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利用密度泛函理论研究锯齿型单、双壁碳纳米管从核到管状团簇直至纳米管的逐层结构衍生.研究结果表明五边形结构在管状团簇生长中发挥关键作用.此外，基于管状团簇的研究，运用周期性边界条件得到锯齿型单、双壁碳纳米管，并通过计算能带和态密度研究其电子特性.对单壁（n，0）和双壁（n，0）@（2 n，0）碳纳米管，当n=3q（q为整数）时，具有金属或窄带隙半导体特性；n3q时，具有较宽带隙半导体特性，且带隙随管径的增加而减小.然而，小管径碳纳米管受曲率效应的明显影响，n3q的（4，0），（4，0）@（8，0）和（5，0）@（10，0）均呈现金属性；n=3q的（6，0）@（12，0）则表现出明显的半导体特性.It is well known that carbon nanotubes (CNTs) have received much attention since they were discovered. With the rapid development of carbon-based electronics and quantum computers, CNTs are required to have their unique physical and chemical properties in many fields. However, due to their uncertain mechanism of growth, it is difficult to achieve high production of CNTs with certain controlled structures. In this paper, we construct the nuclei of specific single- and double-walled zigzag CNTs and study their structural derivatives and electronic properties by using the density functional theory. According to the study of carbon clusters, we find some stable cage-like clusters containing zigzag structure which can be used as the nucleus of the corresponding single-walled CNTs. The nucleus of the double-walled CNTs is composed of the corresponding nucleus of single-walled CNTs. It is possible to obtain a tubular cluster by optimizing the structure of the nucleus with accumulating carbon atoms at one end. The results show that the pentagonal structure plays a key role in the growing of tubular clusters. We find that the tubular clusters are grown in the form of global reconstruction when the clusters are short, but grown by local reconstruction when the clusters are longer. It can provide a theoretical reference to realize numerous CNTs with certain structures. Furthermore, the average binding energy (Eb) of tubular clusters is studied, and we find that their Eb is more and more stable and then close to the corresponding CNTs. At the same time, the study of the thermodynamic quantities of tubular clusters shows that their structures are thermodynamically stable. In addition, the infinite zigzag CNTs can be obtained by using the periodic boundary conditions. Furthermore, the energy bands and density of states are calculated to study their electronic properties. The results show that the energy band structures of zigzag CNTs are closely related to the chiral index n. For zigzag CNTs (n, 0) and (n, 0)@(2n, 0), they show a metal property or narrow band gap semiconductor when n=3q (q is an integer); when n3q, they show a wide band gap semiconductor, and the band gap decreases with the diameter increasing. It is interesting that the two metallic single-walled CNTs (SWCNTs) are nested to obtain metallic double-walled (CNTs) DWCNTs, while the two semiconducting SWCNTs are nested to obtain semiconducting DWCNTs. However, due to the obvious curvature effect, small-diameter CNTs (4, 0), (4, 0)@(8, 0) and (5, 0)@(10, 0) show the metal properties but CNT (6, 0)@(12, 0) shows the obvious semiconductor property.
