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Hydrogen storage and release by bending carbon nanotubes
Computational Materials Science 68 (2013) 121–126
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Hydrogen storage and release by bending carbon nanotubes Zilong Liu a,b, Qingzhong Xue a,b,⇑, Cuicui Ling a,b,⇑, Zifeng Yan a, Jingtang Zheng a a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, Shandong, PR China College of Science, China University of Petroleum, Qingdao 266555, Shandong, PR China
a r t i c l e
i n f o
Article history: Received 20 May 2012 Received in revised form 26 July 2012 Accepted 10 September 2012 Available online 22 November 2012 Keywords: Carbon nanotubes Hydrogen storage Room temperature Bending
a b s t r a c t Efficient storage of hydrogen at room temperature is a bottleneck problem for hydrogen-based energy applications. A simple way of hydrogen storage and release by bending carbon nanotubes (CNTs) at room temperature is demonstrated using molecular dynamics (MD) simulations. A large number of hydrogen molecules can be put in CNTs at low temperatures, and then the hydrogen molecules can be completely encapsulated in the CNTs by bending the CNTs to a critical angle. The critical angle decreases with increasing CNT length, while it increases with increasing hydrogen number and temperature. However, the CNT chirality has a negligible influence on the critical angle and hydrogen storage process. It is demonstrated that the release of the hydrogen molecules also can be controlled accurately at room temperature by changing bending angle. The van der Waals force plays an important role in the hydrogen storage and release process. Compared with the conventional methods for hydrogen storage, the brand-new one occurs at room temperature and the release of the hydrogen molecules can be controlled accurately by changing bending angle. Besides, the special structure of the bent CNTs will also significantly enhance their applications in atomic storage, various chemical and biological sensors and actuators, catalyst and catalyst supports, nanoelectronic devices as well as high-capacity energy storage in solar cells or fuel cells. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction With lightweight, clean-burning nature, zero pollutant emission, high conversion efficiency and potentially abundant production from other renewable resources [1–6], hydrogen is considered to be the most promising alternative energy carrier in the fuel of the future [1–4]. It can be used as fuel both directly in internal combustion engines and, indirectly, to supply electricity using polymer electrolyte membrane fuel cells [6,9]. However, the large-scale application of hydrogen as a fuel is still greatly limited because of its explosive nature and large volume. It is still a big challenge to store hydrogen at low cost and safely. There are several major technologies for storing hydrogen: compressed gas storage, cryogenic (liquefaction) liquid hydrogen, underground storage, metal hydride storage, glass microsphere storage, and adsorbed on high surface area materials [3–5,7–9]. The first three alternatives are either unsafe or extremely high power consuming. What is more, it is difficult to solve many practical difficulties in these techniques related to compression requirements, tank volume [3,9,10]. And the latter two methods ⇑ Corresponding authors at: State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, Shandong, PR China. Tel.: +86 546 8392836; fax: +86 546 8397900. E-mail addresses: [email protected] (Q. Xue), lingcuicui@upc. edu.cn (C. Ling). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.09.025
are hampered with problems of low content storage, large weight, expensive manufacture and high temperatures of decomposition [3,11]. Therefore, people begin to explore new high surface area materials, especially carbon nanostructures, such as carbon nanotubes (CNTs) [4], which possess egregious properties in the gas storage and release. For example, they are mechanically robust and can endure large strain without bond breaking or bond switching [12–16]. Their hollow cylindrical structures allow the molecules or atoms to store either inside or outside of the tube walls [17–19]. Recently, Zhang et al. has proposed a novel molecular sieving model of a kinked CNT for gas separation (nitrogen and oxygen) and the efficiency of molecular sieving has also been demonstrated [20]. From their study, we can know that the resilience of CNTs makes it possible to use the nanotubes as a gas pipeline whose permeability can be tuned by mechanical deformation. And they have done a more detailed research of the molecular sieving model in another paper [21]. Their work not only makes guiding importance in developing molecular sieving mechanisms and devices, but also leads some significance in the gas storage. The hydrogen storage through physisorption [22,23] and/or chemisorption [24] has been demonstrated. Extensive experimental and theoretical investigations have been done to search the mechanisms of hydrogen adsorption on CNTs. For example, Dillon et al. firstly measured the hydrogen adsorption capacity on CNTs at 133 K in order to evaluate the hydrogen adsorption amount of CNTs, and they concluded that CNTs can be considered as the
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rechargeable hydrogen storage medium [25]. Ye et al. analyzed the hydrogen adsorption on high-purity single-walled CNTs (SWNTs) at 80 K and pressure of 4–8 MPa, a gravimetric storage capacity as high as 8.25 wt% was achieved [26]. Nishimiya et al. had reported hydrogen adsorption on SWNTs reached 2.37 wt% at 77 K under 107.9 kPa with the hydrogen uptakes not yet saturated [27]. A volumetric method was performed on an as-grown and heat-treated arc-generated SWNTs by Anson et al., it is found that the amounts of hydrogen adsorbed at atmospheric pressure reach approximately 1 wt% at 77 K [28]. Besides, there are a large number of theoretical studies of the adsorption storage of hydrogen on CNTs at low temperature. Cao et al. used the grand canonical Monte Carlo (GCMC) method to investigate the adsorption storage of hydrogen in the bundle of SWNTs [29]. They found that gravimetric and volumetric capacities of hydrogen in the diamondshaped bundle of SWNTs achieved 7.4 wt% at 105 K and 13.2 MPa. By total-energy density functional theory calculations, Li et al. demonstrated that the contribution from physisorption in nanotubes, though significant at liquid nitrogen temperature, should be negligible at room temperature [30]. Obviously, previous work has demonstrated that hydrogen storage in CNTs is feasible at moderate low temperatures and high pressures. However, these rigorous storage conditions restrict the further application of hydrogen due to the safety, production, transportation and release of hydrogen. Hydrogen storage and release in CNTs at room temperature can be a good choice. At room temperature, the interaction energy between adsorbed hydrogen molecules and the nanotube is very low for hydrogen storage. It can be interpreted that high temperature will increase the kinetic energy of hydrogen molecules, intensify their thermal dynamic motions so that hydrogen molecules can easily move out of the nanotube. Thermodynamic calculations indicate that the optimum interaction energy for efficient but reversible storage under ambient conditions is approximate 7 kcal/mol [31]. In the past, researchers ignored the special structure of the CNTs in hydrogen storage and often paid close attention to the outer conditions such as pressure, temperature, to reach the optimum interaction energy. Despite the significant effort that has been made to store hydrogen at room temperature, the solution has not yet been found. Herein, using molecular dynamics (MD) simulations, we propose a simple method of storage and release a plenty of hydrogen molecules in bent SWNTs at room temperature. It is considered that the van der Waals force plays an important role in the hydrogen storage and release process. Compared with the conventional hydrogen storage methods, the brand-new one occurs at room temperature and the release of the hydrogen molecules can be controlled accurately by changing the bending angle. Moreover, the CNTs can be performed for thousands of times without breaking down because of the remarkable flexibility of CNTs [12]. Another advantage is that such method is suitable for many types of molecules such as O2, NH3.
