在這研究工作中，我們使用郎之萬動力學(Langevin dynamics simulation)來進行分子動力學模擬以探討單一柔軟的高分子鏈從碟形空腔通過奈米通道噴射(eject)到另一個奈米狹縫空間。基於先前用於高分子鏈從球型空腔噴射至另一空間的理論，我們可以發展出一套用於二維空間的高分子噴射理論以預測噴射速度v及噴射時間τ的尺度行為。藉由改變高分子鏈長N和初始體積分率ϕ_0，我們可以觀察到噴射速度在ϕ_0很大時有兩個主要的尺度行為：(1)當m很大時，v ~ 〖ϕ_0〗^2 m^2/N^2.5。(2)當m很小時，v ~ m^(-1.33)。此外，噴射過程主要由壓縮階段和非壓縮階段所組成。當空腔裡的高分子鏈尺寸相當於碟型空腔尺寸時，噴射過程會從壓縮階段轉換至非壓縮階段。從模擬結果裡，我們可以得知噴射時間也有兩個主要的尺度行為：(1)當ϕ_0很大時，τ∼N^1.83 〖ϕ_0〗^(-1.33)。(2)當ϕ_0很小時，τ∼N^2.25。透過使用能量消散理論(energy dissipation)以及減縮空間效應(shrunk space effect)，我們能夠更精準地去解釋這些尺度行為。

In this work, we perform molecular dynamics simulations with Langevin dynamics to investigate the ejection of single flexible polymer chains from a disc-shaped confinement to the nanoslit through a small pore. Based on the previous theories applied in the polymer ejection from a spherical cavity, the ejection theory for two-dimensional space can be developed to predict the scaling behaviors of the translocation speed v and the ejection time τ. By changing the values of the chain length N and the initial volume fraction ϕ_0, the scaling behaviors for translocation speed are v ~ 〖ϕ_0〗^2 m^2/N^2.5 for large m and v ~ m^(-1.33) for small m as ϕ_0 is large. Furthermore, the ejection process is mainly composed of the compressed stage and the uncompressed stage. When the size of the polymer chain inside the confinement is equal to the size of the confinement, the process of the ejection will be transformed from the compressed stage to the uncompressed stage. From our simulation results, the scaling behaviors for the ejection time also can be obtained：τ∼N^1.83 〖ϕ_0〗^(-1.33) for large ϕ_0 and τ∼N^2.25 for small ϕ_0. These scaling behaviors of the ejection time can be precisely explained via the theory of energy dissipation and shrunk space effect.

Chinese Abstract ... i
English Abstract ... ii
Acknowledgments .... iii
Contents ........... iv
List of Figures .... v
List of Tables ..... viii
Chapter 1 Introduction ... 1
Chapter 2 Theory - Literature Review and Application ... 4
2.1 Equilibrium size of a polymer chain ... 4
2.2 Polymer ejection from a spherical cavity ... 5
2.3 Polymer ejection from a quasi-2D confinement ... 11
Chapter 3 Simulation Model and Method ... 14
3.1 Simulation model ... 14
3.1.1 Particle interactions ... 14
3.1.2 Space confinement ... 15
3.2 Simulation method ... 17
3.2.1 Molecular dynamics simulation ... 17
3.2.2 Langevin dynamics ... 18
3.2.3 Reflecting potential at the pore ... 18
3.3 Simulation process ... 18
3.4 Simulation results ... 19
Chapter 4 Results and Discussions ... 21
4.1 Stages of the ejection process for a disc-shaped confinement ... 21
4.2 Prediction of translocation speed ... 21
4.3 The critical number of monomers inside the confinement ... 24
4.4 Prediction of ejection time ... 24
4.5 Scaling behaviors of ejection time ... 27
4.6 The shrunk space effect from the wall of the confinement .. 29
Chapter 5 Conclusion and Future work ... 33
Bibliography ... 35

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