Hydrogen Adsorption and Diffusion in Amorphous, Metal-Decorated Nanoporous Silica

international journal of hydrogen energy 39 (2014) 9241e9253

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Hydrogen adsorption and diffusion in amorphous, metal-decorated nanoporous silica

Nethika S. Suraweera a, Austin A. Albert b, James R. Humble b, Craig E. Barnes b, David J. Keffer c,* a Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA b Department of Chemistry, University of Tennessee, Knoxville, TN 37996, USA c Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA article info abstract

Article history: Amorphous, nanoporous adsorbents composed of spherosilicate building blocks and Received 21 November 2013 incorporating isolated metal sites were investigated for their ability to adsorb and desorb Received in revised form hydrogen. This novel adsorbent contains cubic silicate building blocks (spherosilicate e 24 February 2014 units: Si8O20), which are cross-linked by SiCl2O2 bridges and decorated with either OTiCl3 e Accepted 29 March 2014 or OSiMe3 groups. The models for the structures were generated to describe experi- Available online 27 April 2014 mentally synthesized materials, based on physical properties including density, surface area, and accessible volume. Adsorption isotherms and energies at 77 K and 300 K for Keywords: pressures up to 100 bar were generated via molecular simulation describing physisorption

Grand Canonical Monte Carlo only. The maximum gravimetric capacity of these materials is 5.8 wt% H2, occurring at 77 K e simulation and 89.8 bar. A low density (high accessible volume) material with no OTiCl3 groups e Spherosilicate proved to be the best performing adsorbent. The presence of OTiCl3 did not enhance Metal decorated silica physisorption even on a volumetric basis, while the high molecular weight of Ti provided a Physisorption strong penalty on a gravimetric basis. Pair correlation functions illustrate that the most favorable adsorption sites for hydrogen are located in front of the faces of the spherosilicate cubes. The self-diffusivity of hydrogen was reported and found to be highly correlated with accessible volume. Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

storage issues. Developing a reliable hydrogen storage system Introduction that meets the cost, safety, capacity and discharge rate requirements of the transportation sector is crucial. Methods for Hydrogen is often proposed as a sustainable energy carrier hydrogen storage include compressed gas, liquefaction, e [1 4], which can be produced from fossil fuels or from water adsorption in metal hydrides, activated carbon, and metal e couple with renewable sources of electricity [5 10]. However, organic frameworks (MOFs) [7,11]. The Department of Energy its application, particularly in on-board vehicles, is limited by (DOE) sets the targets for onboard hydrogen storage systems

* Corresponding author. Department of Materials Science and Engineering, University of Tennessee, 301 Ferris Hall, 1508 Middle Drive, Knoxville, TN 37996-2100, USA. Tel.: þ1 865 974 5322; fax: þ1 865 974 7076. E-mail address: [email protected] (D.J. Keffer). http://dx.doi.org/10.1016/j.ijhydene.2014.03.247 0360-3199/Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. 9242 international journal of hydrogen energy 39 (2014) 9241e9253

for light-duty vehicles for gravimetric capacity of 5.5 wt% procedures [15,16,19]. More details about experimental struc- hydrogen and volumetric capacity of 0.04 kg hydrogen/L to be tures are included in our previous work on adsorption prop- achieved by 2017 [12]. These targets will allow some hydrogen- erties for methane and carbon dioxide in the same set of fueled vehicle platforms to meet customer performance ex- adsorbents [25]. Here we report the results of molecular-level pectations, while the “ultimate full fleet” targets of 7.5 wt% simulations to study physisorption and diffusion of hydrogen and 0.07 kg hydrogen/L are intended to facilitate the broad in these materials, with the purpose of developing funda- adoption of hydrogen-fueled propulsion systems. mental structure/property relationships. Particularly, we are A good storage media for hydrogen should perform both as interested in the impact of surface area (SA), accessible vol- e an efficient adsorber and desorber, because it is not only the ume (AV) and OTiCl3 content on the adsorptive and diffusive storage capacity that matters, but also the discharge rate. behavior of H2. Hydrogen storage adsorbents that have been investigated so far either adsorb via chemisorption and display high capacities with slow discharge rates (e.g.: metal hydrides), or adsorb Simulation methods via physisorption with lower capacities but higher discharge rates (e.g.: single-walled carbon nanotubes (SWNTs) and Model for spherosilicate structures MOFs) [13]. Neither category currently meets both the adsorptive and desorptive requirements effectively. In 1997, Developing an atomistic model of an amorphous adsorbent is Bushnell et al. [14] performed quantum mechanical studies to more challenging than for a crystalline material because in identify the favorable binding energies for both adsorption the latter case one can rely on atomic coordinates and unit cell and desorption of hydrogen in the structures with isolated Ti parameters obtained from diffraction whereas in the former centers. Ti metal centers have binding energies that are be- case, one must propose atomic coordinates and validate the tween those associated with physisorption and chemisorp- resulting model through comparison to physical properties tion, making materials that incorporate them potentially with those available from experiments (such as the chemical interesting storage materials. stoichiometry, pore size distribution, surface area, fraction of Motivated by this idea a synthetic strategy to make porous accessible volume and density of the material). In order to spherosilicate matrices that contain isolated titanium metal generate an atomistic structure for these amorphous, metal- centers has been developed [15,16]. These materials have an decorated spherosilicate structures, we developed a multi- inorganic cross-linked polymer-like structure with atomically scale procedure which includes a mesoscale level modeling dispersed Ti acting as isolated metal centers. In a reduced step followed by a molecular level modeling step. A detailed state, the Ti metal centers provide catalytic sites, which mimic description of this procedure is included in our previous work those described by Bushnell et al. [14]. In an oxidized state, the [25]. Briefly, in the mesoscale level modeling step, four e Ti metal centers appear as OTiCl3, which still impacts the different coarse grain beads representing four different 3 adsorption of H2. In this study we computationally investigate atomic groups were placed in a 50 50 50 A cubic simu- the spherosilicate structures made up of polyhedral oligo- lation box according to the relevant distances and angles be- meric silsesquioxane (POSS), which has the shape of a cube tween connected beads, so that the system agrees with the and the empirical chemical formula (RSiO3/2)8 where R is experimentally determined stoichiometry, density, surface either a functional ending group or a cross linker connecting it area and accessible volume. The four groups are spher- to another spherosilicate unit. POSS are part of a large family osilicate cubes (Fig. 1(a)), O2SiCl2 connecting bridges (Fig. 1(b)) of polycyclic compounds consisting of siliconeoxygen bonds and two groups that terminally binds to the vertices of the e e [17,18]. spherosilicate cubes: OTiCl3 (Fig. 1(c)) and OSi(CH3)3 (tri- e Metal-containing POSS compounds have been experi- methylsilyl or OSiMe3)(Fig. 1(d)). A mesoscale level energy mentally studied as metal catalyst supports [19]. Numerous minimization in which the coarse grain beads were translated elements throughout the periodic table have been incorpo- was performed using canonical Monte Carlo simulation to rated successfully into POSS [15,16] opening paths to facilitate avoid overlap between the beads and to obtain a stable broad applications. Theoretical modeling of synthesis, as- structure. In the molecular level modeling step the coarse sembly and properties for POSS systems have been previously grain beads were replaced with their relevant atomic de- investigated by McCabe et al. [20]. The adsorptive capability of scriptions and rotated to obtain the correct orientation using POSS-based structures has been investigated in several the downhill simplex method [26]. Fig. 1(e) and (f) illustrates a studies. A PdePOSS system has been analyzed by Maiti et al. coarse grain structure and an atomistic structure respectively. [21] to investigate hydrogen catalysis and sequestration. They Using this procedure we modeled nine materials for this report density functional theory results on POSS binding en- study, by varying two physical properties at three levels. The ergies at the Pd(110) surface, hydrogen storing ability of POSS first property is density of the adsorbent. Of course, a change and possible pathways of hydrogen radicals from the catalyst in density corresponds to a change in the fraction of accessible surface to unsaturated bonds away from the surface. Shan- volume in the adsorbent as well as a commensurate change in e mugam et al. studied CO2 adsorption [22], Xie et al. studied surface area. The second property is OTiCl3 content. As copper and nickel ions adsorption [23], Hongbo et al. studied noted above there are two types of non-connecting end groups e N2 adsorption [24], in different variations of POSS-based attached to the vertices of the spherosilicate cube, OTiCl3 e structures. and OSi(CH3)3. Values of 0%, 50% and 100% Ti correspond to e The family of cross-linked matrices of spherosilicate cubes the fraction of end groups which were OTiCl3. For each level e used in this work has been prepared according to published of OTiCl3 content, there are three levels of material density, international journal of hydrogen energy 39 (2014) 9241e9253 9243

