed above that the synthesis method for PAF-1 would not give a thermodynamic product, although it is possible that a solventtemplating effect prevents interpenetration. The majority of the noninterpenetrating structures have similar SASAs in the range of ∼5000−5500 m2 g−1, including the amorphous model with a surface area of 5152 m2 g−1 (Figure 2b). This suggests that the specific crystalline form has little influence on the surface area and furthermore that there is little to be gained in surface area alone from a crystalline rather than amorphous structure. This contradicts the claims that a high degree of crystallinity is a requirement of ultrahigh surface area materials. We suspect that, in contrast to inorganic 4connected materials where a single atom is the linker, the fact that the PAF-1 structure has a biphenyl linker of ∼9 Å means that typically all of the linker surface area is exposed in all of the structures and therefore the surface area is similar across the structures. By contrast, there is a difference in the pore volume across the noninterpenetrated models, with an increase in pore volume observed, as expected, with decreasing density (Figure 2c). The largest pore volume found of 1.94 cm3 g−1 is for the ATN structure (Figure 2c and Figure S25, Supporting Information), which is 56% greater than the amorphous model’s pore volume of 1.22 cm3 g−1. The ATN structure appears to have a high pore volume as a result of consisting of a series of large cavities of very similar size (rather than a mixture of small and large cages), including cavities of ∼22 Å diameter and channels with diameters above 16 Å. Therefore, if it were synthetically feasible to template toward a desired crystalline structure, such as ATN, there is the potential to increase the pore volume of a PAF-1 material. On the basis of the surface area and pore volume, we can now rule out many of the structures that are not representative of the experimental results for those properties. We chose the following criteria: a surface area greater than 5000 m2 g−1 and a pore volume between 0.80 and 1.50 cm3 g−1 (see section S2, Supporting Information, for further discussion of the correlation of experimental and calculated surface area and pore volumes and the selection criteria). Table 1 shows the eight candidate structures based upon these criteria; they are all noninterpenetrating networks and are clustered within a small region of the relative energy per T-site versus density plot (shown by filled circles in Figure 2a). As structural determination through the SA and pore volume properties alone is not possible, we must also consider the additional structural characterization methods: the PXRD pattern, pore size distribution (PSD), and nitrogen gas uptake. The experimental and simulated PXRD patterns for all candidate structures were simulated using Mercury 3.1 and are shown in sections S6 and S7, Supporting Information. It is challenging to simulate accurately the properties of amorphous

Figure 2. (a) Relative energy as a function of crystallographic density for the structures of PAF-1. Filled points highlight the candidate structures from Table 1. The amorphous structure is highlighted in green and the dia series is highlighted red and labeled. (b) Solventaccessible surface area as a function of density. (c) Pore volume as a function of density. Surface area and pore volume calculated using a probe radius of 1.82 Å. Circles represent noninterpenetrated structures, while triangles represent interpenetrated structures.

syntheses where bonds are formed through irreversible chemistry will tend to form kinetic products that lack longrange order. Thus, if the reaction to form PAF-1 were thermodynamically controlled, then we would expect, in the absence of other factors, in particular solvent templating effects, that an interpenetrating structure based upon a dia-cN net would be formed. As PAF-1 is synthesized through irreversible Yamamoto type Ullmann cross-coupling reactions, we would not expect the reaction product to have a thermodynamically controlled structure.52−54 Nevertheless, we now evaluate all possible structures for their surface area and pore volumes and test these against the experimentally obtained values. Solvent-accessible surface area (SASA) and pore volume (PV) were calculated for each structure using Accelrys C

