- 學位論文
軟物質之反離子凝聚暨電泳行為
Counterion Condensation and Electrophoresis of Soft Matter
摘要
本研究以假性光譜法數值模擬軟物質之靜電力學與電動力學現象，包含反離子凝聚現象及電泳行為的探討。反離子凝聚理論解釋了許多生物界重要現象發生的機制，如DNA凝聚、RNA摺疊等。反離子凝聚現象亦可於生物體外由人為引發，並於DNA疫苗、基因轉殖領域中都有重要應用。過去幾年Manning反離子凝聚理論已被普遍接受，然而其僅適用於無限長圓柱系統(或表面帶電的硬球)，然而當生物粒子(如DNA、RNA)摺疊後會形成內部帶電的球型粒子，此時則無法直接使用Manning理論。Yamasaki等人以實驗結果指出，若直接使用Manning理論預測凝聚DNA分子的反離子凝聚比率，將產生極大誤差。除了由於生物聚電解質(DNA、RNA、蛋白質)，在水溶液中並非伸展的長圓柱，而是蜷曲成3D的立體球形之外，由DNA磷酸根官能基的均勻分布亦可知，其為整體均勻帶電的球體。因此本研究在此重新提出一個更符合生物粒子構造形狀的模型－多孔球模型來探討聚電解質的反離子凝聚現象，且與Yamasaki等人所做的DNA反離子凝聚實驗數據比對相當吻合，驗證了本研究的可信度及成功地使用多孔球模型模擬聚電解質靜電力學行為(第四章)。 我們於第五章以軟球模型探討新興材料spherical polyelectrolyte brush的反離子凝聚現象，此新興材料可應用於藥物釋放、功能性生物粒子、觸媒載體、奈米微反應器、薄膜通透率調控…等領域。為驗證模型的可靠度，我們將理論預測與Poly(styrene)-block-poly(styrene sulfonate)反離子凝聚實驗做數據比對，結果相當吻合實驗數據，因此本理論預測提供了實驗者可靠的參考依據。當實驗可操作參數(Qfix、 (b-a)/a、κa)為已知，即可藉本研究理論預測反離子凝聚比率，以利進一步的實驗設計與應用，如：調控SPB的構造形狀、濕潤度、摩擦係數、吸附、脫附強度、靜電排斥力，並應用於前述先驅領域。此外，當內硬核過小時，實驗可能無法準確測量出SPB的內核半徑，此時可藉理論協助推測溶液中真實的軟球層厚度。 第六章探討了單一聚電解質的電泳行為，由於許多天然聚電解質如DNA、蛋白質等，在水溶液中常呈現3D的立體球形，且其帶電官能基為均勻分布，因此我們以均勻帶電的球體聚電解質。另外，此種生物粒子常具有流體可穿透的特性，因此採用Brinkman提出的多孔模型描述流體穿透粒子時提供的摩擦力。我們使用完整的非線性Poisson方程式探討單一聚電解質的電泳行為，並聚焦於極化效應(電動力學)與非線性遮蔽效應(靜電力學)各自對泳動度造成的影響。當粒子為高穿透度時，由於粒子移動較快，且流體流經粒子時所受到的摩擦力較小，因此球內對流旺盛，進而誘發強烈的極化效應。當此作用夠強烈時，甚至可使得帶電較小的聚電解質移動速度較高帶電聚電解質還快!我們以擾動離子場圖及誘發電場圖觀察極化效應的發生(離子雲變形)與其導致的電動力學現象。另一方面，當粒子穿透度極低時，流體流經球體時所受摩擦力較大，球內對流弱，極化效應不重要，此時，遮蔽效應的影響較為重要。我們進一步將理論預測與文獻中的poly(sodium styrene-p-sulfonate)電泳實驗數據做比對，結果相當吻合，說明了本研究的可信度及成功地使用帶電多孔球模擬聚電解質電泳行為。本研究在此提供了方便實驗者查閱的圖表，以預測聚電解質的內部結構、帶電密度或電泳動度等。且本研究提供了標籤溶液電泳實驗所需的基礎資料，即單一聚電解質的電泳動度。 第七章則是探討聚電解質垂直氣液交界面的電泳行為，並檢視極化效應、遮蔽效應、邊界效應對粒子電泳行為造成的影響。氣液交界面的存在使電雙層變形或崩潰而對粒子運動造成阻力，在此稱邊界效應。當電雙層越厚或粒子離交界面越近時，邊界效應越甚。我們觀察到帶電密度 、摩擦係數 的粒子，在電雙層很厚( )時，邊界效應的存在( )使其電泳動度下降了45%。當電雙層極薄時，邊界效應消失。此外我們觀察到一有趣現象：雖然邊界效應與極化效應都對粒子泳動造成阻力，但某些情況下邊界效應會弱化極化效應的影響，使粒子越接近交界面時，反而泳動地越快。換言之，當粒子非常接近氣液交界面時，邊界效應某種程度上削弱了極化效應的誘發電場，然而當粒子更靠近氣液交界面時，邊界效應的阻力變地更強使泳動度再度下降。兩效應競爭下，電泳動度隨粒子－氣液交界面距離h變化出現區域極大值。我們以平衡電位場圖及擾動電場圖觀察極化效應、邊界效應造成電雙層變形甚至崩潰的情況。本研究在此提供了方便實驗者查閱的圖表，以預測聚電解質電泳受邊界效應的影響。 由於靜電力學現象隸屬於電動力學現象的一種極限情況，我們將相通的主控方程式，於第二章理論分析一併介紹，而各種物理模型所對應的不同邊界條件，則於各章節各自介紹；第三章則是詳述本論文所採用的數值方法與計算流程。
並列摘要
Counterion condensation phenomenon and electrophoretic behabior of soft matter are investigated in this study. General electrokinetic equations including the full nonlinear Poisson-Boltzmann equation are employed as the governing equations which are then solved with a pseudo-spectral method based on Chebyshev polynomials. Counterion condensation phenomenon of a highly charged polyelectrolyte, which is directly related to DNA condensation and RNA folding, has great importance and potential use in biological science, electrokinetic phenomenon, and medical science. To further understand this fascinating phenomenon, the polyelectrolyte particle is modeled as a charged porous sphere based on the experimental observation of the DNA and protein conformations in free solution, both are major polyelectrolytes of interest. The full nonlinear Poisson– Boltzmann equation is used to describe the interaction between the counterions in the electrolyte solution and the backbone macroion of the polyelectrolyte itself. The fraction of total charges condensed is analyzed in particular, with its dependence on the charged condition of the polyelectrolyte as well as the ionic strength of the solution investigated in detail. Comparison with limited experimental data available in the literature for DNA neutralization fraction is excellent in the asymptotic sense, suggesting the reliability of the analysis in this study, as well as the promising