臺灣博碩士論文加值系統

本論文中推導出在兩平面、圓柱以及球的內部為不含鹽類的介質系統下，膠體內部的空間電位分佈近似解析解；根據兩平面內部的空間電位分佈解析解，本論文使用變數變換的方法近似導出圓柱座標以及球座標的近似解析解。結果顯示近似條件所需要設定的距離，在幾何中心距離假想空間電位衰變至零的面超過100倍粒子徑長時誤差相當低。並且當表面電位較高的時候，近似解析解對於空間電位的分佈會有較好的描述，即和數值解的結果會有較少的誤差；而在表面電位較低的情況下，圓柱座標以及球座標的近似解可以乘上一個校正函數來修正，則可以有效的大幅降低誤差，更可以正確的描述膠體粒子內部的空間電位分佈。而在同樣的參數下，空間電位隨著距離膠體表面的距離增加而下降，而空間電位下降的速率依序平面座標>圓柱座標>球座標。而在反離子價數提升的狀況下，當有越大的反離子價數會得到越低的空間電位，而同樣空間的電位分佈隨距離表面的距離增加有更快速度的衰減。最後並導出有關固定表面電位和固定表面電荷密度在此方程式上的轉換式，並且可以應用邊界條件相關表面官能基解離的情況。

Approximation analytical expression for the potential of planar, cylindrical, and spherical surfaces are derived for the case when the inside medium contains counterions only. Based on the results for planar, those for two identical surfaces can be derived. The error of a surface on the electrical potential distribution can be neglected when the order of the distance which from center to the surface we assume the potential decay to zero about 102 of its radius. This effect also can be neglected when the potential is high, but it can be taken into account by multiplying a correction function to the potential of surface when the surface potential is low. For the same set of parameters, the magnitude of the degree of the potential decay for various type of surface follows the order planar surface>cylindrical surface>spherical surface.
Furthermore, the boundary condition exchange equation of constant surface potential change to constant charge density is derived for these equations. So it can be used with two types of boundary condition.

中文摘要…………………………………………………………………………………I
英文摘要………………………………………………………………………………...II
目錄………………………………………………………………………….…………III
圖目錄………………………………………………………………….……………….V
第一章 緒論………………………………………………………………...…………1
第二章 文獻回顧…………………………………………………...………………....3
2-1 電雙層理論………………………………………………...……………….....3
2-1.1波茲曼分佈……………………………………………………………..3
2-1.2 波松方程式…………………………………...………………………..4
2-1.3 波松—波茲曼方程式………………………...………………………..5
2-1.4 Debye-Hückel 理論………………………………………………….....6
2-1.5 單一電雙層的Gouy-Chapman 理論……...………………………......7
2-2電動力學現象……………………....……………………………………….....8
2-3 Modified Poission-Boltzmann equation….………………………………….....8
2-4 不含鹽類的膠體分散系統…………….….…………………………………..9
第三章 理論分析…………………………………………………………………..12
3-1 兩平板系統內部的電位分佈………………………………………………12
3-2 球座標內部的電位分佈………………...…………………………………13
3-3 圓柱座標內部的電位分佈……...…………………………………………...14
3-4 官能基解離的邊界條件…………..…………………………………………16
第四章 結果與討論………………………………………………………………17
4-1 F對於近似解誤差的修正性…………………………………………………17
4-2 a的大小對於膠體粒子內部電位分佈的影響…..………………………..…18
4-3 ys的大小對於膠體粒子內部電位分佈的影響………………………………18
4-4 ω對於膠體粒子內部電位分佈的影響.……………………………………...19
4-5 b對於膠體粒子內部電位分佈的影響…………….………………………...19
第五章 結論………………………………………………………………………..21
符號說明……………………………………………………………………………23
參考文獻……………………………………………………………………………26
附錄A…………………………………………………………………..………………47
附錄B……………………………………………………………..……………………49
附錄C……………………………………………………………………………..……51

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