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NPN-1 (the closest equivalent to PAF-1) forms a 4-fold interpenetrated diamondoid net similarly to the dia-c4 structure. NPN-1 has a node-to-node distance of 12.26 Å, 2.46 Å longer than the PAF-1 node-to-node distance of 9.80 Å. It is therefore expected that the energetic ordering of the structures will differ, with the more open structure of the NPN1 framework perhaps favoring the more interpenetrated dia-c4 topology. No porosity information was given for this material. The PSD was calculated for the eight candidate structures using Poreblazer v1.2 (as shown in section S8, Supporting Information).62 The experimental pore size distribution shows a broad distribution of peaks with a maxima between 13−15 Å. A sharp edge is observed to the lower values with no pores observed with a diameter less than 12 Å and a broad tail extended smoothly to pore diameters greater than 30 Å. Only the amorphous structure is able to represent the distribution of pore sizes observed experimentally, with a maxima in the distribution located at a pore size of ∼15 Å (as shown in Figure 2b). The dia, cri, 52_2_39194, and 61_2_8903 structures exhibit a sharp peak at ∼15 Å but with no pore sizes greater than this. The 74_3_1891598 structure exhibits a distribution of pore sizes but with a maxima in the distribution at ∼18−20 Å. The quartz and 145_1_30 structures have pore sizes below those observed experimentally with a maxima in the distribution at ∼12 Å and none above this value. Finally, we calculated the nitrogen isotherms at 77 K for the eight candidate models using Grand Canonical Monte Carlo (GCMC) simulations with the Sorption module in Materials Studio 5.048 and PCFF.47 The nitrogen molecule was modeled with a quadrupole moment according to Potoff and Siepmann.63 Experimental sorption isotherms show that at a pressure of 1 bar and a temperature of 77 K there is an uptake of around 1800 cm3 g−1. Section S9, Supporting Information, shows the isotherms for all candidate structures in comparison to the experimentally obtained isotherm.20 The isotherms simulated here fall into three categories, shown in Figure S64, Supporting Information: 1. Those that have agreement with experiment in highpressure regions but do not agree at low-pressure regions where the uptake is too high and the curve too sharp; these include the dia, 61_2_8903, and cri structures. 2. Those that exhibit an overall agreement with experiment but are slightly too high in low-pressure regions and slightly too low in high-pressure regions; these include the amorphous, 52_2_39194, and 74_3_1891598 structures. 3. Those where the overall uptake is too low; these include the quartz and 145_1_30 structures. These groupings correlate to the simulated pore volume groupings of 1.40−1.48, 1.22−1.24, and 0.87−0.90 cm3 g−1, respectively. We can now consider which of our candidate structures can best explain the experimentally observed properties and structural characterization of PAF-1. The amorphous structure best reproduces both the PXRD pattern and PSD, shown in Figure 3a,b, respectively. The amorphous structure’s PSD reproduces the broad distribution with a maxima at ∼15 Å. The PXRD pattern for the amorphous model has several features that could correlate well with the experimental PXRD: a hump at 2θ = 13°, with a d-spacing of 6.45 Å which correlates well with the length of the biphenyl of the strut of 6.90 Å; a broad set of peaks observed at 2θ = 5−10° with a d-spacing of 9.40 Å,

Table 1. Properties of the Selected Candidate Structures for PAF-1 structure

density [g cm−3]

relative energy [kJ mol−1 T -site−1]

SASA [m2 g−1]a

PV [cm3 g−1]a

52_2_39194 61_2_8903 74_3_1891598 quartz 145_1_30 cri amorphous dia experiment

0.36 0.33 0.37 0.42 0.42 0.34 0.37 0.34 −

55.7 77.1 111.1 81.4 79.1 79.1 110.1 49.9 −

5452 5417 5104 5372 5394 5401 5152 5422 5600b

1.24 1.48 1.22 0.90 0.87 1.41 1.22 1.40 0.89−1.44c

a c

Calculated with a N2 probe radius of 1.82 Å. bBET surface area. Experimentally determined pore volume from the t-plot.20,23

