Physisorption of molecular hydrogen on carbon nanotube with vacant defects Gang Sun, Jirawat Tangpanitanon, Huaze Shen, Bo Wen, Jianming Xue, Enge Wang, and Limei Xu Citation: The Journal of Chemical Physics 140, 204712 (2014); doi: 10.1063/1.4879656 View online: http://dx.doi.org/10.1063/1.4879656 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/20?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydrogen adsorption/desorption in functionalized single-walled carbon nanotubes AIP Conf. Proc. 1447, 253 (2012); 10.1063/1.4709975 On the hydrogen storage capacity of carbon nanotube bundles Appl. Phys. Lett. 95, 163111 (2009); 10.1063/1.3253711 Prediction of energetically optimal single-walled carbon nanotubes for hydrogen physisorption Appl. Phys. Lett. 95, 013116 (2009); 10.1063/1.3158597 Quantum dynamics of hydrogen interacting with single-walled carbon nanotubes J. Chem. Phys. 130, 064701 (2009); 10.1063/1.3068411 High pressure saturation of hydrogen stored by single-wall carbon nanotubes Appl. Phys. Lett. 84, 918 (2004); 10.1063/1.1646728

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THE JOURNAL OF CHEMICAL PHYSICS 140, 204712 (2014)

Physisorption of molecular hydrogen on carbon nanotube with vacant defects Gang Sun,1,2 Jirawat Tangpanitanon,3 Huaze Shen,1,2 Bo Wen,1,4 Jianming Xue,5,6 Enge Wang,1,2 and Limei Xu1,2,a) 1

International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China Collaborative Innovation Center of Quantum Matter, Beijing, China 3 University of Cambridge, Cambridge, Cambridgeshire CB2 1TP, United Kingdom 4 Beijing Computational Science Research Center, Heqing Street, Haidian District, Beijing 100084, China 5 State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China 6 Center for Applied Physics and Technology, Peking University, Beijing 100871, China 2

(Received 14 March 2014; accepted 8 May 2014; published online 30 May 2014) Physisorption of molecular hydrogen on single-walled carbon nanotubes (SWCNTs) is important for its engineering applications and hydrogen energy storage. Using molecular dynamics simulation, we study the physisorption of molecular hydrogen on a SWCNT with a vacant defect, focusing on the effect of the vacant defect size and external parameters such as temperature and pressure. We find that hydrogen can be physisorbed inside a SWCNT through a vacant defect when the defect size is above a threshold. By controlling the size of the defects, we are able to extract hydrogen molecules from a gas mixture and store them inside the SWCNT. We also find that external parameters, such as low temperature and high pressure, enhance the physisorption of hydrogen molecules inside the SWCNT. In addition, the storage efficiency can be improved by introducing more defects, i.e., reducing the number of carbon atoms on the SWCNT. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4879656] I. INTRODUCTION

Since carbon nanotube (CNT) was discovered in 1991,1 a large number of studies have been carried out due to its unique physical,2–5 optical,6 and mechanical properties.7–9 Recently, CNT has been considered for hydrogen storage due to the need for green sources of energy. Since the study on hydrogen storage in SWCNTs by Dillon et al.,10 the adsorption of diverse gases on various types of CNTs, i.e., single- or multiwalled, closed- or open-ended,11–14 has become an active research field. Different mechanisms have been proposed,15–18 among which physisorption is believed to be one of the mechanisms for storage in SWCNTs.17–22 Recently, various molecular simulation techniques have been employed to understand the hydrogen physisorption on CNTs18, 23 and improve the storage efficiency with a target of mass ratio 6.5 wt. % specified by the US Department of Energy. Many of these studies mainly focus on storage in ideal carbon nanotubes. However, in reality, CNTs are barely found in the form of perfect structures due to the presence of topological defects,24 specifically vacant defects, which are commonly present during the formation of carbon nanotubes (CNTs) and also likely to occur due to the stress generated during synthesis.25 Therefore, the study of physisorption of hydrogen inside the SWCNT with vacant defects is of crucial importance for the understanding of hydrogen storage. In this work, using molecular dynamics (MD) simulations, we study the adsorption of hydrogen molecules inside SWCNTs with vacant defects, which are obtained by taking a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2014/140(20)/204712/6/$30.00

