BCR2

Chapter 4Molecular Computations of Adsorptionin Nanoporous Materials

Ravichandar Babarao and Jianwen Jiang

Abstract Adsorption lies at the heart of many industrially important applicationssuch as purification, separation, ion exchange, and catalysis. As the number ofnanoporous materials synthesized to date is extremely large, rationally choosinga high-performance material from discovery to specific application is a substan-tial challenge. Computational approaches at the molecular scale can provide micro-scopic insight into adsorption behavior from the bottom-up, complement and securecorrect interpretation of experimental results, and are imperative to new materialdesign and advanced technological innovation. We review the recent computationalstudies of adsorption in nanoporous materials with a wide variety of building blocksand physical topologies, ranging from zeolites, carbonaceous materials to hybridframeworks.

4.1 Introduction

Nanoporous materials play a pivotal role in many engineering processes and indus-trial applications, for instance, the separation of impurities from natural gas toimprove energy efficiency, the catalytic cracking of hydrocarbons, and the removalof toxic heavy metals from wastewater [1]. An overwhelmingly large number ofporous materials have been and are being synthesized and characterized in the labo-ratory; consequently, theoretical guidelines are highly desired to properly choosea material for specific use. Due to the spatial confinement and surface interac-tions, fluids in nanodomain behave significantly different from bulk phases. A clearmechanistic understanding of fluid behavior in nanoporous materials is not onlyof fundamental interest but also of central importance for practical use. In the past,analytical approaches like density-functional theory (DFT) based on the advances in

J. Jiang (B)Department of Chemical and Biomolecular Engineering, National University of Singapore,Singapore 117576, Singaporee-mail: [email protected]

69L.J. Dunne, G. Manos (eds.), Adsorption and Phase Behaviour in Nanochannelsand Nanotubes, DOI 10.1007/978-90-481-2481-7_4,C© Springer Science+Business Media B.V. 2010

70 R. Babarao and J. Jiang

statistical mechanics have been developed to examine the equilibrium properties offluids in simple slit-like and cylindrical pores [2–4]. With an appropriate weightingfunction, DFT can accurately predict the density profiles, isotherms, configurations,layerings, etc. [5–7]. However, the extension of DFT to three-dimensional complexgeometries is formidable. With ever-growing computational power, the state-of-the-art molecular simulation has increasingly become a versatile tool to investigate theunderlying properties of fluids confined in porous materials [8]. Simulation providesmicroscopic insight from the bottom-up that is otherwise experimentally inaccessi-ble or difficult, if not impossible. In addition, simulation can be used to comple-ment and secure fundamental interpretation of experimental results and establishthe structure–function relations based on molecular description. Therefore, molecu-lar simulation is indispensable in the rational design of novel materials of increasingcomplexity for new applications.

In this chapter, we review the recent simulation studies of adsorption in zeo-lites, carbonaceous structures, and hybrid organic–inorganic frameworks. They rep-resent three classes of fascinating nanoporous materials that are being widely usedin chemical industries and/or exhibit unique properties for emerging applications.Experimental studies of adsorption in these materials have been comprehensivelyaddressed; however, simulation studies are relatively less. Due to page limitation,the technical details of simulation principles are not described here, which are welldocumented elsewhere [9, 10]. Nevertheless, the commonly used simulation meth-ods for adsorption in porous media are briefly introduced below.

Stochastic Monte Carlo (MC) instead of deterministic molecular dynamics (MD)method is most frequently used for adsorption studies [11]. The reason is thatMD is not straightforward to simulate adsorption isotherm as a function of bulkpressure, which is considered as one of the most important adsorption propertiesbecause isotherm can be readily determined from experiment. MD motion mim-ics the natural behavior of molecules through Newton’s equation of motion, that is,molecules diffuse into a porous material before adsorption equilibrium is reached.This is a slow process particularly for large molecules, such as alkanes and aro-matics. In contrast, MC does not need to follow the natural pathway and thusallows random trial move so that a successful move may correspond to a largejump in phase space, thereby reaching equilibrium rapidly. Most MC simulationstudies of adsorption are carried out in canonical or grand-canonical ensemble. Incanonical ensemble, temperature, volume, and number of adsorbate molecules arefixed. MC simulation in canonical ensemble is usually used to simulate the distri-bution and energetics of adsorption sites, isosteric heat, and Henry’s constant. Ingrand-canonical ensemble, temperature, volume, and chemical potential of adsor-bate are fixed. Grand-canonical Monte Carlo (GCMC) simulation permits adsorbatemolecules to exchange between adsorbed phase and bulk fluid reservoir, and canprovide adsorption isotherm easily. To compare GCMC results with experimentaldata, the chemical potential has to be converted into pressure using an equationof state or additional simulation. Widely used to simulate phase equilibria, Gibbsensemble Monte Carlo (GEMC) method [12] has recently been used to simulateadsorption at a given pressure. GEMC is performed in two microscopic cells, one

4 Molecular Computations of Adsorption in Nanoporous Materials 71

cell with the adsorbent and the other with the bulk fluid. At a given pressure, thevolume of the bulk fluid is allowed to change. The total number of molecules isfixed, but molecules can be transferred from one cell to the other. In the studiesreviewed here, these simulation techniques have been used to elucidate adsorptionphenomena at the molecular level in zeolites, carbonaceous materials, and hybridframeworks.

4.2 Zeolites

Zeolites are three-dimensional crystalline aluminosilicate materials [13, 14]. Theprimary building blocks in zeolites are tetrahedral oxides SiO4 and AlO4 that con-nect together via corner-sharing oxygen atoms to form well-defined open pores. Thepores are precisely uniform, which distinguishes zeolites from many other porousmaterials. Figure 4.1 shows three typical structures: MFI, FAU, and LTA. Some zeo-lites are not stable upon removing nonframework species, and the stability varieswith topology and composition. Zeolites have been extensively used in industrialapplications such as molecular sieving, catalysis, and ion exchange. Progress till2001 in the computation of thermodynamic properties of guest molecules in zeo-lites was reviewed [15].

