Disorder to order transition of layering and intralayer  structures in confined three-dimensional Yukawa liquids

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趙翊丞(Yi-Cheng Zhao) 查詢紙本館藏

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物理學系

論文名稱

(Disorder to order transition of layering and intralayer structures in confined three-dimensional Yukawa liquids)

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摘要(中)

強耦合多體系統在液態下，微觀結構與動力行為，由三基本要素決定，分別為背景熱擾動、粒子間交互作用、及外在拓樸侷限。粒子間交互作用與平面邊界造成拓樸侷限，粒子垂直於平面的運動受到抑制並沿邊界排列，進而促使層狀結構形成，然而，熱擾動驅使粒子無序運動，導致層狀排列惡化，因此隨垂直邊界之距離減少，侷限效應增強，促使結構逐漸由液體轉變為層狀。此層化轉換未曾從微觀尺度被探討。
近世研究發現，非平衡延展系統在外界驅動增強所展現的非平衡有序-無序(或無序-有序)相轉變可遵循展透理論(percolation theory)的普世規範。在非平衡狀態下，有序與無序點在空間中形成團簇般非均質(heterogeneous)分布，隨外加驅動增強(減弱)，系統異質性增加，無序(有序)結構增加促使無序(有序)團塊擴張，進而形成巨大的團塊展透(percolate)至整個空間。然而，在對冷液體在微觀尺度下，受邊界侷限效應增強所誘發的層化與微結構之無序-有序相轉變是否亦遵循上述展透相變行為，仍為未被探討之重要議題。
此研究中，我們透過數值模擬受兩對稱平面邊界侷限之三維湯川(Yukawa)液體，分析計算局部結構有序性，訂出各層中層化秩序點(layering order site, LOS)與粒子排列結構秩序點(intralayer structural order site, SOS)，探討隨至邊界距離縮短，如何由均相液體到分層結構中其層中 LOSs 與 SOSs 如何演變，並從其中了解溫度扮演角色及重要性。
研究發現 LOSs 與 SOSs 展現高度空間關聯，在固定溫度下，LOSs 與 SOSs在與邊界平行之二維層中形成團簇，隨平面與邊界距離縮減，逐漸占據整個平面，最終形成一個展透空間的巨型團簇，層化團簇大小呈現無尺(scale-free)冪次分布，且在臨界點的尺度指數(scaling exponent)亦展現類似在非線性系統中由規則至紊亂展透轉換的普世規律。

摘要(英)

For liquids confined by flat boundaries, microscopic structures and particle motions are determined by three important factors: thermal agitation, mutual interaction, and topological constraint of the flat boundary. Due to the interplay of mutual interaction and the topological constraint from the flat boundary, the particles nearby the boundary are lined up and their transverse motions are suppressed, leading to the formation of stacked layered structures nearby the boundary. Conversely, thermal agitation serves as the disordered source deteriorating layering. As the distance to the boundary decreases, the confinement effect intensifies, leading to a transition in micro-structures from a liquid state to layered arrangements. Despite its importance, understanding this layering transition down to the microscopic level is still an unexplored issue.
Recent studies in various nonlinear extend systems, such as forest fire, power grid failure, epidemic spread, colloids gelation, solid exhibiting yielding, and turbulent transitions in hydrodynamic flow and nonlinear waves, have demonstrated the order-disorder/disorder-order transitions under varying control parameters belong to the general category of percolating transition, the formation of a spanning network through the connection of active (inactive) sites, associated with the rapid smooth rise of the fraction of active (inactive) sites. With increasing (decreasing) drives, those systems exhibit smooth rapid increases in the fraction of disordered (ordered) sites, associated with the heterogeneous emergence of ordered (disordered) sites in the form of clusters, which can grow and form a percolating cluster spanning over the system. However, the generic behaviors of layering transition in cold liquids under confinement down to the microscopic level, and whether the generic transition behaviors also follow those governed by percolation theory remain unexplored.
Here, the above unexplored issues are investigated in a 3D Yukawa liquid confined by two parallel flat boundaries, using molecular dynamic simulation. The layered order sites (LOSs) and intralayer structural order sites (SOSs) in each layer are identified by calculating local layering and intralayer structural orders. Their correlation and the role of temperature on the layering transition are also studied.
It is found that, LOSs and SOSs exhibit strong positive spatial correlation. At a fixed low temperature, the fraction of LOSs (SOSs) shows a smooth rapid growth with decreasing distance to the boundary. LOSs (SOSs) emerge in the form of clusters with various sizes exhibiting power-law cluster size distributions. The scaling exponents of the power-law distribution gradually increase before a large percolating cluster spanning over the space appears, akin to the transition governed by percolation theory.

關鍵字(中)

★ 滲流理論
★ 湯川液體
★ 層化
★ 無序-有序相變

關鍵字(英)

★ Percolation theory
★ Yukawa liquid
★ Layering transition
★ Disorder-order transition

論文目次

Chapter 1 Introduction...1
Chapter 2 Background...5
Chapter 2.1 Microscopic liquids under confinement...5
Chapter 2.1.1 Microstructures and motions of 2D cold liquids...5
Chapter 2.1.2 3D liquids under confinement from flat boundary...6
Chapter 2.2 Non-equilibrium order-disorder transition...7
Chapter 2.2.1 Percolating transition...8
Chapter 3 Simulation method and data analysis...9
Chapter 3.1 Simulation method...9
Chapter 3.1.1 Langevin type equations of motion...9
Chapter 3.2 Identification of structural order and disorder sites...10
Chapter 3.2.1 Identification of layering order site...10
Chapter 3.2.2 Identification of intralayer structural order site...12
Chapter 4 Result and Discussion...13
Chapter 4.1 Formation of layer structures under different temperatures...13
Chapter 4.2 Heterogeneous distributions of layering and intra-slab structures orders...14
Chapter 4.3 Percolating transition from disorder to order...17
Chapter 4.4 Scaling behavior of multiscale clusters...19
Chapter 4.5 Effect of changing thresholds for binarizing local orders...21
Chapter 4.6 Correlation of heterogeneities in structural orders...23
Chapter 5 Conclusion...26
Reference...28

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指導教授

伊林(I Lin)

審核日期

2023-7-26

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