out carbon atoms from the SWCNT surface. Specifically, we focus on the effects of vacant defect size, temperature, and pressure on the adsorption of hydrogen molecules inside the SWCNTs. We find that hydrogen can be physisorbed inside the SWCNT through a vacant defect when the defect size is above a threshold. The storage of hydrogen molecules and its selection from a gas mixture is applicable by controlling the size of the defect. Low temperature and high pressure enhance the physisorption of hydrogen molecules inside the SWCNT. In addition, the storage efficiency can be improved by introducing more defects, i.e., by reducing the number of carbon atoms on the SWCNT. This paper is organized as follows. Section II contains the simulation details. Section III presents the effect of vacant size and external parameters, such as temperature and pressure, on the hydrogen physisorption in the SWCNT as well as the selection of hydrogen molecules from a gas mixture. Section IV contains the brief summary.

II. METHOD

Molecular dynamics (MD) simulations are performed to study the hydrogen adsorption in singled walled carbon nanotubes (SWCNTs) with vacant defects. An armchair (10, 10) SWCNT with diameter R = 6.75 Å and length L = 24.43 Å is employed in our study. The vacant defect on each SWCNT is obtained by taking out NV carbon atoms from the surface, where NV is defined as the size of the vacant defect. The SWCNT with a vacant defect is then relaxed to obtain a configuration at its potential-energy local-minimum.

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TABLE I. Lennard-Jones parameters.

Pair

 (kcal/mol)

σ (Å)

C-H H-H N-N C-N H-N

0.06296 0.07172 0.19069 0.10252 0.11695

3.19 2.96 3.56 3.49 3.26

The initial configuration contains N gas molecules (e.g., H2 ) randomly distributed outside the SWCNT. The interaction between atoms are characterized by two types of interactions, that is the intra-molecule interactions characterizing the covalent bonds, such as H-H interaction for H2 and N − N interaction for N2 , and the inter-molecule interactions without covalent bond, such as van der Waals interactions between two atoms, e.g., carbon-hydrogen (C-H), carbon-nitrogen (C-N), hydrogen and hydrogen (H-H), hydrogen-nitrogen (H-N), and nitrogen-nitrogen (N-N). The inter-molecule interactions are described by the LennardJones potential   σ 12 σ6 − 6 , (1) U (rij ) = 4 rij12 rij where σ and  are the size and energy parameters, respectively, rij is the distance between two atoms. The parameters for the intra-molecule interactions are listed in Table I.26 The inter-molecule interactions between two atoms within each molecule, e.g., H2 , N2 , are modeled by harmonic springs with parameters listed in Table II. A cutoff distance of rc = 18 Å (5 times larger than the largest σ ) is used in the calculation of pair interactions with the LAMMPS software.27 We note that the features described in this work will not be essentially affected by a more involved force field.28 We also note that there are many studies employing ab initio approaches,29–34 which have advantages in obtaining the static properties of physisorption, e.g., accurately calculating the binging energy, the coverage and the degrees of structural relaxation of H2 physisorbed on the nanotube. However, in terms of the dynamic process of the uptake and release of several hundred hydrogen molecules, the ab initio method is very expensive and time consuming. In this case, simple models as mentioned above are more suitable. The SWCNT is kept rigid within a periodic simulation box of size Lx × Ly × Lz , where Lx = Ly = 48.87 Å and Lz = 24.43 Å [Fig. 1]. The lengths in x-, y-, and z-directions are chosen such that they are sufficiently large to eliminate the nearest neighbor H2 − H2 interactions with periodic im-

H-H bond N-N bond

ages. Especially, the length of Lz is to make sure that it is sufficiently large to avoid periodic reflections in z-direction. Molecular dynamics simulations are performed using NVTensemble. Each MD trajectory is equilibrated for long enough time (60-100 ns) with a time step of 1 fs. For the characterization of the physisorption of gas molecules, the distribution of gas molecules inside and outside the SWCNT is calculated by dividing the system into a series of cylinders with a thickness of 0.5 Å coaxial to the axis of the SWCNT. The possibility of finding one hydrogen molecule in the range of r ∼ r + r is calculated as N (r) , (2) N r where N(r) is the number of hydrogen molecules in the range of r ∼ r + r. During the process of physisorption, the adsorption energy Eb of a gas molecule is also calculated when the molecule passes along the center line of the vacant defect. It is defined as P (r) =