(a) (b) (c)

Fig. 4.1 Zeolites: (a) MFI, (b) FAU, and (c) LTA. Color code: red, O; yellow, Si; pink, Al

4.2.1 Light Gases

N2, O2, and Ar in zeolites LTA, X-, and Y-FAU were studied using GCMC simu-lation; the predicted N2/O2 selectivity in LTA was in accordance with experiment[16]. With the appropriate force field parameters, experimentally determined isos-teric heats of NH3 adsorption in MOR, MFI, and Y-FAU were reproduced by sim-ulation [17]. Adsorption of CH4 and CF4 in silicalite was measured and simulatedas a function of phase composition, total pressure, and temperature; the simulatedisotherms and isosteric heats were in good agreement with experiments [18]. A hier-archical modeling approach combining atomistic and coarse-grained simulations


was proposed to predict adsorption thermodynamics of single components andbinary mixtures in silicalite. The results agreed well with full atomistic simula-tion, but the hierarchical approach saved an order of magnitude of computationaleffort [19]. Long-range corrections were evaluated for simulation of CH4 and SF6in silicalite at 298 K. A consistent use of cutoff radius was shown to be more impor-tant than the inclusion or the neglect of long-range corrections to potential energy[20]. Nonpolar (Ar and CH4) and quadrupolar gases (N2 and CO2) in pure siliceousFAU were investigated both experimentally and theoretically at ambient tempera-ture and high pressures [21]. A systematic simulation study was reported for H2in 12 purely siliceous zeolites, in which the cell parameters and framework flexi-bility were allowed to vary upon progressive filling of gas molecules, and then themaximum H2 adsorption capacity in each framework was examined [22]. CO2 andN2 both as single component and as binary mixture were studied in MFI, ITQ-3,and ITQ-7. The CO2/N2 selectivity varies strongly with the crystal structure. Sim-ulated binary adsorption agrees well with prediction by the ideal adsorbed solutiontheory (IAST) based on single-component adsorption [23]. Thermodynamics andsiting of CO2, CH4, and their mixtures were studied in ITQ-1 which consists oftwo independent pores of different geometry. At the three temperatures considered,a preferential adsorption of CO2 over CH4 was found. The equilibrium selectivitywas distinctly higher in its sinusoidal channel pore system than in the large cav-ity system over a wide range of pressures starting from the Henry law regime. Amaximum in selectivity was observed at low temperature, high pressure, and CH4-rich gas-phase composition [24]. H2O adsorption in X- and Y-FAU as well as insilicalite was computed. The isotherms and heats of adsorption were in good agree-ment with available experiments. The existence of cyclic H2O hexamers located inthe 12-ring windows of NaX, recently disclosed by neutron diffraction experiments,was observed [25]. A joint experimental and simulation study of H2O adsorptionin silicalite was reported. The simulation qualitatively reproduced experimentallyobserved condensation thermodynamic features. A shift and a rounding in the con-densation transition were found with an increasing hydrophilicity of the local defect,but the condensation transition was observed above the saturation pressure of H2O[26]. Simulation of H2O in MFI by reducing the dipole moment of H2O matchedwell with the experimental isotherm at 300 K. The work suggests that the effectiveintermolecular potential parameterized for bulk water is insufficient to describe theultraconfined water molecules [27].

4.2.2 Alkanes and Alkenes

With the development of configurational-bias Monte Carlo (CBMC) algorithm[28–30], adsorption of alkanes has been studied efficiently. Instead of inserting amolecule at a random position, a molecule in CBMC is grown atom-by-atom bias-ing toward the energetically favorable configurations while avoiding overlap withother atoms, and the bias is then removed by adjusting the acceptance rules [10].Using the united-atom (UA) model for alkanes, Smit et al. observed an inflection


in the adsorption isotherms of n-hexane and n-heptane in MFI, but not of shorteror longer alkanes. This inflection was attributed to the “commensurate freezing”effect as the size of the zigzag channel in MFI is commensurate with the size ofn-hexane and n-heptane [31, 32]. Apart from MFI, alkanes were also simulated inother zeolites such as FER, MTW, TON, and DON using the same force field as forMFI and good agreement with experiments was found [33]. Linear alkanes rang-ing in length from C2 to C7 in AlPO4-11 were examined and the isosteric heatsat infinite dilution matched well with experimental data [34]. The UA model wasalso used to study adsorption of alkenes and their mixtures in silicalite-1, theta-1,and deca-dodecasil. For C3H6/C3H8 mixture in Na-LTA, adsorption isotherm fromsimulation agrees well with experimentally measured results in cation-free LTA,but not in Na+-exchanged LTA [35, 36]. The anisotropic united-atom (AUA) poten-tial for hydrocarbons was adopted to calculate the adsorption isotherms of linearand branched alkanes in MFI; good agreement was observed with experiments andother simulation results [37]. Also, with the AUA potential, adsorption isotherms ofpure alkenes and alkane/alkene mixtures in MFI were found to be closely consis-tent with experimental results [38]. Adsorption of n-pentane and n-hexane in FERshowed that the prediction of UA potential is inconsistent with experiment, whereasthe AUA potential can reproduce the subtle change in adsorption site occupanciesof n-alkanes (n = 3−7) [39]. Simulation isotherms of cycloalkanes like cyclopen-tane, -hexane, and -heptane in MFI reproduced most features in experiments andrevealed an inflection for cyclopentane but not for cyclohexane [40]. Comparingmeasured and simulated adsorption properties, a decrease in the Gibbs free energyof formation and adsorption was observed. Based on this observation, the selectiveproduction and adsorption of the most compact, branched paraffins in n-hexadecanehydroconversion in molecular sieves with pore diameters of ~0. 75 nm was satisfac-torily elucidated [41]. Krishna et al. screened different zeolites for the separation ofCH4/CO2 mixture and of hexane isomers. The linear n-hexane has a longer “foot-print” and occupies a longer segment in the zeolite channel; 2,2-dimethylbutane isthe most compact isomer and has the smallest “footprint.” Consequently, a greaternumber of 2,2-dimethylbutane molecules were observed to be located within theMOR channels, in which the length entropy effect dictates [42, 43].

4.2.3 Aromatics

Adsorption of aromatic molecules that fit tightly into zeolite frameworks has beeninvestigated by simulations. Different guest–host force fields including all-atom,UA, and AUA models were used to simulate the adsorption of benzene, xylene,and cyclohexane. The force field considerably affects the locations of benzene andcyclohexane. This suggests that care should be taken in choosing the force field, par-ticularly when the guest–host ratio is near the value defined for the levitation effect[44]. Benzene adsorption in different ORTHO silicalite structures was analyzed todetermine the origin of a surprising factor of 3.1 difference in Henry’s constants.The results indicate that a slight change in the lattice oxygen atom positions can


reposition the sorbates enough to sizably affect the electrostatics. The small shiftsare magnified by the partial cancellation of large electrostatic terms on the hydrogenand carbon atoms [45]. Binary adsorption was simulated in silicate for benzene/CH4and benzene/cyclohexane mixtures. Benzene and cyclohexane display preferred sit-ing in the channel intersections, while CH4 adsorbs preferentially in the channels. Inbenzene/cyclohexane mixture, cyclohexane adsorbs in the intersections and benzeneis pushed to the zigzag channels [46]. Adsorption in silicalite from binary mixturesof p-xylene, m-xylene, and toluene was investigated using simulation. Experimentalisotherms can be well reproduced if MFI is modeled in the para form, but not inthe native ortho form. This reveals that zeolite structure undergoes a transition fromortho to para in the presence of aromatic molecules [47]. Using a nine-site modelfor benzene, adsorption isotherms of benzene, propene, and their mixture in zeo-lites MOR, FAU, BEA, MFI, and MCM-22 were computed and in excellent accor-dance with measured results [48]. Benzene and benzene/thiophene mixtures werestudied in FAU, MFI, MOR, and Na-FAU using energy-biased GCMC, and the cal-culated isotherms and heats in Na-FAU were consistent with experiments [49, 50].Adsorption properties of xylenes in X- and Y-FAU were reproduced by simulationusing a potential derived from Pellenq and Nicholson scheme. m-Xylene was foundto be adsorbed preferentially and the p-xylene/m-xylene selectivity predicted fromsimulation was in good agreement with experiment [51–53]. Preferential adsorp-tion of o-xylene over p-xylene in AlPO4-11 was predicted by simulations, agreeingwith experimental data. The selective adsorption comes from the smaller length ofo-xylene along the crystallographic c-axis in AlPO4-11 compared to p-xylene, dif-ferent from the case in AlPO4-5 and AlPO4-8 [54].

