高分子在溶液中，受到外加電場作用而影響其高分子的運動情形，在實驗上已陸續地被研究出；本篇論文則利用分子動力模擬方法，計算並探討類聚乙烯（PE-like）高分子在氯甲烷（methyl chloride）溶劑中，施以外加直流電場後，造成類聚乙烯運動改變的情形，並進一步瞭解其動力行為。計算系統包含一般溶液、稀釋溶液及低密度溶液，每個系統再分別對以下四種條件進行模擬，即非極性或極性高分子溶於極性或非極性溶劑，極性的變化係藉由改變高分子或溶劑本身的電荷分佈所構成。
藉由計算類聚氯乙烯的質心擴散係數，可以觀察其運動速率隨著外加電場強度的變化。一般而言，極性分子受外加電場作用，應增加分子的流動性（mobility），致使質心擴散係數隨著電場強度增大，然而比較各個模擬系統的計算結果，並未顯示出如此的一致性，甚至有部分系統的高分子質心擴散係數會隨著電場強度的增加而降低。根據電流變效應（electro-rheological, ER, effect)及計算高分子周圍溶劑分子的徑向分佈函數，可解釋各系統中高分子的動力行為，係由於外加電場引起極性分子間的偶極-偶極作用力而導致分子規則排列（alignment）與分子的流動性產生競爭所造成。
溶液中高分子的質心擴散係數隨外加電場強度而增加或減少的趨勢，與系統密度、高分子濃度、溶劑或高分子的極性大小以及外加電場強度有關。適當選擇並搭配以上各種性質，則可利用外加電場控制高分子在溶液中的運動行為。

By means of molecular dynamics simulation the effect of external direct current electric field on the polyethylene-like (PE-like) polymer and methyl chloride solvent system is investigated. Three systems include normal solution, dilute solution, and lower-density solution are simulated. For each system, four conditions include non-charged polymers in nonpolar solvents, non-charged polymers in polar solvents, charged polymers in nonpolar solvents, and charged polymer in polar solvents are simulated.

The diffusion behavior of polymer in solvent is as functions of electric field, polarity of solvent molecules, and polarity of polymer. When an electric field is applied to the system include dielectric molecules, our calculation shows that the center of mass diffusion constant of polymer depends on the alignment of charged polymer or polar solvent molecules, the mobility of charged polymer or solvent molecules and the density of the system. The mobility of polar molecules results in the increase of the center of mass diffusion constant of polymer. The alignment of polar molecules results in the increase of fluid viscosity. This decreases the center of mass diffusion constant of polymer.

Table of Contents

Chapter 1 Introduction ------------------ 1
1-1 Progress about Computer Simulation 2
1-2 Dynamics of Polymer under External
Electric Field ------------------ 4

Chapter 2 Molecular Dynamics Simulation --- 7
2-1 Basic Principle of MD ------------- 8
2-2 Numerical Methods ----------------- 9
2-3 Image Box Dimensions ------------ 10
2-4 Cutoff Radius --------------------- 12
2-5 Nearest Image Convection ---------- 12
2-6 System Equilibrium ---------------- 13
2-7 Application of Reduced Unit ------- 14
2-8 Procedure of MD Simulation -------- 15

Chapter 3 System Construction & Analytical
Methods ------------------------- 17
3-1 Mixture of Polymers and Solvents -- 18
3-2 Force Field in Systems ------------ 19
3-3 Indispensable Information to the MD
Simulation ------------------------ 22
3-4 Simulated Properties ------------ 23
3-4-1 Center of Mass of Polymer ------ 23
3-4-2 Diffusion Coefficient ----------- 24
3-4-3 Radial Distribution Function ---- 25

Chapter 4 Results & Discussion ------------ 26
4-1 Diffusion Coefficient ---------- 27
4-1-1 AI, BI, CI Systems ---------- 27
4-1-2 AII, BII, CII Systems ------------- 28
4-1-3 AIII, BIII, CIII Systems ---------- 29
4-1-4 AIV, BIV, CIV Systems ------------- 29
4-2 Radial Distribution Function -------- 30
4-3 Discussions --------------------------- 31

Chapter 5 Conclusions ------------------- 35

References --------------------------------- 37


List of Figures

Figure 2.1. Two-dimensional periodic boundary
condition ----------------------- 42
Figure 2.2. Two-dimensional interaction among
units --------------------------- 43
Figure 2.3. The integrated processes of MD
simulation ---------------------- 44
Figure 3.1. The subjects in the simulation -- 45
Figure 3.2. Three simulated systems --------- 46
Figure 3.3. Four varieties of polymer-solvent
mixture --------------------- 47
Figure 4.1. Mean square displacement of unit in
polymer for AI, BI, and CI systems --- --------------------------------- 48
Figure 4.2. Mean square displacement of polymer
center of mass for AI, BI, and CI
systems ------------------------- 49
Figure 4.3. Diffusion constants of polymer in AI,
BI, and CI systems -------------- 50
Figure 4.4. Mean square displacement of unit in
polymer for AII, BII, and CII
systems -------------------------- 51
Figure 4.5. Mean square displacement of polymer
center of mass for AII, BII, and CII
systems -------------------------- 52
Figure 4.6. Diffusion constants of polymer in
AII, BII, and CII systems -------- 53
Figure 4.7. Mean square displacement of unit in
polymer for AIII, BIII, and CIII
systems -------------------------- 54
Figure 4.8. Mean square displacement of polymer
center of mass for AIII, BIII, and
CIII systems ----------------------55
Figure 4.9. Diffusion constants of polymer in
AIII, BIIII, and CIII systems----- 56
Figure 4.10. Mean square displacement of unit in
polymer for AIV, BIV, and CIV
systems -------------------------- 57
Figure 4.11. Mean square displacement of polymer
center of mass for AIV, BIV, and CIV
systems -------------------------- 58
Figure 4.12. Diffusion constants of polymer in
AIV, BIV, and CIV systems -------- 59
Figure 4.13. Radial distribution function for
AII, BII, and CII systems -------- 60
Figure 4.14. Radial distribution function for
AIII, BIII, and CIII systems ----- 61
Figure 4.15. Radial distribution function for
AIV, BIV, and CIV systems --------- 62
Figure 4.16. Mean square displacement of unit in
polymer for AII’, AII, AII’’ and
AII’’’ systems ---------------- 63
Figure 4.16. Mean square displacement of polymer
center of mass for AII’, AII,
AII’’ and AII’’’ systems ---- 64



List of Tables

Table 2.1. Conversion with reduced unit in MD
simulation ------------------------ 65
Table 3.1. The classification of simulated
systems ------------------------ 66
Table 3.2. Constants used for the potential
functions ------------------------- 67
Table 4.1. Diffusion constants of AII, BII, and
CII systems ------------------- 68
Table 4.2. Diffusion constants of AIII, BIII, and
CIII systems ------------- 69
Table 4.3. Diffusion constants of AIV, BIV, and
CIV systems ---------------- 70

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