Baowan Duangkamon, Cox Barry J, Hill James M
Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia.
Nanotechnology. 2008 Feb 20;19(7):075704. doi: 10.1088/0957-4484/19/7/075704. Epub 2008 Jan 31.
For future nanoelectromechanical signalling devices, it is vital to understand how to connect various nanostructures. Since boron nitride nanostructures are believed to be good electronic materials, in this paper we elucidate the classification of defect geometries for combining boron nitride structures. Specifically, we determine possible joining structures between a boron nitride nanotube and a flat sheet of hexagonal boron nitride. Firstly, we determine the appropriate defect configurations on which the tube can be connected, given that the energetically favourable rings for boron nitride structures are rings with an even number of sides. A new formula E = 6+2J relating the number of edges E and the number of joining positions J is established for each defect, and the number of possible distinct defects is related to the so-called necklace and bracelet problems of combinatorial theory. Two least squares approaches, which involve variation in bond length and variation in bond angle, are employed to determine the perpendicular connection of both zigzag and armchair boron nitride nanotubes with a boron nitride sheet. Here, three boron nitride tubes, which are (3, 3), (6, 0) and (9, 0) tubes, are joined with the sheet, and Euler's theorem is used to verify geometrically that the connected structures are sound, and their relationship with the bonded potential energy function approach is discussed. For zigzag tubes (n,0), it is proved that such connections investigated here are possible only for n divisible by 3.
对于未来的纳米机电信号装置而言，了解如何连接各种纳米结构至关重要。由于氮化硼纳米结构被认为是良好的电子材料，因此在本文中，我们阐明了用于组合氮化硼结构的缺陷几何形状的分类。具体而言，我们确定了氮化硼纳米管与六方氮化硼平板之间可能的连接结构。首先，鉴于氮化硼结构在能量上有利的环是边数为偶数的环，我们确定了可在其上连接管子的合适缺陷构型。为每个缺陷建立了一个新的公式(E = 6 + 2J)，该公式将边数(E)与连接位置数(J)相关联，并且可能的不同缺陷的数量与组合理论中所谓的项链和手镯问题相关。采用两种最小二乘法，即涉及键长变化和键角变化的方法，来确定锯齿形和扶手椅形氮化硼纳米管与氮化硼片的垂直连接。在此，将三根氮化硼管，即((3, 3))、((6, 0))和((9, 0))管，与该片连接，并使用欧拉定理从几何角度验证连接结构是合理的，并且讨论了它们与键合势能函数方法的关系。对于锯齿形管((n,0))，证明了此处研究的这种连接仅在(n)能被(3)整除时才可能实现。
