多價鹽對高分子電解質在構形上的影響｜國立清華大學博碩士論文庫

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研究生：	魏瑜甫 Yu-Fu Wei
論文名稱：	多價鹽對高分子電解質在構形上的影響 Effect of added multivalent salt on conformation of a polyelectrolyte
指導教授：	蕭百沂 Pai-Yi Hsiao 李四海 Shih-Hai Li
口試委員:
學位類別：	碩士 Master
系所名稱：	原子科學院 - 工程與系統科學系 Department of Engineering and System Science
論文出版年：	2006
畢業學年度：	94
語文別：	英文
論文頁數：	63
中文關鍵詞：	高分子電解質、DNA濃縮、基因治療、分子模擬
外文關鍵詞：	DNA condensation, redissolution, gene therapy, reentrant condensation, Langevin dynamics simulations
相關次數：	點閱：2 下載：0
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本研究以朗日凡動力學(Langevin dynamics)模擬方法探討多價鹽類以及高分子鏈之硬度對高分子電解質在構形上的影響。根據高分子電解質其尺寸(旋轉半徑Radius of gyration) 隨鹽濃度變化的方式，我們可以將不同硬度的高分子電解質分為了三類：包括易彎曲鏈(flexible chain)、半易彎曲鏈(semiflexible chain)、以及剛硬鏈(stiff chain)。易彎曲鏈的尺寸隨鹽濃度變化曲線呈現了一個類似向左傾斜的L字型的曲線，半易彎曲鍊的尺寸隨鹽濃度變化曲線呈現了一個類似U字型的曲線，而剛硬鏈的尺寸隨鹽濃度變化曲線則是一條近乎水平的直線。本研究觀察發現不同硬度的高分子電解質在加鹽溶液中其局部結構有明顯的差異。易彎曲鏈呈現了鋸齒狀(zigzag)的局部結構，半易彎曲鏈在反離子(counterion)沈澱處會有大角度的彎曲，剛硬鏈則是平滑的延伸開來。在多價鹽濃度的效應方面，於系統中加入多價鹽，高分子鏈會先收縮進而發生濃縮(condensation)的現象，當鹽濃度升高到一定程度時高分子鏈會發生再張開(reexpansion)的現象。易彎曲鏈的濃縮結構是一個無序的球狀物。半易彎曲鏈則會濃縮成有序的結構，包括了環狀和棒狀的結構。本研究的結果顯示在溶液中加入越多的多價鹽可以幫助這兩個有序結構間的互相轉變。本研究發現高分子鍊的硬度在兩方面影響了高分子鏈的構形。一方面它決定了高分子電解質的濃縮現象是否會發生，另一方面也決定了其濃縮物的結構。除此之外，高分子鏈的硬度也影響了“coil-globule transition” 的形式，硬度低的高分子鏈進行連續式的coil-globule transition，硬度較高的高分子鏈則進行了不連續的coil-globule transition。最後，本研究將以上的多價鹽對不同硬度的高分子鏈在構形上的效應合併，總結在一個狀態圖(state diagram)中

Effect of multivalent salt and effect of chain stiffness on conformation of a single polyelectrolyte were investigated using Langevin dynamics simulations. A polyelectrolyte is classified into three categories according to its chain stiffness, based upon the variation of chain size (radius of gyration Rg) against the concentration of multivalent salt Cs. The variation of Rg for a flexible chain shows a tilted-L-shaped Rg curve. That for a semiflexible chain is characterized by a U-shaped curve. A stiff chain exhibits
an almost straight Rg curve. A polyelectrolyte at different stiffness shows different local structure. A flexible chain exhibits a zigzag local structure; a semiflexible chain reveals large-angle turns at the place where the counterions condense; a stiff chain stretches out smoothly. Upon addition of multivalent salt, a polyelectrolyte collapses and is then followed by chain reexpansion. The condensed structure of a flexible chain is disordered and spheroid-like. On the other hand, a semiflexible chain collapses into an ordered structure, such as rod or toroid. An increase in salt concentration is found to enhance the transition between these two ordered structures. The chain stiffness determines the occurrence of a condensation of a polyelectrolyte and the morphology of a condensate. It also affects the nature of the ‘coil-globule transition’. A flexible chain undergoes a continuous transition but a semiflexible chain undergoes a discrete transition. A state diagram is proposed in this study according to the prescribed effects.

Contents
Title Page . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgments  . . . . . . . . . . . . . . . . . . . . . v
Table of Contents  . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . x
Introduction 1
1 Polyelectrolyte and DNA . . . . . . . . . . . .. . . . 1
2 DNA condensation and redissolution . . . . . . . . . . 2
2.1 DNA condensation . . . . . . . . . . . . . . . . . . 2
2.2 Redissolution of condensed DNA . . . . . . . . . . . 3
2.3 Reentrant condensation of polyelectrolytes . . . . . 4
3 Applications of DNA condensation . . . . . . . . . . . 4
4 Difficulties in study polyelectrolytes . . . . . . . . 5
5 Coarse-grained model . . . . . . . . . . . . . . . . . 5
6 Review of recent research  . . . . . . . . . . . . . . 6
7 Motivation . . . . . . . . . . . . . . . . . . . . . . 8
Model and Method 9
1 Model  . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1 The system . . . . . . . . . . . . . . . . . . . . . 9
1.2 The interactions  . . . . . . . . . . . . . . . . . 11
2 Method  . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Molecular dynamics  . . . . . . . . . . . . . . . . 15
2.2 Langevin dynamics . . . . . . . . . . . . . . . . . 16
2.3 Sampling the phase space  . . . . . . . . . . . . . 17
2.4 Boundary condition  . . . . . . . . . . . . . . . . 18
2.5 Integration algorithm . . . . . . . . . . . . . . . 18
2.6 LAMMPS  . . . . . . . . . . . . . . . . . . . . . . 19
Simulation Setup 20
Result and Discussion 23
1 Size of a polyelectrolyte . . . . . . . . . . . . . . 23
1.1 Radius of gyration  . . . . . . . . . . . . . . . . 24
1.2 Size relation between charged and uncharged chain . 26
1.3 End-to-end distance . . . . . . . . . . . . . . . . 29
2 Snapshots . . . . . . . . . . . . . . . . . . . . . . 31
3 Shape of a polyelectrolyte  . . . . . . . . . . . . . 34
3.1 Shape factor Re2/Rg2 . . . . . . . . .  . . . . . . 34
3.2 Asphericity . . . . . . . . . . . . . . . . . . . . 35
4 Distribution of conformational quantities . . . . . . 37
5 Effects of multivalent salt . . . . . . . . . . . . . 45
6 Effects of chain stiffness  . . . . . . . . . . . . . 47
7 State diagram . . . . . . . . . . . . . . . . . . . . 56
Conclusion 58
Bibliography 61

                                

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