ELASTICITY OF MAIN CHAIN LIQUID CRYSTAL ELASTOMERS AND ITS RELATIONSHIP TO LIQUID CRYSTAL MICROSTRUCTURE A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Sonal Dey December, 2013 Dissertation written by Sonal Dey B.Sc., Cotton College, Gauhati University, India, 2004 M.Sc., Indian Institute of Technology Roorkee, India, 2006 M.A., Kent State University, USA, 2012 Ph.D., Kent State University, USA, 2013 Approved by , Chair, Doctoral Dissertation Committee Dr. Satyendra Kumar , Members, Doctoral Dissertation Committee Dr. Elizabeth Mann Dr. Brett D. Ellman Dr. Edgar Kooijman Dr. Jonathan V. Selinger Accepted by , Chair, Department of Physics Dr. James T. Gleeson , Associate Dean, College of Arts and Sciences Dr. Janis Crowther ii TABLE OF CONTENTS LIST OF FIGURES ........................................................................................................ VI DEDICATION.............................................................................................................. XVI ACKNOWLEDGEMENTS ...................................................................................... XVII CHAPTER 1 INTRODUCTION ..................................................................................... 1 1.1 Classical rubber elastic theory ................................................................................... 2 1.1.1 Entropic elasticity of a single chain of macromolecules ................................. 7 1.1.2 Gaussian elasticity of a crosslinked macromolecular network ..................... 12 1.1.3 Non-Gaussian chain statistics of elastomers at high extensions ................... 14 1.2 Liquid Crystals ........................................................................................................ 20 1.3 Liquid Crystal Elastomers ....................................................................................... 26 1.3.1 Neo-classical theory of nematic rubber elasticity ......................................... 29 1.4 Chapter Summary .................................................................................................... 33 REFERENCES ................................................................................................................ 34 CHAPTER 2 SOFT ELASTICITY AND SHAPE MEMORY EFFECT .................. 38 2.1 Soft elasticity of nematic elastomers ....................................................................... 38 2.1.1 Soft elasticity in monodomain nematic elastomers ....................................... 40 2.1.2 Semi-soft elasticity: effect of non-ideal network .......................................... 45 2.1.3 Soft elasticity in polydomain nematic elastomers ......................................... 46 2.2 Domain rotation in smectic elastomers ................................................................... 51 2.3 Shape memory effect in polydomain main-chain smectic-C elastomers ................ 56 2.4 Chapter Summary .................................................................................................... 59 iii REFERENCES ................................................................................................................ 61 CHAPTER 3 X-RAY DIFFRACTION: THEORY AND EXPERIMENTAL TECHNIQUE ...................................................................................................... 63 3.1 Bragg’s law of diffraction ....................................................................................... 63 3.2 Basic theory of X-ray scattering .............................................................................. 66 3.3 X-ray diffraction pattern of common liquid crystal phases ..................................... 71 3.4 Elastomer Liquid Crystals ....................................................................................... 76 3.5 Mechanical properties of LCE1 and LCE2 ............................................................. 78 3.6 Experimental Set-up ................................................................................................ 80 3.6.1 Synchrotron X-ray source ............................................................................. 80 3.6.2 Beam optics and the X-ray spectrometer ...................................................... 83 3.6.3 Application of Uniaxial Strain ...................................................................... 84 3.6.4 Image plate detector ...................................................................................... 86 3.6.5 Data collection, calibration, and analysis ...................................................... 88 3.6.6 Determination of orientational order parameter ............................................ 89 3.6.7 Experimental Details ..................................................................................... 91 3.7 Chapter Summary .................................................................................................... 92 REFERENCES ................................................................................................................ 94 CHAPTER 4 SOFT ELASTICITY IN A MAIN CHAIN SMECTIC-C ELASTOMER ..................................................................................................... 97 4.1 Discussion of Results ............................................................................................ 100 4.2 Polydomain-monodomain transition by uniaxial strain ........................................ 101 iv 4.3 Mechanism behind polydomain-monodomain transition ...................................... 109 4.4 Relaxation at constant strain ................................................................................. 112 4.5 Strain retention ...................................................................................................... 118 4.6 Thermal shape recovery ........................................................................................ 120 4.7 Chapter Summary .................................................................................................. 125 REFERENCES .............................................................................................................. 127 CHAPTER 5 THE EFFECT OF TRANSVERSE RIGID SEGMENT ON STRAIN RETENTION..................................................................................................... 129 5.1 Effect of TR3 on the polydomain-monodomain transition ................................... 129 5.2 TR3 and strain retention ........................................................................................ 136 5.3 Effect of TR3 on thermal shape recovery ............................................................. 138 5.4 Chapter Summary .................................................................................................. 142 REFERENCES .............................................................................................................. 144 CHAPTER 6 CONCLUSIONS AND FUTURE WORK .......................................... 145 6.1 Conclusions ........................................................................................................... 145 6.2 Suggestions for future work .................................................................................. 147 REFERENCES .............................................................................................................. 150 v LIST OF FIGURES Figure 1.1.1 Schematic diagram showing a network of macromolecular chains cross- linked (the black blobs) at various positions. .............................................................. 3 Figure 1.1.2 A typical force-extension curve of a classical elastomer, adapted with permission from [3]. .................................................................................................... 5 Figure 1.1.3 (a) Freely-jointed model of a macromolecular chain. Each segment is of length d and there are p junction points so that the maximum extension-length is D = pd. β is the angle between two adjacent segments. (b) A particular macromolecular chain conformation with an end-to-end distance l (l D). ............. 8 Figure 1.1.4 Non-linear force extension curve for elastomers is shown according to the eqn. (1.12). The relation is valid until the polymer chains remain Gaussian. But it fails to explain the upward turn in the force-extension curve at higher extensions as depicted in Figure 1.1.2. ............................................................................................ 15 Figure 1.1.5 Force-extension curve of an elastomer under three different models. The upward curve in the force-extension plot (Figure 1.1.2) is explained by taking into account the finite extensibility of the elastomer network. ......................................... 18 Figure 1.2.1 Schematic showing the orientation of a rod-like nematic mesogen in the laboratory frame of reference. The macroscopic director n is taken along the z-axis; m is the axis of the molecule; θ and ϕ are respectively the polar and azimuthal angles made by the molecule in this frame. The graph to the left shows a smoothly behaving form of the molecular distribution function where it reaches the minimum value in the direction orthogonal to n. ..................................................................................... 21 vi Figure 1.2.2 A plot of the Landau-de Gennes nematic free energy density for three different temperatures. For T TNI, the system is in the isotropic state with free energy minimum at S = 0. The transition