Eb = ESW CNT +H2 − ESW CNT − EH2 ,

(3)

where ESW CNT +H2 is the total potential energy when H2 goes through the vacant defect into the SWCNT, EH2 and ESW CNT are the energy of H2 and SW CN T , respectively. III. RESULTS A. The size effect of the vacant defect on physisorption

TABLE II. Harmonic springs parameters.

Harmonic spring

FIG. 1. Snapshot of an initial configuration of the simulated system. Hydrogen molecules (colored in purple) distribute randomly in space outside the SWCNT with a vacant defect. The vacant defect is denoted by the carbon atoms (colored in cyan) on the edge of vacant defect. The nanotube is placed along z-direction. The green line is the center line of the nanotube.

Spring constant (k) (kcal mol−1 Å−2 )

r0 (Å)

104.2 3227.3

0.752 1.098

By performing MD simulations on a system consisting of 156 hydrogen molecules and a SWCNT with the defect size NV , we first investigate the size effect on the distribution of physisorbed gas molecules. Figure 2(a) shows the number of molecules, Nin , physisorbed inside a SWCNT with a vacant

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0.3

25

(a)

NV=4 NV=13

P3 Distribution

20

Nin

15 10

0.2

0.1

P1

5 0 3

4

5

6

7

8

9 10 11 12 13 14 15 16

NV 4

-1

Eb (Kcal mol )

3

(b)

NV=7 NV=9

1 0 -1 -2 2

4

6

8

10 12 14 16

0 0

2

4

6

8 10 12 14 16 18 20 22 24

r (Å)

2

-3 0

P2

18 20

r (Å) FIG. 2. (a) Dependence of H2 physisorption on the size of vacant defect at T = 300 K. (b) The energy needed to move a hydrogen molecule to a distance r away from the axis of the SWCNT with different defect sizes NV . H2 is adsorbed only when the defect size is larger enough, e.g., NV ≥ 8, due to higher energy barrier to overcome for NV < 8 . We note that the number of H2 physisorbed inside the SWCNT is independent of the size of a vacant defect.

defect of size, NV , at T = 300 K. We find that when the vacant defect size is small, e.g., NV < 8, there is no hydrogen molecule inside the SWCNT. When the defect size is large, e.g., NV ≥ 8, hydrogen molecules are able to be physisorbed inside the SWCNT. Thus, a critical defect size, NVC (∼ 8 in this study), exists below which physisorption inside the SWCNT is forbidden. To explain the existence of such a critical defect size on the physisorption, Figure 2(b) shows the adsorption energy Eb as a function of the distance r away from the axis of the SWCNT. For a small defect (e.g., NV = 7 < NVC ), Eb first decreases and then reaches a minimum at r ∼ 8 Å, when the hydrogen molecule is moved from the distance r > 8 towards the SWCNT. As r further decreases, Eb increases sharply and reaches a maximum at r ∼ 6 Å, which is the energy barrier for a hydrogen molecule to overcome to enter the SWCNT. For a larger defect (e.g., NV = 9 > NVC ), Eb follows a similar trends as above. However, Eb is negative, indicating that no extra cost is needed for a hydrogen molecule to enter the SWCNT. Thus, increasing the vacant defect on the SWCNT lowers the energy barrier for physisorption of hydrogen molecules. The size effect can also be seen from the spatial distribution of hydrogen molecules inside and outside the SWCNT. Figure 3 shows the spatial distribution of hydrogen molecules at T = 100 K. For the small defect, NV = 4, hydrogen molecules are preferentially distributed only outside of the

FIG. 3. Spatial distribution of H2 for a SWCNT with a defect of different sizes at T = 100 K. The vacant-defect size determines the distribution of hydrogen inside, but has very minor effect on the storage outside the SWCNT. For instance, for NV = 4, no H2 exists inside, yet the distribution outside the SWCNT is similar to that for NV = 13.

