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The armchair (n,n) single walled carbon nanotubes with n=2—20 are studied by using the first principle density functional theory at the B3LYP/3-21G(d) level of theory combined with the periodic boundary conditions in simulating the ultra long tube model. The structure parameter, the energy, the band structure, and the energy gaps are obtained. The results show that the tube diameter and the energy of formation are closely related to n. The fitted analytical equations are developed with a correlation coefficient larger than 0.999. The energy gaps of (2,2) and (3,3) carbon nanotubes are 1.836 eV and 0.228 eV and the tubes have indirect energy gaps. For n=4 to 20, the energy gaps are quite small (between 0.027 eV and 0.079 eV), showing metal conductivity as well as direct energy gaps.
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Keywords:
- armchair carbon nanotubes /
- periodic boundary condition(PBC) /
- ultra long /
- band structure
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[32] Verlag C,Weinheim 1968 Handbuch der Anorganischen Chemie (vol. 14B/2) p143
[33] Mashreghi A, Moshksar M M 2010 Computational Materials Science 49 871
[34] Budyka M F, Zyubina T S, Ryabenko A G, Lin S H, Mebel A M 2005 Chem. Phys. Lett. 407 266
[35] Dresselhaus M S, Dresselhaus G, Saito R 1995 Carbon 33 883
[36] Roberto S, Mauro B, Takahisa O 2009 Chem. Phys. Lett. 480 215
[37] Zhao X, Liu Y, Inoue S, Suzuki T, Jones RO, Ando Y 2004 Phys Rev. Lett. 92 125502
[38] Qin L C, Zhao X L, Hirahara K, Miyamoto Y, Ando Y,lijima S 2000 Nature 408 50
[39] Wang L, Tang Z K, Li G D, Chen J S 2000 Nature 408 50
[40] Satio R, Dresselhaus G, Dresselhaus M S 1998 Physical properties of carbon nanotubes (London: Imperial College Press)
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[1] Iijima S 1991 Nature 354 56
[2] Ilijima S 1993 Mater. Sci. Eng. B 19 172
[3] Robertson J 2007 Mater Today 10 36
[4] Oku T, Narita I 2002 Physica B 323 216
[5] Bahram B Shirvani, Javad Beheshtian, Mehdi D Esrafili, Nasser L Hadipour 2010 Physica B 405 1455
[6] Saeidi M, Vaezzadeh M 2009 Physica E 41 1723
[7] Ayala P, Arenal R, Rümmeli M, Rubio A, Pichler T 2010 Carbon 48 575
[8] Tien L G, Tsai C H, Li F Y, Lee M H 2008 Diamond Relat. Mater. 17 563
[9] Kawakami Y, Nojima Y, Doi K, Nakamura K, Tachibana A 2004 Electrochim. Acta 50 739
[10] Barone V, Heyd J, Scuseria G E 2004 Chem. Phys. Lett. 389 289
[11] Satio R,Fujita M, Dresselhaus G 1992 Appl. Phys. Lett. 60 2240
[12] Behabtu N, Green M J, Pasquali M 2008 Nano Today 3 24
[13] Geoffrey M Spinks, Su Ryon Shin, Gordon G Wallace, Philip G Whitten, In Young Kim, Sun I Kim, Seon Jeong Kim 2007 Sens. Actuators B 121 616
[14] Yao M G., Liu B B, Zou Y G, Wang L, Li D M, Cui T, Zou G T, Sundqvist B 2005 Carbon 43 2894
[15] Chen C W, Lee M H, Clark S J 2004 Appl. Surf. Sci. 228 143
[16] Liu B C, Lyu S C, Jung S I, Kang H K, Yang C W, Park J W, Park C Y, Lee C J 2004 Chem. Phys. Lett. 383 104
[17] Seifi M, Ross D K, Giannasi A. 2007 Carbon 4 1871
[18] Charlotte T M, Kwok B J, Reizman D E, Agnew, Gurjit S S, Weistroffer J, Michael S S, Edmund G S 2010 Carbon 48 1279
[19] Matthew R M, Placidus B A, Amit G, Zafar I, Timothy S F 2006 Carbon 44 2758
[20] Gabriel G, Sauthier G, Fraxedas J, Moreno-Maas M, Martínez M T, Miravitlles C, Casabó J 2006 Carbon 44 1891
[21] Christian Klinke, Ali Afzali, Phaedon Avouris 2006 Chem. Phys. Lett. 430 75
[22] Chen L N, OuYang F P, Ma S S, Wu X Z, Xiao J, Xu H 2010 Phys. Lett. A 374 4343
[23] Budyka M F, Zyubina T S, Ryabenko A G, Lin S H, Mebe A M 2005 Chem. Phys. Lett. 407 266
[24] Xu H, Xiao J, Ouyang F P 2010 Acta Phys. Sin. 59 4186 (in Chinese)[徐 慧、肖 金、欧阳方平 2010 物理学报 59 4186]
[25] Wei Y, Hu H F, Wang Z Y, Cheng C P, Chen N T, Xie N 2011 Acta Phys. Sin. 60 (in Chinese)[魏 燕、胡慧芳、王志勇、程彩萍、陈南庭、谢 能 2011 物理学报 60 ](已接受)
[26] Wang S F, Chen L Y, Zhang Y, Zhang J M, Xu K W J 2010 Mol. Struct. 962 108
[27] Zhou G, Yoshiyuki Kawazoe 2002 Physica B 32 196
[28] Ouyang F P, Peng S L, Chen L N, Sun S Y, Xu H 2011 Chin. Phys. 20 027102
[29] Wang Y L, Yan H X, Huang Y, Zhang J P 2010 J. Mol.Sci. 27 34 (in Chinese)[王艳丽、颜红侠、黄 英、张军平 2010 分子科学学报 27 34]
[30] Dovesi R, Civalleri B, Orlando R, Roetti C, Saunders V R, in: Lipkowitz K B, Larter R, Cundari T R. (Eds.) 2005 Reviews in Computational Chemistry Wiley (New York) 21 1
[31] Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J L, Hada M, Ehara M, K Toyota G, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery J A, Jr, Peralta J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam J M, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A, Farkas O, Foresman J B, Ortiz J V, Cioslowski J, Fox D J, Gaussian 09, Revision A.02, Gaussian, Inc Wallingford CT 2009
[32] Verlag C,Weinheim 1968 Handbuch der Anorganischen Chemie (vol. 14B/2) p143
[33] Mashreghi A, Moshksar M M 2010 Computational Materials Science 49 871
[34] Budyka M F, Zyubina T S, Ryabenko A G, Lin S H, Mebel A M 2005 Chem. Phys. Lett. 407 266
[35] Dresselhaus M S, Dresselhaus G, Saito R 1995 Carbon 33 883
[36] Roberto S, Mauro B, Takahisa O 2009 Chem. Phys. Lett. 480 215
[37] Zhao X, Liu Y, Inoue S, Suzuki T, Jones RO, Ando Y 2004 Phys Rev. Lett. 92 125502
[38] Qin L C, Zhao X L, Hirahara K, Miyamoto Y, Ando Y,lijima S 2000 Nature 408 50
[39] Wang L, Tang Z K, Li G D, Chen J S 2000 Nature 408 50
[40] Satio R, Dresselhaus G, Dresselhaus M S 1998 Physical properties of carbon nanotubes (London: Imperial College Press)
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