奈米碳管的力學性質數值模擬

Abstract

本文以碳-碳鍵的能量曲線為出發點，配合結構力學模擬的方法，對奈米碳管的基本力學性質做了一些初步的研究。本文簡單描述有關於奈米碳管的結構外觀，包含扶手椅型、鋸齒型和對掌型奈米碳管，以及從石墨片到碳管的映射關係。並且以數學公式建立起管壁上碳原子的位置，配合以Tersoff 能量公式的計算發現不同類型的奈米碳管有不一樣的鍵結長度和鍵角，但都和石墨片十分接近。本文也用了Tersoff 能量公式配合碳-碳鍵間的幾何變形關係，計算出不同晶格向量的單壁鋸齒型奈米碳管的拉伸、撓曲和扭轉力場常數。再以能量函數相等的方法，把分子力學和結構力學連接起來，以此建立起數值模型。並以結構力學的方法計算出奈米碳管的軸向彈性模數、剪力模數和自然振頻等奈米碳管的基本力學性質。結果都顯示和碳管的管徑大小相關，不同幾何型式的奈米碳管力學行為也會因此有些許差異。

This paper starting on the potential energy curve of carbon-carbon bond with combination of the analytic method of structural mechanics researches preliminarily on the property of the mechanics in carbon nanotube. This paper briefly describes the structural shape of carbon nanotube, including armchair, zigzag, chiral of carbon nanotube, and the transformation through mathematic formula from graphene sheet to carbon nanotube. In addition, this paper establishes the position of carbon atom on the wall of carbon nanotube by mathematical formula, and discovers that under Tersoff potential formula the different types of carbon nanotube have different bond lengths and bond angles; however, they all very approach to graphene sheet. This paper also combines Tersoff potential formula with the deformation sharp of carbon-carbon bond to calculate the bond stretching, bond angle bending, bond torsional of constants of force fields of different chiral vectors of single-walled carbon nanotube. Than by energy equivalence links molecular mechanics and structural mechanics to establish analytic model. And using the method of structural mechanics to calculate the axial Young’s modulus, shear modulus, natural frequency and so on, these properties of the mechanics in carbon nanotube. The result all displays that they are related to the diameter of carbon nanotube, and there would be some slight differences from different forms of the function of the mechanics in carbon nanotube.