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Structural Design and Two-Dimensional Conductivity of Sheet-Tube Frameworks C. H. Hu,† S. Q. Wu,*,† Y. H. Wen,† Y. Yang,‡ and Z. Z. Zhu*,† Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen UniVersity, Xiamen 361005, China, and State Key Lab for Physical Chemistry of Solid Surfaces, Xiamen UniVersity, Xiamen 361005, China ReceiVed: September 1, 2010; ReVised Manuscript ReceiVed: October 14, 2010
In this study, a family of defect-free and structurally analogous sheet-tube frameworks (STFs) constructed by tailored graphene sheets and (3n, 3n) armchair single-walled carbon nanotubes (SWCNTs) was proposed. First-principles calculations have been employed to investigate the structural and electronic properties of two typical STFs, namely, STF(6, 6)-I and STF(6, 6)-II. The results show that both are energetically stable and two-dimensionally conductive on the graphene sheets, a result of charge transfer from the tubes to the graphene sheets. All other defect-free STFs have thus been expected to be energetically stable and similar in electronic behaviors as they are structurally analogous to STF(6, 6)-I or STF(6, 6)-II. In addition, the present STFs are all in porous networks with high surface areas, promising their potential applications in the field of energy storage. The two-dimensional (2-D) conductivity of STFs is also expected to find important potential application in nanoelectronics. 1. Introduction Over the past decade, the increasing demand for energy and the desire for the reduction of air pollution have led to the urgent quest for novel renewable energy source that is environmentally friendly. Hydrogen1-3 has already been recognized as a promising energy carrier, especially for automotive applications, but it has not yet been used as a fuel on a large scale. Lithium-ion batteries are another energy storage instrument of utmost importance that have been widely commercialized but only for portable electronic devices. One of the crucial reasons for this has been the difficulty in finding safe and efficient energy storage materials. The solution to this problem, as revealed in much research, will be the design and synthesis of innovative targeted materials or the development of already existing materials with specific properties.4-8 Under the above-mentioned circumstances, a great many efforts have been made to design novel materials possibly propitious to enhance the capacity of energy storage. Previous investigations have suggested that high porosity4-6 and high surface area8,9 are the key elements to enhance the hydrogen’s storage capacity. For example, two typical highly porous materials, namely, metal organic frameworks (MOFs)10-12 and covalent-organic frameworks (COFs),8,13 have each exhibited exceptional capacity for hydrogen storage. Promising, revolutionary materials with high surface areas have also been applied in lithium-ion batteries.7 Nowadays, graphene (an all-surface material) and carbon nanotubes have been commonly recognized as attractive electrode materials in energy storage devices because of their outstanding electrical properties, high surface area, chemical stability, and mechanical strength.14-16 In addition, they can also be tailored chemically and/or structurally due to their high flexibility. In order to enhance the capacity of energy storage, the design of the targeted material is of special * Corresponding authors. Tel./Fax: +86 592 2189426. E-mail: zzhu@ xmu.edu.cn (Z.Z.Z.);
[email protected] (S.Q.W.). † Department of Physics and Institute of Theoretical Physics and Astrophysics. ‡ State Key Lab for Physical Chemistry of Solid Surfaces.
importance. Therefore, a family of materials of STFs, constructed by tailored graphene sheets and SWCNT, is proposed in this study. The present STFs are all in porous networks with high surface areas, thus promising their potential applications in the field of energy storage. However, the pristine STFs, like the pristine MOFs and COFs,17-19 are chemically too inert to bind enough H2 molecules at ambient conditions. Two main strategies could then be suggested for enhancing capacity of hydrogen storage in the present STFs: forming micropore sizes comparable to gas molecules20 by guest material and introducing coordinatively unsaturated metal centers.21,22 For example, the use of tritopic bridging ligand 1,3,5-benzenetristetrazolate in MOFs (with exposed metal coordination sites) successfully produced a stable and microporous material exhibiting exceptional H2 uptake.23 Recent inelastic neutron scattering studies suggest that high-affinity H2 binding sites are metal-based.24,25 On the other hand, because of their distinctive 2-D conductive properties, present defect-free STFs also hold the promise for application in nanoelectronics, such as nanocircuits. Practically, nanocircuits are composed of three different fundamental components, i.e., transistors, interconnections, and architecture.26 The STFs should be of special importance in interconnection and architecture of nanocircuits. 2. Structural Design and Calculation Method The newly designed STFs, characterized by both high porosity and high surface area (including most of the surface of graphene and SWCNT), are shown in Figure 1. The figure illustrates two typical structures of STFs, i.e., STF(6, 6)-I and STF(6, 6)-II. The pentagons and hexagons formed by atoms from both the sheet and the tube are highlighted in green and blue. All other polygons are formed by atoms of either the sheet or the tube only. The STF(m, m), where (m, m) represents the wrapping index of armchair SWCNT, is constructed by the tailored graphene sheets and the (m, m) armchair SWCNTs. In this structure, the graphene sheets are punched periodically and properly according to the size of the corresponding SWCNTs, creating the holes of an appropriate size on the sheet to bind
10.1021/jp1083289 2010 American Chemical Society Published on Web 11/03/2010
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Figure 1. Optimized structures of (a) STF(6, 6)-I and (b) STF(6, 6)-II. The pentagons and hexagons formed at the intersections are represented in green and blue, respectively.
