LiquidCrystals
ThirdEdition
IAM-CHOONKHOO
PennsylvaniaStateUniversity
UniversityPark,Pennsylvania
Thiseditionfirstpublished2022 ©2022JohnWiley&Sons,Inc.
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Names:Khoo,Iam-Choon,author.
Title:Liquidcrystals/Iam-ChoonKhoo,PennsylvaniaStateUniversity, UniversityPark,Pennsylvania.
Description:Thirdedition.|Hoboken,NJ:JohnWiley&Sons,Inc.,[2022] |Series:Wileyseriesinpureandappliedoptics|Includes bibliographicalreferencesandindex.
Identifiers:LCCN2021038545(print)|LCCN2021038546(ebook)|ISBN 9781119705826(hardback)|ISBN9781119705857(adobepdf)|ISBN 9781119705796(epub)
Subjects:LCSH:Liquidcrystals –Congresses.
Classification:LCCQD923.L531592021(print)|LCCQD923(ebook)|DDC 530.4/29–dc23
LCrecordavailableathttps://lccn.loc.gov/2021038545
LCebookrecordavailableathttps://lccn.loc.gov/2021038546
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10987654321
1.2.1.ElectronicOpticalTransitionsandUVAbsorption3
1.2.2.VisibleandInfraredAbsorption;Terahertz,Microwave4 1.3.Lyotropic,Polymeric,andThermotropicLiquidCrystals6
1.3.1.LyotropicLiquidCrystals
1.3.3.ThermotropicLiquidCrystals:Smectic,Nematic, Cholesteric,andBlue-phaseLiquidCrystals
1.4.2.Dye-dopedLiquidCrystals
1.4.3.Polymer-dispersedandPolymer-stabilizedLiquidCrystals14
1.5.4.PhotosensitiveandTunableOpticalWaveguide,Photonic Crystals,andMetamaterialNanostructures
1.5.5.IsotropicLiquidCrystalCoredFiberArray
2.3.MolecularTheoriesandResultsfortheLiquidCrystallinePhase34 2.3.1.Maier–SaupeTheory:OrderParameterNear Tc
2.3.2.NonequilibriumandDynamicalDependenceoftheOrder
2.4.2.FreeEnergyinthePresenceofanAppliedField41
3.1.Introduction
3.2.1.TheVectorField:DirectorAxis
3.2.2.ElasticConstants,FreeEnergies,andMolecularFields46
3.3.DielectricConstantsandRefractiveIndices
3.3.1.DCandLow-frequencyDielectricPermittivity, Conductivities,andMagneticSusceptibility
3.3.2.FreeEnergyandTorquesbyElectricandMagneticFields52
3.4.OpticalDielectricConstantsandRefractiveIndices
3.4.1.LinearSusceptibilityandLocalFieldEffect
3.4.2.EquilibriumTemperatureandOrderParameter DependencesofRefractiveIndices
3.5.FlowsandHydrodynamics
3.5.1.HydrodynamicsofOrdinaryIsotropicFluids
3.5.2.GeneralStressTensorforNematicLiquidCrystals64
3.5.3.FlowswithFixedDirectorAxisOrientation
3.5.4.FlowswithDirectorAxisReorientation
3.6.Field-inducedDirectorAxisReorientationEffects
3.6.1.Field-inducedReorientationWithoutFlowCoupling: FreederickszTransition
4.1.CholestericLiquidCrystals
4.1.1.FreeEnergies
4.1.2.Field-inducedEffectsandDynamics
4.1.3.TwistandConicModeRelaxationTimes
4.2.OpticalPropertiesofCholesterics
4.2.1.BraggRegime(OpticalWavelength Pitch)
4.2.2.ReflectionandTransmissionofPolarizedLight:Normal Incidence 79
4.2.3.CholestericLiquidCrystalasaOne-dimensionalPhotonic Crystal,PhotonicBandgap,andDispersion 84
4.2.4.CholestericLiquidCrystalswithMagneto-opticActivity: NegativeIndexofRefraction 89
4.2.5.PolarizationRotationandSwitchingbyHighPeriod NumberCLC – AdiabaticRotation and CircularBragg Resonance 90
4.3.CholestericBluePhaseLiquidCrystals 97
4.3.1.FreeEnergiesandEquationofMotionunderanApplied Field 97
4.3.2.Field-inducedLatticeDistortionandNewCrystalline Structures 98
4.3.3.Polymer-stabilizationandElectro-opticalProperties ofNon-cubicBPLC 99
4.4.SmecticandFerroelectricLiquidCrystals:ABriefSurvey100
4.4.1.Smectic-ALiquidCrystals 101
4.4.2.Smectic-CLiquidCrystals 104
4.4.3.Smectic-C ∗ andFerroelectricLiquidCrystals 106
4.4.4.Smectic-C ∗ – Smectic-APhaseTransition111
5.1.Introduction
5.2. Electroma gneticFormalismofLightScatteringinLiquid Crystals
5.3.ScatteringFromDirectorAxisFluctuationsinNematicLiquid Crystals
5.4.LightScatteringintheIsotropicPhaseofLiquidCrystals122
5.5.Temperature,Wavelength,andCellGeometryEffectson Scattering 125
5.6.SpectrumofLightandOrientationFluctuationDynamics127
5.7.RamanScatterings
5.7.1.Introduction
5.7.2.QuantumTheoryofSpontaneousandStimulated RamanScattering:ScatteringCross-section
5.7.3.SpontaneousRamanScattering
5.7.4.StimulatedRamanScattering
5.8.BrillouinandRayleighScatterings
5.8.1.BrillouinScattering
5.8.2.RayleighScattering
5.9.ABriefIntroductiontoNonlinearLightScattering
6.1.Introduction
6.2.Review ofElectro-OpticsofAnisotropicandBirefringent
6.2.1.Anisotropic,UniaxialandBiaxialOpticalCrystals143