2. Model and methods A zigzag-type (8, 0) SWNT with diameter of 6.26 Å, which is energetically optimal candidates for physisorption of molecular hydrogen [32], is used in our simulation. Each C–C bond length is 1.42 Å, while H–H bond length is 0.75 Å. Preliminary instability analysis shows that the hydrogen molecules could not stay in the CNTs without bending at room temperature. It is well known that hydrogen molecules can be put in CNTs at moderate low temperatures and high pressures. In this study, we focus on how to store and release hydrogen molecules at room temperature. Using MD simulations, we perform a simple method of encapsulating hydro-
gen molecules by bending CNTs to a critical angle. The encapsulation process consists of three major steps: (1) the hydrogen molecules are put in a CNT, (2) labeling the two ends of CNT with green color while rotating the two ends step-wisely with one angle each time, and (3) fixing the atoms at the two ends of the nanotube. Fig. 1a shows the morphology of the CNT and the encapsulated molecules with the well-distributed pattern after the minimization process. Subjected to an external bending moment M, the final structures of the CNTs with different bending angles are respectively depicted in Fig. 1b. In each simulation, the labeled atoms are held rigid at their rotated positions while the rest are relaxed to a minimum energy. The MD simulations are carried out by the DISCOVER code in MATERIALS STUDIO software. The interatomic interactions are described by force field of condensed-phased optimized molecular potential for atomistic simulation studies (COMPASSs) [23], which is a general all-atom force field for atomistic simulation of organic molecules, small molecules and polymers. It is the first ab initio force field that has been parametrized and validated using condensed-phase properties in addition to various ab initio and empirical data, which has been proven to be applicable in describing the mechanical properties of CNTs [33,34]. The model was put into an NVT [19,35,36] ensemble simulation at 300 K, which were generally applied in other MD simulations. The Andersen method [37] was applied to control the thermodynamic temperature. The time step in MD simulation was 1 fs, and data were collected every 1 ps. All the simulations were calculated long enough to detect several cycles of thermal vibration, and the full-precision trajectory was recorded. 3. Results and discussion The bonding strength between the CNTs and hydrogen molecules is evaluated by the interaction energy of the system. Generally, the interaction energy can be estimated by the distinction between the potential energy of the bending system and the potential energy of the hydrogen molecules and the relevant CNTs as follows [38]:
Einteraction ¼ Etotal ðEH2 þ ECNTs Þ;
ð1Þ
where Etotal is the energy of the system including the hydrogen molecules and the CNT, EH2 is the energy of hydrogen molecules without the CNT, and ECNTs is the energy of CNT without the hydrogen molecules, respectively. 3.1. The bending process Fig. 2 shows the final structures of CNTs with different encapsulated hydrogen molecules at the bending angle changing from 35° to 40° and the bending center are indicated by dashed line with arrows. And the top view of the atomic system clearly shows changes of the alignment of hydrogen molecules in nanotube. Fig. 3 shows the relationship between the bending angle and the proportion of encapsulated hydrogen molecules in the CNTs. Proportion of H2 is defined as the ratio of the amount of the encapsulated molecules to the total molecules put in the CNTs. From the figure, we can easily observe that the proportion of encapsulated hydrogen molecules increases sharply with the increase of bending angle. And, the whole hydrogen molecule cluster is encapsulated when the bending angle reaches 40°. In other words, the hydrogen molecules can be completely encapsulated by bending CNT. The effect of the bending angle on encapsulating process is carefully described in the following. At the beginning, bending the ends of the nanotube is smooth at small bending angles, hydrogen molecules can gradually move out of the nanotubes due to the
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Fig. 1. (a) Simulation model of the CNT (8 0) under bending at two ends. 20 hydrogen molecules are put in the CNT with red color highlighted. Two ends of the CNTs are held rigid with green color labeled. (b) Snapshoot the CNTs at different bending angles after energy minimization. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Side view (a) and top view (b) of final structures of CNTs with different encapsulated hydrogen molecules at the bending angle changing from 35° to 40° and the bending center are indicated by dashed line with arrows.
