- Email: [email protected]
Hydrogenation of ultrasmall carbon nanotubes: A first principle study
Chemical Physics Letters 480 (2009) 215–219
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Hydrogenation of ultrasmall carbon nanotubes: A first principle study Roberto Scipioni a,*, Mauro Boero b,c, Takahisa Ohno d a
International Center for Materials Nanoarchitectonics, MANA, 1-1 Namiki, Tsukuba 305-0044, Japan Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS-UDS, 23 rue du Loess, F-67034 Strasbourg, France c JAIST, 1-1 Asahidai, Nomi-shi, Ishikawa 923-1292, Japan d Computational Materials Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan b
a r t i c l e
i n f o
Article history: Received 6 July 2009 In final form 25 August 2009 Available online 4 September 2009
a b s t r a c t We analyze, via molecular dynamics, the hydrogenation of the smallest zigzag and armchair carbon nanotubes. These tubes with radii smaller than 0.4 nm, contrary to larger tubes, upon exposure to molecular hydrogen have an exothermic hydrogenation. First principles simulations show that these tubes are thermally stable up to temperatures of 1500 K. The free energy profiles for hydrogen abstraction, computed via constrained dynamics for the case of the (2, 2) tube, show that the energy barrier for hydrogenation from a single H2 molecule is about 1.5–2.0 eV, thus amounting to half (or less) the dissociation energy of H2 in gas phase. Ó 2009 Elsevier B.V. All rights reserved.
Carbon nanotubes have attracted considerable attention because of their peculiar electronic and mechanical properties [1]. Recently, some efforts have been devoted to the fabrication of ultra-small carbon nanotubes (USCNTs). Qin and coworkers [2] and Zhao et al. [3] found tubes with diameters of 0.4 and 0.3 nm. These were identified as inner layers of multiwalled nanotubes. More recently the USCNT (2, 2) was discovered in some confined zeolite structures where they were found to be stable [4]. These tubes would not be stable in empty space where they are expected to be damaged even at small temperatures. Carbon nanotubes (CNTs) owe some of the interest to the fact they can be filled with various molecules ranging from fullerenes [5] to fibers [6] and water [7]. Suggestions have been given to their usage for hydrogen storage [8,9]. Unfortunately the yield of this storage have been found not to exceed a few per cent at most. The major drawback seems to be the fact that molecular hydrogen is weakly bound to the tube and, due to the small size of the H2 molecule, characterized by a high diffusivity even inside a small CNT, thus making the escape from the tube a very easy process. A possibility to overcome this difficulty is to use hydrogen chemisorption rather than physisorption. Some previous theoretical studies [10] found that the hydrogenation from the exterior (exohydrogenation) of a CNT is energetically favorable. However, although the reaction is exothermic with respect to atomic hydrogen, it is endothermic with respect to the more common molecular hydrogen due to the high dissociation energy of the H2 molecule. Experimentally it was observed, via XAS and XPS, a reversible atomic hydrogenation for CNTs with diameters ranging from 1 to 1.8 nm [11].