6.2.2.IndexEllipsoidinthePresenceofanElectric Field–Electro-opticsEffect 145
6.2.3.PolarizersandRetardationPlate 146
6.2.4.BasicElectro-opticsModulation
6.3.Electro-OpticsofNematicLiquidCrystals
6.3.1.DirectorAxisReorientationinHomeotropicand PlanarCell;DualFrequencyLiquidCrystals
6.3.2.FreederickszTransitionRevisited
6.3.3.Field-inducedRefractiveIndexChangeandPhaseShift154
6.4.NematicLiquidCrystalSwitchesforDisplayApplication156
6.4.1.LiquidCrystalSwitch – onAxisConsiderationforTwist, Planar,andHomeotropicAlignedCells 156
6.4.2.Off-axisTransmission,ViewingAngle,and BirefringenceCompensation 157
6.4.3.LiquidCrystalDisplayElectronics 159
6.5.Electro-OpticalEffectsinOtherPhasesofLiquidCrystals159
6.5.1.SurfaceStabilizedFLC 160
6.5.2.Soft-modeFLCs 161
6.6.Non-DisplayApplicationsofLiquidCrystals
6.6.1.LiquidCrystalSpatialLightModulator
6.6.2.TunablePhotonicCrystalswithLiquidCrystal InfiltratedNanostructures
6.6.3.TunableFrequencySelectiveStructures,Metamaterial, andMetasurfaces 167
6.6.4.LiquidCrystalsforMolecularSensingandDetection168
6.6.5.BeamSteering,Routing,andTunableMicro-ring Resonator,andHigh-powerLaserOptics
7.1.ElectromagneticFormalismsforOpticalPropagation 175
7.1.1. Maxwell EquationsandWaveEquationsinAnisotropic Media 176
7.1.2.ComplexRefractiveIndex – RealandImaginary Components 177
7.1.3.NegativeIndexMaterial 178
7.1.4.NormalModes,PowerFlowandPropagationVectors inaLosslessIsotropicMedium 179
7.1.5.NormalModesandPropagationVectorsinaLossless AnisotropicMedium 181
7.2.PolarizedLightPropagationinLiquidCrystalDisplayPanel185
7.2.1.PanePolarizedWaveandJonesVectors 185
7.2.2.JonesMatrixMethod 189
7.2.3.ObliqueIncidence – 4×4MatrixMethods 191
7.3.ExtendedJonesMatrixMethod 193
7.4.Finite-differenceTime-domaintechnique 196
7.5.NonlinearLightPropagationinLiquidCrystals – aFirstLook197
7.6.SystemsofUnits 198 References 200
Chapter8.Laser-inducedReorientationNonlinearOpticalEffects203
8.1.Introduction 203
8.2. Laser-InducedMolecularReorientationsintheIsotropicPhase204
8.2.1.IndividualMolecularReorientationsinAnisotropic Liquids 204
8.2.2.CorrelatedMolecularReorientationDynamics 207
8.2.3.InfluenceofMolecularStructureonIsotropicPhase ReorientationNonlinearities 210
8.3.MolecularReorientationsintheNematicPhase 212
8.3.1.SimplifiedTreatmentofOpticalField-inducedDirector AxisReorientation 213
8.3.2.MoreExactTreatmentofOpticalField-inducedDirector AxisReorientation 215
8.3.3.NonlocalDirectorAxisReorientationandNonlocal OpticalNonlinearity 217
8.4.NematicPhaseReorientationDynamics 219
8.4.1.PlaneWaveOpticalField 219
8.4.2.SinusoidalOpticalIntensity 222
8.4.3.PolarizationGratingwithUniformOpticalIntensity224
8.5.Laser-InducedDirectorAxisRealignmentinDye-Doped LiquidCrystals 225
8.5.1.ReorientationCausedbyInter-MolecularTorque225
8.5.2.Laser-inducedTrans–CisIsomerisminDye-doped LiquidCrystals 226
8.6.DCFieldAidedOpticallyInducedNonlinearOpticalEffects inLiquidCrystals – Photorefractivity 226
8.6.1.OrientationPhotorefractivity – BulkEffects 229
8.6.2.ExperimentalResultsandSurfaceCharge/Field Contribution 233
8.7.ReorientationinOtherPhasesofPristine(Undoped)Liquid Crystals 234
8.7.1.SmecticPhase 234
8.7.2.CholestericandBlue-phaseLiquidCrystals 235 References 236
Chapter9.Thermal,Density,LatticeDistortionOpticalNonlinearities inNematic,Cholesteric,andBlue-phaseLiquidCrystals241
9.1.Introduction
9.2.Electrostricti onandFlowsinNon-AbsorbingLiquidCrystals –aGeneralOverview
9.3.Laser-InducedDensityandTemperatureModulationsinLiquid Crystals
9.3.1.ModulationsbySinusoidalOpticalIntensity
9.3.2.RefractiveIndexChanges:TemperatureandDensity Effects
9.4.OpticalNonlinearitiesofNematicLiquidCrystals
9.4.1.Steady-StateThermalNonlinearityofNematicLiquid Crystals
9.4.2.ShortLaserPulse-inducedThermalIndexChangein NematicsandNear-Tc Effect
9.4.3.OpticalNonlinearitiesofIsotropicLiquidCrystals258
9.5.CoupledNonlinearOpticalEffectsinNematic LiquidCrystals
9.5.1.ThermalOrientationCouplingEffect
9.5.2.Flow-reorientationEffect
9.6.NonlinearOpticalResponsesofCholestericBlue-PhaseLiquid Crystals
9.6.1.GeneralOverview
9.6.2.Non-electronicsOpticalNonlinearitiesofBPLC268
10.1.IntroductiontoQuantumMechanicalTreatmentofMolecules275
10.2. DensityMatrixFormalismforOpticalInducedMolecular ElectronicPolarizabilities
10.2.1.Field-inducedPolarizations – FirstandHigherOrders280
