臺灣博碩士論文加值系統

由於奈米碳管具有許多優異之材料、機械、熱傳及電學特性，近年來引起廣泛的研究。本論文旨在建立一等效連體力學分析模式以快速、準確的反算單層奈米碳管材料性質，如等效楊氏模數(Young’s modulus)及柏松比(Poisson’s ratio)等。
本論文首先以連體力學分析為基礎，分別推導等效彈簧及梁單元以模擬碳原子間之鍵結力，並以之建立有限單元分析模型，配合不同負載，以反算石墨及鋸齒型與扶手型單層奈米碳管之材料性質。所得結果與文獻中之實驗及模擬結果相較，顯示應用等效梁單元之有限單元分析模型具有較高的準確性。
最後，本論文應用等效梁單元之有限單元分析模型進一步探討凡得瓦力(van der Waals force)對於單層奈米碳管材料性質的影響。凡得瓦力係以等效非線性彈簧單元模擬。研究結果發現，凡得瓦力對於單層奈米碳管之材料性質具有相當程度的影響。

Carbon nanotubes (CNTs) have stimulated wide research activities in recent years because of the merits of their special material, mechanical, thermal and electric properties. The objective of this work is to develop an equivalent continuum mechanics analysis model to make an in-verse-calculation of the material properties of single-walled CNTs fastly and accurately, such as equivalent Young’s modulus and Poisson’s ratio.
Firstly, based on the continuum mechanics analysis, the equivalent spring and beam elements are derived to simulate the bond forces be-tween carbon atoms, respectively. By establishing the finite element mod-els using respective equivalent elements, the inverse-calculation of the material properties of graphite and single-walled CNTs with zigzag and armchair type can be made subjected to different loadings. The compari-sons between the present results and available experimental and simulat-ing data show that the finite element analysis model using equivalent beam elements has higher accuracy.
Finally, the finite element analysis model using equivalent beam elements is adopted to further study the influence of the van der Waals forces on the material properties of single-walled CNTs. The van der Waals forces are simulated by equivalent nonlinear spring elements. It is found that the van der Waals forces have significant influence on the ma-terial properties of single-walled CNTs.

目錄
摘要 I
目錄 III
圖表目錄 V
第一章、 導論 1
第二章、 奈米碳管之介紹 4
2.1 奈米碳管之製備 4
2.2 單層奈米碳管結構 4
2.3 奈米碳管之應用 5
第三章、 等效連體力學分析模式 7
3.1 分子力學 7
3.2 等效彈簧單元 9
3.3 等效梁單元 10
第四章、 凡得瓦力對奈米碳管材料性質的影響 12
4.1 凡得瓦力（van der Waals force） 12
4.2 凡得瓦力之等效模擬 12
第五章、 結果與討論 14
5.1 石墨等效楊氏模數之計算 14
5.2 奈米碳管材料性質之計算 15
5.3 等效楊氏模數之計算 16
5.4 柏松比之結果比較 18
5.5 等效彈簧及梁單元之比較 19
5.6 凡得瓦力之影響 19
第六章、 結論與未來展望 21
參考文獻 22

圖表目錄
表一、有限單元分析模型之單元數及節點數 29
表二、等效楊氏模數及柏松比與文獻比較 30
圖一、奈米碳管之電子顯微鏡圖 31
圖二、奈米碳管結構型式 32
圖三、鍵結能量形式 33
圖四、等效彈簧單元 34
圖五、等效梁單元 35
圖六、凡得瓦能及力與原子間距離之關係 36
圖七、奈米碳管之鍵結及非鍵結原子 37
圖八、凡得瓦力影響範圍 38
圖九、石墨之有限單元分析模型 39
圖十、奈米碳管之有限單元分析模型 40
圖十一、奈米碳管之等效梁分析 41
圖十二、等效楊氏模數與半徑之關係 42
圖十三、柏松比與半徑之關係 43
圖十四、等效楊氏模數與半徑之關係 (考慮凡得瓦力效應) 44
圖十五、柏松比與半徑之關係 (考慮凡得瓦力效應) 45

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