4.2.4 Cation-Exchanged Zeolites

A large number of simulation studies have been reported for adsorption in cation-exchanged zeolites. Isotherms of H2 adsorption in Na-, Ni-, and Rh-exchanged X-FAU were calculated at different temperatures and compared with measured data[55]. Adsorption of alkanes in two different Na-MOR zeolites from simulation wasfound to agree with experiment with the adequate inclusion of cations and realisticcharges in Al atoms [56]. CH4, C2H6, and C3H8 in Na-exchanged MFI and MORwere simulated. The predicted positions of nonframework Na+ cations are in agree-ment with those determined by X-ray diffraction and so are the computed isothermsand Henry’s constants. Adsorption of alkanes is largely influenced by the positionand the density of nonframework ions [57]. For a given type of cation, adsorptionof alkanes in ZSM-5 was found to increase with decreasing density of the non-framework cations; for a given Si/Al ratio, adsorption increases with decreasingatomic weight of the cation [58]. Isotherm and enthalpy of N2 adsorption in X-FAUwere simulated at ambient temperature, and qualitative agreement was observedwith experiments for a series of monovalent and divalent cations [59]. Adsorptionof CH4 in X- and Y-FAU was investigated using a newly derived force field in whichthe Lennard-Jones parameters between CH4 and FAU were obtained by fitting the


potential energies from ab initio cluster calculations. The calculated isotherms andenthalpies were in good agreement with those experimentally obtained [60]. Redis-tribution of nonframework cations was observed to occur upon adsorption of waterand aromatics in NaY, and in turn the selectivity of p-xylene over m-xylene wasenhanced by a fact of 4 [61].

Single- and binary-component adsorption of CO2, N2, and H2 in dehydratedNa-4A was examined, and the strong selectivity for CO2 over both N2 and H2was observed and also compared with that in MFI [62]. Supercritical CO2 adsorp-tion in NaA and NaX was studied using GEMC, and the adsorption isotherms andenthalpies were discussed in detail and compared with available measured data [63].Combining experimental and simulation techniques, adsorption of N2, O2, and Arin Mn-exchanged zeolite-A and -X was studied. It was observed that the selectivityof O2 over Ar was higher in both zeolite-A and -X [64]. Ar, N2, and O2 in Na-and Ca-exchanged LTA were studied both experimentally and theoretically. Thepredicted isotherms match well with measured data and the extent of adsorptionincreases with increasing Ca ions in LTA [65]. Selectivity of CO2 over N2 in fluegas was found to rise remarkably in Na-ZSM-5, particularly at low pressures. Thisis because CO2 has a large quadrupolar moment and its adsorption is enhanced dueto the electric field of cations [66]. Adsorption and enthalpy of CO2 in various typesof FAU including purely siliceous DAY, NaY, and NaLSX were simulated. Typicalarrangements of CO2 molecules were identified from low to high pressures [67].Figure 4.2 shows that Na+ ions interact with a few CO2 molecules at a low pressure.With increasing pressure, Na+ ions are more and more solvated by the surround-ing CO2 molecules. Consequently, CO2/NaY interaction slightly decreases due tothe solvation process, whereas CO2/CO2 interaction increases. The combination ofthese two contributions leads to a relatively constant value of adsorption enthalpy aspressure rises [67]. CO2 adsorption was further simulated in LiY and NaY at vari-ous temperatures with Li+–CO2 interaction derived from ab initio calculations. Theresults revealed two different types of adsorption behavior in NaY and LiY at 323and 373 K, respectively [68].

Table 4.1 summarizes the simulation studies of adsorption for a wide variety ofguest molecules in different zeolites.

Fig. 4.2 Typical arrangements of CO2 molecules in NaY at (a) 0.1 bar, (b) 1 bar, and (c) 25 bar.Na+ cations are represented in green, and the typical distances of Na–Oz and O–Oz are in Å.Reproduced with permission from [67]. Copyright (2005) American Chemical Society


Table 4.1 Simulation studies of adsorption in zeolites

Guests MFI X-FAU Y-FAU Other zeolitesComputedquantities

Rare gases [69–76] [16, 77, 78] [16, 78–80] [81–89] P, I, Q, K, SN2 [74, 90] [16, 78,

91–93][16, 78] [16, 77] P, I, Q, K, S

O2 [90] [16, 78,91–93]

[16, 78] P, I, Q, K, S

CO [92] P, I, Q, K, SCO2 [94] [78] [78] P, I, Q, K, SSF6 [76] P, I, Q, K, SNH3 [17] [17] [17] Q, SH2O [26, 95] [96] [96, 97] P, I, Q, K, SMethane [31, 70, 76, 90,

98–101][80] [76, 81, 83, 84,

86, 88, 98,102–104]

P, I, Q, K, S

Ethane [31, 32, 105,106]

[103] P, I, Q, K, S

Propane [31, 32, 105] [103, 107, 108] P, I, Q, K, Sn-Butane [32, 105,

109–113][87, 109, 110] [87, 103,

107–110]P, I, Q, K, S

i-Butane [111, 114, 115] P, I, Q, K, Sn-pentane [105, 109, 110,

116][109, 110] [103, 107–110] P, I, Q, K, S

n-Hexane [32, 105, 109,110, 114, 116]

[87, 109, 110] [87, 107–110,114]

P, I, Q, K, S

Cyclohexane [117] P, I, Q, K, Sn-Heptane [32, 105,

109–111, 114,116]

[87, 109, 110] [87, 107–110,114]

P, I, Q, K, S

n-Octane [109, 110, 118] [109, 110,118]

[109, 110, 118] P, I, Q, K, S

n-Nonane [109, 110, 118] [109, 110,118]

[109, 110, 118] P, I, Q, K, S

n-Decane [109–112, 118] [109, 110,118]