Fig. 3. Proportion of H2, defined as the ratio of the amount of the encapsulated molecules to the total molecules put in the CNTs, as a function of the bending angle.
self-diffusion of molecules and relatively weak interaction energy. Interestingly, hydrogen molecules go out almost one by one at one time. Bending the CNTs continually, we observe that one or two remaining molecules pace up and down in the nanotube, eventually move out. This phenomenon may attribute to the fact that as molecules concentration decreases, the remaining hydrogen has less molecular collision and they have more space to diffuse, therefore it needs more time to move out. It is not until the bending angle of 35° that two kinks appear at the both ends of the CNTs and few molecules start to be encapsulated in the nanotube. During the bending CNT process, while the bending angle is less than 40°, hydrogen molecules will run out of the nanotube in a certain proportion but some molecules still stay in it. When the bending angle is up to 40°, hydrogen molecules are successfully encapsulated in the nanotube even after a longer simulation time. Keeping on bending the CNTs, hydrogen molecules constantly change its orientation and oscillate all the time with no molecules fleeing. It is considered that the bending angle of CNTs is the critical angle when hydrogen molecules are successfully encapsulated. When the
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bending angle is less than the critical angle, molecules will move out and the bent CNTs fail to encapsulate the hydrogen molecules. Conversely, if the bending angle is larger than the critical angle, the hydrogen molecules can be entirely encapsulated in CNTs. It is well known that CNTs are mechanically robust and can endure large strain without bond breaking or bond switching. Removing the restriction on the two ends of the CNTs, the CNTs reversibly returns its initial straight geometry and hydrogen molecules are all released from the tube. Furthermore, the CNTs can be reused through the same method, which reflects a great recycle characteristic of CNTs in hydrogen storage. Based on above discussions, a conclusion can be drawn that the bent CNTs could be used for hydrogen storage at room temperature and the release of the hydrogen molecules can be controlled accurately by changing the bending angle. It is worth to further explore the molecular storage mechanism of the encapsulation process. From Fig. 2, hydrogen molecules nearly present a homogeneous distribution rather than the congregated pattern in the bending CNTs process after energy minimization and dynamic simulation. Many axial symmetric potential wells are formed in bent CNTs, due to the interactions of C–H2 and H2–H2, which is the dominating contributions [39]. Molecules mostly trend to assemble at low-energy place which makes the system more stable. Therefore, hydrogen molecules present a clearly homogeneous distribution at potential wells. Moreover, there are two kinks appearing at the both ends of the CNT during bending process, which is considered as the main factors to prevent molecules to move out. The kink structure is changed by the variation of the bending angle. It is not until the bending angle of 35° that the kinks appear at the both ends of the CNTs. From Fig. 2a, it can be seen that the kinks decrease gradually with increasing the bending angle. Since the ends of the nanotubes are held rigid, the critical bending angle changes with the position of bending center. A symmetry structure as the CNT is, we only indicate the bending center by dashed lines with arrows on the left end of the nanotubes. When the bending angle varies from 35° to 40°, accordingly, the bending center tends to shift slightly to the ends of the nanotubes. It can be clearly seen that the bending center locates at about the fourth layer carbon atoms on the ends of the nanotubes. Furthermore, a reflecting wall located at the kink is introduced to impede the gas molecules from passing through the kink [21]. In order to interpret the storage mechanism of the encapsulation process, we analyzed this phenomenon from the point of interatomic interaction. One hydrogen molecule is put in the centre of the SWNT (8, 0) with the bending angle of 40°, we cal-
culate the interaction energy every time after the molecule is moved at a small scale to one end. As shown in Fig. 4, we can see that there is an energy barrier forming at the kinks of the nanotube, which prevents encapsulated molecules to run out of the CNTs. Stronger interaction between molecules and the bent nanotube restricts self-diffusion of molecules. The kinks form gatecontrolled tunnel barriers and the existence of the layered structure in the kinked model also make self-diffusion of molecules more difficult. As a result, when the bending angle reaches 40°, the energy barrier is bigger enough to impede all the hydrogen molecules to flee out of the CNTs. 3.2. Structure effect 3.2.1. Chirality effect It is well known that the chirality of CNTs has a significant effect on the properties of CNTs, for example, the chirality of CNTs can vary its type from metallic to semiconductor [40]. To investigate the effect of the chirality on the hydrogen storage capacity of the bending CNT, the hydrogen molecules interact with four types of CNTs, whose chiral angles range from 0° to 30°. The corresponding chiral angle h and diameter Dn of CNTs with ðn; mÞ indices can be determined by using the rolling graphene model [41].
pffiffiffi ! 3m h ¼ arctan ; 2n þ m
pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 b ðn2 þ m2 þ nmÞ; Dn ¼
p
6 m 6 nÞ
ð0 ð2Þ
where b is the C–C bond length. The total number of the atoms, diameter, length of each chiral CNT are given in Table 1. Variation of the critical angle with CNT chirality is shown in Fig. 5. From the figure, we can observe that the CNT chirality has a negligible influence on the critical angle and the bending process. In the hydrogen storage, there is no essential difference among armchair, zigzag and chiral CNTs as concerns their ability to store H2. Our work explain the negligible influence on hydrogen storage from another curious sight, which confirms well with the works [19,32]. 3.2.2. Length effect To investigate the influence of CNT length on the encapsulation ability of hydrogen storage, the bending process of CNTs with different lengths (6.39, 8.52, 10.65, 14.91, and 19.17 nm) are performed using MD simulations. From Fig. 6, it can be seen that the whole hydrogen molecules can be completely encapsulated at different critical angles during the bending process. When the CNT length is less than approximate 10.5 nm, the critical angle decreases sharply with increasing CNT length, which is caused by the reduction of the molecular concentration. As the concentration of molecules decreases in CNTs, molecules interaction is becoming weak as well as molecular collision. Beyond the limitation of 10.5 nm, a further increase of the CNT length leads to a slight decrease of the critical angle. Based on previous discussion, it is not until the bending angle of 35° that two kinks appear at the both ends of the CNTs. To store all the hydrogen molecules, the kinks are needed to be formed when the bending angle approaches to or above 35°. At the same time, the longer CNTs length has a
Table 1 Total number of atoms, diameter, and length of each chiral nanotube used in MD simulations.