Three types of moves: (i) center-of-mass translation, (ii) molecule insertion and (iii) molecule deletion, were randomly attempted for hydrogen molecules in a ratio of 3:2:2. For each simulation, 20 million conﬁgurations were used with the last half of the conﬁgurations were performed to obtain the desired average ensemble properties. Three dimensional standard periodic boundary conditions and the minimum image convention were employed. The size of the simulation box was chosen such that the average number of hydrogen molecules in the system is between 300 and 2000.

At cryogenic temperatures for light molecules like H2 quantum effects become non-negligible [34,35]. Even at 300 K, quantum effects could lead to an overestimation of adsorption by several percent [36]. To account for the quantum effects, we adopted the FeynmaneHibbs (FH) effective Buch potential method [37,38] in the GCMC simulations. This is computationally more efﬁcient than the Path Integral Monte Carlo method [39], used in our earlier study for isoreticular metal organic frameworks (IRMOFs) [27]. The FH effective Buch potential is capable of accurately reproducing properties from Path Integral Monte Carlo [40,41]. We previously validated that points on the adsorption isotherms could be reproduced using either the FH effective Buch potential or the Path Integral (PI)

method to within 0.06% for H2 in IRMOF-1 at 300 K and 1 bar [27]. Since we are interested in generating an isotherm as a function of T and pressure (p), the chemical potential of the bulk phase at a given temperature and pressure was esti- mated using the LennardeJones equation of state by Johnson et al. [42]. To eliminate the error arising from the approximate e e nature of the equation of state, for each choice of chemical Fig. 1 (a) Spherosilicate cube, (b) O2SiCl2 bridge, (c) OSiMe3 e potential and temperature, we performed two simulations: end group and (d) OTiCl3 end group. (e) Course grain e e one in the bulk phase and one in the adsorbed phase. structure (Cubes: gray, bridges: red, OTiCl3: green, OSiMe3: Adsorption isotherms were generated by plotting the amount blue). (f) Atomic structure (Cl e green, Ti e dark gray, Si e of hydrogen in the system obtained from the adsorbed phase yellow/orange, O e red, C e light gray, H e white). (For interpretation of the references to color in this figure legend, simulation as a function of the pressure obtained from the the reader is referred to the web version of this article.) bulk phase. The hydrogen molecule is treated as a single Len- nardeJones (LJ) particle (united atom model) and Buch Len- e s ¼ ε = ¼ nard Jones parameters ( H2 2.96 A and H2 kB 34.2 K) were designated low, medium and high. The densities change, as used to model the interaction potentials [43]. The framework e the name implies, for a given OTiCl3 content, although there atoms of the structures are assumed to be rigid, hence only are examples where the density of a “low density” material the non-bonded interactions between the molecular hydrogen e with 100% OTiCl3 end groups is higher than a “medium and the atoms of the adsorbent were calculated. The LJ pa- e density” material with 0% OTiCl3 end groups due to the high rameters for the atoms in the framework were taken from molecular weight of Ti. Accessible volume and surface area for universal force field (UFF) [44] (values are listed in Table 2). each structure were calculated using geometrical methods Interaction parameters between different types of atoms were that have been used for MOFs [27] and polymer membranes determined using the LorentzeBerthelot mixing rules [45]. [28,29] in our previous studies. These geometrical methods are Previous studies shows that the hydrogen adsorption capac- based on published approaches [30]. Additional details and ities for MOFs calculated with UFF agree with experimental physical properties of these structures are included in Table 1. values and the calculated values with other force fields [27,46].

Atomistic structures for adsorbents modeled are available in No electrostatic interactions were included as justiﬁed for H2 an online archive [31]. adsorption in MOFs in literature [46,47]. We note that there is work that has shown that MOFs with highly ionic character Grand Canonical Monte Carlo simulation may require an explicit description of electrostatic in-

teractions between H2 and the framework atoms [48,49]. Standard Grand Canonical Monte Carlo (GCMC) simulation [32,33] was used for adsorption simulations, in which the Quantum mechanical calculations chemical potential (m), volume (V) and temperature (T) of the system are ﬁxed and the simulation delivers the number of In order to validate that only physisorption, rather than e hydrogen molecules in the system and the potential energy. chemisorption, of hydrogen occurs with OTiCl3 groups, 9244 international journal of hydrogen energy 39 (2014) 9241e9253

