Amorphous PAF-1: Guiding the Rational Design of UltraporousMaterialsJens 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-1are compared with an amorphous structure for PAF-1,reproducing the ultrahigh surface area and pore volumeobserved experimentally. We compare the porosity propertiesof these structures and discuss potential structural strategiesfor increasing porosity and gas uptake properties. The PAF-1network formation mechanism is simulated through use of anautomated 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 frameworkmaterials.

■ INTRODUCTION

The high surface area and pore volume of microporousmaterials has led to their widespread use in applications such asgas adsorption, heterogeneous catalysis, and chemical separa-tions.1−5 There is a pressing need for the discovery of materialswith ultrahigh porosity to attain the advanced functionalitydemanded by these increasingly important applications. It iswidely believed that ultrahigh porosity can only be achieved forframework materials with a high degree of crystallinity,including metal−organic frameworks (MOFs)6−8 and covalentorganic frameworks (COFs),9−13 the obvious example beingthe highest reported surface area for any material (over 7000m2 g−1) for MOF NU-110.14 Design strategies for futureframework materials with increasingly high porosity includeincreasing the strut length of the crystalline framework andhence increasing the interspatial void. However, this strategyoften results in framework interpenetration and ironically areduction in the porosity. Increasingly, the stability and theability to further functionalize a framework is of greaterimportance for the materials’ applications. In this sense, thephysical and chemical stability and the potential for vastsynthetic diversity of amorphous materials, including micro-porous organic polymers (MOPs), hyper-cross-linked polymers(HCPs),15 conjugated microporous polymers (CMPs),16,17

polymers of intrinsic microporosity (PIMs),18 and covalenttriazine-based frameworks (CTFs)19 have many advantagesover other classes of porous materials. However, these materialshave typically not yet attained the ultrahigh porosity of theircrystalline 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 BETsurface area of over 5600 m2 g−1 was reported with porevolume ranging 0.89−1.44 cm3 g−1 for PAF-123 and withexceptional physical and chemical stability. A number of recent

reports demonstrate the synthetic diversity and scope forpostsynthetic modification.21,24−30 However, the structuralmodel of these framework materials has not yet beenconclusively determined. A crystalline diamondoid structurewas presented that can account for the surface area and gasuptake properties observed but does not explain the lack oflong-range order evident in the powder X-ray diffraction(PXRD) pattern. Here, we explore a number of potentialalternative crystalline and amorphous topologies. We show thatof these, only the amorphous PAF-1 structure is able to fullyrationalize the properties of the PAF-1 material. Furthermore,we are able to rationalize the synthetic route to the amorphousstructure. We are able to suggest some broad design strategiesthat increase the pore volume and hence the gas uptakecapacity of the material. This implies that there are newdirections in the design strategy of functional materials withhigh porosity available to be exploited.

■ STRUCTURE IDENTIFICATIONTopologically, PAF-1 is similar to the 4-connected nets thatunderlie the structures of silica, aluminosilicate zeolites, andsimple tetrahedral solids (e.g., carbon diamond and zinc oxidewurtzite structures). For silicate structures, these tetrahedralSiO4 units are termed T-sites; here we use the same term forthe PAF-1 tetrahedral unit, tetraphenylmethane (Figure 1a,b,bottom left). Where silicate T-sites are connected by fouroxygen atoms to four other tetrahedral silicon sites, for PAF-1 abiphenyl group connects the tetrahedral carbon atoms. Such atopological mapping between nets and structures hassuccessfully been exploited in structure prediction for a range

Received: March 7, 2014Revised: July 30, 2014

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of materials, including bulk oxides, sulfides and nitrides,inorganic microprous materials, and MOFs.31−36 In the specificcase of PAF-1, we previously showed that an amorphous PAF-1structure generated through topological mapping from anamorphous silica structure provided an alternative to theproposed diamondoid structure for PAF-1.37 This amorphousPAF-1 structure rationalized the surface area, lack of endgroups, and the lack of experimental evidence for long-rangeorder.Computational Method. In this study, we compare these

amorphous and dia PAF-1 structures with 31 other topologicalstructures for networks. These were selected from threedifferent databases that collate both experimentally realizedand hypothetical crystal structures: the Zeolite Atlas of theInternational Zeolite Association38−40 (topologies of exper-imentally synthesized microporous (alumino) silicates andrelated materials, with a three capital letter code, e.g., SOD foreach structure), Treacy’s database of hypothetical zeolitestructures40−42 (hypothetical siliceous zeolite topologiesenumerated through a graph search, with a xx_y_zzzzz code,where xx is the space group in which the topology was foundand y the number of symmetry unique tetrahedral atoms), andthe Reticular Chemistry Structure Resource Database43−46