materials, as a simulation cell is required that artificially imposes periodicity and thus cannot reproduce the full range of potential structural topologies within the finite limits of the simulation cell. Hence, when comparing experimental data with the simulated data, the noise of the amorphous structure is due to its artificially small size (66 × 68 × 69 Å) and periodicity must be taken into consideration. The raw PXRD experimental data were processed (see section S6), and the resulting plot shows a broad hump at 2θ = 12−13° and a large broad hump with a shoulder at 2θ ∼ 10°. The peak at 2θ ∼ 38° is due to the sample holder and can be ignored. PXRD patterns can be generally classed into three distinct types: those that are clearly crystalline with defined Bragg reflection peaks, those that are disordered nanocrystalline materials with broadened peaks centered on the Bragg reflection peaks of the ideal crystalline structure with amorphous halos that are related to the crystalline microstructure (crystal size, microstrain and defects), and those that are amorphous where the humps have no relation to the Bragg reflection peaks of an ideal crystalline structure.56 The humps observed in the processed PXRD for PAF-1 do not center on any of the Bragg reflection peaks of the crystalline candidate structures, including the dia structure. This suggests that the structure is not a crystalline or nanocrystalline form of the candidate structures. We note, however, that we have processed the experimental PXRD pattern from Ben et al. with an automated background detection tool, and the features observed, such as the small hump at 2θ = 13°, may not be real features, and equally some weak peaks may be obscured at low angles. Ideally, SAXS measurements would give more information as to whether there is any long-range order in PAF-1, but no SAXS studies have been reported to our knowledge. We conclude therefore that the experimental PXRD pattern shows no evidence of long-range order, but we cannot conclusively rule this out for the pattern of Ben et al. Where PAF-1, PAF derivatives, and similar materials such as element organic frameworks (EOF)57,58 and porous polymer networks (PPN)59 have been synthesized elsewhere, these are also found to have similar amorphous PXRD patterns. There are some PAF-type frameworks that do show evidence of long-range order and do have the associated peaks in their respective PXRD patterns, but these are synthesized via an alternative route that utilizes reversible chemistry.60 This includes the recently reported nitroso polymer networks (NPNs) that have a similar tetraphenyl tetrahedral unit (a C, Si, or adamantane core) but a different linker consisting of a nitroso group formed through a reversible polymerization reaction.61 Interestingly, D

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the model and experiment may be possible if an amorphous structure was generated specifically for the PAF-1 system. We now comment on the lack of network interpenetration and further turn our attention to the automated generation of specific amorphous frameworks for the PAF-1 building unit. Network Interpenetration. Network interpenetration increases dispersive interactions between frameworks and hence is favorable. The degree of network interpenetration depends upon the topology of the interpenetrating nets and steric factors. For amorphous networks such as CMPs, nets with flexible node-strut topology have increased density and lower surface area.64,65 Conversely, those with short rigid linkers or restricted node topology have decreased density and higher surface area. The flexibility of the net allows increased network interpenetration and more efficient packing, thereby increasing the density of the material. CMP-1, with a short, rigid, node-strut topology, has a surface area of 834 m2 g−1 and a density of 0.94 g cm−3.64 CMP-5, with longer more flexible struts, has a surface area of 512 m2 g−1 and a density of 1.16 g cm−3.64 The PAF-1 node-strut topology is relatively short and rigid with a node-tonode distance of 9.80 Å. This is shorter than for CMP-1, which has a node-to-node distance of 11.10 Å.64 We would therefore expect PAF-1 to follow the same trend as for the CMP series of materials and to have a decreased density and a corresponding increased surface area. However, while we would expect network interpenetration to be reduced, we would not expect it to be missing entirely on the basis of steric factors alone. Network topology of crystalline materials can be controlled by use of a template.66−68 The template is a molecule or group of molecules that directs the network topology to a specific form and interacts favorably with the framework. It can prevent network interpenetration by blocking volume that would otherwise be occupied by an interpenetrating net. Often the template is also a solvent with an intermediary solvate being formed, where the solvent template is an integral part of the crystalline structure.69,70 Upon desolvation, this can result in an open crystalline structure,71 or more often, framework collapse occurs, leading to a dense nonporous material.72 For PAF-1, no specific templating molecule was used in the synthesis method. However, we note that DMF is used as a solvent. DMF has been known to increase the porosity in other porous materials, including MOFs72 and in CMPs by over 300%.73 The mechanism by which DMF influences the final density of the porous material is yet to be determined. Molecular dynamic simulations have suggested that liquid DMF contains significant structure and local order.74−76 It is also known to form aggregates of four DMF molecules arranged in a flat oval-like shape in solution similarly to those found in the crystalline solid-state form, described in Figure S73, Supporting Information.75,77 It is not unreasonable to consider that the DMF molecule, or the DMF cluster, may act as a template to network formation, filling space and thereby preventing network interpenetration. Automated Generation of Amorphous PAF-1 Models. Structure identification through network mapping to topologically similar silica- and carbon-based framework materials have shown that the most realistic structure is based upon amorphous silica. Here we generate amorphous models specifically using the PAF-1 building block, shown in Figure S74, Supporting Information. A Python code was written to automate the model generation process. The Python code seeds an initial simulation