10.2.2.LinearandNonlinearAbsorptions
10.3.LinearandNonlinearElectronicSusceptibilities
10.3.1.LinearOpticalPolarizabilitiesofaMolecule
10.3.2.ComplexSusceptibilitiesandIndexofRefraction –Dispersion,Absorption,andAmplificationofLight, Lasers
10.3.3.Second-orderElectronicPolarizabilities
10.3.4.Third-orderElectronicPolarizabilities
10.3.7.PermanentDipoleandMolecularOrdering
10.3.8.QuadrupoleContributionandField-inducedSymmetry Breaking
10.3.9.InfluenceofMolecularStructures
10.4.Intensity-DependentRefractiveIndexChangeandnonlinear Absorption
10.4.1.NonlinearAbsorption
References
Chapter11.NonlinearOptics
11.1.Introduction
11.1.1 GeneralNonlinearPolarizationandSusceptibility302
11.1.2.ConventionandSymmetry
11.2.CoupledMaxwellWaveEquations
11.3.NonlinearOpticalPhenomena
11.3.1.StationaryDegenerateOpticalWaveMixing
11.3.2.OpticalPhaseConjugation
11.3.3.TransientandNearlyDegenerateWaveMixing316
11.3.4.NondegenerateOpticalWaveMixing;Harmonic Generations 320
11.3.5.StationarySelf-phaseModulationandSelf-action323
11.4.StimulatedScatterings
11.4.1.StimulatedRamanScatterings
11.4.2.StimulatedBrillouinScatterings
11.4.3.StimulatedOrientationScatteringinLiquidCrystals336
11.4.4.StimulatedThermalScattering 341
11.5.UltrafastLaserPulseSelf-ActionEffectsinCholestericLiquid Crystals 342
11.5.1.CoupledWaveEquationsforForwardandBackward PropagatingWaves 342
11.5.2.UltrafastPulseModulations – Compression,Stretching, andRecompressionwithCholestericLiquidCrystals344
12.1.Self-ActionNonlinearOpticalProcesses
12.1.1. Self-inducedSpatialandTemporalPhaseShift348
12.1.2.Self-phaseModulation,Self-focusing,-defocusing ofContinuous-Wave(CW)orPulsedLaser
12.1.3.Self-guiding,SpatialSolitonandPatternFormation353
12.1.4.PulseModulations,PolarizationRotationofand SwitchingbyUltrafast(Picosecond–Femtoseconds) Laser
12.2.OpticalWaveMixings
12.2.1.StimulatedOrientationalScatteringandPolarization Self-switching–SteadyState
12.2.2.StimulatedOrientationalScattering – Nonlinear Dynamics
12.2.3.OpticalPhaseConjugationwithOrientationand ThermalGratings
12.2.4.Self-startingOpticalPhaseConjugation
12.3.LiquidCrystalsforAll-OpticalImageProcessing
12.3.1.LiquidCrystalsasAll-opticalInformationProcessing Materials
12.3.2.All-opticalImageProcessing
12.4.HarmonicGenerationsandSum-FrequencySpectroscopy374
12.5.OpticalSwitching
12.6.NonlinearAbsorptionandOpticalLimitingofLasersfor Eye/SensorProtection
12.6.1.Introduction
12.6.2.NonlinearFiberArray – An IntensityDependentSpatial FrequencyFilter
12.6.3.OpticalLimitingActionofFiberArrayContainingRSA
12.6.4.OpticalLimitingActionofFiberArrayContainingTPA
Preface
Importantprogressandadvanceshavebeenmadeinthemultidisciplinarystudyof liquidcrystalssincethelasteditionofthisbookwentintoprintin2007.Thisnew editionconsistsof12chapters,mostofwhichhavebeencompletelyrevampedwith thelatestfundamentalbreakthroughandunderstandingofoptical,electro-,andnonlinearopticalpropertiesofliquidcrystals.
Chapters1–5coverthebasicphysicsandopticalpropertiesofliquidcrystals. Besidesnematicsthatarewidelyusedinubiquitousdevices,Ihaveincludedsufficientdiscussionsonothermesophasesofliquidcrystalssuchasthesmectics,ferroelectrics,cholesterics,andtheBlue-phasetoenablethereaderstoproceedtomore advancedorspecializedtopicselsewhere.Severalnewsectionshavebeenadded. Forexample,inChapter1,Ihaveincludedadetailedaccountofthefabrication methodsforgrowingmassivesingle-crystallinechiral1-Dand3-Dphotoniccrystals basedoncholestericandBlue-phaseliquidcrystalsandthefeasibilityofusingcholestericliquidcrystalsforultrafastmodulationofpicosecondandfemtosecondlasers ofcomplexvectorfields.
InChapter6,weexplorethefundamentalsofliquidcrystalsforelectro-opticsand displayandnon-display-relatedapplicationssuchassensing,switching,andspecializednanostructuredtunablephotoniccrystals,frequencyselectivesurfaces,and metamaterials.InChapter7,weprovideathoroughaccountoftheoreticalandcomputationaltechniquesusedtodescribeopticalpropagationthroughliquidcrystals andanisotropicmaterials.Chapters8–12provideacomprehensive,self-contained treatmentofnonlinearopticsofliquidcrystals,fromclassicalaswellasquantum mechanicalstandpoints,andhavegreatlyexpandedonthecoverageofthesamesubjectmatterinthepreviouseditionofthebookwithupdatedliteraturereviewsand fundamentaldiscussions.
