臺灣博碩士論文加值系統

本研究著重於高電位的單一軟球擴散泳系統。文中，我們首先回顧擴散泳理論與軟球電動力學發展相關文獻與相關應用，再針對近年軟球擴散泳理論做延伸，利用得以處理高度非線性問題的數值方法，發展出計算高電位單一軟球擴散泳之程式系統，打破以往單一軟球擴散泳解析解低電位之限制。參數上，我們討論電解質濃度κa的影響，亦探討在軟球結構對電動力學的相應變化，我們深入剖析了軟球層(硬球核)比例b/a與軟球層摩擦係數λa對擴散泳的影響。

研究結果發現於電性上，在電雙層厚度適中時(約0.1<κa<10)，雖然此時電雙層變形驅動的極化效應(化學泳效應)較強，然而我們仍必須同時考慮流動貢獻的極化效應，特別是硬球核σ*帶高電荷量，抑或軟球層電荷密度Qfix帶高電荷量皆會造成嚴重的流動貢獻極化效應，會使得擴散泳動度大幅降低，也就是說若使用低電位的解析解會嚴重高估擴散泳動度。其中有趣的是，當硬球核電荷密度帶非常高電量時，擴散泳可能會發生反向運動的狀況，其原因可以由其誘發的不均勻擾動電位解釋。

在結構上，軟球中硬球核的存在的影響應同時考慮流力與電力的共同作用，此外，軟球層摩擦係數λa大至1以上時，擴散泳動度才會有明顯的變化，特別的是當λa過大時，擴散泳亦會發生反向運動的現象，其原因來自於兩旁流動造成的渦漩，使其往反方向運動。

考慮現今大量高帶電量的奈米複合型軟球粒子應用於生技、藥物控制、生物影響標記等技術，發展高電位(高帶電量)軟球擴散泳模型對於軟球粒子發展與應用有其必要性，我們的計算結果對單一軟球擴散泳而言，無論在電性上與流力性質上皆無任何限制，在此情況下許多特殊的非線性現象會發生:流動貢獻極化效應、速度反轉等現象，我們期望本研究結果能給予軟球系統研究者無論在理論與實驗上更準確定性與定量上的預測。

The diffusiophoretic motion of a uniformly distributed charge soft particle suspended in an infinite medium of electrolyte solution is studied in this paper. The resulted nonlinear electrokinetic equations governing the diffusiophoretic motion are solved numerically with a pseudo-spectral method based on Chebyshev polynomials. In particular, the convection contribution of the ion flux and the polarization effect are taken into account.

Key parameters of electrokinetic interest are examined for their respective effect on the particle motion, and the results presented here show the particle diffusiophoretic mobility deviates significantly from the analytical prediction using linear Poisson-Boltzmann equation. Meanwhile, it is also found that a soft particle may reverse its direction with a high surface charge condition of the hard core, which significantly influences the diffusiophoretic motion. These results provide more information about the general electrokinetic behavior of a soft particle such as sphere polyelectrolyte brushes, polymer-coated colloidal particles and other engineered nanoparticles (ENPs), which has a great potential in treating systems of biochemical or microfluidic interests.

中文摘要 I
Abstract III
目錄 V
圖目錄 VIII
Chapter 1 緒論 1
1.1 膠體系統 1
1.2 軟球粒子 7
1.3 擴散泳理論 10
1.4 膠體粒子擴散泳現象的相關應用 13
1.5 擴散泳文獻回顧 17
1.6 軟物質擴散泳模型 20
1.7 研究動機 23
Chapter 2 理論分析 24
2.1 電動力學方程組 25
2.1.1 電位方程式 26
2.1.2 離子守恆式 27
2.1.3 流場方程式 28
2.2 平衡態與擾動態 32
2.2.1 平衡態 35
2.2.2 擾動態 36
2.3 邊界條件 39
2.4 二維系統的一維化 45
2.5 系統無因次化分析 47
2.6 數值無窮遠邊界處理方法 52
2.7 粒子受力計算 56
2.8 泳動度之計算 57
Chapter 3 數值方法 60
3.1 正交配位法 60
3.2 空間映射 64
3.3 多區聯解問題 66
3.4 牛頓-拉福森 (Newton-Raphson) 疊代法 69
3.5 擾動態多變數聯解 72
3.6 數值積分 74
Chapter 4 結果討論 76
4.1 驗證程式正確性 77
4.1.1 比對Keh軟球擴散泳解析解 77
4.2 軟球層帶電之影響 80
4.3 硬球核存在之影響 84
4.4 硬球核比例之影響 89
4.5 摩擦係數之影響 91
Chapter 5 結論 94
參考資料 97
附錄A 常見電解質水溶液參數值 104
附錄B　座標系統簡介 107
附錄C　力積分之推導 111
附錄D 擴散泳相關邊界條件推導 115

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