LiquidCrysta 36.LiquidCrystalsLiquidCrysta 933 PartD|36.1 36.LiquidCrystals GeoffreyLuckhurst,DavidDunmur Thischapteroutlinesthebasicphysics,chemical natureandpropertiesofliquidcrystals.Thesema-

Liquid Crysta933Part

D|36.1

36. Liquid Crystals

Geoffrey Luckhurst, David Dunmur

This chapter outlines the basic physics, chemicalnature and properties of liquid crystals. These ma-terials are important in the electronics industry asthe electro-optic component of flat-panel liquid-crystal displays, which increasingly dominate theinformation display market.

Liquid crystals are intermediate states of mat-ter which flow like liquids, but have anisotropicproperties like solid crystals. The formation ofa liquid-crystal phase and its properties are deter-mined by the shape of the constituent moleculesand the interactions between them. While manytypes of liquid-crystal phase have been identified,this Chapter focuses on those liquid crystals whichare important for modern displays.

The electro-optical response of a liquid crys-tal display (LCD) depends on the alignment ofa liquid-crystal film, its material properties andthe cell configuration. Fundamentals of the physicsof liquid crystals are explained and a number ofdifferent displays are described.

In the context of materials, the relationshipbetween the physical properties of liquid crystalsand their chemical composition is of vital impor-tance. Materials for displays are mixtures of manyliquid-crystal compounds carefully tailored to op-timise the operational behaviour of the display.Our current understanding of how chemical struc-ture determines the physical properties is outlined,and data for typical liquid-crystal compounds aretabulated. Some key references are given, but ref-erence is also made to more extensive reviewswhere additional data are available.

36.1 Introduction to Liquid Crystals........... 93336.1.1 Calamitic Liquid Crystals ..................... 93536.1.2 Chiral Liquid Crystals . ......................... 93736.1.3 Discotic Liquid Crystals ....................... 938

36.2 The Basic Physics of Liquid Crystals .... 94036.2.1 Orientational Order ............................ 94036.2.2 Director Alignment ............................ 94036.2.3 Elasticity ........................................... 94136.2.4 Flexoelectricity .................................. 94436.2.5 Viscosity ........................................... 945

36.3 Liquid-Crystal Devices ....................... 94736.3.1 A Model Liquid-Crystal Display:

Electrically ControlledBirefringence (ECB) Mode.................... 948

36.3.2 High-Volume Commercial Displays:The Twisted Nematic (TN)and Super-Twisted Nematic (STN)Displays ............................................ 951

36.3.3 Complex LC Displaysand Other Cell Configurations ............. 952

36.4 Materials for Displays ........................ 95636.4.1 Chemical Structure and Liquid-

Crystal Phase Behaviour ..................... 95636.4.2 The Formulation

of Liquid-Crystal Display Mixtures ....... 95736.4.3 Relationships Between Physical

Properties and Chemical Structuresof Mesogens...................................... 958

References ................................................... 964

36.1 Introduction to Liquid Crystals

Liquid crystals have been known for almost 130 yearsbut it is only in the last 40 years or so that their uniqueapplication in display devices has been recognised.Now they are seen as extremely important materialshaving made possible the development of thin screensfor use with personal computers (PCs) and in televi-

sions. In fact a wide range of different liquid-crystal(LC) display devices has been developed. The commonfeature for each of these is that the optical character-istics of the display are changed on application of anelectric field across a thin liquid-crystal film. The pro-cess causing this change is associated with a variation

© Springer International Publishing AG 2017S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_36

PartD|36.1

934 Part D Materials for Optoelectronics and Photonics

OO

O

O

F F

NC

NC O

N

NC

Cr 401 C N 445 C I Cr 63 C SmC 74 C N 91 C I

Cr 49 C SmC 77 C SmA 93 C N 108 C I

Cr 187 C N 221 C I

Cr 62 C N 85 C I

a) b)

c)

d)

e) f)

Cr 24 C N 35 C I

O C

Fig. 36.1 The molecular structures for a selection of compounds which form calamitic liquid crystals

a) b)

c)

Fig. 36.2a–c The molecular organisation in (a) theisotropic phase (b) the nematic phase and (c) the smec-tic A phase obtained from the simulation of a Gay–Bernecalamitic mesogen

in the macroscopic organisation of the liquid crystalwithin the cell. The liquid crystal is, therefore, strictlybehaving as a molecular material and not an electronicone. Nonetheless the display itself is closely integratedwith electronic components. Since liquid crystals maybe unfamiliar to those concerned with conventionalelectronic materials, this section begins with an intro-duction to liquid crystals and the compounds that form

them. The following section describes the basic physicsfor liquid crystals which are needed to understand theiruse in display devices. The functioning of the most im-portant displays is described in Sect. 36.3, which makescontact with the basic physics outlined in Sect. 36.2.The liquid-crystal materials used in display devices arediscussed in the final section, where the necessary opti-misation of a wide range of properties is addressed.

The majority of chemical compounds can exist inthree states of matter, namely crystal, liquid or gas,each with its defining characteristics. There is a fourthstate known as a liquid crystal and, as the name sug-gests, this state has characteristics of both crystals andliquids. Thus a liquid crystal flows when subject toa stress, like a liquid, but certain of its properties areanisotropic, like a crystal. This macroscopic behaviour,often used to identify the phase, implies that at the mi-croscopic or molecular level the material has an elementof long-range orientational order together with sometranslational disorder at long range. It is this combina-tion of order and disorder that makes liquid crystals sofascinating and gives them their potential for applica-tions, especially in the field of electro-optic displays.

A variety of different classes of materials are knownto form liquid crystals at some point on their phase di-agram [36.1]. These include organic materials wherethe liquid crystal is formed, on heating, between thecrystal and isotropic liquid phases. Such materials areknown as thermotropic liquid crystals and are thesubject of this Chapter. Another class is formed byamphiphilic organic materials in which part of the con-stituent molecules favours one solvent, normally water,while the other part does not. When the amphiphile is

Liquid Crystals 36.1 Introduction to Liquid Crystals 935Part

D|36.1

a) b) c)

Fig. 36.3a–c Typical optical textures observed with a polarising microscope for (a) nematic, (b) smectic A and(c) columnar liquid-crystal phases

dissolved in the water, the molecules form aggregateswhich then interact to give the liquid-crystal phase, theformation of which is largely controlled by the con-centration of amphiphile. These are known as lyotropicliquid crystals; they underpin much of the surfactantindustry, although they are not used in displays andso will not be considered further. Colloidal disper-sions of inorganic materials such as clays can alsoform liquid-crystal phases depending on the concen-tration of the colloidal particles. Solutions of certainorganic polymers also exhibit liquid-crystal phases and,like the colloidal systems, the solvent acts to increasethe separation between polymer chains but does notsignificantly affect their state of aggregation. A primeexample of such a system is the structural polymerKevlar, which for the same weight is stronger than steel;it is formed by processing a nematic solution of thepolymer.

The following sections return to thermotropic liquidcrystals and describe the molecular organisation withinthe phases, mention some of their properties and brieflyindicate the relationship between the phase and molec-ular structures.

36.1.1 Calamitic Liquid Crystals

In view of the anisotropic properties of liquid crystals,it seems reasonable that a key requirement for their for-mation is that the molecules are also anisotropic. Thisis certainly the case, with the majority of liquid crys-tals having rod-like molecules, such as those shownin Fig. 36.1. One of the simplest nematogenic rod-like molecules is p-quinquephenyl (Fig. 36.1a), whichis essentially rigid. However, flexible alkyl chains canalso be attached at one or both ends of the molecule(Fig. 36.1b,c) or indeed in the centre of the molecule

(Fig. 36.1d), and rigid polar groups such as a cyano(Fig. 36.1d–f) may be attached at the end of themolecule. The rigid part is usually constructed fromplanar phenyl rings (Fig. 36.1a–e) but they can be re-placed by alicyclic rings (Fig. 36.1f) which enhancethe liquid crystallinity of the compound. The termcalamitic, meaning rod-like, is applied to the phases thatthey form. There are, in fact, many different calamiticliquid-crystal phases but we shall only describe thosewhich are of particular relevance to display applica-tions.

At an organisational level the simplest liquid crys-tal is called the nematic and in this phase the rod-like molecules are orientationally ordered, but there isno long-range translational order. A picture showingthis molecular organisation, obtained from a computersimulation of a Gay–Berne mesogen [36.2] is givenin Fig. 36.2b. The molecular shape is ellipsoidal andthe symmetry axes of the ellipsoids tend to be parallelto each other and to a particular direction known as thedirector.

In contrast there is no ordering of the molecularcentres of mass, except at short range. The essentialdifference between the nematic and isotropic phases(Fig. 36.2a) is the orientational order, which is onlyshort range in the isotropic liquid. At a macroscopiclevel the nematic phase is characterised by its high flu-idity and by anisotropy in properties such as the refrac-tive index. The anisotropic properties for a nematic havecylindrical symmetry about the director, which providesan operational definition of this unique axis and is theoptic axis for the phase. The anisotropy in the refractiveindex combined with the random director distributionresults in the turbidity of the phase, which contrastswith the transparency of the isotropic liquid. This on itsown would not be sufficient to identify the liquid crys-

PartD|36.1


tal as a nematic phase but identification is possible fromthe optical texture observed under a polarising micro-scope. These textures act as fingerprints for the differentliquid-crystal phases. An example of such a texture fora nematic phase is shown in Fig. 36.3a; it is created bythe anisotropy or birefringence in the refractive indexcombined with a characteristic distribution of the direc-tor in the sample.

The next level of order within liquid crystal phasesis found for the smectic A phase. Now, in addition tothe long-range orientational order, there is translationalorder in one dimension, giving the layered structureshown in Fig. 36.2c [36.2]. The director associated withthe orientational order is normal to the layers. Withina layer there is only short-range translational order asin a conventional liquid. In this structure the layer spac-ing is seen to be comparable but slightly less than themolecular length, as found experimentally for manysmectic phases.

At a macroscopic level the layer structure meansthat the fluidity of a smectic A phase is consider-ably less than for a nematic phase. The properties areanisotropic and the birefringence is responsible for theturbidity of the phase, as found for a nematic. How-ever, under a polarising microscope the optical textureis quite different to that of a nematic, as is apparent fromthe focal conic fan texture shown in Fig. 36.3b.

A variant on the smectic A is the smectic C phase.The essential difference to the smectic A phase is thatthe director in the smectic C phase is tilted with respectto the layer normal. The defining characteristic of thesmectic C phase is then the tilt angle, which is takenas the angle between the director and the layer normal.This tilt in the structure reduces the symmetry of thephase to the point group C2 h in contrast to D1h for ne-matic and smectic A phases. This lowering in symmetrynaturally influences the symmetry of the properties. Thefluidity of the smectic C phase is comparable to that ofa smectic A phase. However, the optical texture can bequite different and it has elements similar to a nematicphase and to a smectic A; the focal conic fan structure isless well defined and is said to be broken. The nematic-like features result from the fact that the tilt direction ofthe director is not correlated between the smectic layersand so it adopts a distribution analogous to that of thedirector in a nematic phase.

The molecular factors which influence the ability ofa compound to form a liquid-crystal phase have beenwell studied both experimentally [36.3] and theoreti-cally [36.4]. Consider the simple nematic as formed, forexample, by p-quinquephenyl (Fig. 36.1a); this melts at401 ıC to form the nematic phase, which then under-goes a transition to the isotropic phase at 445 ıC; thetransition temperatures are denoted by TCrN and TNI, re-

spectively. The very high value of TNI, which is a mea-sure of the stability of the nematic phase, is attributed tothe large length-to-breadth ratio of p-quinquephenyl. Incontrast p-quaterphenyl, formed by the removal of justone of the five phenyl rings, does not exhibit a liquid-crystal phase at atmospheric pressure, even though itsshape anisotropy is still relatively large. This occurs be-cause, on cooling, the isotropic liquid freezes beforethe transition to the nematic phase can occur. Indeedmany compounds with anisotropic molecules might beexpected to form liquid-crystal phases, but do not be-cause of their high melting points. As a consequencethe molecular design of liquid crystals needs to fo-cus not only on increasing the temperature at whichthe liquid crystal–isotropic transition occurs but alsoon lowering the melting point. One way by which thiscan be achieved is to attach flexible alkyl chains to theend of the rigid core (Fig. 36.1). In the crystal phasethe chain adopts a single conformation but in a liq-uid phase there is considerable conformational disorder,and it is the release of conformational entropy on melt-ing that lowers the melting point. The addition of thechain also affects the nematic–isotropic transition tem-perature, which alternates as the number of atoms inthe chain passes from odd to even. This odd–even ef-fect is especially dramatic when the flexible chain linkstwo mesogenic groups (Fig. 36.1d) to give what isknown as a liquid-crystal dimer [36.5]. The odd–eveneffect is particularly marked because the molecularshapes for the dimers with odd and even spacers differsignificantly on average, being bent and linear, respec-tively.

The attachment of alkyl chains to the rigid coreof a mesogenic molecule has another important conse-quence, as it tends to promote the formation of smec-tic phases (Fig. 36.1b,c). The reason that the chainslead to the formation of such layered structures isthat, both energetically and entropically, the flexiblechains prefer not to mix with the rigid core, and so byforming a layer structure they are able to keep apart.Indeed it is known that biphenyl (a rigid rod-like struc-ture) is not very soluble in octane (a flexible chain).The lack of compatibility of the core and the chainincreases with the chain length and so along a ho-mologous series it is those members with long alkylchains that form smectic phases. For example, 4-pentyl-40-cyanobiphenyl (Fig. 36.1e) forms only a nematicphase whereas the longer-chain homologue, 4-decyl-40-cyanobiphenyl only exhibits a smectic A phase. Toobtain a tilted smectic phase such as a smectic Cthere clearly needs to be a molecular interaction whichfavours an arrangement for a pair of parallel moleculesthat is tilted with respect to the intermolecular vector.Such a tilted structure can be stabilised by electrostatic


D|36.1

interactions; for example by off-axis electric dipoles(Fig. 36.1b,c) [36.6] or with a quadrupolar charge dis-tribution.

