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Systematic periodicity in waviness of vertically aligned carbon nanotubes explained by helical buckling

机译：通过螺旋屈曲解释的垂直对齐碳纳米管波动的系统性周期性

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摘要

A hypothesis is proposed in this work to account for the geometry of individual vertically aligned carbon nanotubes (VACNTs) that not only justifies the directionality of their growth, but also explains the origin of the waviness frequently reported for these nanotube forests. Such waviness has fundamental effects on the transport/conduction properties of VACNTs, either through or along them, regarding phenomena such as mass, stress, heat and electricity. Despite the general opinion about randomness of carbon nanotubes (CNTs) tortuosity, we demonstrate here that rules of helical buckling of tubular strings is applicable to VACNTs, based on which a regular 3D helical geometry is proposed for VACNTs, with a 2D sine wave shape side-profile. In this framework, gradual increase of the total free surface energy by growth of CNTs ensues their partial cohesion, driven by van der Waals interactions, to reduce the excess surface energy. On the other hand, their cohesion is accompanied by their deformation and loss of straightness, which in turn, translates to buildup of an elastic strain energy in the system. The balance of the two energies along with the spatial constraints on each CNT at its contact points with neighboring CNTs, is manifested in its helical buckling, that is systematically influenced by nanostructural characteristics of VACNTs, such as their diameter, wall thickness and inter-CNT spacing.
机译：一个假设是在这项工作中，以账户为个人垂直排列的碳纳米管（VACNTs），不仅证明其生长的方向性的几何形状提出，但也说明了经常报道这些纳米管森林波纹的起源。这样波纹对VACNTs的传输/传导性能基本作用，无论是通过或沿着它们，关于等现象的质量，压力，热和电。尽管对碳纳米管（CNT）的曲折的随机性一般认为，我们在这里展示的是管柱的螺旋屈曲的规则适用于在其上提出了VACNTs规则的三维螺旋几何VACNTs，基础，以二维正弦波形侧-轮廓。在此框架下，通过CNT的生长的总自由表面能的逐渐增加随之而来它们的部分的凝聚力，通过范德华相互作用驱动，以减少过量的表面能。在另一方面，它们的内聚力是伴随着它们的变形和直线度的损失，这又，转换为在系统中的弹性应变能量的积累。与相邻的CNT在各CNT的空间限制在其接触点沿着所述两个能量的平衡，表现在其螺旋屈曲，即系统地VACNTs的纳米结构的特性，如它们的直径，壁厚和帧间CNT影响间距。

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