* Corresponding author. E-mail address: [email protected] (R. Scipioni). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.08.078
Here we concentrate on the smallest non chiral CNTs, which are likely to be very reactive to hydrogen, also thanks to their small curvature radius. We focus on their mechanical and thermal stability and on their interaction with H atoms and H2 molecules. In particular, we investigate the properties of fully exohydrogenated USCNTs (2, 2), (3, 3), (4, 0) and (5, 0) having radii never exceeding 0.4 nm. We remind here that a generic carbon nanotube can be specified giving its chiral indices (n, m) which give the lattice vector of the tube as Cnm ¼ a1 n þ a2 m with a1 and a2 the lattice parameters of a graphitic plane. We used static relaxations within the density functional theory (DFT) framework, as implemented in the PHASE code [12] as well as Car–Parrinello molecular dynamics simulations [13,14]. In the first case we used ultrasoft pseudopotentials [15] and a plane-wave basis set with a cut-off of 29 Ry to represent the valence electrons wavefunctions, the generalized gradient approximation (GGA) within the scheme of Becke and Lee et al. was used [17,18]. In order to reduce the number of K points necessary for the calculation, we used three unit cells along the tube axis. With a number of atoms ranging from 60 to 80, A good convergence was achieved using meshes within the Monkhorst Pack scheme [16] of (1, 1, 20) or (2, 2, 20) points. Geometry optimizations were continued until residual forces on the atoms were less than 0.001 Ha/Bohr. Test calculations were also performed allowing the cell parameter along the tube axis to vary, without noticing any significant difference. Large cell simulations were used to keep a separation between neighbor images of at least 0.6 nm, since periodic boundary conditions were imposed. These static calculations showed that these materials have big gaps of the order of 2–3 eV therefore a Car–Parrinello approach is adequate for dynamical simulations. These were also performed within the Becke [17] and Lee et al. [18] gradient corrected exchange and correlation functionals, respectively. Since in this case
216
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
Table 1 Relaxed radii (Å), binding energies for atomic and molecular hydrogen and band gaps (eV) for different armchair and zigzag tubes. Tube
R
H
H2
Eg
(2, 2) (3, 3) (4, 0) (5, 0)
3.2 4.7 3.7 4.5
4.35 3.50 4.0 3.6
1.0 0.2 0.7 0.3
3.5 2.5 3.4 2.9
norm-conserving pseudopotentials were used [19] a larger planewave cut-off (50 Ry) was used, sampling the Brillouin zone at the C point only. Simulations were started from the same static struc-
tures obtained within the former computational scheme, using larger supercells with at least 60 atoms. The temperature which was controlled by a Nosé–Hoover thermostat [20,21], was increased starting from room temperature by steps of 300 K up to 1500 K for a total simulation time of 20 ps. The fictitious electronic mass and the time step were set to 400 a.u and 4 a.u. respectively. These finite temperature simulations displayed deformations of the tubes during the dynamics, however kept their structure without undergoing any bond breaking and without showing any sign of permanent geometrical modification. In Table 1 we report the binding energies per atom with respect to atomic hydrogen, expressed as
Fig. 1. Stable geometries and band structure of the fully exohydrogenated tubes (2, 2) and (3, 3).
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
EBH ¼ ðECH EC nEH Þ=n
ð1Þ
and with respect to molecular hydrogen, given by
1 EBH2 ¼ ðECH EC nEH2 Þ=n: 2
ð2Þ
We can see that all tubes are stable not only against atomic hydrogen, but also with respect to H2 , with energy gains per atom ranging from 0.2 to 1.0 eV, the latter occurring for the tube (2, 2). In an attempt at rationalizing these results, we observe that the smaller the tube, the larger is the deviation from the sp2 bonding and the stronger is the sp3 hybridization, since each C atom forms four bonds, three with other C atoms and one with H. Hence, smaller tubes are more stable since they have a stronger sp3 nature.
217
These results agree with what previously found in the theoretical work by Yildirim et al. [10] on exohydrogenation of bigger tubes. There it was observed that binding energy of hydrogens to carbon nanotubes increases as the tube diameter decreases suggesting that for smaller CNTs hydrogenation should be stable also with respect to molecular hydrogen, as found here. Fig. 1 shows the results for the band structure and optimized geometry of the fully exohydrogenated armchair USCNTs (2, 2) and (3, 3). The computed band gap is over 2 eV for both tubes. An analogous trend holds also for the zigzag tubes (4, 0) and (5, 0), where the computed band gaps are larger than 2.9 eV (Fig. 2). These wide gaps confer a high stability to these hydrogenated tubes with respect to their non-hydrogenated structures.
Fig. 2. Stable geometries and band structure of the fully exohydrogenated tubes (4, 0) and (5, 0).
