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Energy Minimization in Nematic Liquid Crystal Systems Driven ENERGY MINIMIZATION IN NEMATIC LIQUID CRYSTAL SYSTEMS DRIVEN BY GEOMETRIC CONFINEMENT AND TEMPERATURE GRADIENTS WITH APPLICATIONS IN COLLOIDAL SYSTEMS A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Jakub Kolacz December 2015 © Copyright All rights reserved Except for previously published materials Dissertation written by Jakub Kolacz B.S., DePaul University, USA 2010 Ph.D., Kent State University, USA 2015 Approved by Dr. Qi-Huo Wei , Chair, Doctoral Dissertation Committee Dr. Antal I. Jákli , Members, Doctoral Dissertation Committee Dr. Robin L. Selinger , Dr. Elizabeth Mann , Dr. Mietek Jaroniec , Accepted by Dr. Hiroshi Yokoyama , Chair, Chemical Physics Interdisciplinary Program Dr. James L. Blank , Dean, College of Arts and Sciences TABLE OF CONTENTS LIST OF FIGURES ..................................................................................................... VIII LIST OF TABLES .........................................................................................................XX ACKNOWLEDGEMENTS ........................................................................................ XXI CHAPTER 1 INTRODUCTION ..................................................................................... 1 1.1 Liquid Crystals in Confined Geometry ..................................................................... 1 1.2 Transport Phenomena in Colloidal LC Systems ....................................................... 3 1.3 Active Colloidal Systems .......................................................................................... 5 1.4 Motivations, Applications and Brief Summary of the Dissertation .......................... 6 CHAPTER 2 TOPOLOGY IN NLCS ............................................................................. 8 2.1 From Topology to NLCs ........................................................................................... 8 2.1.1 Defects ............................................................................................................. 9 2.1.2 Homotopy Groups in Sn ................................................................................ 12 2.1.3 NLCs: Homotopy in RPn ............................................................................... 14 2.1.4 Schlieren Textures ......................................................................................... 18 2.1.5 Elastic Free Energy ....................................................................................... 19 2.2 Simulation Methods ................................................................................................ 21 2.3 NLCs under External Geometric Confinement ....................................................... 27 2.3.1 Pair Annihilation in RPm ............................................................................... 29 2.3.2 Spherical Caps on Planar and Homeotropic Surfaces ................................... 31 2.3.3 Spherical Caps on 2D Defects ....................................................................... 33 iii 2.4 Summary ................................................................................................................. 36 CHAPTER 3 NLC ON CHEMICAL PATTERNS ...................................................... 37 3.1 NLC Drops on Surfaces .......................................................................................... 37 3.1.1 Contact Angle ................................................................................................ 37 3.1.2 Fluid Droplets on Chemically Patterned Surfaces ........................................ 39 3.1.3 Surface Energy of LCs .................................................................................. 42 3.1.4 Surface Alignment of NLCs .......................................................................... 43 3.2 Materials, Methods and Characterization ................................................................ 44 3.2.1 Materials ........................................................................................................ 44 3.2.2 Contact Angle Measurement ......................................................................... 45 3.2.3 Pre-Tilt Angle Measurement ......................................................................... 47 3.2.4 Monolayer Self-Assembly............................................................................. 50 3.2.5 Cell Fabrication ............................................................................................. 51 3.3 Characterization of 5CB on SAMs .......................................................................... 53 3.3.1 SAM Morphology ......................................................................................... 53 3.3.2 Contact Angle Results ................................................................................... 53 3.3.3 Pre-Tilt Angle Results ................................................................................... 55 3.4 Chemical Patterning ................................................................................................ 56 3.5 Droplet Self-Organization ....................................................................................... 58 3.5.1 Spincoating .................................................................................................... 59 3.5.2 Cell Breaking................................................................................................. 61 iv 3.5.3 Solvent Evaporation ...................................................................................... 63 3.5.4 Dragged Drop ................................................................................................ 65 3.5.5 Droplets on Patterned Domains..................................................................... 68 3.6 Internal Director Structures ..................................................................................... 70 3.6.1 Defect Position and Annihilation in Ellipsoidal Caps ................................... 72 3.6.2 Spherical Caps of Chiral LCs ........................................................................ 74 3.7 Simulations of Internal Director Structure .............................................................. 75 3.7.1 Effect of Contact Angle and System Size ..................................................... 75 3.7.2 NLCs on Circular Domains ........................................................................... 76 3.7.3 SAM Surfaces ............................................................................................... 78 3.8 Summary ................................................................................................................. 81 CHAPTER 4 THERMOPHORESIS IN NEMATIC LIQUID CRYSTALS ............. 84 4.1 Thermophoresis: Background ................................................................................. 84 4.1.1 Thermophoresis in Fluids .............................................................................. 87 4.1.2 Temperature-Dependent Thermophoresis ..................................................... 89 4.1.3 Applications .................................................................................................. 91 4.2 Colloids in Nematic Liquid Crystals: Background ................................................. 94 4.2.1 Colloidal Liquid Crystals .............................................................................. 95 4.2.2 Observations of Motion by Elastic Forces .................................................. 101 4.3 Motivations ............................................................................................................ 103 4.4 Methods ................................................................................................................. 103 v 4.4.1 Cell Fabrication ........................................................................................... 103 4.4.2 Gradient Heat Stage .................................................................................... 104 4.4.3 Particle Tracking ......................................................................................... 107 4.5 Control Experiments: Negative Thermophoresis in NLCs ................................... 108 4.6 Thermophoretic Motion of Colloids in NLCs ....................................................... 110 4.6.1 Positive and Negative Thermophoresis in 5CB .......................................... 113 4.6.2 Homeotropically Anchored Colloids in 5CB .............................................. 115 4.6.3 Theory ......................................................................................................... 119 4.6.4 Additional Observations .............................................................................. 122 4.6.5 Elastophoresis vs Traditional Thermophoresis ........................................... 127 4.7 Summary ............................................................................................................... 128 CHAPTER 5 SELECTIVE POLYMERIZATION OF LC COLLOIDS ................ 130 5.1 Introduction ........................................................................................................... 130 5.1.1 Self-Folding Structures ............................................................................... 130 5.1.2 LC Polymers ................................................................................................ 131 5.1.3 Motivations.................................................................................................
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