Study of Heterogeneous Aggregation, Packing, and Self-Assembly of Colloids using Discrete Elements

膠體粒子(colloid)均勻分散於某種介質中就是所謂的膠體分散系(colloidal dispersion)，應用膠體系統於陶瓷製程已有數百萬年的歷史，而在各種陶瓷製程中，本研究主要著眼於光閘晶體(photonic bandgap crystals, 簡稱PBG crystals)的相關製程，其中，如何維持膠體系統的穩定則是最關鍵的課題。 應用電腦模擬來研究膠體系統的穩定是一個相當有趣的方式，文獻中可以找到不少膠體系統的模擬方法，然而，至今尚未有一個較具代表性的模擬工具，要取得程式碼來根據我們的應用需求加以修改也相當困難。因此，本研究的第一個目標就是開發一個研究膠體粒子動態行為的數值模擬工具。在本研究中，我們根據布朗動力學（Brownian dynamics）的Langevin Equation，整合粒間作用力（主要為DLVO理論）、布朗運動（Brownian motion）和系統力場（field forces），開發了一個物件導向的離散元素模擬程式。程式開發中，解決了模擬過程中的幾何衝突、聚結的形成與移動、碰撞效率等課題，模擬結果並與文獻中的模擬案例以及smoluchowski的聚結理論相比較，來驗證程式的適用性。 本研究的第二個目標是利用上述膠體粒子模擬程式來模擬光閘晶體相關的製程，從觀察模擬過程中的微結構變化來掌握合成光閘晶體的關鍵因素，並以異質聚結(heterogeneous aggregation)、光閘晶體的堆疊(packing of PBG crystals)、利用樣板的自我組裝(template-directed self-assembly)為研究案例。 在異質聚結的案例研究中，對於奈米到次微米等級的膠體粒子，受到布朗運動與DLVO作用的交互影響有深入的探討，從而推論布朗運動對於奈米等級的膠體粒子有顯著的重要性。另外，從對異質聚結製程的模擬，我們也提供合成SiO2/TiO2核殼結構(core/shell structure)複合粒子的重要因素。 在光閘晶體的堆疊案例研究中，我們觀察SiO2顆粒在水中從沉降到聚結成形的過程。藉由觀察堆疊過程中顆粒排列微結構與RDF分析的變化，可以發現當沉積體形成後，顆粒間仍不斷地調整顆粒與顆粒間排列的位置；而當顆粒間的表面互斥能量較大時，可以形成區域性的整齊排列。 在利用樣板的自我組裝的案例研究中，利用簡單的幾何分析，搭配1000顆SiO2取向附生(epitaxy)的模擬驗證，我們認為用來合成三維光閘晶體的樣板，其最佳排列模式為具有2.45r間距的方形排列。 總和而言，利用電腦模擬配合實驗觀察的研究方法，十分適合膠體系統製程的研究，後續將可期待更廣泛的應用。A colloidal dispersion is a system in which the dispersed particles through the medium are much larger than the molecules of the medium. Ceramic manufacturing has been processed by means of the colloidal system for several millennia. The colloidal system applications in this study focus on photonic bandgap (PBG) crystal related processes where the maintenance of the stability is critical. Computer simulation offers a potential means to study colloidal stability. Several simulation methods have been presented in the literature for the colloidal system simulation. However, none of them is eminent and none of the source code is available for further modification to conduct our application cases of interests. Thus, the first objective of this study is to develop a simulation program which can properly mimic the dynamic behaviors of colloids in a finite system. In this study, an Object-Oriented DEM (discrete element method) based Brownian dynamics simulation system is developed to mimic the integrated behavior of colloidal particles in a suspension. The Langevin-type equations of motion are employed in the DEM simulation program to govern the movement of colloidal particles subjected to inter-particle interactions (mainly DLVO interaction), field forces, and the Brownian motion (in diffusive scale). Several techniques are proposed to solve the relating problem during the simulation, including the overlapping of particles, formation of agglomerations, and the collision efficiency. Simulation cases of a centrifugal casting and a rapid Brownian coagulation have been conducted to verify the feasibility of the program. The simulation results agree well with the simulation results reported in the literature and the theoretical predictions of Smoluchowski’s kinetics of coagulation theory. The second objective is to seek the implications of the recipe for synthesizing the PBG crystals by monitoring transformation during simulation. To this end, three simulation cases were conducted; these include coating PBG particles by heterogeneous aggregation, packing of PBG crystals, and template-directed crystallization of PBG crystals. For the case of heterogeneous aggregation, intensive studies have been