- Email: [email protected]
Structural and electronic properties of bamboo-like carbon nanostructure
ARTICLE IN PRESS
Physica E 31 (2006) 62–66 www.elsevier.com/locate/physe
Structural and electronic properties of bamboo-like carbon nanostructure S- akir Erkoc- Department of Physics, Middle East Technical University, 06531 Ankara, Turkey Received 26 August 2005; accepted 21 September 2005 Available online 10 November 2005
Abstract The structural and electronic properties of bamboo-like carbon nanostructure have been investigated qualitatively by performing semiempirical self-consistent-field molecular orbital calculations at the level of the PM3 method within the RHF formulation. It has been found that these structures are stable and endothermic. Bamboo-like carbon nanostructures resemble zigzag carbon nanotubes capped with a plane graphine sheet. r 2005 Elsevier B.V. All rights reserved. PACS: 61.48.+c; 61.46.+w; 31.15.Ct Keywords: Carbon nanotubes; Carbon bamboo structures; SCF-MO calculation; PM3 method
1. Introduction Carbon-based materials became important early in the century [1,2]. Since then, there has been an ever-growing number of proposed forms and commercial applications. Rather recently, this trend reached the size of nanometers [3,4], and gained a whole new aspect with the introduction of the famous fullerene molecule [5]. There are many fullerene-related carbon nanostructures, such as carbon nanotubes (CNTs) [6], nanorods [7–11], nanotori [12,13], etc. These structures exhibit intriguing electronic properties, along with unusual structural stability, and this makes them highly popular in future commercial applications that may come to pass. One interesting point is that the nonplanar carbon macromolecules were not unknown to society before the introduction of fullerene itself. In fact, the basic building block of C60, namely corannulene, was found and extensively studied in the 1970s [14,15]. Even a structure in the shape of a football was proposed [16,17], which was called the buckministerfullerene after 1990. The common point in many carbon nanostructures is that they Tel.: +90 312 210 32 85; fax: +90 312 210 12 81.
E-mail address: [email protected]. 1386-9477/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.09.008
possess unusual aromaticity due to hybridization of carbon atoms. CNTs seem to have more technological applications than other carbon nanostructures. CNTs were synthesized on a large scale for the first time in 1992 [18]. Then superfine structures of single-walled CNTs (SWCNTs) were introduced [19], followed by work on the large-scale synthesis of these SWCNTs by the same method used for creating bucky balls [20]. There is still much research to be done for this promising material. Ideal SWCNTs consist of rolled graphine sheet-like hexagonal structures [21]. Graphine has a very special structure, and SWCNTs have some very interesting properties, especially some unique electronic properties [22]. Since unit cells have a circular symmetry such that only standing waves of electrons can occur along the perimeter [22], and conduction along the axis is a function of these standing waves [23]. Thus, conductivity of an SWCNT is dependent on its diameter and the type of unit cell [21,23]. Actually, an SWCNT can be a conductor or a semi-conductor with varying diameter and unit cell [21]. Experimental works proved this semi-conductor effect [24,25] and some key electronic devices have already been designed [24,25]. Their electronic properties may also be
ARTICLE IN PRESS S. Erkoc- / Physica E 31 (2006) 62–66
adjusted mechanically such as by twisting [25]. Owing to its nanometer scale, these electronic properties may show great potential in many areas in the years to come [26]. In addition to these unique electronic properties, SWCNTs have some unique structural properties too [27]. Carbonbased fibers have been well known for their strength and durability in industry for a long time; CNTs are even better, and they are roughly up to 100 times stronger in tensile strength than steel on a nanometer scale [27,28]. A dream fiber of infinite length may be the ultimate rope for multiple purposes [28]. Adding all these features, along with a chemically inert nature and thermal conductivity [24], CNTs may have wide industrial applications in the future. Most of the tubules that have been discussed in the literature have closed caps; however, open-ended tubules with dangling bonds have also been reported [29,30]. The growth mechanism for cylindrical fullerene tubules is still being debated regarding whether the tubules are always capped [31,32] or open during the growth process and whether carbon atoms are added at the open ends of the tubules [29,33,34]. For the growth of CNTs by the arc discharge method, it has been proposed that the tubules grow at their open ends [33,35]. CNTs are named according to integers defining their chiral vectors for the unit cells. The general notation used to define an SWCNT is Cðn; mÞ, where n and m are integers ðmpnÞ. When m ¼ 0 the tube is called a zigzag model, when m ¼ n the tube is called armchair model, and all the other combinations ð0omonÞ form the chiral models [36]. The physical properties of CNTs are strongly dependent on the tubule diameter. These predictions still remain to be well tested experimentally. Because of the difficulty in making physical measurements on individual single-wall nanotubes, a number of exploratory studies have been performed on bundles of tubules [36]. On the other hand, carbon tubules are interesting as examples of a 1D periodic structure along the tubule axis. It is predicted that small-diameter nanotubes will exhibit either metallic or semiconducting electrical conduction depending on their diameter [37]. On the other hand, multi-wall CNTs can be produced with less yield with respect to single-wall nanotubes. Singlewall nanotubes were first made by the electric-arc discharge method through the introduction of a catalyst species along with the evaporated carbon [6]. Recently, it has been reported that well-aligned multi-wall CNTs can be grown, in addition to the arc-discharge method, by chemical-vapor deposition catalyzed by iron nanoparticles embedded in mesoporous silica [38]. In the case of multi-wall CNTs the spacing between cylinders increases with decreasing diameter of the graphine cylinders which is due to the increasing curvature of the graphine sheets. The stability and physical properties of nanotubes could be affected by curvature in nanotubes. The morphology and stability at the growing edge of double-wall CNTs have been recently studied theoretically [39]. The nanometer-scale tubular