The ability of a compound to form a liquid crys-tal is not restricted to just one phase. The delicatebalance of the intermolecular interactions responsiblefor the various liquid-crystal phases means that transi-tions between them can result from modest variationsin temperature. This is apparent for the 4,40-dialkyl-20,30-difluoroterphenyl shown in Fig. 36.1c, which oncooling the isotropic liquid forms nematic, smectic Aand smectic C phases; such a compound is said to bepolymorphic. Materials which form even more liquid-crystal phases are known [36.1]. The occurrence ofseveral liquid-crystal phases in a single system can beof value in processing the material for display applica-tions.

36.1.2 Chiral Liquid Crystals

The mesogenic molecules that have been considered sofar are achiral in the sense that the molecule is super-imposable on its mirror image. Molecules may also bechiral in that they are not superimposable on their mir-ror images; this chirality can result from the tetrahedralarrangement of four different groups around a singlecarbon atom. This is illustrated in Fig. 36.4a whichshows such an arrangement together with its mirrorimage; these are known as enantiomers. The presenceof a chiral centre will certainly change the nature ofthe interactions between the molecules and it is rele-vant to see whether the chiral interactions might notinfluence the structure of the liquid-crystal phases ex-hibited by the material. From a formal point of viewit might be expected that the molecular chirality ofa mesogen should be expressed through the symme-try of the liquid-crystal structure. This proves to be thecase, provided no other interactions oppose the chiraldeformation of the liquid-crystal phase. In fact the firstliquid crystal to be discovered [36.7] was chiral; thiswas cholesteryl benzoate where the cholesteryl moietycontains many chiral centres. The structure of the liq-uid crystal is nematic-like in that there is no long-rangetranslational order but there is long-range orientationalorder. However, the difference between this phase anda nematic formed from achiral materials is that the di-rector is twisted into a helix. The helix may twist ina left-handed or a right-handed sense and these struc-tures, shown in Fig. 36.4b, are mirror images of eachother. The phase structure is certainly chiral and so isknown as a chiral nematic, although originally it wascalled a cholesteric phase. The symbol for the phaseis N�, where the asterisk indicates that the phase hasa chiral structure.

a) b)NC

H

CH3

CN

H3C

H

Fig. 36.4 (a) A chiral mesogenic molecule, (R) 2-[40-cyano-4-biphenyl]-hexane, together with its mirror im-age, (S) 2-[40-cyano-4-biphenyl]-hexane. (b) The left- andright-handed helical organisation of the director for a chiralnematic

The helical structure is characterised by the pitchof the helix p which is the distance along the helixaxis needed for the director to rotate by 2 . Since thedirections parallel and antiparallel to the director areequivalent the periodicity of the chiral nematic is p=2.For many chiral nematics the helical pitch is compa-rable to the wavelength of visible light. This, togetherwith the periodic structure of the phase, means thatBragg reflection from a chiral nematic will be in thevisible region of the spectrum and so this phase willappear coloured with the wavelength of the reflectedlight being related to the pitch of the helix. This pitch issensitive to temperature, especially when the chiral ne-matic phase is followed by a smectic A. This sensitivityhas been exploited in the thermochromic application ofchiral nematics, where the reflected colour of the phasechanges with temperature [36.1].

The chirality of cholesteryl benzoate clearly re-sults from the chiral centres present in the mesogenicmolecule. However, the chirality can also be intro-duced indirectly to a mesogen by simply adding a chiraldopant, which does not need to be mesogenic. Themixture will be chiral and this is sufficient to lead toa chiral nematic. The pitch of this mixture depends onthe amount of the dopant and the inverse pitch, p�1,proves to be proportional to its concentration. The hand-edness of the helix induced by the dopant will dependon its stereochemical conformation and will be oppositefor the two enantiomers. Accordingly, if both enan-tiomers are present in equal amounts, i. e., as a racemicmixture, then doping a nematic with this will not con-vert it to a chiral nematic.

Chiral smectic phases are also known in which thedirector adopts a helical structure as a result of in-troducing molecular chirality into the material either

PartD|36.1


C6H13

Cr 124 C ND 142 C I

C9H19

O

O

O

O

C9H19

OO

OO

C9H19

C9H19C9H19

O

OO

O

C6H13

C6H13

C6H13C6H13

C6H13

C9H19

b)

Cr 175 C Colrd 183 ND 192 C

Cr 68 C Colro85 ND 138 C Colho 280 C

c)

a)

C9H19 O

O

O

OC9H19

C9H19

O

OO

O

C9H19

C9H19O

O

C9H19

O O

C I

C I

Fig. 36.5 A selection of molecular structures for compounds that form discotic liquid crystals

as a dopant or as an intrinsic part of the mesogenicmolecule. The chiral smectic C phase, denoted SmC�,provides an appropriate example with which to illus-trate the structure of such phases. In an achiral smec-tic C phase the tilt direction of the director changesrandomly from layer to layer, analogous to the randomdirector orientation in an achiral nematic. For the chiralsmectic C phase, as might be anticipated, the tilt direc-tion of the director rotates in a given sense, left-handedor right-handed, and by a small, fixed amount fromlayer to layer. Other structural features of the smec-tic C phase remain unchanged. Thus, the director ofthe chiral smectic C phase has a helical structure withthe helix axis parallel to the layer normal. The pitch ofthe helix is somewhat smaller than that of the associ-ated chiral nematic phase. The magnitude of the pitchis inversely related to the tilt angle of the smectic C,and since this grows with decreasing temperature so thepitch decreases. The reduced symmetryC2 of the SmC�

phase leads to the introduction of a macroscopic electri-cal polarisation [36.8]. This is of potential importancefor the creation of fast-switching displays.

The ability of the SmC� phase to adopt a helicalstructure results from the fact that the tilt direction forthe director acts in an analogous manner to the direc-tor in a nematic, and importantly that the layer spacingis preserved in the helical structure. In marked con-trast there are strong forces inhibiting the creation ofa twisted structure for a smectic A composed of chi-

ral molecules. The director is normal to the layers andso the creation of a twisted structure would requirea variation in the layer thickness but this has a highenergy penalty associated with it. Accordingly manyof the smectic A phases formed from chiral moleculeshave the same structure as those composed of achiralmolecules. There are, however, exceptions and these oc-cur when the chiral interactions are especially strongand, presumably, the translational order of the layersis small. Under such conditions the smectic A struc-ture is partially destroyed, creating small SmA-likeblocks about 1000Å wide, separated by screw disloca-tions [36.9, 10]. These defects in the organisation allowthe directions for the blocks to rotate coherently to givea chiral helical structure; the pitch of the helix is foundto be larger than that in an analogous chiral nematicphase. This chiral phase is just one example of a liquid-crystal structure stabilised by defects; it is known asa twist grain-boundary phase and denoted by TGBA�.The letter A indicates that the director is normal to thelayers in the small smectic blocks; there is a compa-rable phase in which the director is tilted, denoted byTGBC�.

36.1.3 Discotic Liquid Crystals

The key requirement for the formation of a liquid crys-tal is an anisotropic molecule, as exemplified by therod-like molecules described in the previous sections.


D|36.1

b)

a)

c)

Fig. 36.6a–c The molecular organisation in discotic liq-uid-crystal phases, (a) nematic, (b) hexagonal columnarand (c) rectangular columnar

However, there is no reason why disc-like moleculesshould not also exhibit liquid-crystal phases. Nonethe-less, it was not until 1977 that the first example ofa thermotropic liquid crystal formed from disc-likemolecules was reported [36.11]. Since that time sev-eral liquid-crystal phases have been identified and thesephases are known collectively as discotic liquid crys-tals. The range of compounds that exhibits these phasesis now extensive and continues to grow [36.12], al-though it does not match the number that form calamiticliquid crystals. The molecular structures of three com-pounds which form discotic liquid crystals are shownin Fig. 36.5.

As for rod-like molecules, the simplest liquid-crystal phase formed by disc-like molecules is thenematic, usually denoted ND, where the D indicates thedisc-like nature of the molecules. Within the nematicphase, shown in Fig. 36.6a, the molecular centres ofmass are randomly distributed and the molecular sym-metry axes are orientationally correlated. The nematicstructure is the same as for that formed from rod-likemolecules, the only difference being that the symme-try axes which are orientationally ordered are the shortaxes for the discs and the long axes for the rods. The

point symmetry of the discotic and calamitic nematic isthe same, namely D1h. The discotic nematic is recog-nised in the same way as the calamitic nematic; thatis it flows like a normal fluid and its anisotropy is re-vealed by a characteristic optical texture analogous tothat shown in Fig. 36.3a. In fact, the refractive indexof a discotic nematic along the director is smaller thanthat perpendicular to it, which is the opposite to that fora calamitic nematic. It has been suggested that this dif-ference may be of value in display devices [36.13] butthis concept has not as yet been commercialised.

The other class of discotic liquid crystals possessessome element of long-range translational order andthese are known as columnar phases, two examplesof which are sketched in Fig. 36.6b,c. The disc-likemolecules are stacked face-to-face into columns. A sin-gle column has a one-dimensional structure, and as suchis not expected to exhibit long-range translational or-der, although this can result from interactions betweenneighbouring columns in the liquid-crystal phase. Thecolumn–column interactions will result in the columnsbeing aligned parallel to each other; these interactionswill also determine how the columns are packed. Whenthe discs are orthogonal to the column axis the crosssection is essentially circular and so the columns packhexagonally, as shown in Fig. 36.6b. The symbol givento this phase is Colhd, where h denotes hexagonalpacking of the columns and d indicates that the ar-rangement along the column is disordered. The pointgroup symmetry of this phase is D6 h. The disc-likemolecules may also be tilted with respect to the columnaxis, giving an elliptical cross section to the columns.As a result the columns are packed on a rectangu-lar lattice; there are four possible arrangements andjust one of these is indicated in Fig. 36.6c. In generalthe mnemonic used to indicate a rectangular columnarphase is Colrd. The point group symmetry of the rect-angular columnar phase is D2 h and the extent to whichthe structure deviates from that of the Colhd phase willdepend on the magnitude of the tilt angle within thecolumn. The columnar phases can be identified fromtheir optical textures and an example of one is shownin Fig. 36.3c.

The columnar phases have potential electronicapplications because of the inhomogeneity of themolecules that constitute them, i. e., the central part isaromatic while the outer part is aliphatic. As a resultof the overlap between the �-orbitals on the centresof neighbouring discs it should be possible for elec-trical conduction to take place along the core of thecolumn. This should occur without leakage into adja-cent columns because of the insulation provided by thealkyl chains. It should also be possible to anneal thesemolecular wires because of their liquid-crystal prop-

PartD|36.2


erties [36.14]. This and the ability to avoid defects inthe columns which can prevent electronic conductionin crystals mean that the columnar phase has manypotential advantages over non-mesogenic materials. Inaddition, discotic systems are also used as compensat-ing films to improve the optical characteristics for someliquid-crystal displays.

At a molecular level the factors that are respon-sible for the formation of the discotic liquid-crystalphases are similar to those for calamitic systems. Thus,the molecular design should aim to increase the liquidcrystal–isotropic transition temperature while decreas-ing the melting point. The latter is certainly achievedby attaching flexible alkyl chains to the perimeter of therigid disc. The creation of the columnar phases shouldbe relatively straightforward provided the central coreis both planar and large. Then, because of the strongattractive forces between the many atoms in the rigidcore the molecules will wish to stack face-to-face ina column. The formation of the columns will also befacilitated by the flexible alkyl chains attached to thecore. Clearly then it may prove to be difficult to cre-ate the nematic phase before the columnar phase is

formed unless the disc–disc interactions can be weak-ened. One way in which this can be achieved is bydestroying the planarity of the core, for example, byusing phenyl rings attached to the molecular centre sothat they can rotate out of the plane (Fig. 36.5a). It isto be expected that the columnar phases should occurbelow the nematic phase, corresponding to an increasein order with decreasing temperature. This is usuallyobserved, for example, for the hexasubstituted triph-enylenes (Fig. 36.5b). However, the truxene derivatives,with long alkyl chains on the perimeter, (Fig. 36.5c)exhibit quite unusual behaviour. For these compoundsthe crystal melts to form a discotic nematic and thenat a higher temperature a columnar phase appears. Thisdeviates from the expected sequence, and because thenematic phase appears at a lower temperature thanthe columnar phase it is usually referred to as a re-entrant nematic. The occurrence of a re-entrant phaseis often attributed to a conformational change whichstrengthens the molecular interactions with increasingtemperature thus making the more ordered phase ap-pear at higher temperatures.

36.2 The Basic Physics of Liquid Crystals

36.2.1 Orientational Order

The defining characteristic of a liquid crystal isthe long-range orientational order of its constituentmolecules. That is, for rod-like molecules, the molec-ular long axes tend to align parallel to each other evenwhen separated by large distances. The molecules tendto be aligned parallel to a particular direction knownas the director and denoted by n. This is an apolarvector, that is n D �n, because the nematic does notpossess long-range ferroelectric order. The propertiesof the nematic phase are cylindrically symmetric aboutthe director, which provides a macroscopic definition ofthis. The anisotropy of the properties results from theorientational order and the extent of this is commonlydefined [36.15] by

S D 1

2

�3 cos2 ˇ � 1

��; (36.1)

although other definitions are possible [36.16]. Here ˇis the angle made by a molecule with the directorand the angular brackets indicate the ensemble aver-age. In the limit of perfect order S is unity while inthe isotropic phase S vanishes. The temperature depen-dence of S is shown in Fig. 36.7 for the nematogen,4,40-dimethoxyazoxybenzene; this behaviour is typicalof most nematic liquid crystals. At low temperatures S

is about 0:6 and then decreases with increasing temper-ature, reaching about 0:3 before it vanishes discontin-uously at the nematic–isotropic transition, in keepingwith the first-order nature of this transition. It is alsofound, both experimentally and theoretically, that theorientational order of different nematic liquid crystals isapproximately the same provided they are compared atcorresponding temperatures, either the reduced, T=TNI,or shifted, TNI � T , temperatures [36.16]. Since manyproperties of liquid crystals are related to the long-rangeorientational order these also vary with temperature es-pecially in the vicinity of the transition to the isotropicphase.

