二維微粒電漿液體之剪力誘發微傳導及等效溫度

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姓名

姚松偉(Chong-wai Io) 查詢紙本館藏

畢業系所

物理學系

論文名稱

二維微粒電漿液體之剪力誘發微傳導及等效溫度
(Shear Induced Micro-Transports and Effective Temperature in 2D Dusty Plasma Liquid)

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摘要(中)

液體在微觀尺度下都被視為一個受到熱擾動作用的非線性多體耦合系統，它的行為非常複雜。此外，當外加剪力的時候，它會偏離平衡態，所以它的微觀行為將變得更複雜。不論在複雜系統或奈米科學，液體的微觀行為一直都是一個重要問題。由於真實系統的尺度太小，所以缺乏良好的直接觀察工具，以致於目前仍然沒有一個很清楚的物理圖像可以描述它的微觀行為。因此，我們藉著實驗室故有的庫倫微粒電漿液體來比照真實系統，從而了解液體分子的微觀行為。
我們將微粒丟入充滿電漿的二維長形空腔中。由於電子有較高的移動力，故空腔與微粒會帶負電，透過庫倫力的交互作用，進而形成二維庫倫液體。由於它獨特的時空結構，具有次毫米級的微粒間距，所以提供了一個光學顯微鏡就可以直接觀察的平台。在這個工作中，我們利用兩度反平衡的雷射來推動腔體最外層的粒子，透過追蹤粒子的運動軌跡及借用擾動－耗散理論的觀念，我們探討了：
(1) 動量的傳導(粘稠度)：它是粒子的平均位移對剪力的比值。在小剪力的情況下，系統有著線性反應，動量傳導是均勻的。在大剪力的情況下，因為粒子間的作用是非線性的，系統的反應也變得不線性，結果動量的傳導變得不均勻。
(2) 粒子的傳導(擴散系數)：它是粒子的均方位移對觀察時間的比值，亦同時反映了熱擾動的強度。儘管剪力的沿著縱方向加在腔體的邊界上，但中間區域及橫向的擾動還是被加強了。原因是分配到每個區域中的動量最後都被轉化為熱擾動。
(3) 等效溫度：透過愛因斯坦方程，我們估算了系統的等效溫度。它具有類似熱力學溫度的物理意義，但可用在不平衡系統中。它能夠反映出系統中每一毎模的能量及能量傳遞的方向從低頻到高頻模。

摘要(英)

We experimentally investigate particle micro-motion and the effective temperature in a quasi-2D dusty plasma Coulomb liquid confined in a narrow mesoscopic channel sheared by two parallel counter laser beams along the opposite boundaries. Liquid at the discrete level can be treated as a strongly coupled many-body system driven by stochastic noise. In addition, under an external shear, it deviates from equilibrium and becomes more complicate. Its micro-dynamics is an interesting and important issue in the study of complex systems and nano-science. However, it is difficult to construct the picture of the particle micro-motion due to the lack of proper direct observation tools and the complexity under the large degrees of freedom. Recently, the development of the dusty plasma liquid formed by the charged micro-meter sized particles suspended in low pressure discharges provides an inspiring experimental platform to study this issue. Due to the proper scale, the spatiotemporal evolutions of particle positions can be directly observed by optical microscope. In this work, by applying two laser shears to push the particle and using the idea of fluctuation-dissipation theorem, we investigate the shear induced micro-transport and the effective temperature:
1. The momentum transport (viscosity) is acquired from the ratio of mean velocity to the shear stress. For small shear, the system has a linear response, and the momentum loaded each region is uniformly. For large shear, the momentum transport is non-uniform due to the non-linear mutual coupling.
2. The particle transport (diffusivity) is acquired from the ratio of mean square displacement to the observation interval which indicates the strength of thermal fluctuation. Although the external shear is applied to the boundary and along the longitudinal direction, the transverse diffusivity is enhanced no matter the boundary and the center region. The momentum loaded to each region is finally converted to heat through the mutual coupling network.
3. The effective temperature of the system is estimated through the Einstein relation. It has similar physical meaning to the thermodynamics temperature, which indicates the energy contained in each mode and the energy cascading direction from low frequency to high frequency modes.

關鍵字(中)

★ 電漿液體
★ 等效溫度
★ 微傳導

關鍵字(英)

★ micro-transports
★ effective temperature
★ dusty plasma liquid

論文目次

Chapter 1 Introduction 1
Chanter 2 Background and Theory 6
2.1 Fluctuation-Dissipation Theorem·····················································6
2.1.1 Fluctuation-dissipation theorem················································7
2.1.2 Einstein relation········································································9
2.1.3 FDT in non-equilibrium system ~ Effective temperature··········11
2.1.4 Multi-time scale characteristics of effective temperature··········12
2.2 Liquids·····························································································16
2.2.1 Microscopic view of liquid·······················································16
2.2.2 Shear-free micro-motion···························································17
2.2.3 Sheared liquid···········································································18
2.3 Dusty plasma liquid·········································································22
2.3.1 Weakly ionized dusty plasma····················································22
2.3.2 Quasi 2D dusty plasma liquid···················································22
2.3.3 Laser shear for a dusty particle·················································24
Chapter 3 Experimental setup 26
3.1 Experimental setup············································································26
3.2 Data analysis······················································································30
Chapter 4 Result and Discussion 31
4.1 Shear-free motions of 2D dusty plasma liquid···································31
4.2 Shear Induced micro-transport···························································37
4.2.1 Particle mean velocity and viscosity·········································37
4.2.2 Particle MSD and diffusion coefficient·····································42
4.3 Effective Temperature of 2D dusty plasma liquid······························49
4.3.1 Multi-time scale characteristics·················································50
4.3.2 Randomization of momentum···················································51
Chapter 5 Conclusion 54
Bibliography 57

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指導教授

伊林(Lin I)

審核日期

2007-7-16

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