高分子鏈在交流電場或流場下的行為｜國立中央大學博碩士論文系統

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研究生：	曾柏剛 Po-kang Tseng
論文名稱：	高分子鏈在交流電場或流場下的行為 Properties of a polymer chain under an oscillatory driveor flow field
指導教授：	黎璧賢 Pik-Yin Lai
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
畢業學年度：	95
語文別：	英文
論文頁數：	81
中文關鍵詞：	外加力場、鬆弛時間、高分子鏈、振盪
外文關鍵詞：	relaxation time, oscillatory, polymer chain, external drives
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高分子物理研究是一門非常重要的學問，在很多科技上材料和生物材料上有許多應用。而探討高分子鏈的動力學特性正是我研究的目的。我們使用高分子鏈的基本動力學模型，並考慮高分子鏈在溶液中受到不同的外力下做用且給予振盪(例如：外加振盪的電場或流場)。我們的目標是想了解高分子鏈是在加振盪外力的作用下結構和動力學，從中了解到高分子鏈的性質。在這篇論中，我們使用不同型式的外力作用和調整振盪的頻率下，可以來計算高分子鏈被外作用力拉開的程度，並且探討高分子鏈在何種狀態下能被拉的最開。此外還能了解在溶液中高分子鏈達熱力學平衡態的鬆弛時間和外加力作用下之間關係。

Polymer physics is a very important subject whose application can be found in various, which are both materials as well as in biological machinery. The purpose of this research is to investigate the dynamical properties of a polymer chain. We use the dynamical models of a polymer chain consider a polymer under different kinds of an oscillatory external drives in a structure and dynamics of a solution. Our purpose is to understand how the polymer chain are affected by the external oscillatory drive.
In this thesis, we consider a polymer chain under different oscillatory drive and frequencies, and calculate how polymer chain is being elongated, and try to obtain the condition that the chain is maximally elongated. Furthermore, the dynamic behavior
of polymer chain, such as the relaxation time, and how it is related to the external drives are investigated.

Contents
Introduction 1
Theoretical Backgrounds 4
1 Model of an ideal chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1 End-to-end distance . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Gaussian distribution for an ideal polymer chain . . . . . . . .. 6
1.3 Entropic elasticity . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Rouse model: A phantom chain in an immobile solvent . . . . . . 8
2.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . .. 9
2.2 m = 0 and f^e_n = 0 Case . . . . . . . . . . . . . . . . . . . . 12
2.3 m = 0 and f^e_n = F(z)_n coswt Case . . . . . . . . . .. . . . . 16
2.4 m ≠ 0 and f^e_n = F(z)_n coswt Case . . . . . . . . . . . . . . 17
3 The Zimm model: A phantom chain with hydrodynamic interaction .  . 19
3.1 The Navier-Stokes equation in the low reynolds number limit .  . 20
3.2 Equation of motion with pre-averaging of the Oseen tensor . .  . 22
3.3 Results of the normal coordinates . . . . . . . . . . . . . . .. 24
The model . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 27
1 Rouse model under an oscillatory electric field in the z direction 27
2 Rouse model under an oscillatory flow field in the z direction . . 31
2.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
3 Zimm model under an oscillatory flow field in the z direction . . .38
3.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Chain distribution Ansatz(I) . . . . . . . . . . . . . . . . . . 40
3.3 Chain distribution Ansatz (II) . . . . . . . . . . . . . . . . . 52
Discussions and Conclusion . . . . . . . . . . . . . . . . . . . . . 66
Bibliography. . . . . . . . . . . . . . . . . . . . . 70
A The Oseen tensor . . . . . . . . . . . . . . . . . . . . . . . . . . 73
B Gaussian distribution  . . . . . . . . . . . . . . . . . . . . . . . 76
C Integral method for hpq in Ansatz(II)  . . . . . . . . . . . . . . . 79

                                

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