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研究生:廖浩羽
研究生(外文):Hao-Yu Liao
論文名稱:以平衡分子動力學研究石墨烯與石墨烯奈米網格之熱傳性質
論文名稱(外文):An Investigation of Thermal Conductivity of Graphene and Graphene Nanomesh in use of the Equilibrium Molecular Dynamics Simulation
指導教授:黃美嬌黃美嬌引用關係
指導教授(外文):Mei-Jiau Huang
口試委員:呂明璋許麗楊天祥
口試委員(外文):Ming-Chang LuLi XuTian-Shiang Yang
口試日期:2023-01-31
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:111
語文別:中文
論文頁數:113
中文關鍵詞:平衡分子動力學晶格熱傳導係數石墨烯石墨烯奈米網格熱整流現象
外文關鍵詞:Equilibrium Molecular DynamicsThermal ConductivityGrapheneGraphene NanoMeshThermal Rectification
DOI:10.6342/NTU202300623
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  本論文以平衡分子動力學模擬方法,研究單層石墨烯與石墨烯奈米網格的熱傳性質。一方面探討系統尺寸與溫度對石墨烯熱傳導係數之影響,也研究孔隙相關幾何參數對石墨烯奈米網格(GNM)熱傳導係數之影響,另一方面探索熱整流效應是否存在於石墨烯與石墨烯奈米網格兩種材料組合而成的系統。模擬採用最佳化特索夫(Opt. Tersoff)勢能函數來描述原子之間的作用力。
 本文首先以平衡分子動力學模擬單層石墨烯的色散關係與態密度,並與實驗、模擬之文獻結果比較,確認設置的正確性。接著搭配 Green-Kubo 理論計算單層石墨烯的熱傳導係數,進行尺寸效應與溫度相性的分析。尺寸效應模擬於300K下進行,模擬結果顯示當單層石墨烯的尺寸變大的時候,熱傳導係數大約呈指數下降,並且觀察到在系統尺寸16.0nm × 16.2nm以上時達到收斂。溫度相依性模擬則是在16.0nm × 16.2nm的尺寸下,計算溫度在 100K 到 400K 間的熱傳導係數,發現隨著溫度的提升,熱傳導係數劇烈下降。在石墨烯奈米網格模擬中,觀察六個不同孔隙設定之熱傳導係數與諸幾何參數的關係,發現與石墨烯奈米網格之熱傳導係數最相關的參數為孔隙之頸寬,且兩者呈現線性正相關。另外,當頸寬越小,熱傳導係數對溫度的敏感性越弱,在頸寬為 2nm 時,熱傳導係數幾乎不隨溫度改變。
  最後,在得到石墨烯與石墨烯奈米網格熱傳導係數的溫度相依性之後,進一步透過熱擴散方程式探討由石墨烯與石墨烯奈米網格組成之系統的熱整流效應,討論平均溫度、溫差、長度比、熱傳導係數的溫度相依性等因素對熱整流效應之影響。根據結果,歸納可能提升熱整流係數的方向。
  In this study, we investigated the thermal conductivity of graphene and graphene nanomesh (GNM) in use of equilibrium molecular dynamic (EMD) simulations with optimized Tersoff potential. The effect size and temperature dependence were inspected. Besides, the correlations of the thermal conductivity with the geometric parameters of nanoholes on GNM were also explored. Finally, we examined if the thermal rectification exists in the system composed of Graphene and GNM.

  We first validated our simulation setup by comparing the calculated phonon dispersion relation and density of states with those in the literature, including experimental and MD measurements. Then, we investigated the size effect on the graphene thermal conductivity at 300K. The thermal conductivity decreases exponentially with increasing system size and converges as the system size is about 16.0nm × 16.2nm. By fixing the film size at 16.0nm x 16.2nm, we found the thermal conductivity of graphene decreases rapidly with increasing temperature while that of GNMs is much less sensitive to temperature. Among the geometric parameters of nanoholes, the neck width affects mostly. The GNM thermal conductivity decreases approximately linearly with decreasing neck width. Moreover, the smaller the neck width, the weaker the temperature dependence becomes. For those GNMs with neck width of 2nm, the temperature dependence almost completely disappears.

  Based on the obtained temperature-dependent thermal conductivities of graphene films and GNMs, we finally investigated the thermal rectification phenomenon in nanoribbons composed of Graphene and GNM by solving the heat diffusion equation. The effects of the mean temperature, temperature difference, length ratio and temperature dependence of GNMs on the intensity of thermal rectification were studied. According to the results, we summary some possible directions useful for promoting thermal rectification.
致謝 i
中文摘要 ii
Abstract iii
目錄 iv
表目錄 vii
圖目錄 viii
第 1 章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 1
1.2.1 實驗量測 2
1.2.2 分子動力學模擬 4
1.2.3 熱整流效應 9
1.3研究動機與目的 11
1.4分子動力學模擬軟體介紹 12
1.5論文架構 12
第 2 章 平衡分子動力學理論與數值方法 13
2.1晶體結構 13
2.2勢能函數 15
2.2.1 Opt. Tersoff 勢能函數 15
2.3初始與邊界條件 17
2.3.2 初始位置與速度 17
2.3.3 週期性邊界條件 18
2.4 運動方程式 19
2.5 控溫控壓 20
2.5.1 溫度控制 20
2.5.2 壓力控制 21
2.6 聲子頻譜 23
2.6.1 聲子色散關係 23
2.6.2 態密度 24
2.7 熱傳導係數 24
2.7.1 Green-Kubo 理論 24
2.7.2 數值積分 Green-Kubo 公式 25
第 3 章 完美單層石墨烯 27
3.1 模擬時步大小選取 27
3.1.1 原子振動特徵時間 27
3.1.2 時步大小測試 28
3.2 薄膜變形分析 31
3.3 穩態判斷 39
3.4 聲子色散關係與態密度 43
3.4.1 聲子色散關係 43
3.4.2 態密度 46
3.5 熱傳導係數 48
3.5.1 熱流自相關函數 48
3.5.2 誤差分析 51
3.5.3 尺寸效應 52
3.5.4 態密度分析 57
3.6 溫度相依性 58
第 4 章 石墨烯奈米網格 64
4.1 有孔隙石墨烯模擬系統 64
4.2 穩態判斷 65
4.3 熱傳導係數 69
4.3.1 尺寸效應 69
4.3.2 孔隙設置與熱傳導係數 72
4.3.3 態密度分析 77
4.4 溫度相依性 80
第 5 章 熱整流效應 83
5.1 一維穩態熱擴散方程式 83
5.2 熱整流係數 84
5.2.1 平均溫度 86
5.2.2 GS 及 GNM 區域長度占比 88
5.2.3 溫差 89
第 6 章 結論與未來展望 91
6.1 結論 91
6.1.1 完美單層石墨烯 91
6.1.2 石墨烯奈米網格 92
6.1.3 熱整流效應 92
6.2 未來展望 93
附錄 A 非平衡分子動力學模擬 94
A.1 石墨烯奈米帶 94
A.2 熱傳導係數 94
A.2.1 Langevin 控溫法 95
A.2.2 Nose-Hoover 控溫法(NH) 100
參考文獻 107
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