Table 1 e Structural details for selected silsesquioxane structures. Structure Number of groups in Volume Density Accessible volume Surface area 3 a50 50 50 A simulation box fraction (g/cc) 3 3 2 2 Cubes Bridges TiCl3 TMS (cm /g) A per (m /g) A per simulation box simulation box e 0% OTiCl3 low density 40 41 0 248 0.73 0.59 1.23 90,800 4810 35,500 e 50% OTiCl3 low density 40 41 124 124 0.74 0.72 1.02 92,100 4090 37,000 e 100% OTiCl3 low density 40 41 248 0 0.75 0.86 0.88 94,200 3350 35,900 e 0% OTiCl3 medium 50 51 0 308 0.66 0.73 0.90 82,400 4790 44,000 density e 50% OTiCl3 medium 50 51 154 154 0.67 0.90 0.75 84,400 3990 44,900 density e 100% OTiCl3 medium 50 51 308 0 0.69 1.07 0.65 86,800 3320 44,200 density e 0% OTiCl3 high density 60 61 0 368 0.59 0.88 0.68 74,400 4680 51,400 e 50% OTiCl3 high density 60 61 184 184 0.61 1.08 0.57 76,500 3970 53,400 e 100% OTiCl3 high density 60 61 368 0 0.64 1.27 0.50 79,500 3270 52,000

quantum mechanical calculations were performed making additional 8 ns was simulated for data production. Self- use of the B3LYP functional in combination with the standard diffusivities were calculated via the Einstein relation using 6-311G(d,p) basis set utilizing Gaussian 03 [50]. This is a level of the center-of-mass positions of the hydrogen molecules saved theory used by other researchers [51] to calculate properties at 5 ps intervals during data production. The activation energy for similar structures. We ﬁrst performed unconstrained ge- for each structure was calculated via linear regression of the ometry optimization on an isolated spherosilicate cube with a Arrhenius equation using the self-diffusivities calculated at e OTiCl3 group attached into it and an isolated H2 molecule, four temperatures (300 K, 400 K, 500 K and 600 K). We did not e Then the optimized H2 was placed near the OTiCl3 group and explore the density dependence for the diffusivity. Instead, the geometry of the combined structure was optimized. The self-diffusivities corresponding to an inﬁnite dilution density bond length of the H2 molecule in the isolated state and near were calculated. e the OTiCl3 group was respectively 0.7440 and 0.7442. From this we conclude that, since no distortion of the HeH bond occurred, there is no chemisorption in this system. We also Results and discussion note that when Ti exists in this oxidized state, experimentally we and others have observed no hydrogen chemisorption Adsorption isotherms [52e54]. Consequently, the use of a potential in the classical GCMC and MD simulations that describes physisorption is Adsorption isotherms were generated at 300 K and 77 K for a appropriate. pressure range up to 100 bar. There is value in examining isotherms on gravimetric and volumetric bases and in terms Molecular dynamics simulations of absolute and excess loading [58e62]. All the isotherms presented in this work were analyzed on both gravimetric Classical equilibrium MD simulations in the canonical (NVT) basis (weight percentage wt%) and volumetric basis (kg of ensemble were used to calculate transport properties of H2 in hydrogen/l). Only gravimetric isotherms are included in this the spherosilicate structures. The two-time step r-RESPA al- manuscript, except Fig. 4(c), where we discuss some volu- gorithm [55] was used to integrate equations of motion with metric isotherms. A complete and analogous set of volumetric 2 fs for a large time step and 0.2 fs for intramolecular in- isotherms is available in the corresponding Supplementary teractions. The same interaction potentials were used in the information. All the isotherms presented are absolute iso- e GCMC and MD simulations. The Nose´ Hoover thermostat therms except Fig. 11, in which we present excess isotherms [56,57] method was used to maintain the temperature at a to compare simulation results with experiment. Absolute constant value. The system was equilibrated for 2 ns and an isotherms can reveal trends that are obscured when plotted on an excess basis [27]. Isotherms on an excess basis have the advantage of easier comparison with experimental results Table 2 e LennardeJones parameters for atoms in the and are presented in the Supplementary information. silsesquioxane framework matrices. Adsorption isotherms can be understood in terms of the s ε Atom (A) /kB (K) general thermodynamic considerations outlined in H 2.571 22.142 Supplementary information, Section 1. C 3.431 52.839 Gravimetric isotherms at 300 K are shown in Fig. 2 for low O 3.118 30.194 density structures (Fig. 2(a)), middle density structures Si 3.826 202.43 (Fig. 2(b)) and high density structures (Fig. 2(c)). At 300 K, the Cl 3.516 114.31 highest weight percentage of hydrogen is less than 1.1 wt% for Ti 2.829 8.5604 all the structures studied and volumetric quantity adsorbed is international journal of hydrogen energy 39 (2014) 9241e9253 9245

weight. However, this is not the sole reason because an analysis of the volumetric isotherms shown in the Supplementary information also shows less adsorption with e increasing OTiCl3 content. Considering the relevant thermodynamics (Supplementary information), the adsorption behavior at 300 K is approaching the inﬁnite temperature limit, where adsorption is governed by entropic effects, which e are characterized by AV [27]. Although OTiCl3 groups add relatively more free volume to the system, they can also add

inaccessible volume. Therefore, the amount of H2 adsorbed e becomes lower in the frameworks with more OTiCl3. Further the value of well depth (ε) of the Lennard Jones potential for Ti

is relatively low resulting in less H2 adsorbed by physisorption e at OTiCl3 sites. The conclusion here is that the presence of Ti e as OTiCl3 does not enhance physisorption. It should be noted, however, that no conclusion can be drawn from the

present work on H2 chemisorption in matrices with reduced Ti sites. Gravimetric isotherms at 77 K are shown in Fig. 3 for low density structures (Fig. 3(a)), middle density structures (Fig. 3(b)) and high density structures (Fig. 3(c)). At 77 K, the maximum weight percentage of hydrogen adsorbed is 5.8 wt % and maximum volumetric quantity adsorbed is 0.036 kg of hydrogen/l at the maximum bulk pressure studied (89.8 bar). The isotherms of all nine materials are clearly nonlinear. e Again, it is clear that the replacement of OSi(CH3)3 e with OTiCl3 does not enhance physisorption at low temperature. In order to better judge the impact of material density (or equivalently accessible volume) on the adsorption isotherms, some of the isotherms plotted in Figs. 2 and 3 are re-plotted in e Fig. 4, grouped now according to OTiCl3 content, so that the impact of density is more easily seen. Fig. 4 presents iso- e therms for 0% OTiCl3 structures: gravimetric isotherms at 300 K (Fig. 4(a)), gravimetric isotherms at 77 K (Fig. 4(b)) and volumetric isotherms at 77 K (Fig. 4(c)). In Fig. 4(a), the gravimetric plots of the adsorption isotherms indicate that the structures with higher AV adsorb more hydrogen on a wt% basis at 300 K. For these materials, adsorption is already dominated by entropic factors (AV) at 300 K. The low density material contains a greater fraction of accessible volume, allowing for a higher adsorption capacity on both a gravimetric and volumetric basis at high temperature, although the difference is emphasized on a gravimetric basis. At 77 K, the impact of material density is more complicated but still understandable in terms of the underlying thermodynamics (Supplementary information). At low pressures, e Fig. 2 Gravimetric H2 adsorption isotherms at 300 K for (a) adsorption is dominated by energetic effects. Therefore, the low density structures, (b) middle density structures and (c) high density materials, which present deeper energy wells at high density structures. the walls of the pores, have an advantage. Therefore, on a