Ihavelimitedmostdiscussionstoonlythefundamentalsanddeviceworking principlesthatcanwithstandthepassageoftime.Whereverpossibleandforthesake ofclarity,Ihavereplacedvigoroustheoreticalformalismswiththeirsimplifiedversions.Almostalloftheresultscontainedinthebookaretakenfrommyresearch projects,whichhavebeensupportedovertheyearsbygrantsandcontractsfrom theNationalScienceFoundation,AirForceOfficeofScientificResearch,Army ResearchOffice,the(PatuxentRiver)NavalAirDevelopmentCenter,theDefense AdvancedResearchProjectsAgencyandWrightPattersonResearchLaboratory. Iwouldliketothankmygraduatestudentsfortheirvaluableparticipationinthese projects,andsupportfromcolleaguesandcollaboratorsfromallovertheworld IhavebefriendedandinteractedwithinthefourdecadessinceIventuredinto thewonderfulworldofliquidcrystals. xiii
IamgratefultothePennsylvaniaStateUniversityforgrantingasabbaticalleave whenmostofthewritingisdone.Duringthecourseofwritingthiseditionofthe book,Ihaveenjoyedconstantencouragementandsupportfrommywife,Chor San;occasionalvisitsbymygrandsonLeoandgranddaughterKairi,anddailyvisits bylivelydovesandhummingbirdstofloweringplantsoutsidemyCarlsbadhome haveprovidedbriefbutmuchneededanddelightfulbreaks.
IAM-CHOON KHOO
Carlsbad,California,June2021
IntroductiontoLiquidCrystals
Liquidcrystalsarewonderfulmaterials.Inadditiontothesolidcrystallineandisotropicliquidphases,theyexhibitmanyso-calledmesophasesinwhichtheyflowlike ordinaryliquidsyetpossesscrystallineproperties[1].Thesemesophasesarecharacterizedbymanyuniquephysicalandopticalpropertiesandofferafertileground forseveralareasoffundamentalpursuits,aswellasapplicationsindisplayscreensof ubiquitousdevices,photonics,THzandmicrowaveandbiomedicalsystems[2–8].
1.1.MOLECULARSTRUCTURESANDCHEMICALCOMPOSITIONS
Withfewexceptions,liquidcrystalsarecomposedoforganicsubstanceswitha typicalstructure,asdepictedinFigure1.1.Theyarearomaticand,iftheycontain benzenerings,theyareoftenreferredtoasbenzenederivatives.Ingeneral,aromatic liquidcrystalmoleculessuchasthoseshowninFigure1.1compriseasidechainR, twoormorearomaticringsAandA ,connectedbylinkagegroupsXandY,andat theotherendconnectedtoaterminalgroupR
Examplesofsidechainandterminalgroupsarealkyl(CnH2n+1),alkoxy (CnH2n+1O),andotherssuchasacyloxyl,alkylcarbonate,alkoxycarbonyl,andthe nitroandcyanogroups.TheXsofthelinkagegroupsaresimplebondsorgroupssuch asstilbene( CH==CH ),ester( O C O ),tolane( C C ),azoxy ( N==N ),Schiffbase( CH==N ),acetylene( C C ),anddiacetylene( C C C C ).Thenamesofliquidcrystalsareoftenfashionedafterthelinkagegroup(e.g.Schiff-baseliquidcrystal).Therearequitea numberofaromaticrings.Theseincludesaturatedcyclohexaneorunsaturated phenyl,biphenyl,andterphenylinvariouscombinations.
Themajorityofliquidcrystalsarebenzenederivatives;therestincludeheterocyclics,organometallics,sterols,andsomeorganicsaltsorfattyacids.Theirtypical structuresareshowninFigures1.2–1.4.Heterocyclicliquidcrystalsaresimilarin
LiquidCrystals,ThirdEdition.Iam-ChoonKhoo. ©2022JohnWiley&Sons,Inc.Published2022byJohnWiley&Sons,Inc.
2 INTRODUCTIONTOLIQUIDCRYSTALS
Side Chain Terminal Group Aromatic Ring Aromatic Ring Linkage Group
'
' =Cl,Br,I,...etc.
structuretobenzenederivatives,withoneormoreofthebenzeneringsreplacedbya pyridine,pyrimidine,oranothersimilargroup.Cholesterolderivativesarethemost commonchemicalcompoundsthatexhibitthecholesteric(orchiralnematic)phase ofliquidcrystals.Organometalliccompoundsarespecialinthattheycontainmetallicatomsandpossessinterestingdynamicalandmagneto-opticalproperties.
Allthephysicalandopticalpropertiesofliquidcrystalssuchasdielectric constants,elasticconstants,viscosities,absorptionspectra,transitiontemperatures, theexistenceofmesophases,anisotropies,andopticalnonlinearitiesaregovernedby thepropertiesoftheseconstituentgroupsandhowtheyarechemicallysynthesized together.Sincethesemoleculesarequitelargeandanisotropic,andthereforevery complex,itwouldtakeatreatisetodiscussallthepossiblevariationsinthemoleculararchitectureandtheresultingchangesintheirphysicalproperties.Nevertheless, therearesomegeneralobservationsonecanmakeonthedependenceofthephysical propertiesonthemolecularconstituents[2].Forexample,thechemicalstabilityof liquidcrystalsdependsverymuchonthecentrallinkagegroup.Schiff-baseliquid
Figure1.1. Molecularstructureofatypicalliquidcrystal.
