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Grand canonical Monte Carlo simulation of hydrogen physisorption in single-walled boron nitride nanotubes
International Journal of Hydrogen Energy 32 (2007) 3402 – 3405 www.elsevier.com/locate/ijhydene
Grand canonical Monte Carlo simulation of hydrogen physisorption in single-walled boron nitride nanotubes Jinrong Cheng a,∗ , Libo Zhang a,b , Rui Ding a , Zhenfeng Ding a , Xiao Wang a , Zhi Wang a a School of Physics and Material Science, Anhui University, Hefei 230039, China b Department of Mathematics and Physics, Hefei College, Hefei 230022, China
Received 11 June 2006; received in revised form 26 February 2007; accepted 27 February 2007 Available online 1 May 2007
Abstract The properties of hydrogen physisorption in single-walled boron nitride nanotubes (SWBNNTs) and single-walled carbon nanotubes (SWCNTs) are investigated in detail by the grand canonical Monte Carlo simulations. A great deal of our computational results show that the hydrogen storage capacity of SWBNNTs is slightly larger than the capacity of SWCNTs at any time when their diameters were equal and in the same conditions, and indicate that the hydrogen storage capacity of SWBNNTs at 293 K and 10 MPa with a diameter of more than 30 nm or at 293 K and 15 MPa with a diameter of more than 25 nm could exceed the 2010 goal of 6 wt%, which is presented by the U.S. Department of Energy. In addition, these results are discussed in theory. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Single-walled boron nitride nanotubes; Physisorption; Hydrogen storage; Grand canonical Monte Carlo simulation
1. Introduction Since their discovery by Iijima in 1991 [1], carbon nanotubes (CNTs) have been found to be new suitable materials for hydrogen storage [2–7]. However, most experimental and theoretical results indicate that the hydrogen storage capacity of CNTs and CNT arrays at room temperature and moderate pressure cannot reach the U.S. Department of Energy (DOE) targets for vehicular fuel cells. The DOE 2010 targets are reported to be 6 wt% (the ratio of stored hydrogen weight to system weight) [8]. In 1994, Rubio et al. predicted the existence of boron nitride nanotubes (BNNTs) [9,10]. Before long, Chorpa et al. [11] synthesized the BNNTs for the first time in 1995. Based on the current theoretical and experimental results, the energy for hydrogen storage in BNNTs is less than that in CNTs [12], and the diameters of BNNTs can reach hundreds of nanometers [13,14], which are much more than the diameters of CNTs, and the stability of BNNTs’ chemical properties are better [15]. Therefore, BNNTs would be the better candidate for hydrogen storage. ∗ Corresponding author. Tel.: +86 551 510 7284; fax: +86 551 510 7237.
E-mail address: [email protected] (J. Cheng).
In order to compare the hydrogen storage capability of BNNTs with that of CNTs numerically, we adopted the grand canonical Monte Carlo (GCMC) method [7] to research the properties of hydrogen physisorption in single-walled boron nitride nanotubes (SWBNNTs). The hydrogen storage capacity (weight percent) of SWBNNTs at room temperature and moderate pressure as a function of the tube diameter, tube length, tube chirality and pressure is drawn, which is compared with that in single-walled carbon nanotubes (SWCNTs). 2. GCMC simulation details Lennard–Jones (LJ) potential is adopted to model the interactions between two particles. In its simplest form, it is given by (rij ) = 4ij [(ij /rij )12 − (ij /rij )6 ],
(1)
where ij and ij are the energy and length parameters in LJ potentials, and rij denotes the distance between the centers of particle i and particle j. The parameter ii of nitrogen, boron, and carbon atom and hydrogen molecule is 72.888, 47.764, 28.2 and 36.7 kB , and ii is 0.3365, 0.3453, 0.34 and 0.2958 nm,
0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.02.037
J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3403
All the parameters are reduced to adapt for computer simulation. The reduced length, mass, energy, temperature and chemical potential are L∗ = L/H , m∗ = m/mH , E ∗ = E/H , T ∗ =T k B /H and ∗ =/H , respectively. The other reduced parameters are determined by the formulary about reduced units in computer simulations [20]. In this article, the simulation iterations are 5 × 107 . The first 2.5 × 107 iterations are used to set up equilibrium of the system, and the last ones are available for calculating ensemble average values of thermodynamics parameters. 3. Results and discussion (1) By fixing temperature and length of nanotubes, and varying pressure and tube diameter, we can draw a tuft of adsorption isotherms of hydrogen physisorption in SWBNNTs and SWCNTs. Some of adsorption isotherms of SWBNNTs and SWCNTs with the length of 4 nm at 293 K are shown in Fig. 2, which show that the hydrogen storage capacity of SWBNNTs and SWCNTs increase with increasing pressure. However, for
1.0
(15,15)SWBNNT
Fig. 1. GCMC simulation cell: (a) armchair SWBNNT; (b) zigzag SWBNNT.
