Biaxial Nematic Liquid Crystals

Theory, Simulation and Experiment
Herausgegeben von Luckhurst, Geoffrey R.; Sluckin, Timothy J.

• Gebundenes Buch

Produktbeschreibung

Liquid Crystals are a state of matter that have properties between those of conventional liquid and those of a solid crystal. Thermotropic liquid crystals react to changes in temperature or, in some cases, pressure. The reaction of lyotropic liquid crystals, which are used in the manufacture of soaps and detergents, depends on the type of solvent they are mixed with.
Since the accidental discovery of the chiral nematic (ordered) phase in 1888 many liquid crystal phases have been found, sometimes by chance and sometimes by design. The existence of one such phase was predicted by Freiser in 1970, this was the biaxial nematic phase which has biaxial symmetry in contrast to that of the ubiquitous nematic phase which ix uniaxial. The biaxial symmetry of the predicted phase confers on it an additional layer of fascinating complexity.

This book is devoted to the biaxial nematic phase, both lyotropic and thermotropic, formed by low molar mass as well as polymeric systems. It brings together theory, simulations and experimental studies. The book opens with a general introduction to the biaxial nematic phase, while chapters 2-7 discuss current theories and predictions. Chapters 8 and 9 report on alignment and applications, while chapters 10.1 -10.5 detail characterization with the goal of unambiguous identification. Final chapters (11-14) cover Lyotropic, Colloidal, Thermotropic and Low Molar Mass Thermotropic Systems respectively.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 408
• Erscheinungstermin: 4. Mai 2015
• Englisch
• Abmessung: 246mm x 191mm x 25mm
• Gewicht: 930g
• ISBN-13: 9780470871959
• ISBN-10: 0470871954
• Artikelnr.: 41845412

Autorenporträt

GEOFFREY R. LUCKHURST School of Chemistry, University of Southampton, UK TIMOTHY J. SLUCKIN School of Mathematics, University of Southampton, UK

