Struct Chem DOI 10.1007/s11224-013-0267-4

ORIGINAL RESEARCH

Computational design of tetrahedral silsesquioxane-based porous frameworks with diamond-like structure as hydrogen storage materials Xiao-Dong Li • Hong Zhang • Yoshiyuki Miyamoto Yong-Jian Tang • Chao-Yang Wang

•

Received: 5 September 2012 / Accepted: 3 April 2013  Springer Science+Business Media New York 2013

Abstract A novel type of three-dimensional (3D) tetrahedral silsesquioxane-based porous frameworks (TSFs) with diamond-like structure was computationally designed using the density functional theory (DFT) and classical molecular mechanics (MM) calculations. The hydrogen adsorption and diffusion properties of these TSFs were evaluated by the methods of grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The results reveal that all designed materials possess extremely high porosity (87–93 %) and large H2 accessible surface areas (5,268–6,544 m2 g-1). Impressively, the GCMC simulation results demonstrate that at 77 K and 100 bar, TSF-2 has the highest gravimetric H2 capacity of 29.80 wt%, while TSF-1 has the highest volumetric H2 uptake of 65.32 g L-1. At the same time, the gravimetric H2 uptake of TSF-2 can reach up to 4.28 wt% at the room temperature. The extraordinary performances of these TSF materials in hydrogen storage made them enter the rank of the top hydrogen storage materials so far.

X.-D. Li  H. Zhang (&) College of Physical Science and Technology, Sichuan University, Chengdu 610065, China e-mail: [email protected] X.-D. Li College of Science, Henan University of Technology, Zhengzhou 450001, China Y. Miyamoto Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki, Japan Y.-J. Tang  C.-Y. Wang Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China

Keywords Porous material  Hydrogen storage  Grand canonical Monte Carlo  Self-diffusivity

Introduction Due to the negative effects such as ecological disruption, environmental pollution, and global warming caused by the exploitation and utilization of fossil fuels [1, 2], new energy sources must be explored to substitute for the traditional energy sources. Hydrogen has been long viewed as an ideal alternative to fossil fuels because it is abundant, pollution-free, and cost effective in comparison with other possible fuels [3, 4]. For the wide use of hydrogen as an energy carrier, the safe and efficient storage is an essential prerequisite and one of main obstacles to be resolved [5]. However, conventional storage methods, i.e., high pressure gas cylinders and liquid hydrogen, are not suitable for commercial application owning to their high costs. During the past decades, materials-based physisorption or chemisorption of hydrogen has been considered as a new strategy to achieve the effective hydrogen storage [5–8]. Toward this direction, many types of materials, especially porous materials, have been proposed as hydrogen storage materials [5, 7–9]. Therefore, an increasing number of porous materials are constructed through various reactions by rational choice of chemical building blocks [10–17]. A computational investigation is a powerful tool for exploring novel nanoporous materials as hydrogen storage media. Abundant computational studies have been performed either to modify the existing porous materials [10, 18, 19] or to design new types of porous materials [16, 20–23] with enhanced hydrogen storage properties. For example, Cha et al. [24] studied the hydrogen storage capacity of Fe-decorated, OH-functionalized IRMOF-16 by the methods of DFT

