Liquid Crystal Materials. Lyotropics Thermotropics amphiphilic molecules, polar and non-polar parts form liquid crystal phases over certain concentration

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<ul><li><p>Liquid Crystal Materials</p></li><li><p> Lyotropics Thermotropicsamphiphilic molecules, polar and non-polarparts form liquid crystal phases over certainconcentration ranges when mixed with a solventmolecules consisting of a rigid core and flexible tail(s) form liquid crystal phasesover certain temperature ranges.+-hydrophilic polar headhydrophobic non-polar tailflexible tailrigid coreBroad Classification</p></li><li><p>The Lyotropic Phasesmicellereverse micellecross sectioncross section</p></li><li><p>Chemists ViewPhysicistsEngineers View Shape Anisotropy Length &gt; WidthThe molecule above (5CB) is ~2 nm 0.5 nmThe Thermotropic Liquid Crystal Molecule</p></li><li><p>Geometrical Structures of Mesogenic MoleculesLow Molecular Weight High Molecular Weight (polymers)( )n( )ndisk-like</p><p>rod-likemost practical applications</p></li><li><p>nTemperature Crystal Nematic LC Isotropic The Liquid Crystal Phase</p></li><li><p> The Nematic Director nnThe local average axis of the long molecular axisdirector</p></li><li><p>nTemperature Smectic C Smectic A Nematicnzqn Other Liquid Crystal Phases</p></li><li><p> left-handed right-handedmirror imagesnon-superimposableH-C-C-C-C-CC NHHHHHHHHHHH-C-C-C-C-CC NHHHCH3HHHHHHnon-chiralchiral (RH)The methyl group on the 2nd carbon atomon the alkyl chain of the molecules extendsout of the plane of the paper and the hydro-gen atom extends into the plane of the paper.Therefore the 2nd carbon can be thought ofas a right or left handed coordinate system Chirality</p></li><li><p>CNpitchPOrdinary NematicChiral NematicdirectornThe Chiral Nematic</p></li><li><p>The Chiral Doped NematicYou can create a cholesteric material by doping a conventionalnematic with a chiral dopant.For dilute solutionsChiral DopantHTP (mm)-1</p><p> S-811 -14 IS-4651 -13.6</p><p> - indicates left twist sense</p><p>For a 10% doping of S-811</p></li><li><p>The Chiral Smectic C: FerroelectricsqmEye- dipole moment m fin - chiral</p><p>ferroelectric LC has adipole moment perp-endicular to its longaxis, and is chiral.</p></li><li><p>The Chiral Smectic: TGBTwisted Grain Boundary (TGB)A twisted grain boundary smectic A phase (frustrated) - TGBA*</p></li><li><p>OCRCOCROOCOROCOROCOROCORDiscotic Liquid Crystalexample: R=OCOC11H23</p></li><li><p>Columnar, columns of molecules in hexagonal latticeNematic discotic phasenDiscotics Liquid Crystalsn</p></li><li><p>Polymer Liquid CrystalsCombining the properties of liquid crystals and polymersMain Chain Side Chainmesogenic moieties are connected head-to-tailmesogenic moietiesattached as side chainson the polymer backbonerigidsemi-flexible</p></li><li><p>Polymer Liquid Crystalsforming nematic liquid crystal phasesnmain-chainside-chain</p></li><li><p>O C-O-(CH2)n-OR2C-OOExample of Side-Chain Polymer LCs-(-CH2-C-)X-R1 Too slow for display applications (switching times ~ 0.5-1 s Useful for other applications such as: Optical filters Optical memory Alignment layers for low molecular weight LCs Non-linear optic devices (optical computing)</p></li><li><p>qnThe Order Parameter</p><p>n</p><p>no order</p><p>perfect orderperfect crystal</p><p>isotropic fluid</p></li><li><p>Interactions between individual molecules are represented by a potential of average forceFrom Statistical Mechanics (Self Consistency)Maier-Saupe Theory - Mean Field Approach {V: minimum} when phase is ordered (-P2(cosq)) {V: V=0} when phase is disordered () factor for intermolecular strength ( n)b=(kT)-1qnfy</p></li><li><p>Maier-Saupe Theory - Mean Field ApproachTemperatureNematic LiquidCrystalIsotropic Fluid-0.60.01.0Order Parameter, S</p></li><li><p>Landau-de Gennes Theorya=ao(T-T*), ao, b, c, T*, L are phenomenological constantsG is a surface interaction strengthOrder Parameter, STemperatureGood near NI transitionsurfacePredicts order nearsurface</p></li><li><p>The Order Parameter: How does it affects display performance ?The order parameter, S, is proportional to a number of importantparameters which dictate display performance. ParameterNomenclature Elastic ConstantKii S2BirefringenceDn SDielectric AnisotropyDe SMagnetic Anisotropy Dc SViscosity AnisotropyDh SExample: Does the threshold switching voltage for a TN increase or decrease as the operating temperature increases.