63
forms of various materials other than carbon have also been synthesized in recent years [40–55]. The tubular forms of all CNTs investigated so far in the literature, both experimentally and theoretically, have been made of graphine sheet. In the formation of graphine sheet both sp- and sp2-type hybridizations play an important role. Carbon atom is a unique element possessing almost all types of hybrizidation (sp, sp2, sp3). A combination of sp and sp2 hybridization allows carbon atoms to form graphine sheets. Carbon may also form a sheet structure different from graphine with a different hybridization combination. For example, a combination of sp and sp3 hybridization may allow carbon atoms to form a sheet structure different from graphine. Graphine sheet has hexagonal unit cells; another type of carbon sheet may be constructed from square unit cells. Such a nongraphine tube was recently proposed and investigated theoretically [56]. CNTs can also be grown in bamboo-like structures. The bamboo structures observed in multiwalled CNTs (MWCNTs) is characterized by segmented compartments, which appear similar to a bamboo. Bamboo structures are usually observed in vertically aligned CNT arrays [57–65]. Several studies have presented explanations for the origin of these periodic structures [58,66,67]. It was suggested that the bamboo structures might be due to effects related to the catalyst particle shape, the bulk diffusion of carbon in the catalyst, or the slow movement of the catalyst compared to the growth rate of the CNT [63]. The dividing wall in bamboo structures is apparently common to the two sets of inner tubes. It was assumed that along the periphery of this common wall sp3-bonded carbon is present [68]. In the present study the structural and electronic properties of a bamboo-like carbon nanostructure model formed from SWCNT have been investigated qualitatively for the first time by performing PM3-type semi-empirical self-consistent-field (SCF) molecular-orbital (MO) calculations. 2. Method of calculation In the present paper, a bamboo-like carbon nanostructure model formed from SWCNT has been considered theoretically by performing molecular-mechanics, and PM3-RHF-type semi-empirical molecular orbital calculations. We present here for the first time a theoretical study of a bamboo-like carbon nanostructure formed from SWCNT. The molecular-mechanics method [69] using the MMþ force field [70], and the Modified Niglect of Differential Overlap Parametric Method Number 3 (PM3) semiempirical method [71] within the Restricted Hartree–Fock (RHF) formalism [72] are sufficient to study carbon systems. All the structures were subjected to conjugate gradient geometry optimization (Polak–Ribiere method [73], convergence limit and RMS gradient were 103 kcal=mol and 103 kcal=ðA˚ molÞ, respectively). All these computations
ARTICLE IN PRESS 64
S. Erkoc- / Physica E 31 (2006) 62–66
were performed by using the Hyperchem-7.5 package program [74]. In the first step of the calculations we optimized the geometry of the bamboo structure by performing molecular-mechanics calculation using an MMþ force field; this makes it easier to perform full optimization by extended methods. Geometry optimization was carried out by a
Fig. 1. The views of the optimized structure of the carbon nanobamboo model from various directions (PM3 results).
conjugate gradient method (Polak–Ribiere algorithm). In the next step we calculated the electronic structure of the tube by applying the semi-empirical molecular orbital method PM3-RHF considering full optimization again. 3. Results and discussion In the construction of a bamboo structure the coronene molecule has been chosen as the common wall of the two tubes. The C(12,0) zigzag tube matches the coronene molecule exactly. The connection between the C(12,0) zigzag tube and the corenene molecule is possible by simply connecting the corresponding atoms. The interface region contains six pentagons and six hexagons on both sides of the common wall (coronene). We have taken C(12,0) tube as the tube parts of the bamboo structure on both sides of the common wall. One sequence of hexagons has been taken to construct the tube parts. The dangling bonds at the end carbon atoms of the tubes are saturated by hydrogen atoms; there are 12 hydrogen atoms at each end. The optimized structure of the carbon nanobamboo model is shown in Fig. 1. The highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and the molecular orbital eigenvalue spectrum are shown in Fig. 2. Both HOMO and LUMO localized on carbon atoms having sp2 hybridization, namely on atoms on the tube part. There was no HOMO and LUMO localization on the atoms at the common wall. 3D and 2D total charge density and electrostatic potential plots are shown in Fig. 3. The charge density distributes uniformly over the surfaces (both inner and outer); on the other hand, a negative electrostatic potential occurs at the interface
Fig. 2. 3D HOMO and LUMO plots, and molecular orbital eigenvalue spectrum of the carbon nanobamboo model (PM3 results).
ARTICLE IN PRESS S. Erkoc- / Physica E 31 (2006) 62–66
65
Fig. 3. 3D and 2D charge density (CD) and electrostatic potential (EP) plots of the carbon nanobamboo model (PM3 results).