respectively [16,17], where kB is Boltzmann constant. The parameters ij and ij between different particles are calculated by the following Lorentz–Berthelot rules. √ ij = i j , ij = (i + j )/2. (2)
Hydrogen/System wt%
(15,15) SWCNT
During GCMC simulation, SWBNNT with given diameter and length are taken as a simulation cell, as shown in Fig. 1. Three types of operations with equal probability are performed randomly in the GCMC simulation cell: displacement, creation and deletion [7]. The steps are repeated until the number of hydrogen molecules in the cell comes to the equilibrium. Considering the kinetic diameter of 0.289 nm for a molecule of hydrogen and the B–N length of 0.144 nm in a boron nitride hexagon, the tube wall can screen hydrogen molecules, that is, hydrogen molecules inside the tube cannot cross the tube walls. Furthermore, periodic boundary conditions are set on the open end of SWBNNT during displacement [20]. GCMC simulation of hydrogen physisorption in SWCNTs is similar to that in SWBNNTs [7].
0.4
0.0 0
2
4
6
8
10
12
14
16
12
14
16
Pressure/MPa 1.4 (22,22)SWBNNT
1.2
(22,22) SWCNT Hydrogen/System wt%
(3) (4)
0.6
0.2
Before GCMC simulation, Widom test particle method [18] and computing method of pressure for fluid systems with periodic boundary conditions [19] are used to determine the relations between the reduced chemical potentials and the bulk pressures (units in MPa), which are ∗BNNT = −71.85935 + 6.90146 × ln P , ∗CNT = −72.99359 + 7.36494 × ln P .
0.8
1.0 0.8 0.6 0.4 0.2 0.0 0
2
4
6
8
10
Pressure/MPa Fig. 2. Adsorption isotherm of hydrogen physisorption in SWBNNTs and SWCNTs at 293 K.
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J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3.5
(15,15) SWBNNT (26,0) SWBNNT
Armchair SWBNNT 3.0
0.8
Hydrogen/System wt%
H2/(H2+B+N) wt%
1.0
0.6 0.4
Armchair SWCNT
2.5 2.0 1.5 1.0
0.2 0.5
293K 0.0
293K, 10MPa
0.0
0
2
4
6 8 10 Pressure/MPa
12
14
16
0
2
4
6
8
10
12
14
16
Diameter of Nanotube/nm
Fig. 3. Influence of tube chirality on hydrogen physisorption in SWBNNTs.
Fig. 5. Influence of tube diameter on hydrogen physisorption in SWBNNTs and SWCNTs.
2.0 (15,15) SWBNNT (15,15) SWCNT
Hydrogen/System wt%
1.5
1.0
0.5
0.0 293K, 10MPa -0.5 2
4
6
8
10
Length of Nanotube/nm Fig. 4. Influence of tube length on hydrogen physisorption in SWBNNTs and SWCNTs.
physisorption the hydrogen storage capacity of SWBNNTs is more than that of SWCNTs at any time when their diameters are equal and have same conditions. (2) By fixing temperature, tube diameter and tube length, the influence of tube chirality on hydrogen storage capacity of SWBNNTs is investigated, and some of our results are shown in Fig. 3. We can see that the adsorption isotherms of hydrogen physisorption in armchair and zigzag SWBNNT at 293 K accord with each other. That is, the influence of tube chirality on hydrogen storage capacity of SWBNNTs can be ignored. (3) By fixing temperature, pressure and tube diameter, we investigate the dependence of hydrogen storage capacity of SWBNNTs and SWCNTs on the tube length. Some of our results are drawn in Fig. 4. The hydrogen storage capacity of SWBNNTs and SWCNTs almost hold the line when the tube length increases, that is to say, the axial distribution of hydrogen molecules stored in the nanotubes is approximately uniform. Therefore, only by changing of the tube length cannot vary the weight percent of hydrogen physisorption in SWBNNTs and SWCNTs.