(topologies of both hypothetical nets and experimentallyknown minerals, with three lowercase letter codes, e.g., diafor diamond). A PERL script was written to automate theisomorphic substitution of PAF nodes for the other tetrahedralnodes. The structures were initially optimized using PCFF47 inAccelrys’ Materials Studio 5.048 using the Forcite module. Theresultant structure was then optimized using the TINKERmolecular modeling package49 with the MM350 force field,which was recently extended by Schmid et al. for COFs51 andfollowed by Monte Carlo (MC) conformational searches (this

procedure is described in full in section S1, SupportingInformation).

Results. Figure 2a−c shows a plot of the relative energy perT-site, surface area, and pore volume versus density for thestructures explored, respectively. An additional fully labeled plotfor energy versus density is shown in Figure S1, SupportingInformation. 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 thenoninterpenetrated structures, there is a general trend that withincreasing density, the relative energy decreases, with the diatopology lying lowest in energy. In general, interpenetratingstructures are lower in energy than those without networkinterpenetration. The dia and interpenetrated dia topologyseries (dia-c, dia-c3, dia-c6, and dia-c4, where N of dia-cNindicates the number of increasing interpenetrating nets) havelow relative energy. The relative energy decreases considerablyfrom dia to dia-c (by 50 kJ mol−1 per T-site), presumablythrough the gain of favorable dispersive interactions betweenthe two networks. The relative energy continues to decreaseslightly through further interpenetration in the dia-c3 structure(by 7 kJ mol−1 per T-site). Further interpenetration to formdia-c4 then causes an increase in energy (by 51 kJ mol−1 per T-site). We assume this results from there being no further spacefor additional networks without introducing strain into thestructures. The dia-c3 structure is the lowest energy structurefor all those investigated here and thus the thermodynamicallyfavored structure, with dia being the most energeticallyfavorable of the noninterpenetrating structures.Reaction mechanisms under thermodynamic control, such as

those with reversible reactions, should result in the formation ofthe lowest energy structure, as the breaking and making ofbonds allows self-healing and energetically unfavorablestructural imperfections to be removed over time. By contrast,

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

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syntheses where bonds are formed through irreversiblechemistry will tend to form kinetic products that lack long-range order. Thus, if the reaction to form PAF-1 werethermodynamically controlled, then we would expect, in theabsence of other factors, in particular solvent templating effects,that an interpenetrating structure based upon a dia-cN netwould be formed. As PAF-1 is synthesized through irreversibleYamamoto type Ullmann cross-coupling reactions, we wouldnot expect the reaction product to have a thermodynamicallycontrolled structure.52−54 Nevertheless, we now evaluate allpossible structures for their surface area and pore volumes andtest these against the experimentally obtained values.Solvent-accessible surface area (SASA) and pore volume

(PV) were calculated for each structure using Accelrys

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 thedegree of interpenetration increases through dia to dia-c4, thesurface area of the structures decreases from 5422 m2 g−1 fordia to 2283 m2 g−1 for dia-c, until finally the dia-c3 and dia-c4structures have effectively zero surface area, as the networkinterpenetration efficiently fills all void space. A similar decreasewith increasing interpenetration is also observed for the models’calculated pore volumes. These observations effectively rule outa fully interpenetrated experimental structure, as they are atodds with the experimentally observed high surface area ofPAF-1. This is also consistent with the expectation discussedabove that the synthesis method for PAF-1 would not give athermodynamic product, although it is possible that a solvent-templating effect prevents interpenetration.The majority of the noninterpenetrating structures have

similar SASAs in the range of ∼5000−5500 m2 g−1, includingthe amorphous model with a surface area of 5152 m2 g−1

