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Experimental Confirmation of a Kibble- Zurek Scaling Law in a Nematic Liquid Crystal

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Experimental Confirmation of a Kibble- Zurek Scaling Law in a Nematic Liquid Crystal Experimental confirmation of a Kibble- Zurek scaling law in a nematic liquid crystal A thesis submitted to The University of Manchester for the degree of Master of Science (by Research) in the Faculty of Engineering and Physical Sciences 2014 Nicholas Fowler School of Physics and Astronomy Contents Chapter 1: Introduction ......................................................................................................... 11 References ......................................................................................................................... 13 Chapter 2: Defect formation in the early universe and condensed matter systems .......... 14 2.1 The Kibble mechanism ................................................................................................ 14 2.1.1 Symmetry breaking in the early universe ........................................................... 15 2.1.2 The Higgs field and defect formation in the early universe ............................... 15 2.2 The Kibble-Zurek Mechanism ..................................................................................... 16 2.2.1 Defect formation in condensed matter systems ................................................. 16 2.2.2 Defect annihilation in condensed matter systems ............................................. 18 2.3 Previous experimental work ....................................................................................... 18 2.3.1 Scaling laws in liquid crystals ............................................................................... 19 2.3.1.1 Defect annihilation in liquid crystals ............................................................ 19 2.3.1.2 Defect formation in liquid crystals ............................................................... 20 2.3.2 Scaling laws in other condensed matter systems ............................................... 22 2.3.3 Scaling laws in other experimental systems ....................................................... 24 2.4 Using a liquid crystal system to test the Kibble-Zurek mechanism ........................... 24 References ......................................................................................................................... 26 Chapter 3: Liquid crystals ...................................................................................................... 29 3.1 Definition of a liquid crystal ........................................................................................ 29 3.2 Types of liquid crystals ................................................................................................ 29 3.2.1 Thermotropic liquid crystals ................................................................................ 30 3.2.2 Lyotropic liquid crystals ....................................................................................... 31 3.2.3 Liquid crystal polymers ........................................................................................ 31 3.3 Liquid crystal phases ................................................................................................... 32 3.4 Birefringence in liquid crystals .................................................................................... 33 3.5 Order in liquid crystals ................................................................................................ 34 3.6 Phase transitions ......................................................................................................... 35 3.7 The Fréedericksz transition ......................................................................................... 36 3.8 Defects in nematic liquid crystals ............................................................................... 37 3.8.1 Point defects ......................................................................................................... 37 3.8.2 The Schlieren texture ........................................................................................... 38 2 3.8.3 Generation of defects following phase transitions ............................................. 40 3.8.4 Umbilic defects ..................................................................................................... 40 3.9 Topological classification of defects............................................................................ 41 3.10 Defect dynamics and annihilation ............................................................................ 43 References ......................................................................................................................... 46 4. Experiment ........................................................................................................................ 48 4.1 Overview ...................................................................................................................... 48 4.2 Materials used ............................................................................................................. 48 4.2.1 ZLI-2806 ................................................................................................................ 48 4.2.2 4-butyl-N-[methoxy-benzylidene]-aniline (MBBA) ............................................. 50 4.3 Cell fabrication ............................................................................................................ 50 4.3.1 Glass cleaning ....................................................................................................... 50 4.3.2 The alignment layer ............................................................................................. 51 4.3.3 Device assembly ................................................................................................... 52 4.3.4 Quality control ...................................................................................................... 53 4.4 Experimental set up .................................................................................................... 55 4.4.1 Signal generators and amplitude modulation..................................................... 56 4.4.2 Linkham hot stage and temperature controller .................................................. 58 4.4.3 Nikon Optiphot-pol polarising microscope ......................................................... 58 4.4.3 IDS uEye GigE camera ........................................................................................... 59 4.5 Experimental parameters ........................................................................................... 61 4.5.1 Time delay before measurement of defect density ............................................ 61 4.5.2 Range of ramp rates ............................................................................................. 62 4.5.3 Temperature ......................................................................................................... 63 4.6 Frame selection ........................................................................................................... 65 4.7 Finding the transition point with ImageJ ................................................................... 67 4.7.1 Mean pixel value .................................................................................................. 67 4.7.2 Validating the imageJ method ............................................................................. 68 4.7.3 Measuring the threshold voltage ........................................................................ 69 4.8 Defect counting ........................................................................................................... 71 4.8.1 Algorithm or counting by eye? ............................................................................ 71 4.8.2 Method for counting defects ............................................................................... 73 4.9 Errors............................................................................................................................ 74 References ......................................................................................................................... 75 Chapter 5: Results and discussion ........................................................................................ 76 3 5.1 Defect formation in ZLI-2806 ...................................................................................... 76 5.1.1 Deviation from expected scaling at higher ramp rates ....................................... 79 5.1.3 Earlier deviation from expected scaling at lower temperatures ........................ 86 5.2 Defect formation in MBBA .......................................................................................... 86 References ......................................................................................................................... 88 Chapter 6: Conclusion and future work ................................................................................ 90 Total word count: 20010 4 List of figures 2.1. Results from previous experiments using liquid crystals to confirm the scaling relationship between defect density and time ...................................................................... 20 2.2. String defect formation in 5CB cooled below its transition temperature ...................... 21 2.3. The results from computer simulations comparing the number of defects generated at different quench rates in systems with overdamped and underdamped dynamics ............. 24 3.1. A 4’-pentyl-4-cyanobiphenyl (5CB) molecule . ..............................................................
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