ELECTROOPTIC STUDIES OF LIQUID CRYSTALLINE PHASES AND MAGNETICALLY LEVITATED AQUEOUS BRIDGES by NEHA MEHUL PATEL Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Dr. Charles Rosenblatt Department of Physics CASE WESTERN RESERVE UNIVERSITY May 2004 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents List of Figures 3 Acknowledgments 6 Abstract 8 Chapter 1. Introduction to Liquid Crystals 10 1. Introduction ……….……………………………………………………. 10 2. Building Blocks …….....…………………………………..................... 14 3. Phases of Liquid Crystals ……..…………………………………….... 17 4. Static Distortions in Nematic Liquid Crystals ……..……………….. 23 5. Anisotropy-related Properties of Liquid Crystals ……...…………... 25 6. Outline of Experiments …….……………………………………........ 27 Chapter 2. Velocity of an Electric-field-induced Synclinic Solitary Wave Invading the Anticlinic Liquid Crystal Phase 29 1. Antiferroelectric Liquid Crystals ……….……………………………. 29 2. Motivation ……….……………………………………………………... 32 3. Experimental Design …………..………………………………………. 33 4. Results ……….………………….………………………………………. 38 5. Conclusion ……….………..……………………………………………. 39 6. Future Work .……………..……………………………………………. 40 Chapter 3. Reentrant Synclinic Phase for Enantiomeric Mixtures of an Antiferroelectric Liquid Crystal 43 1. Reentrant Phases ……….………………...……………………………. 43 2. Antiferroelectric Liquid Crystals ……….…………………………….. 44 3. Experimental Design ……….……………………………………….…. 47 4. Discussion ……….………………………………………………………. 49 5. Theoretical Model ……...………………………………………………. 54 6. Conclusion ……….…………………………………..…………………. 63 7. Future Work …….………………………………………………..……. 63 Chapter 4. Twist Elasticity and Anchoring in a Lamellar Nematic Phase 66 1. Introduction to Lamellar Phases …….……………………...…..……. 66 2. Experimental Design ……………………………………………..……. 69 3. Discussion …….………………………….………………………..……. 80 4. Conclusions and Future Work …………………………………..……. 81 Chapter 5. Possible Structures for the Lamellar Isotropic and Lamellar Nematic Phases 85 1. Introduction …….………………………………………………………. 85 2. Experimental Design …….……………………………………….……. 87 3. Discussion …….……………….…………………………………..……. 95 4. Conclusions and Future Work …….…………………………....……. 103 1 Chapter 6. Transient Dynamics of Liquid Bridges in Simulated Microgravity 106 1. Introduction …….………………….……………………………..……. 106 2. Experimental Technique ………..………………………………..……. 109 3. Results and Discussion …….………………………………………….. 118 4. Conclusion …….…………………………………………………..……. 123 Chapter 7. Stability Limits of Connected Liquid Bridges 128 1. Introduction …….………………………………………………..…….. 128 2. Experimental Design …….…………………………………………….. 132 3. Theoretical Predictions …………………………………………..……. 139 4. Discussion …….………………………………………………..……….. 140 5. Conclusion ……….………………………………………………..……. 143 Appendix A 147 Appendix B 149 2 List of Figures Figure 1 - 1: Schematic illustration of the solid, liquid crystal, and liquid phases. The elliptical shapes represent molecules. 11 Figure 1 - 2: Liquid crystal molecule with polar angle θ and azimuthal angle φ with respect to n 12 Figure 1 - 3: Structure of PAA. 14 Figure 1 - 4: Generic structure of organic molecules forming either nematic or smectic phases. 15 Figure 1 - 5: Example of discoid molecular structure 16 Figure 1 - 6: Schematic of Main Chain Polymer structures 16 Figure 1 - 7: Schematic of Side Chain Polymer structures 17 Figure 1 - 8: Structure of the Nematic Phase 18 Figure 1 - 9: Structure of the Cholesteric or Chiral Nematic Phase 19 Figure 1 - 10: Structure of the Smectic-A Phase 20 Figure 1 - 11: Structure of the Smectic-C Phase 21 Figure 1 - 12: Structure of the Smectic-CA* Phase 22 Figure 1 - 13: Common distortions in liquid crystals 24 Figure 2 - 1: Sm-CA*phase (left) for an infinitely long helical pitch at electric field E=0. The angle θ describes the polar tilt of the molecules with respect to the layer normal and P is the layer polarization. For a moderately large electric field E, a transition to a synclinic phase Sm-C* phase (right) occurs. 31 Figure 2 - 2: Chemical structure of TFMHPOBC. 35 Figure 2 - 3: Experimental Apparatus: The smectic layers lie in the x-y plane. The image of the liquid crystal is enlarged by a factor of 35 at the two optical fibers F1 and F2, placed behind the analyzer. 35 Figure 2 - 4: Typical trace of the two optical signals temporally separated by ms. With a virtual fiber separation x = (2980 m/35) = 85 m, we deduce a velocity v=14.2 cm/s. 37 Figure 2 - 5: Time-of-flight versus virtual fiber separation x for several values of reduced field Er at T=113 degrees C: the symbol key is shown. 