(Figure 2b). This suggests that the specific crystalline form haslittle influence on the surface area and furthermore that there islittle to be gained in surface area alone from a crystalline ratherthan amorphous structure. This contradicts the claims that ahigh degree of crystallinity is a requirement of ultrahigh surfacearea materials. We suspect that, in contrast to inorganic 4-connected materials where a single atom is the linker, the factthat the PAF-1 structure has a biphenyl linker of ∼9 Å meansthat typically all of the linker surface area is exposed in all of thestructures and therefore the surface area is similar across thestructures. By contrast, there is a difference in the pore volumeacross the noninterpenetrated models, with an increase in porevolume observed, as expected, with decreasing density (Figure2c).The largest pore volume found of 1.94 cm3 g−1 is for the

ATN structure (Figure 2c and Figure S25, SupportingInformation), which is 56% greater than the amorphousmodel’s pore volume of 1.22 cm3 g−1. The ATN structureappears to have a high pore volume as a result of consisting of aseries of large cavities of very similar size (rather than a mixtureof small and large cages), including cavities of ∼22 Å diameterand channels with diameters above 16 Å. Therefore, if it weresynthetically feasible to template toward a desired crystallinestructure, such as ATN, there is the potential to increase thepore 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 representativeof the experimental results for those properties. We chose thefollowing criteria: a surface area greater than 5000 m2 g−1 and apore volume between 0.80 and 1.50 cm3 g−1 (see section S2,Supporting Information, for further discussion of thecorrelation of experimental and calculated surface area andpore volumes and the selection criteria). Table 1 shows theeight candidate structures based upon these criteria; they are allnoninterpenetrating networks and are clustered within a smallregion 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 theadditional structural characterization methods: the PXRDpattern, pore size distribution (PSD), and nitrogen gas uptake.The experimental and simulated PXRD patterns for allcandidate structures were simulated using Mercury 3.1 andare shown in sections S6 and S7, Supporting Information. It ischallenging to simulate accurately the properties of amorphous

Figure 2. (a) Relative energy as a function of crystallographic densityfor the structures of PAF-1. Filled points highlight the candidatestructures from Table 1. The amorphous structure is highlighted ingreen and the dia series is highlighted red and labeled. (b) Solvent-accessible surface area as a function of density. (c) Pore volume as afunction of density. Surface area and pore volume calculated using aprobe radius of 1.82 Å. Circles represent noninterpenetratedstructures, while triangles represent interpenetrated structures.

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materials, as a simulation cell is required that artificially imposesperiodicity and thus cannot reproduce the full range ofpotential structural topologies within the finite limits of thesimulation cell. Hence, when comparing experimental data withthe simulated data, the noise of the amorphous structure is dueto its artificially small size (66 × 68 × 69 Å) and periodicitymust be taken into consideration. The raw PXRD experimentaldata were processed (see section S6), and the resulting plotshows a broad hump at 2θ = 12−13° and a large broad humpwith a shoulder at 2θ ∼ 10°. The peak at 2θ ∼ 38° is due to thesample holder and can be ignored. PXRD patterns can begenerally classed into three distinct types: those that are clearlycrystalline with defined Bragg reflection peaks, those that aredisordered nanocrystalline materials with broadened peakscentered on the Bragg reflection peaks of the ideal crystallinestructure with amorphous halos that are related to thecrystalline microstructure (crystal size, microstrain and defects),and those that are amorphous where the humps have norelation to the Bragg reflection peaks of an ideal crystallinestructure.56 The humps observed in the processed PXRD forPAF-1 do not center on any of the Bragg reflection peaks of thecrystalline candidate structures, including the dia structure. Thissuggests that the structure is not a crystalline or nanocrystallineform of the candidate structures. We note, however, that wehave processed the experimental PXRD pattern from Ben et al.with an automated background detection tool, and the featuresobserved, such as the small hump at 2θ = 13°, may not be realfeatures, and equally some weak peaks may be obscured at lowangles. Ideally, SAXS measurements would give moreinformation as to whether there is any long-range order inPAF-1, but no SAXS studies have been reported to ourknowledge. We conclude therefore that the experimental PXRDpattern shows no evidence of long-range order, but we cannotconclusively rule this out for the pattern of Ben et al. WherePAF-1, PAF derivatives, and similar materials such as elementorganic frameworks (EOF)57,58 and porous polymer networks(PPN)59 have been synthesized elsewhere, these are also foundto have similar amorphous PXRD patterns. There are somePAF-type frameworks that do show evidence of long-rangeorder and do have the associated peaks in their respectivePXRD patterns, but these are synthesized via an alternativeroute that utilizes reversible chemistry.60 This includes therecently reported nitroso polymer networks (NPNs) that havea similar tetraphenyl tetrahedral unit (a C, Si, or adamantanecore) but a different linker consisting of a nitroso group formedthrough a reversible polymerization reaction.61 Interestingly,

