博碩士論文 87222035 詳細資訊




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姓名 孫富國( Fu-Kuo Shun)  查詢紙本館藏   畢業系所 物理學系
論文名稱 高分子在二元混合溶劑之二維蒙地卡羅模擬研究
(Polymers In a BinaryMixture Solvent:Monte Carlo Simulation StudiesOn A Two Dimensional System)
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摘要(英) (or be called monomer). Polymers in binary mixture solvent belong to the class of multicomponent
system and present a fundamental interest. They show peculiar properties
near the critical region. The critical point will shift to another point and critical exponents
also change to another value. The polymer structure and its location has different
change when the temperature decrease over the critical point gradually.
In chapter one, Introduction, the history of polymer development will be mentioned
and the briefly properties of binary mixture are also be mentioned.
In chapter two, Theoretical and Experimental Backgrounds, the mathematical
properties will be mentioned to realize some polymer physics. The critical phenomenon
is also an important background.
In chapter three, The Simulation Method, we will study how to simulate the
dynamical system in the computer and our system–binary mixture with linear polymers
– will also be introduced.
In chapter four, Result and Discussions, we will analyse our data and try to explain
the physical mechanism in the system.
論文目次 Abstract ii
Acknowledgement iii
1 Introduction 1
1.1 Introduction to Polymer . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introducion to BinaryMixture . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Introduction to this system. . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Theoretical and Experimental Backgrounds 10
2.1 Polymer Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Polymer properties . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 The physical picture of a polymer chain . . . . . . . . . . . . . . 13
2.1.3 The dynamic properties of polymers . . . . . . . . . . . . . . . . 27
2.2 The Critical Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 The Definition of Phase Transition . . . . . . . . . . . . . . . . . 29
2.2.2 The Classification of Phase Transition . . . . . . . . . . . . . . . 30
2.2.3 Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.4 Correlation Function . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.5 Critical Behavior and Exponents . . . . . . . . . . . . . . . . . . 36
3 The Simulation Method 38
3.1 TheMonte Carlomethod . . . . . . . . . . . . . . . . . . . . . . . . . . 38
iv
3.1.1 RandomVariables and Stochastic Process . . . . . . . . . . . . . 40
3.1.2 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.3 TheMetropolisMethod . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 The Bond FluctuationModel . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Model for the Polymer Systemwith a binarymixture solvent . . . . . . . 47
4 Results and Discussions 50
4.1 Pure BinaryMixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 BinaryMixture with Polymers . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 PolymersWhich Has No Interaction. . . . . . . . . . . . . . . . . 56
4.2.2 Polymers InteractingWith The BinaryMixture Solvent . . . . . . 59
4.3 Polymer Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.1 Polymers have no interactions . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Polymers have interactions . . . . . . . . . . . . . . . . . . . . . . 68
Appendices 80
A The Program for Binary Mixture with Polymers 80
Bibliography 91
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指導教授 黎璧賢(Pik-Yin Lai) 審核日期 2001-7-19
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