Liquid Crystals

Chapter 2 - Order Parameter, Phase Transition, and Free Energies


2.1.1.   Introduction

Generally speaking, we can divide liquid crystalline phases into two distinctly
different types: the ordered and the disordered. For the ordered phase, the theoretical
framework invoked for describing the physical properties of liquid crystals is closer
in form to that pertaining to solids; it is often called elastic continuum theory. In this
case various terms and definitions typical of solid materials (e.g., elastic constant,
distortion energy, torque, etc.) are commonly used. Nevertheless, the interesting fact
about liquid crystals is that in such an ordered phase they still possess many properties
typical of liquids. In particular, they flow like liquids and thus require hydrodynamical
theories for their complete description. These are explained in further detail
in the next chapter.

Liquid crystals in the disordered or isotropic phase behave very much like
ordinary fluids of anisotropic molecules. They can thus be described by theories pertaining
to anisotropic fluids. There is, however, one important difference.

Near the isotropic → nematic phase transition temperature, liquid crystals
exhibit some highly correlated pretransitional effects. In general, the molecules
become highly susceptible to external fields, and their responses tend to slow down

In the next few sections we introduce some basic concepts and definitions,
such as order parameter, short- and long-range order, phase transition, and so on,
which form the basis for describing the ordered and disordered phases of liquid


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