volumetric basis, the high density materials adsorb more H2 than do the low density materials, as shown in Fig. 4(c). less than 0.007 kg of hydrogen/l. Adsorption up to 100 bar However, on a gravimetric basis, the low density materials are occurs within the linear regime for all structures. This rela- favored due to the lighter mass of the framework, as shown in tively low adsorption capacity at room temperature is Fig. 4(b). Taking these two competing effects into account re- consistent with the physisorption mechanism included in the sults in little impact of the density of the material on the simulations. What is also obvious from these simulations is gravimetric isotherm. At high pressures, adsorption is gov- that the presence of Ti does not enhance adsorption on a erned by entropic considerations, which is enhanced by the gravimetric basis. Obviously, there is a gravimetric penalty greater accessible volume of the low density adsorbent. associated with the inclusion of Ti based on its molecular Therefore, the low densities materials show a greater 9246 international journal of hydrogen energy 39 (2014) 9241e9253

e e Fig. 4 H2 adsorption isotherms for 0% OTiCl3 structure.

(a) Gravimetric H2 adsorption isotherms at 300 K. (b) e Fig. 3 Gravimetric H2 adsorption isotherms at 77 K for (a) Gravimetric H2 adsorption isotherms at 77 K. (c) Volumetric low density structures, (b) middle density structures and (c) H2 adsorption isotherms at 77 K. high density structures.

cubes was never observed. This observation also agrees with adsorption capacity on both gravimetric and volumetric bases the studies done by Maiti et al. to analyze the stability of a H2 at high pressure and low temperature. Based on the analysis molecule in a spherosilicate cube [21]. They found that a H2 above, the best adsorbent for a physisorption process is a low molecule inside the POSS cage is less stable than outside e density material with 0% OTiCl3 content. the cage. The possibility of stabilization and trapping of Hydrogen was always adsorbed around the framework hydrogen by POSS cages has also been discussed in the and in the pore areas. H2 adsorption inside the spherosilicate literature [63]. international journal of hydrogen energy 39 (2014) 9241e9253 9247

e Energetics of adsorption favorable energy for the low 0% OTiCl3 material; the presence of Ti does not enhance physisorption, as reflected in the e The impact of material density and OTiCl3 content on en- isotherms. Fig. 5(b) shows that the high density materials have ergies of adsorption are important in terms of understanding deeper energy wells, as noted above but the energetic structure/property relationships in adsorbents. The ener- enhancement is not sufficient to overcome the entropic pen- getics of adsorption are frequently described in terms of an alty of high-density materials due to the reduced accessible isosteric heat of adsorption [64,65]. Herein, we report two volume as shown in the isotherms. At 300 K the energies of properties: the potential energy due to adsorbateeadsorbent adsorption range in magnitude from 1 to 5 kJ/mol. interactions and the potential energy due to adsorbate- In Fig. 6, the potential energy due to adsorbateeadsorbent e eadsorbate interactions. In practice, the interaction energies interactions is plotted for three OTiCl3 contents in the low e between hydrogen molecules are negligible compared to the density material (a) and for three densities in the 0% OTiCl3 interaction energies between hydrogen and framework material (b) at 77 K. The energies of adsorption are much atoms. Therefore, adsorbateeadsorbent interaction yield the stronger functions of pressure, since the loadings are now dominant term on which we now focus. Focusing on this much higher. The deep sites near the walls are occupied first. component of the energy of adsorption allows us to identify Then the energetically less favorable pore interior is filled. the molecular mechanisms underlying observed energetics of Fig. 6(a) again clearly shows a more favorable energy for the e adsorption. low 0% OTiCl3 material across the entire pressure range. In Fig. 5, the potential energy due to adsorbateeadsorbent Fig. 6(b) shows that the high density materials have deeper e interactions is plotted for three OTiCl3 contents in the low energy wells across the entire pressure range and the differ- e density material (a) and for three densities in the 0% OTiCl3 ence increases with increasing pressure. At 77 K the energies material (b) at 300 K. Both plots show only a weak loading- of adsorption range in magnitude from 2 to 7 kJ/mol. dependence on the energy of adsorption, due to the rela- In Fig. 7, the potential energy due to adsorbateeadsorbate e tively low loadings at 300 K. Fig. 5(a) clearly shows a more interactions is plotted for three OTiCl3 contents in the low e density material (a) and for three densities in the 0% OTiCl3

e Fig. 5 Potential energy between H2 and framework at e e 300 K for (a) low density structures and (b) 0% OTiCl3 Fig. 6 Potential energy between H2 and framework at 77 K e structures. for (a) low density structures and (b) 0% OTiCl3 structures. 9248 international journal of hydrogen energy 39 (2014) 9241e9253

* + X X V gðrÞ¼ d r r (1) DVN2 ij i jsi

V is the system volume, r is the separation distance between two particles i and j, and N is the number of particles in the system. The use of three-dimensional density distributions to identify adsorption sites in crystalline IRMOFs in our previous study [27] cannot be used for amorphous spherosilicate structures because they do not have periodic unit cells.

e Fig. 7 Potential energy between adsorbed H2 for (a) low e density structures and (b) 0% OTiCl3 structure.

material (b) at both 77 and 300 K. Note that the adsorbateeadsorbate energies are measured in Joules, while the adsorbateeadsorbent energies in Figs. 5 and 6 were measured in kJ. At 300 K, the magnitude of the adsorbateeadsorbate energy never exceeds 0.05 kJ/mol, while at 77 K it never exceeds 0.5 kJ/mol. There is no signiﬁcant structural impact on the adsorbateeadsorbate energy at 300 K. At 77 K, the 0% e OTiCl3 material shows a more favorable adsorbateeadsorbate energy (a) and the high density material shows a more favorable adsorbateeadsorbate energy at low loadings only (b). Essentially, adsorbateeadsorbate energies reﬂect the same trends as observed in the volumetric isotherms, because under the conditions examined here, the adsorbateeadsorbate energies is strongly correlated to the concentra- tion of the adsorbed phase.