[109, 110, 118] P, I, Q, K, S

Ethane/butane [106] [119] P, I, SCF4 [76] [120] [76] P, I, Q, SCF3Cl [120] P, Q, SCF2Cl2 [120, 121] P, Q, SCFCl3 [120] P, Q, SCHF3 [120] P, Q, SCHCl3 [122] [122, 123] P, Q, SIsopropylamine [17] [17] [17] Q, SAcetonitrile [124] P, SBenzene [45, 125, 126] [122, 127] [127, 128] P, I, Q, K, So-Xylene [54, 128] P, Sm-Xylene [53] [51, 52, 80,

128, 129]P, I, Q, S

p-Xylene [125] [53] [51, 52, 80,128, 129]

[54] P, I, Q, S


Table 4.1 (continued)

Guests MFI X-FAU Y-FAU Other zeolitesComputedquantities

Other alkylbenzenes P, I, Q, K, Sm-Dinitrobenzene [130] P, SPhenol [126] P, I, Q, K, SPyridine [17] [17] [17] Q, S

P : interaction energy, I: adsorption isotherm, Q: heat of adsorption, K: Henry’s constant, S: struc-ture of adsorbed phase.

4.3 Carbonaceous Materials

Carbon atoms can possess different extents of aromatic sp2 or aliphatic sp3

hybridization and have different bonding and ring structures. As a consequence,there are several stable carbon forms ranging from naturally occurring bulk struc-tures such as graphite, diamond, activated carbons [131] to discrete structures suchas fullerenes and nanotubes [132]. Among these, activated carbons and nanotubeshave been extensively studied as adsorbents for gas purification and separation.

4.3.1 Activated Carbons

Activated carbon is a synthetic carbonaceous material, constructed by thermaldecomposition and activation at elevated temperature. Activated carbon consistsof elementary graphitic crystallites and amorphous structures. In many theoreticalstudies, the simplified carbon slit-like pores have been used to mimic activated car-bons. Simulation of pure and mixed CH4 and CO2 adsorption in slit pores gaveresults close to the measured data in A35/4 activated carbon [133]. CO2/CH4/N2mixtures in slit pores showed that CO2 is preferentially adsorbed and the simula-tion results are consistent with the predictions from DFT at various temperaturesand pressures [134]. Adsorption of alkanes in slit pores was studied over a widerange of temperature, pressure, alkane chain length, and slit width to evaluate theireffects. The behavior of long alkanes at high temperatures was found to be similarto short alkanes at lower temperatures [135]. The performance of 1- and 5-site mod-els of CH4 adsorption in slit pores was evaluated. Although the two models yieldcomparable pore densities, the number of particles predicted by the 1-site modelis always greater, regardless of whether temperature is subcritical or supercritical[136]. Adsorption and desorption of H2O in a platelet model for activated carbonwere simulated. The model included the effects of structural disorder which aremissing in the slit pore model. Hysteresis observed was in good agreement withexperimental results [137]. Simulation of pentane isomers and their ternary mixturesin a series of carbon nanoslits demonstrated competitive adsorption. With decreas-ing slit width, first shape selective adsorption occurs due to the configurational


entropy effect, followed by inverse-shape selective adsorption that occurs due tothe area entropy effect, and finally no adsorption occurs [138]. Using hypotheti-cal C168 schwarzite to represent an amorphous nanoporous carbon, N2, O2, andtheir mixtures were investigated by GCMC and GEMC simulations [139, 140]. Inaddition to six-member rings, C168 schwarzite has some seven-member rings ratherthan five-member rings as in buckyball C60. The curvatures of C168 and amorphousnanoporous carbon are similar; therefore, C168 may provide a similar environmentfor adsorbates as that found in real samples. The predictions of mixture adsorptionusing IAST based solely on the adsorption of pure gases agree well with simula-tion results. The energetic effect, by itself, cannot explain the large difference in thepermeation rates of O2 and N2 observed experimentally. The entropic effect, whicharises due to the size difference, is the dominant factor for the large selectivity favor-ing O2 over N2[141].

4.3.2 Carbon Nanotubes

A carbon nanotube (CNT) can be envisaged as a cylinder rolled from a graphenesheet and exists in three types, namely armchair, zigzag, and chiral. In 1991, Iijimadiscovered the first CNT [142] and has ever since triggered extensive interest inCNTs for a variety of applications. A number of earlier simulation studies werecarried out in CNTs for the adsorption of N2, O2, CO2, Ar, Kr, Xe, CH4, etc. Theadsorption isotherms of N2[143], Xe [144], CH4, and C2H6 [145] were found to beof type I regardless of temperature, inconsistent with experimentally observed typeII at subcritical temperatures. This is because the infinite periodic CNT bundleswere used in these simulations; however, real CNT samples have finite diameters.As a result, the external surface of the finite CNT bundle was not included, whichis available for gas adsorption as evidenced experimentally by gas adsorption onclosed-ended CNTs.

A handful of simulations were carried out to examine the role of external surfaceof CNT bundle on adsorption. Gas molecules were observed to form a quasi-one-dimensional phase in the grooves at low pressures, whereas a “three-stripe” phaseparallel to the grooves at high pressures, followed by monolayer and bilayer phases.The adsorption isotherms were predicted to be type II, consistent with experiment[146–148]. This suggests that the external surface must be accounted for to correctlypredict adsorption in CNTs. The role of external surface was thoroughly explodedfor N2 adsorption in two types of single-walled CNT bundles, as shown in Fig. 4.3[149]. In the infinite periodic bundle, adsorption follows type I at both sub- andsupercritical temperatures and occurs inside CNTs, first at the annuli and then at thecenters. In the finite isolated bundle, adsorption follows type II at subcritical tem-peratures, as observed experimentally. Adsorption occurs first at the annuli and thenat the grooves. At high pressures, adsorption also occurs at the ridges surroundingCNTs and at the centers, and on the external surface at still higher pressures. Astemperature increases from sub- to supercritical, adsorption in the finite isolatedbundle changes from type II to type I [149]. Adsorption of N2 and O2 mixture was


Fig. 4.3 Energy contours of a nitrogen atom along the xy plane in (a) periodic infinite bundle and(b) isolated finite bundle. The vdW gap between CNTs is 3.2 Å. Adapted with permission from[149]. Copyright (2003) American Physical Society

further studied in the two types of CNT bundles mentioned above. The selectivitydepends strongly on temperature but only weakly on the type of the bundle, and airmight be separated by competitive adsorption in CNT bundles [150].