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calculation and GCMC simulation. The modified IRMOF-16 has the hydrogen storage capacity of 6.0 wt% at 298 K and 100 atm reversibly. Also, by comprehensively using the MP2, CCSD, and GCMC methods, Sagara et al. proposed several novel MOFs with gravimetric hydrogen storage density up to 6.5 wt% and volumetric hydrogen storage density up to 40 kg m-3 at room temperature [21]. Meanwhile, with the help of classical MM optimization and GCMC simulation, four 3D COFs were designed with enhanced hydrogen storage properties by Klontzas et al. [20]. At the same time, Ben et al. [16] subsequently synthesized a PAF-1 framework with exceptional thermal and hydrothermal stabilities in experiment with the guide of computational simulation. All these experiences demonstrate that the computational design of nanoporous materials can not only cover the shortage of experiment but also make the experimental synthesis goal-directed and effective. Herein, inspired by these studies, we computationally designed one new type of tetrahedral silsesquioxane based porous frameworks by combining the DFT and classic MM calculations. The TSF materials proposed here are constructed by two types of building moieties, tetrahedral silsesquioxane, and aromatic organic linkers (phenyl, biphenyl, naphthalene, and pyrene). It is well-known that the selected aromatic moieties have been widely used to construct porous materials such as MOFs, COFs, PAFs, and so on [15, 16, 25–27]. Besides, polyhedral silsesquioxanes are also one type of structures capable of forming nanocomposites [28, 29]. They are nanoscopic cages in size and are comprised of a rigid 3D Si–O frameworks with the form of (RSiO3/2)n, (n = 4, 6, 8,…), where R can be typically an alkyl or an aryl organic group, etc. [30, 31]. The organic groups of polyhedral silsesquioxanes can be made reactive for polymerization, and hence, they are very promising building blocks for constructing porous materials [31–33]. Not long ago, several octahedral silsesquioxane (R8Si8O12)-based 3D porous frameworks with specific net topology have been reported [34–36]. All these experiences forebode the attractive prospect of porous materials based on polyhedral silsesquioxanes. The tetrahedral silsesquioxane (R4Si4O6) is the simplest polyhedral silsesquioxane, and thus it has the potential to build low-density porous materials. However, to the best knowledge, there is devoid of report on the tetrahedral silsesquioxane-based porous materials up to now. Therefore, in this contribution, we select the tetrahedral silsesquioxane and four aromatic organic linkers as build units to computationally design one novel type of porous materials as hydrogen storage media. Design and computational details Figure 1a shows the optimized geometry of the simplest tetrahedral silsesquioxane, tetrahedral H-silsesquioxane

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(H4Si4O6). The geometrical parameters of the basic model H4Si4O6 are consistent with the results derived from the inelastic neutron scattering of various silsesquioxane: ˚ and d(Si–O) = 1.671 A ˚ as compared d(Si–H) = 1.463 A ˚ ˚ experito d(Si–H) = 1.48 A and d(Si–O) = 1.62(1.61) A mentally [37]. Seen from Fig. 1a, the structure of tetrahedral H-silsesquioxane has very high symmetry and seems like a cage. The four silicon atoms are located at the culminations of a tetrahedron, while each of the six oxygen atoms is bridged between two silicon atoms. As referred previously, the positions of four hydrogen atoms can be replaced by organic groups with various potential applications. It is well-known that diamond is one of the most stable materials in the nature world. In diamond structure, each carbon atom is saturated with four neighboring carbon atoms through sp3 hybridization forming an extremely stable structure. Conceptually, replacing the carbon atoms with tetrahedral chemical units and the C–C bonds with linear organic linkers in diamond structure should not only build a framework with diamond-like net structure but also retain a diamond-like structural stability. Moving toward this direction, we have designed the four 3D TSFs by replacing the carbon atoms with tetrahedral silsesquioxanes and the C–C bonds with phenyl, biphenyl, naphthalene, and pyrene linkers in diamond structure, respectively. Here, we term the TSFs with phenyl, biphenyl, naphthalene, and pyrene linkers as TSF-1, TSF-2, TSF-3, and TSF-4, respectively. All the 3D TSFs were constructed using the Materials Visualizer [38] with the guide of EPINET [39, 40]. The geometry structures of the TSFs and the corresponding design schemes are presented in Fig. 2. Ahead of constructing these TSFs, the first-principles calculations were used to optimize several small clusters comprised of tetrahedral silsesquioxane and organic linkers to obtain the chemical building blocks of these TSFs. We typically show the optimized clusters for TSF-1 in Fig. 1. The clusters for constructing other TSFs are similar to that of TSF-1, just by replacing the phenyl in Fig. 1 with the corresponding organic linkers. Then, based on these basic units, the 3D periodic TSFs were preliminarily constructed and then optimized using the classical MM method. At last, the GCMC simulations were employed to study the hydrogen storage properties and the MD simulations were used to investigate the diffusion properties of the adsorbed H2 molecules in these TSFs. First-principles all-electron calculations for geometry optimizations were performed by the method of generalized gradient approximation (GGA) within the framework of DFT. The gradient-corrected exchange and correlation functions of Perdew–Wang (PW91) with the double numeric basis sets including polarization functions (DNP) on all atoms were employed here [41]. The first-principles calculations were carried out using the Dmol3 module of