39 Figure 2 - 6: Velocity v as a function of Er obtained from a linear fit of the data in Figure 2-5. 40 Figure 3 - 1: Sm-CA*phase (left) for an infinitely long helical pitch at electric field E=0. The angle θ describes the polar tilt of the molecules with respect to the layer normal and P is the layer polarization. For a moderately large electric field E, a transition to a synclinic phase Sm-C* phase (right) occurs. 45 Figure 3 - 2: Chemical structure of TFMHPOBC. 46 3 Figure 3 - 3: The phase diagram of Temperature versus X for TFMHPOBC shows a transition from Sm-A- Sm-CA* for X>0.6 and a transition from Sm-A - Sm-C* - Sm-CA* for X<0.6. 46 Figure 3 - 4: Phase boundary curves TC is the upper Sm-C* - Sm-CA* phase transition temperature at E=0, corresponding to TC =101°C for X=0.20, 108°C for X=0.42, and 111°C for X=0.58. 49 Figure 3 - 5: Coupling coefficient U plotted versus T-TC shows a monotonic behaviour with X. 50 Figure 3 - 6: a) Possible pairs between two right handed molecules in adjacent layers, b) possible pairs between a right handed and a left handed molecule( the solid rectangle is the right handed molecule and the open rectangle is the left handed molecule). 53 Figure 3 - 7: Possible molecular pairings for (a) rr pairs, (b) rs pairs, and (c) ss pairs. r are respresented by solid rectangles and s enantiomers by open rectangles. dipole moments are represented by a dot or a cross 56 Figure 3 - 8: Measured polar tilt angle θ versus T. 57 Figure 3 - 9: The phase diagram from our simple theory. Parameter -19 choices: To=85 °C, Tf = 280 K, dipole moment= 7*10 esu cm, -18 k=2.3*10^-16 erg/K, U0=5.75*10 erg. 62 Figure 4 - 1: Molecule1 (mpp88) showing mesogenic moiety and side group. 67 Figure 4 - 2: Schematic representation of lamellar phases: (a) Lam-I phase (b) Lam-N phase (c) Lam-A phase. 68 Figure 4 - 3: Side view of shear set-up. 69 Figure 4 - 4: Top view of shear set-up. 70 2 Figure 4 - 5: Azimuthal rotation φS at the surface versus E . Solid curve -8 represents fit using Eqs. (11) and (12) and K22=1.8+/-0.3 * 10 dyne. 77 Figure 5 - 1: Molecule1 (mpp88) showing mesogenic moiety and side group. 85 Figure 5 - 2: Schematic representation of lamellar phases: (a) Lam-I phase according to our understanding before this experiment (b) Lam-N phase (c) Lam-A phase. 86 Figure 5 - 3: Optical Setup for Retardation Measurement 91 Figure 5 - 4: Measured values of birefringence ∆nSO(T) vs. temperature 92 Figure 5 - 5: Retardation αSOP vs. rotation angle β for cell rotated about the shear axis. 93 Figure 5 - 6: Retardation αSOP vs. temperature for cell rotated by angle β =18° about the shear axis. 95 4 Figure 5 - 7: Derived refractive indices nS, nO, and nP versus temperature. The error bars reflect the uncertainty in the determination of αSOP at β =18° n the Lam-I phase, but not in the determination of nISO. Errors in nS and nO due to errors in measurement of ∆nSO may be inferred Figure 5-4. 96 Figure 5 - 8: X-ray reflections in a) the Lam-I phase and b) the Lam-A phase. Notice that (b) shows an extremely weak 04 reflection, which apparently is absent in (a). 98 Figure 5 - 9: Schematic view of Lam-I phase in which there is considerable out-of-sublayer orientational disorder of mesogenic director. 99 Figure 6 - 1: (a) Liquid Bridge levitated against gravity χHH=∇ ρg, (b) Liquid Bridge with χHH<∇ ρg, (c) Liquid Bridge with χHH>∇ ρg. 109 Figure 6 - 2: Static surface tension versus surfactant concentration. Notice that CMC occurs at X=0.7. Typical error bar is shown. 112 Figure 6 - 3: Schematic diagram of the experimental setup (top view). 113 Figure 6 - 4: Schematic diagram of the experimental setup (side view). 113 Figure 6 - 5: The bridge length was decreased by a distance Li-Lf=0.13 -4 cm to its final length Lf n small but rapid steps (step size =1.3*10 cm, dwell time=0.5 ms) over time T=500 ms, causing a decrease in its resistance and a bulge in shape. 114 Figure 6 - 6: Schematic diagram of experimental setup to measure electrical resistance. 115 Figure 6 - 7: Typical trace of VR versus time. Rapid rise occurs during the T=500 ms translation of support rod, followed by exponential relaxation. The solid curve represents a single exponential fit to the relaxation. 118 Figure 6 - 8: Relaxation time τ vs. concentration. Typical error bar is shown. 119 Figure 7 - 1: Open equilibrium system with