Figure 2. Building blocks for (a-d) STF(6, 6), (e) STF(9, 9), (f) STF(15, 15), and (g-h) STF(12, 12), where the pentagons and hexagons formed at the intersections are shown in green and blue, respectively. In panels c and d, the tube’s atoms locating at the graphene plane are highlighted by red spheres for STF(6, 6)-I and STF(6, 6)-II, respectively.
the (m, m) armchair SWCNTs. Due to the symmetry of the graphene and the armchair SWCNT, a series of structurally defect-free STFs could be constructed and described as STF(3n, 3n) (with n g 2). All the STF(3n, 3n) are structurally analogous to each other, and the representative examples for STF(3n, 3n) are shown in Figure 2. The STF(3n, 3n) can be further classified structurally into two groups based on the odevity of n. When n ) 2m + 1 (where m is an integer), there is only one structural model for each STF(6m + 3, 6m + 3). In this structure, the polygons around the intersection area are arranged repeatedly by the unit of one hexagon and 2m pentagons [see examples shown in Figure 2, panels e and f]. When n ) 2m, there are two structural models for each STF(6m, 6m), namely, STF(6m, 6m)-I and STF(6m, 6m)-II. The former is represented by 6m pentagons in the intersection area, while the latter is distinguished by one hexagon and (m - 1) pentagons repeated periodically in the intersection area [see examples in Figure 2,
panels a, b, g, and h]. However, since the diameter of SWCNT obtained experimentally is always less than ∼3 nm,27,28 large STF(3n, 3n) may not be possible. As the representatives, two typical STFs, namely, STF(6, 6)-I and STF(6, 6)-II, are investigated by using first-principles calculations in terms of their electronic and structural properties. The unit cell is modeled by a “horizontal” (8 × 8) graphene sheet and a “vertical” tube consisting of six primitive cells of (6, 6) armchair SWCNT as shown in Figure 2a-d (the size of unit cell is tunable, i.e., the size of induced pores is tunable). The 24 central carbon atoms of the (8 × 8) graphene sheet are removed, creating holes of an appropriate size to bind the (6, 6) armchair SWCNT. Structurally, the STF(6, 6)-I and STF(6, 6)-II can be obtained from one another by fixing the tailored graphene sheet and rotating the (6, 6) armchair SWCNT along the tube’s axial direction by a suitable angle. The present calculations are performed by using the projector augmented wave (PAW) formalism based on the density functional theory as implemented in the Vienna ab initio simulation package (VASP).29-31 The generalized gradient approximation (GGA)32,33 for the exchange-correlation energy functional is employed. Brillouin zone integrations are approximated by using a special k-point sampling of the Monkhorst-Pack scheme34 with a 1 × 1 × 3 Γ-centered grid. The wave functions are expanded by the plane waves with a kinetic energy cutoff Ecut ) 400 eV. All of the structures are fully relaxed until the Hellmann-Feynman forces on all atoms are smaller than 0.005 eV/Å. Considering that graphene with a small vacancy could be magnetic,35,36 the spin-polarized calculations have been first performed to investigate whether the present tailored graphene and the STF(6, 6) are magnetic. The calculation results show that both the STF(6, 6)-I and STF(6, 6)-II are insensitive to the spin-polarized effects. Therefore, all of the following calculations are based on the nonspin-polarization scheme. 