Simulation of CO2 trapped in CNT bundles showed a sequential filling of adsorp-tion sites in CNT with the interstitial sites preceding endohedral sites. The drasticchanges predicted from simulation in the binding energy distributions and densityprofiles qualitatively explained the frequency shifting, broadening, and integratedintensity changes in experimental infrared spectra [151]. Adsorption of an equimo-lar CO2/CH4 mixture was determined in five CNTs with various diameters to inves-tigate the effects of temperature, pressure, and pore size. The results revealed thatpressure and temperature have little effect, in contrast to the pore size [152]. CH4adsorption was examined in triangular bundles of armchair CNTs with the vdW gapvarying from 0.335 to 1.0 nm. The results demonstrated that (15,15) CNT bundlewith the vdW gap of 0.8 nm is optimal for CH4 storage at 300 K [153]. Adsorptionand separation of linear and branched alkanes in CNTs were studied at room tem-perature. The results suggested the possible separation of alkane mixtures based ondifference in either size or configuration, as a consequence of competitive adsorp-tion [154]. Shape and inverse-shape selectivity were observed for C5 isomers inCNTs and the tube size was identified to be crucial as to which type of selectiveadsorption might occur. In (7,7) CNT, inverse-shape selective adsorption occurs dueto the length entropy effect, whereas in large-size CNT, shape selective adsorptionoccurs due to the configurational entropy effect [155].

Real CNT samples consist of heterogeneous rather than homogeneous bundle.Shi and Johnson proposed an optimization method to construct a heterogeneousCNT bundle with different diameters, as illustrated in Fig. 4.4. At low coverages,simulated isosteric heats in the heterogeneous bundle were consistent with experi-mental data. In contrast, the isosteric heats in the homogeneous bundle were about25% lower. Therefore, an accurate description of adsorption in CNT bundle must


(a)(b)

Fig. 4.4 (a) A heterogeneous CNT bundle. (b) Isosteric heat for Ar. Circles and triangles areexperiments, diamonds (squares) are simulations in the heterogeneous (homogeneous) bundles.Reproduced with permission from [156]. Copyright (2003) American Physical Society

account for the heterogeneity [156]. Displacement of CO2 by Xe was simulated inthe heterogeneous bundle also. The spectral information constructed from simula-tion qualitatively reproduced experimental intensity. The good agreement betweensimulation and experiment suggested that the adsorption sites associated with theintensity peaks and changes upon Xe exposure are the consequence of CO2 beingdisplaced from the sites [157].

4.3.3 H2 Storage

High-capacity H2 storage is an essential prerequisite for the widespread deploy-ment of next-generation fuel cells, particularly in portable devices and future auto-mobiles. Considerable research has been undertaken over the past two decades todetermine H2 capacity in different carbon structures like activated carbons, car-bon nanofibers, and CNTs. Experimental studies have been reviewed recently bya few researchers [158–161]. H2 storage in primitive, gyroid, diamond, CNT, andquasi-periodic icosahedral nanoporous carbons was examined by simulation. Noneof these satisfies storage target, except the quasi-periodic icosahedral nanoporouscarbon, which could accommodate 6 wt% H2 at 3.8 MPa and 77 K but the volu-metric density does not exceed 24 kg/m3 [162]. It is clear from this work that thegeometry of carbon surface can enhance capacity only to a limited extent, and thecombination of most effective structure with appropriate additives should be incor-porated to improve capacity. H2 adsorption in CNTs was simulated at 293 K and77 K with an effective quantum potential derived from the Feynman–Hibbs pertur-bative approach [163, 164]. The capacity at 298 K predicted by quantum simulationis several percent smaller than that by classical simulation, and the quantum effectcontributes 15–20% of adsorption amount at 77 K. Carbon nanohorn (CNH) is a


tube of typically 2–6 nm in diameter and 40–50 nm long and has a conical cap atone end. H2 isotopes in CNHs were simulated at 77 K, and the adsorption, incor-porating quantum effect through the Feynman–Hibbs potential, was predicted to bein good agreement with experimental results [165]. This indicates that the quan-tum effect at 77 K is accurately represented by the Feynman–Hibbs potential. Theeffects of size, vdW gap, and CNT arrangement were investigated on H2 adsorp-tion. Interestingly, it was observed that the size of CNT has significant influenceon the amount adsorbed inside CNT and distribution in the vicinity of CNT wall,regardless of the type of CNT and vdW gap [166].

To enhance H2 storage capacity in CNTs, several approaches such as elementdoping [167], incorporating defects, spilling over [168], changing the size and gapof CNTs [166], introducing heteroatoms [169] as well as using silicon nanotubes(SiNTs) [170] were proposed. Both N and B doping in single-walled CNTs decreaseH2 adsorption energy. The effect of alkali doping on H2 adsorption was simulated byincorporating K or Li ions into CNT arrays. H2 capacity was found to be 3.95 wt%with K doping and 4.21 wt% with Li doping, in fairly good agreement with theexperimental data determined at room temperature and 100 atm [171]. There is aconsiderable increase in H2 binding energy by a factor of 50% in the presence ofstructural defects in CNTs, which in turn enhances capacity [172]. H2 adsorption inSiNTs was studied at 298 K over pressure range from 1 to 10 MPa. SiNTs exhibita stronger attraction to H2 both inside and outside the tube compared to the isodi-ameter CNTs; consequently, the capacity in SiNTs is enhanced [170]. Carbon nano-scroll (CNS) structure is formed by jelly roll-like wrapping of a graphene sheet.H2 adsorption in CNSs was found to reach 5.5 wt% at 150 K and 1 MPa. Dopingalkali in CNSs leads to H2 capacity of 3 wt% at ambient temperature and pressure[173, 174]. Recent analysis of thermodynamic constraints for H2 adsorption with afocus on porous carbon suggested that an optimal adsorption enthalpy of 15 kJ/molis required to meet H2 storage target at room temperature. The enthalpy in mostcarbon structures is about 4–6 kJ/mol, too weak to satisfy the desired goal for H2storage at ambient temperature. Structural modification of carbon revealed the com-plex relationship between adsorption enthalpy, pore volume, and the amount of H2stored. It was observed that increasing adsorption enthalpy might reduce storage aswell as delivery [175].

Numerous studies investigated the interaction of H2 with CNTs using quan-tum mechanics methods. Periodic DFT calculations of H2 chemisorption in CNTsshowed two chemisorption sites, one inside and the other outside. H2 capacity inan empty space increases linearly with CNT diameter, and the maximum capacityis limited by the repulsive energies between H2 molecules inside CNT and thosebetween H2 molecules and CNT wall [176]. Ab initio calculations in a cleaved clus-ter model revealed that boron nitride nanotubes are preferable to CNTs for H2 stor-age due to their heteropolar binding nature of their atoms. In addition, more efficientbinding energy can be achieved by increasing nanotube diameter or equivalentlydecreasing the curvature [177]. H2 physisorption inside and outside achiral CNTswas examined with the CNTs modeled as curved coronene-like (C24H12) graphenesheets. It was found that physisorption depends mainly on CNT diameter being


virtually independent of chirality [178]. Another commonly used method is thetwo-level quantum mechanics/molecular mechanics (QM/MM) approach, in whicha system is divided into two different sections; the inner section is treated by ahigh-level QM method and the outer section by MM method. With this method, H2binding to the side of a (10,0) CNT was studied, in which B3LYP hybrid functionalwas used for the accurate calculation of reaction sites, while the universal force field(UFF) was used to describe the neighboring atoms [179]. This approach was alsoapplied to a (4,4) CNT with 200 atoms by treating 64 carbon atoms and 32 hydro-gen atoms in the inner section with a high-level theory and the outer section with alow-level theory. This study was focused on H2 coverage in CNT and the intercala-tion of H2 inside CNT [180]. Recently, Froudakis reviewed the existing theoreticalliterature on H2 adsorption in CNTs, in which the importance of simulations forunderstanding H2 adsorption mechanism and for improving storage capacity wasunderlined, and the advantages and disadvantages of both statistical and quantummechanics modeling were discussed [181].