218
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
The big gap originates from the localization of the electronic bands caused by the saturation of the carbon p dangling bonds saturated by H. It was shown that by using different rates of coverage the band gap of carbon nanotubes changes from metallic to semiconducting, and the other way around [22]. The thermodynamic and mechanical stability evidenced by our finite temperature simulations suggest that these structures are actually laboratory-realizable and are deemed to be stable even if not inserted in host structures or larger tubes. However, they must be first synthesized. One possibility could be the hydrogenation of USCNTs contained inside one of these hosts. Since the most abundant form of H available is the H2 molecule and since its dissociation energy in gas phase can be over 6 eV, the simple approach of adding H2 to the USCNT walls would require the overcoming of a very high activation barrier to hydrogenate the tube. However, we have to observe that very small carbon nanotubes have strained and dangling bonds that are very reactive because of the large deviations from the sp2 geometry. Therefore, we can expect that the carbon atoms themselves can act as catalysts for the process. To check whether this is true or not, we sampled the free energy profile of this reaction using the thermodynamic integration approach [23–26] for the tube (2, 2). We started from the case where all the carbons are saturated by H but two (see Fig. 3). This choice was motivated by the fact the almost fully saturated tube is very stable and with big HOMO LUMO gap, therefore the Car–Parrinello MD procedure was feasible for the long calculation which is necessary to accumulate statistics and to compute the Free Energy
profile of the reaction. The same analysis with very small coverage requires for the metallic (2, 2) nanotube a Born–Oppenheimer procedure and therefore it would be computationally more expensive. In the next forthcoming work the dependence of the energy barriers on the coverage will be reported. As shown in panel (a) of Fig. 3 (lateral view), the center of mass of a H2 molecule, which is initially placed at a distance of about 2.5 Å from two adjacent unsaturated C atoms, is moved toward the tube via constrained dynamics [24]. As it approaches the unsaturated C atoms (panel (b) of Fig. 3) it starts forming bonds with one of the two C atoms. This weakens the H-H bond of the H2 molecule (panel (c) of Fig. 3) which start to dissociate (panel (d) of Fig. 3) until the two H atoms are completely bound to the tube in positions geometrically equivalent to all the other H atoms already bonded to the tube (panel (e) of Fig. 3). The free and total energy profiles, computed at 300 K and at 600 K (Fig. 4), show that the final state, corresponding to a fully hydrogenated tube (and dissociated H2 ) is located to a lower energy with respect to the reactant (undissociated H2 ). In particular, by looking at the differences between the total and free energy curves, since DF ¼ DEtot T DS, we notice that the entropy contribution is large before the molecule approaches the tube and is of course larger in the case higher temperature. In fact the total energy curve is above the free energy one. Then, when the molecule is captured, there is a decrease in the entropy, as expected and already remarked in other system using an identical approach [26]. Finally, when the molecule is completely dissociated and the tube fully hydrogenated, at both temperature the system show a total energy
Fig. 3. Snapshots of the main phases of the hydrogenation of the tube (2, 2). Panels from (a) to (e) go from the reactant to the product. Details are given in the text. For the sake of clarity the H atoms of the incoming hydrogen molecule are evidenced as red spheres. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
219
hydrogenation and mechanically stable up to a temperature of 1500 K. The free energy profile, computed on the tube (2, 2) for its last hydrogenation step, shows that unsaturated C dangling p bonds can lower the dissociation energy of H2 by more than 2 eV, thus serving as an intrinsic catalyst leading to the full hydrogenation of the USCNT. This suggests that if a proper catalytic mechanism is found to grow these structures they can effectively be hydrogenated and behave like very stable materials. A detailed study of the dependence on coverage, bond positions, reaction paths, etc.; is under way and will be reported elsewhere. Acknowledgements
Fig. 4. Free (solid lines, filled circles) and total (dashed lines, open squares) energy profiles for the approach of an H2 molecule to the (2, 2) CNT at different temperatures. The lower panel refers to a simulation performed at 300 K, the upper panel to an identical simulation performed at 600 K.