36.2.2 Director Alignment

The director in a bulk liquid crystal is distributed ran-domly unless some constraint is applied to the system;a variety of constraints can be employed and two ofthese are of special significance for display applica-tions. One of them is an electric field and because ofthe inherent anisotropy in the dielectric permittivity ofthe liquid crystal the director will be aligned. The elec-tric energy density controlling the alignment is givenby [36.17]

Uelec D �"0 "

2.n �E/2 : (36.2)

Liquid Crystals 36.2 The Basic Physics of Liquid Crystals 941Part

D|36.2

Here "0 is the permittivity of a vacuum and the scalarproduct n �E is E cos , where E is the magnitude of thefield E and is the angle between the director and thefield, " is the anisotropy in the dielectric tensor

" D "jj

� "? ; (36.3)

where the subscripts denote the values parallel (jj)and perpendicular (?) to the director. If the dielectricanisotropy is positive then the director will be alignedparallel to the electric field and, conversely, if " isnegative, then the director is aligned orthogonal to thefield. The molecular factors that control the sign of " will be discussed in Sect. 36.4. Of course, intenseelectric fields are also able to align the molecules inan isotropic phase but what is remarkable about a ne-matic liquid crystal is the very low value of the fieldneeded to achieve complete alignment of the director.Thus for a bulk nematic free of other constraints theelectric field necessary to align the director is typicallyabout 30 kV=m, although the value does clearly dependon the magnitude of the dielectric anisotropy. This rel-atively small value results because of the long-rangeorientational correlations which mean that the field acts,in effect, on the entire ensemble of molecules and notjust single molecules.

The other constraint, essential for display devices,is the interaction between the director and the sur-face of the container [36.18]. At the surface there aretwo extreme arrangements for the director. One is withthe director orthogonal to the surface, the so-calledhomeotropic alignment. In the other the director is par-allel to a particular direction in the surface; this isknown as uniform planar alignment. The type of align-

360

1

0.8

0.6

0.4

0.2

0

370 380 390 400 410 420

S

T(K)

Fig. 36.7 The temperature variation of the orientationalorder parameter S for 4,40-dimethoxyazoxybenzene; thedifferent symbols indicate results determined with differ-ent techniques

ment depends on the way in which the surface has beentreated. For example, for a glass surface coated withsilanol groups a polar liquid crystal will be alignedhomeotropically, while to achieve this alignment fora non-polar nematic the surface should be covered withlong alkyl chains. In these examples the direct interac-tion of a mesogenic molecule with the surface producesan orthogonal alignment which is then propagated bythe long-range order into the bulk. To achieve uniformplanar alignment of the director the surface is coatedwith a polymer, such as a polyimide, which on its ownwould result in planar alignment. To force the directorto be parallel to a particular direction in the surfacethe polymer is rubbed which aligns the director par-allel to the direction of rubbing. There is still someuncertainty about the mechanism responsible for uni-form planar alignment. It might result from alignmentof the polymer combined with anisotropic intermolecu-lar attractions with the mesogenic molecules, althoughit had been thought [36.19] to have its origins in surfacegroves and the elastic interactions which are describedlater.

The energy of interaction between the surface andthe director clearly depends on the nature of the sur-face treatment and the particular nematic. Rapini andPapoular [36.20] have suggested the following simpleform for the surface energy density

US D �A

2.n � e/2 ; (36.4)

where A is the anchoring energy and e is the easyaxis or direction along which the director is aligned.Clearly it has an analogous form to that for theanisotropic interaction between the nematic and anelectric field (36.2) but is essentially phenomenological.The anchoring energy is determined to be in the range10�7�10�5 J=m2 [36.21]. The upper value correspondsto strong anchoring in that typical values of the electricfield would not change the director orientation at thesurface. In contrast the lower value is associated withweak anchoring and here the director orientation at thesurface can be changed by the field.

36.2.3 Elasticity

As the name suggests, a liquid crystal has some proper-ties typical of crystals and others of liquids. The elasticproperties of crystals should, therefore, be reflected inthe behaviour of liquid crystals. Here it is the directororientation which is the analogue of the atomic posi-tions in a crystal. In the ground state of a nematic liquidcrystal the director is uniformly aligned. However, theelastic torques, responsible for this uniform ground

PartD|36.2


z

x

δnx

δny

y

z

x

y

δny

δnx

n n

z

x

δnx

–δnyy

a) b) c)

Fig. 36.8a–c The three fundamental deformations for the nematic director (a) splay, (b) twist and (c) bend

–20

12

9

6

3–15 –10 –5 0

K(10–12N)

(T–TNI) (C)

K3

K1

K2

Fig. 36.9 The temperature dependence of the three elasticconstants, K1, K2 and K3, for the nematogen 5CB

state, are weak and, at temperatures within the nematicrange, the thermal energy is sufficient to perturb thedirector configuration in the bulk. This perturbed statecan take various forms depending on a combination offactors but, whatever the form, it can be representedas a sum of just three fundamental distortion modes.These are illustrated in Fig. 36.8 and are the splay,twist and bend deformations [36.22]. At a more for-mal level these modes are also shown in terms of thesmall deviations of the director from its aligned stateat the origin as the location from this is varied. For ex-ample, for the twist deformation away from the originalong the x-axis there is a change in the y-componentof the director, ny, and the displacement along the y-axis causes a change in nx. The magnitude of the twist

deformation is measured by the gradients @ny=@x and@nx=@y.

The energy needed to stabilise a given distortion ofthe director field is clearly related to the extent of thedeformation via the gradients. This distortion energydensity for a bulk nematic liquid crystal is given by con-tinuum theory [36.22] as

f D 1

2

�K1.r � n/2 CK2.n � r � n/2

CK3.n� r � n/2�; (36.5)

where the terms r � n, n � r � n and n� r � n cor-respond to the splay, twist and bend deformations,respectively. The contribution each makes to the freeenergy is determined by the proportionality constantsK1, K2 and K3, which are usually known as the Frankelastic constants for splay, twist and bend, respec-tively. They are small, typically 5�10�12 N, and theirsmall magnitude explains why the thermal energy isable to distort the uniform director arrangement soreadily. The elastic constants are not in fact constantbut vary with temperature and nor are they equal asthe results for 4-pentyl-40-cyanobiphenyl (5CB) shownin Fig. 36.9 demonstrate. The twist elastic constant isseen to be the smallest while the largest is the bendelastic constant. This means that it is easiest to in-duce a twist deformation in a nematic while a benddeformation is the most difficult to create. All threeelastic constants decrease with increasing temperaturein keeping with the decreasing order as the transi-tion to the isotropic phase is approached. Like theorientational order the elastic constants vanish discon-tinuously at the first-order nematic–isotropic transi-


D|36.2

E

a) b)

Fig. 36.10a,b The geometry for the Fréedericksz experi-ment used to determine the twist elastic constant, K2; (a) inzero field and (b) above the threshold value

tion.The continuum theory is especially valuable in pre-

dicting the behaviour of display devices and this isillustrated by considering one of the ingenious exper-iments devised by Fréedericksz to determine the elasticconstants [36.23]. In these a thin slab of nematic is con-fined between two glass plates with a particular directorconfiguration, either uniform planar or homeotropicproduced by surface forces. These forces control thedirector orientation just at the two surfaces and thealignment across the slab is propagated by the elasticinteractions. A field is then applied which will move thedirector away from its original orientation and the vari-ation of the director orientation with the field strengthprovides the elastic constant. To employ the contin-uum theory in order to describe the experiment it isnecessary to add the field energy density (36.2) tothe elastic free-energy density in (36.5). The directorconfiguration is then obtained by integrating the free-energy density over the volume of the sample, andminimising this, subject to the surface constraints. Thegeometry of the experiment is shown in Fig. 36.10and provided the dielectric anisotropy " is positivethe director will move from being orthogonal to thefield to being parallel to it. However, the extent of thistwist deformation will vary across the cell, being great-est at the centre and zero at the surfaces, in the limitof strong anchoring. The dependence of the directororientation, at the centre of the slab, with respect tothe electric field is shown in Fig. 36.11. As the fieldstrength is increased from zero the director orienta-tion remains unchanged until a threshold value Eth isreached when the angle between the director and thefield starts to decrease continuously. At very high val-ues of the field the director at the centre of the slabtends to be parallel to the field. This behaviour canbe understood in the following simple terms. Belowthe threshold field the elastic energy exceeds the elec-trical energy and so the director retains its uniformplanar alignment. Above the threshold field strength theelastic energy is less than the electrical energy and so

0.0

90

80

70

60

50

40

30

20

10

0

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Θm()

E*

Fig. 36.11 The dependence of the director orientation mat the centre of a nematic slab on the scaled field strength,E� D E=Eth

the director begins to move to be parallel to the elec-tric field. The threshold electric field is predicted tobe

Eth D

l

sK2

"0 "; (36.6)

where l is the slab thickness. Once the thresholdfield has been measured and provided the dielec-tric anisotropy is known, the twist elastic constantwould be available. Other Fréedericksz experimentswith analogous expressions for the threshold field leadto the determination of the splay and bend elastic con-stants.

For real display applications (Sect. 36.3) the di-rector alignment at the surface deviates from eitheruniform planar or homeotropic alignment. This devi-ation is known as a surface pre-tilt and is illustratedin Fig. 36.12a for near-uniform planar alignment withthe tilt direction on the two surfaces differing by 180ı.The cell with this arrangement has what is known asantiparallel alignment, so named because of the dif-ference in the tilt direction caused by the directionof rubbing on the surfaces being antiparallel. In zerofield, therefore, the director is uniformly aligned acrossthe cell but tilted with respect to the x-axis set in thesurface. A continuum theory calculation analogous tothe case when the pre-tilt angle 0 is zero allows thedependence of the director orientation m in the cen-tre of the cell to be determined as a function of thestrength of the field applied across the cell. The resultsof these calculations, for a nematic with positive ",are shown in Fig. 36.12b as a function of the scaled

PartD|36.2


0.0

90

80

70

60

50

40

30

20

10

0

0.5 1.0 1.5 2.0 2.5

02

10

Θm ()

E/Eth

Θ0

Ea)

b)

Fig. 36.12 (a) The director alignment in a cell with pre-tiltat the two surfaces assembled so that the rubbing directionsare antiparallel. (b) The electric field dependence of thedirector orientation m at the centre of the cell for valuesof the pre-tilt angle of 0ı (solid line), 2ı (dashed line) and10ı (dash-dotted line)

field strength E=Eth, where Eth is the threshold fieldfor zero pre-tilt. The theoretical dependence for a tiltangle of zero is analogous to that considered for thetwist deformation. In other words, below the thresh-old field the director is parallel to the easy axis andthen above this threshold the director moves to be-come increasingly parallel to the field. When there isa surface pre-tilt the behaviour is quite different andthis is especially apparent for a pre-tilt angle of 10ı

(Fig. 36.12b). In zero field the angle m made by thedirector with the x-axis is 10ı and, as the field in-creases, so does m. The rate of increase grows asthe threshold field is approached and then is reducedas E=Eth increases beyond unity. Comparison of thisbehaviour with the conventional Fréedericksz experi-ment (Fig. 36.12b) shows that a pre-tilt of 10ı hasa significant effect on the way in which the director ori-entation changes with the field strength. Indeed, evenfor a pre-tilt of just 2ı, there is a pronounced differ-ence in behaviour in the vicinity of the threshold field.This clearly has important implications for the accuratedetermination of the elastic constants [36.20]. It alsoshows how unique the behaviour is when the surfacepre-tilt angle is zero.

Chiral nematics are often employed in liquid-crystaldisplay devices. Locally, their structure is analogous toa nematic but the director is twisted into a helical struc-ture. The continuum theory for the chiral nematic must,therefore, be consistent with the helical ground statestructure of the phase. To achieve this, a constant is

a)

b)

Fig. 36.13a,b The orientational distribution of bentmolecules in (a) a uniformly aligned nematic and (b) onesubject to a bend deformation; the x-axes are denoted byarrows

added to the twist term in the elastic free-energy den-sity. Thus (36.5) for a nematic becomes

f D 1

2

"

K1.r � n/2 CK2

�n � r � n� 2

p

�2

CK3.n� r � n/2#

(36.7)

for a chiral nematic, where p is the pitch of the helix.

36.2.4 Flexoelectricity

Another property of solids which is mimicked by liquidcrystals is piezoelectricity. For solids this is the genera-tion of a macroscopic electrical polarisation as a resultof the deformation of certain ionic materials. It is to beexpected, therefore, that deformation of the director dis-tribution for a liquid crystal will create a macroscopicpolarisation; this proves to be the case [36.24] and thephenomenon is known as flexoelectricity. The origin offlexoelectricity can be understood in the following way.It is generally assumed that mesogenic molecules arecylindrically symmetric but examination of the molec-ular structure of real mesogens shows that this is not thecase. The molecules are asymmetric and at one extreme


D|36.2

can be thought of as bent, as shown in Fig. 36.13; herez is the molecular long axis and x is the axis bisectingthe bond angle. When the director is uniformly alignedthe z-axis will be parallel to the director and the x-axiswill be randomly arranged orthogonal to it (Fig. 36.13).If the director is now subject to a bend deformationthe molecular long axis will still tend to be parallel tothe local director, however, the x-axis will tend to alignparallel to a direction in the plane formed by the bentdirector. This change in the distribution function for thex-axis will introduce polar order into the system andif there is an electrical dipole moment along the x-axisthen the deformed nematic will exhibit a macroscopicpolarisation P. A similar argument shows that, if themolecule is wedge-shaped, a splay deformation of thedirector distribution will also induce a polarisation inthe nematic [36.24].

