臺灣博碩士論文加值系統

本文針對由N個單體所組成的聚電解質，分別就未添加鹽類(salt free)、添加一價鹽類(monovalent salt)、添加多價鹽類(multivalent salt)等三個不同方向進行蒙地卡羅模擬法，並藉由計算其解離度(α)去探討其於水溶液中的反離子凝聚現象。在此模擬之中，於未添加鹽類的部份中，我們用Wigner-Seitz cell法進行模擬，發現解離度會隨著聚電解質的分子量上升而下降，與實驗組用離子濃度選擇性電極所做出的結果是相符合的，並對單體帶負一價伴隨帶正一價或正二價電荷的反離子進行解離度與結構上的討論，並比較用此兩種不同方法所計算出來的結果其差異性何在；添加一價鹽類及多價鹽類則就相同濃度不同單體數聚電解質於添加不同價數的鹽類濃度中進行Wigner-Seitz cell的模擬，加入一價鹽類之後，使得聚電解質的反離子凝聚現象較為明顯，添加多價鹽類後，因為所帶的價數較高，彼此之間的靜電作用力較原先聚電解質本身一價的反離子要來的更加強烈，因此取代反離子的能力也越強。除了從反離子的解離度去觀察外，亦由計算迴旋半徑、結構因子以及堅持長度去觀察聚電解質在添加不同價數鹽類後，鏈長與聚電解質鍵結柔軟度之變化。
在本篇論文的最後，我們亦對Ewald summation與Cell model對不同價數的charged particle進行計算，並比較兩種方法於不同價數與不同反離子濃度下，其結果會有何差異性，並發現於低價數與低濃度的狀況下，運用Cell model算出的結果與Ewald summation是幾乎相同的。

Abstract

The phenomenon of counterion condensation around a linear polyelectrolyte chain with N monomers is investigated by Monte Carlo simulation in terms of a degree of ionization α, which is proportional to the effective charge. It is define as the ratio of observed to intrinsic counterion concentration, α=co/ci..In order to know the effect of salt addition, we add different valent salts in the system. Fixing polyelectrolyte in the center of the Wigner-Seitz cell, we calculate the degree of ionization, radius of gyration and persistence length. We observe that multivalent salt make radius of gyration, persistence length and degree of ionization decrease rapidly. The driven mechanism of counterion condensation is primarily the electrostatic internal energy, manifested by the effect of dielectric constant, while the counterion entropy influences the degree of ionization as well.

In the last of the thesis, we compare the difference with Ewald summation and Cell model. We set different valent charged particles in two systems and calculate the degree of ionization. As low valent and low concentration, the results of cell model and Ewald summation are the same.

目錄
摘要 ..............................................................I
誌謝 .............................................................IV
目錄 ..............................................................V
圖目錄 ...........................................................VI
第一章 緒論與文獻回顧 …..........................................1
1-1 聚電解質 .....................................................1
1-1-1四大類聚電解質 – 依官能基分類 .......................1
1-1-2常見的天然聚電解質 …………..........................3
1-1-3應用 ……………...…………………..........................5
1-2 反離子凝聚現象 ................................................5
1-2 反離子的動態平衡 .............................................8
第二章 理論與名詞簡介 ..........................................10
2-1 理論介紹 .......................................................10
2-2庫侖作用力 ………...................................................11
2-3 介電常數 .....................................................12
2-4卜松-波滋曼方程式 ……….....................................13
2-5 化學勢能 ........................................................15
2-6 高分子的特性簡介 ................................................15
2-6-1結構因子 …………………………….......................16
2-6-2迴旋半徑 …………………………….......................17
2-6-3堅持長度 …………………………….......................18

第三章 模擬方法 ...................................................19
3-1 分子模擬 ........................................................19
3-2 蒙地卡羅法 ....................................................22
3-3 Wingner-Seitz Cell ………………………........................24
3-4 週期性邊界條件 ………………….........................................27
3-5 內能計算 ............................................................29
3-6 Ewald summation ….....................................................30
3-7 化學勢能與解離度 ................................................32
第四章 結果與討論 .....................................................34
4-1 聚電解未添加鹽類 ............................................34
4-2 一價鹽類效應 .........................................................39
4-3 多價鹽類效應 .......................................................43
4-4 Cell model與Ewald summation 的比較 ........................49
第五章 結論 .......................................................51
� � 參考文獻 ...................................................52

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