Figure 3. Simulated porous properties of the amorphous structure (a) PXRD, (b) pore size distribution, and (c) N2 isotherm at 77 K. The black line corresponds to simulation and the red lines to experimental results.

close to the node-to-node distance of 9.80 Å. A comparison of the amorphous model to the experimental results for PXRD, PSD, and N2 uptake is shown in Figure 3 (and in Figures S65− 72, Supporting Information, for other candidate models). Figure 4 shows the simulated loading of N2 at maximum uptake.

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STRUCTURE RATIONALIZATION In the first section, we have modeled the structure of a number of potential crystalline and amorphous topologies for PAF-1 based upon mapping the PAF-1 node and strut atomic structure to the topology of a set of silica- and carbon-based structures. This topological mapping raises two interesting conclusions. First, we find that it is impossible to rationalize the high surface area and pore volume if there is interpenetration of frameworks, despite the fact that interpenetration is energetically favorable. Second, the structure based on amorphous silica is found to be the most realistic. A better correlation between E

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Figure 4. Simulated sorption of N2 at maximum loading in the amorphous PAF structure. Each N2 molecule is shown in blue. A solvent-accessible surface is shown in yellow (right), calculated with a probe radius of 1.82 Å, to highlight the pore topology of the amorphous PAF structure.

Figure 5. Models of amorphous PAF-1 generated through an automated methodology: (a) Model-1a generated in the presence of DMF; (b) model2a generated with no DMF present. The top panel shows the underlying topological connectivity for model-1a and -2a. Each gray rod highlights the connectivity between each carbon T-site. The bottom panel shows the full structure with a solvent-accessible surface shown in blue. Gray spheres, carbon; white spheres, hydrogen; brown spheres, bromine.

cell with PAF building blocks and DMF solvent molecules. A molecular dynamics (MD) simulation is then undertaken with regular structural sampling for bond formation. This approach is similar to that taken successfully previously by Colina for the HCP polyDCX.78 The HOOMD-blue GPU-based code79−81 is used as the MD engine, enabling long simulation times and easy integration with the Python code. Optimization of the

structure geometry uses the Fast Inertial Relaxation Engine (FIRE) rigid-body minimizer within HOOMD-blue.81 A full description of the automated generation process can be found in the Supporting Information. The automated generation process is designed to provide qualitative insight into potential mechanisms of structure formation for amorphous materials, and the types of topological F

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features that can be formed within them. Unlike the previous structures examined in this paper, which are experimental or hypothetical crystal structures (and therefore minimum energy structures), the automated process currently cannot generate fully condensed structures and so energy comparisons with the earlier structures will not be made. We generate four amorphous PAF-1 structures. Model-1a and -1b are generated with DMF solvent molecules present in the system and model-2a and -2b without. The resulting structures for model-1a and model-2a are shown in Figure 5, depicting the underlying topology and the full structure with a solvent-accessible surface. The properties for each model are shown in Table 2. For each system, we do not obtain a full condensation of the network, with between 120 and 140 Br end groups remaining in the simulation cells. Table 2. Properties of the Amorphous PAF-1 Models Generated through an Automated Process and Compared to the Amorphous and dia Models Generated through Topological Mapping

a

structure

density [g cm−3]

