柱狀自泳動粒子之擴散行為與沉降平衡

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姓名

陳冠中(Kuan-Chung Chen) 查詢紙本館藏

畢業系所

化學工程與材料工程學系

論文名稱

柱狀自泳動粒子之擴散行為與沉降平衡
(Diffusion and Sedimentation Equilibrium of Rodlike Nano-Swimmers)

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摘要(中)

自泳動粒子為具備有自我推進而通過周遭流體能力的物體，在自然界中諸如魚類群游、鳥類群飛，或是許多常見細菌如大腸桿菌、衣藻等，近年來許多科學家極力探討有關這些細菌的運動行為。在微觀尺度上，這些自泳動粒子大多有著類似的運動方式，它們會朝著一個方向做直線運動，經過一段時間後，以極短暫的時間停住然後轉向，接著再重複同樣的過程，這種運動模式我們稱之為run-and-tumble motion。在微觀尺度下布朗運動(Brownian motion)會對粒子運動產生影響，布朗運動所造成的轉動擴散(Rotation diffusion)會影響到自泳動粒子行直線運動的時間，意即自泳動粒子在還未tumble之前，其運動方向就已經不再是直線。
　　本研究採用耗散粒子動力學法，模擬pusher類型的桿狀自泳動奈米粒子於有限及無限邊界系統中的運動行為。首先，在無限邊界系統中研究一般奈米硬桿的轉動擴散以及傳送擴散。較長的奈米硬桿擁有較大的轉動擴散係數(rotational diffusivity, Dθ)，意即較長的硬桿較難改變運動方向，而傳送擴散係數(translational diffusivity, D)會隨著奈米硬桿的長度增加而變小，意即較長的硬桿其擴散速率較小。接著，我們施予奈米硬桿一個作用力(active force, FA)，使其獲得泳動的能力，並在無限邊界系統中討論其轉動擴散以及傳送擴散。自泳動奈米硬桿與一般奈米硬桿擁有相同的轉動擴散係數，此外，自泳動硬桿的傳送擴散係數則會與作用力平方及硬桿轉彎所需時間成正比。最後，將自泳動硬桿置於有邊界系統中，以觀察沉降平衡時的變化。當系統達平衡時，自泳動硬桿的濃度分布較為膨潤，且自泳動硬桿的運動方向與重力所施加的方向相反，產生polar order的現象。

摘要(英)

Self-propelled micro-swimmers are biological organisms or synthetic objects that propel themselves through the surrounding fluids. Examples are swimming fish, flying birds, or various swimming bacteria such as Escherichia coli and the green alga Chlamydomonas reinhardtii, etc. In the microscale living system, most of self-propelled bacteria have the same pattern of motion, which they move along one direction with linear motion, after a period of time, they stop suddenly and turn to another direction, and then they repeat the same process. This motion mode is called run-and-tumble motion. The trajectory of its motion is linear in a short interval, then punctuated by sudden and rapid randomizations in direction. However, the motion of the particles will be affect by Brownian motion in microscopic study. The particle will change the direction of the movement because rotational Brownian motion. In other words, the particle won’t move straightly before it tumbles.
In this study, dissipative particle dynamics (DPD) is employed to simulate the rod-like self-propelled nano-swimmers in bounded/unbounded system. For the unbounded system, it is found that the longer nano-rods have the lower rotational diffusivity (Dθ), and the lower translational diffusivity (D). It means, the longer nano-rods need more time to change the direction of the movement, and the rate of the diffusion is lower. Additionally, the nano-rods become the self-propelled nano-swimmers from the active force (FA). The rotational diffusivity of the nano-swimmers is the same as the nano-rods. Both the square of the amount of active force and the time of the nano-swimmers changing the direction of the movement are directly proportional to the diffusivity of the nano-swimmers. For the sedimentation equilibrium, it is found that the sedimentation length of the nano-swimmers is higher than the nano-rod. In addition, the nano-swimmers exhibit polar order under gravity. It means, the nano-swimmers proceed toward reverse direction of gravity.

關鍵字(中)

★ 自泳動粒子
★ 擴散行為
★ 沉降平衡

關鍵字(英)

★ Nano-Swimmers
★ Diffusion
★ Sedimentation Equilibrium

論文目次

摘要.......................................................I
Abstract..................................................II
致謝.....................................................III
目錄......................................................IV
圖目錄.....................................................VI
表目錄.....................................................IX
第一章　緒論.................................................1
　1-1　　簡介...............................................1
　1-2 奈米硬桿的布朗運動....................................1
　1-3 常見的自泳動粒子......................................2
　1-4 Run-and-tumble motion模型..........................4
　1-5 自泳動粒子與周遭流體作用方式............................5
　1-6 自泳動粒子的特性與應用.................................8
　　1-6-1 自泳動粒子的擴散與沉降平衡.....................8
　　1-6-2 自泳動粒子與物質表面間的作用...................12
第二章　模擬原理與方法........................................15
　2-1 耗散粒子動力學(Dissipative Particle Dynamics).......15
　2-2 DPD原理...........................................17
　　2-2-1 DPD作用力 ..................................17
　　2-2-2 噪訊與時間尺度(Noise and Time Step).........21
　　2-2-3 斥力參數(Repulsion Parameters).............21
　　2-2-4 弗洛里-哈金斯理論(Flory-Huggins Theory)......23
　　2-2-5 長度、速度、時間尺度的無因次化.................26
　　2-2-6 積分法求解.................................28
　　2-2-7 週期性邊界條件..............................30
　　2-2-8 Cell List表列法............................31
　2-3 模擬系統與參數......................................32
　　2-3-1 系統基本參數設定.............................32
　　2-3-2 自泳動粒子的設定.............................33
　　2-3-3 牆粒子的設定................................35
　2-4 擴散係數(Diffusion Coefficient, D).................36
　　2-4-1 平均平方位移(Mean Square Displacement, MSD)......................................................37
　　2-4-2 速度自相關函數(Velocity Autocorrelation Function, VAF)............................................38
　2-5 沉降平衡(Sedimentation Equilibrium, SE)............40
第三章　無邊界系統中奈米硬桿擴散行為............................42
　3-1 硬桿的關聯時間......................................42
　3-2 硬桿的轉動擴散係數...................................44
　3-3 硬桿的擴散係數......................................48
第四章　無邊界系統中自泳動奈米硬桿擴散行為.......................51
　4-1 自泳動奈米硬桿的轉動擴散..............................51
　4-2 自泳動硬桿的傳送擴散.................................52
第五章　奈米硬桿的沉降平衡....................................60
　5-1 奈米硬桿的沉降平衡...................................60
　5-2 奈米自泳動硬桿的沉降平衡..............................62
第六章　結論................................................69
第七章　參考文獻.............................................71

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指導教授

曹恆光(Heng-Kwong Tsao)

審核日期

2014-6-11

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