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arXiv 1102.2066cond-mat.mes-hall
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碳纳米管的一维连续模型

A one-dimensional continuous model for carbon nanotubes

Xiaohua Zhou

摘要:

将Tu和Ou-Yang在[Phys. Rev. B \textbf{65},235411(2003)]中提出的单壁碳纳米管(SWNTs)的连续二维(2D)弹性模型严格简化为一维(1D)曲率弹性模型。该模型符合各向同性克希霍夫弹性杆理论。在此模型中忽略面内应变能,它适合于研究大变形的碳纳米管(CNTs)的性质,并且可以简化为[Phys.Rev.Lett. \textbf{76},4055(1997)]。对于直手征形状,该一般模型表明,两个平衡态之间的手征角差约为$π/6$,这与晶格模型一致。在相同条件下,螺旋形的原子能量比直形的原子能量低。通过求解相应的平衡形状方程,螺旋管的解与实验结果吻合较好,得到了超螺旋形状,希望在今后的实验中能够发现。

英文摘要:

The continuous two-dimensional (2D) elastic model for single-walled carbon nanotubes (SWNTs) provided by Tu and Ou-Yang in [Phys. Rev. B \textbf{65}, 235411 (2003)] is reduced to a one-dimensional (1D) curvature elastic model strictly. This model is in accordance with the isotropic Kirchhoff elastic rod theory. Neglecting the in-plane strain energy in this model, it is suitable to investigate the nature features of carbon nanotubes (CNTs) with large deformations and can reduce to the string model in [Phys. Rev. Lett. \textbf{76}, 4055 (1997)] when the deformation is small enough. For straight chiral shapes, this general model indicates that the difference of the chiral angle between two equilibrium states is about $π/6$, which is consistent with the lattice model. It also reveals that the helical shape has lower energy for per atom than the straight shape has in the same condition. By solving the corresponding equilibrium shape equations, the helical tube solution is in good agreement with the experimental result, and super helical shapes are obtained and we hope they can be found in future experiments.

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