微粒電漿液體之微觀運動與結構重整

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姓名

詹佳玲(Chia-ling Chan) 查詢紙本館藏

畢業系所

物理學系

論文名稱

微粒電漿液體之微觀運動與結構重整
(Micro-motions and structuralrearrangements in dustyplasma liquids)

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摘要(中)

在巨觀尺度下，不同於固體受到微小外力時，產生彈變，在兩平行侷限板中的液體受到微小外加剪力時，不僅緩慢流動，產生塑變，且速度場在橫向位置成線性直線分佈。然而，隨著把兩平行侷限板間距降到介觀(~ 幾個分子)尺度時，研究者發現，在狹窄狹縫中的液體不僅動力行為變的十分緩慢，且臨侷限板邊界的液體分子傾向沿侷限板排列成整齊的層狀結構。此外，當施予微小外加剪力時，此超薄液體除呈現黏彈反應，而且展現非線性剪薄與剪帶的物理現象。超越連續極限的觀念，液體無法視為均勻的連續體；液體的密度與固體相近，分子與分子間的作用力，仍然強大，而分子的質量甚小，背景的熱擾動無法再被忽略。在不連續組成分子和侷限板所形成的拓普侷限，與隨機熱擾動和外加剪力所組成的驅動力間的交互作用下，介觀剪力液體不但在結構上，並且在動力行為上，皆展現異質特性。瞭解上述超薄液體的奇異現象，不僅對基礎物理研究有貢獻外上，且在奈米科技應用上，也著實重要。
微粒電漿液體是由一群米級帶負電的粒子懸浮在低壓力的弱游離氣體中組成。由於微粒之間的間距約0.3豪米，故能透過光學顯微鏡直接觀察微粒電漿液體的微觀結構並且能追蹤每個粒子的運動軌跡。我們將微粒電漿液體侷限在幾個微粒寬的兩平行板間，並利用兩平行的雷射光束施加連續穩定或週期交頻的剪力在此介觀液體的邊界。
我們發現在不連續組成分子和侷限版所形成的拓撲侷限，與隨機熱擾動和外加剪力所組成的驅動力間的交互作用下，當介觀液體受到連續穩定和週期交頻的剪力時，同樣呈現非線性剪薄和剪帶，與黏彈反應。藉由一些統計運算分析，例如：速度場與黏滯係數對外力的關係，時空結構關連函數，位移與結構重整的相關機率等，我們深入探討形成上述現象的本源並加以比較其他玻璃態系統的異同性。

摘要(英)

Macroscopically, liquid °ows smoothly under external shears. Neverthe-
less, the physical picture of a sheared liquid beyond the continuous limit
remains elusive. The studies of micro-motions and structures in a sheared
liquid have been mainly limited to the macroscopic force and the velocity
measurement on the con¯ning boundary because of the lack of microscopic
measures at the small scale, which is insu±cient to provide an obvious mi-
croscopic picture at the discrete molecular level.
A dusty plasma liquid (DPL) formed by micrometer sized dust particles
negatively charged and suspended in a low-pressure weakly ionized discharge
background is an inspiring system to mimic and understand the generic dy-
namical behaviors of a liquid in nature at the kinetic level because of the
capability of directly visualization. Vertically, the suspended dust particles
are aligned through the wake-¯eld e®ect of the downward ion °ow. Thus,
these particles cannot hop vertically. When the number of particles in each
chain is less than 10, particles in the same chain move together horizontally.
Consequently, it can be regarded as a quasi-2D system. In this work, us-
ing a con¯ned mesoscopic quasi-2D DPL sheared by two counter steadily
or periodic chopped laser beams along the opposite boundaries, we investi-
gate the shear banding and thinning, and explore the physical origins of the
visco-elastic response of a thin liquid through correlating the micro-structural
evolution and displacements using a novel correlation probability method.
We demonstrate the shear banding and the enhanced avalanche-type lo-
cal topological transitions with stress relaxation in the form of clusters in
steadily sheared mesoscopic dusty plasma liquids. The frequently avalanche-
type structural rearrangements exhibiting in the outer sheared zone dissipate
i
the external stress and screen the momentum cascaded into the center. It
leaves two outer thin regions a few inter-particle distance in width with high
shear rate sandwiching a plug-like central region with low shear rate. When
we use the periodic moderated shear-pulse instead of a constant stress, the
visco-elastic response is observed. The relations of the elastic (reversible)
and viscous (irreversible) responses and the topological structural memory
are further identi¯ed by correlating the micro-structural evolutions and dis-
placements in the laser-on and -o® durations. The plastic deformation is
generated by bond breaking, kinking, and reconnection through hopping.
The strain energy accumulation in the twisted regions without topological
rearrangement is the source for local rebound. The reorganized structure ex-
hibits di®erent spatiotemporal response in the next stress-on and -o® cycle.
In addition, increasing the number of particles, we can turn the quasi-2D
DPL into the ’’2+1’’D DPL which is composed the bundles of long vertical
particle chains. A digital stereo video particle imaging system is constructed
to directly track the trajectories of particles in the xy planes at di®erent
heights. We present the micro-motions of the ’’2+1’’D DPL at the di®erent
heights, identify its basic excitations. The preliminary observation of the
dynamical behaviors of the entanglement, breaking and reconnection are also
investigated and discussed in this thesis.

