博碩士論文 100222014 詳細資訊




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姓名 余思萱(Szu-Hsuan Yu)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(Dynamics of monomers and dimers in melting transition in an air table system)
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摘要(中) 我們建立了一個二維氣墊床顆粒系統,可以利用控制氣流大小來模擬顆粒系 統中的“溫度”,藉此可利用 此系統來做升溫或降溫的相變實驗。我們設計一 種顆粒monomer是由壓克力材質切割成圓盤狀,裡面嵌 了弱磁性的圓餅狀小 磁鐵,其磁力方向是垂直於monomer表面的。這種顆粒在磁鐵的排斥力和彼 此之間 氣流的作用力下,可以在低溫狀態,均勻地分佈在氣墊床上,並且 是排成六角晶格形狀。晶格線的長度 是2.2公分。除此之外,我們還利用兩 個monoer連接而成一個dimer顆粒,並且重覆升溫相變實驗。

分析這兩組實驗,我們發現monomer的實驗可以進入到液態,但dimer不行。 但兩組實驗都在 Lindemann融化參數約為0.01時,從晶體開始融化。有趣的 現象發生在monomer 跟 dimer 在融化的 過程中。像是monomer有兩種狀態交 錯發生,而dimer有三種。其中 “moving” 狀態和 ”frozen“狀 態是兩種顆粒條 件都有的,而第三種“stuck”只有在dimer條件下發生。“moving”狀態如其名, 顆粒可 以自由的移動跟碰撞。當顆粒移動一陣子後,它們調整自己的位置排 回六角晶格狀,可以維持幾分鐘。 這就是”frozen“狀態。“stuck”發生原因是 一些dimer排成相同的方向,並且限制住附近的dimer也都 無法移動,形成了 區域性的同向。更多的細節我們會在接下來幾章討論。
摘要(英) We built up a 2D air table granular system. We adjust the airflow rate to simulate the granular temperature and operate a melting transition experiment by putting granular particles on it. The mono-particles are designed with a weak magnet embedding in an acrylic disk. Under the affection of the dipolar repulsion from magnet and intermediated air jet between particles, monomers distributed uniformly on the slab and arranged in a hexangular lattice with inter-particle length of 2.2 cm under lower airflow rate. Furthermore, we con- nected two monomers with the length of lattice constant as a dimer particle and repeated the melting experiment.

Analyzing these two experiments, monomer melts from crystal phase to liquid phase, dimer melts, too, but it doesn’t enter liquid phase. Both of their melting point γM is close to 0.01. The behavior of monomers and dimers is interest- ing in melting transition. There are two (monomer) and three (dimer) state switching. They are moving, frozen state. Stuck state only exist in dimer case. In moving state, particles diffuse and collide each other freely and randomly. Particles diffuse for a while, they start re-arranging to form positional disorder into hexangular order and stay in this state for few minutes. Stuck state is due to some oriented dimers restricted their neighbors activities and make locally orientational order. More details of dynamic of these will be discussed in this thesis.
關鍵字(中) ★ 氣墊床
★ 顆粒系統
★ 軟物質
關鍵字(英) ★ airbed
★ granule
★ soft condense matter
論文目次 1 Introduction 1

2

Apparatus and Methods 3

2.1 TheExperimentSetup ............................. 3

2.1.1 Two-dimensionalgas-fluidizedairtable . . . . . . . . . . . . . . . . 3

2.1.2 Monomerparticlesanddimerparticles . . . . . . . . . . . . . . . . 4

2.1.3 Hexagonalmagneticboundary..................... 6

2.2 Videoprocessing ................................ 6

2.3 MeasureofExperiment............................. 6 2.3.1 Meansquaredisplacement ....................... 6 2.3.2 Topologicaldefectsanddefectfraction . . . . . . . . . . . . . . . . 7

2.3.3 Bondorientationalorder........................ 7 2.3.4 Lindemannparameter ......................... 8

2.3.5 Orientationalorderparameter..................... 8

Results and Discussions 10

3.1 Monomer: Transition from crystal to liquid states by heating . . . . . . . . 10

3.1.1 Trajectoryanddefects ......................... 10 3.1.2 Mean-squaredisplacement ....................... 12 3.1.3 Evolution of defect fraction and bond orientational order . . . . . . 14

3.1.4 Lindemannparameter ......................... 16

3.2 Dimer: Transition from crystal to liquid states by heating . . . . . . . . . . 19

3.2.1 Trajectoryanddefects ......................... 19 3.2.2 Mean-squaredisplacement ....................... 20 3.2.3 Evolution of defect fraction and bond orientational order . . . . . . 23

3.2.4 Lindemannparameter ......................... 26

3.2.5 Orientationalorderparameter..................... 26

3.2.6 Evolution of angle correlation with di↵erent boundary . . . . . . . 27

3.3 Dimer:Nucleationindi↵erentdensity..................32 3.3.1 OrientationParameter ......................... 32 3.3.2 AngleCorrelation............................ 32

4 Conclusion 38
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[11] Chen-Hung Wang. Universal scaling laws of di↵usion in two-dimensional granular liquids in an airtable granule system. PhD thesis, National Central University, Jan 2015.

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for 2d melting. Physics Letters, 109A(6):289, June 1985.
指導教授 陳培亮(Peilong Chen) 審核日期 2015-8-26
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