</p><p> Scales as the square root of S therefore lowers with increasing temperatureproportional to</p></li><li><p>Anisotropy: Dielectric ConstantbOff-axis dipole moment, angle b with molecular axisN: number densityh,f: reaction field, reaction cavity parametersS: order parameterDa: anisotropy in polarizabilitym: molecular dipole momentkB: Boltzman constantT: TemperatureFor values of the angle b54.7o, the dipolar term isnegative, and may result in a materials with an overall -De.</p></li><li><p>Anisotropy: Dielectric Constant+++++- -- --EeeDe = e - e &gt; 0EDe = e - e &lt; 0++++----</p><p>positivenegativeall angles inthe plane to E arepossible for the-De materialsE</p></li><li>Anisotropy: Duel Frequency MLC-2048 (EM Industries), Duel Frequency Material Frequency (kHz)0.11.01050100Dielectric Anisotropy (De)3.283.220.72-3.0-3.4low frequency, De&gt;0high frequency, De</li><li><p>Dielectric Constants (@20oC, 1kHz)*Mixture Application Deee</p><p>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</p></li><li><p>Dielectric Constants: Temperature Dependence4-pentyl-4-cyanobiphenylTemperature DependenceAverage Dielectric Anistropy</p></li><li><p>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. </p><p>Ring currents associated witharomatic units give a largenegative component to c for directions to aromatic ringplane. Dc is usually positive since:</p></li><li><p>Magnetic Anisotropy: DiamagnetismCompound</p></li><li><p>Optical Anisotropy: Birefringenceordinary ray (no, ordinary index of refraction)extraordinary ray (ne, extraordinary index of refraction)</p></li><li><p>Optical Anisotropy: Birefringenceordinary waveqextraordinary waveFor propagation along the opticaxis, both modes are nooptic axis</p></li><li><p>Optical Anisotropy: Phase Shiftanalyzerpolarizerliquid crystallight</p><p> f = 2pdno,e/l</p><p>Df = fe - fo=2pdDn/l</p><p> Dn = ne - no</p><p> 0 &lt; Dn &lt; 0.2depending on deformation</p><p>380 nm &lt; l &lt; 780 nm visible light </p></li><li><p>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</p></li><li><p>Birefringence: Temperature Dependence Average IndexTemperatureDependence</p></li><li><p>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</p></li><li><p> Nematic Elasticity: Frank Elastic Theory 11 Splay, K Twist, K22 Bend, K33</p></li><li><p>Surface Anchoringmicrogrooved surface -homogeneous alignment (//)rubbed polyimide ensemble of chains -homeotropic alignment ()surfactant or silaneAlignment at surfaces propagates over macroscopic distances</p></li><li><p>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</p></li><li><p>Creating Deformations with a Field and Surface - Bend DeformationE or B</p></li><li><p>Creating Deformations with a Field and Surface - Splay DeformationE or B</p></li><li><p>Creating Deformations with a Field and Surface - Twist DeformationE or B</p></li><li><p>Magnitudes of Elastic ConstantsEM Industry K11K22K33 Mixture(pN)(pN)(pN)Application</p><p>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</p><p>U: intermolecular interaction energya: molecule distance</p></li><li><p>Elastic Constant K22: Temperature Dependence</p></li><li><p>The Flexoelectric Effect-</p><p>+-</p><p>+Polar AxisUndeformedstate of bananaand pear shapedmoleculesSplayBendPolar structure corresponds tocloser packingof pear and banana molecules</p></li><li><p>xeeyEnqEffects of an Electric FieldElectric Free Energy DensityElectric Torque DensityUsing De = 5 and E=0.5 V/mm</p></li><li><p>xccyBnqEffects of an Magnetic FieldMagnetic free energy densityMagnetic torque densityUsing Dc = 10-7 m3kg-1 and B= 2 T = 20,000 G</p></li><li><p>Deformation TorqueOrientation of molecules obeys this eq.Free energy density from elastic theoryTorque density</p></li><li><p>SurfaceDeformation Torqueqdx Material Shear Modulus Steel 100 GPa Silica 40 GPa Nylon 1 GPaShear modulus Youngs modulus</p></li><li><p>Coherence Length: Electric or MagneticEBalance torqueFind