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Student Number 87222035
Author Fu-Kuo Shun(®]´I°ê)
Author's Email Address No Public.
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Department Physics
Year 2000
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title Polymers In a Binary
Mixture Solvent:
Monte Carlo Simulation Studies
On A Two Dimensional System
Date of Defense 2001-07-19
Page Count 93
Keyword
  • none
  • Abstract 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¡Vbinary mixture with linear polymers
    ¡V 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.
    Table of Content 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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    Advisor
  • Pik-Yin Lai(¾¤Âz½å)
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    Date of Submission 2001-07-19

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