Struct Chem

Fig. 1 The optimized the build clusters for constructing the TSF-1 material, a tetrahedral H-silsesquioxane, b teraphenyl silsesquioxane, and c one phenyl terminated by two tetrahedral silsesquioxane. The dangling bonds are terminated by –SiH3 or –CH3 groups to maintain the corrected hybridization environment

the Materials Studio [38]. During the calculations, the ‘‘fine’’ criterion was adopted for energy and force convergence without any symmetry restrictions. Besides, the classical MM calculations were implemented using the Forcite module of Materials Studio [38]. The COMPASS [42, 43] force field and the ‘‘ultra-fine’’ criterion were adopted for the geometry optimization of the 3D periodic TSFs. Most parameters of the COMPASS force field were derived from the ab initio data and the COMPASS force

field had been parameterized to well-predict various properties for a variety of materials including most common organics, small inorganic molecules, and polymers in isolation and in condensed phases [42, 43]. The van der Waals (VDW) interactions between the H2 molecule and TSFs atoms are treated as Lennard-Jones (LJ) potential shown in Eq. (1). The potential parameters of H2 molecule are from the work of Buch [44], where a united-atom model is used. The potential parameters for the atoms of TSFs are from the DREIDING force field of Mayo et al. [45]. All the parameters used in this study are listed in Table 1. The cross-interaction potential parameters between different atoms are calculated by the Lorentz– Berthelot mixing rules in Eqs. (2) and (3). "    # rij 6 rij 12 Uij ¼ 4eij  ð1Þ rij rij   ð2Þ rij ¼ rii þ rjj 2 pffiffiffiffiffiffiffiffi eij ¼ eii ejj ð3Þ The GCMC simulations were carried out using the multipurpose simulation code (Music) [46]. The 2 9 2 9 2 simulation cells for all TSF materials were adopted and the periodic boundary conditions were applied for all three dimensions. The TSFs were kept rigid with the frozen atoms during the processes of simulations. The LJ interactions were ˚ . The input evaluated with a spherical cut-off value of 13.0 A gas-phase fugacity for hydrogen was computed by the PengRobinson equation of state [47]. Each Monte Carlo step is consisted of three types of trial moves for H2 molecule including insertion of a new molecule, deletion of an existing

Fig. 2 The schemes of processes for constructing the TSF materials. By the diamond net topology, the TSF structures are constructed by replacing the C atom with tetrahedral silsesquixane and the C–C bond with phenyl, biphenyl, naphthalene or pyrene in diamond, respectively. The center large spheres denote the largest spherical cavities in these 3D TSFs

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molecule, or translation of an existing molecule. Maximum of 2 9 107 steps were implemented in a typical GCMC simulation. The first half steps were used for equilibration, and the subsequent half steps were used for ensemble averages. The veracity of the employed force field parameters and the simulation method were validated in our previous paper [23]. In many studies, the excess adsorbed amounts are often calculated from absolute adsorbed amounts to compare with the experiments. So we also calculated the excess adsorbed amounts (Nexc) based on the absolute adsorbed amounts (Nabs) obtained from the simulation results by Eq. (4), Nexc ¼ Nabs  qVp ;

average number of molecules in the simulation system, R is the ideal gas constant, and T is the temperature. Furthermore, equilibrium molecular dynamics simulations were carried out in the canonical ensemble (NVT) to probe the self-diffusion of the adsorbed H2 molecules in these TSF materials. The self-diffusivity (Ds) describes the motion of individual, tagged particles. In an isotropic threedimensional material, Ds is related to the mean-squared displacement (MSD) of tagged particles after time t by the Einstein relation [51, 52], E 1D r  ~ð0Þ r j2 Ds ¼ lim ð7Þ j~ðtÞ t!1 6t