lower than the free energy. This is due both to the fact that after the reaction the constraint forces are vanishing, thus no longer contributing to DF [27], and to the fact that by the reassessment of the newly formed C–H bonds the system is entropy-stabilized, again in agreement with previous findings [26]. This is another confirmation that hydrogenation is thermodynamically favored and stabilizes the system. interestingly, the free energy barrier to dissociate the H2 molecule leading to the full hydrogenation is about 1.5–2.0 eV per atom, i.e. about 3.0–4.0 eV, much lower than the dissociation energy of the H2 molecule alone, which amounts to 6–7 eV. Of course, the energy barrier depends on many factors, beside the temperature, as evidenced by these calculations. Namely, on the percentage of H coverage, the positions of the bonds, the reaction path, etc. However, it is remarkable the effect of the dangling p bonds in lowering the dissociation energy of H2 by almost 3 eV with respect to the bare molecule, indicating that potential hydrogenation mechanisms for USCNTs can be realized via metallic clusters and/or surfaces acting as a catalyst for H2 . On the other hand, USCNTs have so far only be found in confined structures. It can then be inferred that the confining hosts can serve as a catalyst, thus not requiring any external triggering agent. It would be important to estimate the hydrogenation rate however, as mentioned, energy barriers are highly influenced by the coverage and other factors. A more thorough study of this dependence is therefore required. We plan to do that in the near future. Summarizing, the smallest non chiral USCNT, namely (2, 2), (3, 3), (4, 0), (5, 0), have been shown to be energetically stable upon
We acknowledge H. Momida for his help with the code PHASE, Cesar P. Gomez for stimulating discussions on the problem of hydrogenation of nanotubes. This work was performed using Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology of the Japan. Calculations were performed on the NIMS supercomputer and on the Linux ICYS Cluster Shizuwo. References [1] S. Iijima, Nature 354 (1991) 56. [2] X. Zhao, K. Hirahara, Y. Miyamoto, Y. Ando, S. Iijima, L-C. Qin, Nature 408 (2000) 50. [3] X. Zhao, Y. Liu, S. Inoue, T. Suzuki, R.O. Jones, Y. Ando, Phys. Rev. Lett. 92 (2004) 125502. [4] Z.K. Tang, J.P. Zhai, Y.Y. Tong, X.J. Hu, R. Saito, Y.J. Feng, P. Sheng, Phys. Rev. Lett. 101 (2008) 047402. [5] B.W. Smith, M. Mothiou, D.E. Luzzi, Nature 396 (1998) 323. [6] F. Ko et al., Adv. Mater. 15 (2003) 1161. [7] Y. Maniwa et al., Nature Mater. 6 (2007) 135. [8] A.C. Dillon, K.M. Jones, T.A. Bekkedahl, C.H. Kiang, D.S. Bethune, M.J. Heben, Nature 386 (1997) 377. [9] G. Gundiah, A. Govindaraj, N. Rajalakshimi, K.S. Dhathathreya, C.N.R. Rao, J. Mater. Chem. 13 (2003) 209. [10] T. Yildirim et al., Phys. Rev. B 64 (2001) 075404. [11] A. Nikitin et al., Phys. Rev. Lett. 95 (2005) 225507. [12] See
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Hydrogenation of ultrasmall carbon nanotubes: A first principle study Roberto Scipioni a,*, Mauro Boero b,c, Takahisa Ohno d a
International Center for Materials Nanoarchitectonics, MANA, 1-1 Namiki, Tsukuba 305-0044, Japan Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS-UDS, 23 rue du Loess, F-67034 Strasbourg, France c JAIST, 1-1 Asahidai, Nomi-shi, Ishikawa 923-1292, Japan d Computational Materials Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan b
a r t i c l e
i n f o
Article history: Received 6 July 2009 In final form 25 August 2009 Available online 4 September 2009
a b s t r a c t We analyze, via molecular dynamics, the hydrogenation of the smallest zigzag and armchair carbon nanotubes. These tubes with radii smaller than 0.4 nm, contrary to larger tubes, upon exposure to molecular hydrogen have an exothermic hydrogenation. First principles simulations show that these tubes are thermally stable up to temperatures of 1500 K. The free energy profiles for hydrogen abstraction, computed via constrained dynamics for the case of the (2, 2) tube, show that the energy barrier for hydrogenation from a single H2 molecule is about 1.5–2.0 eV, thus amounting to half (or less) the dissociation energy of H2 in gas phase. Ó 2009 Elsevier B.V. All rights reserved.
Carbon nanotubes have attracted considerable attention because of their peculiar electronic and mechanical properties [1]. Recently, some efforts have been devoted to the fabrication of ultra-small carbon nanotubes (USCNTs). Qin and coworkers [2] and Zhao et al. [3] found tubes with diameters of 0.4 and 0.3 nm. These were identified as inner layers of multiwalled nanotubes. More recently the USCNT (2, 2) was discovered in some confined zeolite structures where they were found to be stable [4]. These tubes would not be stable in empty space where they are expected to be damaged even at small temperatures. Carbon nanotubes (CNTs) owe some of the interest to the fact they can be filled with various molecules ranging from fullerenes [5] to fibers [6] and water [7]. Suggestions have been given to their usage for hydrogen storage [8,9]. Unfortunately the yield of this storage have been found not to exceed a few per cent at most. The major drawback seems to be the fact that molecular hydrogen is weakly bound to the tube and, due to the small size of the H2 molecule, characterized by a high diffusivity even inside a small CNT, thus making the escape from the tube a very easy process. A possibility to overcome this difficulty is to use hydrogen chemisorption rather than physisorption. Some previous theoretical studies [10] found that the hydrogenation from the exterior (exohydrogenation) of a CNT is energetically favorable. However, although the reaction is exothermic with respect to atomic hydrogen, it is endothermic with respect to the more common molecular hydrogen due to the high dissociation energy of the H2 molecule. Experimentally it was observed, via XAS and XPS, a reversible atomic hydrogenation for CNTs with diameters ranging from 1 to 1.8 nm [11].