H19C9C9H19 NN NN
Figure1.2. Molecularstructureofaheterocyclicliquidcrystal.
OH3CHg CHN
Figure1.3. Molecularstructureofanorganometallicliquidcrystal. H3CCH3 CH3
Figure1.4. Molecularstructureofasterol.
crystalsareusuallyquiteunstable.Ester,azo,andazoxycompoundsaremorestable butarealsoquitesusceptibletomoisture,temperaturechange,andultraviolet(UV) radiation.Compoundswithoutacentrallinkagegroupareamongthemoststable liquidcrystalseversynthesized.Themostwidelystudiedoneis5CB(pentyl cyanobiphenyl),whosestructureisshowninFigure1.5.Othercompoundssuch aspyrimideandphenylcyclohexanearealsoquitestable.
1.2.OPTICALPROPERTIES
Ingeneral,opticalpropertiesofliquidcrystalsfallintotwodistinctcategories:those characteristicsof individual constituentmoleculesandthoseuniquetothe bulkcrystalline mesophases.Herewediscussopticalpropertiesthatarelargelydecidedbythe individualconstituentmolecules;opticalpropertiesassociatedwithvariousordered mesophasesofliquidcrystalsareelaboratedinlaterchapters.
1.2.1.ElectronicOpticalTransitionsandUVAbsorption
Sinceliquidcrystalconstituentmoleculesarequitelarge,theirenergylevelstructuresarerathercomplex.Inessence,thebasicquantummechanicaltheoryissimilar totheonedescribedinChapter10foramultilevelmolecule.Generally,theenergy levelsarereferredtoasorbitals: π , n,and σ orbitalsforthegroundandlow-lying levelsand π ∗ , n ∗,and σ ∗ fortheirexcitedcounterparts.Sincemostliquidcrystals arearomaticcompounds,containingoneormorearomaticrings,theenergylevels ororbitalsofaromaticringsplayamajorrole.Inparticular,the π π ∗ transitions inabenzenemoleculehavebeenextensivelystudied.Figure1.6showsthreepossible π π ∗ transitionsinabenzenemolecule.
Ingeneral,thesetransitionscorrespondtotheabsorptionoflightinthenear-UV spectralregion(≤200nm)[2].Theseresultsforabenzenemoleculecanalsobeused forinterpretingtheabsorptionofliquidcrystalscontainingphenylrings.Onthe otherhand,inasaturatedcyclohexaneringorband,usuallyonly σ electronsare involved.The σ σ ∗ transitionscorrespondtoabsorptionoflightofshorterwavelength(≤180nm)incomparisontothe π π ∗ transitionmentionedpreviously.
Theseopticalpropertiesarealsorelatedtothepresenceorabsenceofconjugation (i.e.alternationsofsingleanddoublebonds,asinthecaseofabenzenering).Insuch conjugatedmolecules,the π electron’swavefunctionisdelocalizedalongthe conjugationlength,resultinginabsorptionoflightinalongerwavelengthregion comparedto,forexample,thatassociatedwiththe σ electronincompoundsthat
Figure1.5. Molecularstructureof5CB(pentylcyanobiphenyl).
donotpossessconjugation.Absorptiondataandspectraldependenceforavarietyof molecularconstituents,includingphenylrings,biphenyls,terphenyls,tolanes,and diphenyl-diacetylenes,maybefoundin[2].
1.2.2.VisibleandInfraredAbsorption;Terahertz,Microwave
Thespectraltransmissiondependenceoftwotypicalliquidcrystalsisshownin Figure1.7aandb.LiquidcrystalsarequiteabsorptiveintheUVregion,asaremostorganicmolecules/liquids.Inthevisibleandnear-infrared(IR)regime(i.e.from 0.4to~2 μm),therearenoabsorptionbands,andthusliquidcrystalsarequitetransparentinthisregime.Inthemid-IR(3–5 μm)andIR(9–12 μm),rovibrationaltransitionsbegintodominate,andliquidcrystalsarequiteabsorptiveinthisspectral area(Table1.1).
TABLE1.1.AnisotropicPhysicalParametersofaTypicalNematicLiquidCrystals(E7)
Thermaldiffusionconstant:
Elasticconstants:
Figure1.6. The π π ∗ electronictransitionsinabenzenemolecule.
Figure1.7. Transmissionspectraofnematicliquidcrystals:(a)5CB;(b) N-(4-methoxybenzylidene)-4butylaniline(MBBA).
Theabsorptioncoefficient α intheUV(~0.2 μm)regimeisontheorder of10 3 cm 1 ;inthevisible(~0.5 μm)regime, α 10 0 cm 1 ;inthenear-IR (~3 – 5 μmand~9 – 12 μm)regime, α ~10 2 cm 1 .Thereare,ofcourse,largevariationsamongthethousandsofliquidcrystalsthathavebeensynthesized.Itispossibletoidentifyliquidcrystalswiththe desirableabsorption/transparencyfora wavelengthofinterest.Forexample,theterahertzandmicrowaveregime,[5,6] haveidentified/synthesizedliquidcrystals(LC’ s)withrelativelylowabsorption coefficient α ~100 cm 1;lowabsorptionisimportantsinceapplicationsinsuchlong-wavelength regimesrequiremuchthickerinteractionlength(cellthickness).
6INTRODUCTIONTOLIQUIDCRYSTALS
Auniqueadvantageofliquidcrystalsi sthesizeablebirefringencethroughout theentirevisible – IR-terahertz-microwavespectrum.Atthe20 – 60GHzregion, [6]hasshownthatforatypicalliquidcrystalsuchasE7, εe =3.17(refractive index ne =1.78)and ε0 =2.72(refractiveindex n 0 =1.65),i.e.abirefringence Δn ~0.13.