ð4Þ

Here, the angular bracket indicates an ensemble average, and ~ðtÞ r is the position of a tagged H2 molecule at the time t. During the MD simulations, the frameworks were still kept rigid with frozen atoms and the 3D periodic boundary conditions were applied, as did in many other studies [53– 55]. The 2 9 2 9 2 to 4 9 4 9 4 simulation cells were adopted to insure at least fifty H2 molecules in the simulation box for each simulation. The same LJ potential parameters and the cut-off radius as GCMC simulations were used. The velocity Verlet algorithm [56, 57] was used to integrate Newton’s equations of motion. The initial configurations for MD simulations were taken from the snapshots saved during the GCMC simulations. The time step used in the MD simulations was taken as 1.0 fs. First, 50,000 steps were performed on the initial configuration to make the ensemble equilibration for each simulation. Then, a total of 2,000,000 steps were performed and the trajectory of the system was saved every 100 steps to subsequently calculate the self-diffusivity Ds by MSD. For each loading, up to 10 independent simulations were performed to estimate the statistical error. It was checked that MD simulations conducted in microcanonical (NVE) ensemble gave the equivalent results. The molecular dynamics simulations were implemented using the code LAMMPS [58].

where q is the density of the hydrogen under the thermodynamics conditions studied, and Vp denotes pore volume of the adsorbent. Here, q is calculated by the Peng– Robinson equation of state under the given temperature and pressure [47]. The Vp is estimated by the method proposed by Myers and Monson [48] who suggest that the pore volume of the porous material could be estimated by the amounts of helium molecules (Na) per unit mass adsorbent from GCMC simulation at low pressures (P) and room temperature (T0) with the following Eq (5), ð5Þ

Vp ¼ Na KB T0 =P;

where Kb refers to the the Boltzmann constant. The potential parameters of helium are the same as those in the work of Myers and Monson [48] and are also listed in Table 1. Meanwhile, with the method suggested by Frost et al. [49], the accessible surface areas of the TSFs were calculated using a numerical Monte Carlo integration. It was performed by ‘‘rolling’’ a probe molecule with a diameter equal to the Lennard-Jones r parameter of H2 molecule ˚ ) over every framework atom. The accessible (2.958 A surface area is highly dependent on the probe size used for measurement, and calculating the surface area in this manner provides the amount of area accessible to hydrogen molecules. In addition, the isosteric heat of adsorption (Qst) of H2 molecule was calculated by the Eq (6) [50], Qst ¼ RT 

hmN i  hmihN i hN 2 i

 hN i

2

Results and discussion First of all, we begin to discuss the optimized structures of four 3D TSF materials. Based on the basic chemical blocks shown in Fig. 1, the 3D TSFs were preliminarily designed and then optimized using the classical MM method. During the optimization, no symmetry restriction is imposed to

ð6Þ

;

where the angular bracket indicates an ensemble average, m is the potential energy of the adsorbed phase, N is the

Table 1 The LJ potential parameters for H2 molecule, helium molecule and the TSF atoms using in this study

˚) r(A e/kB (K)

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H2

C

H

O

Si

He

2.956 36.7

3.473 47.856

2.846 7.649

3.033 48.156

3.804 155.997

2.64 10.9

Struct Chem

modify the frameworks with rational bond lengths, angles, and cell parameters. The geometry optimization generated four well-converged structures bearing the cubic lattices without more symmetry within the error range of 0.01. In order to facilitate the subsequent molecular simulations, the cubic cells for all TSFs are adopted in the whole study. The detailed structural parameters of four TSFs are listed in Table 2 and the structural models are presented in Fig. 2. Analyzing the chemical formulas in Table 2, we can find that each TSF unit cell contains same number of silicon and oxygen atoms which form the tetrahedral silsesquioxanes blocks in these frameworks. Hence, the different cell lengths of the TSFs are attributed to the different lengths of their organic linkers. In this sense, the TSF materials here have the tunable pore size, and hence more TSF materials can be designed with desired pore sizes by rational choice of the organic linkers. As listed in Table 2, the four TSFs here all have very low density (0.19–0.39 g cm-3) and satisfy the sequence TSF-1 [ TSF-3 [ TSF-4 [ TSF-2. To the best of our knowledge, the porous materials with the lowest density are reported for COF-108 (0.17 g cm-3) and COF-105 (0.18 g cm-3) in experiment [25, 59]. Impressively, TSF-2 owns the lowest density of 0.19 g cm-3, which reflects that it has entered the lists of the porous materials with the lowest density. The pore size is indeed a great important index to judge the performance of porous materials. Here, the distances between the center of largest cavity and the nearest hydrogen atom in TSF-1 to TSF-4 are 7.46, 11.42, 9.35, ˚ , respectively. Taking account of the VDW and 10.35 A ˚ ) [60], the diameters of the radius of hydrogen atom (1.2 A spherical cavities of TSF-1 to TSF-4 shown in Fig. 2 are ˚, determined to be 12.53, 20.43, 16.31, and 18.29 A respectively. According to IUPAC notation [61], mesoporous materials have pore diameter between 20 and 500 ˚ , while the microporous and macroporous materials have A ˚ and greater than 500 A ˚, the pore diameters less than 20 A respectively. Clearly, the pore size of TSF-2 exceeds the ˚ for mesoporous material. In addition, lower limit of 20 A the pore volumes of these TSFs estimated by the adsorption amounts of helium molecules at the low pressure of 0–1 bar and the room temperature of 298 K are presented