* Corresponding author. E-mail address: [email protected] (R. Scipioni). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.08.078
Here we concentrate on the smallest non chiral CNTs, which are likely to be very reactive to hydrogen, also thanks to their small curvature radius. We focus on their mechanical and thermal stability and on their interaction with H atoms and H2 molecules. In particular, we investigate the properties of fully exohydrogenated USCNTs (2, 2), (3, 3), (4, 0) and (5, 0) having radii never exceeding 0.4 nm. We remind here that a generic carbon nanotube can be specified giving its chiral indices (n, m) which give the lattice vector of the tube as Cnm ¼ a1 n þ a2 m with a1 and a2 the lattice parameters of a graphitic plane. We used static relaxations within the density functional theory (DFT) framework, as implemented in the PHASE code [12] as well as Car–Parrinello molecular dynamics simulations [13,14]. In the first case we used ultrasoft pseudopotentials [15] and a plane-wave basis set with a cut-off of 29 Ry to represent the valence electrons wavefunctions, the generalized gradient approximation (GGA) within the scheme of Becke and Lee et al. was used [17,18]. In order to reduce the number of K points necessary for the calculation, we used three unit cells along the tube axis. With a number of atoms ranging from 60 to 80, A good convergence was achieved using meshes within the Monkhorst Pack scheme [16] of (1, 1, 20) or (2, 2, 20) points. Geometry optimizations were continued until residual forces on the atoms were less than 0.001 Ha/Bohr. Test calculations were also performed allowing the cell parameter along the tube axis to vary, without noticing any significant difference. Large cell simulations were used to keep a separation between neighbor images of at least 0.6 nm, since periodic boundary conditions were imposed. These static calculations showed that these materials have big gaps of the order of 2–3 eV therefore a Car–Parrinello approach is adequate for dynamical simulations. These were also performed within the Becke [17] and Lee et al. [18] gradient corrected exchange and correlation functionals, respectively. Since in this case
216
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
Table 1 Relaxed radii (Å), binding energies for atomic and molecular hydrogen and band gaps (eV) for different armchair and zigzag tubes. Tube
R
H
H2
Eg
(2, 2) (3, 3) (4, 0) (5, 0)
3.2 4.7 3.7 4.5
4.35 3.50 4.0 3.6
1.0 0.2 0.7 0.3
3.5 2.5 3.4 2.9
norm-conserving pseudopotentials were used [19] a larger planewave cut-off (50 Ry) was used, sampling the Brillouin zone at the C point only. Simulations were started from the same static struc-
tures obtained within the former computational scheme, using larger supercells with at least 60 atoms. The temperature which was controlled by a Nosé–Hoover thermostat [20,21], was increased starting from room temperature by steps of 300 K up to 1500 K for a total simulation time of 20 ps. The fictitious electronic mass and the time step were set to 400 a.u and 4 a.u. respectively. These finite temperature simulations displayed deformations of the tubes during the dynamics, however kept their structure without undergoing any bond breaking and without showing any sign of permanent geometrical modification. In Table 1 we report the binding energies per atom with respect to atomic hydrogen, expressed as
Fig. 1. Stable geometries and band structure of the fully exohydrogenated tubes (2, 2) and (3, 3).