Table 1 Some of the calculated energy values (in kcal/mol) of the carbon nanobamboo model (according to the molecular-mechanics method with an MMþ force field) Quantity
Value
Bond stretching energy Angle bending energy Dihedral bending energy Vdw interaction Stretch–bend energy Electrostatic energy Total energy
19.862 113.424 247.812 80.625 2.573 0.000 459.150
Table 2 Calculated energy values (in kcal/mole unless otherwise stated) of the carbon nanobamboo model (according to the PM3 method) Quantity
Value
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation HOMO (eV) LUMO (eV) E g (eV)
335559.906 20515.468 315044.438 7304260.212 6968700.306 1241.780 6.801 3.075 3.725
region as if a ring-like, and positive electrostatic potential occurs at the tube parts. Molecular mechanics with an MMþ force field and PM3-RHF semi-empirical SCF-MO calculations reveal
that the structure of present interest is stable, and endothermic. According to the PM3 method the system considered has 120 C atoms and 24 H atoms. The number of electrons is 504, the number of double-occupied levels is 252, and the number of total orbitals is 504. The system is neutral, and the optimized structure has the molecular point group (Symmetry) C6h . Tables 1 and 2 show certain calculated energies of the carbon nanobamboo considered according to molecular mechanics and PM3 methods, respectively. The frontier molecular orbital energies, namely the HOMO and the LUMO energies, and the interfrontier molecular energy gap values (HOMO–LUMO gap, E g ) of the system studied are also given in Table 2. Excess charge localization shows an interesting feature. Negative charge development takes place on the carbon atoms placed at the tube wall; on the other hand, positive charge development takes place only on the carbon atoms forming the common wall. Acknowledgments The author would like to thank METU (Middle East Technical University) for their partial support through the project METU-BAP-08-11-DPT-2002-K120-510. References [1] R. Bacon, J. Appl. Phys. 31 (1960) 283. [2] M.S. Dresselhaus, G. Dresselhaus, K. Sugihara, I.L. Spain, H.A. Goldberg, Graphite Fibers and Filaments, Springer Series in Materials Science, vol. 5, Springer, Berlin, 1988. [3] A. Oberlin, M. Endo, T. Koyama, Carbon 14 (1976) 133. [4] A. Oberlin, M. Endo, T. Koyama, J. Crystal Growth 32 (1976) 335. [5] H.W. Kroto, J.R. Heath, S.C. Obrien, R.F. Curl, R.E. Smalley, Nature 318 (1985) 162.
ARTICLE IN PRESS 66
S. Erkoc- / Physica E 31 (2006) 62–66
[6] S. Iijima, Nature 354 (1991) 56. [7] Y.K. Kwon, Y.H. Lee, S.G. Kim, P. Jund, D. Tomanek, R.E. Smalley, Phys. Rev. Lett. 79 (1997) 2065. [8] S. Erkoc, Int. J. Mod. Phys. C 11 (2000) 1247. [9] S. Erkoc, O.B. Malcioglu, Int. J. Mod. Phys. C 13 (2002) 367. [10] O.B. Malcioglu, S. Erkoc, Int. J. Mod. Phys. C 14 (2003) 441. [11] S. Erkoc, J. Mol. Struc. (Theochem) 639 (2003) 157. [12] S. Itoh, S. Ihara, J. Kitakami, Phys. Rev. B 47 (1993) 1703. [13] E. Yazgan, E. Tasci, S. Erkoc, Int. J. Mod. Phys. C 15 (2004) 267. [14] W.E. Barth, R.G. Lawton, J. Am. Chem. Soc. 88 (1966) 380. [15] W.E. Barth, R.G. Lawton, J. Am. Chem. Soc. 93 (1971) 1730. [16] E. Osawa, Kagaku 25 (1970) 854. [17] Z. Yoshida, E. Osawa, Kagaku Dojin (Kyoto) (1971) 174. [18] T.W. Ebbesen, P.M. Ajayan, Nature 358 (1992) 220. [19] S. Iijima, T. Ichihashi, Nature 363 (1993) 603. [20] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, A.G. Rinzler, D.T. Colbert, G. Scuseria, D. Tomanek, J.E. Fischer, R.E. Smalley, Science 273 (1996) 483. [21] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, Singapore, 1998. [22] http://link.springer-ny.com/link/service/series/0560/bibs/0080/ [23] M. Dresselhaus, G. Dresselhaus, P. Eklund, R. Saito, Phys. World 11(1) (Article 9) (1998). [24] http://www.lbl.gov/Science-Articles/Archive/nanotubes.html [25] http://www.research.ibm.com/nanoscience/ [26] A. Globus, D. Bailey, J. Han, R. Jaffe, C. Levit, R. Merkle, D. Srivastava, J. Br. Interplanetary Soc. 51 (1998) 145. [27] http://www.wag.caltech.edu/foresight/ [28] http://cnst.rice.edu/IUPAC.html [29] K. Salter, Carbon 33 (1995) 915. [30] S. Iijima, Mater. Sci. Eng. B 19 (1993) 172. [31] R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Mater. Sci. Eng. B 19 (1993) 185. [32] M. Endo, H.W. Kroto, J. Phys. Chem. 96 (1992) 6941. [33] S. Iijima, T. Ichihashi, Y. Ando, Nature 356 (1992) 776. [34] R.E. Smalley, Acc. Chem. Res. 25 (1992) 98. [35] R.E. Smalley, Mater. Sci. Eng. B 19 (1993) 1. [36] M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerens and Carbon Nanotubes, Academic Press, New York, 1996. [37] R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Appl. Phys. Lett. 60 (1992) 2204. [38] W.Z. Li, S.S. Xie, L.X. Qian, B.H. Chang, B.S. Zou, W.Y. Zhou, R.A. Zhao, G. Wang, Science 274 (1996) 1701. [39] Y.K. Kwon, Y.H. Lee, S.G. Kim, P. Jund, D. Tomanek, R.E. Smalley, Phys. Rev. Lett. 79 (1997) 2065. [40] C.R. Martin, Science 266 (1994) 1961. [41] T.J. Trentler, K.M. Hickman, S.C. Goel, A.M. Viano, P.C. Gibbons, W.E. Buhro, Science 270 (1995) 1791. [42] A. Loiseau, F. Willaime, N. Demoncy, G. Hug, H. Pascard, Phys. Rev. Lett. 76 (1996) 4737.