in Table 2. It can be found that TSF-1 has the smallest pore volume (2.27 cm3 g-1) while TSF-2 possesses the largest one (4.96 cm3 g-1). At the same time, the pore volume of four TSFs obeys the sequence TSF-1 \ TSF-3 \ TSF-4 \ TSF-2, which is contrary to the sequence of the density. To gain a concrete image of porosity, the percent pore volume is also evaluated and it is 88, 93, 91, and 93 % for TSF-1 to TSF-4, respectively. Impressing, all four TSFs have high porosity comparable with COF-105 (88.22 %), COF-108 (88.84 %), and PAF-1 (77.60 %) [16, 25, 59], which are all high-porosity materials with excellent hydrogen storage properties. Besides the extraordinarily high porosity, these TSFs also have extremely high surface area which is one of the key factors for porous materials to store hydrogen efficiently [8]. To our knowledge, the highest surface area reported for MOF materials is claimed for MOF-210 [62], which has a BET surface area of 6,240 m2 g-1 and a Langmuir surface area of 10,400 m2 g-1. In addition, the highest surface area reported for COF materials is 4,210 m2 g-1 (BET) in COF-103 up to now [25]. Also, PAF-1 owns a very high BET surface area of 5,600 m2 g-1 and a Langmuir surface area of 7,100 m2 g-1 [16]. Obviously, the 3D TSFs reported here are on a par with the porous materials with the highest surface area, as judged by the accessible surface areas in Table 2. All these properties indicate the excellent hydrogen storage potential of these TSF materials. Both the gravimetric and volumetric H2 adsorption isotherms for four TSFs at 77 K were calculated up to 100 bar using the GCMC simulation, as depicted in Fig. 3. As shown in Fig. 3a, the absolute gravimetric H2 capacity increases gradually with the rise in H2 pressure. The maximum absolute gravimetric H2 capacity for TSF-1 to TSF-4 are, respectively, 16.86, 29.80, 22.27, and 25.65 wt% at 100 bar. Other than the absolute adsorption capacity, the excess H2 uptake achieves maximum at a relatively low pressure for four TSFs, namely, 11.13 wt% at 40 bar, 13.71 wt% at 60 bar, 12.32 wt% at 50 bar, and 12.65 wt% at 60 bar for TSF-1 to TSF-4, as shown in Fig. 3a. In addition, in contrary to the gravimetric capacity, TSF-1 exhibits the highest absolute (65.32 g L-1) and

Table 2 Chemical formula, unit cell parameters, molar mass (M), density (q), pore volume (Vp), and hydrogen accessible surface (S) of designed 3D TSF materials Materials