The magnitude of P, the induced dipole per unit vol-ume, clearly depends on the extent of the deformationin the director distribution. In the linear response regimethe induced polarisation for mesogenic molecules of ar-bitrary asymmetry is given by [36.25]

P D e1nr � nC e3n� r � n ; (36.8)

where the vectors nr � n and n� r � n represent thesplay and bend deformations, respectively. Since thepolarisation per unit volume is also a vector then theproportionality constants, e1 and e3, are scalars. Theseare known as the splay and bend flexoelectric coeffi-cients, respectively, and their dimensions are Cm�1.The determination of individual flexoelectric coeffi-cients is challenging [36.26], however, it seems that(e1 C e3) is of the order of 10�12�10�11 Cm�1, al-though from the previous discussion their magnitudeshould vary amongst the mesogens because of their de-pendence on the molecular asymmetry and the size andlocation of the dipole moment. The molecular modelproposed to understand the flexoelectricity of nematicssuggests that, for rod-like molecules, devoid of asym-metry, the flexoelectric coefficients should vanish, butthat does not seem to be the case. Indeed, it has beenproposed that polarisation can result even for rod-likemolecules if they possess an electrostatic quadrupolemoment [36.27]. This is not inconsistent with the po-larisation predicted by (36.8) which follows from thereduced symmetry of a nematic with splay and benddeformations of the director [36.24]. Although the exis-tence of flexoelectricity is of considerable fundamentalinterest the inverse effect in which the director is de-formed from a uniform state by the application of anelectric field is of relevance for liquid-crystal displays(Sect. 36.3). This deformation occurs because the polar-isation induced by the director deformation can couple

Velocitygradient

Flow direction

η3η2η1

a) b) c)

Fig. 36.14a–c The principal flow geometries of the Mie-sowicz experiments with the director pinned (a) parallelto the flow direction, (b) parallel to the velocity gradientand (c) orthogonal to both the flow direction and velocitygradient

with the applied electric field and so stabilise the de-formation [36.26]. Since the coupling is linear in theelectric field then reversal of the field will simply re-verse the deformation; a novel bistable device basedsolely on this reversal is described in Sect. 36.3.

36.2.5 Viscosity

For a nematogen the fluidity of the nematic phase iscomparable to that of the isotropic phase appearing ata higher temperature. It is this fluidity, similar to thatof a liquid, which is responsible, in part, for the displayapplications of nematics. An indication of the fluidityof conventional liquids is provided by a single viscos-ity coefficient �, measured from the flow of the liquidsubject to an applied stress in a viscometer. The flowbehaviour of a nematic is made more complex by itsdefining long-range orientational order and the resultantanisotropy of the phase.

This complexity can be appreciated at a practicallevel in terms of the Miesowicz experiments to deter-mine the viscosity coefficients of a nematic [36.28].In these experiments it is helpful to consider flow ina viscometer with a square cross section such that thereis a velocity gradient orthogonal to the direction offlow. For a nematic, flow through the viscometer willnow depend on the orientation of the director withrespect to these two axes. A magnetic field is em-ployed to align the director along a particular axisand it must be sufficiently strong that flow does notperturb the director alignment. There are three rel-atively simple flow geometries and these are shownin Fig. 36.14: with the director parallel to the flow di-rection (Fig. 36.14a), with the director parallel to thevelocity gradient (Fig. 36.14b), and with the direc-

PartD|36.2


20

150

100

70

40

20

1030 40 50 60

η(mPa s)

T(C)

TNI

η2

η3

η1

Fig. 36.15 The temperature dependence of the three Mie-sowicz viscosity coefficients, �1, �2, and �3, for the ne-matic phase of MBBA; the viscosity coefficient for theisotropic phase is also shown

tor orthogonal to both the flow direction and velocitygradient (Fig. 36.14c). The viscosity coefficients weredenoted by Miesowicz as a) �1, b) �2, and c) �3,although other notation has been proposed in which�1 and �2 are interchanged [36.29]. The three vis-cosity coefficients are clearly expected to differ giventhe anisotropy of the nematic phase and these differ-ences are found to be large. They are illustrated for theroom-temperature nematogen 4-methoxybenzylidene-40-butylaniline (MBBA) [36.30] in Fig. 36.15 where theviscosities are plotted against temperature.

It is immediately apparent that flow is easiest whenthe director is parallel to the direction of flow, as mighthave been anticipated. Conversely flow of the nematicis most difficult when the director is orthogonal to theflow direction but parallel to the velocity gradient. Theintermediate viscosity �3 occurs when the director isorthogonal to both the flow direction and the velocitygradient. Here it is seen that this third viscosity coef-ficient for the nematic is very similar to the viscositycoefficient for the isotropic phase extrapolated to lowertemperatures.

The viscosity coefficient �.; �/ for an arbitraryorientation (; �) of the director with respect to theflow direction and velocity gradient can be related tothe director orientation. It might be expected that thisorientation dependence would involve just the threeMiesowicz viscosity coefficients, rather like the trans-formation of a second-rank tensor from its principal

axis system. In fact this is not quite the case and a fourthviscosity coefficient �12 needs to be introduced. The ori-entation dependence is then [36.28]

�.; �/ D �1 cos2 C �

�2 C �12 cos2

�

� sin2 cos2 � C �3 sin2 sin2 � : (36.9)

We see that for the principal orientations (0, =2), ( =2,0) and ( =2, =2) the expression gives �1, �2, and �3, asrequired. The optimum director orientation with whichto determine �12 is with the director at 45ı to both theflow direction and the velocity gradient; the viscositycoefficient for this is

� 4; 0�

D �12

4C �1 C �2

2: (36.10)

The value of �12 determined for MBBA proves to besignificantly smaller than the other three viscosity coef-ficients.

The four viscosity coefficients have been defined ata practical level in terms of flow in which the directororientation is held fixed. The converse of these exper-iments, in which the director orientation is changed inthe absence of flow, allows the definition of the fifthand final viscosity coefficient. This is known as the rota-tional viscosity coefficient; it is denoted by the symbol�1 and plays a major role in determining the responsetimes of display devices (Sect. 36.4). To appreciate thesignificance of �1, it is helpful, as for the other fourviscosity coefficients, to consider an experiment withwhich to measure it. In this an electric field is suddenlyapplied an angle to a uniformly aligned director, thenproviding the dielectric anisotropy is positive the direc-tor orientation will be changed and rotates towards thefield direction. The electric torque responsible for thealignment is given by

�elec D �"0 "

2sin 2 ; (36.11)

which is the derivative of the electric energy in (36.2).The rotation of the director is opposed by the viscoustorque

�visc D �1d

dt; (36.12)

which is linear in the rate at which the director orien-tation changes, with the proportionality constant being�1. Provided the only constraint on the director is theelectric field and provided, 0 45ı, the director willmove as a monodomain so that the elastic terms van-ish. The inertial term for a nematic is small and so themovement of the director is governed by the equation

Liquid Crystals 36.3 Liquid-Crystal Devices 947Part

D|36.3

in which the two torques are balanced. That is, the elec-tric torque causing rotation is balanced by the viscoustorque opposing it; this gives

�1d

dtD �"0 "

2E2 sin2 : (36.13)

The solution to this differential equation is

tan D tan 0 exp� t

�

�; (36.14)

where 0 is the initial orientation of the director withrespect to the electric field and � is the relaxation time

� D �1

"0 "E2: (36.15)

Measurement of the time-dependent director orienta-tion allows � to be determined and from this �1, given

values of ". For MBBA the rotational viscosity coef-ficient is found to be slightly less than �2 and to parallelits temperature dependence [36.31].

The five independent viscosity coefficients neces-sary to describe the viscous behaviour of a nematic havebeen introduced in a pragmatic manner by appealingto experiments employed to measure these coefficients.However, the viscosity coefficients can be introducedin a more formal way as has been shown by Ericksenand then by Leslie in their development of the the-ory for nematodynamics [36.32]. The Leslie–Ericksentheory in its original form contained six viscosity coef-ficients, but subsequently Parodi has shown, using theOnsager relations, that there is a further equation link-ing the viscosity coefficients, thus reducing the numberof independent coefficients to five [36.33]. These fivecoefficients are linearly related to those introduced byreference to specific experiments.

36.3 Liquid-Crystal Devices

The idea to use liquid crystals as electro-optic de-vices goes back to the early days of liquid-crystalresearch. In 1918 Björnståhl, a Swedish physicist,demonstrated that the intensity of light transmitted bya liquid crystal could be varied by application of anelectric field [36.34]. As optical devices of various typesbecame established in the first decades of the 20thcentury, mainly in the entertainment industry, ways ofcontrolling light intensity became important to the de-veloping technologies. One device that soon found

VV

Electrodes and surface aligning layers

Liquidcrystal

No electric field applied With electric field applied

a) b)

Fig. 36.16 Electrically controlled birefringence (ECB)cell

commercial application was the Kerr cell shutter, inwhich an electric field caused the contained fluid (usu-ally nitrobenzene) to become birefringent. Placing sucha cell between crossed polarisers enabled a beam oflight to be switched on and off very rapidly. The firstreport of liquid crystals being of interest for electro-optic devices was in 1936, when the Marconi Com-pany filed a patent [36.35] which exploited the highbirefringence of nematic liquid crystals in an electro-optic shutter. However, it was another 35 years beforecommercial devices became available which used theelectro-optic properties of liquid crystals. The long in-terruption to the development of liquid-crystal devicescan be attributed to the lack of suitable materials. Weshall see in this Section how the physical propertiesof liquid crystals determine the performance of de-vices.

The optical properties of liquid crystals are ex-ploited in displays, although the operational character-istics of such devices also depend crucially on manyother physical properties (Sect. 36.2). Since the devicesto be described all depend on the application of an elec-tric field, their operation will be influenced by electricalproperties such as dielectric permittivity and electricalconductivity. There is a range of electro-optic effectsthat can be used in devices, and the precise mannerin which the properties of the liquid-crystal materialsaffect the device behaviour depends on the effect andthe configuration of the cell. Thus there is not a singleset of ideal properties that can define the best liquid-crystal material, rather the material properties have to

PartD|36.3


be optimised for a particular application. In this section,different devices will be described, and their depen-dence on different properties will be outlined. The wayin which the material properties can be adjusted for anyapplication will be discussed in the final section of thischapter.

36.3.1 A Model Liquid-Crystal Display:Electrically ControlledBirefringence (ECB) Mode

If an electric field is applied across a film of planar-aligned liquid crystal having a positive dielectricanisotropy, then the director of the liquid crystal willtend to align along the electric field. Thus the direc-tor will rotate into the field direction, and the opticalretardation or birefringence of the film will change.If the film is placed between crossed polarisers, thenthe change in optical retardation will be observed asa change in the intensity of transmitted light. The con-figuration for an ECB-mode display is schematicallyillustrated in Fig. 36.16. This illustrates the principalcomponents of a liquid-crystal display. The liquid crys-tal is contained between two glass plates that havebeen coated with a transparent conducting layer, usu-ally an indium–tin oxide alloy. Such treatment allowsthe application of an electric field across the liquid-crystal film, which can then be viewed along the fielddirection. For most applications, the surfaces of theelectrodes are treated so that a particular director ori-entation is defined at the surface. This can be achievedin a variety of ways, depending on the desired sur-face director orientation. For the ECB-mode displayunder consideration, the director alignment should beparallel to the glass substrates and along a defineddirection, which is the same on both surfaces. The stan-dard technique to produce this alignment is to coatthe glass plates with a thin (0:5 nm) layer of poly-imide, which is mechanically rubbed in a particulardirection. The cell is then placed between crossed po-larisers, the extinction directions of which make anglesof ˙45ı with the surface-defined director orienta-tion.

The unperturbed state of the liquid-crystal film willbe determined by the surfaces which contain it. If thesehave been treated in such a way that the liquid-crystaldirector is parallel to the surface along a particular di-rection, then the film will act as an optical retardationplate. Thus incident polarised light will, in general,emerge elliptically polarised, and there will be a phaseretardation between components of the light wave par-allel to the fast and slow axes of the retardation plate.For electromagnetic waves polarised at ˙45ı to thedirector the phase retardation �, in radians, will be

determined by the intrinsic birefringence of the liq-uid crystal ( n D ne � no), the film thickness ` and thewavelength of the light �

� D 2 `

�.ne � no/ I (36.16)

ne and no are respectively the extraordinary (slow) andordinary (fast) refractive indices of the liquid crystal(assuming that n is positive). If the emergent ellipti-cally polarised light passes through a second polariser,crossed with respect to the incident polarisation direc-tion, only a proportion of the incident intensity will betransmitted. The normalised intensity of light transmit-ted by a pair of crossed polarisers having a birefringentelement between them, the axis of which is at ˙45ı tothe extinction directions of the polarisers is given by

T D�1

2

�sin2

�

2(36.17)

(the factor of one half appears for incident unpolarisedlight – if the light is polarised, as from a laser, then thefactor is one).

Thus the initial appearance of the cell will be bright-est if the cell thickness, birefringence and wavelengthare chosen to give � equal to , 3 , 5 etc. It is nor-mal to select the cell thickness to give � D , and underthese conditions the display is known as normally white.It is possible, though less satisfactory, to configure thedisplay so that it operates in a normally black state, cor-responding to a phase retardation of a multiple of 2 .