(4) By fixing temperature, pressure and tube length, we study the influence of tube diameter on hydrogen storage capacity of SWBNNTs and SWCNTs, and some of our results are plotted in Fig. 5. It is clear that the hydrogen storage capacity of SWBNNTs and SWCNTs increase with the increasing diameter. This is because the space inside nanotube increases with the increasing diameter, and at the same time, the number of boron, nitrogen or carbon atoms also increases, which promote the exertion of the potential effect and the space effect of hydrogen storage in nanotubes [7]. These results indicate that increasing the tube diameter properly can improve the hydrogen storage capacity of SWBNNTs and SWCNTs effectively. (5) The above results (Figs. 2, 4 and 5) show that for physisorption the hydrogen storage capability of SWBNNTs is better than that of SWCNTs at room temperature and moderate pressure. In addition, we have calculated the weight percents of hydrogen physisorption in SWBNNTs and SWCNTs with different diameters of 20, 25 and 30 nm at 293 K and different pressures of 10 and 15 MPa, and obtained the computational results as shown in Table 1. From Table 1, we can see that the hydrogen storage capacity of SWBNNTs and SWCNTs at 293 K exceed the DOE 2010 goal of 6 wt% when the nanotube diameter is more than 30 nm (at 10 MPa) or 25 nm (at 15 MPa). Considering that it has difficulty in synthesizing SWCNT whose diameter is more than 25 nm at present, and the SWBNNT with a diameter of more than 30 nm has been synthesized [13], so, if the tube diameter can be controlled efficiently when we synthesize SWBNNTs, the total weight percent of hydrogen physisorption inside and outside (waiting for future work) SWBNNTs at room temperature and moderate pressure could exceed the commercial standard presented by the U.S. DOE. 4. Theoretic interpretation Our former work [7] indicated that the mechanism of hydrogen physisorption in nanotubes could be described by the potential effect and the space effect. The potential effect comes
J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3405
Table 1 Hydrogen storage capacity of SWBNNTs and SWCNTs with large diameters Type and diameter of nanotube
Hydrogen storage capacity (wt%)
D = 19.99 nm D = 19.94 nm D = 24.95 nm D = 24.96 nm D = 30.05 nm D = 29.97 nm
(145,145)BNNT; (147,147)CNT; (181,181)BNNT; (184,184)CNT; (218,218)BNNT; (221,221)CNT;
At 293 K and 15 MPa
4.43 4.18 5.41 5.16 6.38 6.13
5.85 5.63 7.11 6.96 8.39 8.20
more than 25 nm could exceed the DOE 2010 goal of 6 wt%. Therefore, BNNTs must be more suitable materials for hydrogen storage than CNTs.
100 0 -100 Potential(KB)
At 293 K and 10 MPa
References
-200 -300 -400 -500 -600
(15,15)SWBNNT
-700
(15,15) SWCNT
-800 -0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Distance from the tube center/nm
Fig. 6. LJ potential wells located in the SWBNNT and SWCNT.