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[1] Iijima S 1991 Nature 354 56
[2] Iijima S, Ichihashi T 1993 Nature 364 603
[3] Peng L M, Zhang Z L, Xue Z Q, Wu Q D, Gu Z N, Pettifor D G 2000 Phys. Rev. Lett. 85 3249
[4] Rao A M, Richter E, Bandow S, Chase B, Eklund P C, Williams K A, Fang S, Subbaswamy K R, Menon M, Thess A, Smalley R E, Dresselhaus G, Dresselhaus M S 1997 Science 275 187
[5] Alvarez L, Righi A, Guillard T, Rolsa S, Anglareta E, Laplazea D, Sauvajolaet J L 2000 Chem. Phys. Lett. 316 186
[6] Burda C, Chen X B, Narayanan R, El-Sayed M A 2005 Chem. Rev. 105 1025
[7] Che J, Cagin T, Goddard W 2000 Nat. Nanotech. 11 2083
[8] Gong X F, Wang Y, Ning X J 2008 Chin. Phys. Lett. 25 468
[9] Wang X, Zheng F, Lu J, Bai J M, Wang Y, Wei F L 2011 Acta Phys. Sin. 60 017505 (in Chinese) [王璇, 郑富, 芦佳, 白建民, 王颖, 魏福林 2011 60 017505]
[10] Fan J, Wan M, Zhu D, Chang B, Pan Z, Xie S 1999 J. Appl. Polym. Sci. 74 2605
[11] Kuzumaki T, Ujiie O, Ichinose H, Ito K 2000 Adv. Eng. Mater. 2 416
[12] Service R F 1999 Science 285 682
[13] Collins P G 1997 Science 278 100
[14] Tans S J, Verschueren A R M, Dekker C 1998 Nature 393 49
[15] Ma W, Liu L, Yang R, Zhang T, Zhang Z, Song L, Ren Y, Shen J, Niu Z, Zhou W, Xie S 2009 Adv. Mater. 21 603
[16] Lin Y M, Appenzeller J, Chen Z, Chen Z G 2005 IEEE Electr. Dev. Lett. 26 823
[17] Ding L, Tselev A, Wang J, Yuan D, Chu H, McNicholas T P, Li Y, Liu J 2009 Nano Lett. 9 800
[18] de Volder M F, Tawfick S H, Baughman R H, Hart A J 2013 Science 339 535
[19] Shulaker M M, Hills G, Patil N, Wei H, Chen H Y, Wong H S, Mitra S 2013 Nature 501 526
[20] Hatta N, Murata K 1994 Chem. Phys. Lett. 217 393
[21] Morales A M, Lieber C M 1998 Science 279 208
[22] Ajayan P M 1999 Chem. Rev. 99 1787
[23] Popov V N 2004 New J. Phys. 6 279
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[27] Fischer J E, Johnson A T 1999 Curr. Opin. Solid St. M. 4 28
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[29] 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
[30] Cheng H M, Li F, Su G, Pan H Y, He L L, Sun X, Dresselhaus M S 1998 Appl. Phys. Lett. 72 3282
[31] Yao Y, Feng C, Zhang J, Yao Y G, Feng C Q, Zhang J, Liu Z F 2009 Nano Lett. 9 1673
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[34] Yang F, Wang X, Li M, Liu X, Zhao X, Zhang D, Zhang Y, Yang J, Li Y 2016 Acc. Chem. Res. 49 606
[35] Kiang C H 2000 J. Chem. Phys. 113 4763
[36] Yu X, Zhang J, Choi W, Choi J Y, Kim J M, Gan L, Liu Z 2010 Nano Lett. 10 3343
[37] Lu X X, Hu Z 2012 Compos. Part B: Eng. 43 1902
[38] An W, Shao N, Bulusu S, Zeng X C 2008 J. Chem. Phys. 128 084301
[39] Jensen F, Toftlund H 1993 Chem. Phys. Lett. 201 89
[40] Jensen F, Koch H 1998 J. Chem. Phys. 108 3213
[41] Wu H S, Jia J F, Xu X H 2004 Acta Chim. Sin. 62 105
[42] Galli G, Gygi F, Golaz J C 1998 Phys. Rev. B 57 1860
[43] Chen Z, Heine T, Jiao H, Hirsch A, Thiel W, Schleyer P 2004 Chem.-Eur. J. 10 963
[44] Lu X, Chen Z 2006 Chem. Rev. 105 3643
[45] Jin Y F, Hao C 2005 J. Phys. Chem. A 109 2875
[46] Nose S 1991 Prog. Theor. Phys. Supp. 103 1
[47] Liu Z F, Zhu H J, Chen H, Liu L R 2011 Acta Phys.-Chim. Sin. 27 2079
[48] Ouyang M, Huang J L, Cheung C L, Lieber C M 2001 Science 292 702
[49] Ding J W, Yan X H, Cao J X 2002 Phys. Rev. B 66 429
[50] Liu X H, Zhu C C, Zeng F G, He Y N, Bao W X 2006 Acta Phys. Sin. 55 2830 (in Chinese) [刘兴辉, 朱长纯, 曾凡光, 贺永宁, 保文星 2006 55 2830]
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