關鍵字(中)

★ 微粒電漿
★ 流變學
★ 黏彈性
★ 庫輪液體
★ 剪薄
★ 剪帶

關鍵字(英)

★ Dusty plasma
★ Coulomb liquid
★ shear banding
★ visco-elastic response
★ rehology

論文目次

1 Introduction 1
2 Background and theory 7
2.1 Rheology of liquids . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Responses to a moderate constant shear . . . . . . . . 7
2.1.2 Responses to a moderate time-dependent shear: Visco-
elastic response . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 Liquid in a tight gap . . . . . . . . . . . . . . . . . . . 10
2.2 Micro-motions and structural arrangements in liquids . . . . 11
2.2.1 Pictures beyond the continuous limit of the liquid . . 11
2.2.2 Micro-dynamics in '2+1'D vortex liquids . . . . . . . 16
2.3 Dusty plasma system . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Radio frequency glow discharges and dusty plasmas . 18
2.3.2 Previous studies on quasi-2D strongly coupled dusty
plasma liquids . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Topological defects, Bond-orientational order and spatiotem-
poral correlation functions . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Topological defects . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Bond-orientational order and its spatiotemporal cor-
relations, g6(r) and g6(¿ ) . . . . . . . . . . . . . . . . 22
2.4.3 Joint probabilities and correlation probabilities of suc-
cessive events . . . . . . . . . . . . . . . . . . . . . . . 24
3 Experiment and data analysis 28
3.1 Quasi- 2D sheared mesoscopic dusty plasma liquids . . . . . 28
3.1.1 Experimental setup . . . . . . . . . . . . . . . . . . . 28
3.1.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 The dynamics of '2+1'D dusty plasma liquids . . . . . . . . . 32
3.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . 37
4 Result and Discussion 38
4.1 Shear responses to mesoscopic dusty plasma liquids . . . . . 39
4.1.1 Shear-free mesoscopic dusty plasma liquids . . . . . . 39
4.1.2 Non-linear velocity response to steady shears . . . . . 41
4.2 The ¯nite size e®ect . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Micro-motions to time-dependent shear stresses . . . 48
4.2.2 Visco-elastic response to the periodically moderate shear 49
4.2.3 Histograms of longitudinal displacements . . . . . . . 57
4.2.4 Finite-size e®ect . . . . . . . . . . . . . . . . . . . . . 61
4.3 Micro-origins of the elastic, the viscous, and the visco-elastic
responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.1 The correlation probability of micro-motions in one
laser-on and -o® cycle . . . . . . . . . . . . . . . . . . 65
4.3.2 Motions associated with local structural changes and
temporal correlation . . . . . . . . . . . . . . . . . . . 69
4.3.3 The correlation of micro-motions and structural changes
under a shear-pulse . . . . . . . . . . . . . . . . . . . . 71
i
4.3.4 Micro-origin of the visco-elastic response . . . . . . . . 78
4.3.5 The correlation between longitudinal displacement and
structural arrangement . . . . . . . . . . . . . . . . . . 83
4.4 '2+1'D dusty plasma liquids . . . . . . . . . . . . . . . . . . . 85
4.4.1 Micro-motions in '2+1'D liquids . . . . . . . . . . . . 85
5 Conclusion..............95

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指導教授

伊林(Lin I)

審核日期

2008-4-29

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