Fig. 4. Change of the interaction energy between the hydrogen molecule and the CNT with position.
Type of SWNTs
C
Nanotube (D)
Length
Angle
(5, 5) (6, 3) (7, 2) (8, 0)
520 474 502 480
6.78 6.41 6.21 6.26
63.95 62.53 63.23 63.90
30.00 19.11 12.22 0.00
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Fig. 5. Variation of the critical angle with CNT chirality.
Fig. 7. (a) Final structures of the bent CNTs containing various encapsulated hydrogen molecules (20, 35, 50, 70, 100) at different critical angles. (b) The critical angle as functions of amounts of the encapsulated hydrogen molecules.
larger the number of molecules is, the stronger interaction between C–H2 and H2–H2 is. The nanotube with more encapsulated H2 molecules has larger bending stiffness. To store all the hydrogen molecules, it needs a bigger bending angle.
Fig. 6. The relation between the critical angle, defined as the bending angle when the hydrogen molecules are completely encapsulated in the CNT, and CNT length.
negligible influence on the critical angle, and the distribution of molecules is much more decentralized. Many axial symmetric potential wells in the longer CNTs provide molecules more space to self-diffusion. When molecules’ distance is becoming short, repulsive force among molecules increases visibly to separate hydrogen molecules. Thus, it presents a decentralized distribution in the nanotube. 3.3. H2 number effect In this section, we focus on the effect of the number of hydrogen molecules in a CNT on the critical angle. It has been demonstrated that more hydrogen molecules can also be successfully encapsulated through bending the CNTs to a certain critical angle, as shown in Fig. 7a. The bending center still shifts to the ends and locates at between the third layer carbon atoms and the fifth layer carbon atoms. With different molecules encapsulated in CNTs, the major difference of the bending process is the critical angle, which is shown in Fig. 7b. From the figure, we can find that when the number of molecules is smaller than 35, the critical angle keeps a constant. In other words, the nanotube is enough to hold more molecules in this limitation, which is attributed to the axial symmetric potential wells formed in CNTs. To investigate the phenomenon thoroughly, more simulations are performed with more molecules encapsulated in CNTs. The critical angle varies sharply as encapsulated molecules increase. It can be explained that the
3.4. Temperature effect The influence of the temperature on the bending process is considered while keeping other parameters constant. On one side, temperature will change the kinetic energy of the molecules, intensify/retard their thermal dynamic motions and induce larger/ smaller random displacements of molecules. On the other side, temperature influences the geometry of kinks in the nanotube [21] and it allows the molecules to reach low potential energy locations more quickly/slowly. By varying the temperature from 100 to 500 K, the proportion of molecules stored in CNTs with different bending angles is shown in Fig. 8a. In order to interpret the varying relationship between temperature and the critical angles, a clear description is given in Fig. 8b. From Fig. 8a, it can be seen that the total amount of the stored molecules increases obviously as the bending angles increase, when the temperature ranges from 100 to 300 K. However, a relatively slow increase of the proportion of stored molecules is observed as the temperature varies from 300 to 500 K. The hydrogen molecules can be fully encapsulated at any temperature when the bending angle approaches to a certain angle. Based on our previous consideration, in a relatively low temperature range, molecules have stable thermal dynamic motions at low kinetic energy. As a result, the critical angle is easy to reach as well as the encapsulation of molecules during the bending process. When the nanotubes are bent at the same bending angle, the geometry of kinks deformed smaller at 500 K than that at lower temperatures. In addition, high kinetic energy gives molecules more chance to flee, but the larger bending angle restricts the molecules. In order to encapsulate the whole molecules, a bigger bending angle
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Acknowledgements This work is supported by Natural Science Foundation of China (10974258), Natural Science Foundation of Shandong province (ZR2010AL009), and the Fundamental Research Funds for the Central Universities (11CX05002A). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] Fig. 8. (a) Variation of proportion of H2 with bending angle under different temperatures. (b) Variation of critical angle with temperature.
is needed. From Fig. 8b, the critical angle increases relatively fast with increasing temperature under 300 K, while it increases slowly with increasing temperature from 300 to 500 K.
4. Conclusion In summary, we have studied the encapsulated process of hydrogen molecules in CNTs at room temperature using MD simulations. Bending the nanotubes to a critical angle, an energy barrier would be formed at the kinks of CNTs, which impedes the hydrogen molecules from fleeing out of the CNTs. Thus, hydrogen molecules are successfully encapsulated in the CNTs at room temperature. The simulations show that, by increasing number of hydrogen molecules encapsulated into the CNTs and the ambient temperature, the critical angle increases accordingly. The CNT length also greatly influences the critical angle. However, it is demonstrated that the chirality of the CNTs has no strong influence on the critical angle and hydrogen storage process. Using this method, many other molecules can also be encapsulated. Due to the special structure of bent CNTs, the release of the hydrogen molecules can be controlled accurately.