NPN-1 (the closest equivalent to PAF-1) forms a 4-foldinterpenetrated diamondoid net similarly to the dia-c4structure. 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 thestructures will differ, with the more open structure of the NPN-1 framework perhaps favoring the more interpenetrated dia-c4topology. 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, SupportingInformation).62 The experimental pore size distribution showsa broad distribution of peaks with a maxima between 13−15 Å.A sharp edge is observed to the lower values with no poresobserved with a diameter less than 12 Å and a broad tailextended smoothly to pore diameters greater than 30 Å. Onlythe amorphous structure is able to represent the distribution ofpore sizes observed experimentally, with a maxima in thedistribution located at a pore size of ∼15 Å (as shown in Figure2b). The dia, cri, 52_2_39194, and 61_2_8903 structuresexhibit a sharp peak at ∼15 Å but with no pore sizes greaterthan this. The 74_3_1891598 structure exhibits a distributionof pore sizes but with a maxima in the distribution at ∼18−20Å. The quartz and 145_1_30 structures have pore sizes belowthose observed experimentally with a maxima in thedistribution 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 MaterialsStudio 5.048 and PCFF.47 The nitrogen molecule was modeledwith a quadrupole moment according to Potoff andSiepmann.63 Experimental sorption isotherms show that at apressure of 1 bar and a temperature of 77 K there is an uptakeof around 1800 cm3 g−1. Section S9, Supporting Information,shows the isotherms for all candidate structures in comparisonto the experimentally obtained isotherm.20 The isothermssimulated here fall into three categories, shown in Figure S64,Supporting Information:

1. Those that have agreement with experiment in high-pressure regions but do not agree at low-pressure regionswhere 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 experimentbut are slightly too high in low-pressure regions andslightly too low in high-pressure regions; these includethe amorphous, 52_2_39194, and 74_3_1891598structures.

3. Those where the overall uptake is too low; these includethe quartz and 145_1_30 structures.

These groupings correlate to the simulated pore volumegroupings 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 andstructural characterization of PAF-1. The amorphous structurebest reproduces both the PXRD pattern and PSD, shown inFigure 3a,b, respectively. The amorphous structure’s PSDreproduces the broad distribution with a maxima at ∼15 Å. ThePXRD pattern for the amorphous model has several featuresthat could correlate well with the experimental PXRD: a humpat 2θ = 13°, with a d-spacing of 6.45 Å which correlates wellwith the length of the biphenyl of the strut of 6.90 Å; a broadset of peaks observed at 2θ = 5−10° with a d-spacing of 9.40 Å,

Table 1. Properties of the Selected Candidate Structures forPAF-1

structuredensity[g cm−3]

relative energy[kJ mol−1 T-site−1]

SASA[m2 g−1]a

PV[cm3 g−1]a

52_2_39194 0.36 55.7 5452 1.2461_2_8903 0.33 77.1 5417 1.4874_3_1891598 0.37 111.1 5104 1.22quartz 0.42 81.4 5372 0.90145_1_30 0.42 79.1 5394 0.87cri 0.34 79.1 5401 1.41amorphous 0.37 110.1 5152 1.22dia 0.34 49.9 5422 1.40experiment − − 5600b 0.89−1.44c

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

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close to the node-to-node distance of 9.80 Å. A comparison ofthe 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 maximumuptake.