Application of an electric field causes the directororientation to change such that the optical retardationof the cell decreases to zero, and hence the cell be-comes non-transmitting, at least in the normally whiteconfiguration. Under these circumstances the optical re-tardation across the cell becomes

� D 2

�

`Z

0

.ne Œ .z/�� n0/ dz ; (36.18)

where the effective extraordinary refractive indexneŒ.z/� depends on the angle Œ90ı � .z/� between thedirector and the field and is a function of position z inthe cell. This effective index is given by

1

n2eŒ.z/�D sin2Œ.z/�

n2oC cos2Œ.z/�

n2eI (36.19)

when the director is along the field direction D 90ı,so ne.90ı/ D no, and � D 0.


D|36.3

Transmitted light intensity

Vth0 Voltage applied to cellVon Voff

Ion

Ioff

Fig. 36.17 Variation of optical transmission with voltagefor an ECB cell between crossed polarisers

The orientational distribution of the director in thecell in the presence of an applied electric field isdetermined by the strength of the field, the electric per-mittivity and elastic constants of the liquid crystal, andmost importantly by the properties at the interface be-tween the liquid crystal and the aligning surfaces. Ifthe director at the surface satisfies the strong-anchoringcondition, i. e., it is unaffected by the applied electricfield, and the surface director is strictly perpendicular tothe electric field, then the reorientation of the directorexhibits a threshold response, known as a Fréeder-icksz transition. The change in transmitted intensity asa function of voltage can be calculated using continuumtheory and simple optics [36.36], and a typical transmis-sion curve for an ECB cell is illustrated schematicallyin Fig. 36.17.

The threshold voltage for director reorientation isindependent of cell thickness, and is given by

Vth D

sK1

"0 "; (36.20)

where " is the anisotropy in the dielectric permittiv-ity and K1 is the splay elastic constant. However, it isclear from (36.17) and (36.18) that the intensity of lighttransmitted by the ECB cell depends on the cell thick-ness and the wavelength of light. This undermines theusefulness of displays based on the ECB mode, sincethey require cells of uniform thickness and also theywill tend to show colouration in white light. Anotherimportant operating characteristic of displays is the an-gle of view, i. e., how the image contrast changes as theangle of incidence moves away from 90ı with respectto the plane of the cell. This is clear from Fig. 36.16,where the optical paths in the distorted state for obser-

Fig. 36.18Schematicof a directlyaddressed seven-segment liquid-crystal display

vation to the left or right of the perpendicular to theelectrodes are clearly different.

In order to construct a useful display from a simpleon=off shutter, it is necessary to consider how imagedata will be transferred to the display. This is knownas addressing, and to a large extent it is determinedby the circuitry that drives the display. However, weshall see that certain properties of liquid crystals alsocontribute to the effectiveness of different types of ad-dressing. The simplest method of displaying images ona liquid-crystal display is to form an array of sepa-rate cells of the type illustrated by the ECB cell, eachhaving a separate connection for the application of anelectric field. Images can then be created by switchingon, or off, those cells required to form the image. Thistechnique is known as direct addressing, and can be il-lustrated by the seven-segment displays used in watchesand numerical instrument displays (Fig. 36.18).

To create complex displays, a large number of sep-arate cells, known as picture elements or pixels, mustbe fabricated, usually in the form of a matrix. Provid-ing separate electrical connections for these pixel arrays(e.g., 640� 480) for a standard visual graphics array(VGA) computer screen, is impossible, and so othermethods of addressing have had to be developed. His-torically, the first was the technique known as passivematrix addressing, in which the array of cells are iden-tified in rows and columns, and connections are onlymade to the rows and columns: for an array of n�m pix-els, only nCm connections are made instead of n�m,as required for direct addressing. Each row is activatedin turn (sequentially), and appropriate voltage pulsesapplied to the columns. Only those pixel elements forwhich the sum of column and row voltages exceedsa threshold are switched to an on-state. However, theproblem with this method is that many unwanted pix-els in the off-state still have a voltage applied, and may

PartD|36.3


be partially activated in the display: so-called crosstalk.The time-sharing of activating signals is known as mul-tiplexing, and it relies on the addressed pixels holdingtheir signal while other pixels which make up the im-age are activated. Provided that the multiplexing is ona time scale of milliseconds, any fluctuation in theimage goes unnoticed. However, if the multiplexing be-comes too slow, the image starts to flicker. In fact thereis a limit to the number of rows of the matrix whichcan be addressed (nmax), which is related to the ratio ofthe on-voltage to off-voltage by a result due to Alt andPleshko [36.37]:

Von

VoffD

sn1=2max C 1

n1=2max � 1: (36.21)

The cell characteristic which determines the values ofVon and Voff is the optical transmittance curve, as illus-trated in Fig. 36.17. Depending on the desired contrastratio Ion=Ioff for a pixel, then the voltages Von=Voff

are determined. Thus, in the operation of a passivelyaddressed matrix display, there is a tradeoff betweenthe contrast ratio (Ion=Ioff) and the number of rows,i. e., the complexity of the display. The shape of thetransmittance curve is determined by the liquid-crystalmaterial properties, and so these affect the resolutionof the image displayed. For a desired contrast ra-tio of 4, the corresponding on=off ratio for an ECBcell might be 1:82. This gives a maximum numberof rows as four, which corresponds to a very-low-resolution display, which would be unusable except fora very basic device. This brief description of a sim-ple electro-optic display operating in the ECB modeillustrates that its performance depends on the dielec-tric, optical and elastic properties of the liquid-crystalmaterial used. Additionally, the properties at the liquid-crystal-substrate interface and the geometry of thecell will influence the electro-optic response of thecell.

One performance characteristic that is of very greatimportance is the speed with which the display informa-tion can be changed, since this determines the qualityand resolution of moving images. The dynamics of flu-ids are related to their viscosity, and it has already beenshown that the viscous properties of liquid crystals arecomplicated to describe, and are correspondingly diffi-cult to measure. The complication arises because liquidcrystals are elastic fluids, and so there is a coupling be-tween the flow of the fluid and the orientation of thedirector within the fluid. We have seen that the motionof the director can be described in terms of a rotationalviscosity, and the optical properties exploited in dis-plays are related to changes in the director orientation.Thus it is the rotational viscosity that is of primary im-

portance in determining the time response of displays.However, the fact that changes of director orientationcause fluid flow in liquid crystals complicates the pro-cess.

The time response of a liquid-crystal display pixelcan be illustrated by reference to the ECB display, al-though other cell configurations modify the behaviourto some extent. In what follows, we shall assume thatthe reorientation of the director within a display pixeldoes not cause the nematic liquid crystal to flow. Fora uniform parallel-aligned nematic-liquid-crystal film,the time for the director to respond depends on the mag-nitude of the electric field (or voltage) applied to thecell. If the voltage applied is only just greater than thethreshold voltage, then the time is very long, while ifa large voltage is applied, then the director respondsquickly. It is found that the time response can usuallybe represented as an exponential behaviour, althougheffects of flow will change this. Neglecting these, a re-sponse time �on can be defined in terms of the change intransmitted-light intensity as

I.t/� I.0/

Ion � I.0/D 1� exp

��

t

�on

�: (36.22)

and the relaxation time for switching on the display isgiven approximately by [36.38, 39]

�on D �1`2

2Keff

"�Von

Vth

�2

� 1

#�1

: (36.23)

On removing the applied voltage, the display elementreturns to its off-state, but with a different relaxationtime which is independent of the applied voltage, suchthat

�off D �1`2

2KeffI (36.24)

here �1 is the rotational viscosity coefficient, and theeffective elastic constant Keff that appears in theseexpressions is the splay elastic constantK1 for the ECB-mode display. These equations can be modified forother display configurations by changing Keff.

Although the ECB-mode display is the simplestthat can be envisaged, based on the Fréedericksz ef-fect, there are many disadvantages, in particular withrespect to its viewing characteristics, and it has not beenused commercially to any significant extent. However,the apparently simple modification of twisting the upperplate by 90ı has resulted in the phenomenally success-ful twisted nematic display, which represents a largepart of today’s multi-billion-dollar market.


D|36.3

V V

Glass substrate

Surfacealigning layersand electrodes

Off state: twisted,light transmitted

Top polarizersGlass substrate

Bottompolarizers

On state: untwisted,no light transmitted

Fig. 36.19 Schematic of a twisted nematic display

36.3.2 High-Volume Commercial Displays:The Twisted Nematic (TN)and Super-Twisted Nematic (STN)Displays

The simple twisted-nematic display is essentially thesame as the ECB display depicted in Fig. 36.16, exceptthat the orientations of the surface director at the con-taining glass plates are rotated by 90ı. However, the TNcell, invented by Schadt and Helfrich in 1970 [36.40],represented a considerable improvement over earlierdevices, and rapidly became the preferred configurationfor commercial displays. A schematic representation ofthe TN cell is given in Fig. 36.19.

This twisted configuration for a liquid crystal filmwas discovered by Mauguin, who found that insteadof producing elliptically polarised light, such a twistedfilm could rotate the plane of polarisation by an angleequal to the twist angle between the surface directorsof the glass plates [36.41]. In fact by working throughthe optics of twisted films, Mauguin showed that per-fect rotation of the plane of polarisation only resulted ifthe film satisfied the following condition

2 n` � � : (36.25)

Thus for the cell illustrated in Fig. 36.19, the off-state would be perfectly transmitting. This is knownas the normally white mode. In reality the cells usedfor TN displays do not meet the Mauguin condition,and the transmission for a 90ı twisted cell betweencrossed polarisers and incident unpolarised light is

given by [36.42]

T D 1

2

0

@1�sin2

2

p1C u2

�

1C u2

1

A ; (36.26)

where u D 2n`�

. Equation (36.26) shows that, for suffi-ciently large u, the transmission T is indeed a maximumof 0:5, however it is also a maximum for u D p

3,p15,p

35, etc. These points on the transmission curve corre-spond to the Gooch–Tarry minima; they are labelled asminima, since they were found for a TN cell operatingin the normally black state. Most commercial cells op-erate under conditions of the first or second minima sothat thin cells can be used, which give faster responses.It is, therefore, important that the birefringence of theliquid-crystal material can be adjusted to match the de-sired cell thickness, so that the display can have the bestoptical characteristics in the off-state.

Application of a sufficiently strong electric fieldacross the twisted film of a nematic liquid crystal hav-ing a positive dielectric anisotropy causes the directorto align along the field direction. Under these circum-stances the film no longer rotates the plane of polarisedlight, and so appears dark. The transmission as a func-tion of voltage for a twisted cell is similar to that shownin Fig. 36.17, except that the transmission varies morestrongly with change in voltage above the threshold,and drops to zero much more rapidly. In contrast tothe ECB cell discussed above, the threshold voltage fora TN cell depends on all three elastic constants

VTNth D

vuut

K1 C �

2 .K3 � 2K2/�

"0 "; (36.27)

where ( is the twist angle (usually =2). The relativechange of the transmission intensity with voltage of theTN cell is greater than for the ECB cell, and it canbe shown that the steepness of the transmission curveincreases as the property ratios K3=K1 and "="? de-crease. The on=off voltage ratio for a TN cell is closer tounity, than for an ECB cell, and so for similar contrastratios more lines can be addressed: up to about 20 fortypical cells and materials. This is significantly largerthan for the ECB cell, and so the TN cell allows morecomplex images to be displayed. There is still a wave-length dependence for the transmission, although thisis less marked than for the ECB mode. However, evenwith the improved multiplexing capabilities of the TNdisplay over the ECB cell, it is still not good enoughto use for computer screens. One very successful ap-proach to solve this problem was to modify the TN cellgeometry so that instead of a 90ı twist, the directors

PartD|36.3


on opposite sides of the cell are rotated by about 270ı.This is known as a super-twisted nematic cell.

The concept of the 270ı super-twisted nematic(STN) display seems at first sight to be irrational [36.43,44]. The director is an apolar vector and so there shouldbe no difference between a 270ı and a 90ı twistedcell. However, it is possible to maintain a director twistgreater than 90ı if the liquid crystal is chiral. The use ofchiral additives in 90ı TN cells was already established,since a very small quantity of chiral dopant added toa TN mixture would break the left/right twist degen-eracy in the cell and so remove patches of reversedtwist, giving a much improved appearance to the dis-play. If the amount of chiral dopant was increased, thenthe chiral liquid-crystal mixture would develop a sig-nificant intrinsic pitch. By adjusting the concentrationof the chiral dopant, the pitch of the mixture could bematched to the 270ı twist across the cell thickness of `,i. e., p � 4`=3. An STN cell operates in the same wayas a TN cell, so that an applied electric field causes thedirector to rotate towards the field direction, therebychanging the optical retardation through the film andthe transmission between external crossed polarisers.However, the additional twist in the STN cell has a sig-nificant effect on the optical properties of the nematicfilm.