Inhaltsangabe

About the Editors xiii List of Contributors xv Preface xvii 1 Introduction
1 Geoffrey R. Luckhurst and Timothy J. Sluckin 1.1 Historical Background 1
1.2 Freiser Theory 3 1.3 Nematic Order Parameters 4 1.4 Nematic Tensor
Order Parameters 5 1.5 Theoretical Phase Diagrams 6 1.6 Landau-de Gennes
Theory 9 1.7 Computer Simulation 10 1.8 Other Theoretical Issues 11 1.9
Applications 12 1.10 Characterisation 12 1.11 Lyotropic and Colloidal
Systems 14 1.12 Molecular Design 15 References 19 2 Biaxial Nematics: Order
Parameters and Distribution Functions 25 Geoffrey R. Luckhurst 2.1
Introduction 25 2.2 The Cartesian Language 26 2.2.1 Order Parameters 26
2.2.2 Molecular Symmetry 28 2.2.3 Measurement 30 2.3 The Spherical Tensor
Language 31 2.3.1 The Order Parameters of Biaxial Molecules in a Uniaxial
Phase 31 2.3.2 Molecular Symmetry 33 2.3.3 Measurement 33 2.4 Extension to
Biaxial Nematics 35 2.4.1 Orientational Order Parameters 35 2.4.2 Systems
with D2h Point Group Symmetry 36 2.4.3 Measurement of the Order Parameters
37 2.4.4 Systems with C2h Point Group Symmetry and Their Order Parameters
38 2.4.5 Systems with C2h Point Group Symmetry: The Cartesian Language 39
2.5 Fourth-Rank Order Parameters 42 2.6 The Singlet Orientational
Distribution Function 44 2.7 Appendices 47 2.7.1 Point Group Symmetry and
the Associated Symmetry Operations 47 2.7.2 Legendre Polynomials, Modified
Spherical Harmonics and Wigner Rotation Matrices 48 Acknowledgements 51
References 51 3 Molecular Field Theory 55 Epifanio G. Virga 3.1
Introduction 55 3.2 General Mathematical Theory 57 3.2.1 Two-Particle
Hamiltonian 57 3.2.2 Ensemble Potentials 62 3.2.3 Molecular Field
Approximation 65 3.2.4 Variational Principles 69 3.2.5 Local Stability
Criterion 71 3.3 Non-Polar Molecules 74 3.3.1 Quadrupolar Hamiltonians 74
3.3.2 Phase Transitions 80 3.3.3 Universal Phase Diagram 87 3.3.4 Steric
Effects 91 3.4 Polar Molecules 99 3.4.1 Dipolar Fluids 100 3.4.2 Dipolar
Hamiltonian 102 3.4.3 Condensed Polar Phases 107 References 112 4 Hard
Particle Theories 117 Andrew J. Masters 4.1 Introduction 117 4.2
Theoretical Approaches 119 4.3 Board-Like Models 122 4.4 Bent-Core Models
124 4.5 Rod-Plate Mixtures 125 4.6 Conclusions and Speculations 128
Acknowledgements 129 References 129 5 Landau Theory of Nematic Phases 133
Lech Longa 5.1 Introduction 133 5.2 Symmetry of Biaxial Nematics and
Primary Order Parameters 134 5.3 Landau Expansion 136 5.3.1 Generic NU -I
Phase Transition 136 5.3.2 Generic NB -NU and NB -I Phase Transitions 138
5.3.3 Role of Coupling between Nematic Order Parameters 141 5.3.4 Landau-de
Gennes Expansion in Terms of the Alignment Tensor 145 5.4 Conclusion 149
Acknowledgements 149 References 149 6 Computer Simulations of Biaxial
Nematics 153 Roberto Berardi and Claudio Zannoni 6.1 Introduction 153 6.2
Order Parameters 156 6.3 Model Potentials and Applications 159 6.3.1
Lattice Models 159 6.3.2 Atomistic Models 162 6.3.3 Molecular Models 163
6.4 Conclusion 171 Acknowledgements 173 6.5 Appendices 173 6.5.1
Quaternions 173 6.5.2 Angular Momentum Operator 174 6.5.3 Kinematic and
Dynamic Equations of Rotational Motion 175 6.5.4 Propagator/Integrator of
Rotational Equations of Motion 176 6.5.5 Gradient of the Biaxial Gay-Berne
Potential 176 6.5.6 Torques of the Biaxial Gay-Berne Potential 177
References 178 7 Continuum Theory of Biaxial Nematic Liquid Crystals 185
Iain W. Stewart 7.1 Introduction 185 7.2 Continuum Model and Energies 186
7.2.1 The Elastic Energy 187 7.2.2 The Magnetic and Electric Energies 187
7.2.3 The Total Energy 189 7.3 Dynamic Equations 189 7.3.1 Balance Laws 190
7.3.2 The Viscous Stress 192 7.3.3 The Dynamic Equations 194 7.3.4 Euler
Angle Description 195 7.3.5 A Simple Shear Flow 196 7.4 Equilibrium
Equations 198 7.4.1 The Equilibrium Equations 199 7.4.2 Alignment Induced
by a Magnetic Field 200 7.5 Conclusion 202 References 202 8 The Alignment
of Biaxial Nematics 205 Demetri J. Photinos 8.1 Introduction 205 8.2
Alignment by an External Electric or Magnetic Field 206 8.3 Surface