■ STRUCTURE RATIONALIZATIONIn the first section, we have modeled the structure of a numberof potential crystalline and amorphous topologies for PAF-1based upon mapping the PAF-1 node and strut atomicstructure to the topology of a set of silica- and carbon-basedstructures. This topological mapping raises two interestingconclusions. First, we find that it is impossible to rationalize thehigh surface area and pore volume if there is interpenetration offrameworks, despite the fact that interpenetration is energeti-cally favorable. Second, the structure based on amorphous silicais found to be the most realistic. A better correlation between

the model and experiment may be possible if an amorphousstructure was generated specifically for the PAF-1 system. Wenow comment on the lack of network interpenetration andfurther turn our attention to the automated generation ofspecific amorphous frameworks for the PAF-1 building unit.

Network Interpenetration. Network interpenetrationincreases dispersive interactions between frameworks andhence is favorable. The degree of network interpenetrationdepends upon the topology of the interpenetrating nets andsteric factors.For amorphous networks such as CMPs, nets with flexible

node-strut topology have increased density and lower surfacearea.64,65 Conversely, those with short rigid linkers or restrictednode topology have decreased density and higher surface area.The flexibility of the net allows increased network inter-penetration and more efficient packing, thereby increasing thedensity of the material. CMP-1, with a short, rigid, node-struttopology, has a surface area of 834 m2 g−1 and a density of 0.94g cm−3.64 CMP-5, with longer more flexible struts, has a surfacearea of 512 m2 g−1 and a density of 1.16 g cm−3.64 The PAF-1node-strut topology is relatively short and rigid with a node-to-node distance of 9.80 Å. This is shorter than for CMP-1, whichhas a node-to-node distance of 11.10 Å.64 We would thereforeexpect PAF-1 to follow the same trend as for the CMP series ofmaterials and to have a decreased density and a correspondingincreased surface area. However, while we would expectnetwork interpenetration to be reduced, we would not expectit 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 groupof molecules that directs the network topology to a specificform and interacts favorably with the framework. It can preventnetwork interpenetration by blocking volume that wouldotherwise be occupied by an interpenetrating net. Often thetemplate is also a solvent with an intermediary solvate beingformed, where the solvent template is an integral part of thecrystalline structure.69,70 Upon desolvation, this can result in anopen crystalline structure,71 or more often, framework collapseoccurs, leading to a dense nonporous material.72

For PAF-1, no specific templating molecule was used in thesynthesis method. However, we note that DMF is used as asolvent. DMF has been known to increase the porosity in otherporous materials, including MOFs72 and in CMPs by over300%.73 The mechanism by which DMF influences the finaldensity of the porous material is yet to be determined.Molecular dynamic simulations have suggested that liquid DMFcontains significant structure and local order.74−76 It is alsoknown to form aggregates of four DMF molecules arranged in aflat oval-like shape in solution similarly to those found in thecrystalline solid-state form, described in Figure S73, SupportingInformation.75,77 It is not unreasonable to consider that theDMF molecule, or the DMF cluster, may act as a template tonetwork formation, filling space and thereby preventingnetwork interpenetration.

Automated Generation of Amorphous PAF-1 Models.Structure identification through network mapping to topolog-ically similar silica- and carbon-based framework materials haveshown that the most realistic structure is based uponamorphous silica. Here we generate amorphous modelsspecifically using the PAF-1 building block, shown in FigureS74, 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. Theblack line corresponds to simulation and the red lines to experimentalresults.

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cell with PAF building blocks and DMF solvent molecules. Amolecular dynamics (MD) simulation is then undertaken withregular structural sampling for bond formation. This approachis similar to that taken successfully previously by Colina for theHCP polyDCX.78 The HOOMD-blue GPU-based code79−81 isused as the MD engine, enabling long simulation times andeasy 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 fulldescription of the automated generation process can be foundin the Supporting Information.The automated generation process is designed to provide

qualitative insight into potential mechanisms of structureformation for amorphous materials, and the types of topological

Figure 4. Simulated sorption of N2 at maximum loading in the amorphous PAF structure. Each N2 molecule is shown in blue. A solvent-accessiblesurface 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) model-2a generated with no DMF present. The top panel shows the underlying topological connectivity for model-1a and -2a. Each gray rod highlights theconnectivity 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.

