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Molecular modelling of adsorption in novel nanoporous metal–organic materials

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Molecular modelling of adsorption in novel nanoporous metal–organic materials
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  Molecular modelling of adsorption in novelnanoporous metal–organic materials LEV SARKISOV, TINA DU ¨ REN and RANDALL Q. SNURR*Northwestern University, Department of Chemical Engineering,2145 Sheridan Road, Evanston, Illinois 60208, USA ( Received 6 July 2003; revised version accepted 28 November 2003 )Grand canonical Monte Carlo and molecular dynamics simulations have been performed formethane, n-alkanes, cyclohexane and benzene in two novel nanoporous metal–organicmaterials. The first material, bipyridine molecular squares, consists of discrete squaremolecules with corners formed by rhenium complexes and edges formed by bipyridine links,giving a small cavity within each square. The material is considered in both its crystalline formand an amorphous packing of squares. The second material is IRMOF-1, a periodic,crystalline structure also with metal corners and organic bridging units. Adsorption isothermsand self-diffusion coefficients are reported and provide insight into molecular interactions inthese materials. 1. Introduction Recently several new classes of nanoporous materialshave been developed from ligand-bridged metal–organiccompounds [1–10]. These materials may have applica-tions in adsorption separations, membranes, sensingand catalysis. They are united by a common synthesisapproach via simple self assembly from a solution of building blocks. The building blocks for these materialsare provided by metal complexes (usually six coordi-nated) and various organic molecules capable of bindingto these metal complexes via weak coordination bonds.Upon mixing these building blocks, the metal complexesare spontaneously connected together by the organiccomponents, which serve as linking units. This process,driven by weak coordination forces, results in theformation of various well-defined geometric structures,such as discrete triangles, squares, cubes, cycles, as wellas periodic three-dimensional grids, with the vertices of these structures being metal complexes connected byorganic links. Examples of these structures are shown infigure 1.The cavities in these materials suggest that they can beused in a variety of technological applications. Fordiscrete entities, such as molecular squares, severalresearch directions have been pursued. For example,Keefe  et al  . [11] investigated the possibility of using filmsassembled from molecular squares as sensors for volatileorganic compounds. Be ´langer  et al  . [4] and Czaplewski et al  . [12] have examined application of molecularsquares, like those shown in figure 1, as membranematerials for size selective chemical separations. Some of the molecular squares developed by Hupp and Nguyen[5] have large enough cavities to encapsulate variousmetalloporphyrin catalysts, such as manganese dipyridylporphyrin, used in the catalytic epoxidation of olefins[13]. Encapsulation of a catalytic site by the molecularsquare leads to better stability and extended lifetime of the catalyst and also creates a route for attachingadditional ligands to the sides of the molecular square torestrict access of certain compounds to the catalytic site,leading to catalytic selectivity. The possibility of usingsimilar compounds for enantioselective sensing wasexplored by Lee and Lin [9]. In contrast to discretemolecular units, such as squares, it is also possible toconstruct three-dimensional periodic metal–organicframeworks with significant porosity. Yaghi andco-workers have developed isoreticular metal–organicframeworks (IRMOFs), as shown in figure 1( d  ), for gasstorage and other applications [6, 7]. Other interestingexamples of functionalized metal–organic frameworksinclude nanoporous molecular magnets with reversiblemechanical and magnetic properties (MOROF materi-als) [10] and zeolite-like materials assembled of metallo-porphyrins (PIZA), recently reported by Kosal  et al  . [8].Metal–organic materials may have a tremendouspotential impact as novel, highly effective recognition,separation, adsorption and catalytic materials due totheir cage-like structure, the simplicity of their synthesisvia self assembly and their structural diversity. However,development