Chemical formula

a = b = c/ ˚ A

M/ g mol-1

q/ g cm-3

Vp/ cm3 g-1

S/ m2 g-1

TSF-1

C96H64O48Si32

23.12

2884.23

0.39

2.27

5264.39

TSF-2

C192H128O48Si32

33.10

4101.80

0.19

4.96

6544.03

TSF-3 TSF-4

C160H96O48Si32 C256H128O48Si32

28.28 33.02

3685.19 4870.50

0.27 0.22

3.37 4.15

5929.83 6169.71

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excess (43.14 g L-1 at 40 bar) volumetric H2 adsorption capacities, while TSF-2 possesses the lowest ones (absolute: 55.95 g L-1, excess: 25.74 g L-1 at 60 bar), as shown in Fig. 3b. This mainly ascribe to the fact that the TSF with small pores generally accommodate more dense H2 molecules, yet the TSF with large pores has more space and thus contains relatively dilute H2 molecules in its cavities, especially at the positions far from the framework atoms. For the practical application of hydrogen should be at the room temperature, we have calculated the hydrogen adsorption capacities in four TSF materials at the temperature of 298 K as well. As depicted in Fig. 4, both the gravimetric and volumetric H2 adsorption capacities increase linearly with the rising of H2 pressure. The slopes of these curves are the Henry law constants [63, 64]. The Henry’s law linear isotherm equation is n = KP, where n is

the adsorbed amounts per unit weight of adsorbent (wt%), P is the adsorbate gas pressure at equilibrium (bar), and K is the Henry law constant (wt% per bar). Here, we have performed linear fittings on the absolute gravimetric H2 adsorption isotherms of four TSFs at 298 K. Both the fitted equations and their corresponding degrees of linear correlation (r) are listed in Fig. 4a. The subscripts 1–4 in these equations denote the corresponding equations and degrees of linear correlation are for TSF-1 to TSF-4. The excellent linearity of these curves implies that the amount of adsorbed H2 molecules is relevant to the pore volume and the surface area. As shown in Fig. 4, the H2 adsorption capacities do assuredly obey the sequence TSF-1 \ TSF3 \ TSF-4 \ TSF-2 in the whole process. The highest absolute gravimetric (volumetric) H2 adsorption capacities for TSF-1 to TSF-4 are 2.23 wt% (8.64 g L-1), 4.28 wt%

Fig. 3 The calculated absolute and excess H2 adsorption isotherms in the 3D TSF materials at 77 K. a Gravimetric H2 adsorption isotherms and b volumetric H2 adsorption isotherms

Fig. 4 The calculated absolute and excess H2 adsorption isotherms in the 3D TSF materials at 298 K. a Gravimetric H2 adsorption isotherms and b volumetric H2 adsorption isotherms

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Struct Chem Table 3 The isosteric heat of adsorption (kJ mol-1) in four TSFs under pressure from 0.1 to 100 bar at both 77 and 298 K Pressure/bar TSF-1 TSF-2 TSF-3 TSF-4

0.1

0.5

1

2.5

5

7.5

10

20

30

40

50

60

70

80

90

100

77 K

4.99

4.62

3.55

3.92

3.76

3.39

3.24

3.42

4.44

4.45

4.26

4.08

4.84

3.79

4.09

4.26

298 K

3.65

4.20

4.95

4.85

4.38

4.54

4.40

4.23

4.74

4.20

4.55

4.60

4.50

4.93

5.12

3.91

77 K

2.80

3.92

3.96

3.18

3.19

2.97

2.21

2.55

2.66

2.34

2.40

2.36

3.06

2.09

2.68

3.16

298 K

2.55

4.26

3.42

3.76

3.25

3.58

3.36

3.52

3.54

3.63

3.43

3.95

3.73

3.01

4.17

1.83

77 K

4.79

4.49

3.36

3.18

2.99

2.91

2.60

2.86

2.50

3.11

2.24

3.30

2.65

3.92

3.33

3.64

298 K

3.35

3.81

3.60

3.90

3.94

4.31

4.72

2.53

3.21

3.70

3.47

4.25

4.42

4.18

4.32

3.58

77 K

4.97

4.82

4.20

3.67

3.08

3.26

2.74

3.23

3.29

2.70

2.28

2.79

3.04

3.47

3.83

2.99

298 K

3.39

3.83

4.40

3.83

3.55

3.84

3.65

3.27

3.40

3.35

3.62

3.21

3.06

3.41

4.00

3.80

Fig. 5 The equilibrium snapshots of TSF-1 structure with adsorbed H2 molecules under a series of pressures

(8.03 g L-1), 3.07 wt% (8.31 g L-1), and 3.69 wt% (8.28 g L-1), respectively. Furthermore, the absolute volumetric H2 capacities for TSFs are all very low and are close to each other at 298 K, which verify that the amount of hydrogen adsorbed is mainly dependent of pore volume. For many studies the excess H2 adsorption capacity is always not mentioned at room temperature, since it is always very low. However, to make the investigation comprehensively, we also present the excess H2 adsorption capacities at room temperature in Fig. 4. As shown in Fig. 4, the maximum excess gravimetric H2 capacities are almost the same (0.4 wt%) for all TSFs, and the volumetric H2 capacities are all located in the range of 0.8–2 g L-1.

