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The static and dynamic mechanical characteristics of carbon nanotubes with double and multiple vacancy defects are simulated by the molecular dynamics method. Firstly, the effects of diatomic and polyatomic vacancy defects on the quasi-static mechanical properties of carbon nanotubes are discussed. Then, the effects of defects and axial pre-stress on the dynamics of C60 molecular oscillation in carbon nano-peapods are discussed. The results show that the ultimate stress, ultimate strain and elastic modulus of carbon nanotube containing different types of diatomic vacancies are significantly reduced as compared with those of non-defective carbon nanotubes. When the carbon nanotubes have many defective atoms and the defects are connected together to form a crack, the axial compressive properties of the carbon nanotubes are greatly reduced. Compared with the circumferential development of cracks, the cracks along the axis greatly reduce the compressive capacity of carbon nanotubes, which is similar to that of shell models with cracks. The oscillation frequency of C60 molecular in defective carbon nano-peapods is affected by the number of missing atoms. The single vacancy defect increases the oscillation frequency of C60 molecule, while with the further increase of vacancy number, the oscillation frequency of C60 molecule decreases gradually. When the defective carbon nano-peapod has axial tensile or compressive pre-stress, the oscillation of the C60 molecule is affected not only by the defects, but also by the axial pre-stress, which makes the oscillation of C60 molecule more complicated.
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Keywords:
- carbon nanotubes /
- carbon nano-peapods /
- defects /
- static and dynamic mechanical characteristics
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图 1 (a) (10 10)无缺陷扶手椅型碳纳米管; (b) 六元环中碳原子编号
Figure 1. (a) (10 10) Non-defective armchair carbon nanotube; (b) numbering of carbon atoms in six-membered ring.
图 3 含多原子空位缺陷碳纳米管模型 (a) 沿轴向分布的多原子空位缺陷; (b) 沿周向分布的多原子空位缺陷
Figure 3. Carbon nanotubes with polyatomic vacancy defects: (a) Polyatomic vacancy defects distributed along the axial direction; (b) polyatomic vacancy defects distributed along the circumferential direction.
图 4 无缺陷碳纳米豆荚模型
Figure 4. Non-defective carbon nano-peapod.
图 5 含缺陷碳纳米豆荚模型
Figure 5. Defective carbon nano-peapod.
图 6 含多原子空位缺陷碳纳米管在轴向荷载作用下屈曲失稳构型 (a) 沿轴向分布的含多原子空位缺陷管; (b) 沿周向分布的含多原子空位缺陷管
Figure 6. Buckling instability configuration of carbon nanotubes with polyatomic vacancy defects under axial loading: (a) Carbon nanotubes with polyatomic vacancy defects distributed along the axial direction; (b) carbon nanotubes with polyatomic vacancy defects distributed along the circumferential direction.
图 7 含多原子空位缺陷碳纳米管的弹性模量随原子缺失数的变化
Figure 7. Variation of elastic modulus of carbon nanotubes with the number of missing atoms when polyatomic vacancy defects occurs.
图 8 C60在一个运动周期内的受力随运动距离的变化
Figure 8. The variation of force on C60 molecule with the distance of its motion in a cycle.
图 9 C60分子的振荡频率随碳管中原子缺失数的变化
Figure 9. Variation of the oscillation frequency of C60 molecule with the number of missing atoms in carbon tubes.
图 10 缺陷碳纳米豆荚内C60分子的振荡频率随轴向预应力的变化
Figure 10. Variation of the oscillation frequency of C60 molecules in the defective carbon nano-peapods with axial pre-stress.
表 1 含双原子空位缺陷碳纳米管
Table 1. Carbon nanotubes containing diatomic vacancy defects.
编号 缺陷类型 间隔碳原子数 1 缺失1, 2位置原子 0 2 缺失1, 3位置原子 1 3 缺失1, 4位置原子 2 4 缺失1, 5位置原子 1 5 缺失1, 6 位置原子 0 6 缺失3, 6位置原子 2 
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表 2 轴压下双原子空位缺陷对碳纳米管力学性能影响
Table 2. Effect of diatomic vacancy defects on mechanical properties of carbon nanotubes under axial compression.
