Dielectric Constants (@20oC, 1kHz)*Mixture Application Deee

BL038PDLCs16.721.75.3MLC-6292TN AMLCDs7.411.13.7ZLI-4792TN AMLCDs5.28.33.1TL205AM PDLCs59.14.118523Fiber-Optics2.774.395-465-De material-4.23.67.8*EM Materials

Dielectric Constants: Temperature Dependence4-pentyl-4-cyanobiphenylTemperature DependenceAverage Dielectric Anistropy

Magnetic Anisotropy: DiamagnetismDiamagnetism: induction of a magnetic moment in opposition to an applied magnetic field. LCs are diamagnetic due to thedispersed electron distribution associated with the electron structure.Delocalized charge makesthe major contribution to diamagnetism.

Ring currents associated witharomatic units give a largenegative component to c for directions to aromatic ringplane. Dc is usually positive since:

Magnetic Anisotropy: DiamagnetismCompound

Optical Anisotropy: Birefringenceordinary ray (no, ordinary index of refraction)extraordinary ray (ne, extraordinary index of refraction)

Optical Anisotropy: Birefringenceordinary waveqextraordinary waveFor propagation along the opticaxis, both modes are nooptic axis

Optical Anisotropy: Phase Shiftanalyzerpolarizerliquid crystallight

f = 2pdno,e/l

Df = fe - fo=2pdDn/l

Dn = ne - no

0 < Dn < 0.2depending on deformation

380 nm < l < 780 nm visible light

Birefringence (20oC @ 589 nm)EM Industry Dn ne no Application Mixture BL0380.27201.79901.5270 PDLCTL2130.23901.76601.5270PDLCTL2050.21751.74551.5270 AM PDLCZLI 54000.10631.59181.4855STNZLI 37710.10451.59651.4920TNZLI 47920.09691.57631.4794 AM TN LCDsMLC-62920.09031.56081.4705AM TN LCDsZLI 60090.08591.55551.4696AN TN LCDsMLC-66080.08301.55781.4748ECB95-4650.08271.55841.4752-De devicesMLC-66140.0770------------------IPSMLC-66010.0763------------------IPS185230.04901.50891.4599Fiber OpticsZLI 28060.04371.51831.4746 -De device

Birefringence: Temperature Dependence Average IndexTemperatureDependence

Birefringence Example: 1/4 Wave PlateUnpolarizedlinear polarizedcircular polarizedpolarizerLC: Dn=0.05dWhat is minimum d forliquid crystal 1/4 wave plate ?Takes greater number of e-waves than o-waves to span d, use Dn=0.05

Nematic Elasticity: Frank Elastic Theory 11 Splay, K Twist, K22 Bend, K33

Surface Anchoringmicrogrooved surface -homogeneous alignment (//)rubbed polyimide ensemble of chains -homeotropic alignment ()surfactant or silaneAlignment at surfaces propagates over macroscopic distances

Surface AnchoringfqNn polar anchoring Wqazimuthalanchoring WfsurfaceStrong anchoring 10-4 J/m2Weak anchoring 10-7 J/m2Wq,f is energy needed to move director n from its easy axis

Creating Deformations with a Field and Surface - Bend DeformationE or B

Creating Deformations with a Field and Surface - Splay DeformationE or B

Creating Deformations with a Field and Surface - Twist DeformationE or B

Magnitudes of Elastic ConstantsEM Industry K11K22K33 Mixture(pN)(pN)(pN)Application

BL03813.7------27.7PDLCTL20517.3------20.4AM PDLCZLI 479213.26.518.3TN AM LCDZLI 5400105.419.9TNZLI-600911.55.416.0AM LCDOrder of magnitude estimate of elastic constant

U: intermolecular interaction energya: molecule distance

Elastic Constant K22: Temperature Dependence

The Flexoelectric Effect-

+-

+Polar AxisUndeformedstate of bananaand pear shapedmoleculesSplayBendPolar structure corresponds tocloser packingof pear and banana molecules

xeeyEnqEffects of an Electric FieldElectric Free Energy DensityElectric Torque DensityUsing De = 5 and E=0.5 V/mm

xccyBnqEffects of an Magnetic FieldMagnetic free energy densityMagnetic torque densityUsing Dc = 10-7 m3kg-1 and B= 2 T = 20,000 G

Deformation TorqueOrientation of molecules obeys this eq.Free energy density from elastic theoryTorque density

SurfaceDeformation Torqueqdx Material Shear Modulus Steel 100 GPa Silica 40 GPa Nylon 1 GPaShear modulus Youngs modulus

Coherence Length: Electric or MagneticEBalance torqueFind distance dCoherence length xUsing E = 0.5 V/mmand De = 20

Viscosity: Shear Flow Viscosity Coefficientn n nn h11h33h22Typically h22 > h33 >h11 nnn

Viscosity: Flow Viscosity CoefficientDynamic Viscosity (h) 1 kg/ms = 1 Pas 0.1 kg/ms = 1 poiseKinematic Viscosity (n) 1 m2/s

LC specification sheets givekinematic viscosity in mm2/sApproximate density

Viscosity: Flow Viscosity CoefficientTypical Conversion Density Conversion Flow r 0.1 kg/ms = 1 poiseViscosityEM Industry Kinematic (n) Dynamic (h) MIXTURECONFIGURATION (mm2/s) (Poise)ZLI-4792TN AM LCDs 15 0.15ZLI-2293STN 20 0.20MLC-6610ECB 21 0.21MLC-6292TN AM LCDs (Tc=120oC) 28 0.2818523Fiber Optics (no=1.4599) 29 0.29TL205PDLC AM LCD 45 0.45BL038PDLCs (Dn=0.28) 72 0.72

Viscosity: Temperature DependenceFor isotropic liquids E is the activation energy for diffusion of molecular motion.H3CONC4H9

nViscosity: Rotational Viscosity CoefficientTimennRotation of the director n bv externalfields (rotating fields or static).