The optical characteristics of the STN off-state areusually outside the Mauguin condition, which meansthat polarised light passing through the cell is notguided, and emerges elliptically polarised. The degreeof ellipticity is wavelength dependent, and so in whitelight the off-state appears coloured, as does the on-state.An ingenious solution to this problem is to have twoidentical STN cells, one behind the other, but wherethe second compensating cell has a twist of the oppo-site sense. In operation, only the first of the cells hasa voltage applied to it. The compensation cell acts tosubtract the residual birefringence of the liquid crys-tal layer, and the display now switches between whiteand black. Despite this additional complexity, the hugeadvantage of the STN display is the rapid change inoptical transmission with increasing voltage, and a fulloptical analysis shows that under optimum conditionsthe rate of change of transmission with voltage can be-come infinite. In modern implementations of the STNdisplay, the residual birefringence can be compensatedby an optical film, avoiding the need for double cells.It is easy to operate an STN display with a Von=Voff ra-tio of 1.1, which corresponds to an nmax of 100. Theshapes of the transmission=voltage curve of ECB, TNand STN cells are a direct consequence of the dielectricand elastic properties of the liquid-crystal material, butalso depend strongly on the configuration of the cellsand the surface alignment

In the description given of displays and their perfor-mance, some important aspects have been ignored. Thesurface orientation of the directors has been assumedto be pinned in the surface plane, which is the require-ment for a threshold response. However, it has beenfound that the performance of displays can be greatlyimproved if this condition is relaxed, and a pre-tilt is in-troduced to the cell, such that the surface director maymake an angle of up to 60ı to the plane of the con-taining glass plates. This pre-tilt can be introduced bydifferent surface treatments, and it depends on the in-terfacial properties of the liquid crystal. An importantperformance characteristic of displays is the angle de-pendence of the contrast ratio, or more simply how theappearance of the displayed image changes with angleof view. This is largely determined by the display de-sign, and can be accurately calculated from the opticalproperties of the cell. The refractive indices of the liquidcrystal will affect the contrast ratio and angle of view,but precise control of these performance parameters isdifficult. Improvements to the appearance in terms ofthe angle of view or brightness of displays have beenachieved by placing precisely manufactured birefrin-gent polymer films behind or in front of liquid-crystalcells.

36.3.3 Complex LC Displaysand Other Cell Configurations

The STN configuration described above used passivematrix addressing, and this opened up the possibilityof relatively large-area, high-resolution displays, whichcould be used in laptop computers and other hand-helddisplays. The next step was to introduce colour by di-viding each picture element into three sub-pixels withred, green and blue filters. However, the demand insome market sectors for larger displays with improvedappearance having higher resolution (extended graphicsarray (XGA) displays have 1024� 768 pixels) over-whelmed the capability of passive matrix addressing,and the alternative method of active matrix addressingis now used for more complex displays. This tech-nique requires each pixel to have its own switch, asin the simple seven-segment display already described.For high-resolution displays hundreds of thousandsof switches are provided by thin-film transistors de-posited onto the glass substrate, which forms the screen.These are known as thin-film-transistor twisted-nematic(TFT-TN) displays [36.45]. The sophistication of thesedisplays relies on the capabilities of integrated cir-cuit technology, but the properties of the liquid-crystalmaterials must still be optimised for the device config-uration. A representation of a TFT-TN display is givenin Fig. 36.20.


D|36.3

Colourfilterarray

Trans-parentelectrode

Gatebuslines

Transparentpixelelectrode

Glass substrate

Source bus lines Polarizer Glass substrate

Polarizer

Thin-filmtransistor

(TFT)

Fig. 36.20 Schematic of a complex colour TFT-TN dis-play

Although being described as an active matrix, theTFT-TN display still uses sequential addressing of pixelrows, and so activated pixels must remain switched onwhile the rest of the display image is created. The TFTsprovide a source of voltage to each liquid-crystal pixel,which must then hold its charge, as a capacitor, until theimage is changed. So another property of liquid crystalsbecomes important, that of low electrical conductivity,since the charge on a pixel will be lost by conductionthrough the liquid crystal. This determines the choice ofmaterials for TFT-TN displays. Generally, high dielec-tric anisotropy is a desirable property for liquid-crystaldisplay mixtures, since it reduces the operating voltage.However, materials with a high dielectric constant tendto have a high electrical conductivity, since charges ei-ther from impurities or leached from surfaces will bestabilised in high-dielectric-constant fluids. Thus theselection of suitable materials requires a compromisebetween its dielectric and conductance properties, and,of course, the all important refractive indices.

Many different cell configurations, which exploitthe optical properties of liquid crystals in differentways, have been tried, and some of these have beencommercialised to meet particular market requirements.One rather successful approach to the problem of re-stricted viewing angle has been the development ofthe in-plane switching (IPS) mode twisted-nematic dis-play [36.46, 47]; this is illustrated in Fig. 36.21. The twooptical states of the cells are (i) twisted, and (ii) pla-nar (parallel aligned film), and the director is switchedbetween these states by application of an electric fieldacross electrodes on a single plate of the cell. The statethat is stabilised by the electric field depends on thedielectric anisotropy of the liquid-crystal material. Thepreferred configuration uses materials having a negative

V V

Glass substratesurface aligning

layer

On state: light transmitted

Polarizers

Electrodes

Off state:no light transmitted

Liquidcrystal

Liquidcrystal

Fig. 36.21 Schematic of an in-plane switching mode dis-play

dielectric anisotropy, so that the off-state is a planar-aligned liquid-crystal film. Application of an electricfield to the in-plane electrodes will cause the directorat the bottom surface to align perpendicularly to its ini-tial direction, and so induce a twist through the cell(Fig. 36.21).

From an optical point of view, the director is alwaysin the plane of the cell, and this means there is less dis-tortion of an image when viewed at angles other than90ı. Another advantage of the IPS device is that theelectric field is confined to the lower plate, and the linesof force do not extend across the cell to the groundedupper plate. This means that a very low electrical con-ductivity of the liquid-crystal material is less importantthan for conventional TFT-TN displays. The thresholdvoltage for the IPS-mode device is given by

V IPSth D d

`

sK2

"0 "; (36.28)

where ` is the thickness of the liquid-crystal film, and dis the separation of the in-plane electrodes. Not surpris-ingly the threshold depends only on the twist elasticconstant, which is usually smaller by about a fac-tor of two than the splay and bend elastic constants.While this helps to reduce the operating voltage, thesmaller elastic energy associated with the pure twistdeformation results in longer switching times. A fur-ther disadvantage of the IPS display is that the opticaltransmission of the cell is reduced by the requirementto have both electrodes deposited on one plate, thereby

PartD|36.3


V

On state:light transmitted

Polarizer

Polarizers

V

Off state:no light transmitted

Glasssubstratesandelectrodes

Glasssubstratesandelectrodes

Polarizer

Liquidcrystal

Fig. 36.22 Schematic of a twisted vertically aligned dis-play

making smaller the active area available to display theimage.

A configuration which shares some of the charac-teristics of the IPS cell and has been successfully com-mercialised is the twisted vertically aligned nematic(TVAN) cell. The two optical states for this configu-ration are uniform vertical (homeotropic) alignment ofthe director for the off-state, and a twisted geometryfor the on-state (Fig. 36.22). The liquid-crystal materialused has a negative dielectric anisotropy, so applicationof an electric field between the plates causes the di-rector to align perpendicularly with respect to the fielddirection. A small quantity of optically active material(chiral dopant) is added to the liquid-crystal mixtureto ensure that the switched director adopts a twistedconfiguration through the cell. The advantages of thiscell are good viewing-angle characteristics and highoptical contrast. Improvements in display technologycontinue to be made, often simplifying earlier devices.For example, high-quality displays described as verti-cally aligned nematic (VAN) devices are now availablebased on the TVAN configuration, but without the twist.The material requirement here is for a liquid crystal ofnegative dielectric anisotropy, that will align perpendic-ularly to an applied electric field.

In the devices described above, one state is de-fined by the surface conditions of the cell, while theother is defined by the action of the applied electricfield. A bistable device is one in which two stablefield-free states exist, both of which are accessible

Homeotropic aligning surface

Hybrid aligned state Vertically aligned state

Grating surface treated with homeotropic alignment agent

Fig. 36.23 Schematic of a zenithal bistable device

by switching with an external field. The first bistableliquid-crystal display to be developed was based ona ferroelectric effect observed in chiral tilted smectic Cliquid crystals [36.48]. This ferroelectric smectic dis-play has achieved some limited commercial success inspecialist markets, but relies on a surface stabilisationof smectic layers, which is very sensitive to mechanicalshock. Recently [36.49], bistable nematic displays havebeen developed in which two alignment states withina liquid-crystal cell, having different optical transmis-sion, can be stabilised. If one of the substrates ofa normal cell is replaced by a surface which has po-tentially two states of minimum energy correspondingto two surface alignments of the director, then it be-comes possible to switch these states selectively usingan electric field. A suitable bistable surface is providedby a grooved surface (grating) which has been treatedwith a surfactant to favour homeotropic alignment ofthe director at its surface [36.50]. Thus the two surfacestates correspond to (i) that determined by the grat-ing, and (ii) that determined by the surfactant wherethe director is perpendicular to the substrate. Combin-ing this intrinsically bistable substrate with a secondsubstrate having a director alignment direction perpen-dicular to the grating direction gives a cell configura-tion capable of supporting two optically distinct stablestates, which can be switched between using an appliedvoltage. Various director configurations are possiblewith this type of cell, and one example is illustratedin Fig. 36.23.

In the absence of any perturbation, the directororientation within the cell will be determined by thehomeotropic alignment at one substrate and the align-ment at the grating substrate. This hybrid (uniformplanar and homeotropic) alignment causes a spatiallyvarying director tilt through the sample. Application of


D|36.3

an electric field to a positive-dielectric-anisotropymate-rial will cause the director to align parallel to the appliedfield, and eventually a fully homeotropic configurationfor the director is stabilised. The switch back from thehomeotropic state to the hybrid state is thought to bedue to a flexoelectric interaction. Other alignment con-figurations are also possible for the so-called zenithalbistable nematic (ZBD) cell. Displays based on theseconfigurations share the good viewing characteristics ofboth the IPS and TVAN configurations, but they havethe great advantage that the image is retained when thevoltage is removed.

All the displays described so far rely on the cou-pling between an applied electric field and the dielectricproperties of the liquid-crystal material, but, as we haveshown, other material properties are just as importantto the operating characteristics of the display. The ap-pearance of a display depends on the optical propertiesof the liquid crystal and the cell configuration, but theoperating voltage and switching times of a display arecrucial in determining the types of application. Chang-ing the nature of the interaction between the switchingelectric field and the liquid crystal gives rise to anotherrange of possibilities for liquid-crystal devices. Undercertain circumstances, a liquid crystal can be made toexhibit permanent ferroelectric (or spontaneous) polari-sation, and this couples linearly with an external electricfield, in contrast to dielectric properties which couplewith the square of the electric field strength. Not sur-prisingly this makes a big difference to the switchingbehaviour of liquid crystals.

The final display to be considered is based on flex-oelectric coupling between the electric field and theliquid crystal. Flexoelectricity occurs, in principle, withall liquid crystals, chiral or not, and shows itself asa bulk electric polarisation induced by an elastic strain.Conversely application of an electric field can cause anelastic strain. In general, flexoelectricity is rather smalland difficult to detect, however it is thought to be re-sponsible for an electro-optic effect observed in chiralnematic liquid crystals, which is being investigated fordisplay applications. The effect, sometimes known asthe deformed helix mode [36.51], is similar in some re-spects to the ferroelectric switching observed in chiralsmectic C phases, but there is no longer a requirementfor a layered structure. Chiral nematic liquid crystalsspontaneously form helical structures in which the di-rector rotates with a pitch determined by the molecularstructure. If an electric field is applied perpendicularlyto a chiral-nematic helix, then there is a tendency for thehelix to unwind, depending on the sign of the dielec-tric anisotropy. Even if the dielectric anisotropy of thematerial is zero, there is an elastic strain which can gen-erate a polarisation (flexoelectric polarisation), which

Opticaxis

Helix axisHelix axisand optic axis

Uniform lying helixNo field

Deformed helixField applied

Fig. 36.24 Schematic of a deformed helix mode flexoelec-tric display

will interact with an applied electric field. This may beexploited in a device configuration, where a thin film ofa chiral nematic liquid crystal, having a small or zerodielectric anisotropy, is aligned such that its helix axisis parallel to the containing glass plates (Fig. 36.24).

Application of an electric field across the plates willcause a distortion of the helix through the splay andbend flexoelectric coefficients, which appears as a ro-tation of the optic axis in the plane of the film [36.25].Reversal of the electric field direction will reverse therotation of the optic axis, with an intrinsic switchingtime about one hundred times faster than conventionalnematic displays. Optically, the effect observed is verysimilar to that exhibited by smectic ferroelectric dis-plays.

There are many cell configurations that can beused with liquid crystals to produce optical switches,displays or light modulators, and some of the moreimportant have been described. The precise operationand performance of these liquid-crystal devices de-pends on both the cell design and the material propertiesof the liquid crystal. To a large extent the configura-tion of the liquid crystal within the cell is determinedby such factors as the surface treatment of the platesenclosing the liquid crystal and the interactions be-tween the surfaces and the liquid crystal. Our under-

PartD|36.4


standing of these interactions is very limited at thepresent time, and much more research is necessary be-fore a quantitative theory can be formulated. However,given the cell configuration, the performance of theliquid-crystal device depends critically on the physi-cal properties of the liquid-crystal material. Thus theelectrical switching characteristics will depend on thedielectric properties, while the optical appearance ofthe device will be determined by the refractive in-

dices. Elastic properties contribute to both the electricfield response and the optical appearance, since anydeformation of the director will be determined by theelastic properties of the liquid crystal. Finally, the all-important dynamical behaviour will be controlled bythe viscous properties of the liquid crystal. All thesematerial properties will be discussed in the next sec-tion.