of particular technological applicationsbased on metal–organic materials requires fundamental *Author for correspondence. e-mail: snurr@northwestern.edu M OLECULAR  P HYSICS , 20 J ANUARY  2004, V OL.  102, N O.  4, 211–221 Molecular Physics  ISSN 0026–8976 print/ISSN 1362–3028 online  # 2004 Taylor & Francis Ltdhttp://www.tandf.co.uk/journalsDOI: 10.1080/00268970410001654854  understanding of their properties on a microscopic level.Molecular modelling can be a powerful complement toexperiment in obtaining this molecular-level under-standing. Adsorption and permeation characteristics of small molecules in novel metal–organic structures can beexplored and understood via molecular simulations. Inaddition this approach can be extended to hypotheticalstructures, not yet prepared in experiments, to screen theselection of cavities for binding of desired molecules.The overall goal of this strategy is to develop a generalapproach to  rational design  of novel adsorption andseparation materials with tailored functional character-istics. As a first step, we explore adsorption anddiffusion of small hydrocarbons in two interestingnanoporous metal–organic materials in this work.The materials of interest here are crystalline bipyr-idine molecular squares, shown in figure 1( a ) andfigure 1( b ), amorphous random packings of bipyridine Figure 1. Structures of various metal–organic porous materials. ( a ) Bipyridine molecular squares, showing a single square (top)and the crystal packing (bottom) from two directions [4]. The size of a single square measured as the distance between the twonearest rhenium atoms located in the corners of a square is 11.4A ˚. ( b ) Schematic depiction of bipyridine molecular squares,where the structure is represented by links between rhenium corner atoms. ( c ) A sample of random packing of bipyridinemolecular squares of 30A ˚  30A ˚  30A ˚. (D) IRMOF-1 [7]. Each cubic cavity has a side of 12.42A ˚in length, measured as thedistance between two zinc–oxygen clusters located in the vertices of the framework. 212 L. Sarkisov  et al.  molecular squares (figure 1( c )) and IRMOF-1, shownin figure 1( d  ). A single bipyridine molecular squareconsists of four  cis -ligated Re(CO) 3 Cl corners, linked bybipyridine edges. Owing to its crystallinity, its nano-porosity and the neutrality of the squares (which meansthey are not blocked by counter-ions as in some metal– organic structures), this material is a promising candi-date for adsorption and separation applications. Twocrystal structures of bipyridine molecular squares havebeen observed, one of them involving a planarconformation of the square (not shown) and the other,more stable one, involving a distorted, or puckeredconformation [2, 4]. In the crystal, puckered bipyridinemolecular squares stack on top of each other, withtheir cavities aligned, forming channels of about 4.58A ˚in diameter, measured as a hard sphere inscribed inthe channel. These channels run in the  z -direction of figures 1( a ) and 1( b ), through the centres of the squares.Parallel to these channels, another set of highlycorrugated pores is formed in the gap  between  fourneighbour squares, as shown in figure 1( a ), with thewidest parts being about 4.1A ˚in diameter and about10.5A ˚in length, separated by very narrow windows of only 1.9A ˚in diameter. We chose bipyridine molecularsquares for a case study to explore the relationshipbetween the crystal structure of metal–organic materialsand their adsorption and diffusion characteristics.Specifically, we hypothesized that the one-dimensionalnature of the pore space in bipyridine molecular squarecrystals should result in high affinity of these materialstoward chain molecules. On the other hand, we werealso interested in understanding the high affinity of these materials toward aromatic compounds observedexperimentally [11]. Many of the specific features of adsorption and diffusion behaviour in this material areexpected to be a direct result of the extreme confine-ment experienced by molecules adsorbed in the narrowone-dimensional pores. In addition, we contrast ourinvestigations on crystalline molecular squares withsimilar investigations in IRMOF-1 materials, shown infigure 1( d  ). IRMOF materials consist of zinc–oxygenclusters linked by molecular struts (such as 1,4-benzenedicarboxylate in IRMOF-1), forming a regular,three-dimensional lattice of cubic cavities. The size of these cavities can be tuned by