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研究生:巫昆懋
研究生(外文):Kun-Mao Wu
論文名稱:外加電場下多價鹽溶液中高分子電解質之行為模擬
論文名稱(外文):Unfolding of polyelectrolytes in tetravalent salt solutions in electric fields: A computer simulation study.
指導教授:蕭百沂
指導教授(外文):Pai-Yi Hsiao
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工程與系統科學系
學門:工程學門
學類:核子工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:52
中文關鍵詞:高分子電解質電泳分離基因定序郎日凡動力學
外文關鍵詞:polyelectrolyteelectrophoresisDNA sequenceLangevin dynamics simulations
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我們利用Langevin dynamics模擬方法探討外加電場對多價鹽溶液中高分子電解質性質的影響。高分子電解質的尺寸,包含旋轉半徑(radius of gyration)及末端距(end-to-end distance),隨著電場變化而改變。在低電場下,旋轉半徑與末端距約為一定值,不會影響高分子電解質的行為;當電場加大超過某一臨界值,部分吸附在高分子上的反離子脫離高分子電解質束縛成為非吸附反離子,高分子電解質開始被拉伸;電場持續加大,聚離子鏈最後會被拉伸成棒狀。形狀因子Rg^2/Re^2與偏球率(Asphericity)的數值也反映出此一事實。臨界電場的值增加隨著鹽濃度增加而變大。當外加鹽濃度大約等於對等電荷濃度有最大臨界電場。在最緊密狀態高分子電解質球的拉伸臨界電場強度E*可由極化能與熱擾動能量相等時的電場求得,其結果顯示出與鏈長的相依性,E*~N^(-1/2) ,可以運用於電泳分離帶電且緊密摺疊的生物分子。非緊密摺疊的高分子電解質被拉伸的過渡行為較不明顯。在伸長狀態下高分子電解質的拉伸臨界電場與鏈長相依性的關係式約為E*~N^(-1) 。最後我們分析聚離子鏈以及吸附離子的動態行為,包含電泳遷移率,與吸附離子在聚離子鏈上分佈的情形。在低電場下,吸附反離子緊緊吸附在聚離子鏈上,減低了聚離子鏈的遷移率,吸附離子平均分佈在聚離子鏈上。在大電場下,電場對吸附反離子加速的力大於聚離子鏈的靜電力,吸附反離子在聚離子鏈上產生滑動現象,吸附反離子在聚離子上分佈產生不均勻現象,有較多吸附反離子分佈在順著電場方向的聚離子鏈一端。
By means of Langevin dynamics simultion,we investigated the properties of a flexible polyelectrolyte (PE) at different salt concentration in external electric fields. The radius of gyration (Rg) and end-to-end distance (Re) alter with the strength of electric field. At weak electric field, the values of Rg and Re are roughly constant. The field does not affect PE behavior. Further increasing electric field over a critical value, part of condensed counterions escape from the PE and become free counterions. The PE starts to be stretched and displays a rod like structure. The values of shape factor and asphericity of the chain show these behaviors too. Moreover, the higher the salt concentration, the higher the critical electric field will be. The critical electric field attains a maximum value when the salt concentration is around equivalence point. For the most compact PE globule, the unfolding critical field E* is determined by equaling the polarization energy and thermal energy(kT). The result gives the relation between the critical field E* and the chain length,E*~N^(-1/2) ,which can be used in electrophoretic separating of charged, globule biopolymers. The unfolding transition for noncollapsed PE is less pronounced. For elongated PE, we obtained a scaling law,E*~N^(-1). In the last section of study, we analyzed dynamic quantities including mobility of PE, and of condensed ions, and distribution of condensed ions on PE backbone. For small field, condensed counterions bind to PE and slow the mobility of PE. Condensed counterions distribute uniformly on PE backbone. For large field, the condensed counterions overcome the electrostatic interaction and can decondense or glide on the PE backbone. Condensed counterions thus distribute non-uniformly and prefer to stay on one side of PE backbone along the field direction.
