臺灣博碩士論文加值系統

本研究主要討論密集硬球膠體粒子於離子液體溶液中之電泳行為，並比較其與單一系統間的異同。
離子液體於近期被廣泛應用於各領域。在電泳上的主要應用如塗佈毛細管電泳的管壁、作為毛細管電泳或微胞電泳的添加劑、非水相電泳之背景電解質或添加劑等。但由於會造成背景電流過強、黏度過高等問題，並不會被直接當作電泳的溶劑使用。
而離子液體由於離子體積較大、離子間交互作用力較強等特性，傳統上用以分析電動力學現象的點電荷模型將存在誤差：較大的體積將導致離子無法大量集中於帶電表面，進而使電雙層增厚，稱為離子體積效應；離子間交互作用力將使電位分布出現反轉，而非隨距離增加單調遞減，稱為電荷過度遮蔽效應。
本研究使用Bazant、Storey、Kornyshev (BSK)三人所提出之模型，引入平均離子體積分率ν和無因次靜電校正長度δ_c，進而將離子體積和離子間交互作用力納入考慮。此模型被廣泛用於電雙層結構模擬，近年來亦有學者應用此模型求出單一粒子時，薄電雙層、低表面帶電等極限條件下的電泳動度解析解。但離子液體在應用上的濃度數量級約為〖10〗^(-1)~〖10〗^2 mM，薄電雙層條件存在疑慮。本研究藉由數值方法解除前述的濃度限制，並利用cell model納入粒子間彼此的干擾，以期能對電雙層極化現象及其對電泳運動的影響有更深的了解。
研究結果顯示，離子體積效應和電荷過度遮蔽效應均在粒子表面電位較高時較為顯著。前者影響如：電位分布趨緩而增加電雙層厚度、放大高密集度時電雙層重疊效應的影響、增加擴散而削弱電雙層極化效應、降低離子間交互作用力的影響等。而後者影響則如：電位或電荷分布出現反轉層而增加電雙層厚度、使電泳動度往負向增加、使擾動電荷出現多層結構等。但在密集度增加時，受到電位反轉層重疊影響，電荷過度遮蔽效應的影響將被削弱。

This thesis investigates the electrophoresis behavior of spherical rigid colloidal particles in ionic liquid solutions, including the differences and similarities between single particle system and concentrated suspensions.
Recently ionic liquid has been used widely in various fields. The applications of electrophoresis are particularly of interest, such as coating on the wall of capillary electrophoresis, modifiers in capillary electrophoresis or microemulsion electrokinetic chromatography, background electrolyte or modifiers in non-aqueous electrophoresis. Note that ionic liquids themselves are not used directly as the solvent of electrophoresis in general, because this will lead to large background current and heavily viscous solutions.
Due to the large volume of ionic liquid ions and strong interaction between them, the point-charge model, which is traditionally used to analyze the electrokinetic phenomena, is no-longer suitable. The larger volume leads to a much dispersive distribution of ions, which is referred to as the steric effect. Moreover, the stronger interaction between ions will affect the original monotonically decreasing electric potential distribution and a layer with reversed electric potential may appear, which is referred to as the overscreening effect.
The modified model proposed by Bazant, Storey, and Kornyshev (BSK model) is used in this study. This model introduces mean volume fraction of ions (ν) and dimensionless electrostatic correlation length (δ_c) to take into account the steric and overscreening effects. It has been widely used in the analysis of the double layer structure. In the past decade, some researches start to use it in the derivations of analytical solutions of a single rigid particle electrophoretic mobility, under either thin double layer or low surface charge conditions. However, the order of ionic liquid concentration is about 〖10〗^(-1)~〖10〗^2 mM in practice, which may unjustify the adoption of the thin-double-layer assumption. This thesis uses numerical method to remove the constraint on concentration, and adopts the cell model to explore the interaction between particles in concentrated suspension in order to better understanding the double layer polarization in particular and electrophoresis phenomena in general.
According to the result, we found that the steric effect and overscreening effect are both more profound in high surface electric potential situations. The steric effect leads to an electric potential distribution smoother hence results in thicker double layer thicker, which in turn enhances the double layer overlapping effect at high particle concentrations as well as the diffusion rate which reduces the double layer polarization. Moreover, this also reduces the effects of interaction between ions, etc. The overscreening effect, on the other hand, induces reversed layers in electric potential and charge distributions, which results in a thicker double layer and may even reverse the direction of particle motion. Multi-layer structure in disturbance charge density distribution is also observed as a result. However, due to the overlapping of these charge-reversed multi-layers, overscreening effect will be reduced in the concentrated suspensions.

致謝 I
摘要 III
Abstract V
目錄 VII
圖目錄 X
表目錄 XII
Chapter 1 緒論 1
1.1 膠體粒子與電雙層 1
1.2 離子液體簡介 2
1.3 電動力學理論文獻回顧 7
1.3.1 傳統電泳理論 7
1.3.2 離子體積效應(Steric effect) 9
1.3.3 電荷過度遮蔽效應(Overscreening effect) 10
1.3.4 離子體積效應及電荷過度遮蔽效應對電動力學現象的影響 12
1.4 研究動機 13
Chapter 2 理論分析 14
2.1 系統描述 14
2.2 主控方程式 15
2.2.1 離子分布關係式 15
2.2.2 電位方程式 16
2.2.3 流場方程式 17
2.2.4 離子守恆方程式 18
2.2.5 無因次化 19
2.2.6 擾動法分析(perturbation analysis) 20
2.3 邊界條件 22
2.3.1 粒子表面 22
2.3.2 無窮遠處 23
2.3.3 虛擬外邊界 24
2.4 方程式與邊界條件一維化 25
2.4.1 主控方程式 26
2.4.2 粒子表面邊界條件 27
2.4.3 密集系統虛擬外邊界條件 27
2.4.4 單一系統虛擬外邊界條件 27
2.5 泳動度計算 29
2.6 總結 31
Chapter 3 數值方法 33
3.1 正交配位法(orthogonal collocation method) 33
3.1.1 簡介 33
3.1.2 計算格點與函數展開 34
3.1.3 微分矩陣 35
3.2 空間映射與多變數聯解 35
3.3 Newton-Raphson迭代法 37
Chapter 4 結果與討論 39
4.1 程式比對 39
4.2 參數選擇 45
4.3 不同條件下平衡電位之分布情形 47
4.3.1 離子體積效應(ν) 47
4.3.2 電荷過度遮蔽效應(δc) 50
4.4 不同條件對電泳動度之影響 54
4.4.1 離子體積效應(ν) 54
4.4.2 電荷過度遮蔽效應(δc) 58
4.4.3 使用Lc*而非δc作為參數 63
4.4.4 密集度影響(H) 65
4.5 結論 67
附錄 69
(A) 室溫水溶液參數列表 69
(B) 曲線座標(curvilinear coordinate)簡介 71
(C) BSK模型推導 76
(D) 主控方程式與邊界條件推導細節 79
(E) 力積分推導 84
(F) 名詞中英對照表與符號列表 86
參考文獻 91

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