36.4 Materials for Displays

The most important requirement for a liquid-crystal dis-play material is that it should be liquid crystalline overthe temperature range of operation of the device. De-spite this, some of the first experimental display devicesincorporated heaters in order to maintain the mate-rial in the liquid-crystal phase: for example, the firstliquid-crystal shutter patented by Marconi and earlyprototype displays developed by the Radio Corporationof America (RCA). It was not until the late 1960s thatroom-temperature nematic liquid crystals suitable fordisplay applications were discovered. The first of thesewere based on Schiff’s bases, which although easy toprepare, were difficult to purify and were susceptibleto chemical decomposition in a device. One materialwhich attracted particular attention from experimentalphysicists was MBBA, which has a nematic range of22�47 ıC (Table 36.1). The basic two-ring core linkedby an imine group was the structural unit of many com-pounds having different terminal groups which wereprepared for display mixtures in the early 1970s. Itwas found that mixtures of Schiff’s bases often hadlower crystal-to-nematic transition temperatures thanany of the components, and furthermore would often re-main liquid crystalline even below the thermodynamiccrystallisation temperature. These two phenomena ofeutectic behaviour and super-cooling have been ex-ploited in the development of materials for devices. Theearly experiments on liquid-crystal displays were pri-marily focused on nematic or chiral compounds, butwe have seen that other displays have been developedwhich use different liquid-crystal phases, most impor-tantly the chiral smectic C phase.

Early studies established guiding principles for thedevelopment of display materials. First, the phase be-haviour must be acceptable, i. e., the right phase stableover a suitable temperature range. Secondly, the mate-rial must have the correct electrical and optical prop-erties for the particular display application envisaged,and above all must be of sufficient chemical purityto prevent any deterioration in performance over time.

Again, guided by the early experiments, suitable dis-play materials require the synthesis of compounds ofappropriate chemical structure, and then the formu-lation of mixtures to optimise the properties. Therehave been a number of reviews of liquid-crystal ma-terials for displays [36.53, 54, 56–59] and these con-tain many tables of data on a wide range of com-pounds. In this Section, we will give a brief accountof the basic chemical structures used for materials inmodern liquid-crystal displays, and then show howmixtures are devised to give the best possible perfor-mance characteristics for different displays. It has tobe recognised that many of the details of display ma-terials are matters of commercial confidentiality, andso it is not possible to give precise accounts of mate-rials currently used or under investigation. However,the generic chemical structures and principles usedin developing suitable mixtures are generally applica-ble.

36.4.1 Chemical Structureand Liquid-Crystal Phase Behaviour

There is a huge literature on the relationship betweenthe structure of mesogens and the nature and stability ofthe liquid-crystal phases they form [36.60]. The stud-ies have embraced empirical correlations of chemicalstructure and phase behaviour, theoretical calculationsfor simple particles (hard rods, spherocylinders etc.)representing mesogens, and computer simulations ofcollections of particles of varying complexities. Forthe display applications considered in this Chapter, thedesired phases are nematic, and occasionally chiral ne-matic or chiral smectic C. Such phases are formed bymolecules having extended structures, which usuallyrequire the presence of terminal alkyl chains to re-duce the crystallisation temperatures. Components innematic display mixtures typically have two, three orfour carbocyclic rings joined directly or through a vari-ety of linking groups.

Liquid Crystals 36.4 Materials for Displays 957Part

D|36.4

Table 36.1 Some typical liquid-crystal materials, including selected physical properties ((ex) – extrapolated from mea-surements on a nematic solution)

Compound �" �n Rotational viscosityTransition temperatures (ıC) [reference] (T ıC) (T ıC) (1=mPa s)

� 1 0.2 �1 D 109 [36.52]

TCrN 22 ıC TNI 47 ıC [36.53] (37 ıC)8.5 0.18 �1 D 102 [36.52]

TCrN 22 ıC TNI 35 ıC [36.53] (29 ıC) (25 ıC) (25 ıC)3.2 (ex) 0.05 (ex)

TCrI 34 ıC [36.54]9.9 0.12

TCrN 31 ıC TNI 55 ıC [36.53] (48 ıC) (40 ıC) �1 D 128 [36.52]3.5 0.05

TCrN 62 ıC TNI 85 ıC [36.53] (78 ıC)19.9 0.15

TCrN 44 ıC TNI 57 ıC [36.53] (40 ıC)� 0 0.15

TCrN 67 ıC TNI 82 ıC [36.55]

36.4.2 The Formulationof Liquid-Crystal Display Mixtures

The two requirements for a liquid crystal to be usedin a display are a suitable temperature range of phasestability and appropriate physical properties. These re-quirements cannot be satisfied for complex displaysby a single compound, and commercial display mate-rials may contain up to twenty different components.The formulation of these mixtures is essentially anempirical process, but guided by the results of ther-modynamics and experience. The principles behindthe preparation of multicomponent mixtures can be

illustrated initially by consideration of a binary mix-ture.

It is well-known that the melting point of a bi-nary mixture of miscible compounds is depressed,sometimes below the melting points of both compo-nents. Furthermore, the melting point of the binarymixture may exhibit a minimum at a particular compo-sition, known as the eutectic. This occurs with liquid-crystalline compounds, and provides a method of re-ducing the lower temperature limit for liquid-crystalphase stability in mixtures. The upper temperature limitof the liquid-crystal range is fixed by the transition toan isotropic liquid. The phase rule of Willard Gibbs

PartD|36.4


predicts that in binary mixtures there will always bea region of two-phase coexistence in the vicinity ofa phase transition; that is, the transition from liquidcrystal to isotropic occurs over a range of temperaturesfor which both the isotropic liquid and liquid crystal arestable in the mixture. Because of the weak first-ordernature of most liquid crystal to isotropic phase transi-tions, the two-phase region is small. The character ofphase transitions is determined by the correspondingentropy change, and a weak first-order transition hasa small

� � 2 JK�1 mol�1�associated entropy. If the

latter were zero, then the transition would be second or-der, and there would no longer be a region of two-phasecoexistence. The phase diagrams of multicomponentnematic mixtures can be calculated by thermodynamicmethods [36.61, 62] and the transition temperatures ofthe mixtures can vary with composition in a variety ofways. For mixtures of two liquid-crystalline compoundsof similar chemical constitution, the variation of thenematic to isotropic transition temperature is approxi-mately linear with composition [36.63].

It is possible to calculate the variation of the melt-ing point with composition using an equation attributedto Schroeder and van Laar. For each component i, themixture composition (mole fraction xi/ and the meltingpoint of the mixture T are related by

ln xi D � Hi

R

�1

T� 1

Ti

�; (36.29)

where Hi and Ti are, respectively, the latent heat offusion and melting point of the pure component i. Fora binary mixture there are two such equations whichcan be solved to give the eutectic temperature andcomposition. In a multicomponent mixture, the set ofequations (36.29) can be solved subject to the condi-tion,

X

i

xi D 1 (36.30)

to predict the eutectic of the mixture.While there is a reasonable thermodynamic basis

to the prediction of the phase diagrams of mixtures,the determination of the physical properties of mix-tures from the properties of individual components ismuch more difficult. Given the absence of any bet-ter theories, it is common to assume that in mixtures,physical properties such as dielectric anisotropy, bire-fringence and even viscosity vary linearly with theamount of any component, at least for small concen-trations. While this may give an indication of the effectof different components on the properties of a displaymixture, it can also be very misleading. One theoretical

problem is that, for a mixture at a particular tempera-ture, the orientational order parameters of the differentcomponents are not equal. The more anisometric com-ponents (e.g., three-ring mesogens) are likely to havea larger orientational order parameter than smaller (two-ring) mesogens. Since the various physical propertiesof interest in displays depend on the order parameterin different ways, it is difficult to predict the contri-bution of different components to the overall mixtureproperties. Despite this, many tables of data for liquid-crystal compounds of interest for display mixtures areprepared [36.60] on the basis of extrapolated mea-surements on mixtures at low composition, normally< 20wt%. There is always a problem concerning thetemperatures at which to compare the physical prop-erties of liquid crystals and their components. Manymeasurements are made at room temperature, so thatthis becomes the temperature for comparison. How-ever, a more useful approach is to compare propertiesat equal reduced temperatures (or at the same shiftedtemperatures, TNI �T), since under these conditions theorientational order parameters are likely to be simi-lar.

36.4.3 Relationships Between PhysicalProperties and Chemical Structuresof Mesogens

Electrical and Optical PropertiesThese properties include the dielectric permittivity,electrical conductivity and refractive indices. The mag-nitude of the dielectric anisotropy determines thethreshold voltage necessary to switch a display, andinfluences the transmission=voltage characteristics ofthe cell. Depending on the particular display config-uration, a positive or negative dielectric anisotropymay be required. Refractive indices strongly affectthe appearance of a display. Usually the refractiveindices or birefringence must be adjusted for a par-ticular cell configuration to give the optimum on=offcontrast ratio. Coloration in displays can sometimesoccur in materials of high refractive index, and so itis desirable to keep the birefringence as low as pos-sible, compatible with an acceptable contrast ratio.For twisted structures, the magnitude of the birefrin-gence also determines the efficiency of light guiding,and so close control of the values of the principalrefractive indices of a display mixture is important.For non-conducting materials, the refractive indicesare measures of the dielectric response of a mate-rial at very high, i. e., optical frequencies, and it ispossible to formulate a single theory which relatesthe dielectric and optical properties of a liquid crys-tal to its molecular properties. Unfortunately this is


D|36.4

Table 36.2 Materials of high, low and negative birefringence

Compound Transition temperatures �n [reference](T ıC)

TNI 112 ıC 0.31 [36.64](92 ıC)

TCrSmB 23 ıC TSmBN 35 ıC TNI 49 ıC 0.052 [36.59]

TNI 93:5 ıC 0.074 [36.64](58:5 ıC)

TCrN 80 ıC TNI 96 ıC �0:193 [36.64](61 ıC)

not possible for the electrical conductivity. The lat-ter is largely determined by the purity of the liquidcrystal, but it is found that the higher the value ofthe permittivity, the larger the electrical conductivity.Materials of high electrical conductivity tend to leakcharge, and so an image may deteriorate during a mul-tiplexing cycle. In general it is desirable to minimisethe conductivity of a display mixture, although thiswas not the case for the first liquid-crystal displaysreported [36.65]. These utilised the strong light scat-tering which results when an electric field is appliedto certain nematic materials. The scattering is due toelectrohydrodynamic instabilities in liquid-crystal ma-terials which have a significant electrical conductivity.Such materials are not suitable for use in modern, fast-multiplexed displays.

The dielectric anisotropy " and birefringence nof a nematic can be related to molecular propertiesof polarisability and dipole moment using a theoryoriginally developed by Maier and Meier [36.66]. The

birefringence is given by

n � NS

"0

�˛l �˛t

�; (36.31)

where N is the density in molecules per m3 and ˛ D.˛l �˛t/ is the anisotropy of the molecular polarisabil-ity. S is the order parameter, defined in Sect. 36.2.1, andsmall corrections due to the local field anisotropy havebeen neglected. Such corrections cannot be ignored inthe corresponding expression

" D NhFS

"0

� ˛ C �2

2kBT.3 cos2 ˇ � 1/

(36.32)

for the dielectric anisotropy, especially for materialsof high permittivity. In (36.32) h and F are local-fieldcorrection factors, while � is the molecular dipole mo-ment, and ˇ is the angle between the dipole directionand the long axis of the molecule. For molecules con-taining a number of dipolar groups, � is the root mean

PartD|36.4


Table 36.3 Materials of high, low and negative dielectric anisotropy; the inset figure indicates the direction of the total dipolemoment with respect to the core of the molecule .1D D 3:33564�10�30 Cm/

Compound Transitiontemperatures

�" [reference](T ıC)

Total dipolemoment� (D)

TCrN 22:5 ıC TNI 35 ıC 11.5 [36.67](25 ıC)

4.8

TCrN 143 ıC TNI 150 ıC �10:0 [36.68](145 ıC)

6.4

TCrN 13 ıC TNI 64 ıC 0.0 [36.69](58 ıC)

1.4

square of the vector sum of all contributing groups.Both the birefringence and the dielectric anisotropy in-crease with decreasing temperature, and the detailedvariation with temperature is largely determined by thetemperature dependence of the order parameter S.

The manipulation of birefringence is achieved bychanging the chemical constitution of the mesogen.Thus extending the electronic conjugation along theaxis of a mesogen will result in an increase in lon-gitudinal polarisability, and hence an increase in bire-fringence. Saturated carbocyclic rings, such as cy-clohexane, and aliphatic chains generally have smallpolarisabilities and mesogens containing a predomi-nance of such moieties form low-birefringence liquidcrystals. Mixtures for displays require a positive bire-fringence, which is associated with calamitic or rod-likemesogens. In order to improve the viewing characteris-tics of displays, optically retarding films are placed infront of the display, and depending on their function,these may be of negative or positive birefringence. Thelatter can be fabricated by encapsulation or polymeri-sation of suitable molecules of an extended structure.On the other hand, films of negative birefringence havebeen made using discotic materials, i. e., mesogenicmolecules formed from disc-like structures which havea negative polarisability anisotropy (Sect. 36.1.3). Someexamples of liquid crystals having different birefrin-gence are shown in Table 36.2.

The introduction of chirality into liquid crystals hasimportant consequences for their optical properties. Theselective reflection of coloured light from the helicalstructure of a chiral nematic has already been men-tioned in Sect. 36.1.2. All chiral materials will rotatethe plane of incident polarised light, and the particularoptical properties associated with chiral thin films areexploited in many liquid-crystal device applications.

The dipole moment of a molecule is increasedif strongly electronegative or electropositive groupsare substituted into the structure, with the result thatthe dielectric permittivity increases. For mesogenicmolecules, the locations of the electropositive or elec-tronegative groups are important, since not only themagnitude but also the orientation of the molecu-lar dipole strongly influences the dielectric anisotropy.From (36.32) it can be seen that the dipolar contributionto the dielectric anisotropy may be positive or negativedepending on the value of the angle ˇ, since for val-ues of ˇ greater than 54:7ı the dipolar contribution tothe permittivity anisotropy becomes negative. This is il-lustrated by the mesogens shown in Table 36.3, wheredifferent structures can be designed to give large posi-tive, negative or zero dielectric anisotropy.