4.4 Hybrid Frameworks

Novel hybrid inorganic–organic porous materials have been recently developed,most notably, the metal–organic frameworks (MOFs) synthesized by Yaghi andcoworkers [182]. The primary building blocks in MOFs (also known as coordinationnetworks or coordination polymers) are metal-oxide clusters and organic linkers.MOFs possess extremely high porosities (up to 90%) and large surface areas (from500 to 6500 m2/g). The controllable length of organic linker and the variation ofmetal oxide allow for tailoring the functionality, pore volume, and size over a wideatomic-scale range, as shown in Fig. 4.5 [183]. In contrast to the spherical or slit-shaped pores usually observed in carbon and zeolite materials, MOFs incorporatecrystallographically well-defined pores including squared, rectangular, triangular,and window-connected cages. Therefore, MOFs provide a wealth of opportunitiesfor engineering new functional materials with tunable properties [184].

4.4.1 Light Gases

In conjunction with experiment, simulation was performed to investigate the pore-filling mechanism of Ar in Cu-BTC. The results agreed quantitatively with experi-mental isotherm up to almost complete filling of the pore network [185]. Similarly,the predicted positions and occupancies of Ar adsorption in IRMOF-1 were foundto match well with experiments [186]. Binding energies of Ar, N2, O2, CH4, C2H6,and C3H8 were computed separately. The most preferred site is near the metal-oxide cluster in the cavity where the organic linker points outward, the second pre-ferred site is where the linker points inward, and the least preferred site is aboveand beneath the linker [186]. Adsorption of nonpolar gases like CH4, N2, and O2was extensively studied in MOFs, particularly IRMOF-1. Different MOFs were


Fig. 4.5 IRMOF-n (n = 1−6) structures. Zn (blue polyhedra), O (red spheres), C (black spheres),Br (green spheres in 2), amino groups (blue spheres in 3). The large yellow spheres representthe largest vdW spheres that would fit into the cavities without touching the frameworks. Repro-duced with permission from [183]. Copyright (2002) American Association for the Advancementof Science

characterized for CH4 storage and compared with MCM-41, zeolites, and CNTs.The complex interplay of various factors that affect CH4 adsorption was uncoveredand new, not yet synthesized, MOFs were proposed [187]. Adsorption of He, Ar, H2,and CH4 was examined in various MOFs, including Cu-BTC, IRMOF-1, IRMOF-6, IRMOF-8, IRMOF-14, MOF-2, MOF-3, and Cu-MMOM, and good agreementwas observed between simulations and experiments for a number of cases and verypoor agreement in other cases [188]. Simulation was performed on CH4 adsorptionin a series of MOFs. The accessible surface area and the free volume were found toplay a major role in adsorption at 298 K and moderate pressures [189]. From simu-lated adsorption isotherms of N2, the BET surface areas of microporous MOFs werefound to agree very well with the accessible surface areas estimated in a geomet-ric fashion directly from the experimental crystal structures. In addition, the surfaceareas matched well with experimental reports in the literature. These results providea strong validation that BET theory can be used to obtain surface areas of MOFs[190].

Mixture separation of CH4 and nC4 in IRMOFs was investigated to study theinfluence of organic linkers. The predicted selectivity was as good as or better thanexperimentally observed selectivity in other adsorbents, suggesting that IRMOFsare promising for hydrocarbon separation [191]. Adsorption of a mixture of pen-tane isomers in IRMOF-1 was simulated. Each isomer exhibits increased extentof adsorption with rising pressure, though there is less adsorption of the branchedisomer due to the configurational entropy effect. Compared to CNT bundle and MFI,


the adsorption selectivity in IRMOF-1 is smaller [192]. Gas mixtures containingCO2, CH4, C2H6 in Cu-BTC were studied, and it was observed that the selectivityof CO2 over CH4 increases due to the electrostatic interaction between CO2 andthe framework [193]. Mixture adsorption of CO2 and CH4, H2 simulated in Cu-BTC and IRMOF-1 showed that the geometry, the pore size, and the electrostaticinteraction in MOFs largely affect separation efficiency [194].

4.4.2 CO2 Storage

The combustion of fossil fuels such as coal and petroleum has generated a hugeamount of greenhouse gas CO2. This has substantially led to severely adverseimpacts on environment like air pollution and global warming. One of the techni-cally feasible approaches for CO2 sequestration is to use porous media, and CO2storage in MOFs has been explored using molecular simulations. Adsorption inthree different types of materials – silicalite, C168 schwarzite, and IRMOF-1 –revealed that IRMOF-1 has the largest adsorption capacity for CO2 [195]. A dif-ferent class of MOFs, based on the assembly of presynthesized molecular buildingunits, were produced and named as MIL (Material Institut Lavoisier) series. Sim-ulation of CO2 in MIL-53 and MIL-47 confirmed that there is a structural inter-change between large and narrow pore forms of MIL-53, but not in MIL-47 [196].CO2 adsorption was simulated in IRMOF-1 at five different temperatures and inIRMOF-3 and MOF-177 at 298 K. The results matched well with experimental dataand suggested that the attractive electrostatic interactions between CO2 moleculesare responsible for inflections and steps observed in the adsorption isotherms [197].A computational study of CO2 storage was reported in MOFs with various linkers,pore sizes, and topologies. The capacity was a complex interplay of these structuralproperties, and the suitable pore size was found to be between 1.0 and 2.0 nm [198].CO2 storage in a series of MOFs was simulated systematically and compared withthose in CNT and Na-exchanged ZSM-5 [199]. Figure 4.6 (left) shows the snapshotfor CO2 adsorption in IRMOF-1 and Fig. 4.6 (right) shows the adsorption isothermsin different MOFs. The organic linkers play a critical role in tuning the free vol-ume and accessible surface area, which largely determine the CO2 adsorption athigh pressures. As a combination of the high capacity and low framework density,IRMOF-10, IRMOF-14, and UMCM-1 were identified to be the best among thosestudied and even surpass the experimentally reported highest capacity in MOF-177.The simulation showed that the larger the surface area and pore volume, the higherthe storage capacity achieved. Various factors like surface area, free volume, poros-ity, and framework density were found to correlate well with CO2 capacity nearsaturation [199].