Hydrogen adsorption sites

In this work, pair correlation functions (PCFs), which repre- sent a conditional probability of ﬁnding two particles at a given separation, normalized to unity at long distances, were e e used to identify the adsorption sites in the spherosilicate Fig. 8 Pair correlation function between H2 H2 at (a) 77 K structures. and 1 bar, (b) 77 K and 100 bar and (c) 300 K and 100 bar. international journal of hydrogen energy 39 (2014) 9241e9253 9249

e e Pair correlation functions were generated for pair of par- 0% OTiCl3). Furthermore, in Figs. 8 10, three thermody- e e e ticles of different types. The H2 H2,H2 Si and H2 Ti PCFs are namic state points are examined, (a) low temperature and low show in Figs. 8e10 respectively. At the top of each figure, a pressure (77 K and 1 bar), (b) low temperature and high pres- snapshot of a configuration representative of the peak is sure (77 K and 89.84 bar) and (c) high temperature and high provided. For each case PCFs for three materials are examined pressure (300 K and 99.39 bar). to investigate the best adsorbent (low density and 0% Using these pair correlation functions we identified that e e OTiCl3), the impact of OTiCl3 content (low density and 100% the preferred adsorption sites are located at the exterior faces e OTiCl3) and the impact of material density (high density and of the spherosilicate cubes. In Fig. 8, there are two prominent e peaks in the H2 H2 PCF, centered at 3.2 A and 7 A. The first e peak corresponds to the H2 H2 nearest neighbor distance when both occupy internal pore area. The second peak cor-

responds to H2 located on adjacent faces of the same spherosilicate cube. At low temperature and low pressure (Fig. 8(a)), we observe that the relative magnitude of the two peaks is impacted by the presence of Ti, but the position is not. Ti

groups allow relatively more H2 bindings near to the cubes at low pressure and low temperature. As the loading is increased at low temperature (Fig. 8(b)), one obtains a PCF structure typical of a high-density gas or liquid. The impact of the adsorbent on the PCF has been drastically diminished as the

H2 arrange themselves in the limited accessible volume. The peaks for the high density material are higher since the PCF is

normalized by the total density (number of H2 per simulation

volume) but the accessible volume where H2 may be found is lower in the high density material. At high temperature (Fig. 8(c)), one obtains a PCF structure typical of a gas, capturing the low density of the adsorbed phase. e In Fig. 9, there are two prominent peaks in the H2 Si PCF, centered at 4 and 6.8 A. The ﬁrst peak corresponds to the H2 interacting with a Si on the adsorbed face and the second peak corresponds to a Si located in the same spherosilicate cube but

on a different face than the one on which the H2 is adsorbed. At low temperature and low pressure (a), we observe that the relative magnitude of the two peaks is impacted by the pres- e ence of Ti, but the position is not. In 0% OTiCl3 structures Si is e also provided by the OSiMe3 groups. Therefore, we see a peak at 5.1 A, which corresponds to the H2 interacting with a Si in e OSiMe3 group connected to the face of the spherosilicate e cube. The peaks for the 100% OTiCl3 structure are higher

since the PCF is normalized by the total density (number of H2

e e Fig. 9 Pair correlation function between H2 Si at (a) 77 K e e and 1 bar, (b) 77 K and 100 bar and (c) 300 K and 100 bar. Fig. 10 Pair correlation function between H2 Ti. 9250 international journal of hydrogen energy 39 (2014) 9241e9253

per simulation volume) but the accessible volume where H2 Ti within the matrix, which is a key feature that is important e may be found is lower in 100% OTiCl3 structures. Values for for an analogous material with reduced Ti, that can act as inaccessible volumes for all the structures are presented in dependent chemisorption sites for hydrogen molecules. Table 1. At high temperature and high pressure (Fig. 9(c)), the relationship between the adsorbed hydrogen and framework Self-diffusivity atoms is relatively weak because the adsorption is governed by entropic effects and H2 is located in available pore area. For each structure self-diffusivities were calculated at four e In Fig. 10, there are two prominent peaks in the H2 Ti PCF, temperatures: 300 K, 400 K, 500 K and 600 K. The values are centered at 4.9 and 9.1 A. The first peak corresponds to the H2 presented in Table 3. Calculated self-diffusivities were vali- e interacting with a Ti in a OTiCl3 group connected to the dated using two methods. First, it was verified that all the MD adsorbed face of the spherosilicate cube and the second peak simulations were run to the infinite-time limit, where a linear e corresponds to a Ti in a OTiCl3 group connected to the same relationship between MSD and observation time is observed. spherosilicate cube but on a different face than the one on Second, long time limit behavior was verified by showing that which the H2 is adsorbed. At low temperature and low pres- the distance traveled by H2 molecules is large enough sure we observe high probability for H2 to stay near to the compared to the pore size of the structure (Table 3; Average e OTiCl3 groups, in other words near to the surface of the distance traveled is the square root of the final MSD). adsorbent. At high pressures, the effect of the presence of Ti In calculating diffusivities we observed a significant dif- diminishes, as in this entropically dominant regime, H2 fills ference between the diffusivities in x direction component, y pores and the binding to the surface of the adsorbent is direction component and z direction component. (We reduced. confirmed the accuracy of these results by getting the same e e e Additional PCFs, H2 OH2 Cl and Ti Ti are presented in the results with a rotated structure.) This happens due to the Supplementary information in Figs. S7eS9 respectively. The anisotropic effects of the structure. Being amorphous, these TieTi PCF demonstrates the atomistically dispersed nature of matrices have a structure with irregular pores in every

Table 3 e Self-diffusivity and activation energies. Structure Temperature Diffusivity Standard deviation Average Activation energy 7 2 7 2 (K) (10 m /s) (10 m /s) displacement (A) (kcal/mol) e 0% OTiCl3 low density 300 3.60 0.98 265 0.850 400 5.05 1.38 315 500 6.33 2.03 351 600 7.34 2.11 380 e 50% OTiCl3 low density 300 2.57 0.74 226 0.798 400 3.57 1.09 264 500 4.28 1.25 290 600 5.10 1.53 316 e 100% OTiCl3 low density 300 3.99 2.50 269 0.712 400 5.41 3.35 314 500 6.52 4.25 344 600 7.20 4.70 361 e 0% OTiCl3 medium density 300 1.82 0.35 190 0.861 400 2.61 0.51 227 500 3.18 0.60 251 600 3.80 0.75 274 e 50% OTiCl3 medium density 300 1.50 0.60 170 0.803 400 2.08 1.07 200 500 2.50 1.29 219 600 2.98 1.50 239 e 100% OTiCl3 medium density 300 2.07 1.65 186 0.812 400 2.72 2.18 213 500 3.32 2.67 235 600 4.19 3.46 262 e 0% OTiCl3 high density 300 0.93 0.41 134 0.861 400 1.36 0.63 161 500 1.62 0.74 177 600 1.94 0.93 193 e 50% OTiCl3 high density 300 0.47 0.19 95 0.775 400 0.66 0.24 113 500 0.77 0.28 123 600 0.91 0.31 134 e 100% OTiCl3 high density 300 1.01 0.86 128 0.755 400 1.40 1.16 151 500 1.67 1.40 165 600 1.91 1.57 177 international journal of hydrogen energy 39 (2014) 9241e9253 9251

