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研究生： 房哲名
Che-Ming Fang
論文名稱： 利用耗散粒子動力學探討星形高分子溶液的滲透壓及維里係數
Osmotic pressure and virial coefficients of star polymer solutions : dissipative particle dynamics
指導教授： 曹恒光
Heng-Kwong Tsao
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 化學工程與材料工程學系
Department of Chemical & Materials Engineering
畢業學年度： 96
語文別： 中文
論文頁數： 72
中文關鍵詞： 耗散粒子動力學 、滲透壓 、維里係數
外文關鍵詞： osmotic pressure, scaling law, DPD, virial coefficient
相關次數： 點閱：9  下載：0 
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    • 本篇論文主要以一種介觀尺度下的模擬方法-分散粒子動力學(
    Dissipative Particle Dynamics )來探討於good solvent中線性與星形高分子的滲透壓、第二維里係數( second virial coefficient, B2 )、第三維里係數( third virial coefficient, B3 )變化以及證明DPD模擬於滲透壓實驗的可行性。
    本文利用半透膜將系統分為兩部份針對稀薄( dilute )溶液及半稀薄( semi-dilute )溶液兩種溶液之滲透壓進行討論。由模擬結果可得，線性高分子在稀薄溶液中，B2、迴旋半徑(radius of gyration, Rg)的關係式 ;在半稀薄溶液中，Π與Φ的關係式Π~Φ2.7，由於軟球模型之因此值大於理論值9/4。對星形高分子而言，於稀薄溶液中，一樣遵守 關係式；在半稀薄溶液中，Π~λΦα。λ與α值與手臂數有關但與手臂長度無關。當手臂數增加，α值會由2.70增加至3.07，這個結果與實驗結果吻合。

    The osmotic pressure Π and virial coefficients ( B2 and B3 ) of linear and star polymers in good solvents are studied by dissipative particle dynamics simulations.
    The dependence of the osmotic pressure on the concentration c is directly caculated by considering two reservoirs separated by a semi-
    permeable, fictitious membrane. For linear polymers with chain length N, our simulation results confirm the scaling relations that B2 ~ N3ν in the dilute regime and Π ~ c2.70 in the semi-dilute regime. The exponent is greater than 9/4 due to the nature of soft beads. For star polymers, the scaling relations become B2 ~ Rg3 in dilute regime and Π λcα in semi-dilute regime. Both the prefactor λ and exponent α vary with the arm number but is independent of the arm length. As the arm number is increased, the exponent may rise from 2.7 to 3.07, which is qualitatively consistent with the experimental result.

    摘要 ………………………………………………………...……...…I Aabstract …………………………………………………...……...…II 致謝 ………………………………………………………...….....…III 目錄 …………………………………………………………..……..IV 圖目錄 …………………………………………………………...….VI 表目錄 ……………………………………………………...…....…VII 第一章 緒論 …………………………………………………..……1 第二章 理論基礎 ……………………………………………..……3 2-1 介觀尺度模擬簡介 ………………………………………….…3 2-2 週期性邊界條件(Periodic Boundary Condition ) ……………5 2-3 分散粒子動力學(DPD)簡介及理論 ……………………..…..7 2-3-1 移動方程式(Equations of motion) ……………………..8 2-3-2長度、速度、時間的尺度(Scaling of length, velocity and time) ……………………………………………..……12 2-3-3 積分法求解(Integration scheme) ……………………14 2-3-4 噪訊和時間尺度(Noise and Timestep) …………...…15 2-3-5 斥力參數的選擇(Choosing the repulsion parameters) ...16 2-3-6 Flory-Huggins Theory …………………………………..18 第三章 文獻回顧 …………………………………………………22 3-1 滲透壓理論 ………….………………………………....…..22 3-2 Good Solvent下溶液的性質表現 ………………..…...……25 3-3 尺度理論(Scaling Theory) ………………………………..…27 3-3-1稀釋範圍(Dilute regime) ……………..……………..…27 3-3-2半稀釋範圍(semi-dilute regime) …………..………..…28 3-4無因次維里比率(dimensionless virial ratio, g) …..……..…30 3-5 模擬法求滲透壓 …………………………………………...31 第四章 模擬系統設定 ……………………………………………33 第五章 結果與討論 ………………………………………………38 5-1線性高分子的探討及DPD模擬的驗證 …………………...38 5-2星形高分子於水溶液的行為探討 ………………………....46 第六章 結論 …………………………………………...………….59 參考文獻 …………………………………………………...……….60

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