Optical Applications of Liquid Crystals

L Vicari

• Publisher: CRC Press
• Year: 2016
• ISBN:
  9781000687477
• Edition: 1
• Topic: Ciencias físicas
• Subtopic: Química industrial y técnica

In recent years, there has been increasing activity in the research and design of optical systems based on liquid crystal (LC) science. Bringing together contributions from leading figures in industry and academia, Optical Applications of Liquid Crystals covers the range of existing applications as well as those in development. Unique in its thorou

Chapter 1

Optical properties and applications of ferroelectric and antiferroelectric liquid crystals

Emmanouil E Kviezis, Lesley A Parry-Jones and Steve J Elston

1.1 Introduction

1.1.1 Smectic liquid crystals

The most simple liquid crystal phase is the nematic phase, in which the molecules possess orientational ordering (like a crystal) but no positional ordering (like a liquid). However, there are some liquid crystal phases in which the molecules do exhibit a degree of positional ordering. In the smectic phases, this positional ordering is in one dimension only, forming layers of two-dimensional nematic liquids.

The most simple smectic phase is the smectic A (SmA) phase, in which the direction of average molecular orientation (the director, n) is along the smectic layer normal (see figure 1.1(a)). In addition, there is a family of tilted smectic liquid crystal phases, in which the director is at a fixed angle θ with respect to the layer normal. Each phase differs in the relationship between the azimuthal angles of the director in adjacent layers. The simplest cases are the smectic C and smectic C_A phases (SmC and SmC_A), which are illustrated in figures 1.1(b) and (c), respectively. In the SmC phase, the director is constant from one layer to the next, whereas in the SmC_A phase the director alternates in tilt direction from layer to layer, forming a herringbone structure.

When the phases comprise chiral molecules, chiral versions of these phases are formed: SmA*, SmC* and SmCA*. One of the effects of the chirality of the molecules in the case of the tilted smectics SmC* and SmCA* is to cause the azimuthal angles of the directors to precess slowly from one layer to the next. This creates a macroscopic helical structure with its axis along the layer normal, which tends to have a pitch of around 100–1000 layers.

Figure 1.1 The three most simple smectic phases (a) SmA, where the director is perpendicular to the layer normal, (b) SmC where the director tilts at a constant angle θ to the layer normal, and (c) SmC_A where the direction of tilt alternates from one layer to the next, forming a herringbone structure.

1.1.2 Typical molecular structure

Like a typical nematic liquid crystal molecule, a smectic mesogen comprises a rigid core (which tends to be made up of two or three ring structures) with flexible chains at either end. For example, 8CB (see figure 1.2(a)) forms a SmA phase below its nematic phase. DOBAMBC, a typical SmC* material, and MHPOBC, a typical SmCļ material, are illustrated in figures 1.2(b) and (c), respectively. In order to form a layered, smectic phase, there must be significant intermolecular interactions (either hydrogen or van der Waals in origin) [1].

Figure 1.2 Typical molecular structure of smectic liquid crystals, as exemplified by (a) 8CB, which forms an SmA phase, (b) DOBAMBC, which forms an SmC* phase, and (c) MHPOBC, which forms an SmCA* phase.

1.1.3 Order parameters

Just like the orientational ordering in a nematic liquid crystal, the positional ordering of a smectic material is not perfect. In some cases a plot of the density of the molecular centres of mass as a function of distance along the normal to the layers, x, follows a sinusoidal variation,

ρ(X)=ρ0(1+ψsin⁡(2πxδ)),

where ρ₀ is the mean density and δ is the layer spacing, which is typically a few nanometers, ψ is the smectic order parameter, which is the ratio of the amplitude of oscillation to the mean layer density, and hence expresses the extent to which the material is layered, typically ψ ≪ 1.

Within each layer, the orientational ordering about the director is characterized by a nematic-like order parameter, S, defined as

S+〈 P2(cos⁡ω) 〉=〈 32cos⁡2ω−12 〉,

where ω is the angle between the molecule and the director, n, and P₂ is the second-order Legendre polynomial. S is an ergodic variable, so that the average can be performed either over many molecules at one point in time, or for one molecule over a period of time.

The order parameters S and ψ are sufficient to describe the SmA phase. However, for the tilted smectic phases, two further order parameters are required to fully describe the phase: the tilt of the director with respect to the layer normal (usually given the symbol θ), and the azimuthal angle of the director with respect to some fixed coordinate system (often given the symbol ϕ). These angles are illustrated in figure 1.3.

Figure 1.3 The smectic cone: an illustration of the tilt (θ) and azimuthal (ϕ) angles in a tilted smectic liquid crystal layer, θ is the half angle of the smectic cone, and ϕ describes the position of the director on the surface of the cone, with respect to some (arbitrary) reference point. Also shown are a set of coordinate axes, x, y and z, which are useful for defining the physical properties of the material.

1.1.4 Point symmetries of the smectic phases

As well as translational symmetry, the SmA phase has the following point symmetries:

1. mirror symmetry about any plane parallel to the smectic layers that is either exactly between planes or exactly midplane;

2. two-fold rotational symmetry about any axis contained within any of the above mirror planes;

3. mirror symmetry about any plane perpendicular to the smectic layers;

4. complete rotational symmetry about the axis perpendicular to the layers.

This set of point symmetries corresponds to the symmetry D_∞h in the Schoenflies notation. The chiral version of the SmA phase (SmA*) has only the rotational symmetries in the list above: the mirror symmetries no longer exist because the constituent molecules are chiral. This reduces the symmetry of the SmA* phase to D_∞.

The high symmetry of the SmA and SmA* phases precludes the existence of any net spontaneous polarization, just like a nematic. They can therefore only respond to an applied field via an induced electric dipole.

The point symmetries of the SmC phase are as follows:

1. mirror symmetry in the tilt plane of the molecules;

2. two-fold rotational symmetry about the axis perpendicular to the tilt plane of the molecules, either exactly between layers or exactly mid-layer.

This combination of point symmetries corresponds to the C_2h symmetry group in the Schoenflies notation, and also preclude the existence of any net spontaneous polarization in the SmC liquid crystal phase.

However, in the chiral version of the SmC phase (SmC*), the mirror symmetry is no longer present (due to the chirality of the molecules) and hence only the rotational symmetry remains. The symmetry group is reduced to C₂, and it is hence possible for a spontaneous polarization to exist along the C₂ axis, that is, along the direction of the two-fold rotation axis.

1.1.5 Ferroelectricity and antiferroelectricity in liquid crystals

As discussed above, the symmetry of the SmC* phase is such that a spontaneous polarization is permitted along the C₂ axis of each smectic layer. The net spontaneous polarization arises due to the lack of rotatio...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1 Optical properties and applications of ferroelectric and antiferroelectric liquid crystals
• 2 Electro holography and active optics
• 3 On the use of liquid crystals for adaptive optics
• 4 Polymer-dispersed liquid crystals
• 5 New developments in photo-aligning and photo-patterning technologies: physics and applications
• 6 Industrial and engineering aspects of LC applications
• Index
• Abbreviations