Alignment 208 8.3.1 Macroscopic Description 208 8.3.2 Molecular Scale
Description 210 8.4 Flow Alignment 210 8.5 Lower Symmetry Biaxial Nematics
and Hierarchical Domain Structures 211 Acknowledgements 212 References 212
9 Applications 215 Paul D. Brimicombe 9.1 Introduction 215 9.1.1 Materials
Considerations 215 9.1.2 Surface Alignment 216 9.2 Thin-Film Electro-Optic
Devices 217 9.2.1 Minor-Director In-Plane Switching Devices 218 9.2.2
Electric Field-Induced Biaxiality Effects 220 9.2.3 Planar Biaxial Nematic
Devices 221 9.2.4 Twist Effects in Biaxial Nematics and Biaxial Pi-Cells
222 9.2.5 Bistable Biaxial Nematic Devices 223 9.2.6 Spontaneous Chirality
Effects 224 9.3 Non-Device Applications of Biaxial Nematic Liquid Crystals
225 9.3.1 Optical Compensation Films 225 9.4 Conclusion 225 References 226
10 Characterisation 229 10.1 Textures of Nematic Liquid Crystals 230 Ingo
Dierking 10.1.1 Polarising Microscopy 230 10.1.2 Simple Liquid Crystal
Optics 230 10.1.3 Optical Biaxiality 232 10.1.4 Textures 234 References 240
10.2 Refractive Index Studies 242 Antonio J. Palangana 10.2.1 Introduction
242 10.2.2 Optical Indicatrix 242 10.2.3 Optical Conoscopy 244 10.2.4
Results 246 10.2.5 Acknowledgements 250 References 250 10.3 Orientational
Order Parameters of Nematic Liquid Crystals Determined by Infrared and
Raman Spectroscopy 251 Jagdish K. Vij and Antoni Kocot 10.3.1 Introduction
252 10.3.2 Polarised IR Spectroscopy 252 10.3.3 Scalar Order Parameters of
a Second-Rank Tensor 252 10.3.4 IR Absorbance Components 254 10.3.5
Experimental Method 256 10.3.6 Results for the Order Parameters for the
Tetrapodes 256 10.3.7 Discussion of the Order Parameters 258 10.3.8 Raman
Spectroscopy 259 10.3.9 Comparisons of IR and Raman Spectroscopy for
Determining Order Parameters 263 References 264 10.4 NMR Spectroscopy 265
Louis A. Madsen 10.4.1 Introduction: NMR Basics, Advantages and Limitations
265 10.4.2 Probing Orientational Order 266 10.4.3 Creating a Director
Distribution to Observe Biaxiality 267 10.4.4 Spectral Analysis
Considerations: Fitting and Rotational Modulations 268 10.4.5 Incorporating
Deuterium: Direct Mesogen Labelling Versus Probe Solutes 270 10.4.6 Powder
Spectra and Monodomain Spectra: Examples 271 10.4.7 Alternative and
Emerging Methods 272 References 274 10.5 Structural Studies of Biaxial
Nematics: X-Ray and Neutron Scattering 276 Patrick Davidson 10.5.1
Introduction 276 10.5.2 Theoretical Considerations 276 10.5.3 Experimental
Details 279 10.5.4 Specificities of the Scattering by Different Kinds of
Biaxial Nematics 280 References 283 11 Lyotropic Systems 285 Antonio M.
Figueiredo Neto and Yves Galerne 11.1 Introduction 285 11.2 Phase Diagrams
286 11.3 The Potassium Laurate-Decanol-Water Mixture: A Working Example 287
11.4 The Intrinsically Biaxial Micelles Model 294 11.5 Theoretical
Reconstruction of the Lyotropic Nematic Phase Diagram: a Landau-Like
Approach 298 11.6 Conclusions 302 Acknowledgements 302 References 302 12
Colloidal Systems 305 Gert Jan Vroege 12.1 Introduction 305 12.2 Onsager
Theory and Extensions 306 12.3 Special Features of Colloids and Colloidal
Liquid Crystals 307 12.4 Biaxiality in Mixtures of Rods and Plates 308 12.5
Particles with Inherent Biaxial Shape 311 12.6 Concluding remarks 315
References 316 13 Thermotropic Systems: Biaxial Nematic Polymers 319 Anke
Hoffmann, Felicitas Brömmel, and Heino Finkelmann 13.1 Introduction 319
13.2 Main-Chain Liquid Crystal Polymers 321 13.3 Side-Chain Liquid Crystal
Polymers 321 13.4 Comparison of Attachment Geometries - Influence of
Molecular Dynamics and Molecular Shape 327 13.5 Conclusion 330 References
330 14 Low Molar Mass Thermotropic Systems 333 Matthias Lehmann 14.1
Preamble 333 14.2 Introduction and General Considerations 333 14.3 Single
Component 336 14.3.1 Biaxial Board-Shaped Mesogens 336 14.3.2 V-Shaped
Nematogens 338 14.3.3 Multipodes 350 14.4 Mixtures 354 14.5 Concluding
Remarks 360 References 360 15 Final Remarks 369 Geoffrey R. Luckhurst and
Timothy J. Sluckin References 373 Index 375