臺灣博碩士論文加值系統

本文主要利用數值方法，並建構相場模型對奈米柱陣列誘導樹枝狀結構自主成長進行三維模擬，三維模擬能夠觀察樹枝狀結構在奈米柱陣列上的成長趨勢以及空間填補關係，使模擬更接近真實狀況。透過建立不同形狀及排列的奈米柱陣並在不同散熱通量條件下模擬，分析各結果的差異以及探討奈米柱與樹枝狀結構分支的影響，並與實驗作比較。

從模擬結果得知，樹枝狀結構分支會沿著奈米柱邊緣成長，並嘗試以最短路徑成長至下一個奈米柱，不同形狀的奈米柱具有不同的分支成長趨勢，這也顯示了奈米柱對樹枝狀結構分支的影響，而在空間填補關係，分支會優先填補奈米柱附近的空間或表面。在加入散熱通量條件後，觀察到隨著散熱通量的增加，空間填補更快速且更布滿整個空間。此研究可以為智慧自組裝結構的提供一個指標性的發展。

In this study, three-dimensional simulation of the nanopost-guided self-organization of dendritc structure by using numerical method. The three-dimensional simulation can observe the growth trend and the spatial filling of the dendritic structure on the nanoposts and make the simulation closer to the real situation. We established the different shapes and arrangement of nanoposts and simulated under different negative heat flux conditions. Further, we analysis the results of simulation and the effects between nanoposts and dendritic branches.
The results show that the dendritic branch will grow along the edge of the nanopost and grow to the next nanopost with the shortest path. Different shapes of nanoposts have different branch growth trends that it show the effects between nanoposts and dendritic branches. After adding the heat flux condition, it is observed that as the heat flux increases, the space filling is faster and more full of space.

摘　要 i
ABSTRACT ii
誌　謝 iii
目　錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 前言 1
1.2 研究動機 2
1.3 文獻回顧 3
1.3.1 自我組織 3
1.3.2 樹枝狀結構 5
1.3.3 奈米柱陣誘導自組裝之無機鹽樹枝狀結構 6
1.3.4 相場模型 14
1.4 本文架構 19
第二章 數值分析與控制方程 20
2.1 數值方法 21
2.1.1 有限差分法 22
2.1.2 有限體積法 22
2.1.3 有限元素法 23
2.2 相場模型與控制方程 24
2.3 網格 28
第三章 模擬步驟與模型建立 30
3.1 求解步驟 30
3.2 幾何形狀建立 32
3.2.1 圓形奈米基柱 33
3.2.2 28∘橢圓奈米基柱 35
3.2.3 38∘橢圓奈米基柱 38
3.3 奈米基柱邊緣之散熱通量條件 40
3.4 參數與網格設置 41
3.5 初始條件設置 42
第四章 結果與討論 46
4.1 界面寬度 46
4.2 奈米柱陣列在零通量條件下的樹枝狀結構 53
4.3 奈米柱陣列在散熱通量條件下的樹枝狀結構 72
4.4 液固相在求解域的體積覆蓋率 82
第五章 結論 97
5.1 結論 97
參考文獻 97

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