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
EBH ¼ ðECH EC nEH Þ=n
ð1Þ
and with respect to molecular hydrogen, given by
1 EBH2 ¼ ðECH EC nEH2 Þ=n: 2
ð2Þ
We can see that all tubes are stable not only against atomic hydrogen, but also with respect to H2 , with energy gains per atom ranging from 0.2 to 1.0 eV, the latter occurring for the tube (2, 2). In an attempt at rationalizing these results, we observe that the smaller the tube, the larger is the deviation from the sp2 bonding and the stronger is the sp3 hybridization, since each C atom forms four bonds, three with other C atoms and one with H. Hence, smaller tubes are more stable since they have a stronger sp3 nature.
217
These results agree with what previously found in the theoretical work by Yildirim et al. [10] on exohydrogenation of bigger tubes. There it was observed that binding energy of hydrogens to carbon nanotubes increases as the tube diameter decreases suggesting that for smaller CNTs hydrogenation should be stable also with respect to molecular hydrogen, as found here. Fig. 1 shows the results for the band structure and optimized geometry of the fully exohydrogenated armchair USCNTs (2, 2) and (3, 3). The computed band gap is over 2 eV for both tubes. An analogous trend holds also for the zigzag tubes (4, 0) and (5, 0), where the computed band gaps are larger than 2.9 eV (Fig. 2). These wide gaps confer a high stability to these hydrogenated tubes with respect to their non-hydrogenated structures.
Fig. 2. Stable geometries and band structure of the fully exohydrogenated tubes (4, 0) and (5, 0).
218
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
The big gap originates from the localization of the electronic bands caused by the saturation of the carbon p dangling bonds saturated by H. It was shown that by using different rates of coverage the band gap of carbon nanotubes changes from metallic to semiconducting, and the other way around [22]. The thermodynamic and mechanical stability evidenced by our finite temperature simulations suggest that these structures are actually laboratory-realizable and are deemed to be stable even if not inserted in host structures or larger tubes. However, they must be first synthesized. One possibility could be the hydrogenation of USCNTs contained inside one of these hosts. Since the most abundant form of H available is the H2 molecule and since its dissociation energy in gas phase can be over 6 eV, the simple approach of adding H2 to the USCNT walls would require the overcoming of a very high activation barrier to hydrogenate the tube. However, we have to observe that very small carbon nanotubes have strained and dangling bonds that are very reactive because of the large deviations from the sp2 geometry. Therefore, we can expect that the carbon atoms themselves can act as catalysts for the process. To check whether this is true or not, we sampled the free energy profile of this reaction using the thermodynamic integration approach [23–26] for the tube (2, 2). We started from the case where all the carbons are saturated by H but two (see Fig. 3). This choice was motivated by the fact the almost fully saturated tube is very stable and with big HOMO LUMO gap, therefore the Car–Parrinello MD procedure was feasible for the long calculation which is necessary to accumulate statistics and to compute the Free Energy
profile of the reaction. The same analysis with very small coverage requires for the metallic (2, 2) nanotube a Born–Oppenheimer procedure and therefore it would be computationally more expensive. In the next forthcoming work the dependence of the energy barriers on the coverage will be reported. As shown in panel (a) of Fig. 3 (lateral view), the center of mass of a H2 molecule, which is initially placed at a distance of about 2.5 Å from two adjacent unsaturated C atoms, is moved toward the tube via constrained dynamics [24]. As it approaches the unsaturated C atoms (panel (b) of Fig. 3) it starts forming bonds with one of the two C atoms. This weakens the H-H bond of the H2 molecule (panel (c) of Fig. 3) which start to dissociate (panel (d) of Fig. 3) until the two H atoms are completely bound to the tube in positions geometrically equivalent to all the other H atoms already bonded to the tube (panel (e) of Fig. 3). The free and total energy profiles, computed at 300 K and at 600 K (Fig. 4), show that the final state, corresponding to a fully hydrogenated tube (and dissociated H2 ) is located to a lower energy with respect to the reactant (undissociated H2 ). In particular, by looking at the differences between the total and free energy curves, since DF ¼ DEtot T DS, we notice that the entropy contribution is large before the molecule approaches the tube and is of course larger in the case higher temperature. In fact the total energy curve is above the free energy one. Then, when the molecule is captured, there is a decrease in the entropy, as expected and already remarked in other system using an identical approach [26]. Finally, when the molecule is completely dissociated and the tube fully hydrogenated, at both temperature the system show a total energy
Fig. 3. Snapshots of the main phases of the hydrogenation of the tube (2, 2). Panels from (a) to (e) go from the reactant to the product. Details are given in the text. For the sake of clarity the H atoms of the incoming hydrogen molecule are evidenced as red spheres. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
R. Scipioni et al. / Chemical Physics Letters 480 (2009) 215–219
219
hydrogenation and mechanically stable up to a temperature of 1500 K. The free energy profile, computed on the tube (2, 2) for its last hydrogenation step, shows that unsaturated C dangling p bonds can lower the dissociation energy of H2 by more than 2 eV, thus serving as an intrinsic catalyst leading to the full hydrogenation of the USCNT. This suggests that if a proper catalytic mechanism is found to grow these structures they can effectively be hydrogenated and behave like very stable materials. A detailed study of the dependence on coverage, bond positions, reaction paths, etc.; is under way and will be reported elsewhere. Acknowledgements
Fig. 4. Free (solid lines, filled circles) and total (dashed lines, open squares) energy profiles for the approach of an H2 molecule to the (2, 2) CNT at different temperatures. The lower panel refers to a simulation performed at 300 K, the upper panel to an identical simulation performed at 600 K.