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Hydrogen storage and release by bending carbon nanotubes Zilong Liu a,b, Qingzhong Xue a,b,⇑, Cuicui Ling a,b,⇑, Zifeng Yan a, Jingtang Zheng a a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, Shandong, PR China College of Science, China University of Petroleum, Qingdao 266555, Shandong, PR China
a r t i c l e
i n f o
Article history: Received 20 May 2012 Received in revised form 26 July 2012 Accepted 10 September 2012 Available online 22 November 2012 Keywords: Carbon nanotubes Hydrogen storage Room temperature Bending
a b s t r a c t Efficient storage of hydrogen at room temperature is a bottleneck problem for hydrogen-based energy applications. A simple way of hydrogen storage and release by bending carbon nanotubes (CNTs) at room temperature is demonstrated using molecular dynamics (MD) simulations. A large number of hydrogen molecules can be put in CNTs at low temperatures, and then the hydrogen molecules can be completely encapsulated in the CNTs by bending the CNTs to a critical angle. The critical angle decreases with increasing CNT length, while it increases with increasing hydrogen number and temperature. However, the CNT chirality has a negligible influence on the critical angle and hydrogen storage process. It is demonstrated that the release of the hydrogen molecules also can be controlled accurately at room temperature by changing bending angle. The van der Waals force plays an important role in the hydrogen storage and release process. Compared with the conventional methods for hydrogen storage, the brand-new one occurs at room temperature and the release of the hydrogen molecules can be controlled accurately by changing bending angle. Besides, the special structure of the bent CNTs will also significantly enhance their applications in atomic storage, various chemical and biological sensors and actuators, catalyst and catalyst supports, nanoelectronic devices as well as high-capacity energy storage in solar cells or fuel cells. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction With lightweight, clean-burning nature, zero pollutant emission, high conversion efficiency and potentially abundant production from other renewable resources [1–6], hydrogen is considered to be the most promising alternative energy carrier in the fuel of the future [1–4]. It can be used as fuel both directly in internal combustion engines and, indirectly, to supply electricity using polymer electrolyte membrane fuel cells [6,9]. However, the large-scale application of hydrogen as a fuel is still greatly limited because of its explosive nature and large volume. It is still a big challenge to store hydrogen at low cost and safely. There are several major technologies for storing hydrogen: compressed gas storage, cryogenic (liquefaction) liquid hydrogen, underground storage, metal hydride storage, glass microsphere storage, and adsorbed on high surface area materials [3–5,7–9]. The first three alternatives are either unsafe or extremely high power consuming. What is more, it is difficult to solve many practical difficulties in these techniques related to compression requirements, tank volume [3,9,10]. And the latter two methods ⇑ Corresponding authors at: State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, Shandong, PR China. Tel.: +86 546 8392836; fax: +86 546 8397900. E-mail addresses: [email protected] (Q. Xue), lingcuicui@upc. edu.cn (C. Ling). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.09.025
are hampered with problems of low content storage, large weight, expensive manufacture and high temperatures of decomposition [3,11]. Therefore, people begin to explore new high surface area materials, especially carbon nanostructures, such as carbon nanotubes (CNTs) [4], which possess egregious properties in the gas storage and release. For example, they are mechanically robust and can endure large strain without bond breaking or bond switching [12–16]. Their hollow cylindrical structures allow the molecules or atoms to store either inside or outside of the tube walls [17–19]. Recently, Zhang et al. has proposed a novel molecular sieving model of a kinked CNT for gas separation (nitrogen and oxygen) and the efficiency of molecular sieving has also been demonstrated [20]. From their study, we can know that the resilience of CNTs makes it possible to use the nanotubes as a gas pipeline whose permeability can be tuned by mechanical deformation. And they have done a more detailed research of the molecular sieving model in another paper [21]. Their work not only makes guiding importance in developing molecular sieving mechanisms and devices, but also leads some significance in the gas storage. The hydrogen storage through physisorption [22,23] and/or chemisorption [24] has been demonstrated. Extensive experimental and theoretical investigations have been done to search the mechanisms of hydrogen adsorption on CNTs. For example, Dillon et al. firstly measured the hydrogen adsorption capacity on CNTs at 133 K in order to evaluate the hydrogen adsorption amount of CNTs, and they concluded that CNTs can be considered as the
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rechargeable hydrogen storage medium [25]. Ye et al. analyzed the hydrogen adsorption on high-purity single-walled CNTs (SWNTs) at 80 K and pressure of 4–8 MPa, a gravimetric storage capacity as high as 8.25 wt% was achieved [26]. Nishimiya et al. had reported hydrogen adsorption on SWNTs reached 2.37 wt% at 77 K under 107.9 kPa with the hydrogen uptakes not yet saturated [27]. A volumetric method was performed on an as-grown and heat-treated arc-generated SWNTs by Anson et al., it is found that the amounts of hydrogen adsorbed at atmospheric pressure reach approximately 1 wt% at 77 K [28]. Besides, there are a large number of theoretical studies of the adsorption storage of hydrogen on CNTs at low temperature. Cao et al. used the grand canonical Monte Carlo (GCMC) method to investigate the adsorption storage of hydrogen in the bundle of SWNTs [29]. They found that gravimetric and volumetric capacities of hydrogen in the diamondshaped bundle of SWNTs achieved 7.4 wt% at 105 K and 13.2 MPa. By total-energy density functional theory calculations, Li et al. demonstrated that the contribution from physisorption in nanotubes, though significant at liquid nitrogen temperature, should be negligible at room temperature [30]. Obviously, previous work has demonstrated that hydrogen storage in CNTs is feasible at moderate low temperatures and high pressures. However, these rigorous storage conditions restrict the further application of hydrogen due to the safety, production, transportation and release of hydrogen. Hydrogen storage and release in CNTs at room temperature can be a good choice. At room temperature, the interaction energy between adsorbed hydrogen molecules and the nanotube is very low for hydrogen storage. It can be interpreted that high temperature will increase the kinetic energy of hydrogen molecules, intensify their thermal dynamic motions so that hydrogen molecules can easily move out of the nanotube. Thermodynamic calculations indicate that the optimum interaction energy for efficient but reversible storage under ambient conditions is approximate 7 kcal/mol [31]. In the past, researchers ignored the special structure of the CNTs in hydrogen storage and often paid close attention to the outer conditions such as pressure, temperature, to reach the optimum interaction energy. Despite the significant effort that has been made to store hydrogen at room temperature, the solution has not yet been found. Herein, using molecular dynamics (MD) simulations, we propose a simple method of storage and release a plenty of hydrogen molecules in bent SWNTs at room temperature. It is considered that the van der Waals force plays an important role in the hydrogen storage and release process. Compared with the conventional hydrogen storage methods, the brand-new one occurs at room temperature and the release of the hydrogen molecules can be controlled accurately by changing the bending angle. Moreover, the CNTs can be performed for thousands of times without breaking down because of the remarkable flexibility of CNTs [12]. Another advantage is that such method is suitable for many types of molecules such as O2, NH3.