SASA [m2 g−1]a

model-1a model-1b model-2a model-2b amorphous dia experiment

0.48 0.49 0.55 0.54 0.37 0.34 −

3832 3907 2562 2916 5152 5422 5600b)

PV [cm3 g−1]a wt % Br 0.74 0.65 0.61 0.60 1.22 1.40 0.89−1.44c)

11.6 11.8 12.3 12.1 0 0 0

Calculated with a N2 probe radius of 1.82 Å. b)BET surface area. Experimentally determined pore volume from the t-plot.20,23

Figure 6. Growth process for automated generation of PAF model-1a highlighting the size of each PAF cluster as the growth of the framework progresses. Yellow, unbonded PAF build units; green, two bonded PAF build units; blue, three bonded PAF build units; purple, four bonded PAF build units; pink, five or more bonded PAF build units. Hydrogen and bromine atoms are not shown for clarity. The DMF solvent molecules are shown for steps 11 and 77.

c)

involve bonding of the remaining end groups within the extended cluster. Figure 7 shows a cluster taken from step 15 with the nearby DMF solvent molecules to the PAF cluster. The DMF molecules occupy the space between the PAF build units of the cluster blocking the space between the build units. For model-2a, the PAF build units are clustered together after equilibration. This behavior is expected as the PAF build units attempt to maximize intermolecular interactions. This simulates the phase separation behavior that would occur if synthesis was performed in solvent within which the PAF build units are not fully miscible.82 Simulation of the growth process for PAF-1 with solvents within which we would not expect the PAF build units to be fully miscible will be important to further clarify the role of the solvent in the network formation. We have not performed these simulations within the scope of this study, but this will be the focus for future work. Figure S76, Supporting Information, plots the number of bromine atom end groups available within the simulation cell against the simulation step. The number of end groups initially drops rapidly and then decreases more slowly before tailing off. Longer MD simulation time may lead to additional bonds being found that could further reduce the final number of bromine atom end groups. However, it is unlikely that full condensation of the network will reached. PXRD and PSD for model-1a and model-2a are shown in Figures S77 and S78, Supporting Information, respectively, and compared to experiment. The PXRD for both model-1a and model-2a are a reasonable match to experiment similarly to the amorphous model generated through topological mapping. The PSD for model-1a shows a broad distribution of peaks with a maximum centered between 10 and 15 Å. For model-2a, the

Model-1a and model-1b have open structures with the PAF building units well dispersed throughout the simulation cell. Some interpenetration of the network is observed for both model-1a and model-1b. Model-2a and model-2b show regions of the simulation cell where the PAF building units have condensed and are densely packed with a high degree of network interpenetration. Model-1a and model-1b have pores that are accessible throughout the simulation, although some regions exhibit network interpenetration. Model-2a and model2b has one large pore with some additional accessible porosity within the densely packed PAF building units. This difference in porosity is reflected in the surface area of the models. Model1a and model-1b have a higher surface area at 3800−3900 m2g−1 than model-2a and model-2b at 2500−2900 m2g−1. Figure S75, Supporting Information, shows the growth process for model-1a and model-2a sampled after equilibration of the respective seeded simulation cell, subsequent to the PAF bonding process, and at the end of the growth steps. Figure 6 shows the growth process in detail for model-1a. Step 11 (the first bonding step after equilibration) shows the PAF build units are dispersed evenly throughout the simulation cell for model-1 with the DMF molecules occupying the volume between the PAF build units. The PAF-1 build units quickly form bonds to neighboring units to form small clusters of two or three PAF units. These small clusters bond together to form extended clusters of more than five PAF build units. At step 30, the extended cluster extends throughout the simulation cell with unbonded PAF build units still present. Half way through the growth process at step 40, all PAF build units are bonded to at least one other PAF build unit. The remaining growth steps G

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Figure 7. A cluster of bonded PAF-1 build units (pink) formed during the growth process of the PAF-1 framework for model 1a taken from step 15 showing the DMF solvent units within the framework structure. Gray spheres, carbon; blue spheres, nitrogen; red spheres, oxygen; white spheres, hydrogen.

