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研究生:孫富國
研究生(外文):Fu-Kuo Shun
論文名稱:高分子在二元混合溶劑中之二維蒙地卡羅模擬研究
論文名稱(外文):Polymers in a Binary Mixture Solvent: Monte Carlo Simulation Studies on a Two-Dimessional System
指導教授:黎璧賢黎璧賢引用關係
指導教授(外文):Pik-Yin Lai
學位類別:碩士
校院名稱:國立中央大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:英文
論文頁數:105
中文關鍵詞:高分子二元混合溶劑蒙地卡羅
外文關鍵詞:polymerbinary mixtureMonte Carlo
相關次數:
  • 被引用被引用:0
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  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:1
本文以蒙地卡羅方法(Monte Carlo Method)模擬高分子(Polymer)在二維混合溶劑(Binary Mixture Solvent)中之臨界現象(Critical phenomena), 運用Ising Model對應二維混合溶劑模擬, 並且用Finite-Size Scaling的方法來研究其臨界現象. 主要的研究方向有: 第一, 高分子對二維混合溶劑的臨界現的影響; 地二, 高分子在臨界點附近之形態. 研究指出, 高分子會改變二維混合溶劑的臨界點和其臨界指數, 且高分子在臨界點附近會收縮. 加入高分子後也會加快二元混合溶劑的相分離速率.

Polymer is a molecule with high molecular weight consisting of many small repeated units (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.

Abstract ii
Acknowledgement iii
1 Introduction 1
1.1 IntroductiontoPolymer ........................... 1
1.2 IntroduciontoBinaryMixture........................ 4
1.3 Introductiontothissystem.......................... 6
2 Theoretical and Experimental Backgrounds 10
2.1 PolymerPhysics................................ 10
2.1.1 Polymerproperties.......................... 10
2.1.2 Thephysicalpictureofapolymerchain .............. 13
2.1.3 Thedynamicpropertiesofpolymers ................ 27
2.2 TheCriticalPhenomenon .......................... 28
2.2.1 The DefinitionofPhaseTransition ................. 29
2.2.2 The ClassificationofPhaseTransition ............... 30
2.2.3 OrderParameter ........................... 32
2.2.4 CorrelationFunction......................... 35
2.2.5 CriticalBehaviorandExponents .................. 36
3 The Simulation Method 38
3.1 TheMonteCarlomethod .......................... 383.1.1 RandomVariablesandStochasticProcess ............. 40
3.1.2 ImportanceSampling......................... 41
3.1.3 TheMetropolisMethod ....................... 43
3.2 TheBondFluctuationModel ........................ 46
3.3 ModelforthePolymerSystemwithabinarymixturesolvent....... 47
4 Results and Discussions 50
4.1 PureBinaryMixture............................. 50
4.2 BinaryMixturewithPolymers........................ 56
4.2.1 PolymersWhichHasNoInteraction................. 56
4.2.2 PolymersInteractingWithTheBinaryMixtureSolvent...... 59
4.3 PolymerStructures.............................. 66
4.3.1 Polymershavenointeractions.................... 67
4.3.2 Polymershaveinteractions...................... 68
Appendices 80
A The Program for Binary Mixture with Polymers 80
Bibliography 91

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