3. Results and Discussion Figure 1 illustrates the optimized structures of STF(6, 6)-I and STF(6, 6)-II, where the nearest-neighbor distances between the walls of carbon tubes are 12.70 and 12.61 Å, respectively, and the interlayer distances of graphene sheets are 14.88 Å for both cases. After structural optimization, the graphene sheets around the intersections are deformed, whereas the other parts are almost “flat”. The tubes near the intersections are also slightly radially compressed because the sizes of tubes and the punched hole on the graphene sheets do not match perfectly. The tubes in the STF(6, 6)-II are deformed a bit more severely than those in the STF(6, 6)-I. It is well-known that the typical bond length for 3-fold coordinated (sp2) carbon, such as in the graphene and graphite, is 1.42 Å and the bond angle is 120°. As far as the sp3 hybridization (C is 4-fold coordinated) is
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TABLE 1: Binding Energies, Eb, Lattice Parameters, Bond Lengths, d (Å), and Bond Angles, θ, of a Fourfold Coordinated Carbon Atom C4c with Its Nearest Neighbors for STF(6, 6)-I and STF(6, 6)-II, Respectively lattice parameters STF(6, 6)
Eb (eV/atom)
a (Å)
b (Å)
c (Å)
d (Å)
θ
STF(6, 6)-I STF(6, 6)-II
-7.683 -7.675
20.29 20.20
20.29 20.20
14.88 14.88
1.48, 1.48, 1.49, 1.52 1.50, 1.50, 1.49, 1.51
111.8°, 122.3°, 100.4°,107.6° 110.3°, 121.3°, 121.7°, 96.7°
concerned, the bond length is 1.54 Å and the corresponding bond angle is 109.5° as in diamond. In the STF(6, 6)-I and STF(6, 6)-II, all carbon atoms are 3-fold coordinated except those of tubes locating at the graphene plane: they are 4-fold coordinated and highlighted by red spheres in Figure 2, panels c and d. Hereafter, the 4-fold coordinated carbon atoms are denoted as C4c. The bond lengths and bond angles of the C4c atom with its nearest neighbors are presented in Table 1 for STF(6, 6)-I and STF(6, 6)-II, respectively. It can be seen from Table 1 that, for both STF(6, 6)-I and STF(6, 6)-II, the C4c atoms have similar bond lengths with carbon atoms in the sp3 hybridization. The corresponding bond angles of C4c range from 100.4° to 122.3° and from 96.7° to 121.7° for STF(6, 6)-I and STF(6, 6)-II, respectively, suggesting that sp3 bonds are deformed in both STF(6, 6)-I and STF(6, 6)-II. Moreover, STF(6, 6)-I and STF(6, 6)-II have quite similar binding energies (Table 1), with that of STF(6, 6)-I being slightly smaller than STF(6, 6)-II. The binding energy here is defined as Eb ) (ESTF - nEC)/n, where EC represents the atomic energy of a carbon atom, ESTF the total energy of STF(6, 6), and n the number of carbon atoms in the STF(6, 6) supercell. The binding energies of these two STFs (∼-7.68 eV/atom) are both close to those of (6, 6) armchair SWCNT (-7.74 eV/atom), graphite (-7.85 eV/atom) and graphene (-7.86 eV/atom), indicating that both STF(6, 6)-I and STF(6, 6)-II could be energetically stable. In order to better understand the bonding characteristics in STF(6, 6), the charge density differences of tailored graphene planes and the planes perpendicular to the graphene sheet passing through two C4c atoms are shown in Figure 3 for STF(6, 6)-I and STF(6, 6)-II, respectively. The charge density difference b- b Rµ), where F(r b) is defined as ∆F(r b) ) F(r b) - ∑µFatom(r b represents the total charge density of STF(6, 6) and ∑µFatom(r
Figure 3. Charge density differences of (a and c) the tailored graphene planes and (b and d) the planes passing through two C4c atoms for STF(6, 6)-I and STF(6, 6)-II, respectively.
