根據高分子物理 ，關於高分子 侷限 在奈 微管 道(polymer confinement )中的 伸長量 ，從較粗的管徑 (weak confinement)到較細的管徑 到較細的管徑 (strong confinement)主要 分為五種 區域 ：bulk regime、de Gennes regime、extended de Gennes regime、 transition regime以及 Odijk regime，雖然這五種 ，雖然這五種 區域的動態與靜行為已經被 許多前人的模擬所驗證， 然而， 目前為止不管是在理論抑或模擬的結果皆是 建立在中性鏈 (Neutral chain) 模型 上，此完全不考慮任何帶電離子相 關的交互作用。即使他們結果顯示， 中性鏈模型 確實 有助簡化實際高分子系 統的複雜結構，但相較於實際應用系仍差甚鉅特別是關生物高分子在奈微 元件 管道中的探測，例如： DNA 、蛋白質以及肽鏈 …等，這類的高分子 不僅通常離子化，且幾乎 生存在充滿多種離子的緩衝液當中，事實上人體內 的血液 就是標準緩衝。因此，為了瞭解實際的高分子 系統我們利用動力學 (Molecular Dynamics simulation)來模擬此真實高分子侷 來模擬此真實高分子侷 限在圓柱狀管道中 的現象 ，而這套系統為了更加貼近實際情況同時引入含有 單一價 電荷的自 由離子與 由離子所串成的 高分子 (polyelectrolyte)，根據 Debye-Huckel theory，這 些自由離子在溶液中會對高分產生 屏蔽效應 ，導致此系統的高分子行為將更 加地複雜且難以預測。而此次研究的目，即是希望藉由管道、 自由離子與高 分子間的交互作用來了解高被侷限在奈微管道中布與型態 ，並 比較簡 易的中性鏈模型，確認 兩種高分子模型之

Currently, the theories of single polymer confined in the micro/nano channel are classfied to five regime, from weak confinement to strong confinement: bulk, de Gennes,
extended de Gennes, transition and Odijk. The behavior of every regime have been
repeatedly verified by many computer simulation, including the static and dynamic properties, but most of these results are all based on the neutral chain model, and ignore the
interaction with ions which include counterion, cation and anion. Although the assumption of neutral chain model is useful to simplify the complex structure of polymer, this
situation is quite different to the real experiment in which researchers are more interested
in understanding confined biomolecules, such as DNA or protein, in micro/nano-scale devices for biological application.
These biomolecules are not only ionized, but also survive
in the buer which contain many kind of ion. Therefore, to understand the more realistic system, the simulation model should employ charged chains and ions. Including ions
accounts for important electrostatic screening and ion condensation effects, which may
lead to complex phenomenon. In this work, we perform molecular dynamics simulations to investigate charged polymers confined in a cylindrical channel with diameter D.
The coarse-grained method is used to model polyelectrolyte chains and monovalent ions in the solutions, and study the configuration of polymer from the interactions between ions,
polymers and the channel wall.

Abstract------------------------------------- i
摘要----------------------------------------- ii
Acknowledgment------------------------------- iii
Contents------------------------------------- iv
List of figures------------------------------ vi
Introduction--------------------------------- 1
Theory--physics of neutral chain------------- 5
Simulation model and method------------------ 13
Results and Discussions---------------------- 19
Conclusion and Future work------------------- 47

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