selecting appropriatestruts [7]. The material formed in this fashion has avery open structure. For example, IRMOF-1 has acrystal density of only 0.59gcm  3 , and about 81% of the structure is free volume (from computer simulationsof the helium porosity [14]). The paddle wheel orienta-tion of the organic edges leads to two alternating cagestructures of about 10.9A ˚and 14.3A ˚in diameter [14].As an example of possible amorphous structures, amodel amorphous morphology was prepared by randompacking of puckered bipyridine molecular squares(figure 1( c )). Random packing of molecular squaresleads to fairly loose structures with low density of 0.795gcm  3 , high free volume of 67.3% and fairlybroad pore distributions with the largest pore being s 13A ˚in diameter [14]. For comparison, crystallinebipyridine molecular squares have 1.755gcm  3 crystaldensity and only 24% free volume. 2. Molecular models In our simulations, the porous materials are modelledas rigid structures. For crystalline bipyridine molecularsquares we considered a system of 64 squares in periodicboundaries. The dimensions of the simulation box were45.434A ˚  45.434A ˚  54.152A ˚. Amorphous packing of bipyridine molecular squares was represented by 56squares randomly placed in a fairly large simulation boxof 60A ˚  60A ˚  60A ˚in periodic boundaries. Randompacking of bipyridine molecular squares was imple-mented via a standard grand canonical Monte Carlo(GCMC) scheme. In this scheme we considered a   VT  ensemble of rigid puckered bipyridine square molecules.The system was placed at arbitrary high constantchemical potential (  ) and arbitrary low, within reason-able limits, temperature ( T  ) to achieve the highestpossible densities of the random packings. Uponequilibration, the structure was quenched and thenused as a porous matrix in further adsorption simula-tions. The structures prepared in this fashion are boundto have some variation in properties owing to the limitedsample size. One way to overcome this problem is toconsider properties (such as adsorption isotherms)averaged over several realizations of the porousstructure. Another way, implemented in this work, isto consider a sufficiently large system. Although somevariations may still persist, the system should capturethe essential features associated with the disorderedmodel morphology. For IRMOF-1 we considered acrystal with dimensions of 51.664A ˚  51.664A ˚  51.664A ˚placed in periodic boundaries. This crystalsample contained 64 cubic cavities.Van der Waals interactions between adsorbents andguest molecules were modelled with a Lennard-Jones12-6 potential between all pairs of sites (atoms or unitedatoms). For the atoms of the molecular squares andIRMOF-1 we used Lennard-Jones parameters from theDREIDING force field [15]. This is a fairly simple forcefield developed to handle a wide range of small organicmolecules, including organometallic systems. The smallnumber of adjustable parameters in this force fieldmakes it easy to extend the force field to more complexsystems with unknown conformational behaviour, and italso creates a friendly platform for further parameteroptimization if desired. These aspects of the force field Molecular modelling of adsorption  213  are important as we plan to extend our studies to flexibleporous materials with incorporated bond stretching,bending, torsional and other degrees of freedom.Methane was modelled using the united atom modelof Goodbody  et al  . [16], applied quite commonly inmethane adsorption studies. We employed the TraPPEforce field [17] to describe normal flexible alkanes, suchas pentane, hexane and heptane. This force field utilizesa united atom representation of CH, CH 2  and CH 3 groups. The bond lengths between the groups are fixed,and flexibility of an alkane molecule is allowed via bondangle and torsional degrees of freedom.For cyclohexane we adopted a six-centre, rigid, unitedatom representation of cyclohexane with Lennard-Jonesparameters for the CH 2  groups coming from theTraPPE force field [17]. We considered only the chairconformation of cyclohexane, since this conformation isdominant in the bulk vapour phase (99.9% to 99.3%depending on the temperature) and in the adsorbedphase of the zeolite silicalite [18], which has pores of comparable size to the structures of interest.Benzene was represented with the rigid, all-atommodel of Shi and Bartell [19]. In addition to Lennard-Jones sites on carbons and