本研究利用分子動力學模擬探討在無/有電場極化下純聚偏氟乙烯(Polyvinylidene fluoride, PVDF)和混合不同比例(4.49 wt%、9.34 wt%及13.23 wt%)的奈米碳管(Carbon Nanotube, CNT )複合物之機械性質與微觀結構變化。為了確保模擬能夠預測出真實材料的物理性質，透過純PVDF系統之密度、溶解度參數與實驗結果做比較，其皆在可接受的誤差範圍內，表示本次研究所建立之分子模型與選用的勢能函數是合理的。此外，分析平衡結構的兩面角分佈，發現透過高溫退火的操作，可以使得結構中β相提升約25%，而結構再經電場極化後，可再進一步誘導約10%的β相形成。模擬拉伸的結果顯示，在PVDF添加CNTs或施加電場使其極化，都可以有效改善純PVDF的楊氏模數(Young’s modulus)以及最大抗拉強度(ultimate tensile strength)。但當碳管添加比例達到13.23 wt%，其機械性質反而會下降。在區域應變與孔隙率的分析，雖然CNTs可以補強局部PVDF的強度，但隨CNTs的含量較高時，其結構脆性亦隨之增加，容易形成孔隙與破裂。然而藉由電場極化，可以有效降低孔隙的生成，且延展性也較佳。再者，拉伸過程可以促進PVDF碳鏈形成trans構型，但在受到電場極化後，拉伸對形成trans構型的增益變的較不明顯。本研究結果可作為設計相關比例之奈米添加劑與各種聚合物混合之參考依據，試圖克服奈米複合物模擬所遭遇之瓶頸。

In this work, the molecular dynamics simulation (MD) simulation was proposed to investigate the microstructure and mechanical properties of pure Polyvinylidene fluoride (PVDF) and PVDF/Carbon Nanotube (CNT) composites(4.49 wt%, 9.34%, 13.23 wt% of CNTs) which are effected by electric field. For proving that the Dreiding force field can well describe the PVDF material, the density and solubility parameters of the pure PVDF system are predicted and compared with the experimental results. According to the results of annealing simulation, the formation of β phase have been increase about 25% during the annealing procedure both in pure PVDF and PVDF/CNTs composite case. The content of β phase in PVDF and PVDF/CNTs composite have been further enhance around 10% under the electric field. According the stress-strain profiles from the tensile simulation, the Young’s modulus and ultimate tensile strength of pure PVDF can be improved by blending with CNTs and polarized by electric field. But the mechanical properties of PVDF/CNTs composite has reduce when the blending ratio of CNTs over 13.23 wt%. The analysis of local shear strain and porosity indicate that the strength of PVDFs which around CNTs have been enhanced but the structure became brittle when CNTs weight fraction increased and easy to be fractured. Moreover, the generation of pores can be effectively reduced and the ductility was also improved due to the applied electric field. The trans configuration ratio in PVDF and PVDF/CNTs composite have been increase during the tensile process, but such enhancement are reduced in electric field polarization system. By taking advantage of this molecular simulation procedure, The properties of PVDF/CNT composites could be fast predicted, and the simulation results can investigate the material in atomistic-level and also provide new pathway to reduce the cost and research time in experiments.

目 錄
論文審定書 i
論文公開授權書 ii
誌謝 iii
中文摘要 iv
Abstract v
圖次 viii
表次 x
第一章 緒論 1
1.1研究動機與目的 1
1.2聚偏氟乙烯與奈米碳管簡介 2
1.2.1聚偏氟乙烯 2
1.2.2奈米碳管 5
1.3文獻回顧 6
1.4本文架構 9
第二章 模擬方法與理論介紹 10
2.1 分子動力學 10
2.1.1 DREIDING力場 11
2.1.2 運動方程式 13
2.1.3 積分法則 14
2.1.4 系綜 15
2.1.5 諾斯-胡佛恆溫法 16
第三章 數值模擬方法 17
3.1 週期性邊界 17
3.2 鄰近原子表列法 18
3.2.1 截斷半徑法 (Cut-off method) 18
3.2.2 維理表列法 (Verlet list) 19
3.2.3 巢室表列法 (Cell Link) 20
3.2.4 維理表列法結合巢室表列法 21
3.3 分子動力學流程圖 22
3.4 統計之參數計算 25
3.4.1 兩面角分佈 (Distribution of dihedral angles) 25
3.4.2分子表面網格 (surface mesh)的建構 27
3.4.3 區域應變分析 (Local shear strain) 28
3.4.4原子級應力計算理論 29
第四章 結果分析與討論 30
4.1 聚偏氟乙烯混和奈米碳管之物理模型 30
4.1.1 純聚偏氟乙烯與奈米碳管分子的建立 30
4.1.2 聚偏氟乙烯與混入不同比例奈米碳管之模型建立 32
4.1.3 電場下之聚偏氟乙烯與混入不同比例奈米碳管之模型建立 36
4.1.4平衡結構之C-C-C-C兩面角分佈 40
4.2拉伸試驗與機械性質探討 44
4.2.1 拉伸模型建立 44
4.2.2 應力應變圖 44
4.2.3 區域應變圖 48
4.2.4 孔隙率分析 53
4.2.5 拉伸過程之兩面角分佈 55
第五章 結論與未來展望 57
5.1 結論 57
5.2 未來展望 58
參考文獻 59

