Nematic and Cholesteric Liquid Crystals : Concepts and Physical Properties Illustrated by Experiments

by Oswald, Patrick; Pieranski, Pawel

• ISBN13: 9780203023013
• ISBN10: 0203023013
• Copyright: 2006-01-18
• Publisher: Taylor & Francis

Summary

This book is a result of personal research and of the graduate lectures given by the authors at the École Normale Supérieure de Lyon and the Paris VII University, respectively. The first part of the book presents historical background, the modern classification of liquid crystals, and mesogenic anatomy; the second part examines liquid crystals with nematic and cholesteric orientational order. Topics include dielectric and magnetic properties, Frederiks transitions and displays, light scattering, flow and electrohydrodynamic instabilities, defects, and surface anchoring transitions, as well as interfaces, equilibrium shapes, and the Mullins-Sekerka instability. Smectic and columnar liquid crystals are covered in more detail by the authors in a separate volume.

Table of Contents

Foreword

Preface to the English edition

Nematic and Cholesteric Liquid Crystals

Overview

Some History

Georges Friedel and Liquid Crystals

The Discovery of Birefringence in Fluid Biological Substances by Buffon, Virchow, and Mettenheimer: Lyotropic Liquid Crystals

Observation of the Surprising Behavior of Cholesteryl Esters by Planer and Reinitzer: Thermotropic Liquid Crystals

Fliessende Kristalle or "The Flowing Crystals" of Otto Lehmann

Modern Classification of Liquid Crystals

The Terminology Introduced by Georges Friedel

Modern Definition of Mesophases; Broken Symmetries; Short- and Long-Distance Order

Classification of Smectic Phases

Classification of Columnar Phases

Chiral Smectic Phases

Mesogenic anatomy

Thermotropic Liquid Crystals

Lyotropic Liquid Crystals

Liquid Crystal Diblock Copolymers

Colloidal Liquid Crystals

Mesophases with an Orientational Order

Structure and Dielectric Properties of the Nematic Phase

Quadrupolar Order Parameter

The Uniaxial Nematic-Isotropic Liquid Phase Transition

The Uniaxial Nematic-Biaxial Nematic Phase Transition

Low-Frequency Dielectric Properties

Optical Properties

Nematoelasticity: Frederiks Transition and Light Scattering

Grupp Experiment

Frank-Oseen Free Energy

Free Energy Minimization: Molecular Field and Elastic Torques

Interpretation of the Grupp Experiment

Magnetic Field Action

Action of an Electric Field: Displays

Elastic Light Scattering and the Determination of the Frank Constants

Nonlinear Optics

Calculating the Scattering Cross-Section

Free Energy Expression in the Fourier Space

Nematodynamics and Flow Instabilities

Preliminary Observations Illustrating Some Fundamental Differences Between a Nematic and an Ordinary Liquid

Equations of the Linear Nematodynamics

Laminary Couette and Poiseuille Flows

Laminary Flows and Their Stability

Convective Instabilities of Electrohydrodynamic Origin

Thermal Instabilities

"Derivation Under the Integral" Theorem

Rotational Identity

Calculation of the Irreversible Entropy Production

Energy Dissipation and Constitutive Laws in the Formalism of Leslie-Ericksen-Parodi

The Rayleigh-Bénard Instability in Isotropic Fluids

Defects and Textures in Nematics

Polarizing Microscope Observations

The Volterra-de Gennes-Friedel process

Energy of a Wedge Planar Line in Isotropic Elasticity

Continuous Core Model: Landau-Ginzburg-de Gennes Free Energy

Interaction Energy Between Two Parallel Wedge Lines

Dynamics of a Planar Wedge Line: Calculating the Friction Force

Wedge line Stability: Escape in the Third Dimension

Bloch and Ising Walls Induced by the Frederiks Instability

Anchoring and Anchoring Transitions of Nematics on Solid Surfaces

Precursors

On the Notion of Interface

Interface Symmetry and Classification of the Different Types of Anchoring

Wetting and Anchoring Selection

Anchoring Transitions

Measuring the Anchoring Energy in the Homeotropic Case

The nematic-isotropic liquid interface:static properties and directional growth instabilities.

Anchoring Angle, Surface Tension, and Width of the Nematic-Isotropic Interface

Landau-Ginzburg-de Gennes Theory

Instabilities in Confined Geometry

Elastic Correction to the Gibbs-Thomson Relation

Directional Growth of the Nematic-Isotropic Liquid Front

Cholesterics: the First Example of a Frustrated Mesophase

Cholesteric Frustration

Cholesteric Order Parameter and the Cholesteric-Isotropic Liquid Phase Transition

Optical Properties of the Cholesteric Phase

Defects and Textures of the Cholesteric Phase

Unwinding Transition

Cholesteric Hydrodynamics

Blue Phases: a Second Example of a Frustrated Mesophase

Experimental Evidence for the Cubic Symmetry of Blue Phases I and II

Uniaxial Models for the Blue Phases: Disclination Lattices

Biaxial Model of the Blue Phases by Grebel, Hornreich, and Shtrikman

Landau Theory of the Blue Phases by Grebel, Hornreich, and Shtrikman

Experiments

BPIII or Blue Fog

Overview of Growth Phenomena and _the Mullins-Sekerka Instability

Gibbs-Thomson Relation and the Phase Diagram of a Diluted Binary Mixture

The Minimal Model

Stationary Plane Front

Plane Front in the Diffusive Regime (ÂúG

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