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features that can be formed within them. Unlike the previousstructures examined in this paper, which are experimental orhypothetical crystal structures (and therefore minimum energystructures), the automated process currently cannot generatefully condensed structures and so energy comparisons with theearlier structures will not be made.We generate four amorphous PAF-1 structures. Model-1a

and -1b are generated with DMF solvent molecules present inthe system and model-2a and -2b without. The resultingstructures for model-1a and model-2a are shown in Figure 5,depicting the underlying topology and the full structure with asolvent-accessible surface. The properties for each model areshown in Table 2. For each system, we do not obtain a fullcondensation of the network, with between 120 and 140 Br endgroups remaining in the simulation cells.

Model-1a and model-1b have open structures with the PAFbuilding units well dispersed throughout the simulation cell.Some interpenetration of the network is observed for bothmodel-1a and model-1b. Model-2a and model-2b show regionsof the simulation cell where the PAF building units havecondensed and are densely packed with a high degree ofnetwork interpenetration. Model-1a and model-1b have poresthat are accessible throughout the simulation, although someregions exhibit network interpenetration. Model-2a and model-2b has one large pore with some additional accessible porositywithin the densely packed PAF building units. This differencein porosity is reflected in the surface area of the models. Model-1a and model-1b have a higher surface area at 3800−3900m2g−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 equilibrationof the respective seeded simulation cell, subsequent to the PAFbonding process, and at the end of the growth steps. Figure 6shows the growth process in detail for model-1a. Step 11 (thefirst bonding step after equilibration) shows the PAF build unitsare dispersed evenly throughout the simulation cell for model-1with the DMF molecules occupying the volume between thePAF build units. The PAF-1 build units quickly form bonds toneighboring units to form small clusters of two or three PAFunits. These small clusters bond together to form extendedclusters of more than five PAF build units. At step 30, theextended cluster extends throughout the simulation cell withunbonded PAF build units still present. Half way through thegrowth process at step 40, all PAF build units are bonded to atleast one other PAF build unit. The remaining growth steps

involve bonding of the remaining end groups within theextended cluster. Figure 7 shows a cluster taken from step 15with the nearby DMF solvent molecules to the PAF cluster.The DMF molecules occupy the space between the PAF buildunits 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 buildunits attempt to maximize intermolecular interactions. Thissimulates the phase separation behavior that would occur ifsynthesis was performed in solvent within which the PAF buildunits are not fully miscible.82 Simulation of the growth processfor PAF-1 with solvents within which we would not expect thePAF build units to be fully miscible will be important to furtherclarify the role of the solvent in the network formation. Wehave not performed these simulations within the scope of thisstudy, 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 cellagainst the simulation step. The number of end groups initiallydrops rapidly and then decreases more slowly before tailing off.Longer MD simulation time may lead to additional bonds beingfound that could further reduce the final number of bromineatom end groups. However, it is unlikely that full condensationof the network will reached.PXRD and PSD for model-1a and model-2a are shown in

Figures S77 and S78, Supporting Information, respectively, andcompared to experiment. The PXRD for both model-1a andmodel-2a are a reasonable match to experiment similarly to theamorphous model generated through topological mapping. ThePSD for model-1a shows a broad distribution of peaks with amaximum centered between 10 and 15 Å. For model-2a, the

Table 2. Properties of the Amorphous PAF-1 ModelsGenerated through an Automated Process and Compared tothe Amorphous and dia Models Generated throughTopological Mapping

structure density [g cm−3]SASA

[m2 g−1]a PV [cm3 g−1]a wt % Br

model-1a 0.48 3832 0.74 11.6model-1b 0.49 3907 0.65 11.8model-2a 0.55 2562 0.61 12.3model-2b 0.54 2916 0.60 12.1amorphous 0.37 5152 1.22 0dia 0.34 5422 1.40 0experiment − 5600b) 0.89−1.44c) 0

aCalculated with a N2 probe radius of 1.82 Å. b)BET surface area. c)