possibility of using the charged porous sphere to model a polyelectrolyte. Results presented here provide useful information in biological systems and can be utilized in practical applications such as DNA vaccines and gene delivery. (Chapter 4) On the other hand, soft sphere, a colloidal particle with a rigid core surrounded by a concentric porous shell, is encountered very often in various colloidal and biocolloidal systems. The fraction of total charges condensed is analyzed in particular, with its dependence on the charged condition of the soft sphere, the thickness of the corona and the ionic strength of the solution investigated in detail. Comparison with experimental data available in the literature for a spherical polyelectrolyte brush (SPB), a special kind of soft particles that has inspired a huge amount of research interest in recent years due to its potential applications, is excellent, indicating the reliability of this analysis, as well as the success of using soft sphere to model an SPB. Results presented here provide crucial information in colloidal/biocolloidal systems and can be utilized in practical applications such as drug delivery, catalyst, functional biomolecules, nanoreactors and carboxylated latex particles. (Chapter 5) Electrophoresis of a polyelectrolyte in an infinite medium of electrolyte solution is investigated in Chapter 6. The porous sphere is treated as a Brinkman medium with uniformly distributed electric charges. Key parameters of electrokinetic interest are examined for their effects on particle motion. Two major motion-deterring nonlinear effects with Poisson equation which consist of the condensation effect and the double layer polarization effect are separated from each other with an approach, for the first time in the literature, and examined in detail for their respective impact on the particle motion. Convenient charts of correction factors are provided to facilitate the usage by interested experimental researchers. Moreover, an interesting phenomenon is observed that a less charged particle may actually move faster than a highly charged one! This is clearly demonstrated as the dominance of the polarization effect there with strong evidences of corresponding contour plots. Excellent agreement with limited experimental data available in the literature is observed, indicating the reliability of this study. Electrophoretic behavior of a single polyelectrolyte normal to an air-water interface is investigated in Chapter 7. Two major motion- deterring effects are thoroughly investigated in particular: The boundary effect due to presence of the air-water face, and the double layer polarization effect due to the convection-induced ion flux. The presence of the air–water interface is found to reduce the particle mobility in general, especially when the double layer is very thick or the particle is close to the interface. This boundary effect diminishes as the double layer gets very thin. However, an interesting phenomenon is observed that a particle closer to the interface may actually move faster than a farther one under some circumstances. The reason behind this is the deformation of the double layer surrounding the particle due to the presence of the air-water interface which further weakens the other motion-deterring polarization effect. This is clearly demonstrated with strong evidences of corresponding contour plots. Convenient charts of correction factors are provided to facilitate the usage by interested experimental researchers.