1.3.LYOTROPIC,POLYMERIC,ANDTHERMOTROPIC LIQUIDCRYSTALS
Thereareseveraldistincttypesofliquidcrystals:lyotropic,polymeric,thermotropic, anddiscotic.Thesematerialsexhibitliquidcrystallinepropertiesasafunction ofdifferentphysicalparametersandenvironmentssuchastemperature,molecular constituents ’ structure,andconcentration.
1.3.1.LyotropicLiquidCrystals
Lyotropicliquidcrystalsareobtainedwhenanappropriateconcentrationofmaterial isdissolvedinsomesolvent.Themostcommonsystemsarethoseformedbywater andamphiphilicmolecules(moleculesthatpossessahydrophilicpartthatinteracts stronglywithwaterandahydrophobicpartthatiswaterinsoluble)suchassoaps, detergents,andlipids.Herethemostimportantvariablecontrollingtheexistence oftheliquidcrystallinephaseistheamountofsolvent(orconcentration).There arequiteanumberofphasesobservedinsuchwater-amphiphilicsystems,asthe compositionandtemperaturearevaried;someappearassphericalmicelles,and otherspossessorderedstructureswith1-,2-,or3-Dpositionalorder.
Examplesofthesekindsofmoleculesaresoaps(Figure1.8)andvariousphospholipidslikethosepresentincellmembranes.Lyotropicliquidcrystalsareofinterestinbiologicalstudies[7]. 3C
Chemicalstructureandcartoonrepresentationofsodiumdodecylsulfate(soap)forming micelles.
Figure1.8.
1.3.2.PolymericLiquidCrystals
PolymericliquidcrystalsarebasicallythepolymerversionsofthemonomersdiscussedinSection1.1.Agoodaccountofpolymericliquidcrystalsmaybefound in[9].Therearethreecommontypesofpolymers,asshowninFigure1.9a–c,which arecharacterizedbythedegreeofflexibility.Thevinyltype(Figure1.9a)isthemost flexible,theDupontKevlarpolymer(Figure1.9b)issemirigid,andthepolypeptide chain(Figure1.9c)isthemostrigid.Mesogenic(orliquidcrystalline)polymersare classifiedinaccordancewiththemoleculararchitecturalarrangementofthemesogenicmonomer.Main-chainpolymersarebuiltbylinkingrigidmesogenicgroupsin amannerdepictedschematicallyinFigure1.10a;thelinkmaybeadirectbondor someflexiblespacer.Liquidcrystalside-chainpolymersareformedbypendantside attachmentofmesogenicmonomerstoaconventionalpolymericchain,asdepicted inFigure1.10b.
Figure1.9. Threedifferenttypesofpolymericliquidcrystals:(a)vinyltype;(b)Kevlarpolymer; (c)polypeptidechain.
1.3.3.ThermotropicLiquidCrystals:Smectic,Nematic,Cholesteric, andBlue-phaseLiquidCrystals
Althoughthemolecularstructuresofthermotropicliquidcrystalsarequitecomplicated,theyareoftenrepresentedas “rigidrods” thatinteractwithoneanothertoform distinctiveorderedstructures(orphases)asafunctionofascendingtemperature: crystals,smectic,nematic,cholesteric(includingblue-phase),andtheisotropicliquidphase.Insmecticliquidcrystals,thereareseveralsubclassificationsinaccordancewiththepositionalanddirectionalarrangementofthemolecules.
Asexplainedingreaterdetailinthefollowingchapters,thesemesophasesare definedandcharacterizedbymanyphysicalparameterssuchaslong-andshortrangeorder,orientationaldistributionfunctions,andsoon.Herewecontinueto usetherigid-rodmodelandpictoriallydescribethesephasesintermsoftheirmoleculararrangement.
Figure1.11adepictsthecollectivearrangementoftherodlikemoleculesinthe nematicphaseschematically.Thesemoleculesare,however,directionallycorrelated;theyarealignedinageneraldirectiondefinedbyaunitvector ñ,theso-called directoraxis,whichmayberegardedasthecrystalaxis.Nevertheless,themolecules arepositionallyrandomandexhibitflowverymuchlikeliquids;X-raydiffraction fromnematicsdoesnotexhibitanydiffractionpeak.
Althoughindividualmoleculesofnematicliquidcrystal(NLC),cholestericliquid crystal(CLC),andblue-phaseliquidcrystal(BPLC)maybepolar,i.e.carryapermanentdipole,theytendtoself-assemblethemselvesinsuchamannerthatbulkliquidcrystalsarecentrosymmetric,cf.Figure1.12;theirphysicalpropertiesarethe sameinthe+ n andtheopticallyuniaxial n directions.
Cholestericliquidcrystals,oftenalsocalledchiralnematicliquidcrystals,resemblenematicliquidcrystalsexceptthatthemoleculesassembledinahelicalmanner, asdepictedinFigure1.11.Thispropertyresultsfromtheadditionofchiralagentsto nematicconstituentsinthestartingmixture.Owingtothespatially(helical)varying refractiveindex,CLCspossessspecialopticalpropertiessuchasphotonicbandgaps
Figure1.10. Polymericliquidcrystals:(a)mainchain;(b)sidechain.
Rod-shapeLCmolecule
others(e.g.BluePhase) 3-DPhotonicCrystals
Naturalself-assembly
nematicsmectic
1-DPhotonicCrystals
cholesteric
Figure1.11. Self-organizationoftherod-shapedLCmoleculesvialocalandlong-rangeordergiving risetovariousorderedphasesofliquidcrystal.