Experimentally determined pore volume from the t-plot.20,23

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

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distribution of peaks is broad with no distinct maxima. A bettermatch 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 thesurface area, pore volume, PXRD, and PSD than model-1a andmodel-2a. The amorphous model shows no network inter-penetration, whereas the models generated through theautomated process (model-1a and -2a) do show networkinterpenetration. To compare the distribution of the networkthrough the simulation cell, the radial distribution function,g(r), was calculated for the T-site carbon atoms for theamorphous model and model-1a, -1b, -2a, and -2b and areshown in Figure S79, Supporting Information. The g(r)calculated for model-1a and -1b are very similar, with verylittle noticeable difference between the models. Similarly formodel-2a and -2b. In all models, a sharp peak at ∼10 Å isobserved, corresponding to the node-to-node T-site−T-sitedistance. Two further very broad peaks are also observed at 17and 25 Å for all models. These correspond to node-to-nodesecond and third neighbor distances, respectively. The regionbetween 5 and 10 Å shows the largest difference between themodels. For the amorphous model, there are no peaks thatcorrespond to distances less than 8 Å and very few that are lessthan 10 Å. For model-1a and -1b, automated structuresgenerated in the presence of DMF, there are no peakscorresponding to distances less than 6 Å, but a greater numberthat are less than 10 Å than for the amorphous model. Whereasfor model-2a and -2b, automated structures generated with noDMF present, there are some peaks corresponding to distancesthat are less than 6 Å and a greater proportion that are below10 Å. This is reflective of the greater degree of interpenetrationobserved in model-2a and -2b compared to model-1a and -1band the amorphous model. A greater degree of networkinterpenetration will result in a greater number of T-site carbonatoms that are less than the node-to-node T-site−T-sitedistance of ∼10 Å.In summary, the automated generation process has suggested

a possible rationalization for the lack of significant networkinterpenetration observed in the experimental structure. TheDMF solvent is an essential part in the formation of an openframework structure, preventing coalescence of the PAF buildunits. However, the generated models do not reproduce the

high surface area and high condensation that is observedexperimentally. Improvement of the generation method mayincrease the condensation of the network and further reducenetwork interpenetration and suggest new insight into themechanism of network formation. These improvements wouldinclude: investigating the ratio of PAF build units to DMFmolecules, fully flexible molecules throughout the seed andgeneration process, use of a force field tailored specifically todescribe the PAF-1 building block and DMF molecule, largersimulation cell, longer simulation run time, consideration of thecatalyst and alternative solvents. This will be the focus forfuture work.

■ CONCLUSIONS

We conclude that the most representative structure for PAF-1is based upon topological mapping from an amorphous silicamodel. We have found that there is nothing to be gained insurface area alone by targeting a specific crystalline topology ofPAF, because most crystalline topologies have a surface areabetween 5000 and 5500 m2 g−1. However, we have found thatthere would be the potential to increase the pore volume bytargeting high pore volume crystalline topologies, potentiallywith an increase of pore volume of ∼50% compared to thatpreviously experimentally reported. We believe the focus on asingle simple crystalline model such as the dia topologysignificantly hinders the rational design of new PAF-familymaterials, as one is envisaging modifications and developmentsupon an incorrect structure.Furthermore, we find that the synthetic conditions, in

particular the solvent, can have a significant role in determiningthe resulting structure by prevention of network inter-penetration and potential templating of cluster formation.This focus on the network formation mechanism suggests thatthere is scope for modification of the synthetic procedure thatcould further reduce network interpenetration and direct thestructure toward larger more open voids within the PAF-1framework. This could result in materials with even highersurface area and pore volume.

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 15showing the DMF solvent units within the framework structure. Gray spheres, carbon; blue spheres, nitrogen; red spheres, oxygen; white spheres,hydrogen.

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■ ASSOCIATED CONTENT*S Supporting InformationCIF files for all PAF-1 models generated through topologicalmapping. Description of topological mapping and simulationmethod. Energy, surface area, pore volume, images, and cellparameters for all structures. Pore size distribution, isothermsimulation, and PXRD simulation for all candidate structures.Description of automated generation process and simulationmethod. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: a.trewin@lancaster.ac.uk.Author ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSA.T. holds a Royal Society University Research Fellowship. A.T.thanks T. Ben and A. I. Cooper for useful discussions andproviding data.

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