from the interactions of nanotube-H2 and H2 .H2 while the space effect comes from the hollow configuration of nanotubes. When SWBNNTs and SWCNTs are of the same length and diameter, the discrepancies between hydrogen physisorption in SWBNNTs and SWCNTs mainly result from the interactions of nanotube-H2 . It is clear that the LJ potential wells’ depth and width of nanotube-H2 interactions in SWBNNTs are both more than the one in SWCNTs, as shown in Fig. 6, so that SWBNNTs possesses of better effectiveness for hydrogen storage. Based on our calculations, we find the lowest points in LJ potential wells of SWBNNTs and SWCNTs are 0.325 nm from the tube walls. Since nanotubes with smaller diameters restrain the exertion of the potential effect and the space effect, so their hydrogen storage capacity will be efficiently increased by the reasonable increase of the diameter of SWBNNTs and SWCNTs. 5. Conclusions A great deal of computer simulation results for hydrogen physisorption in SWBNNTs and SWCNTs indicate that the capacity of SWBNNTs is slightly larger than the capacity of SWCNTs at any time when their diameters were equal and in the same conditions, and show that the hydrogen storage capacity of SWBNNTs at 293 K and 10 MPa with a diameter of more than 30 nm or at 293 K and 15 MPa with a diameter of
[1] Iijima S. Helical microtubules of graphitic carbon. Nature 1991;354:56. [2] Dillon AC, Jones KM, Bekkedahl TA, Kiang CH, Bethune DS, Heben MJ. Storage of hydrogen in single-walled carbon nanotube. Nature 1997;386:377. [3] Liu C, Fan Y-Y, Liu M, Cong H-T, Cheng H-M, Dresselhaus MS. Hydrogen storage in single-walled carbon nanotubes at room temperature. Science 1999;286:1127. [4] Chen P, Wu X, Lin J, Tan KL. High H2 uptake by alkali-doped carbon nanotubes under ambient pressure and moderate temperatures. Science 1999;285:91. [5] Williams KA, Eklund PC. Monte Carlo simulations of H2 physisorption in finite-diameter carbon nanotube ropes. Chem Phys Lett 2000;320:352. [6] Lee SM, Lee YH. Hydrogen storage in single-walled carbon nanotubes. Appl Phys Lett 2000;76:2877. [7] Cheng JR, Yuan XH, Zhao L, Huang DC, Zhao M, Dai L. et al. GCMC simulation of hydrogen physisorption on carbon nanotubes and nanotube arrays. Carbon 2004;42:2019. [8] http://www1.eere.energy.gov/hydrogenandfuelcells/pdfs/h2_stor_mat_ work_proceedings.pdf , http://www1.eere.energy.gov/hydrogenandfuel cells/pdfs/freedomcar_targets_explanations.pdf. [9] Rubio A, Corkill JL, Cohen ML. Theory of graphitic boron nitride nanotubes. Phys Rev B 1994;49:5081. [10] Blasé X, Rubio A, Louie SG, Cohen ML. Stability and band gap constancy of boron nitride nanotubes. Europhys Lett 1994;28:335. [11] Chopra NG, Luyken RJ, Cherrey K, Crespi VH, Cohen ML, Louis SG. et al. Boron nitride nanotubes. Science 1995;269:966. [12] Oku T, Narita I. Calculation of H2 gas storage for boron nitride and carbon nanotubes studied from the cluster calculation. Physica B 2002;323:216. [13] Oku T. Synthesis and atomic structures of boron nitride nanotubes. Physica B 2002;323:357. [14] Xu LQ, Peng YY, Meng ZY, Yu WC, Zhang SY, Liu XM. et al. A Copyrolysis method to boron nitride nanotubes at relative low temperature. Chem Mater 2003;15:2675. [15] Kuno M, Oku T, Suganuma K. Encapsulation of cobalt oxide nanoparticles and Ar in boron nitride nanocapsules. Scr Mater 2001;44:1583. [16] Kang JW, Hwang HJ. Comparison of C60 encapsulations into carbon and boron nitride nanotubes. J Phys: Condens Matter 2004;6:3901. [17] Darkrim F, Levesque D. Monte Carlo simulations of hydrogen adsorption in single-walled carbon nanotubes. J Chem Phys 1998;19:4981. [18] Widom B. Topics in the theory of fluids. J Chem Phys 1963;39:2808. [19] Guo YK, Liang XG, Guo ZY. Methods of pressure for fluid systems with periodic boundary conditions in molecular dynamics. J Tsinghua Univ 2001;41:94 (in Chinese). [20] Allen MP, Tildesley DJ. Computer simulation of liquids. New York: Oxford University Press; 1987.