SWCNT at a distance r ∼ 10 Å. For the larger defect, NV = 13, the hydrogen molecules distribute at several preferential locations, P1 , P2 , and P3 , as shown in Figure 3, which are along the axis of the SWCNT at r ∼ 0 Å, a cylindrical shell inside the SWCNT with r ∼ 3 Å, and a cylindrical shell outside the SWCNT with r ∼ 10 Å, respectively. The peak P1 indicates that hydrogen molecules inside the SWCNT form a chain along the axis of the SWCNT at r ∼ 0 Å. We note that at T = 100 K, the preferential locations of the physisorbed site outside the SWCNT is the same for NV = 13 and NV = 4. This indicates that the vacant-defect size affects the storage of hydrogen inside, but has very minor effect on the storage outside the SWCNT. B. Temperature and pressure effect on physisorption

We next investigate the effect of external parameters, such as temperature and pressure, on the physisorption. For the large defect NV = 13, as temperature increases, hydrogen molecules disperse to larger distance and the preferential arrangement becomes weaker (see Fig. 4(a)). For instance, at high temperatures, e.g., T = 300 K, the hydrogen molecules distribute uniformly outside the SWCNT. We note that, for small defects (NV < NVC ), the spatial distribution of molecular hydrogen physisorbed outside the SWCNT changes with temperature in the same way as that in Figure 4(a), even though no particles are physisorbed inside the SWCNT. Figure 4(b) shows the dependency of the hydrogen storage inside the SWCNT on the size of a vacant defect. As temperature increases, the number of hydrogen molecules inside the SWCNT decreases; however, the number of hydrogen molecules stored inside the SWCNT is rather independent of the defect sizes. This implies that temperature is a key factor in the process of hydrogen storage, that is, hydrogen molecules can be storaged at low temperature and released at high temperature. We also investigate the effect of pressure on hydrogen storage in a SWCNT with a vacant defect,26, 35 specifically, NV = 9 at T = 300 K. By varying the density of H2 , we investigate the number of H2 physisorbed, Nin , in the SWCNT.

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(a)

60

T=100K T=200K T=300K

P3

H2 N2

50 40

0.2

heating Nin

P2

30 20

0.1

10

P1

T=95K

0 0 0

2

4

6

8 10 12 14 16 18 20 22 24

0

100

200

300

66

NV=8 NV=9 NV=10 NV=11 NV=12 NV=13 NV=14 NV=15

(b)

55

Nin

44 33

500

C. Selection of hydrogen molecules from a gas mixture

90 120 150 180 210 240 270 300 330

T (K) FIG. 4. Temperature dependence of the spacial distribution of hydrogen molecules (a) and the number of H2 physisorbed (Nin ) inside a SWCNT with different size of a defect NV (b). The number of H2 inside the SWCNT decreases with increasing temperature, indicated by the drop in the magnitude of peaks for higher temperatures. At the same temperature, the amount of H2 adsorbed inside the SWCNT is independent of the vacant defect size for NV > NVC .

As shown in Figure 5, Nin increases rapidly as pressure increases from P = 0 MPa to 30 MPa and gradually saturates at P > 30 MPa. This indicates that high pressure enhances the storage of hydrogen. We note that for a system of 156 hydrogen molecules, the gas pressure we obtain is about 14 MPa, consistent with a rough estimation of pressure(11 MPa) for 156 ideal gas molecules, which is a reasonable pressure range for real applications.

Particular gaseous mixtures, e.g., H2 and N2 , are common in industry and experiment. The storage of hydrogen molecules in the SWCNT requires the selection of hydrogen molecules from the mixtures.35 We next investigate the selection of hydrogen molecules from the gas mixture with N2 for the SWCNT having a vacant defect of size NV = 9 at T = 300 K. The number of molecules adsorbed inside the SWCNT is presented in Figure 6. It shows that no nitrogen molecule but hydrogen molecules exists inside the SWCNT, thus the SWCNT with vacant defects naturally selects hydrogen molecules from the gas mixture. This selection can be explained by the behavior of the potential energy, Eb , as a function of the distance r from the center of mass of molecule to the axis of the SWCNT. Figure 7 shows that at the defect site, i.e., at R = 6.75 Å, Eb exhibits a positive energy barrier for nitrogen molecules but a negative energy barrier for H2 . Thus, the negative energy barrier allows H2 to enter the SWCNT through a vacant defect without extra energy cost, while the positive energy barrier for N2 disfavors the physisorption of N2 inside the SWCNT. Therefore, the SWCNT with vacant defects can be used to extract smaller molecules (e.g., H2 )