Figure1.12. Arrangementofdipolesinthecentrosymmetricbulkcrystalsuchasnematics.
fortransmissionofcircularlypolarizedlights.MoredetailsonCLCaswellascholestericBPLCsobtainedbyincreasingtheconcentrationofthechiralconstituent [10]inthestartingmixturearepresentedinChapter4.
Smecticliquidcrystals,unlikenematics,possesspositionalorder;thatis,the positionofthemoleculesiscorrelatedinsomeorderedpattern.Wediscussherethree representativeones:smectic-A,smectic-C,andsmectic-C∗ (ferroelectrics)dueto
Layernormal LayernormalLayernormal
Liquidcrystal molecules
Figure1.13. Moleculararrangementsofliquidcrystals:(a)smectic-A;(b)smectic-C;(c)smectic-C∗ or ferroelectric;(d)unwoundsmectic-C
theirrelevancetoopticalandphotonicstudies/applicationsnotingthatmanyother subphasesofsmecticssuchassmecticG,H,I,F Qwithdifferentmolecular arrangementandordershavebeenidentified.
Figure1.13adepictsthelayeredstructureofasmectic-Aliquidcrystal.Ineach layer,themoleculesarepositionallyrandombutdirectionallyordered,withtheir longaxisnormaltotheplaneofthelayer.Similartonematics,smectic-Aliquid crystalsareopticallyuniaxial;thatis,thereisarotationalsymmetryaroundthe directoraxis.
Thesmectic-Cphaseisdifferentfromthesmectic-Aphaseinthatthematerialis opticallybiaxial,andthemoleculararrangementissuchthatthelongaxisistilted awayfromthelayernormal z (cf.Figure1.13b).
MIXTURES,POLYMER-DISPERSED,ANDDYE-DOPEDLIQUIDCRYSTALS
Insmectic-C∗ liquidcrystals,asdepictedinFigure1.13c,thedirectoraxis n is tiltedawayfromthelayernormal z andprecessesaroundthe z axisinsuccessive layers.Thisisanalogoustocholestericsandisduetotheintroductionofopticalactiveorchiralmoleculestothesmectic-Cliquidcrystals.
Smectic-C ∗ liquidcrystalsareinterestinginoneimportantaspect;namely,they compriseasystemthatpermits,bythesymmetryprinciple,theexistenceofspontaneouselectricpolarization.Thiscanbeexplainedsimplyinthefollowingway. Thespontaneouselectricpolarization p isavectorandrepresentsabreakdownof symmetry;thatis,thereisadirectionalpreference.Iftheliquidcrystalproperties areindependentofthedirectoraxis n direction(i.e.+ n isthesameas n ), p , ifitexists,mustbelocallyperpendicularto n .Inthecaseofsmectic-A,which possessesrotationalsymmetryaround n , p mustthereforebevanishing.Inthe caseofsmectic-C,thereisareflectionsymmetry(mirrorsymmetry)abouttheplane definedbythe n and z axes,so p isalsovanishing.Thisreflectionsymmetryis brokenifachiralcenterisintroducedtothemolecule,resultinginasmectic-C∗ system.
Byconvention, p isdefinedaspositiveifitisalongthedirectionof z × n ,and negativeotherwise.Figure1.13cshowsthatsince n precessesaround z , p also precessesaround z .If,bysomeexternalfield,thehelicalstructureisunwound and n pointsinafixeddirection,asinFigure1.12d,then p willpointinonedirection. Clearly,thisandotherdirectoraxisreorientationprocessesareaccompaniedbya considerablechangeintheopticalrefractiveindexandotherpropertiesofthesystem,andtheycanbeutilizedinpracticalelectro-andopto-opticalmodulation devices.MoredetaileddiscussionsofsmecticliquidcrystalsaregiveninChapter4.
1.3.4.FunctionalizedandDiscoticLiquidCrystals
Throughvariouschemicalsynthesistechniquesaswellasnanotechnologies,anentire classofnovelorso-calledfunctionalizedliquidcrystalshaveemerged[11–13]. Figure1.14shows,forexample,theshuttlecock-shapedliquidcrystalformedby incorporatingfullereneC60tovariouscrystalsandliquidcrystalsreportedby Sawamuraetal.[11].Othershaveinvestigatedaspecialclassofliquidcrystalscomprisingdisc-likemolecules,discoticliquidcrystals,thatpossessinterestinganduseful semiconductingpropertiessuitableforoptoelectronicapplications[12,13].
1.4.MIXTURES,POLYMER-DISPERSED,ANDDYE-DOPED LIQUIDCRYSTALS
Ingeneral,temperaturerangesforthevariousmesophasesofsingleconstituent liquidcrystalsarequitelimited.Therefore,whilemanyfundamentalstudiesarestill conductedonsuchliquidcrystallinematerials,industrialapplicationsemploy mostlymixtures,composites,orspeciallydopedliquidcrystalswithlargeoperating temperaturerangeandtailor-madephysicalandopticalproperties.
2:R′O=C12H25O 3:R′O=C14H29O 4:R′O=C16H33O 5:R′O=C18H37O
Figure1.14. Ashuttlecock-shapedliquidcrystalformedbyincorporatingfullereneC60intovarious liquidcrystalswasreported[11].
Therearemanytechniquesformodifyingthephysicalpropertiesofaliquidcrystal.Atthemostfundamentallevel,variouschemicalgroupssuchasbondsoratoms canbeintroducedtomodifytheLCmolecule.Agoodexampleisthecyanobiphenyl homologousseries nCB(n =1,2,3…).As n isincreasedthroughsynthesis,theviscosities,anisotropies,molecularsizes,andmanyotherparametersaregreatlymodified.Someofthesephysicalpropertiescanalsobemodifiedbysubstitution.For example,thehydrogeninthe2,3,and4positionsofthephenylringmaybesubstitutedbysomefluoro(F)orchloro(Cl)group[14].
