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arXiv 0907.2528cond-mat.mes-hallcond-mat.mtrl-sci
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单壁碳纳米管轴向应变扭转的二维连续非谐各向异性弹性模型研究

Study of axial strain induced torsion of single wall carbon nanotubes by 2D continuum anharmonic anisotropic elastic model

Weihua MU, Ming Li, Wei Wang, Ou-Yang Zhong-can

摘要:

最近的分子动力学模拟发现,手性单壁碳纳米管(SWNTs)在拉伸过程中发生扭曲,这类似于螺旋的运动。显然,这种现象是一种曲率-手征效应,不能用通常的单壁碳纳米管各向同性弹性理论来解释。更有趣的是,随着较大的轴向应变(屈曲前),轴向应变诱导扭转(a-SIT)表现出轴向拉伸和压缩应变的不对称行为,这表明单壁碳纳米管的非谐弹性在真正的a-SIT响应中起着重要的作用。为了研究具有实际尺寸的手性单壁碳纳米管的a-SIT,避免由于有限尺寸效应可能导致的计算机模拟结果的偏差,我们提出了一个二维解析连续模型,该模型可以用来描述任意手性、曲率和长度的单壁碳纳米管,考虑了单壁碳纳米管的各向异性和非谐弹性。本模型的弹性能来自于基于第二代反应经验键级势(REBO-II)的晶格能的连续极限,该第二代反应经验键级势是固体碳的公认经验势。我们的模型没有可调的参数,除了那些在REBO-II,模型中的所有系数可以解析计算。利用我们的方法,我们获得了任意半径,手性和手性的单壁碳纳米管的a-SIT响应。我们的结果是在合理的协议与最近的分子动力学模拟。[Liang { \it et.等人,Phys. Rev. Lett,${\bf 96}$,165501(2006).]我们的方法也可以用来计算其他曲率手征依赖的单壁碳纳米管的非谐力学响应。

英文摘要:

Recent molecular dynamic simulations have found chiral single wall carbon nanotubes (SWNTs) twist during stretching, which is similar to the motion of a screw. Obviously this phenomenon, as a type of curvature-chirality effect, can not be explained by usual isotropic elastic theory of SWNT. More interestingly, with larger axial strains (before buckling), the axial strain induced torsion (a-SIT) shows asymmetric behaviors for axial tensile and compressing strains, which suggests anharmonic elasticity of SWNTs plays an important role in real a-SIT responses. In order to study the a-SIT of chiral SWNTs with actual sizes, and avoid possible deviations of computer simulation results due to the finite-size effect, we propose a 2D analytical continuum model which can be used to describe the the SWNTs of arbitrary chiralities, curvatures, and lengths, with the concerning of anisotropic and anharmonic elasticity of SWNTs. This elastic energy of present model comes from the continuum limit of lattice energy based on Second Generation Reactive Empirical Bond Order potential (REBO-II), a well-established empirical potential for solid carbons. Our model has no adjustable parameters, except for those presented in REBO-II, and all the coefficients in the model can be calculated analytically. Using our method, we obtain a-SIT responses of chiral SWNTs with arbitrary radius, chiralities and lengthes. Our results are in reasonable agreement with recent molecular dynamic simulations. [Liang {\it et. al}, Phys. Rev. Lett, ${\bf 96}$, 165501 (2006).] Our approach can also be used to calculate other curvature-chirality dependent anharmonic mechanic responses of SWNTs.

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