lower than the free energy. This is due both to the fact that after the reaction the constraint forces are vanishing, thus no longer contributing to DF [27], and to the fact that by the reassessment of the newly formed C–H bonds the system is entropy-stabilized, again in agreement with previous findings [26]. This is another confirmation that hydrogenation is thermodynamically favored and stabilizes the system. interestingly, the free energy barrier to dissociate the H2 molecule leading to the full hydrogenation is about 1.5–2.0 eV per atom, i.e. about 3.0–4.0 eV, much lower than the dissociation energy of the H2 molecule alone, which amounts to 6–7 eV. Of course, the energy barrier depends on many factors, beside the temperature, as evidenced by these calculations. Namely, on the percentage of H coverage, the positions of the bonds, the reaction path, etc. However, it is remarkable the effect of the dangling p bonds in lowering the dissociation energy of H2 by almost 3 eV with respect to the bare molecule, indicating that potential hydrogenation mechanisms for USCNTs can be realized via metallic clusters and/or surfaces acting as a catalyst for H2 . On the other hand, USCNTs have so far only be found in confined structures. It can then be inferred that the confining hosts can serve as a catalyst, thus not requiring any external triggering agent. It would be important to estimate the hydrogenation rate however, as mentioned, energy barriers are highly influenced by the coverage and other factors. A more thorough study of this dependence is therefore required. We plan to do that in the near future. Summarizing, the smallest non chiral USCNT, namely (2, 2), (3, 3), (4, 0), (5, 0), have been shown to be energetically stable upon
We acknowledge H. Momida for his help with the code PHASE, Cesar P. Gomez for stimulating discussions on the problem of hydrogenation of nanotubes. This work was performed using Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology of the Japan. Calculations were performed on the NIMS supercomputer and on the Linux ICYS Cluster Shizuwo. References [1] S. Iijima, Nature 354 (1991) 56. [2] X. Zhao, K. Hirahara, Y. Miyamoto, Y. Ando, S. Iijima, L-C. Qin, Nature 408 (2000) 50. [3] X. Zhao, Y. Liu, S. Inoue, T. Suzuki, R.O. Jones, Y. Ando, Phys. Rev. Lett. 92 (2004) 125502. [4] Z.K. Tang, J.P. Zhai, Y.Y. Tong, X.J. Hu, R. Saito, Y.J. Feng, P. Sheng, Phys. Rev. Lett. 101 (2008) 047402. [5] B.W. Smith, M. Mothiou, D.E. Luzzi, Nature 396 (1998) 323. [6] F. Ko et al., Adv. Mater. 15 (2003) 1161. [7] Y. Maniwa et al., Nature Mater. 6 (2007) 135. [8] A.C. Dillon, K.M. Jones, T.A. Bekkedahl, C.H. Kiang, D.S. Bethune, M.J. Heben, Nature 386 (1997) 377. [9] G. Gundiah, A. Govindaraj, N. Rajalakshimi, K.S. Dhathathreya, C.N.R. Rao, J. Mater. Chem. 13 (2003) 209. [10] T. Yildirim et al., Phys. Rev. B 64 (2001) 075404. [11] A. Nikitin et al., Phys. Rev. Lett. 95 (2005) 225507. [12] See