2. Model and methods A zigzag-type (8, 0) SWNT with diameter of 6.26 Å, which is energetically optimal candidates for physisorption of molecular hydrogen [32], is used in our simulation. Each C–C bond length is 1.42 Å, while H–H bond length is 0.75 Å. Preliminary instability analysis shows that the hydrogen molecules could not stay in the CNTs without bending at room temperature. It is well known that hydrogen molecules can be put in CNTs at moderate low temperatures and high pressures. In this study, we focus on how to store and release hydrogen molecules at room temperature. Using MD simulations, we perform a simple method of encapsulating hydro-
gen molecules by bending CNTs to a critical angle. The encapsulation process consists of three major steps: (1) the hydrogen molecules are put in a CNT, (2) labeling the two ends of CNT with green color while rotating the two ends step-wisely with one angle each time, and (3) fixing the atoms at the two ends of the nanotube. Fig. 1a shows the morphology of the CNT and the encapsulated molecules with the well-distributed pattern after the minimization process. Subjected to an external bending moment M, the final structures of the CNTs with different bending angles are respectively depicted in Fig. 1b. In each simulation, the labeled atoms are held rigid at their rotated positions while the rest are relaxed to a minimum energy. The MD simulations are carried out by the DISCOVER code in MATERIALS STUDIO software. The interatomic interactions are described by force field of condensed-phased optimized molecular potential for atomistic simulation studies (COMPASSs) [23], which is a general all-atom force field for atomistic simulation of organic molecules, small molecules and polymers. It is the first ab initio force field that has been parametrized and validated using condensed-phase properties in addition to various ab initio and empirical data, which has been proven to be applicable in describing the mechanical properties of CNTs [33,34]. The model was put into an NVT [19,35,36] ensemble simulation at 300 K, which were generally applied in other MD simulations. The Andersen method [37] was applied to control the thermodynamic temperature. The time step in MD simulation was 1 fs, and data were collected every 1 ps. All the simulations were calculated long enough to detect several cycles of thermal vibration, and the full-precision trajectory was recorded. 3. Results and discussion The bonding strength between the CNTs and hydrogen molecules is evaluated by the interaction energy of the system. Generally, the interaction energy can be estimated by the distinction between the potential energy of the bending system and the potential energy of the hydrogen molecules and the relevant CNTs as follows [38]:
Einteraction ¼ Etotal ðEH2 þ ECNTs Þ;
ð1Þ
where Etotal is the energy of the system including the hydrogen molecules and the CNT, EH2 is the energy of hydrogen molecules without the CNT, and ECNTs is the energy of CNT without the hydrogen molecules, respectively. 3.1. The bending process Fig. 2 shows the final structures of CNTs with different encapsulated hydrogen molecules at the bending angle changing from 35° to 40° and the bending center are indicated by dashed line with arrows. And the top view of the atomic system clearly shows changes of the alignment of hydrogen molecules in nanotube. Fig. 3 shows the relationship between the bending angle and the proportion of encapsulated hydrogen molecules in the CNTs. Proportion of H2 is defined as the ratio of the amount of the encapsulated molecules to the total molecules put in the CNTs. From the figure, we can easily observe that the proportion of encapsulated hydrogen molecules increases sharply with the increase of bending angle. And, the whole hydrogen molecule cluster is encapsulated when the bending angle reaches 40°. In other words, the hydrogen molecules can be completely encapsulated by bending CNT. The effect of the bending angle on encapsulating process is carefully described in the following. At the beginning, bending the ends of the nanotube is smooth at small bending angles, hydrogen molecules can gradually move out of the nanotubes due to the
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Fig. 1. (a) Simulation model of the CNT (8 0) under bending at two ends. 20 hydrogen molecules are put in the CNT with red color highlighted. Two ends of the CNTs are held rigid with green color labeled. (b) Snapshoot the CNTs at different bending angles after energy minimization. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Side view (a) and top view (b) of final structures of CNTs with different encapsulated hydrogen molecules at the bending angle changing from 35° to 40° and the bending center are indicated by dashed line with arrows.