The very low excess capacities also state that the isosteric heat and surface area do contribute the lesser effect on the H2 adsorption in these materials at room temperature. Table 3 lists the isosteric heats of H2 adsorption under all pressures studied at 77 and 298 K. From the results, we can deduce that the adsorbed H2 molecules interact with TSF materials through weak VDW interaction. As a whole, the isosteric heat of H2 adsorption for four TSFs is in accordance with the order TSF-1 [ TSF-4 [ TSF-3 [ TSF-2 at both 77 and 298 K. This due to the fact the materials with small pores interact with H2 molecules more strongly. Some previous work have pointed that the value of isosteric heat larger than 15 kJ mol-1 is likely to be

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Struct Chem

and 298 K. The results reveal that Ds for H2 molecules in four TSF materials increases with the rise of pore space, that is, with a sequence TSF-2 [ TSF-4 [ TSF-3 [ TSF-1. This is because the framework atoms of TSF with smaller pores generate relatively the larger steric hindrance effects on the H2 diffusion. On the other hand, the self-diffusivity for H2 molecules in each TSF decreases gradually with the rise in H2 pressure, which is caused by the steric hindrance effects among the adsorbed H2 molecules. In addition, the Ds at 298 K are about one order of magnitude larger than Ds at 77 K, which reveals the difficulty of H2 diffusion at 77 K compared to 298 K.

Conclusions

Fig. 6 The H2 pressure dependence of self-diffusivity, Ds, for H2 molecules in four 3D TSF materials at a 77 K and b 298 K

needed for practical hydrogen storage [65]. Unfortunately, the isosteric heats of H2 are all very low in these TSFs, which is disadvantage for hydrogen storage. So some methods must be adopted to enhance the isosteric heat of H2, which is being carried out in the subsequent studies. In order to understand the adsorption behaviors of H2 molecules in these frameworks at a molecular level, we examined the snapshots of these TSF structures with H2 molecules adsorbed during the simulation processes. Here, we typically show several snapshots of TSF-1 with adsorbed H2 molecules under a series of pressures in Fig. 5. From these snapshots, we can conclude that the H2 molecules are first adsorbed near the organic linkers at low pressure. Then they occupy the corners of the framework as the increase in H2 pressure. At last, they begin to accommodate the cavities far from the frameworks. Finally, Fig. 6 depicts the pressure dependence of the self-diffusivity for H2 molecules in four TSFs at both 77

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In conclusion, four novel 3D porous TSF materials have been computationally designed and proposed as hydrogen storage media. The calculated pore sizes reveal that TSF-2 has leaped into the lists of mesoporous materials, while other TSFs all belong to the microporous materials. Among the four TSFs, TSF-2 possesses the significantly high gravimetric hydrogen uptakes at both 77 and 298 K, which mainly benefit by its low density, large pore volume, and high surface area. In addition, the linear H2 adsorption isotherms reveal that amount of H2 molecules adsorbed is be mainly connected with the pore volume at room temperature. Although the octahedral silsesquioxane-based 3D porous materials have been reported in experiment [31– 33], how to synthesize the tailored tetrahedral silsesquioxanes-based porous materials proposed here still require further efforts in future. It is hoped that knowledge gained from this study will motivate some inspirations for developing the corresponding experiments. Acknowledgments H. Zhang acknowledges financial support from the National Natural Science Foundation of China (NSFC. Grant No. 11074176 and NSAF. Grant No. 10976019) and the support from Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100181110080). X.L. Cheng acknowledges financial support from the National Natural Science Foundation of China (NSAF. Grant No.11176020). The computational resources utilized in this research were provided by Shanghai Supercomputer Center.

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