Topological Formations in Chiral Nematic Droplets (eBook)

Supervisor’s Foreword 6
Acknowledgments 8
Abstract 9
Contents 10
1 Introduction 13
References 15
2 Liquid Crystals—An Overview 16
2.1 Nematic Order 16
2.2 Chiral Nematics 17
2.3 Free Energy Expansion 19
2.4 Anchoring 21
2.5 Topological Defects in Nematics 22
2.5.1 Topological Defects in Two Dimensions 24
2.5.2 Three-Dimensional Topological Defects 25
2.5.3 Topological Defects in Chiral Nematics 30
2.6 Optics of Liquid Crystals 32
2.6.1 Optics of Chiral Nematic Liquid Crystals 34
References 36
3 Liquid Crystal Droplets 39
3.1 Chiral Nematic Droplets 41
3.2 Chiral Nematic Droplets with Homeotropic Anchoring 43
References 46
4 Experimental Inspection of Director Fields 50
4.1 Confocal Microscopy 52
4.2 Fluorescent Confocal Polarising Microscopy 54
References 60
5 Materials and Experimental Setup 61
5.1 Materials 61
5.1.1 Liquid Crystal Mixture 61
5.1.2 Emulsion Matrix 63
5.1.3 Fluorescent Dye 64
5.1.4 Sample Preparation 65
5.2 Microscopy Setup 66
5.2.1 Numerical Processing of Data and Visualisation 68
References 69
6 Simulated Annealing for Determination of z-Component Sign 71
6.1 Testing the Algorithm 72
6.1.1 Continuity as the Evaluating Criterion in the Boltzmann Factor 74
6.1.2 Boltzmann Factor with Landau-de Gennes Free Energy 76
6.2 Implementing the Simulated Annealing Algorithm on Experimental Data 78
6.2.1 Bleaching Corrections 80
6.2.2 Deconvolution 80
6.2.3 Offset Correction and Normalisation 83
6.3 Calibration of the Annealing Algorithm on Experimental Data 85
6.3.1 Nematic Homeotropic Droplet 85
6.3.2 Chiral Nematic Droplet with a Complex Director Structure 88
6.3.3 Skyrmions and Torons in Homeotropic Cells 91
References 94
7 Structures in Chiral Nematic Droplets with Homeotropic Anchoring 96
7.1 Droplet with a Single Point Defect and a Cholesteric Bubble 96
7.2 Droplets with Layered Structures 99
7.2.1 Droplets with Bent Layers 100
7.2.2 Droplets with Flat Layers 102
7.2.3 Cylindrical Layers 103
7.2.4 Cholesteric Finger with a Central Hyperbolic Point Defect 106
7.2.5 The Lyre/Yeti Structure 107
7.2.6 Droplets with Disclination Lines 110
7.2.7 Combinations of Cholesteric Bubbles and Cholesteric Cylinders 119
7.3 Strings of Point Defects 124
7.4 Higher-Charge Topological Point Defects 141
7.4.1 -2 Point Defect 141
7.4.2 -3 Point Defect 145
7.4.3 Structure of the Higher-Charge Point Defects 149
7.5 Topological Molecules 152
7.5.1 Topological Molecules with Higher-Charge Defects 152
7.5.2 Topological Molecules with Disclination Lines 160
7.5.3 Other Topological Molecules 165
References 166
8 Schematic Construction of Droplets with Multiple Cholesteric Bubbles 168
8.1 Construction of String-Like Constellations 168
8.2 Construction of Topological Molecules with Higher-Charge Point Defects 170
Reference 175
9 Discussion 176
References 187
10 Conclusion 189
References 192