direction. Our cubic simulation box with a side length of 50 A is not large enough to overcome the anisotropic effect. For example in one instance we have x, y and z components respectively of 7.92 (0.009) 10 07 m2/s, 9.10 (0.004) 10 07 m2/s and 5.00 (0.001) 10 07 m2/s, such that the average diffusivity is 7.34 (2.11) 10 07 m2/s. Therefore, we observe that the standard deviation of the average diffusivity is significant while the standard deviation of any one component is 3 orders of magnitude smaller. The increased standard deviation in the self-diffusivity is the only manifes- tation of small system size in these simulations. The activation energies calculated are presented in Table 3. As expected from the Arrhenius equation, a negative correlation between the self-diffusivity and activation energy for diffusion is observed. Similar to our previous studies [25,27] we calculated correlation coefficients, a statistical property bounded between Fig. 11 e Comparison of experimental and simulation 1 (perfect negative correlation) and þ1 (perfect positive cor- isotherms at 77 K. relation), to analyze the relationship between self-diffusivity and activation energy with SA, AV and energy of adsorption (at 1 bar to match with the infinite dilution conditions) at 300 K. Calculated values (Table 4) show a strong positive cor- isotherms across samples. The primary purpose of the relation between self-diffusivity and AV. When the pore size is experimental isotherms was to distinguish between phys- large, the hydrogen diffuses faster. Since the SA is negatively isorption and chemisorption. Based on the small amount of H correlated with the AV, the self-diffusivity is also negatively 2 adsorbed, these results clearly indicated physisorption for correlated with the SA. These observations are consistent both materials. The simulated H adsorption for the 0% with the results obtained by Liu et al. [66] and our previous 2 eOTiCl structure is much higher than the experimental study [27] for hydrogen diffusion in metal organic frame- 3 adsorption. This discrepancy must be attributed to failures in works. The self-diffusivity increases as the molecules are either the structure or potential of the model. Since our more weakly bound, in large part due to a commensurate structure has been validated against available experimental decrease in the activation energy. characterization of structure, we suspect that a shortcoming in the UFF potential may be responsible for the discrepancy. Comparison with experiments The UFF well depth (ε) of the Lennard Jones potential for Ti is low relative to Si (Table 2) resulting in more energetically Simulated hydrogen adsorption results were compared with e favorable sites for H2 adsorption in the material with OSiMe3 experimental adsorption for two structures at 77 K up to 1 bar e e groups rather than OTiCl3 groups. Therefore, the simula- (100 kPa). The materials include the high density 0% OTiCl3 e tions show high adsorption in this structure which is not structure and the middle density 100% OTiCl3 structure. The observed experimentally. relevant samples were generated and tested for hydrogen adsorption by the authors. Physical properties of the experimental structures such as accessible volume, surface area and e OTiCl3 content agreed with the selected modeled structures. Conclusions The comparison of adsorption isotherms is shown in Fig. 11.

There is good agreement between the simulated and experi- In this work, we investigated the physisorption of H2 in ad- e mental isotherms for 100% OTiCl3 structure. The difference sorbents containing cubic silicate building blocks (spher- between the two experimental materials is within experi- osilicate units: Si8O20), which are cross-linked by SiCl2O2 e e mental error based on independent measurement of the bridges and decorated with either OTiCl3 or OSiMe3 groups. At 300 K, the highest weight percentage of hydrogen is less than 1.1 wt% for all the structures studied and volumetric Table 4 e Correlation coefﬁcients for self-diffusivity and quantity adsorbed is less than 0.007 kg of hydrogen/l. At 77 K, activation energy with surface area, accessible volume the maximum weight percentage of hydrogen adsorbed is and adsorbate framework energy at 300 K and 1 bar. 5.8 wt% and maximum volumetric quantity adsorbed is Property 1 Property 2 Correlation 0.036 kg of hydrogen/l at the maximum bulk pressure studied coefﬁcient (89.8 bar). The best adsorbent for a physisorption process e Self-diffusivity Accessible volume 0.92 studied herein is a low density material with 0% OTiCl3 e Self-diffusivity Surface area 0.95 content. The presence of Ti as OTiCl3 does not enhance Self-diffusivity Adsorbate framework energy 0.63 physisorption. First, there is a gravimetric penalty associated Activation energy Accessible volume 0.30 with the inclusion of Ti based on its molecular weight. Second, Activation energy Surface area 0.06 Ti is surrounded by 3 Cl atoms limiting the attraction of Ti Activation energy Adsorbate framework energy 0.67 towards the adsorbed H2. However, for an analogous material, 9252 international journal of hydrogen energy 39 (2014) 9241e9253

