摘要
自然界中，帶電高分子(charged polymer)在所有的生物反應扮演了非常重要的角色。除此之外，在工業上帶電高分子也有很廣泛的應用。但是到目前為止，我們對於帶電高分子的了解還是非常的有限。長程(long-range)庫侖交互作用力是使得帶電高分子系統的理論發展困難的主要因素。在這篇論文中，我們透過一個簡單的模型，且利用蒙地卡羅(Monte Carlo)模擬的方法，研究帶電高分子在good solvent條件下的吸附(adsorption)現象。此研究和先前對於帶電高分子吸附現象的研究的最大差別在於我們考慮了重要的環境效應。此研究中的帶電高分子模型是採用非晶格模型之 -- 小珠彈簧模型(Bead-Spring Model)。研究的焦點主要是在吸附相變點附近帶電高分子吸附在帶電表面上的行為，以及比較帶電高分子和短程(short-range)交互作用力之不帶電高分子系統吸附現象的差別。從我們目前研究的結果看來，我們預言帶電高分子的吸附為一階相變。

Abstract

Charged polymers are widely used in industry and are present in nature. They play an important role in many problems of physical chemistry or formulation in a aqueous solvents. Typical examples would be waste water treatment or all the physical problems related to biopolymers. Surface coated with charged polymers also has important applications in industrial and biological technologies such as colloidal stabilization, adhesion, interaction of biopolymers with charged proteins, etc. another widely studied example in material is the formation of multilayers. Previous analytic studies on the adsorption of polyelectrolyte were not focused on the importance of the effect of the medium. In this study, we use a simple model to investigate the adsorption of a charged polymer on a charged impenetrable surface under good solvent conditions using Monte Carlo simulation method. The polymer chain studied in this work is modeled as beads connected by springs. The impenetrable substrate is a semi-infinite plane separating two media of different dielectric properties. We study the behavior near the adsorption phase transition. Our recent results predict that the adsorption of a charged polymer appears to be first-order.

Contents

Contents ……………………………………………………………………………I
Figure captions ……………………………………………………………………III
1 Introduction ……………………………………………………………………..1
1.1 The Historical Development of Polymers ……………………………2
1.2 Introduction to Neutral Polymers ……………………………………...4
1.3 Review of polymer adsorption with short-range attraction ……….11
1.4 Introduction to Charged Polymers …………………………………….12
2 Theory of Charged Polymers …………………………………………….…..15
2.1 Properties of Charged Polymers in Solution ………………………...15
2.2 Charged Polymer in a semi-infinite region bounded by a flat substrate ……………………………………………22
3 The Simulation Method ……………………………………………………….33
3.1 Bead-Spring Model ………………………………………………………34
3.2 Monte Carlo Simulation Method ………………………………………37
3.2.1 Metropolis Monte Carlo Method …………………………………38
3.2.2 Histogram Monte Carlo Method …………………………………44
3.3 Simulation Details ………………………………………………………..46
4 Simulation Results and Discussions …………………………………….….51
4.1 Results for the Static by the Standard Monte Carlo Simulation method ……………………………………………………...51
4.2 Results of the Histogram Monte Carlo Simulations ………………..60
5 Conclusion and Outlook ……………………………………………………...77
Reference ………………………………………………………………………….79

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