conducted to understand the importance of Brownian motion for colloidal particles in nano and sub-micron scales. The importance of Brownian motion was illustrated when the particle size is in the order of ten nm. The recipes for synthesizing core/shell structures by mean of heterogeneous aggregation were suggested. For the case of PBG crystal packing, the processes of self-assembly of the silica spheres on the solid substrate were studied. The evolution of the positional order in the process of the assembly was demonstrated by means of snapshots visualization and RDF analysis. We found that particles inside a sediment cake continue adjusting their positions by inter-particle interactions even after the height of the sediment cake has reached a stable condition. For the case of template-directed crystallization, a simple and heuristic analysis to find the most appropriate template pattern to synthesize well-ordered PBG by colloidal epitaxy was proposed. The analysis was verified by a series of simulations based on a system of 1000 SiO2 particles. The cubic array template provided only one kind of site for the upward layers. A cubic array with lattice spacing of 2.45r was illustrated to be the best designed template for synthesizing the PBG crystals. In conclusion, we have shown that computer simulation is a proper tool to study the colloidal process, for example, to monitor the transformation from the initial state to the consolidated result. The collaboration of simulations and experiments on studying the colloidal processes have been demonstrated in this study, and we believe that further novel advancing through such venue is expected in the future.Table of Contents 誌謝 I 摘要 III Abstract V Table of contents VII List of Figures XI List of Tables XVII Chapter 1 Introduction 1 1.1 General 1 1.2 Colloidal domain and computer simulation 3 1.3 PBG colloidal system for applications 6 1.4 Objectives and outlines 7 Chapter 2 Theories and Simulation Methodologies 9 2.1 Introduction 9 2.2 DLVO theory 10 2.2.1 van der Waals forces 11 2.2.2 Electrostatic forces 13 2.2.3 DLVO theory in force field 15 2.3 Very-short-range force and JKR adhesion theory 16 2.4 Brownian motion 18 2.4.1 Random walk of Brownian motion 18 2.4.2 Brownian dynamics simulation 19 2.5 Object-Oriented colloidal particle simulation system 22 2.5.1 Governing equations over separation distance 23 2.5.2 Particle agglomeration 25 2.5.3 Collision efficiency 26 2.5.4 Verification of the simulation program 27 Chapter 3 Modeling Motion and Interaction of Nanosized Bimodal Colloids 35 3.1 Introduction 35 3.2 Brownian motion v.s. DLVO of silica and tinania 38 3.3 Simulation and discussion 53 3.4 Concluding remarks 57 Chapter 4 Simulation of Colloidal Particle Packing for Photonic Bandgap Crystals 59 4.1 Introduction 59 4.2 Experimental 60 4.3 Simulation process 63 4.4 Simulation results and discussion 69 4.5 Concluding remarks 77 Chapter 5 The Simulation on Synthesizing 3D PBG Crystals by Self-assembly with Proper Template 79 5.1 Introduction 79 5.2 Geometrical analysis for optimum template 81 5.3 Simulation and discussion 87 5.4 Concluding remarks 92 Chapter 6 Conclusions 93 6.1 Summary 93 6.2 Future studies 95 Reference 97 Appendix A Object-Oriented Discrete Element Simulation System of Brownian Dynamics 103 A.1 System design 103 A.2 Classes 104 A.3 Simulation parameters 105 A.4 Post processing 107 Appendix B A Tutorial to Estimat