Fig. 3. Proportion of H2, defined as the ratio of the amount of the encapsulated molecules to the total molecules put in the CNTs, as a function of the bending angle.
self-diffusion of molecules and relatively weak interaction energy. Interestingly, hydrogen molecules go out almost one by one at one time. Bending the CNTs continually, we observe that one or two remaining molecules pace up and down in the nanotube, eventually move out. This phenomenon may attribute to the fact that as molecules concentration decreases, the remaining hydrogen has less molecular collision and they have more space to diffuse, therefore it needs more time to move out. It is not until the bending angle of 35° that two kinks appear at the both ends of the CNTs and few molecules start to be encapsulated in the nanotube. During the bending CNT process, while the bending angle is less than 40°, hydrogen molecules will run out of the nanotube in a certain proportion but some molecules still stay in it. When the bending angle is up to 40°, hydrogen molecules are successfully encapsulated in the nanotube even after a longer simulation time. Keeping on bending the CNTs, hydrogen molecules constantly change its orientation and oscillate all the time with no molecules fleeing. It is considered that the bending angle of CNTs is the critical angle when hydrogen molecules are successfully encapsulated. When the
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bending angle is less than the critical angle, molecules will move out and the bent CNTs fail to encapsulate the hydrogen molecules. Conversely, if the bending angle is larger than the critical angle, the hydrogen molecules can be entirely encapsulated in CNTs. It is well known that CNTs are mechanically robust and can endure large strain without bond breaking or bond switching. Removing the restriction on the two ends of the CNTs, the CNTs reversibly returns its initial straight geometry and hydrogen molecules are all released from the tube. Furthermore, the CNTs can be reused through the same method, which reflects a great recycle characteristic of CNTs in hydrogen storage. Based on above discussions, a conclusion can be drawn that the bent CNTs could be used for hydrogen storage at room temperature and the release of the hydrogen molecules can be controlled accurately by changing the bending angle. It is worth to further explore the molecular storage mechanism of the encapsulation process. From Fig. 2, hydrogen molecules nearly present a homogeneous distribution rather than the congregated pattern in the bending CNTs process after energy minimization and dynamic simulation. Many axial symmetric potential wells are formed in bent CNTs, due to the interactions of C–H2 and H2–H2, which is the dominating contributions [39]. Molecules mostly trend to assemble at low-energy place which makes the system more stable. Therefore, hydrogen molecules present a clearly homogeneous distribution at potential wells. Moreover, there are two kinks appearing at the both ends of the CNT during bending process, which is considered as the main factors to prevent molecules to move out. The kink structure is changed by the variation of the bending angle. It is not until the bending angle of 35° that the kinks appear at the both ends of the CNTs. From Fig. 2a, it can be seen that the kinks decrease gradually with increasing the bending angle. Since the ends of the nanotubes are held rigid, the critical bending angle changes with the position of bending center. A symmetry structure as the CNT is, we only indicate the bending center by dashed lines with arrows on the left end of the nanotubes. When the bending angle varies from 35° to 40°, accordingly, the bending center tends to shift slightly to the ends of the nanotubes. It can be clearly seen that the bending center locates at about the fourth layer carbon atoms on the ends of the nanotubes. Furthermore, a reflecting wall located at the kink is introduced to impede the gas molecules from passing through the kink [21]. In order to interpret the storage mechanism of the encapsulation process, we analyzed this phenomenon from the point of interatomic interaction. One hydrogen molecule is put in the centre of the SWNT (8, 0) with the bending angle of 40°, we cal-
culate the interaction energy every time after the molecule is moved at a small scale to one end. As shown in Fig. 4, we can see that there is an energy barrier forming at the kinks of the nanotube, which prevents encapsulated molecules to run out of the CNTs. Stronger interaction between molecules and the bent nanotube restricts self-diffusion of molecules. The kinks form gatecontrolled tunnel barriers and the existence of the layered structure in the kinked model also make self-diffusion of molecules more difficult. As a result, when the bending angle reaches 40°, the energy barrier is bigger enough to impede all the hydrogen molecules to flee out of the CNTs. 3.2. Structure effect 3.2.1. Chirality effect It is well known that the chirality of CNTs has a significant effect on the properties of CNTs, for example, the chirality of CNTs can vary its type from metallic to semiconductor [40]. To investigate the effect of the chirality on the hydrogen storage capacity of the bending CNT, the hydrogen molecules interact with four types of CNTs, whose chiral angles range from 0° to 30°. The corresponding chiral angle h and diameter Dn of CNTs with ðn; mÞ indices can be determined by using the rolling graphene model [41].
pffiffiffi ! 3m h ¼ arctan ; 2n þ m
pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 b ðn2 þ m2 þ nmÞ; Dn ¼
p
6 m 6 nÞ
ð0 ð2Þ
where b is the C–C bond length. The total number of the atoms, diameter, length of each chiral CNT are given in Table 1. Variation of the critical angle with CNT chirality is shown in Fig. 5. From the figure, we can observe that the CNT chirality has a negligible influence on the critical angle and the bending process. In the hydrogen storage, there is no essential difference among armchair, zigzag and chiral CNTs as concerns their ability to store H2. Our work explain the negligible influence on hydrogen storage from another curious sight, which confirms well with the works [19,32]. 3.2.2. Length effect To investigate the influence of CNT length on the encapsulation ability of hydrogen storage, the bending process of CNTs with different lengths (6.39, 8.52, 10.65, 14.91, and 19.17 nm) are performed using MD simulations. From Fig. 6, it can be seen that the whole hydrogen molecules can be completely encapsulated at different critical angles during the bending process. When the CNT length is less than approximate 10.5 nm, the critical angle decreases sharply with increasing CNT length, which is caused by the reduction of the molecular concentration. As the concentration of molecules decreases in CNTs, molecules interaction is becoming weak as well as molecular collision. Beyond the limitation of 10.5 nm, a further increase of the CNT length leads to a slight decrease of the critical angle. Based on previous discussion, it is not until the bending angle of 35° that two kinks appear at the both ends of the CNTs. To store all the hydrogen molecules, the kinks are needed to be formed when the bending angle approaches to or above 35°. At the same time, the longer CNTs length has a
Table 1 Total number of atoms, diameter, and length of each chiral nanotube used in MD simulations.