-b Rµ) the superposition of atomic charge densities. Figure 3 suggests that all electrons are bonded in either sp2 or sp3 hybridization, leading to the defect-free structures of the STF(6, 6)-I and STF(6, 6)-II. Although the bonding coordinates in the intersections are different from those of other atoms, all bonds in STF(6, 6)-I and STF(6, 6)-II are strongly covalent. In comparison with the pristine graphene, the sp2 hybridization is preserved in the tailored graphene sheets of STF(6, 6)-I and STF(6, 6)-II [Figure 3, panels a and b]. Similarly, all the carbon atoms of tubes are bonded covalently with each other in the manner of sp2 hybridization as indicated in Figure 3, panels c and d, except C4c atoms. For C4c atoms located at the intersection areas, the four bonds are approximately equivalent to one another, as shown in Figure 3a-d. Hence, all the carbon atoms in STF(6, 6)-I and STF(6, 6)-II are in sp2 hybridization except C4c atoms that are in sp3 hybridization. Both graphene and SWCNT are well-known to be characterized by two types of bonds, namely σ bond (combined by s, px, and py orbitals) and π bond (combined by neighboring pz orbitals).37 Such σ bonds are strong and responsible for most binding energies and elastic properties of graphene and SWCNT. Therefore, the strong σ bonds (note: bonds around the intersection areas are also strong σ bonds) should also play the pivotal roles in determining the structural stability and electronic properties of both STF(6, 6)-I and STF(6, 6)-II. Figure 4 presents the band structures of STF(6, 6)-I, STF(6, 6)-II, the pristine graphene and the (6, 6) armchair SWCNT, where the Fermi level has been set as 0 eV. It is clear in Figure 4, panels a and b that, for both STF(6, 6)-I and STF(6, 6)-II, there are bands crossing the Fermi level in the planar directions (i.e., along M-K-Γ and L-H-A in the Brillouin zone), as highlighted by dashed circles, but not in the direction Γ-A (i.e., the axial direction of tube). Such a feature of the band structure indicates that electrons are conductive only in the graphene plane. Furthermore, the analyses of the contribution of electronic states to the band structures show that the bands crossing the Fermi level are predominately from the C-pz states of the graphene sheet, confirming that the electrons are conductive only in the graphene plane although the pristine graphene is semimetallic [Figure 4c] and the (6, 6) armchair SWCNT is metallic [Figure 4d]. In the pristine graphene, the pz orbital, pointing out of the graphene plane, interacts with its neighbors leading to the formation of π band and a zero-gap band structure. However, due to the interaction between the tailored graphene sheets and tubes in the STF(6, 6)-I and STF(6, 6)-II, the Fermi level rises significantly relative to that of the pristine graphene and the corresponding π bands around the Fermi level in graphene turn into “deeper” valence bands, indicating that electrons (of conduction band) have migrated from the tubes to the graphene planes. On the other hand, bands crossing the Fermi level in Figure 4d indicate that the (6, 6) armchair SWCNT is metallic. However, in both STF(6, 6)-I and STF(6, 6)-II, the fact that no band crosses the Fermi level along Γ-A (which corresponds to the Γ-Z in the SWCNT) together with the noticeable band-gaps along Γ-A demonstrate that conductivity along the tubes is not possible (at zero temperature). From
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Figure 4. Band structures of (a) STF(6, 6)-I, (b) STF(6, 6)-II, (c) pristine graphene, and (d) (6, 6) armchair SWCNT, where the Fermi levels are all at 0 eV and indicated by the dashed line.
larger structural deformation near the intersection in the STF(6, 6)-II, the tail of integrated charge redistribution curve of STF(6, 6)-II [Figure 5d] is somewhat more fluctuant than that of STF(6, 6)-I [Figure 5b]. Therefore, STF(6, 6)-I and STF(6, 6)-II are quite similar in both the structural and electronic properties though the polygons formed around the intersection areas are different from each other. Practically, the STF(6, 6)-I and STF(6, 6)-II, as shown in Figure 1, panels a and b, have not only the high surface area but also a large number of pores, ensuring their promising applications in the field of energy storage. In addition, because of the 2-D conductivity, they are also expected to find important potential applications in nanoelectronics. 4. Conclusions
Figure 5. Charge redistribution and the integrated charge redistribution over x-y plane ∆F′(z) as a function of z for (a and b) STF(6, 6)-I and (c and d) STF(6, 6)-II, respectively, where the red dashed lines represent the positions of the tailored graphene sheets.