Grand canonical Monte Carlo simulation of hydrogen physisorption in single-walled boron nitride nanotubes Jinrong Cheng a,∗ , Libo Zhang a,b , Rui Ding a , Zhenfeng Ding a , Xiao Wang a , Zhi Wang a a School of Physics and Material Science, Anhui University, Hefei 230039, China b Department of Mathematics and Physics, Hefei College, Hefei 230022, China
Received 11 June 2006; received in revised form 26 February 2007; accepted 27 February 2007 Available online 1 May 2007
Abstract The properties of hydrogen physisorption in single-walled boron nitride nanotubes (SWBNNTs) and single-walled carbon nanotubes (SWCNTs) are investigated in detail by the grand canonical Monte Carlo simulations. A great deal of our computational results show that the hydrogen storage capacity of SWBNNTs is slightly larger than the capacity of SWCNTs at any time when their diameters were equal and in the same conditions, and indicate that the hydrogen storage capacity of SWBNNTs at 293 K and 10 MPa with a diameter of more than 30 nm or at 293 K and 15 MPa with a diameter of more than 25 nm could exceed the 2010 goal of 6 wt%, which is presented by the U.S. Department of Energy. In addition, these results are discussed in theory. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Single-walled boron nitride nanotubes; Physisorption; Hydrogen storage; Grand canonical Monte Carlo simulation
1. Introduction Since their discovery by Iijima in 1991 [1], carbon nanotubes (CNTs) have been found to be new suitable materials for hydrogen storage [2–7]. However, most experimental and theoretical results indicate that the hydrogen storage capacity of CNTs and CNT arrays at room temperature and moderate pressure cannot reach the U.S. Department of Energy (DOE) targets for vehicular fuel cells. The DOE 2010 targets are reported to be 6 wt% (the ratio of stored hydrogen weight to system weight) [8]. In 1994, Rubio et al. predicted the existence of boron nitride nanotubes (BNNTs) [9,10]. Before long, Chorpa et al. [11] synthesized the BNNTs for the first time in 1995. Based on the current theoretical and experimental results, the energy for hydrogen storage in BNNTs is less than that in CNTs [12], and the diameters of BNNTs can reach hundreds of nanometers [13,14], which are much more than the diameters of CNTs, and the stability of BNNTs’ chemical properties are better [15]. Therefore, BNNTs would be the better candidate for hydrogen storage. ∗ Corresponding author. Tel.: +86 551 510 7284; fax: +86 551 510 7237.
E-mail address: [email protected] (J. Cheng).
In order to compare the hydrogen storage capability of BNNTs with that of CNTs numerically, we adopted the grand canonical Monte Carlo (GCMC) method [7] to research the properties of hydrogen physisorption in single-walled boron nitride nanotubes (SWBNNTs). The hydrogen storage capacity (weight percent) of SWBNNTs at room temperature and moderate pressure as a function of the tube diameter, tube length, tube chirality and pressure is drawn, which is compared with that in single-walled carbon nanotubes (SWCNTs). 2. GCMC simulation details Lennard–Jones (LJ) potential is adopted to model the interactions between two particles. In its simplest form, it is given by (rij ) = 4ij [(ij /rij )12 − (ij /rij )6 ],
(1)
where ij and ij are the energy and length parameters in LJ potentials, and rij denotes the distance between the centers of particle i and particle j. The parameter ii of nitrogen, boron, and carbon atom and hydrogen molecule is 72.888, 47.764, 28.2 and 36.7 kB , and ii is 0.3365, 0.3453, 0.34 and 0.2958 nm,
0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.02.037
J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3403
All the parameters are reduced to adapt for computer simulation. The reduced length, mass, energy, temperature and chemical potential are L∗ = L/H , m∗ = m/mH , E ∗ = E/H , T ∗ =T k B /H and ∗ =/H , respectively. The other reduced parameters are determined by the formulary about reduced units in computer simulations [20]. In this article, the simulation iterations are 5 × 107 . The first 2.5 × 107 iterations are used to set up equilibrium of the system, and the last ones are available for calculating ensemble average values of thermodynamics parameters. 3. Results and discussion (1) By fixing temperature and length of nanotubes, and varying pressure and tube diameter, we can draw a tuft of adsorption isotherms of hydrogen physisorption in SWBNNTs and SWCNTs. Some of adsorption isotherms of SWBNNTs and SWCNTs with the length of 4 nm at 293 K are shown in Fig. 2, which show that the hydrogen storage capacity of SWBNNTs and SWCNTs increase with increasing pressure. However, for
1.0
(15,15)SWBNNT
Fig. 1. GCMC simulation cell: (a) armchair SWBNNT; (b) zigzag SWBNNT.
