Given the widespread interest in macroscopic phenomena in liquid crystals, stemming from their applications in displays and devices. The need has arisen for a rigorous yet accessible text suitable for graduate students, whatever their scientific background. This book satisfies that need.
The approach taken in this text, is to introduce the basic continuum theory for nematic liquid crystals in equilibria, then it proceeds to simple application of this theory- in particular, there is a discussion of electrical and magnetic field effects which give rise to Freedericksz transitions, which are important in devices. This is followed by an account of dynamic theory and elementary viscometry of nemantics Discussions of backflow and flow-induced instabilities are also included. Smetic theory is also briefly introduced and summarised with some examples of equilibrium solutions as well as those with dynamic effects. A number of mathematical techniques, such as Cartesian tensors and some variational calculus, are presented in the appendices.
Author(s): Iain W. Stewart
Series: Liquid Crystals Book Series
Edition: 1
Publisher: Taylor & Francis
Year: 2004
Language: English
Pages: 360\377
Tags: Liquid crystals, Physical Science, Mathematics, statistic
Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgements
1 Introduction
1.1 The Discovery of Liquid Crystals
1.2 Basic Descriptions of Liquid Crystals
1.3 The Development of the Continuum Theory of Liquid Crystals
1.4 Notation and Conventions
2 Static Theory of Nematics
2.1 Introduction
2.2 The Frank-Oseen Elastic Energy
2.2.1 The Nematic Energy
2.2.2 The Cholesteric Energy
2.3 Electric and Magnetic Fields
2.3.1 Electric Fields and the Electric Energy
2.3.2 Magnetic Fields and the Magnetic Energy
2.3.3 Comments on Fields and Units
2.4 Equilibrium Equations
2.4.1 Preliminaries
2.4.2 Derivation of the Equilibrium Equations
2.5 General Equilibrium Solutions
2.6 Anchoring and Boundary Conditions
2.6.1 No Anchoring
2.6.2 Strong Anchoring
2.6.3 Conical Anchoring
2.6.4 Weak Anchoring
2.7 Reformulation of Equilibrium Equations
2.7.1 Bulk Equilibrium Equations
2.7.2 Reformulation of Boundary Conditions
3 Applications of Static Theory of Nematics
3.1 Introduction
3.2 Some Equilibrium Solutions
3.2.1 Elementary Equilibrium Solutions
3.2.2 Tilt and Twist Equilibrium Solutions
3.3 Magnetic Coherence Length
3.4 Freedericksz Transitions
3.4.1 The Classical Freedericksz Transitions in Nematics
3.4.2 Pretilt at the Boundaries
3.4.3 Tilted Fields
3.5 Electric Field Effects
3.6 Weak Anchoring Effects
3.7 The Twisted Nematic Device
3.8 Defects
3.8.1 Axial Line Disclinations
3.8.2 Perpendicular Disclinations
3.8.3 Boundary Line Disclinations
3.8.4 Point Defects at a Surface
Dynamic Theory of Nematics
4.1 Introduction
4.2 The Ericksen-Leslie Dynamic Equations
4.2.1 Kinematics and Material Frame-Indifference
4.2.2 Balance Laws
4.2.3 Constitutive Equations
4.2.4 The Dynamic Equations
4.2.5 Summary of the Ericksen-Leslie Dynamic Equations
4.3 Reformulation of the Dynamic Equations
4.4 The Nematic Viscosities
Applications of Dynamic Theory of Nematics
5.1 Introduction
5.2 A Simple Flow Alignment,
5.3 A Transverse Flow Effect
5.4 The Zwetkoff Experiment
5.5 Shear Flow
5.5.1 Newtonian and Non-Newtonian Behaviour
5.5.2 Governing Equations for Shear Flow
5.5.3 Shear Flow Near a Boundary
5.5.4 Shear Flow between Parallel Plates
5.5.5 Scaling Properties
5.6 Oscillatory Shear Flow
5.6.1 Oscillatory Shear Flow Solutions
5.6.2 Stability and Instability
5.7 Couette Flow
5.7.1 The Anisotropic Fluid Case
5.7.2 The Nematic Liquid Crystal Case
5.8 Poiseuille Flow
5.8.1 The Anisotropic Fluid Case
5.8.2 The Nematic Liquid Crystal Case
5.8.3 Results from a Scaling Analysis
5.9 Dynamics of the Freedericksz Transition
5.9.1 Dynamics in the Twist Geometry
5.9.2 Backflow and Kickback in the Splay Geometry
5.9.3 Backflow in the Bend Geometry
5.10 Light Scattering
6 Theory of Smectic C Liquid Crystals
6.1 Introduction
6.2 Static Theory of Smectic C
6.2.1 The Elastic Energy for Smectic C
6.2.2 The Magnetic and Electric Energies
6.2.3 Equilibrium Equations
6.2.4 Focal Conic Defects: Dupin and Parabolic Cyclides
6.2.5 A Freedericksz Transition in Bookshelf Smectic C
6.2.6 Smectic Layer Compression
6.3 Dynamic Theory of Smectic C
6.3.1 Dynamic Equations for SmC Liquid Crystals
6.3.2 The Smectic C Viscosities
6.3.3 Simple Flow Alignment in Smectic C
6.4 Theory of Smectic C* Liquid Crystals
6.4.1 Energies for Smectic C*
6.4.2 Static and Dynamic Theory for Smectic C*
6.4.3 Director Reorientation in Smectic C*
6.5 Comments on Theories of Smectics
A Results Employing Variational Methods
B Identities
C Physical Components in Cylindrical Polar Coordinates
D Tables
Bibliography
Index