[43] K. Suenaga, C. Colliex, N. Demoncy, A. Loiseau, H. Pascard, F. Willaime, Science 278 (1997) 653. [44] Z. Liliental–Weber, Y. Chen, S. Ruvimov, J. Washburn, Phys. Rev. Lett. 79 (1997) 2835. [45] T.J. Trentler, S.C. Goel, K.M. Hickman, A.M. Viano, M.Y. Chiang, A.M. Beatty, P.C. Gibbons, W.E. Buhro, J. Am. Chem. Soc. 119 (1997) 2172. [46] Y. Kondo, K. Takayanagi, Science 289 (2000) 606. [47] X.F. Duan, C.M. Lieber, Adv. Mater. 12 (2000) 298. [48] M.S. Gudiksen, C.M. Lieber, J. Am. Chem. Soc. 122 (2000) 8801. [49] M.S. Gudiksen, J.F. Wang, C.M. Lieber, J. Phys. Chem. B 105 (2001) 4062. [50] R. Tenne, Proc. Inorg. Chem. 50 (2001) 269. [51] Y. Wu, P. Yang, Adv. Mater. 13 (2001) 520. [52] O.G. Schmidt, K. Eberl, Nature 410 (2001) 168. [53] G.R. Patzke, F. Krumeich, R. Nesper, Angew. Chem. Int. Ed. Engl. 41 (2002) 2446. [54] J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan, H-J. Choi, P. Yang, Nature 422 (2003) 599. [55] C. Tang, Y. Bando, Z. Liu, D. Golberg, Chem. Phys. Lett. 376 (2003) 676. [56] S. Erkoc, Physica E 25 (2004) 69. [57] Y. Saito, Carbon 33 (1995) 979. [58] C. Lee, J. Park, Appl. Phys. Lett. 77 (2000) 3397. [59] C.J. Lee, J.H. Park, J. Park, Chem. Phys. Lett. 323 (2000) 560. [60] M. Jung, K.Y. Eun, Y.J. Baik, K.R. Lee, J.K. Shin, S.T. Kim, Thin Solid Films 398–399 (2001) 150. [61] N. Hayashi, S. Honda, K. Tsuji, K.Y. Lee, T. Ikuno, K. Fujimoto, S. Ohkura, M. Katayama, K. Oura, T. Hirao, App. Surf. Sci. 212–213 (2003) 393. [62] C.H. Lin, H.L. Chang, C.M. Hsu, A.Y. Lo, C.T. Kuo, Diamond Relat. Mater. 12 (2003) 1851. [63] Y.Y. Wang, G.Y. Tang, F.A.M. Koeck, B. Brown, J.M. Garguilo, R.J. Nemanich, Diamond Relat. Mater. 13 (2004) 1287. [64] S.H. Kim, J.C. Park, B. Kim, S.K. Lee, D.U. Kim, Y.H. Kim, Mater. Sci. Eng. C 24 (2004) 297. [65] P. Ding, E. Liang, M. Chao, X. Guo, J. Zhang, Physica E 25 (2005) 654. [66] V.V. Kovalevski, A.N. Safranov, Carbon 36 (1998) 963. [67] G.Y. Zhang, X.C. Ma, D.Y. Zhong, E.G. Wang, J. Appl. Phys. 91 (2002) 9324. [68] G.V. tendeloo, S. Amelinckx, in: Z.L. Wang (Ed.), Characterization of Nanophase Materials, Wiley-VCH, New York, 2000, pp. 353–393. [69] U. Burkert, N.L. Allinger, Molecular Mechanics, ACS Monogr. 177 (1982). [70] N.L. Allinger, J. Am. Chem. Soc. 99 (1977) 8127. [71] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209, 211. [72] C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [73] P. Fletcher, Practical Methods of Optimization, Wiley, New York, 1990. [74] Hypercube, Inc., Gainesville, FL, USA.