respectively [16,17], where kB is Boltzmann constant. The parameters ij and ij between different particles are calculated by the following Lorentz–Berthelot rules. √ ij = i j , ij = (i + j )/2. (2)
Hydrogen/System wt%
(15,15) SWCNT
During GCMC simulation, SWBNNT with given diameter and length are taken as a simulation cell, as shown in Fig. 1. Three types of operations with equal probability are performed randomly in the GCMC simulation cell: displacement, creation and deletion [7]. The steps are repeated until the number of hydrogen molecules in the cell comes to the equilibrium. Considering the kinetic diameter of 0.289 nm for a molecule of hydrogen and the B–N length of 0.144 nm in a boron nitride hexagon, the tube wall can screen hydrogen molecules, that is, hydrogen molecules inside the tube cannot cross the tube walls. Furthermore, periodic boundary conditions are set on the open end of SWBNNT during displacement [20]. GCMC simulation of hydrogen physisorption in SWCNTs is similar to that in SWBNNTs [7].
0.4
0.0 0
2
4
6
8
10
12
14
16
12
14
16
Pressure/MPa 1.4 (22,22)SWBNNT
1.2
(22,22) SWCNT Hydrogen/System wt%
(3) (4)
0.6
0.2
Before GCMC simulation, Widom test particle method [18] and computing method of pressure for fluid systems with periodic boundary conditions [19] are used to determine the relations between the reduced chemical potentials and the bulk pressures (units in MPa), which are ∗BNNT = −71.85935 + 6.90146 × ln P , ∗CNT = −72.99359 + 7.36494 × ln P .
0.8
1.0 0.8 0.6 0.4 0.2 0.0 0
2
4
6
8
10
Pressure/MPa Fig. 2. Adsorption isotherm of hydrogen physisorption in SWBNNTs and SWCNTs at 293 K.
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J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3.5
(15,15) SWBNNT (26,0) SWBNNT
Armchair SWBNNT 3.0
0.8
Hydrogen/System wt%
H2/(H2+B+N) wt%
1.0
0.6 0.4
Armchair SWCNT
2.5 2.0 1.5 1.0
0.2 0.5
293K 0.0
293K, 10MPa
0.0
0
2
4
6 8 10 Pressure/MPa
12
14
16
0
2
4
6
8
10
12
14
16
Diameter of Nanotube/nm
Fig. 3. Influence of tube chirality on hydrogen physisorption in SWBNNTs.
Fig. 5. Influence of tube diameter on hydrogen physisorption in SWBNNTs and SWCNTs.
2.0 (15,15) SWBNNT (15,15) SWCNT
Hydrogen/System wt%
1.5
1.0
0.5
0.0 293K, 10MPa -0.5 2
4
6
8
10
Length of Nanotube/nm Fig. 4. Influence of tube length on hydrogen physisorption in SWBNNTs and SWCNTs.
physisorption the hydrogen storage capacity of SWBNNTs is more than that of SWCNTs at any time when their diameters are equal and have same conditions. (2) By fixing temperature, tube diameter and tube length, the influence of tube chirality on hydrogen storage capacity of SWBNNTs is investigated, and some of our results are shown in Fig. 3. We can see that the adsorption isotherms of hydrogen physisorption in armchair and zigzag SWBNNT at 293 K accord with each other. That is, the influence of tube chirality on hydrogen storage capacity of SWBNNTs can be ignored. (3) By fixing temperature, pressure and tube diameter, we investigate the dependence of hydrogen storage capacity of SWBNNTs and SWCNTs on the tube length. Some of our results are drawn in Fig. 4. The hydrogen storage capacity of SWBNNTs and SWCNTs almost hold the line when the tube length increases, that is to say, the axial distribution of hydrogen molecules stored in the nanotubes is approximately uniform. Therefore, only by changing of the tube length cannot vary the weight percent of hydrogen physisorption in SWBNNTs and SWCNTs.