编号 极限应力/GPa 极限应变/% 弹性模量/GPa 1 27.96 3.76 743.6 2 28.26 4.00 706.5 3 28.28 4.00 707.0 4 29.06 4.24 685.4 5 31.21 4.20 743.1 6 30.34 4.30 705.6 7 40.86 4.85 842.5
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[1] Iijima S 1991 Nature 354 56
Google Scholar
[2] Krishnan A, Dujardin E, Ebbesen T W 1998 Phys. Rev. B 58 14013
Google Scholar
[3] Berber S, Kwon Y K, Tomanek D 2000 Phys. Rev. Lett. 84 4613
Google Scholar
[4] Rinzler A G, Hafner J H, Nikolaev P, Lou L, Kim S G, Tomanek D, Nordlander P, Colbert D T, Smalley R E 1995 Science 269 1550
Google Scholar
[5] Popov V N 2004 Mater. Sci. Eng. R 43 61
Google Scholar
[6] Harris P J F, Hernandez E, Yakobson B I 2004 Am. J. Phys. 72 413
Google Scholar
[7] Stone A J, Wales D J 1986 Chem. Phys. Lett. 128 501
Google Scholar
[8] Nardelli M B, Yakobson B I, Bernholc J 1998 Phys. Rev. B 57 4277
Google Scholar
[9] Hirai Y, Nishimaki S, Mori H, Kimoto Y, Akita S, Nakayama Y, Tanaka Y 2003 Jpn. J. Appl. Phys. 42 4120
Google Scholar
[10] 辛浩, 韩强, 姚小虎 2008 物理学报 57 4391
Google Scholar
Xin H, Han Q, Yao X H 2008 Acta Phys. Sin. 57 4391
Google Scholar
[11] 袁剑辉, 程玉民, 张振华 2009 物理学报 58 2578
Google Scholar
Yuan J H, Cheng Y M, Zhang Z H 2009 Acta Phys. Sin. 58 2578
Google Scholar
[12] Zhang Y Y, Xiang Y, Wang C M 2009 J. Appl. Phys. 106 113503
Google Scholar
[13] Kulathunga D D T K, Ang K K, Reddy J N 2010 J. Phys.: Condens. Matter 22 345301
Google Scholar
[14] 王锋, 曾祥华, 徐秀莲 2002 物理学报 51 1778
Google Scholar
Wang F, Zeng X H, Xu X L 2002 Acta Phys. Sin. 51 1778
Google Scholar
[15] Liu P, Zhang Y W, Lu C 2005 J. Appl. Phys. 97 094313
Google Scholar
[16] Song H Y, Zha X W 2009 Phys. Lett. A 373 1058
Google Scholar
[17] 崔柳, 冯妍卉, 檀鹏, 张欣欣 2015 科学通报 60 1414
Cui L, Feng Y H, Tan P, Zhang X X 2015 Chin. Sci. Bull. 60 1414
[18] 方炜, 王磊 2018 材料导报 32 164
Fang W, Wang L 2018 Mater. Rev. 32 164
[19] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[20] Brenner D W, Shenderova O A, Harrison J A, Stuart S J, Ni B, Sinnott S 2002 J. Phys.: Condens. Matter 14 783
Google Scholar
[21] Stuart S J, Tutein A B, Harrison J A 2000 J. Chem. Phys. 112 6472
Google Scholar
[22] Lennard-Jones J E, Dent B M 1926 Proc. R. Soc. A 112 230
Google Scholar
[23] Girifalco L A, Hodak M, Lee R S 2000 Phys. Rev. B 62 13104
Google Scholar
[24] Rafizadeh H A 1974 Physica 74 135
Google Scholar
[25] Cox B J, Thamwattana N, Hill J M 2007 Proc. R. Soc. A 463 461
Google Scholar
[26] Cox B J, Thamwattana N, Hill J M 2007 Proc. R. Soc. A 463 477
Google Scholar
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