Physica E 31 (2006) 62–66 www.elsevier.com/locate/physe
Structural and electronic properties of bamboo-like carbon nanostructure S- akir Erkoc- Department of Physics, Middle East Technical University, 06531 Ankara, Turkey Received 26 August 2005; accepted 21 September 2005 Available online 10 November 2005
Abstract The structural and electronic properties of bamboo-like carbon nanostructure have been investigated qualitatively by performing semiempirical self-consistent-field molecular orbital calculations at the level of the PM3 method within the RHF formulation. It has been found that these structures are stable and endothermic. Bamboo-like carbon nanostructures resemble zigzag carbon nanotubes capped with a plane graphine sheet. r 2005 Elsevier B.V. All rights reserved. PACS: 61.48.+c; 61.46.+w; 31.15.Ct Keywords: Carbon nanotubes; Carbon bamboo structures; SCF-MO calculation; PM3 method
1. Introduction Carbon-based materials became important early in the century [1,2]. Since then, there has been an ever-growing number of proposed forms and commercial applications. Rather recently, this trend reached the size of nanometers [3,4], and gained a whole new aspect with the introduction of the famous fullerene molecule [5]. There are many fullerene-related carbon nanostructures, such as carbon nanotubes (CNTs) [6], nanorods [7–11], nanotori [12,13], etc. These structures exhibit intriguing electronic properties, along with unusual structural stability, and this makes them highly popular in future commercial applications that may come to pass. One interesting point is that the nonplanar carbon macromolecules were not unknown to society before the introduction of fullerene itself. In fact, the basic building block of C60, namely corannulene, was found and extensively studied in the 1970s [14,15]. Even a structure in the shape of a football was proposed [16,17], which was called the buckministerfullerene after 1990. The common point in many carbon nanostructures is that they Tel.: +90 312 210 32 85; fax: +90 312 210 12 81.
E-mail address: [email protected]. 1386-9477/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.09.008
possess unusual aromaticity due to hybridization of carbon atoms. CNTs seem to have more technological applications than other carbon nanostructures. CNTs were synthesized on a large scale for the first time in 1992 [18]. Then superfine structures of single-walled CNTs (SWCNTs) were introduced [19], followed by work on the large-scale synthesis of these SWCNTs by the same method used for creating bucky balls [20]. There is still much research to be done for this promising material. Ideal SWCNTs consist of rolled graphine sheet-like hexagonal structures [21]. Graphine has a very special structure, and SWCNTs have some very interesting properties, especially some unique electronic properties [22]. Since unit cells have a circular symmetry such that only standing waves of electrons can occur along the perimeter [22], and conduction along the axis is a function of these standing waves [23]. Thus, conductivity of an SWCNT is dependent on its diameter and the type of unit cell [21,23]. Actually, an SWCNT can be a conductor or a semi-conductor with varying diameter and unit cell [21]. Experimental works proved this semi-conductor effect [24,25] and some key electronic devices have already been designed [24,25]. Their electronic properties may also be
ARTICLE IN PRESS S. Erkoc- / Physica E 31 (2006) 62–66
adjusted mechanically such as by twisting [25]. Owing to its nanometer scale, these electronic properties may show great potential in many areas in the years to come [26]. In addition to these unique electronic properties, SWCNTs have some unique structural properties too [27]. Carbonbased fibers have been well known for their strength and durability in industry for a long time; CNTs are even better, and they are roughly up to 100 times stronger in tensile strength than steel on a nanometer scale [27,28]. A dream fiber of infinite length may be the ultimate rope for multiple purposes [28]. Adding all these features, along with a chemically inert nature and thermal conductivity [24], CNTs may have wide industrial applications in the future. Most of the tubules that have been discussed in the literature have closed caps; however, open-ended tubules with dangling bonds have also been reported [29,30]. The growth mechanism for cylindrical fullerene tubules is still being debated regarding whether the tubules are always capped [31,32] or open during the growth process and whether carbon atoms are added at the open ends of the tubules [29,33,34]. For the growth of CNTs by the arc discharge method, it has been proposed that the tubules grow at their open ends [33,35]. CNTs are named according to integers defining their chiral vectors for the unit cells. The general notation used to define an SWCNT is Cðn; mÞ, where n and m are integers ðmpnÞ. When m ¼ 0 the tube is called a zigzag model, when m ¼ n the tube is called armchair model, and all the other combinations ð0omonÞ form the chiral models [36]. The physical properties of CNTs are strongly dependent on the tubule diameter. These predictions still remain to be well tested experimentally. Because of the difficulty in making physical measurements on individual single-wall nanotubes, a number of exploratory studies have been performed on bundles of tubules [36]. On the other hand, carbon tubules are interesting as examples of a 1D periodic structure along the tubule axis. It is predicted that small-diameter nanotubes will exhibit either metallic or semiconducting electrical conduction depending on their diameter [37]. On the other hand, multi-wall CNTs can be produced with less yield with respect to single-wall nanotubes. Singlewall nanotubes were first made by the electric-arc discharge method through the introduction of a catalyst species along with the evaporated carbon [6]. Recently, it has been reported that well-aligned multi-wall CNTs can be grown, in addition to the arc-discharge method, by chemical-vapor deposition catalyzed by iron nanoparticles embedded in mesoporous silica [38]. In the case of multi-wall CNTs the spacing between cylinders increases with decreasing diameter of the graphine cylinders which is due to the increasing curvature of the graphine sheets. The stability and physical properties of nanotubes could be affected by curvature in nanotubes. The morphology and stability at the growing edge of double-wall CNTs have been recently studied theoretically [39]. The nanometer-scale tubular