high surface area and high condensation that is observed experimentally. Improvement of the generation method may increase the condensation of the network and further reduce network interpenetration and suggest new insight into the mechanism of network formation. These improvements would include: investigating the ratio of PAF build units to DMF molecules, fully flexible molecules throughout the seed and generation process, use of a force field tailored specifically to describe the PAF-1 building block and DMF molecule, larger simulation cell, longer simulation run time, consideration of the catalyst and alternative solvents. This will be the focus for future work.

distribution of peaks is broad with no distinct maxima. A better match to the experimental PSD is observed for model-1a. The amorphous model generated from topological mapping to amorphous silica is a better match to experiment for the surface area, pore volume, PXRD, and PSD than model-1a and model-2a. The amorphous model shows no network interpenetration, whereas the models generated through the automated process (model-1a and -2a) do show network interpenetration. To compare the distribution of the network through the simulation cell, the radial distribution function, g(r), was calculated for the T-site carbon atoms for the amorphous model and model-1a, -1b, -2a, and -2b and are shown in Figure S79, Supporting Information. The g(r) calculated for model-1a and -1b are very similar, with very little noticeable difference between the models. Similarly for model-2a and -2b. In all models, a sharp peak at ∼10 Å is observed, corresponding to the node-to-node T-site−T-site distance. Two further very broad peaks are also observed at 17 and 25 Å for all models. These correspond to node-to-node second and third neighbor distances, respectively. The region between 5 and 10 Å shows the largest difference between the models. For the amorphous model, there are no peaks that correspond to distances less than 8 Å and very few that are less than 10 Å. For model-1a and -1b, automated structures generated in the presence of DMF, there are no peaks corresponding to distances less than 6 Å, but a greater number that are less than 10 Å than for the amorphous model. Whereas for model-2a and -2b, automated structures generated with no DMF present, there are some peaks corresponding to distances that are less than 6 Å and a greater proportion that are below 10 Å. This is reflective of the greater degree of interpenetration observed in model-2a and -2b compared to model-1a and -1b and the amorphous model. A greater degree of network interpenetration will result in a greater number of T-site carbon atoms that are less than the node-to-node T-site−T-site distance of ∼10 Å. In summary, the automated generation process has suggested a possible rationalization for the lack of significant network interpenetration observed in the experimental structure. The DMF solvent is an essential part in the formation of an open framework structure, preventing coalescence of the PAF build units. However, the generated models do not reproduce the

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CONCLUSIONS

We conclude that the most representative structure for PAF-1 is based upon topological mapping from an amorphous silica model. We have found that there is nothing to be gained in surface area alone by targeting a specific crystalline topology of PAF, because most crystalline topologies have a surface area between 5000 and 5500 m2 g−1. However, we have found that there would be the potential to increase the pore volume by targeting high pore volume crystalline topologies, potentially with an increase of pore volume of ∼50% compared to that previously experimentally reported. We believe the focus on a single simple crystalline model such as the dia topology significantly hinders the rational design of new PAF-family materials, as one is envisaging modifications and developments upon an incorrect structure. Furthermore, we find that the synthetic conditions, in particular the solvent, can have a significant role in determining the resulting structure by prevention of network interpenetration and potential templating of cluster formation. This focus on the network formation mechanism suggests that there is scope for modification of the synthetic procedure that could further reduce network interpenetration and direct the structure toward larger more open voids within the PAF-1 framework. This could result in materials with even higher surface area and pore volume. H

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ASSOCIATED CONTENT

S Supporting Information *

CIF files for all PAF-1 models generated through topological mapping. Description of topological mapping and simulation method. Energy, surface area, pore volume, images, and cell parameters for all structures. Pore size distribution, isotherm simulation, and PXRD simulation for all candidate structures. Description of automated generation process and simulation method. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.T. holds a Royal Society University Research Fellowship. A.T. thanks T. Ben and A. I. Cooper for useful discussions and providing data.

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REFERENCES

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