Fig. 4. Change of the interaction energy between the hydrogen molecule and the CNT with position.
Type of SWNTs
C
Nanotube (D)
Length
Angle
(5, 5) (6, 3) (7, 2) (8, 0)
520 474 502 480
6.78 6.41 6.21 6.26
63.95 62.53 63.23 63.90
30.00 19.11 12.22 0.00
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Fig. 5. Variation of the critical angle with CNT chirality.
Fig. 7. (a) Final structures of the bent CNTs containing various encapsulated hydrogen molecules (20, 35, 50, 70, 100) at different critical angles. (b) The critical angle as functions of amounts of the encapsulated hydrogen molecules.
larger the number of molecules is, the stronger interaction between C–H2 and H2–H2 is. The nanotube with more encapsulated H2 molecules has larger bending stiffness. To store all the hydrogen molecules, it needs a bigger bending angle.
Fig. 6. The relation between the critical angle, defined as the bending angle when the hydrogen molecules are completely encapsulated in the CNT, and CNT length.
negligible influence on the critical angle, and the distribution of molecules is much more decentralized. Many axial symmetric potential wells in the longer CNTs provide molecules more space to self-diffusion. When molecules’ distance is becoming short, repulsive force among molecules increases visibly to separate hydrogen molecules. Thus, it presents a decentralized distribution in the nanotube. 3.3. H2 number effect In this section, we focus on the effect of the number of hydrogen molecules in a CNT on the critical angle. It has been demonstrated that more hydrogen molecules can also be successfully encapsulated through bending the CNTs to a certain critical angle, as shown in Fig. 7a. The bending center still shifts to the ends and locates at between the third layer carbon atoms and the fifth layer carbon atoms. With different molecules encapsulated in CNTs, the major difference of the bending process is the critical angle, which is shown in Fig. 7b. From the figure, we can find that when the number of molecules is smaller than 35, the critical angle keeps a constant. In other words, the nanotube is enough to hold more molecules in this limitation, which is attributed to the axial symmetric potential wells formed in CNTs. To investigate the phenomenon thoroughly, more simulations are performed with more molecules encapsulated in CNTs. The critical angle varies sharply as encapsulated molecules increase. It can be explained that the
3.4. Temperature effect The influence of the temperature on the bending process is considered while keeping other parameters constant. On one side, temperature will change the kinetic energy of the molecules, intensify/retard their thermal dynamic motions and induce larger/ smaller random displacements of molecules. On the other side, temperature influences the geometry of kinks in the nanotube [21] and it allows the molecules to reach low potential energy locations more quickly/slowly. By varying the temperature from 100 to 500 K, the proportion of molecules stored in CNTs with different bending angles is shown in Fig. 8a. In order to interpret the varying relationship between temperature and the critical angles, a clear description is given in Fig. 8b. From Fig. 8a, it can be seen that the total amount of the stored molecules increases obviously as the bending angles increase, when the temperature ranges from 100 to 300 K. However, a relatively slow increase of the proportion of stored molecules is observed as the temperature varies from 300 to 500 K. The hydrogen molecules can be fully encapsulated at any temperature when the bending angle approaches to a certain angle. Based on our previous consideration, in a relatively low temperature range, molecules have stable thermal dynamic motions at low kinetic energy. As a result, the critical angle is easy to reach as well as the encapsulation of molecules during the bending process. When the nanotubes are bent at the same bending angle, the geometry of kinks deformed smaller at 500 K than that at lower temperatures. In addition, high kinetic energy gives molecules more chance to flee, but the larger bending angle restricts the molecules. In order to encapsulate the whole molecules, a bigger bending angle
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Acknowledgements This work is supported by Natural Science Foundation of China (10974258), Natural Science Foundation of Shandong province (ZR2010AL009), and the Fundamental Research Funds for the Central Universities (11CX05002A). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] Fig. 8. (a) Variation of proportion of H2 with bending angle under different temperatures. (b) Variation of critical angle with temperature.
is needed. From Fig. 8b, the critical angle increases relatively fast with increasing temperature under 300 K, while it increases slowly with increasing temperature from 300 to 500 K.
4. Conclusion In summary, we have studied the encapsulated process of hydrogen molecules in CNTs at room temperature using MD simulations. Bending the nanotubes to a critical angle, an energy barrier would be formed at the kinks of CNTs, which impedes the hydrogen molecules from fleeing out of the CNTs. Thus, hydrogen molecules are successfully encapsulated in the CNTs at room temperature. The simulations show that, by increasing number of hydrogen molecules encapsulated into the CNTs and the ambient temperature, the critical angle increases accordingly. The CNT length also greatly influences the critical angle. However, it is demonstrated that the chirality of the CNTs has no strong influence on the critical angle and hydrogen storage process. Using this method, many other molecules can also be encapsulated. Due to the special structure of bent CNTs, the release of the hydrogen molecules can be controlled accurately.
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