in which the Ti is reduced and can act as a chemisorption site [9] Mantz RJ, De Battista H. Hydrogen production from idle for H2, inclusion of Ti catalytic sites is expected to yield generation capacity of wind turbines. Int J Hydrogen Energy 2008;33(16):4291e300. significantly higher H2 adsorption [14]. [10] Steinfeld A. Solar thermochemical production of hydrogen e We observe that at 300 K and pressures up to 100 bar the a review. Sol Energy 2005;78(5):603e15. adsorption process is governed by entropic considerations. At [11] Lim KL, Kazemian H, Yaakob Z, Daud WRW. Solid-state 77 K, there is more than one adsorption regime. At low pres- materials and methods for hydrogen storage: a critical sures, the adsorption process is governed by energetic con- review. Chem Eng Technol 2010;33(2):213e26. siderations and at the high end of the pressure range the [12] Fuel Cell Technologies Office Multi-Year Research, adsorption becomes a process dominated by entropic con- Development and Demonstration Plan. Available from: siderations. Based on the pair correlation functions we iden- http://www1.eere.energy.gov/hydrogenandfuelcells/mypp/, updated July 2013 [accessed November 2013], cited 2013. tified that favorable adsorption sites for hydrogen are located [13] Yang J, Sudik A, Wolverton C, Siegel DJ. High capacity in front of the face of a spherosilicate cube. Self-diffusivity of hydrogen storage materials: attributes for automotive hydrogen at infinite dilution is correlated with accessible applications and techniques for materials discovery. Chem volume (AV). Soc Rev 2010;39(2):656e75. [14] Bushnell JE, Maitre P, Kemper PR, Bowers MT. Binding energies of Tiþ(H-2)(1-6) clusters: theory and experiment. J Chem Phys 1997;106(24):10153e67. Acknowledgments [15] Clark JC, Barnes CE. Reaction of the Si8O20(SnMe3)8 building block with silyl chlorides: a new synthetic methodology for preparing nanostructured building block solids. Chem Mater This research was supported by the Sustainable Energy and 2007;19(13):3212e8. Education Research Center at the University of Tennessee and [16] Clark JC, Saengkerdsub S, Eldridge GT, Campana C, by a grant from the National Science Foundation (DGE- Barnes CE. Synthesis and structure of functional 0801470). This research project used resources of the National spherosilicate building block molecules for materials e Institute for Computational Sciences (NICS) supported by NSF synthesis. J Organomet Chem 2006;691(15):3213 22. [17] Cordes DB, Lickiss PD, Rataboul F. Recent developments in under agreement number: OCI 07-11134.5. the chemistry of cubic polyhedral oligosilsesquioxanes. Chem Rev 2010;110(4):2081e173. [18] Jaroentomeechai T, Yingsukkamol PK, Phurat C, Somsook E, Osotchan T, Ervithayasuporn V. Synthesis and reactivity of Appendix A. Supplementary information nitrogen nucleophiles-induced cage-rearrangement silsesquioxanes. Inorg Chem 2012;51(22):12266e72. Supplementary information related to this article can be [19] Ghosh NN, Clark JC, Eldridge GT, Barnes CE. Building block found at http://dx.doi.org/10.1016/j.ijhydene.2014.03.247. syntheses of site-isolated vanadyl groups in silicate oxides. Chem Commun 2004;7:856e7. [20] McCabe C, Glotzer SC, Kieffer J, Neurock M, Cummings PT. references Multiscale simulation of the synthesis, assembly and properties of nanostructured organic/inorganic hybrid materials. J Comput Theor Nanosci 2004;1(3):265e79. [21] Maiti A, Gee RH, Maxwell R, Saab AP. Hydrogen catalysis and [1] Jain IP. Hydrogen the fuel for 21st century. Int J Hydrogen scavenging action of Pd-POSS nanoparticles. Chem Phys Lett Energy 2009;34(17):7368e78. 2007;440(4e6):244e8. [2] Mandal TK, Gregory DH. Hydrogen: a future energy vector for [22] Shanmugam N, Lee KT, Cheng WY, Lu SY. Organic-inorganic sustainable development. Proc Inst Mech Eng Part C J Mech hybrid polyaspartimide involving polyhedral oligomeric

Eng Sci 2010;224(C3):539e58. silsesquioxane via Michael addition for CO2 capture. J Polym [3] Kelly NA, Gibson TL, Cai M, Spearot JA, Ouwerkerk DB. Sci Part A Polym Chem 2012;50(13):2521e6. Development of a renewable hydrogen economy: [23] Xie KL, Jing LX, Zhao WG, Zhang YL. Adsorption removal of þ þ optimization of existing technologies. Int J Hydrogen Energy Cu2 and Ni2 from waste water using nano-cellulose 2010;35(3):892e9. hybrids containing reactive polyhedral oligomeric [4] Lee JY, Yoo M, Cha K, Lim TW, Hur T. Life cycle cost silsesquioxanes. J Appl Polym Sci 2011;122(5):2864e8. analysis to examine the economical feasibility of hydrogen [24] Hongbo R, Yuancheng Q, Chengwei S, Yutie B, Lin Z. as an alternative fuel. Int J Hydrogen Energy Adsorption and desorption properties of hybrid aerogels 2009;34(10):4243e55. derived form MPMS-SSO at 77 K. Rare Metal Mater Eng [5] Elnashaie S, Chen ZX, Prasad P. Efﬁcient production and 2010;39:475e8. economics of clean-fuel hydrogen. Int J Green Energy [25] Suraweera NS, Albert AA, Peretich ME, Abbott J, Humble JR, 2007;4(3):249e82. Barnes CE, et al. Methane and carbon dioxide adsorption and [6] Lee KB, Beaver MG, Caram HS, Sircar S. Reversible diffusion in amorphous, metal-decorated nanoporous silica. chemisorption of carbon dioxide: simultaneous production Mol Simul 2014;40(7e9):618e33.

of fuel-cell grade H-2 and compressed CO2 from synthesis [26] Press WH, Flannery BP, Teukolsky SA, Vetterling WT. gas. Adsorpt J Int Adsorpt Soc 2007;13(3e4):385e97. Numerical recipes: the art of scientiﬁc computing. , New [7] Nath K, Das D. Production and storage of hydrogen: present York: Cambridge University Press; 1986. scenario and future perspective. J Sci Ind Res [27] Suraweera NS, Xiong RC, Luna JP, Nicholson DM, Keffer DJ. 2007;66(9):701e9. On the relationship between the structure of metal-organic [8] Pasculete E, Condrea F, Radulescu C. Hydrogen and frameworks and the adsorption and diffusion of hydrogen. sustainable energy. Research for hydrogen production. Mol Simul 2011;37(7):621e39. Environ Eng Manag J 2007;6(1):45e9. international journal of hydrogen energy 39 (2014) 9241e9253 9253

[28] Liu JW, Suraweera N, Keffer DJ, Cui ST, Paddison SJ. On the [49] Pham T, Forrest KA, McLaughlin K, Tudor B, Nugent P,