目錄
中文摘要 ............................................... ii
英文摘要 ...............................................iii
誌謝 ................................................... iv
目錄 .................................................... v
圖目錄 ................................................ vii

第一章 簡介 ......................................... 1
1.1 高分子電解質(Polyelectrolyte) ...................... 1
1.2 濃縮(Condensation)與覆溶(Redissolution)行為 ........ 2
1.3 電泳(Electrophoresis) .............................. 2
1.4 基因定序(Gene mapping) ............................. 3
1.5 研究動機 ............................................ 4
第二章 模型與方法 ...................................... 6
2.1 模型 ............................................... 6
2.1.1 系統 ............................................. 6
2.1.2 粒子作用力 ....................................... 7
2.2 方法 ............................................... 10
2.2.1 分子動力學(Molecular dynamics) ............... 10
2.2.2 郎日凡動力學(Langevin dynamics) ............. 11
2.2.3 邊界條件 .................................. 11
2.2.4 積分演算法 ................................ 12
2.2.5 Ewald summation ........................... 12
2.2.6 LAMMPS ........................................... 13
第三章 模擬參數設定 .................................... 14
第四章 結果與討論 ...................................... 16
4.1 外加電場對高分子電解質構形大小影響 ................. 16
4.1.1 旋轉半徑(Radius of gyration) ................ 16
4.1.2 末端距(End-to-end distance) ................. 18
4.2 高分子電解質外觀形貌圖 ............................. 19
4.3 外加電場對高分子電解質構形形狀影響 ............... 21
4.3.1 形狀因子 Re^2/Rg^2 ........................ 21
4.3.2 偏球率(Asphericity)A ...................... 22
4.4 高分子電解質之拉伸臨界電場 ......................... 23
4.4.1 外加電場對濃縮電荷的影響 .................... 24
4.4.2 鹽濃度對臨界電場的影響 ...................... 28
4.4.3 改變鏈長對臨界電場的影響-尺度率(Scaling law) ..... 31
4.5 動態行為分析 ....................................... 39
4.5.1 鹽濃度對電泳遷移率的影響 ......................... 39
4.5.2 聚離子鏈上離子吸附分佈情形 ....................... 43
第五章 結論 ............................................ 47
參考文獻 ................................................ 49




圖目錄
圖2.1:體積排斥作用力 ................................... 8
圖2.2:鍵結作用力 ....................................... 10
圖4.1:不同電場下高分子電解質均方旋轉半徑隨鹽濃度變化圖形 17
圖4.2:不同電場下高分子電解質末端距與鏈長比值隨鹽濃度變化圖形 ...................................................... 18
圖4.3:不同鹽濃度下末端距與鏈長比值隨電場變化圖形 ....... 19
圖4.4:高分子電解質在未加鹽溶液中的外觀形貌 ............. 20
圖4.5:高分子電解質在對等電荷濃度溶液中的外觀形貌 ....... 20
圖4.6:高分子電解質在高鹽濃度溶液中的外觀形貌 ........... 21
圖4.7:不同鹽濃度下 隨電場變化圖形 ...................... 22
圖4.8:不同鹽濃度下偏球率 隨電場變化圖形 ................ 23
圖4.9:各種鹽濃度下有效吸附電荷與聚離子電荷比值的絕對值隨電場變化圖形............................................... 25
圖4.10:不同鹽濃度溶液中各種粒子吸附於聚離子鏈上的數量隨電場變化圖形................................................. 28
圖4.11:不同電場下高分子複合體產生感應電偶極的圖形 ...... 29
圖4.12:不同鹽濃度溶液高分子電解質拉伸臨界電場的圖形 .... 30
圖4.13:不同鹽濃度下末端距與鏈長比值隨電場變化圖形 ...... 30
圖4.14:對等電荷濃度下不同鏈長高分子複合體感應電偶極對電場分佈圖形................................................... 32
圖4.15:對等電荷濃度下不同鏈長高分子電解質末端距與鏈長比值隨電場變化圖形............................................. 32
圖4.16:對等電荷濃度下臨界電場與鏈長對數-對數座標圖形 ... 33
圖4.17:對等電荷濃度下旋轉半徑與鏈長對數-對數座標圖形 ... 34
圖4.18:零鹽電荷濃度下不同鏈長高分子複合體感應電偶極對電場分佈圖形 .................................................. 34
圖4.19:零鹽濃度下不同鏈長高分子電解質末端與鏈長比值距隨電場變化圖形 ................................................ 35
圖4.20:零鹽濃度下臨界電場與鏈長對數-對數座標圖形 ....... 36
圖4.21:零鹽濃度下旋轉半徑與鏈長對數-對數座標圖形 ....... 36
圖4.22:零鹽濃度下旋轉半徑張量特徵值1與鏈長對數-對數座標圖形
................................................. 37
圖4.23:零鹽濃度下旋轉半徑張量特徵值2與鏈長對數-對數座標圖形
................................................. 38
圖4.24:零鹽濃度下旋轉半徑張量特徵值3與鏈長對數-對數座標圖形
................................................. 38
圖4.25:不同鹽濃度下聚離子鏈遷移率隨電場變化圖形 ......... 40
圖4.26:不同鹽濃度下吸附四價反離子遷移率隨電場變化圖形 ... 41
圖4.27:不同鹽濃度下吸附一價反離子遷移率隨電場變化圖形 ... 42
圖4.28:不同鹽濃度下非吸附一價反離子遷移率隨電場變化圖形 . 42
圖4.29:不同鹽濃度下非吸附四價反離子遷移率隨電場變化圖形 . 43
圖4.30:零鹽濃度下聚離子鏈上吸附一價反離子分佈情形隨電場變化圖形 .................................................... 44
圖4.31:低鹽濃度聚離子鏈上離子分佈情形隨電場變化圖形 ..... 45
圖4.32:對等電荷濃度聚離子鏈上離子分佈情形隨電場變化圖形 . 46
圖4.33:高鹽濃度聚離子鏈上離子分佈情形隨電場變化圖形...... 46
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