63
forms of various materials other than carbon have also been synthesized in recent years [40–55]. The tubular forms of all CNTs investigated so far in the literature, both experimentally and theoretically, have been made of graphine sheet. In the formation of graphine sheet both sp- and sp2-type hybridizations play an important role. Carbon atom is a unique element possessing almost all types of hybrizidation (sp, sp2, sp3). A combination of sp and sp2 hybridization allows carbon atoms to form graphine sheets. Carbon may also form a sheet structure different from graphine with a different hybridization combination. For example, a combination of sp and sp3 hybridization may allow carbon atoms to form a sheet structure different from graphine. Graphine sheet has hexagonal unit cells; another type of carbon sheet may be constructed from square unit cells. Such a nongraphine tube was recently proposed and investigated theoretically [56]. CNTs can also be grown in bamboo-like structures. The bamboo structures observed in multiwalled CNTs (MWCNTs) is characterized by segmented compartments, which appear similar to a bamboo. Bamboo structures are usually observed in vertically aligned CNT arrays [57–65]. Several studies have presented explanations for the origin of these periodic structures [58,66,67]. It was suggested that the bamboo structures might be due to effects related to the catalyst particle shape, the bulk diffusion of carbon in the catalyst, or the slow movement of the catalyst compared to the growth rate of the CNT [63]. The dividing wall in bamboo structures is apparently common to the two sets of inner tubes. It was assumed that along the periphery of this common wall sp3-bonded carbon is present [68]. In the present study the structural and electronic properties of a bamboo-like carbon nanostructure model formed from SWCNT have been investigated qualitatively for the first time by performing PM3-type semi-empirical self-consistent-field (SCF) molecular-orbital (MO) calculations. 2. Method of calculation In the present paper, a bamboo-like carbon nanostructure model formed from SWCNT has been considered theoretically by performing molecular-mechanics, and PM3-RHF-type semi-empirical molecular orbital calculations. We present here for the first time a theoretical study of a bamboo-like carbon nanostructure formed from SWCNT. The molecular-mechanics method [69] using the MMþ force field [70], and the Modified Niglect of Differential Overlap Parametric Method Number 3 (PM3) semiempirical method [71] within the Restricted Hartree–Fock (RHF) formalism [72] are sufficient to study carbon systems. All the structures were subjected to conjugate gradient geometry optimization (Polak–Ribiere method [73], convergence limit and RMS gradient were 103 kcal=mol and 103 kcal=ðA˚ molÞ, respectively). All these computations
ARTICLE IN PRESS 64
S. Erkoc- / Physica E 31 (2006) 62–66
were performed by using the Hyperchem-7.5 package program [74]. In the first step of the calculations we optimized the geometry of the bamboo structure by performing molecular-mechanics calculation using an MMþ force field; this makes it easier to perform full optimization by extended methods. Geometry optimization was carried out by a
Fig. 1. The views of the optimized structure of the carbon nanobamboo model from various directions (PM3 results).
conjugate gradient method (Polak–Ribiere algorithm). In the next step we calculated the electronic structure of the tube by applying the semi-empirical molecular orbital method PM3-RHF considering full optimization again. 3. Results and discussion In the construction of a bamboo structure the coronene molecule has been chosen as the common wall of the two tubes. The C(12,0) zigzag tube matches the coronene molecule exactly. The connection between the C(12,0) zigzag tube and the corenene molecule is possible by simply connecting the corresponding atoms. The interface region contains six pentagons and six hexagons on both sides of the common wall (coronene). We have taken C(12,0) tube as the tube parts of the bamboo structure on both sides of the common wall. One sequence of hexagons has been taken to construct the tube parts. The dangling bonds at the end carbon atoms of the tubes are saturated by hydrogen atoms; there are 12 hydrogen atoms at each end. The optimized structure of the carbon nanobamboo model is shown in Fig. 1. The highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and the molecular orbital eigenvalue spectrum are shown in Fig. 2. Both HOMO and LUMO localized on carbon atoms having sp2 hybridization, namely on atoms on the tube part. There was no HOMO and LUMO localization on the atoms at the common wall. 3D and 2D total charge density and electrostatic potential plots are shown in Fig. 3. The charge density distributes uniformly over the surfaces (both inner and outer); on the other hand, a negative electrostatic potential occurs at the interface
Fig. 2. 3D HOMO and LUMO plots, and molecular orbital eigenvalue spectrum of the carbon nanobamboo model (PM3 results).
ARTICLE IN PRESS S. Erkoc- / Physica E 31 (2006) 62–66
65
Fig. 3. 3D and 2D charge density (CD) and electrostatic potential (EP) plots of the carbon nanobamboo model (PM3 results).