圖次
圖1-1 聚偏氟乙烯化學式 4
圖1-2 聚偏氟乙烯示意圖 4
圖1-3 (a)無壓電性的α相結構以及(b)有壓電性的β相結構 4
圖1-4 (a)奈米碳管示意圖、(b)掃描式電子顯微鏡(SEM)下之奈米碳管及(c)穿透式電子顯微鏡(TEM)下之奈米碳管 5
圖2-1 Velocity Verlet積分法則積分流程示意圖 14
圖3-1 週期性邊界示意圖 17
圖3-2 截斷半徑法示意圖 18
圖3-3 維理表列法示意圖 19
圖3-4 巢室表列法示意圖 20
圖3-5 維理表列結合巢室表列法示意圖 21
圖3-6 分子動力學之流程圖 22
圖3-7模擬退火之流程圖 23
圖3-8模擬拉伸試驗之流程圖 24
圖3-9 PVDF之(a)α相結構(TGTG')及(b)β相結構(TGTG' TTTT)示意圖 26
圖4-1 單一條α-聚偏氟乙烯之結構，其中灰色為碳原子(C)、淡藍色為氟原子(F)、白為氫原子 31
圖4-2 (5,5)單壁奈米碳管之(a)橫面及(b)縱面 31
圖4-3 (a)純PVDF與PVDF混合(b) 4.49 wt%、(c) 9.34 wt%及(d) 13.23 wt%的CNTs複合物在無電場下之穩定結構示意圖。左半部為完整全原子模型，其中灰色為碳原子(C)、淡藍色為氟原子(F)、白色為氫原子(H)，CNTs為紅色。右半部將全原子模型中的PVDF隱藏以便觀察CNTs在空間中的分佈，不同的CNT給予獨立的顏色。 35
圖4-4 (a)純PVDF與PVDF混合(b) 4.49 wt%、(c) 9.34 wt%及(d) 13.23 wt%的CNTs複合物在電場下極化後穩定結構示意圖。左半部為完整全原子模型，其中灰色為碳原子(C)、淡藍色為氟原子(F)、白色為氫原子(H)，CNTs為紅色。右半部將全原子模型中的PVDF隱藏以便觀察CNTs在空間中的分佈，不同的CNT給予獨立的顏色。 38
圖4-5純PVDF系統之中單獨第12條分子在(a)無電場、(b)電場極化後之穩定結構示意圖 39
圖4-6純PVDF及不同混合比例下PVDF/CNTs複合物在(a)無電場及(b)電場極化下之兩面角分佈 43
圖4-7純PVDF與混合不同比例CNTs系統於(a)無電場及(b)有電場極化後之應力應變圖 47
圖4-8 純PVDF在應變為(a) 0.0198、(b) 0.0617、(c) 0.1165、(d) 0.1295、(e) 0.1598和(f) 0.1988下的區域應變圖。 50
圖4-9 PVDF/CNTs(9.34%)在應變為(a) 0.0192、(b) 0.0673、(c) 0.1041、(d) 0.1116、(e) 0.1516和(f) 0.1966下的區域應變圖。 51
圖4-10電場極化後之純PVDF在應變為(a) 0.0198、(b) 0.1176及(c) 0.1999下的區域應變圖。 52
圖4-11 電場極化後之PVDF/CNTs(9.34%)在應變為(a) 0.0199、(b) 0.1127及(c) 0.1999下的區域應變圖。 52
圖4-12 純PVDF與混合不同比例CNTs系統在(a)無電場及(b)有電場極化後於不同應變下的孔隙率變化 54
圖4- 13 純PVDF與混合不同比例CNTs系統在(a)無電場及(b)有電場極化後於不同應變下的系統trans構型比例變化 56

表次
表2-1 DREIDING力場對應符號表 12
表2-2 常見的分子動力學系綜平均模擬準則 15
表4-1 模擬分子之詳細資訊 31
表4-2 不同複合系統之詳細資訊 33
表4-3 PVDF模擬結果與實驗結果比較表 33
表4-4 純PVDF與混合不同比例CNTS複合物之擬合參數 42
表4-5 純PVDF及不同混合比例下PVDF/CNTS複合物之擬合參數 42
表4-6 無電場下之純PVDF與混合不同比例CNTS下之機械性質 46
表4-7 電場極化後之純PVDF與混合不同比例CNTS之機械性質 46

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