10

50

H2 N2

8 -1

Eb (Kcal mol )

40

Nin

30 20

6 4 2 0 -2 -4

10 0 0

600

FIG. 6. Temperature dependence of H2 physisorption inside a SWCNT for a mixture of H2 and N2 . Clearly, N2 is excluded from the SWCNT, thus can be used to purify and store H2 . We note that the physisorption of H2 has a maximum at T = 95 K.

22 11 60

400

T (K)

r (Å)

-6 0

30

60

90

120

150

2

4

6

8

10 12 14

16

18 20

r (Å)

P (MPa) FIG. 5. Pressure dependence of the number H2 physisorbed (Nin ) inside the SWCNT with a vacant defect of size NV = 9 at T = 300 K. Physisorption is preferred at high pressures.

FIG. 7. Comparison of relative potential energy Eb of a SWCNT interacting with hydrogen and nitrogen molecules. Molecules are moved along a straight line in xy plane, perpendicular to the axis of SWCNT, through the center of vacant defect.

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(a) N2

T=80K T=95K T=200K

P1

0.4 0.3

P2

0.2 0.1 0 0

2

4

6

8 10 12 14 16 18 20 22 24

r (Å) 0.4

(b) H2 0.3

Distribution

P2

P4

P5

0.2

0.1 P 1 0 0

P3 2

4

6

8 10 12 14 16 18 20 22 24

r (Å) FIG. 8. Temperature dependence of spatial distribution of N2 (a) and H2 (b) for the SWCNT with a defect of size NV = 9. For N2 , two peaks located at r ∼ 10 Å and r ∼14 Å are observed in the spatial distribution, while for hydrogen molecules, there are five peaks located at r ∼ 0, 3.5 Å, 10 Å, 14 Å, 17 Å, are observed. The different location of peaks (e.g., r < 8 Å) can be used to separate the mixture of N2 and H2 .

from a mixture and efficiently store the selected H2 inside at an optimized temperature (e.g., T = 95 K, see Figure 6 for the case of NV = 9). The selection of H2 from the mixture can also be seen from the spatial distribution of N2 and H2 at different temperatures [Fig. 8]. N2 are distributed outside the SWCNT [Fig. 8(a)], indicated by two preferential peaks located at r ∼ 10 Å and r ∼ 14 Å, respectively. On the other hand, H2 can be stored inside the SWCNT, indicated by two peaks located at r ∼ 0 (P1 ) and r ∼ 3.5 Å (P2 ), respectively. Besides the preferential distribution inside the SWCNT, hydrogen molecules also show other preferential distribution outside. For instance, at T = 80 K, three peaks located at r ∼ 3.5 Å (P2 ), ∼14 Å (P4 ), and ∼17 Å (P5 ) are observed, each of which corresponds to one preferential cylindrical shell occupied by H2 . As temperature changes, the number of H2 molecules inside the SWCNT changes, indicated by the change in the magnitude of each peak. At T = 95 K, the magnitude of peak P1 and P2 are larger than other temperatures below or above, indicating that the storage capacity inside the SWCNT is a maximum at T = 95 K, consistent with the results shown in Figure 6. IV. PHYSISORPTION ON SWCNT WITH MULTIPLE VACANT DEFECTS

The efficiency of hydrogen storage is an important factor to be considered in green energy storage. The higher the

FIG. 9. Illustration of unfolded SWCNTs with one defect and multi-defects. (a) One defect of size NV = 9, and (b) 12 defects of size NV = 6 and 3 defects of size NV = 9. The horizontal and the vertical axes represent θ and z in the cylindrical coordinate, respectively, where the SWCNTs are coaxial with the z-axis. We note that the defect pattern in case (b) is the densest possible defect pattern since adding more defects will result in overlapping between defects.