Table 1 Some of the calculated energy values (in kcal/mol) of the carbon nanobamboo model (according to the molecular-mechanics method with an MMþ force field) Quantity
Value
Bond stretching energy Angle bending energy Dihedral bending energy Vdw interaction Stretch–bend energy Electrostatic energy Total energy
19.862 113.424 247.812 80.625 2.573 0.000 459.150
Table 2 Calculated energy values (in kcal/mole unless otherwise stated) of the carbon nanobamboo model (according to the PM3 method) Quantity
Value
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation HOMO (eV) LUMO (eV) E g (eV)
335559.906 20515.468 315044.438 7304260.212 6968700.306 1241.780 6.801 3.075 3.725
region as if a ring-like, and positive electrostatic potential occurs at the tube parts. Molecular mechanics with an MMþ force field and PM3-RHF semi-empirical SCF-MO calculations reveal
that the structure of present interest is stable, and endothermic. According to the PM3 method the system considered has 120 C atoms and 24 H atoms. The number of electrons is 504, the number of double-occupied levels is 252, and the number of total orbitals is 504. The system is neutral, and the optimized structure has the molecular point group (Symmetry) C6h . Tables 1 and 2 show certain calculated energies of the carbon nanobamboo considered according to molecular mechanics and PM3 methods, respectively. The frontier molecular orbital energies, namely the HOMO and the LUMO energies, and the interfrontier molecular energy gap values (HOMO–LUMO gap, E g ) of the system studied are also given in Table 2. Excess charge localization shows an interesting feature. Negative charge development takes place on the carbon atoms placed at the tube wall; on the other hand, positive charge development takes place only on the carbon atoms forming the common wall. Acknowledgments The author would like to thank METU (Middle East Technical University) for their partial support through the project METU-BAP-08-11-DPT-2002-K120-510. References [1] R. Bacon, J. Appl. Phys. 31 (1960) 283. [2] M.S. Dresselhaus, G. Dresselhaus, K. Sugihara, I.L. Spain, H.A. Goldberg, Graphite Fibers and Filaments, Springer Series in Materials Science, vol. 5, Springer, Berlin, 1988. [3] A. Oberlin, M. Endo, T. Koyama, Carbon 14 (1976) 133. [4] A. Oberlin, M. Endo, T. Koyama, J. Crystal Growth 32 (1976) 335. [5] H.W. Kroto, J.R. Heath, S.C. Obrien, R.F. Curl, R.E. Smalley, Nature 318 (1985) 162.
ARTICLE IN PRESS 66
S. Erkoc- / Physica E 31 (2006) 62–66
[6] S. Iijima, Nature 354 (1991) 56. [7] Y.K. Kwon, Y.H. Lee, S.G. Kim, P. Jund, D. Tomanek, R.E. Smalley, Phys. Rev. Lett. 79 (1997) 2065. [8] S. Erkoc, Int. J. Mod. Phys. C 11 (2000) 1247. [9] S. Erkoc, O.B. Malcioglu, Int. J. Mod. Phys. C 13 (2002) 367. [10] O.B. Malcioglu, S. Erkoc, Int. J. Mod. Phys. C 14 (2003) 441. [11] S. Erkoc, J. Mol. Struc. (Theochem) 639 (2003) 157. [12] S. Itoh, S. Ihara, J. Kitakami, Phys. Rev. B 47 (1993) 1703. [13] E. Yazgan, E. Tasci, S. Erkoc, Int. J. Mod. Phys. C 15 (2004) 267. [14] W.E. Barth, R.G. Lawton, J. Am. Chem. Soc. 88 (1966) 380. [15] W.E. Barth, R.G. Lawton, J. Am. Chem. Soc. 93 (1971) 1730. [16] E. Osawa, Kagaku 25 (1970) 854. [17] Z. Yoshida, E. Osawa, Kagaku Dojin (Kyoto) (1971) 174. [18] T.W. Ebbesen, P.M. Ajayan, Nature 358 (1992) 220. [19] S. Iijima, T. Ichihashi, Nature 363 (1993) 603. [20] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, A.G. Rinzler, D.T. Colbert, G. Scuseria, D. Tomanek, J.E. Fischer, R.E. Smalley, Science 273 (1996) 483. [21] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, Singapore, 1998. [22] http://link.springer-ny.com/link/service/series/0560/bibs/0080/ [23] M. Dresselhaus, G. Dresselhaus, P. Eklund, R. Saito, Phys. World 11(1) (Article 9) (1998). [24] http://www.lbl.gov/Science-Articles/Archive/nanotubes.html [25] http://www.research.ibm.com/nanoscience/ [26] A. Globus, D. Bailey, J. Han, R. Jaffe, C. Levit, R. Merkle, D. Srivastava, J. Br. Interplanetary Soc. 51 (1998) 145. [27] http://www.wag.caltech.edu/foresight/ [28] http://cnst.rice.edu/IUPAC.html [29] K. Salter, Carbon 33 (1995) 915. [30] S. Iijima, Mater. Sci. Eng. B 19 (1993) 172. [31] R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Mater. Sci. Eng. B 19 (1993) 185. [32] M. Endo, H.W. Kroto, J. Phys. Chem. 96 (1992) 6941. [33] S. Iijima, T. Ichihashi, Y. Ando, Nature 356 (1992) 776. [34] R.E. Smalley, Acc. Chem. Res. 25 (1992) 98. [35] R.E. Smalley, Mater. Sci. Eng. B 19 (1993) 1. [36] M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerens and Carbon Nanotubes, Academic Press, New York, 1996. [37] R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Appl. Phys. Lett. 60 (1992) 2204. [38] W.Z. Li, S.S. Xie, L.X. Qian, B.H. Chang, B.S. Zou, W.Y. Zhou, R.A. Zhao, G. Wang, Science 274 (1996) 1701. [39] Y.K. Kwon, Y.H. Lee, S.G. Kim, P. Jund, D. Tomanek, R.E. Smalley, Phys. Rev. Lett. 79 (1997) 2065. [40] C.R. Martin, Science 266 (1994) 1961. [41] T.J. Trentler, K.M. Hickman, S.C. Goel, A.M. Viano, P.C. Gibbons, W.E. Buhro, Science 270 (1995) 1791. [42] A. Loiseau, F. Willaime, N. Demoncy, G. Hug, H. Pascard, Phys. Rev. Lett. 76 (1996) 4737.