the perspective of structural characteristics, the sp3 hybridization of C4c atoms at the intersection areas could also cause the conductivity along the tubes to be cut off, resulting in 2-D conductivities of the STF(6, 6)-I and STF(6, 6)-II. Additionally, the charge redistribution for STF(6, 6)-I and STF(6, 6)-II has also been calculated, as shown in Figure 5, b) - FSWCNT(r b) panels a and c. It is defined as ∆F′(r b) ) FSTF(r b), where FSTF(r b) represents the charge density of the Fgraphene(r b) (Fgraphene(r b)) the charge density of the STF(6, 6), and FSWCNT(r tube (graphene) calculated by removing the graphene (tube) with all the tubes’ (graphene’s) atoms frozen at the positions of optimized STF(6, 6). Figure 5, panels b and d, further display the x-y planar electron charge-density differences, i.e., the integrated charge redistribution over x-y plane, ∆F′(z), as a function of z for both STF(6, 6) structures. Generally, the calculated charge redistribution profiles for the STF(6, 6)-I and STF(6, 6)-II, as shown in Figure 5, are similar on the whole, in consistent with their topologically analogous structures. The charge redistribution mainly occurs in the graphene sheet and its neighboring areas. The redistributed charges around the graphene sheet are verified by the sharp peaks around z ) 0 Å in the Figure 5, panels b and d. Furthermore, the two negative sharp peaks (at about z ) (1 Å) together with a positive sharp peak (at z ) 0 Å) in Figure 5, panels b and d, suggest that the charge redistribution at the tailored graphene sheets is mostly transferred from its very near layers. Nevertheless, due to a bit
We have proposed a series of defect-free and structurally analogous STFs, namely, STF(3n, 3n) (n g 2, n ∈ N), which are constructed by tailored graphene sheets and (3n, 3n) armchair SWCNT according to the symmetry of the graphene sheet and the armchair SWCNT. First-principles calculations have been employed to investigate the structural and electronic properties of STF(6, 6)-I and STF(6, 6)-II. It is found that both can be energetically stable. All of the carbon atoms in the STF(6, 6)-I and STF(6, 6)-II are in sp2 or sp3 hybridization, ensuring their defect-free configuration and structural stability. In addition, STF(6, 6)-I and STF(6, 6)-II are two-dimensionally conductive because of the charge transfer from tubes to graphene sheets. This 2-D conductivity is expected to find important potential applications in nanoelectronics. It is expected that all the STF(3n, 3n) should also be energetically stable and similar in electronic behaviors as they are all structurally analogous to the STF(6, 6). All of the present STFs are in porous networks with high surface areas, thus showing potential applications in the field of energy storage. Acknowledgment. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10774124 and 10702056. References and Notes (1) Coontz, R.; Hanson, B. Science 2004, 305, 957. (2) Schlapbach, L.; Zu¨ttel, A. Nature 2001, 414, 353. (3) Crabtree, G. W.; Dresselhaus, M. S.; Buchanan, M. V. Phys. Today 2004, 57, 39. (4) Bhatia, K. S.; Myers, L. A. Langmuir 2006, 22, 1688. (5) Kowalczyk, P.; Holyst, R.; Terrones, M.; Terrones, H. Phys. Chem. Chem. Phys. 2007, 9, 1786. (6) Jorda´-Beneyto, M.; Sua´rez-Garcı´a, F.; Lozano-Castello´, D.; CazorlaAmoro´s, D.; Linares-Solano, A. Carbon 2007, 45, 293.
Design and Conductivity of Sheet-Tube Frameworks (7) Reddy, A. L. M.; Shaijumon, M. M.; Gowda, S. R.; Ajayan, P. M. Nano Lett. 2009, 9, 1002. (8) Klontzas, E.; Tylianakis, E.; Froudakis, G. E. Nano Lett. 2010, 10, 452. (9) Wu, X. J.; Zeng, X. C. Nano Lett. 2009, 9, 250. (10) Li, H. L.; Eddaoudi, M.; O’Keeffe, M.; Yaghi, O. M. Nature 1999, 402, 276. (11) Klontzas, E.; Mavrandonakis, A.; Froudakis, G. E.; Carissan, Y.; Klopper, W. J. Phys. Chem. C 2007, 111, 13635. (12) Zhao, X. B.; Xiao, B.; Fletcher, A. J.; Thomas, K. M.; Bradshaw, D.; Rosseinsky, M. J. Science 2004, 306, 1012. (13) El-Kaderi, H. M.; Hunt, J. R.; Mendoza-Corte´s, J. L.; Coˆte´, A. P.; Taylor, R. E.; O’Keeffe, M.; Omar, M. Y. Science 2007, 316, 268. (14) Park, J. H.; Ko, J. M.; Park, O. O. J. Electrochem. Soc. 2003, 150, 864. (15) Reddy, A. L. M.; Ramaprabhu, S. J. Phys. Chem. C 2007, 111, 7727. (16) Liao, S. J.; Holmes, K. A.; Tsaprailis, H.; Birss, V. I. J. Am. Chem. Soc. 2006, 128, 3504. (17) Rowsell, J. L. C.; Millward, A. R.; Park, K. S.; Yaghi, O. M. J. Am. Chem. Soc. 2004, 126, 5666. (18) Sillar, K.; Hofmann, A.; Sauer, J. J. Am. Chem. Soc. 2009, 131, 4143. (19) Klontzas, E.; Tylianakis, E.; Froudakis, G. E. J. Phys. Chem. C 2008, 112, 9095. (20) Pan, L.; Sander, M. B.; Huang, X. Y.; Li, J.; Smith, M.; Bittner, E.; Bockrath, B.; Johnson, J. K. J. Am. Chem. Soc. 2004, 126, 1308.
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