weight ratio, the more efficient the energy storage is. For instance, more hydrogen with less storage material is the goal of hydrogen storage. Next, we discuss the hydrogen physisorption of hydrogen on a SWCNT with more than one defect, that is, increasing the weight ratio by reducing the amount of storage materials. Here, we consider an extreme case, e.g., the SWCNT has 15 holes on the SWCNT among which 12 holes are of size NV = 6 and 3 are of size NV = 9 [Figure 9(b)]. We compare its physisorption to that with a single defect of size NV = 9 [Figure 9(a)]. We note that the former one is an extreme case in the sense that additional defects lead to overlapping with the existing defects. The adsorption ratio, defined as the ratio of the number of H2 inside the SWCNT with respect to its total number, is studied at P = 14 MPa. The time evolution of physisorption is present in Figure 10. After equilibration for 1 ns at T = 100 K, 35% (±1%) of H2 is physisorbed inside the SWCNT. As shown in Figure 10(a), the adsorption ratio is the same for the SWCNT with either one defect or multi-defects. This suggests that introducing extra defects does not affect the capacity of the hydrogen adsorption. However, due to the reduction in the weight of the SWCNT, which is now reduced by 24.8% compared to that of the perfect SWCNT, the mass ratio in this case is 3.04 ± 0.07 wt. % at T = 100 K and at 1.19 ± 0.26 wt. % at T = 300 K. Compared to the singledefect case, the mass ratio is improved by 30% at T = 100 K and 27% at T = 300 K. The portion of adsorbed H2 decreases with temperature as expected due to an increase in thermal fluctuations.

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11274012, 91021007, and 11174006) and the National Basic Research Program of China (973 Program) (Grant No. 2012CB921404) for financial supports.

42 36 30

single defect multiple defects

24

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18 12 6 0 0

1 S.

2

4

6

8

10 12 14 16

18 20

t (ns) FIG. 10. Comparison of the H2 physisorption for SWCNTs with one defect and multi-defects at temperatures T = 100 K. The amount of H2 adsorbed inside the SWCNT is the same for one defect and multi-defect. However, due to the reduction in weigh, the weight ratio for energy storage is largely enhanced for the latter case.

V. SUMMARY

To summarize, we study the physisorption of hydrogen molecules on a SWCNT with vacant defects. We systematically explore the defect size and external parameter effects on the hydrogen storage inside the SWCNT. We find that H2 can be physisorbed inside a SWCNT through a vacant defect when the defect size is above a threshold, below which the energy barrier is high thus prevents H2 to enter the SWCNT. Therefore, the storage of hydrogen is applicable by controlling the size of defect on the SWCNT. Specifically, the SWCNT with an appropriate vacant defect can be used to extract H2 from a gas mixture and store H2 inside. We successfully extract H2 from a binary mixture of H2 and N2 , and store H2 inside the SWCNT. By lowering temperature or increasing pressure, one can improve the hydrogen storage capacity, which is a maximum at T = 95 K. Finally, we find that the storage efficiency can be improved by introducing multiple defects to the SWCNT. The percentage of adsorbed H2 for a single defect is close to that for multiple defects at T = 100 K. However, due to a reduction in the mass of the SWCNT, the adsorption of the latter has a 30% higher hydrogen-to-tube weight ratio. As we now know from experiment, generating multiple vacant defects can be rather precisely controlled by bombardment with heavy ions in CNTs and graphene sheets,36–40 such as cutting and patterning graphene using focused ion beams with a high spatial resolution.39, 40 Therefore, our study not only provides a way to extract and store hydrogen which may be applied to industry and laboratory process, but also provide a practical way to improve the storage capacity of hydrogen inside the SWCNT by introducing vacant defects, that is, by reducing carbon atoms. ACKNOWLEDGMENTS

We thank the National Science Foundation of China (NSFC) (Grant Nos. 11290162/A040106, 10974238,

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Physisorption of molecular hydrogen on carbon nanotube with vacant defects.

Physisorption of molecular hydrogen on single-walled carbon nanotubes (SWCNTs) is important for its engineering applications and hydrogen energy stora...
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