The most effective substituent for producingmateri-als of high dielectric anisotropy is the cyano group, andmixtures containing cyano-mesogens were the basis forthe rapid development of complex displays in the 1980s


D|36.4

and early 1990s. However, these mixtures tended tohave relatively high viscosities, which gave rise to slowswitching times. Another disadvantage was the highelectrical conductivity associated with the high dielec-tric anisotropies which caused charge leakage duringmultiplexing, and hence degradation of the image.

As the demands placed on liquid-crystal materi-als by more sophisticated display technologies haveincreased, new families of molecules have been syn-thesised and screened for their physical properties.However, it is no longer the properties of the puremesogens that are of interest, rather how they behavein mixtures. For this reason, the physical properties ofmost components of display mixtures are measured inmixtures, and values for the pure mesogens are obtainedby extrapolation. Data derived in this way are usefulin designing display mixtures and for comparison pur-poses, but cannot be relied upon to give quantitativeinformation about the relationship between molecularstructure and physical properties.

The major display technologies using TN, STN orTFT-TN configurations require display mixtures hav-ing a positive dielectric anisotropy. Many materialshave been developed to improve the electro-opticalbehaviour of these displays, particularly using fluorine-substituted mesogens to provide the required dielectricand optical properties (for examples see [36.54, 58,70]). Some of these fluorinated mesogens are shown inTable 36.4. However, within the past seven years, newdisplay configurations have emerged, such as the in-plane switching (IPS) and vertically aligned (VAN andTVAN) nematic modes, which require mixtures withnegative dielectric anisotropy. Using the design strat-egy illustrated above for simple mesogens, it has beenpossible to prepare a large number of materials with thedesired negative dielectric anisotropy. These are againmostly based on fluorine-substituted compounds, andas before their properties have mostly been determinedby extrapolation of measurements on mixtures.

Elastic PropertiesThe property known as elasticity is characteristic ofliquid crystals, and distinguishes them from isotropicliquids. It has been shown in Sect. 36.2.3 that themacroscopic orientational disorder of the director in liq-uid crystals can be represented in terms of three normalmodes, designated as splay, twist and bend, and as-sociated with each of these deformations is an elasticconstant. Since the elastic properties of display ma-terials contribute to the electro-optic response, theiroptimisation for particular display configurations is im-portant to maximise the performance of commercialdevices. However, despite their importance, the rela-tionships between the magnitudes of elastic constants

and the chemical structure of mesogens are poorly un-derstood. There is a good reason for this; the optical anddielectric properties are to a first approximation singleparticle properties. That is they are roughly proportionalto the molecular number density and are also linearlydependent on the order parameter. Because elastic prop-erties are a measure of the change in energy due todisplacements of the director, they are related to theorientation-dependent intermolecular forces. Thus, ata molecular level, elastic properties are two-particleproperties, and are no longer linearly proportional tothe number density. A further consequence is that theelastic properties depend to lowest order on the squareof the order parameters. Molecular theories of elasticityin nematic liquid crystals have been developed [36.71]and the simplest results suggest that the different elasticconstants can be related to molecular shape

K1 D K2 / hx2i and K3 / hz2i ; (36.33)

where hz2i and hx2i are the average intermoleculardistances parallel and perpendicular to the molecularalignment direction, respectively. Thus theory predictsthat for rod-like molecules the splay elastic constantshould be smaller than the bend elastic constant, and in-creasing the molecular length should increase K3, whileincreasing the molecular width should increase K1. Thisis roughly in accord with experimental results, exceptthat the prediction of equal splay and twist elastic con-stants is not confirmed (Fig. 36.9). In general, the twistelastic constant is about one half of the splay elasticconstant. Hard particle theories [36.72] evaluated forspherocylinders provide further guidance on the rela-tionship of elastic constants to molecular shape. Thesetheoretical results can be presented in a simplified wayas follows

K1 �K

KD �.1� 3�/ I

K2 �K

KD ��.2C �/ I

K3 �K

KD �.1C 4�/ ; (36.34)

where K D 13 .K1 CK2 CK3/. The quantities � and �

are parameters of the theory, where � is approximatelyequal to the square of the length:width ratio of thespherocylinder, and � depends on the degree of orien-tational order. Despite the fact that details of internalchemical structure are ignored, these theoretical resultsfor nematics are in approximate agreement with ex-perimental measurements on simple nematics. If thenematic material has an underlying smectic phase, orif there is a tendency for local smectic-like ordering,

PartD|36.4


Table 36.4 Fluorinated mesogens of positive and negative dielectric anisotropy used in liquid-crystal mixtures for mod-ern displays. All measurements listed have been obtained by extrapolation from measurements on nematic solutions

CompoundTransition temperatures (ıC) [reference]

�" �n Rotational viscosity(1=mPa s)

�6:2 0.1 �1 D 110

TCrN 49 ıC TNI 13 ıC [36.59]�5:9 0.156 �1 D 233

TCrN 80 ıC TNI 173 ıC [36.59]11.3 0.134 �1 D 191 [36.73]

TCrN 30 ıC TNI 58 ıC [36.54]9 0.14 �1 D 180 [36.73]

TCrSmB 43 ıC TSmBN 128 ıC TNI 147 ıC [36.54]�2:7 0.095 �1 D 218

TCrN 67 ıC TNI 145 ıC [36.59]�4:3 0.2 �1 D 210

TCrN 88 ıC TNI 89 ıC [36.59]11.1 0.067 �1 D 175

TCrN 56 ıC TNI 117 ıC [36.59]

this can strongly affect the elastic constants. Both thetwist and bend elastic constants are infinite in a smec-tic phase, and in a nematic phase they diverge as thetransition to a smectic phase is approached.

The elastic constants contribute directly to thethreshold voltage and the response times of displays.Threshold voltages increase with increasing elastic con-

stants, and the elastic constants responsible depend onthe configuration of the display. Thus for the planar-aligned electrically controlled birefringence display(ECB), the threshold voltage depends on K1, while theswitching voltage for TN displays depends on a com-bination of all three elastic constants (36.27). The IPSdisplay voltage depends only on K2, and for VAN and


D|36.4

TVAN devices, the threshold voltage is determinedby K3. Different combinations of elastic constants de-termine the transmission=voltage curves, which areimportant in the multiplexing of complex displays.For example, decreasing the ratio K3=K1 increases thesteepness of the curve for TN displays, and so increasesthe number of lines that may be addressed. On theother hand, for the STN display, if the ratio K3=K1 isdecreased, the number of lines that may be addressedalso decreases. Identification of the important elasticconstants necessary to optimise the operation of thesedisplays is relatively straightforward; however, manip-ulation of the components of displays mixtures to givethe best results is much more difficult.

Ferroelectric and Flexoelectric PropertiesThe electro-optic properties considered so far resultfrom interaction of an electric field with the anisotropicpermittivity of a material. This might be termeda quadratic response since the dielectric term in thefree energy (36.2) is quadratic in the electric field, andas a consequence the electro-optic response does notdepend on the sign of the electric field. For materialshaving a centre of symmetry, such as achiral nematicand smectic liquid crystals, this response is the only onepossible. However, if the centro-symmetry of the liquidcrystal is broken in some way, then a linear electric po-larisation becomes possible, which results in a linearresponse to an applied electric field. One example ofthis, in the context of displays, is the chiral smectic Cphase, which in the surface-stabilised state exhibits fer-roelectricity, i. e., a spontaneous electric polarisation.The origin of the symmetry breaking in this case isthe chirality of the material, and the polarisation is di-rected along an axis perpendicular to the tilt plane ofthe smectic C. Another way in which the symmetry canbe broken is through elastic strain. This effect was firstdescribed by Meyer [36.24], and it can be representedas a polarisation resulting from a splay or bend defor-mation (Sect. 36.2.4). Since at a molecular level, strainis related to molecular interactions, the flexoelectric re-sponse depends on a coupling of intermolecular forcesand the molecular charge distribution. Two molecularmechanisms have been identified which contribute tothe strain-induced polarisation. If the molecules havea net dipole moment, then the longitudinal componentcan couple with the molecular shape to give a splaypolarisation along the director axis, while the trans-verse component couples with the shape to give a bendpolarisation perpendicular to the director axis. Evenin the absence of a net dipole, a quadrupolar chargedistribution in a molecule can result in strain-inducedpolarisation [36.26]. Both contribute to the splay andbend flexoelectric coefficients, but only the dipolar part

γ1/P

Vfg0 0.35

4

3

2

1

0.30

5

4

3

12

Fig. 36.25 Relationship between the rotational viscos-ity coefficient �1 (P D 10�1 Pa s) and the geometric freevolume (Vfg) at 25 ıC for bicyclic polar mesogens.Compound numbers represent alkyl series as follows:1-cyanophenylalkylcyclohexanes; 2-alkylcyanobiphenyls;3-cyanophenylalkylpyridines; 4-cyanophenylalkylbicyclo-octanes; 5-alkoxycyanobiphenyls. (After [36.52])

persists in the sum e1 C e3. Thus it is common to quoteflexoelectric coefficients as a sum and difference ratherthan as separate coefficients.

The measurement of flexoelectric coefficients hasbeen a challenge to experimentalists, and there is a widerange of values in the literature for standard materi-als (Sect. 36.2.4). It is, therefore, premature to drawany conclusions about structure=property relationshipsfor flexoelectricity from the limited experimental dataavailable. There have been attempts [36.74, 75] tomodel flexoelectricity for collections of Gay–Berneparticles simulating wedge-shaped molecules. Applica-tion of the surface interaction model to flexoelectricbehaviour [36.76] has allowed the calculation of flex-oelectric coefficients for a number of molecules; thesecalculations include the quadrupolar contribution. Theimportance of molecular shape is clearly demonstrated,and in particular changes of shape, either through con-formational changes or cis–trans isomerisation, havelarge effects on the magnitude and sign of the flexo-electric coefficients.

Flexoelectric effects contribute to the electro-opticresponse of nematic displays, especially those withhybrid alignment, i. e., planar on one electrode andhomeotropic on the other electrode, but they are notusually considered in the optimisation of mixture prop-

PartD|36


erties. However, flexoelectric properties are of directimportance to the operation of displays based on theswitching of the direction of the optic axis in chiral ne-matics: the so-called deformed helix mode [36.25].

Viscous PropertiesAs explained in Sect. 36.2.5, the flow properties of liq-uid crystals are complicated. Since the materials areanisotropic, the viscosities in different directions aredifferent, furthermore because of the torsional elastic-ity, viscous stress can couple with the director orien-tation to produce complex flow patterns. Thus thereare five viscosity coefficients necessary for nematics,in addition to the elastic constants, and as many as 20viscosities for smectic C liquid crystals [36.77]. To re-late all or indeed any of these to molecular structureis a formidable challenge. However, for most liquid-crystal displays, the only viscosity of interest is thatwhich relates to the reorientation of the director: theso-called rotational viscosity. This depends on the tem-perature and order parameter, and on the forces experi-enced by the rotating director. The rotational viscositiesfor all liquid-crystalline materials can be represented byone or other of the following parameterised relations

�1 D aSx exp�A.T /

kBT

�

or

�1 D bSy exp

�B

T �T0

�; (36.35)

where a, b, A and B are material parameters, and S isthe order parameter raised to a power of x or y between0 and 2. The first of these expressions emphasises thediffusional nature of rotational relaxation in a liquidcrystal, that is molecules rotating in an external poten-tial. The second expression taken from polymer physicsdescribes rotation in terms of free volume, where T0 isthe temperature at which the free volume becomes zero,and the rotational viscosity infinite, i. e., a glass transi-tion.

At the simplest level, the rotational viscosity de-pends on the molecular shape and size. As the lengthof the molecule increases, from two rings to three ringsetc. �1 increases, similarly it increases with the lengthof the alkyl chain. Varying the nature of the rings in the

mesogenic core can have a dramatic effect on the rota-tional viscosity, which correlates well with free volume,as shown in Fig. 36.25, and the glass temperature of thematerial.

There is a correlation between the increasing dielec-tric anisotropy and increasing rotational viscosity whichcan be attributed to local dipolar intermolecular forceswhich impede end-over-end rotation of molecules. Thusmesogens having cyano-groups in a terminal positiontend to have relatively high viscosities. Other dipolargroups such as fluorine do not have such a deleteriouseffect on viscosity as the cyano-group, and so fluorine-containing mesogens are increasingly preferred in theformulation of display mixtures.

As with the determination of other properties, therotational viscosities of mesogenic components are of-ten determined by extrapolation from measurements onmixtures doped with the component under investiga-tion. Such a method only provides approximate valuesto compare different components, but in the formulationof mixtures for display applications it is only the rota-tional viscosity of the final mixture that is important.Rotational viscosities of some mesogens of interest fordisplay mixtures are given in the Tables 36.1 and 36.4accompanying this section. In many instances, the vis-cosities, as with other properties, have been determinedby extrapolation from measurements on mixtures. Themeasurement of rotational viscosities is experimentallydifficult, and some authors prefer to quote the resultsof bulk-viscosity measurements in terms of a kinematicviscosity. In fact there is a good correlation betweenkinematic viscosity and rotational viscosity, and wherepossible both values have been included in the tables.From the various tables, the effect of increasing themolecular length on the viscosity is clearly seen, as isthe effect of replacing an F atom with a CN group. Lat-eral substitution, which produces materials of negativedielectric anisotropy, tends to increase the rotationalviscosity. Despite this the fastest nematic displays nowuse vertical alignment and materials of negative dielec-tric anisotropy. The operating characteristics of displaymixtures depend on the physical properties of indi-vidual components in a very complex manner, andoptimisation of mixture properties has to be carried outin a concerted way.

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LiquidCrysta 36.LiquidCrystalsLiquidCrysta 933 PartD|36.1 36.LiquidCrystals GeoffreyLuckhurst,DavidDunmur Thischapteroutlinesthebasicphysics,chemical natureandpropertiesofliquidcrystals.Thesema-

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