本研究使用分子動力學(MD)模擬，針對單壁奈米碳管之軸向楊氏係數進行估測。MD模擬過程中使用了<NPT>系綜平均準則COMPASS勢能函數，使用其模擬碳管在不同的外加應力場下以100 ps模擬時間步階且截斷半徑設為9.5 Å內，得三斜晶系之單壁奈米碳管晶格軸向平均伸長量及分子應變能，進而求取應變值及應變能與應變之二次曲線方程式。後處理計算是以彈性力學理論之古典力法與應變能與應變關係兩種方法，分別得到各種直徑與幾何之下單壁奈米碳管軸向楊氏係數。本研究所推導之扶手椅、鋸齒以及螺旋型單壁奈米碳管軸向楊氏係數範圍分別介於1.004~1.06 TPa0.97~1.037 TPa與1.0089~1.059 TPa，與文獻中的理論值1.0~1.2 TPa，比較其誤差在20 %以內。管束型單壁奈米碳管方面，因管束間之凡德瓦爾力造成管束晶格內排列的不完美，而導致管束型單壁奈米碳管之軸向楊氏係數下降，模擬出的軸向楊氏係數隨管束直徑與數目增加而減少，推導結果介於0.989±0.07 TPa之間，與文獻結果0.978±0.05 TPa，比較其誤差在20 %以內。
本研究亦使用原子力顯微鏡(AFM)估測管束型單壁奈米碳管之楊氏係數。過程中，因碳管表面化學組成為碳-碳部分雙鍵結之類苯環結構，故原料需經酸洗改質以破壞碳管表面鍵結，產生-COOH官能基(羧基)，-COOH含量的提昇會使碳管於浸沒之乙醇溶劑中親水性增加而不易團簇。運用AFM之接觸式與輕拍式探針交錯搜尋與量測，對管束型單壁奈米碳管定點施予奈米等級之集中作用力，可得管束碳管之作用力與彎曲變形量，經計算可得管束型單壁奈米碳管之楊氏係數，其實驗結果介於0.301~1.034 TPa，其結果與誤差範圍與文獻比較均於50 %之範圍內。最後，亦將AFM實驗值與MD模擬值比較，可發現實驗量測值與數值預測頗為一致。

In this study, molecular dynamics simulation has been performed to determine the axial Young’s modulus of the single-walled carbon nanotubes(SWCNTs) and the ropes of single-walled carbon nanotubes as well. Cases considered in the present study involve the armchair, zigzag, chiral and ropes of SWCNTs. The molecular dynamics simulation with <NPT> ensemble is performed at constant pressure and temperature. The forcefield among the molecules is prescribed by the COMPASS potential. Based on the data of the elongation of the length of the carbon nanotubes crystals under external stress, the strain and the potential energy of SWCNTs could be derived for different geometrical conditions. Then, the values of axial Young’s modulus can be obtained by two methods of elasticity mechanics, namely, the classical mechanics and the energy methods. Results show that the obtained axial Young’s modulus of zigzag, armchair and chiral SWCNTs are among 1.004 to 1.06 TPa, 0.97 to 1.037 TPa and 1.0089 to 1.059 TPa respectively, and their ropes are in general varied in the range of 0.989±0.07 TPa. The predictions and error ranges are in close agreement with the existing information.
In this study, atomics force microscopy (AFM) also has been used to measure the Young’s modulus of ropes of SWCNTs. Since the surface structure of the SWCNTs is referred to the C-C partial double bonds, in order to improve the hydrophilicity of SWCNTs, the acid treatment has been performed to weaken the bonding between carbon atoms to increase the amount of -COOH in the samples. The structure of ropes of SWCNTs after acid treatment is observed by high resolution transmission electron microscopy and field emission scanning electron microscopy. Base on the obtained data of force and deflection by AFM, the Young’s modulus of ropes of SWCNTs has been derived. Results show that the Young’s modulus of ropes of SWCNTs is in general varied in the range of 0.301 to 1.034 TPa, which agrees closely with the predictions by the molecular dynamics simulation.

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