Viscous torque's Gv are exerted on a liquidcrystal during rotation of the director n and by shear flow.g1: rotational viscosity coefficient

nViscosity: Rotational Viscosity CoefficientnnEM IndustryViscosityViscosity MIXTURE CONFIGURATION (mPas) (Poise)ZLI-5400TN LCDs 109 1.09ZLI-4792 TN AM LCDs 123 1.23ZLI-2293STN 149 1.4995-465-De Applications 185 1.85MLC-6608TN AM LCD 186 1.86

Viscosity: ComparisonsMaterialViscosity (poise)

Air10-7Water10-3Light Oil10-1Glycerin1.5

LC-Rotational (g1)1< g1 < 2LC-Flow (hii)0.2< hii

Surfacex Relaxation from DeformationESurfacexfield on statezero field stateRelaxation when field is turned off Relaxation time t

Relaxation from DeformationBalance viscous/deformation torqueAssume small deformationsSolutionFor 100 mm cellFor 5 mm cell

Freedericksz Transition - The Threshold IEczyExAt some critical E field, the director rotates, before Ecnothing happensqnyxnE00d

Freedericksz Transition - The Threshold II E-fieldfree energy totalfree energyMinimize free energy with Euler Equation

Freedericksz Transition - The Threshold III1.0 E/Ecmid-layer tilt (deg)differential equation soln.small qthreshold

Defectss=+1s=+1s=+1s=1/2s=-1/2s=-1s=3/2s=+2The singular line(disclination) is pointing out of the page, and director orientation changes by2ps on going around the line (s is the strength)

Estimate Defect SizeThe simplest hypothesis is that the core or defector disclination is an isotropic liquid, therefore thecore energy is proportional to kBDTc. Let M be themolecular mass, N Avogadadros number and rthe density of the liquid crystal.

Microscopic Fluttering and FluctuationsThermally induced Deformations Characteristic time t of Fluctuations:

Can see fluctuations with microscope: Responsible for opaque appearance of nematic LC

AXYZZ Aromatic or saturated ring core X & Y are terminal groups A is linkage between ring systems Z and Z are lateral substituentsCH3 - (CH2)4C N4-pentyl-4-cyanobiphenyl (5CB) General Structure

Mesogenic Core Linking Groups Ring GroupsNNphenylpyrimidinecyclohexanebiphenylterphenyldiphenylethanestilbenetolaneschiffs baseazobenzeneazoxyben-zenephenylbenzoate(ester)phenylthio-benzoate Common Groups

NomenclatureMesogenic Corephenylbenzylbenzenebiphenylterphenylphenylcyclohexane (PCH)cyclohexane cyclohexylRing Numbering Scheme321654321654

Terminal Groups

(one terminal group is typically an alkyl chain)CH3CH2CH2CH2CH3CH2C*HCH2CH3straight chain

branched chain (chiral)Attachment to mesogenic ring structureDirect - alkyl (butyl)Ether -O- alkoxy (butoxy)

CH3-CH3-CH2-CH3-(CH2)2-CH3-(CH2)3-CH3-(CH2)4-CH3-(CH2)5-CH3-(CH2)6-CH3-(CH2)7-methylethylpropylbutylpentylhexylheptyloctylCH3-O-CH3-CH2-O-CH3-(CH2)2-O-CH3-(CH2)3-O-CH3-(CH2)4-O-CH3-(CH2)5-O-CH3-(CH2)6-O-CH3-(CH2)7-O-methoxyethoxypropoxybutoxypentoxyhexoxyheptoxyoctoxyTerminal Groups

Second Terminal Group andLateral Substituents (Y & Z)H -FflouroClchloroBrbromoIiodoCH3methylCH3(CH2)nalkylCNcyanoNH2aminoN(CH3)dimethylaminoNO2nitro

phenyl

cyclohexyl

Odd-Even EffectClearing point versus alkyl chain length0 1 2 3 4 5 6 7 8 9 10 11 carbons in alkyl chain (n) clearing point 18

16

14

12

10CH3-(CH2)n-OO-(CH2)n-CH3C-OO

4-pentyl-4-cyanobiphenyl4-pentoxy-4-cyanobiphenylNomenclatureCommon molecules which exhibit a LC phase

Structure - PropertyCH3-(CH2)4C Nvary mesogenic coreA AC-N (oC)N-I(oC)DnDe22.5350.1811.571520.1819.731550.109.7

Structure - PropertyCH3-(CH2)4COOvary end groupXXC-N (oC)N-I (oC)HFBrCNCH3C6H587.592.0115.5111.0106.0155.0114.0156.0193.0226.0176.0266.0

Lateral Substituents (Z & Z)AXYZZ Z and Z are lateral substituents Broadens the molecules Lowers nematic stability May introduce negative dielectric anisotropy

ESolidLiquid CrystalIsotropic LiquidConcentration (c2), %0 50 100Why Liquid Crystal MixturesMelt Temperature:Liquid Crystal-Solid

ln ci = DHi(Teu-1 - Tmi-1)/R

DH: enthalpiesTeu: eutectic temperature Tmi: melt temperatureR: constant

Nematic-IsotropicTemperature: TNI

TNI = S ciTNIi

Temperatureeutecticpoint

S-N

PropertyZLI 4792 MLC 6292/000 MLC 6292/100S-N

Thermotropic Liquid Crystal Anisotropy Nematic phase Chirality Order parameters Dielectric Anisotropy Diamagnetism Birefringence Elastic constants Surface Anchoring Viscosity Threshold Defects Eutectic MixtureSummary of Fundamentals