relationship between polymer electrolyte structure and Hogan A, et al. Theoretical investigations of CO2 and H-2 hydrated morphology of perfluorosulfonic acid membranes. J sorption in an interpenetrated square-pillared metal-organic Phys Chem C 2010;114(25):11279e92. material. J Phys Chem C 2013;117(19):9970e82. [29] Wang QF, Suraweera NS, Keffer DJ, Deng SX, Mays J. [50] Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Atomistic and coarse-grained molecular dynamics Cheeseman JR, et al. Gaussian 03, Revision C.02. Wallingford, simulation of a cross-linked sulfonated poly(1,3- CT: Gaussian, Inc.; 2004. cyclohexadiene)-based proton exchange membrane. [51] Chiacchio MA, Borrello L, Di Pasquale G, Pollicino A, Macromolecules 2012;45(16):6669e85. Bottino FA, Rescifina A. Synthesis of functionalized [30] Frost H, Duren T, Snurr RQ. Effects of surface area, free polyhedral oligomeric silsesquioxane (POSS) macromers by volume, and heat of adsorption on hydrogen uptake in microwave assisted 1,3-dipolar cycloaddition. Tetrahedron metal-organic frameworks. J Phys Chem B 2005;61(33):7986e93. 2006;110(19):9565e70. [52] Acatrinei AI, Hartl MA, Eckert J, Falcao EHL, Chertkov G, [31] Keffer DJ. Molecular simulation images from the Daemen LL. Hydrogen adsorption in the Ti-doped computational materials research group at the University of mesoporous silicate SBA-15. J Phys Chem C Tennessee, Knoxville, TN. Available from: https://trace.lib. 2009;113(35):15634e8. utk.edu/home/davidkeffer/sites/atoms/animmn.html; 2013. [53] Prasanth KP, Raj MC, Bajaj HC, Kim TH, Jasra RV. Hydrogen [32] Allen MP, Tildesley DJ. Computer simulation of liquids. sorption in transition metal modified mesoporous materials. Oxford: Oxford Science Publications; 1987. Int J Hydrogen Energy 2010;35(6):2351e60. [33] Frenkel D, Smit B. Understanding molecular simulation. San [54] Simmons JM, Yildirim T, Hamaed A, Antonelli DM, Webb MI, Diego, CA: Academic Press; 1996. Walsby CJ. Direct observation of activated hydrogen binding [34] Basmadjian D. Adsorption equilibria of hydrogen, deuterium, to a supported organometallic compound at room and their mixtures 1. Revue Can de Chimie [Can J Chem] temperature. Chem Eur J 2012;18(14):4170e3. 1960;38(1):141e8. [55] Tuckerman M, Berne BJ, Martyna GJ. Reversible multiple time [35] Freeman MP. The quantum mechanical correction for the scale molecular-dynamics. J Chem Phys high temperature Van Der Waals interaction of light gases 1992;97(3):1990e2001. and surfaces e a new method of determining surface area. J [56] Nose S. A molecular-dynamics method for simulations in the Phys Chem 1960;64(1):32e7. canonical ensemble. Mol Phys 1984;52(2):255e68. [36] Wang QY, Johnson JK. Molecular simulation of hydrogen [57] Hoover WG. Canonical dynamics e equilibrium phase-space adsorption in single-walled carbon nanotubes and idealized distributions. Phys Rev A 1985;31(3):1695e7. carbon slit pores. J Chem Phys 1999;110(1):577e86. [58] Mahdizadeh SJ, Goharshadi EK. Hydrogen storage on [37] Feynman RP. Statistical mechanics: a set of lectures. silicon, carbon, and silicon carbide nanotubes: a combined Reading, MA: W. A. Benjamin; 1972. quantum mechanics and grand canonical Monte Carlo [38] Feynman RP. Quantum mechanics and path integrals. , New simulation study. Int J Hydrogen Energy 2014;39(4): York: McGraw-Hill Companies; 1965. 1719e31. [39] Feynman RP. Space-time approach to non-relativistic [59] Kowalczyk P, Tanaka H, Holyst R, Kaneko K, Ohmori T, quantum mechanics. Rev Mod Phys 1948;20(2):367e87. Miyamoto J. Storage of hydrogen at 303 K in graphite slitlike [40] Liu JC, Culp JT, Natesakhawat S, Bockrath BC, Zande B, pores from grand canonical Monte Carlo simulation. J Phys Sankar SG, et al. Experimental and theoretical studies of gas Chem B 2005;109(36):17174e83. adsorption in Cu-3(BTC)(2): an effective activation procedure. [60] Kaye SS, Dailly A, Yaghi OM, Long JR. Impact of preparation J Phys Chem C 2007;111(26):9305e13. and handling on the hydrogen storage properties of [41] Liu J, Lee JY, Pan L, Obermyer RT, Simizu S, Zande B, et al. Zn4O(1,4-benzenedicarboxylate)(3) (MOF-5). J Am Chem Soc Adsorption and diffusion of hydrogen in a new metal- 2007;129(46):14176. organic framework material: [Zn(bdc)(ted)(0.5)]. J Phys Chem [61] Kuchta B, Firlej L, Mohammadhosseini A, Boulet P, C 2008;112(8):2911e7. Beckner M, Romanos J, et al. Hypothetical high-surface- [42] Johnson JK, Zollweg JA, Gubbins KE. The Lennard-Jones area carbons with exceptional hydrogen storage capacities: equation of state revisited. Mol Phys 1993;78(3):591e618. open carbon frameworks. J Am Chem Soc [43] Buch V. Path-integral simulations of mixed para-D2 and 2012;134(36):15130e7. ortho-D2 clusters: the orientational effects. J Chem Phys [62] Weinberger B, Lamari FD. High pressure cryo-storage of 1994;100(10):7610e29. hydrogen by adsorption at 77 K and up to 50 MPa. Int J [44] Rappe AK, Casewit CJ, Colwell KS, Goddard WA, Skiff WM. Hydrogen Energy 2009;34(7):3058e64. Uff, a full periodic-table force-field for molecular mechanics [63] Sasamori R, Okaue Y, Isobe T, Matsuda Y. Stabilization of and molecular-dynamics simulations. J Am Chem Soc atomic-hydrogen in both solution and crystal at room- 1992;114(25):10024e35. temperature. Science 1994;265(5179):1691e3. [45] Prausnitz JM, Lichtenthaler RN, Avezedo EG. Molecular [64] Myers AL, Siperstein F. Characterization of adsorbents by thermodynamics of fluid-phase equilibria. New Jersey: energy profile of adsorbed molecules. Colloids Surf A Prentice-Hall International Series; 1998. Physicochem Eng Aspects 2001;187:73e81. [46] Garberoglio G, Skoulidas AI, Johnson JK. Adsorption of gases [65] Sircar S, Mohr R, Ristic C, Rao MB. Isosteric heat of in metal organic materials: comparison of simulations and adsorption: theory and experiment. J Phys Chem B experiments. J Phys Chem B 2005;109(27):13094e103. 1999;103(31):6539e46. [47] Jhung SH, Yoon JW, Kim HK, Chang JS. Low temperature [66] Liu B, Yang QY, Xue CY, Zhong CL, Smit B. Molecular adsorption of hydrogen on nanoporous materials. Bull simulation of hydrogen diffusion in interpenetrated metal- Korean Chem Soc 2005;26(7):1075e8. organic frameworks. Phys Chem Chem Phys [48] Belof JL, Stern AC, Eddaoudi M, Space B. On the mechanism 2008;10(22):3244e9. of hydrogen storage in a metal-organic framework material. J Am Chem Soc 2007;129(49):15202e10.