hydrogens, the modelincludes Coulombic contributions, coming from partialcharges of   þ 0.15 and  0.15 placed on aromatic hydro-gens and carbons, respectively. As shown by Shi andBartell, it is possible to reparameterize the combinedLennard-Jones plus Coulombic 12-6-1 potential into amore computationally efficient 12-6-2-0 potential forbenzene–benzene interactions. To incorporate electro-static interaction between benzene molecules and themolecular squares, we considered explicit partial chargesof   þ 0.15 and  0.15 placed on hydrogens and carbons,respectively. The Mulliken partial charges for anindividual puckered molecular square were calculatedusing the GAUSSIAN98 software [20] with the B3LYPdensity functional method [21] and the LANL2DZeffective core potential basis set [22]. The calculatedpartial charges are summarized in the supplementarymaterial (SUP 16151). Calculation of the partial chargesfor a significant sample of the crystal structure inperiodic boundaries is computationally cumbersome.Although the partial charges in this work werecalculated for an isolated molecule of bipyridine square,our preliminary analysis shows that the crystal packinghas little impact on the values of partial charges forbipyridine molecular squares. Finally, issues associatedwith possible charge transfer effects must be considered.We have estimated partial charge distributions for amolecule of benzene passing through a single bipyridinemolecular square using density functional theory.This calculation did not reveal any significant polariza-tion or charge fluctuation effects, and thus the srcinalset of charges can be considered as static in furtheratomistic calculations. Calculation of the electrostaticinteractions between benzene and the molecular squareswas implemented via the standard Ewald summationapproach [23]. Electrostatic interactions were pre-calculated by using a ( þ 1) charged probe on a three-dimensional grid with 0.2A ˚spacing for a simulationbox in periodic boundaries. During the simulation,the energy of interaction was then calculated using athree-dimensional Hermite polynomial interpolationalgorithm [24]. Van der Waals interactions betweenbenzene atoms and the molecular squares were modelledvia a Lennard-Jones potential with values of   "  and    recovered from the 12-6 terms of the 12-6-2-0 model of Shi and Bartell [19].For calculation of cross-species Lennard-Jones para-meters, we used the standard Lorenz–Berthelot mixingrules, with geometric averaging for the "  parameter andarithmetic averaging for the     parameter. In the caseof methane adsorption and diffusion, we also consideredthe geometric mixing rule for    , as recommendedby DREIDING, and found little difference with theother calculations. Lennard-Jones potentials were trun-cated at 12.8A ˚for all calculations. A summary of allLennard-Jones parameters is given in table 1. 3. Computational methods Adsorption isotherms of rigid species were calculatedvia the energy biased GCMC method as developed bySnurr  et al  . [25]. In this method, translation and rotationof molecules are handled as in the conventional GCMC Table 1. Summary of Lennard-Jones parameters.Group or atom type     (A ˚)  " / k B  (K)H (IRMOF, square) [15] 2.85 7.65O (IRMOF, square) [15] 3.03 48.19C (IRMOF, square) [15] 3.47 47.86Zn (IRMOF) [15] 4.04 27.70Cl (square) [15] 3.52 142.57Re (square) a [15] 4.04 27.70CH 4  [16] 3.73 148.00CH 3  (alkanes) [17] 3.77 98.10CH 2  (alkanes) [17] 3.93 47.00H (benzene) b [19] 2.42 15.16C (benzene) b [19] 3.55 35.36 a Rhenium parameters are not given by the standardDREIDING force field and are assumed to be equal to theparameters of other metals in the force field (Fe, Zn, Ru). Wealso performed calculations with Re atoms excluded from theinteraction and found little dependence of the results on theinclusion of rhenium atoms. b These parameters of aromatic atoms were used only tocalculate cross Lennard-Jones terms for benzene–sorbentinteractions. For benzene–benzene interactions the srcinal12-6-2-0 potential of Shi and Bartell [19] was employed. 