4.4.3 H2 Storage

H2 adsorption in MOFs has been extensively simulated toward the development ofnew storage media. A study of H2 in IRMOF-1, IRMOF-8, and IRMOF-18 showed


P(kPa)

0 1000 2000 3000 4000 5000N

ex(m

mol

/g)

0

10

20

30

40

IRMOF-1Mg-IRMOF1Be-IRMOF1IRMOF1-(NH2)4IRMOF10IRMOF13IRMOF14UMCM-1

Fig. 4.6 (left) Snapshot of CO2 adsorbed in IRMOF-1 at 300 K and 2000 kPa. (right) Excessadsorption isotherms of CO2 in different MOFs versus bulk pressure. Reproduced with permis-sion from [199]. Copyright (2008) American Chemical Society

that metal-oxide clusters are the preferential adsorption sites for H2 and the effect oforganic linkers becomes evident with increasing pressure [200]. Simulation of H2in 10 noninterpenetrating MOFs revealed that H2 uptake correlates well with isos-teric heat at low pressures and with the surface area and free volume at intermediateand high pressures [201]. In interpenetrating MOFs, the small pores generated bycatenation play a primary role in densely confining H2 molecules so that the capac-ity is higher in interpenetrating frameworks than in noninterpenetrating frameworks[202]. The interactions between H2 and MOFs were artificially increased in sim-ulation to learn the degree to which the isosteric heat must be increased to meetthe current target for H2 storage. H2 density within the free volume of materialsprovided a useful insight and yielded a graph for the required isosteric heat as afunction of the free volume to meet the storage target at room temperature and120 bar [203].

A number of theoretical studies on the interactions between H2 and MOFs basedon quantum mechanics have been reported. Generally, metal-oxide sites bind H2more strongly (7–8 kJ/mol) than do organic linkers (4–5 kJ/mol). But as the avail-able volume of the metal-oxide sites is small, they tend to be saturated quickly, whileorganic linkers play a more crucial role at higher pressures [204]. The stronger H2binding observed at the metal-oxide sites can be attributed to the electrostatic and,possibly, orbital donation interactions, while the vdW interactions dominate at theorganic linkers [205]. Several polar aromatic linkers of MOFs were examined to pre-dict H2 binding using DFT theory, and the computed binding energies were in goodagreement with experiments [206]. With the approximate resolution of identity MP2(RI-MP2) and triple-zeta valence basis set, H2 binding energies were calculated withvarious substituted benzenes like C6H6, C6H5F, C6H5OH, C6H5NH2, C6H5CH3,and C6H5CN, in which the substituted benzenes were treated as simplified sub-units of the organic linkers in MOFs. The interaction energy with C6H5NH2 was


found to be the strongest (4.5 kJ/mol) [207]. Similarly, the binding energies wereestimated by MP2 with the metal oxide and organic linker in IRMOF-1. GCMCsimulation identified a high-energy binding site at the corner that quickly satu-rated with 1.27 H2 molecules at 78 K, whereas a broad range of binding sites wereobserved at 300 K [208]. Various IRMOFs such as IRMOF-1, IRMOF-3, IRMOF-4NH2, IRMOF-6, IRMOF-8, IRMOF-12, IRMOF-14, IRMOF-18, and IRMOF-993were studied using RI-MP2. The highest binding energy was found in IRMOF-4NH2, even higher than in polybenzoid structures such as IRMOF-14 and IRMOF-993 [209]. A significant enhancement of H2 uptake in Li-decorated IRMOF-1 wasrevealed with 2.9 wt% at 200 K and 2.0 wt% at 300 K. Two Li atoms strongly adsorbon the surfaces of six-carbon rings, one on each side. Each Li atom can cluster threeH2 molecules with a binding energy of 12 kJ/mol [210]. Using both DFT theory andMP2 calculations, the interaction energies of H2 adsorption with benzenoid molec-ular linkers in MOFs were computed. Both the local-density and the generalized-gradient approximated DFT methods were inaccurate in predicting binding energybut gave a qualitatively correct prediction [211]. A strong correlation was demon-strated between H2 surface density and coordinatively unsaturated metal centersin MOFs. Quantum mechanical calculations were performed to estimate the short-est distance achievable between H2 molecules, thereby defining the surface arearequirements for MOFs that can reach the target for H2 storage [212].

Table 4.2 summarizes the simulation studies of adsorption for a wide variety ofguest molecules in different MOFs.

4.4.4 New Hybrid Frameworks

A recent breakthrough in the development of hybrid frameworks is the crystalline,porous, covalent organic frameworks (COFs) [220–223]. Solely synthesized fromlight elements like B, C, O, and H, COFs consist of the organic linkers covalentlybonded with boron-oxide clusters and have high thermal stability, large surface area,and porosity. These boron-oxide clusters can be regarded as analogous to the metal-oxide clusters in MOFs. Composed of light elements, however, COFs have evenlower density than MOFs. Currently, very few simulation studies have been reportedfor COFs. Adsorption isotherms of Ar, CH4, and H2 in COF-102, -103, -105, and-108 were simulated, in which COF-102 and COF-103 showed greater affinity forCH4 due to the compact atomic structures [223]. CO2 storage in various 3D, 2D,and 1D COFs structures was simulated, and exceptionally high capacity in COF-105and -108 was observed. The gravimetric and volumetric capacities at 30 bar corre-lated well with various factors such as framework density, free volume, porosity,and surface area [224]. Another breakthrough is the invention of zeolitic imidazo-late frameworks (ZIFs) [225]. ZIFs have high thermal and chemical stability likezeolites and also high porosity and pore functionality like MOFs. Similar to MOFs,ZIFs showed promising storage and separation capacity [226, 227]. At the time ofpreparing this chapter, we were not aware of any reported simulation work in ZIFs.


