臺灣博碩士論文加值系統

在水中加入陽離子型、陰離子型、兩性離子型等界面活性劑(surfactant)，會解離出反離子(counterion)。當界劑達到CMC時，會聚集形成微胞(micelles)，其散佈在水中的反離子會靠近帶Z價電荷的微胞表面，這就是反離子凝聚(condensation)現象。從遠處感受微胞的電荷也就不再是Z價電荷了，我們以Debye-Hückel進似理論來得到有效電荷Z*，例如計算DLVO位能時就必須考慮到有效電荷Z*。而一個帶電膠體系統擁有效電荷的現象就稱為電荷的重正化(charge renormalization)。
對一個未加鹽類(salt-free)的膠體(colloidal)懸浮溶液，我們採用球型系統(spherical Wigner-Seitz cell) ，在系統的正中心放入帶電粒子，周圍散佈著因帶電粒子解離出的反離子，整個系統視為電中性，改變球型系統的大小，相當於改變真實情況的濃度。以蒙地卡羅模擬法(MC)得到各式各樣的熱力學性質�蝖A並且為了考量在帶電粒子以及水溶液系統中介電常數的不連續，採用restricted primitive model來解算卜松方程式(Poisson equation)以求得反離子之間的靜電作用力。
在產生反離子凝聚現象的兩個相同條件系統中，找到帶較高Z價帶電粒子的�蝖A相等於帶較低Z*價帶電粒子的�蝖A[�� (Z) =�n�� (Z*)]，我們定義Z*就是有效電荷，並且在Z＝Z*時，存在一個���n之最大值。換
而言之，我們藉由���n隨著反離子數目增加，先有上升的趨勢，達到最大值後再下降的圖中找出有效電荷。而從Debye-Hückel進似理論求得�膗H的有效電荷會比上述的有效電荷值來的小。

結果我們從化學勢能(chemical potential)解釋電荷重正化的現象，而化學勢能相當於從實驗上測量到的滲透壓(osmotic pressure)。

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the
charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles,
effective charges Z* is therefore invoked in the models based on Debye-Hückel approximation, such
as the DLVO potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to
obtain various thermodynamic properties ω in a spherical Wigner-Seitz cell. The effect of dielectric
discontinuity is examined. We show that at the same particle volume fraction, counterions around
a highly charged spheres with Z may display the same value of ω as those around a weakly charged
sphere with Z*, i.e., ω(Z) = ω(Z*). There exists a maximally attainable value of ω at which
Z = Z*. Defining Z* as the effective charge, we find that the effective charge passes through a
maximum and declines again due to ion-ion correlation as the number of counterions is increased.
The effective charge is even smaller if one adopts the Debye-Hückel expression ωDH. Our results
suggest that charge renormalization can be performed by chemical potential, which may be observed
in osmotic pressure measurements.

全文目錄
第一章 序論與文獻回顧 1
1-1 電荷重正化(反離子凝聚)的現象 1
1-2 介紹Wigner-Seitz Cell 3
1-3 過去研究中有效電荷的定義 4
1-4 以熱力學性質定義有效電荷 7
第二章 理論介紹 9
2-1 以Partition Function得到系統的熱力學性質 9
2-2 極弱的吸引作用：Debye-Hückel近似理論 14
第三章 蒙地卡羅模擬 17
3-1 Poisson方程式 17
3-2 Metropolis Method 19
3-3 Widom’s Method 20
第四章 結果與討論 22
4-1 比較DH與MC的結果 24
4-2 以化學勢能(滲透壓)定義電荷重正化現象 26
4-3 以表面電位定義電荷重正化現象 30
4-4 系統的內能 32
4-5 界面兩側的介電常數不連續的影響 33

4-6 結論 35
參考文獻 48


圖目錄
圖1-1 7
圖3-1 21
圖4-1 37
圖4-2 38
圖4-3 39
圖4-4 40
圖4-5 41
圖4-6 42
圖4-7 43
圖4-8 44
圖4-9 45
圖4-10 46
圖4-11 47

表目錄
表4-1 36

1.S. Alexander, P. M. Chaikin, P. Grant, G. J. Morales, and P. Pincus, J. Chem. Phys. 80, 5776 (1984).
2.E. Trizac, L. Bocquet, and M. Aubouy, Phys. Rev. Lett. 89, 248301 (2002).
3.J. M. Roberts, J. J O’Dea, and J. G. Osteryoung, Anal. Chem. 70, 3667 (1998).
4.G. S. Manning, J. Chem. Phys. 51, 924 (1969).
5.F. Oosawa, Polyelectrolytes, Dekker: New York, 1971.
6.W. M. Gelbart, R. F. Bruinsma, P. A. Pincus, and V. A. Parsegian, Phys. Today 53, 38 (2000).
7.B. H. Zimm and M. Le Bret, J. Biomol. Struct. Dyn. 1, 461 (1983).
8.M. J. Stevens, M. L. Falk and M. O. Robbins, J. Chem. Phys. 104, 5209 (1996).
9.R. D. Groot, J. Chem. Phys. 95, 9191 (1991).
10.G. V. Ramanathan, J. Chem. Phys. 88, 3887 (1988).
11.L. Belloni, Colloid Surf. A 140, 227 (1998).
12.M. Deserno and C. Holm, in Electrostatic Effects in Soft Matter and Biophyiscs, (Kluwer Academic Publishers, Netherlands, 2001), p. 27.
13.V. Sanghiran and K. S. Schmitz, Langmuir 16, 7566 (2000).
14.E. J.W.Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier:Amsterdam, 1948.
15.D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic Press, New York,1996).
16.Y.-J. Sheng and H.-K. Tsao, Phys. Rev. Lett. 87, 185501 (2001);Y.-J. Sheng and H.-K. Tsao,Phys. Rev. E 66, 040201(R) (2002);C.-H. Ho,H.-K. Tsao and Y.-J. Sheng, J. Chem. Phys.119, 2369 (2003).
17.B. I. Shklovkii, Phys. Rev. E 60, 5802 (1999).