[43] K. Suenaga, C. Colliex, N. Demoncy, A. Loiseau, H. Pascard, F. Willaime, Science 278 (1997) 653. [44] Z. Liliental–Weber, Y. Chen, S. Ruvimov, J. Washburn, Phys. Rev. Lett. 79 (1997) 2835. [45] T.J. Trentler, S.C. Goel, K.M. Hickman, A.M. Viano, M.Y. Chiang, A.M. Beatty, P.C. Gibbons, W.E. Buhro, J. Am. Chem. Soc. 119 (1997) 2172. [46] Y. Kondo, K. Takayanagi, Science 289 (2000) 606. [47] X.F. Duan, C.M. Lieber, Adv. Mater. 12 (2000) 298. [48] M.S. Gudiksen, C.M. Lieber, J. Am. Chem. Soc. 122 (2000) 8801. [49] M.S. Gudiksen, J.F. Wang, C.M. Lieber, J. Phys. Chem. B 105 (2001) 4062. [50] R. Tenne, Proc. Inorg. Chem. 50 (2001) 269. [51] Y. Wu, P. Yang, Adv. Mater. 13 (2001) 520. [52] O.G. Schmidt, K. Eberl, Nature 410 (2001) 168. [53] G.R. Patzke, F. Krumeich, R. Nesper, Angew. Chem. Int. Ed. Engl. 41 (2002) 2446. [54] J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan, H-J. Choi, P. Yang, Nature 422 (2003) 599. [55] C. Tang, Y. Bando, Z. Liu, D. Golberg, Chem. Phys. Lett. 376 (2003) 676. [56] S. Erkoc, Physica E 25 (2004) 69. [57] Y. Saito, Carbon 33 (1995) 979. [58] C. Lee, J. Park, Appl. Phys. Lett. 77 (2000) 3397. [59] C.J. Lee, J.H. Park, J. Park, Chem. Phys. Lett. 323 (2000) 560. [60] M. Jung, K.Y. Eun, Y.J. Baik, K.R. Lee, J.K. Shin, S.T. Kim, Thin Solid Films 398–399 (2001) 150. [61] N. Hayashi, S. Honda, K. Tsuji, K.Y. Lee, T. Ikuno, K. Fujimoto, S. Ohkura, M. Katayama, K. Oura, T. Hirao, App. Surf. Sci. 212–213 (2003) 393. [62] C.H. Lin, H.L. Chang, C.M. Hsu, A.Y. Lo, C.T. Kuo, Diamond Relat. Mater. 12 (2003) 1851. [63] Y.Y. Wang, G.Y. Tang, F.A.M. Koeck, B. Brown, J.M. Garguilo, R.J. Nemanich, Diamond Relat. Mater. 13 (2004) 1287. [64] S.H. Kim, J.C. Park, B. Kim, S.K. Lee, D.U. Kim, Y.H. Kim, Mater. Sci. Eng. C 24 (2004) 297. [65] P. Ding, E. Liang, M. Chao, X. Guo, J. Zhang, Physica E 25 (2005) 654. [66] V.V. Kovalevski, A.N. Safranov, Carbon 36 (1998) 963. [67] G.Y. Zhang, X.C. Ma, D.Y. Zhong, E.G. Wang, J. Appl. Phys. 91 (2002) 9324. [68] G.V. tendeloo, S. Amelinckx, in: Z.L. Wang (Ed.), Characterization of Nanophase Materials, Wiley-VCH, New York, 2000, pp. 353–393. [69] U. Burkert, N.L. Allinger, Molecular Mechanics, ACS Monogr. 177 (1982). [70] N.L. Allinger, J. Am. Chem. Soc. 99 (1977) 8127. [71] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209, 211. [72] C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [73] P. Fletcher, Practical Methods of Optimization, Wiley, New York, 1990. [74] Hypercube, Inc., Gainesville, FL, USA.