Table 4.2 Simulation studies of adsorption in MOFs

Guests HostsaComputedquantitiesb References

Ar M1, Cu-BTC, MI P, I, S [186, 188, 213]N2 M1, Cu-BTC P, I, Q, S [186, 214]O2 Cu-BTC P, I, S [214]CO2 M1-10, MOF-177,

Cu-BTC,UMCM-1,MI, ML1,ML2, ML3, ML4,F-MOF1

P, I, Q, K, S, A, F [193–197, 199, 214, 215]

Methane M1, M3, M5, M6, M9,M10, ML1, Cu-BTC,CPL-2, CPL-5, MI,CU1, CU2

P, I, Q, K, S [187, 191–193, 195, 216]

Ethane M1 P, I, Q, K, S [192]Propane M1, MM1 P, I, Q, K, S [192, 217]n-Butane M1, M5, M6, M7, M8,

MM1P, I, Q, K, S [191, 192, 217]

i-Butane M1 P, I, Q, K, S [192]n-Pentane M1 P, I [218]n-Hexane M1 P, I [218]Cyclohexane M1 P, I [218]n-heptane M1 P, I [218]Methane/butane M1, M4, M5, M8, M9 P, I, S [191]CO2/CH4/H2 M1, Cu-BTC P, I, S [194]CO2/CH4 M1, Cu-BTC P, I, S [193, 195]CO2/N2/O2 Cu-BTC P, I, Q, S [214]C1–C5 alkanes M1 P, I, S [192]C5 isomers M1 P, I, S [192]n-Butane/2-

methylpropaneM1, M4 P, I, S [219]

n-Pentane/2-methylbutane

M1, M4 P, I, S [219]

n-Hexane/2-methylpentane

M1, M4 P, I, S [219]

aM1: IRMOF-1, M2: IRMOF-3, M3: IRMOF-4, M4: IRMOF-6, M5: IRMOF-8, M6: IRMOF-10, M7: IRMOF-11, M8: IRMOF-13, M9: IRMOF-14, M10: IRMOF-16, MI: manganese formate,ML1: MIL-53, ML2: MIL-47, ML3: MIL-100, ML4: MIL-101, MM1: Cu (hfipbb) (H2hfipbb),CU1: Cu(SiF6)(bpy)2, CU2: Cu(GeF6)(bpy)2.b I: adsorption isotherm, Q: heat of adsorption, K: Henry’s constant, A: accessible surface area, F:free volume, P: interaction energy, S: structure in adsorbed phase.

4.5 Outlook

We have reviewed the recent simulation studies of adsorption for a wide varietyof guest molecules in three important classes of nanoporous materials – zeolites,carbons, and hybrid frameworks. The contents reviewed are representative ratherthan exhaustive. From simulations, useful adsorption properties, such as binding


sites, interaction energies, isosteric heats, isotherms, and separation factors, can beobtained and compared with available experimental data. It is important to note that,given a material, the accuracy of simulation is primarily determined by the guest–framework interactions [228]. In a large number of simulation studies, the empiricalforce fields have been used. For example, classical Kiselev [78] and Steele [229]potentials are commonly used for zeolites and carbon materials, respectively. ForMOFs, the universal [230] and Dreiding [231] force fields are often used. Theseforce fields were constructed by fitting to some experimental data over a limitedrange of conditions with certain empirical rules. Their semiempirical nature maylead to inaccurate predictions. A more rational way is to calculate guest–frameworkinteractions from the first-principles methods. DFT has been widely used in solid-state materials; however, it fails to describe the weak physisorption interactionsbecause the dispersion forces are not properly accounted for in the DFT theory.A major obstacle to calculate the guest–framework interactions is that high-levelmethods are usually required, but they are computationally very expensive, partic-ularly for large structures. Consequently, cost-effective hierarchical approaches areadopted as a compromise of accuracy and speed.

Most simulation studies on adsorption have used rigid frameworks. This allowsthe use of grid-interpolation techniques to compute the interactions between guestmolecules and framework very efficiently. Such a simplified treatment is usuallyacceptable but cannot reproduce structural changes that might occur upon adsorp-tion. The effect of framework flexibility on hydrocarbon adsorption in silicalite wasexamined. At low loadings, the effect is small but seems to be increasingly larger athigh loadings [232]. In contrast to the relatively rigid zeolitic and carbon structures,adsorption in MOFs could easily cause structural transformation due to the exis-tence of organic linkers. For example, a hysteresis was observed in a pillared-layerMOF, which undergoes expansion and contraction (27.9% reduction in cell volume)during adsorption and desorption [233]. However, most simulation studies scarcelyinclude the flexibility of MOFs. H2O in IRMOF-1 examined by molecular dynam-ics simulation with a flexible force field revealed that IRMOF-1 is stable at very lowH2O content but unstable upon exposed to ≥4% H2O [234]. Exceptionally negativethermal expansion in IRMOFs was explored and two competing effects were iden-tified. One is a local effect where all bond lengths increase with temperature anda long-range effect where the thermal movement of the linker molecules leads to ashorter average distance between corners upon heating [235].

The review is focused mainly on adsorption. To further elucidate fluid behaviorin porous media, however, dynamic diffusion should be synergistically incorporated[236]. Similar to adsorption, a wealth of simulation studies have been reported fordiffusion in various porous materials. Diffusion of CH4, CO2, and N2 in silicalitewas simulated over a wide range of occupancies and compared with experimentaldata [237, 238]. Comparison of the self-diffusivities of CH4/CF4 mixture in silicalitewas conducted between simulation and NMR experiment, and good agreement wasfound [239]. A dynamically corrected transition-state theory was used in simula-tion to quantitatively compute the self-diffusivity of adsorbed molecules in confinedsystems at nonzero loading [240]. Diffusion of various gases (He, Ne, Ar, Kr, H2,


N2, CO2, and CH4) was investigated in six all-silica zeolites MFI, AFI, FAU, CHA,DDR, and LTA [241]. The self- and transport diffusivities of light gases like H2,CH4, Ar, and Ne were simulated in CNTs and in zeolites with comparable poresizes. It was found that diffusion in CNTs is 1–3 orders of magnitude faster [242,243]. Mass transport of O2, N2, and their mixture in a CNT demonstrated that agood kinetic selectivity could be achieved for air separation by carefully adjustingthe upstream and downstream pressures [244]. Self- and transport diffusions of lightgases in MOF-2, MOF-3, MOF-5, and Cu-BTC as a function of pore loading werefound to be in the same order of magnitude as in silicalite [245]. Simulation of ben-zene in IRMOF-1 revealed that the diffusion and the activation energy of benzeneare considerably smaller in a flexible framework compared to a rigid one [246]. Dif-fusion and separation of CO2 and CH4 in silicalite, C168 schwarzite, and IRMOF-1 were examined. The predictions of self-, corrected-, and transport diffusivitiesfrom the Maxwell–Stefan formulation match well with the simulation results [247].A critical appraisal of current estimation methods was presented to predict binarymixture diffusions in a large number of porous materials, including zeolites (MFI,AFI, TON, FAU, CHA, DDR, MOR, and LTA), CNTs, titanosilicates (ETS-4), andMOFs (IRMOF-1 and Cu-BTC) [248].

In summary, molecular simulations have substantially enhanced the current stateof knowledge for guest molecules in nanoporous materials. Fundamental insight hasbeen provided to bridge the large gap between microscopic and macroscopic prop-erties in the nanodomain. On the basis of molecular description, structure–propertyand function relations can be developed toward high-efficacy material screening.Molecular simulations thus facilitate and accelerate the intelligent design of newporous materials with novel topological and compositional characteristics for indus-trially important applications.

Acknowledgments The authors are grateful for the support from National University ofSingapore (Grants R-279-000-198-112/133 and R-279-000-243-123).

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