Besidesthesemolecularsynthesistechniques,thereareotherwaystodramaticallyimprovetheperformancecharacteristicsofliquidcrystals.Inthefollowingsections,wedescribethreewell-developedmethods,focusingourdiscussionon nematicliquidcrystalsastheyexemplifytheuniquecharacteristicsofliquidcrystals widelyusedinopticalandphotonicapplications.
1.4.1.Mixtures
Alargemajorityofliquidcrystalsinubiquitousdevicesareeutecticmixturesoftwo ormoremesogenicsubstances.AgoodexampleisE7(fromEMChemicals),which isamixtureoffourliquidcrystals(cf.Figure1.15).Theopticalproperties,dielectric anisotropies,viscositiesofE7areverydifferentfromthoseoftheindividualmixture constituents.
Figure1.15. MolecularstructuresofthefourconstituentsmakinguptheliquidcrystalE7(fromEM Chemicals).
Creatingmixturesisanart,guided,ofcourse,bysomescientificprinciples.One oftheguidingprinciplesformakingtherightmixturecanbeillustratedbytheexemplaryphasediagramoftwomaterialswithdifferentmelting(i.e.crystal nematic) andclearing(i.e.nematic isotropic)points,asshowninFigure1.16.Both
Figure1.16. Phasediagramofthemixtureoftwoliquidcrystals.
substanceshavesmallnematicranges(Ti–Tn and T ' i T ' n).Whenmixedattheright concentration[2],however,thenematicrange(T m i T m n )ofthemixturecanbeorders ofmagnitudelarger.Todate,thereisanassortmentofnematicliquidcrystals,for example,withanoperatingtemperaturerangefromsubfreezing(< 30 C)towell over100 Cthatfoundtheirwayinubiquitousdisplaydevices(Figure1.16).
Ifthemixturecomponentsdonotreactchemicallywithoneanother,theirbulk physicalproperties,suchasdielectricconstant,viscosity,andanisotropy,aresome weightedsumoftheindividualresponses.Sinceopticalandotherparameters(e.g. absorptionlinesorbands)arelargelydependentontheelectronicresponsesofindividualmolecules,theygenerallyfollowsuchasimpleadditiverule.Otherphysical parameterssuchasviscosities,transitiontemperature,andelasticconstantsare highlydependentonintermolecularforcesandthereforefollowmorecomplexphysio-chemicalrules(seee.g.[2,13]).
1.4.2.Dye-dopedLiquidCrystals
Anobviouseffectofintroducingdyemoleculetoliquidcrystalsistoincreasethe absorptionofaparticularliquidcrystalatsomespecifiedwavelengthregion.Inparticular,dyemoleculeswithabsorptionanisotropy,orthosethatundergoconformationchangessuchastrans–cisisomorphismorproducephoto-charges,areoften usedforphotonicapplications[15–17].Forexample,dichroicdyemoleculesthat aremoreabsorptiveforopticalfieldpolarizationparallelthanperpendiculartoits longaxisareoftenusedfortheguest–hosteffectastheiroblongshapemakesthem compatiblefordispersinginthehostnematicliquidcrystalswithoutdisturbingthe order.Thesedichroicmoleculescanthenbeorientedandreorientedbyanexternal fieldappliedtothehostNLCtoswitchthetransmissionofthecell(cf.Figure1.17); suchdichroicdye-dopedliquidcrystalshavebeenutilizedtodemonstrateoptical diodeaction[15]inthetransmissionofpolarizedlight.
Ifthedyemoleculesundergosomephysicalchangessuchastrans–cisisomorphismorproducespacechargesfollowingphotonabsorption,theycouldgiverise tononlinearopticaleffects[16];others[17]haveshownthatdyemoleculesdepositedonthecellwindowscanbeopticallyalignedasaneffectivemeansofsurface alignmentmechanismforLCcellfabrication.Theseandothereffectsduetothe presenceofdyemoleculesorotherphotosensitiveagentsinliquidcrystalsarediscussedinmoredetailinChapter8.
1.4.3.Polymer-dispersedandPolymer-stabilizedLiquidCrystals
Justasthepresenceofdyemoleculesmodifiestheabsorptioncharacteristicsofliquidcrystals,theinclusionofliquidcrystalsinthematerialofdifferentrefractive indexesmodifiesthelightscatteringpropertiesoftheresulting “mixed” system. Agoodexampleispolymer-dispersedliquidcrystals(PDLC)formedbyintroducing liquidcrystalsasmicron-orsub-micron-sizeddropletsintoapolymermatrix.The
LowtransmissionHightransmission
Figure1.17. Alignmentofadichroicdye-dopednematicliquidcrystal:(a)beforeapplicationof switchingelectricfield;(b)switchingfieldon.
opticalindicesoftheserandomlyorientedliquidcrystaldroplets,intheabsenceof anexternalalignmentfield,dependontheliquidcrystal–polymerinteractionatthe boundaryandthereforeassumearandomdistribution(cf.Figure1.18a).Thiscauses largescattering[18].Upontheapplicationofanexternalfield,thedropletswillbe aligned(Figure1.18b),andthesystemwillbecomeclearastherefractiveindexof theliquidcrystaldropletsmatchestheisotropicpolymerbackgrounds.
IncidentLight
NoAppliedField (ScatteringState)
(TransmissiveState)
Figure1.18. Schematicdepictionofapolymer-dispersedliquidcrystalmaterial:(a)intheabsence ofanexternalalignmentfield,highlyscatteredstate;(b)whenanexternalalignmentfieldison, transparentstate.