(4) By fixing temperature, pressure and tube length, we study the influence of tube diameter on hydrogen storage capacity of SWBNNTs and SWCNTs, and some of our results are plotted in Fig. 5. It is clear that the hydrogen storage capacity of SWBNNTs and SWCNTs increase with the increasing diameter. This is because the space inside nanotube increases with the increasing diameter, and at the same time, the number of boron, nitrogen or carbon atoms also increases, which promote the exertion of the potential effect and the space effect of hydrogen storage in nanotubes [7]. These results indicate that increasing the tube diameter properly can improve the hydrogen storage capacity of SWBNNTs and SWCNTs effectively. (5) The above results (Figs. 2, 4 and 5) show that for physisorption the hydrogen storage capability of SWBNNTs is better than that of SWCNTs at room temperature and moderate pressure. In addition, we have calculated the weight percents of hydrogen physisorption in SWBNNTs and SWCNTs with different diameters of 20, 25 and 30 nm at 293 K and different pressures of 10 and 15 MPa, and obtained the computational results as shown in Table 1. From Table 1, we can see that the hydrogen storage capacity of SWBNNTs and SWCNTs at 293 K exceed the DOE 2010 goal of 6 wt% when the nanotube diameter is more than 30 nm (at 10 MPa) or 25 nm (at 15 MPa). Considering that it has difficulty in synthesizing SWCNT whose diameter is more than 25 nm at present, and the SWBNNT with a diameter of more than 30 nm has been synthesized [13], so, if the tube diameter can be controlled efficiently when we synthesize SWBNNTs, the total weight percent of hydrogen physisorption inside and outside (waiting for future work) SWBNNTs at room temperature and moderate pressure could exceed the commercial standard presented by the U.S. DOE. 4. Theoretic interpretation Our former work [7] indicated that the mechanism of hydrogen physisorption in nanotubes could be described by the potential effect and the space effect. The potential effect comes
J. Cheng et al. / International Journal of Hydrogen Energy 32 (2007) 3402 – 3405
3405
Table 1 Hydrogen storage capacity of SWBNNTs and SWCNTs with large diameters Type and diameter of nanotube
Hydrogen storage capacity (wt%)
D = 19.99 nm D = 19.94 nm D = 24.95 nm D = 24.96 nm D = 30.05 nm D = 29.97 nm
(145,145)BNNT; (147,147)CNT; (181,181)BNNT; (184,184)CNT; (218,218)BNNT; (221,221)CNT;
At 293 K and 15 MPa
4.43 4.18 5.41 5.16 6.38 6.13
5.85 5.63 7.11 6.96 8.39 8.20
more than 25 nm could exceed the DOE 2010 goal of 6 wt%. Therefore, BNNTs must be more suitable materials for hydrogen storage than CNTs.
100 0 -100 Potential(KB)
At 293 K and 10 MPa
References
-200 -300 -400 -500 -600
(15,15)SWBNNT
-700
(15,15) SWCNT
-800 -0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Distance from the tube center/nm
Fig. 6. LJ potential wells located in the SWBNNT and SWCNT.
from the interactions of nanotube-H2 and H2 .H2 while the space effect comes from the hollow configuration of nanotubes. When SWBNNTs and SWCNTs are of the same length and diameter, the discrepancies between hydrogen physisorption in SWBNNTs and SWCNTs mainly result from the interactions of nanotube-H2 . It is clear that the LJ potential wells’ depth and width of nanotube-H2 interactions in SWBNNTs are both more than the one in SWCNTs, as shown in Fig. 6, so that SWBNNTs possesses of better effectiveness for hydrogen storage. Based on our calculations, we find the lowest points in LJ potential wells of SWBNNTs and SWCNTs are 0.325 nm from the tube walls. Since nanotubes with smaller diameters restrain the exertion of the potential effect and the space effect, so their hydrogen storage capacity will be efficiently increased by the reasonable increase of the diameter of SWBNNTs and SWCNTs. 5. Conclusions A great deal of computer simulation results for hydrogen physisorption in SWBNNTs and SWCNTs indicate that the capacity of SWBNNTs is slightly larger than the capacity of SWCNTs at any time when their diameters were equal and in the same conditions, and show that the hydrogen storage capacity of SWBNNTs at 293 K and 10 MPa with a diameter of more than 30 nm or at 293 K and 15 MPa with a diameter of
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