214 L. Sarkisov  et al.  scheme. For insertions and deletions, the simulationbox is discretized into small cubic cells, each of which isassigned a weighting factor  i  , such that P i   i  ¼ 1. Theninsertions are performed by choosing a cell according tothe weighting factor  i   and placing a molecule withrandom position and orientation within the chosen cell.This move is accepted with a probability scaled by 1/  i  .Consequently, to ensure microscopic reversibility, thedeletion acceptance probability must be scaled by  i  . Alladsorption isotherms were calculated at 300K. For eachpressure point, the system was allowed to equilibrate for5  10 5 moves, where each move consisted of an attemptto insert, delete, translate or rotate a rigid molecule. Thesystem properties were then sampled for another 5  10 5 moves. Longer runs have demonstrated that the chosensimulation length of 1  10 6 total moves is sufficient torecover equilibrium properties of the system.To calculate adsorption of flexible normal alkanes,the energy biased method was combined with theconfiguration bias grand canonical Monte Carlo(CB-GCMC) technique in the fashion described byMacedonia and Maginn [26]. In this approach, to inserta chain molecule we begin with placing the first atom (ora united atom group) of a chain molecule using theenergy biased GCMC scheme. A complete chain is thengrown via a set of sampling schemes as prescribed by theCB-GCMC method. For a molecule deletion, the samecombination of sampling schemes is used to compute theprobability of an attempt to delete a chain molecule.In this procedure, we essentially‘regrow’ the chain inits current configuration and a biased probability of an attempt to delete a molecule is then calculated.In addition to biased insertion and deletion moves,adsorbed phase configurations are sampled by config-uration biased‘cut and regrow’ moves. In this type of move a chain molecule is randomly selected and aportion of this molecule is cut off. The missing fragmentof the molecule is then regrown following the samplingschemes of the CB-GCMC algorithm. The final type of move included is rigid translation of molecules. Thesimulations were usually 5  10 6 moves long, with eachmove consisting of an attempt to insert, delete, translate,or cut and regrow a molecule. Half of the total numberof moves was used for equilibration and the latter half for sampling system properties.Transport properties of various adsorbates wereexploredusingconstanttemperaturemoleculardynamics(MD) simulations. The constant temperature conditionwas implemented via the Nose ´ –Hoover thermostat [27],based on the extended Hamiltonian approach. TheNose ´ –Hoover equations of motion were integrated overtime using Gear’s six-value, five-parameter predictor-corrector method [28]. For bond-length constraintsin flexible normal alkanes and to maintain rigidity of cyclohexane, we employed the method of Edberg  et al  .[29], based on Gauss’s principle of least constraint.Planarity of benzene molecules during moleculardynamics calculations was maintained via the Ciccottialgorithm [30], reformulated in terms of the constraintscheme of Edberg  et al  . [29]. In all cases, moleculardynamics simulations were performed with a 0.5 fstime step and a total run length of 2.5ns. The conser-vation of the total Hamiltonian was monitored andno effect coming from the potential truncation wasobserved. Self-diffusivity coefficients were calculatedusing the Einstein relationship. Diffusivities in micro-porous materials can be strong functions of the adsorbedspecies loading. In this article all transport calculationshave been carried out at low loadings, not exceeding0.25 molecules per molecular square or 1.25 moleculesper cage of IRMOF-1. 4. Results 4.1.  Adsorption Calculated adsorption isotherms for C 5  to C 7  normalalkanes at 300K in crystalline bipyridine molecularsquares are shown in figure 2. Analysis of the hexaneadsorption isotherm reveals several effects. First, thereare two knees in the adsorption isotherm. The first kneestarting its rise from around 10  6 kPa corresponds tohexane molecules filling the intra-square channels, andthe second knee forming around 0.01kPa correspondsto hexane adsorbing in the space between the molecularsquares. An important feature of this process is theapparent independence of the two stages. The widerinterior channels reach saturation first, and only thendo the narrower channels start to take up hexanemolecules. Adsorption of pentane and heptane is Figure 2. Adsorption isotherms at 300K for normal alkanesin bipyridine molecular squares: pentane ( h ); hexane (  );heptane ( i ). Isotherms recalculated to include inaccessi-bility of the exterior set of channels are shown in solidblack lines. Molecular modelling of adsorption  215
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