臺灣博碩士論文加值系統

帶電膠體粒子之間的互相作用是長久以來的研究課題。DLVO理論是其中一個值得注目的研究成果，它結合了凡得瓦吸引力與屏蔽的庫侖排斥力。我們現今的工作中只考慮靜電作用，但吸引力與排斥力部分仍然同時被得到。在我們的模型中，反離子(counter-ions)會在各自的巨離子(macro-ion)附近凝聚(condense)或擾動(fluctuate)。我們利用蒙地卡羅模擬(Monte Carlo simulation)計算並得到在二維系統中兩顆巨離子平均靜電作用與距離之關係。
當一粒巨離子平均所分到反離子的數目較少時，我們可觀察一個短距離的吸引力與長距離的排斥力。然而，當一粒巨離子所分到的反離子數目增加時，吸引力會因此而逐漸消失。在這裡，我們提供引力與斥力來源的可能性方案。

Interaction among charged colloidal particles has been investigated for long. One remarkable success, the so-called DLVO theory, considered the effects of both the van der Waals attraction and the screened Coulomb repulsion. In our current work, both the attractive and repulsive parts of the effective potential energy are observed while we consider the electrostatic effect only. In our model, we investigate the regime where the electrostatic interaction dominates and the counter-ions condense or fluctuate nearby each macro-ion. We use Monte Carlo simulations to obtain the average electrostatic interactions versus the distance between two macro-ions embedded in 2-dimensions.
When the number of counter-ions is small, we obtain a short-range attraction and long-range repulsion. However, the attraction tends to vanish when the number of counter-ions increases. We provide possible scenarios for the sources of the attraction and repulsion.

Contents
1 Introduction 1
2 Background 3
2.1 What are colloids? 3
2.2 Interactions in a colloidal system 4
2.2.1 The Debye-Hückel theory 5
2.2.2 The van der Waals 6
2.2.3 Like-charge attraction 7
3 Model and Algorithm 11
3.1 Our Basic model 11
3.2 Simulation scheme 13
3.2.1 The Monte Carlo methods in statistical physics 13
3.2.2 Definition of dimensionless variables 14
4 Results and discussions 15
4.1 Average electrostatic interactions 15
4.2 Asymmetric distribution of counterions 18
4.3 The effect of confined geometry 20
4.4 The effect of dipole-dipole interaction 22
4.5 A Locked-up model and multipole effects 24
4.6 Physical implementation 31
5 Further results and analysis 34
6 Conclusion 38

[1] Debye P W and H¨uckel E 1923 Phys. Z. 24 185
[2] Derjaguin B V and Landau L 1941 Acta Physicochimica (USSR) 14
[3] Verwey E J W and Overbeek J T G 1948 Theory of the Stability of Lyophobic Colloids (Amsterdam:Elsevier)
[4]Y. Levin, Rep. Prog. Phys. 65 (2002) 1577
[5] G. M. Kepler and S. Fraden, Phys. Rev. Lett. 73, 356 (1994)
[6] Y. Han and D. G. Grier, Phys. Rev. Lett. 91, 038302 (2003)
[7] W. Chen et al., Phys. Rev. Lett. 95, 218301 (2005)
[8] W. Chen et al., Phys. Rev. E 74, 021406 (2006)
[9] T. Liu, J. Am. Chem. Soc. 2003, 125, 312.
[10]G. Liu, J. Am. Chem. Soc. 2004, 126, 16690
[11]A. E. Larsen and D. G. Grier, Nature (London) 385, 230 (1997)
[12] D. G. Angelescu and P. Linse Langmuir 2003, 19, 9661-9668