distance dCoherence length xUsing E = 0.5 V/mmand De = 20</p></li><li><p>Viscosity: Shear Flow Viscosity Coefficientn n nn h11h33h22Typically h22 &gt; h33 &gt;h11 nnn</p></li><li><p>Viscosity: Flow Viscosity CoefficientDynamic Viscosity (h) 1 kg/ms = 1 Pas 0.1 kg/ms = 1 poiseKinematic Viscosity (n) 1 m2/s</p><p>LC specification sheets givekinematic viscosity in mm2/sApproximate density</p></li><li><p>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</p></li><li><p>Viscosity: Temperature DependenceFor isotropic liquids E is the activation energy for diffusion of molecular motion.H3CONC4H9</p></li><li><p>nViscosity: Rotational Viscosity CoefficientTimennRotation of the director n bv externalfields (rotating fields or static).</p><p>Viscous torque's Gv are exerted on a liquidcrystal during rotation of the director n and by shear flow.g1: rotational viscosity coefficient</p></li><li><p>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</p></li><li><p>Viscosity: ComparisonsMaterialViscosity (poise)</p><p>Air10-7Water10-3Light Oil10-1Glycerin1.5</p><p>LC-Rotational (g1)1&lt; g1 &lt; 2LC-Flow (hii)0.2&lt; hii</p></li><li><p>Surfacex Relaxation from DeformationESurfacexfield on statezero field stateRelaxation when field is turned off Relaxation time t</p></li><li><p> Relaxation from DeformationBalance viscous/deformation torqueAssume small deformationsSolutionFor 100 mm cellFor 5 mm cell</p></li><li><p> Freedericksz Transition - The Threshold IEczyExAt some critical E field, the director rotates, before Ecnothing happensqnyxnE00d</p></li><li><p> Freedericksz Transition - The Threshold II E-fieldfree energy totalfree energyMinimize free energy with Euler Equation</p></li><li><p> Freedericksz Transition - The Threshold III1.0 E/Ecmid-layer tilt (deg)differential equation soln.small qthreshold</p></li><li><p> 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)</p></li><li><p> 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.</p></li><li><p>Microscopic Fluttering and FluctuationsThermally induced Deformations Characteristic time t of Fluctuations:</p><p> Can see fluctuations with microscope: Responsible for opaque appearance of nematic LC</p></li><li><p>AXYZZ Aromatic or saturated ring core X &amp; 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</p></li><li><p>Mesogenic Core Linking Groups Ring GroupsNNphenylpyrimidinecyclohexanebiphenylterphenyldiphenylethanestilbenetolaneschiffs baseazobenzeneazoxyben-zenephenylbenzoate(ester)phenylthio-benzoate Common Groups</p></li><li><p>NomenclatureMesogenic Corephenylbenzylbenzenebiphenylterphenylphenylcyclohexane (PCH)cyclohexane cyclohexylRing Numbering Scheme321654321654</p></li><li><p> Terminal Groups </p><p>(one terminal group is typically an alkyl chain)CH3CH2CH2CH2CH3CH2C*HCH2CH3straight chain</p><p>branched chain (chiral)Attachment to mesogenic ring structureDirect - alkyl (butyl)Ether -O- alkoxy (butoxy)</p></li><li><p>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</p></li><li><p>Second Terminal Group andLateral Substituents (Y &amp; Z)H -FflouroClchloroBrbromoIiodoCH3methylCH3(CH2)nalkylCNcyanoNH2aminoN(CH3)dimethylaminoNO2nitro</p><p>phenyl</p><p>cyclohexyl</p></li><li><p>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</p><p>16</p><p>14</p><p>12</p><p>10CH3-(CH2)n-OO-(CH2)n-CH3C-OO</p></li><li><p>4-pentyl-4-cyanobiphenyl4-pentoxy-4-cyanobiphenylNomenclatureCommon molecules which exhibit a LC phase</p></li><li><p>Structure - PropertyCH3-(CH2)4C Nvary mesogenic coreA AC-N (oC)N-I(oC)DnDe22.5350.1811.571520.1819.731550.109.7</p></li><li><p>Structure - PropertyCH3-(CH2)4COOvary end groupXXC-N (oC)N-I (oC)HFBrCNCH3C6H587.592.0115.5111.0106.0155.0114.0156.0193.0226.0176.0266.0</p></li><li><p>Lateral Substituents (Z &amp; Z)AXYZZ Z and Z are lateral substituents Broadens the molecules Lowers nematic stability May introduce negative dielectric anisotropy</p></li><li><p>ESolidLiquid CrystalIsotropic LiquidConcentration (c2), %0 50 100Why Liquid Crystal MixturesMelt Temperature:Liquid Crystal-Solid</p><p>ln ci = DHi(Teu-1 - Tmi-1)/R</p><p>DH: enthalpiesTeu: eutectic temperature Tmi: melt temperatureR: constant</p><p>Nematic-IsotropicTemperature: TNI</p><p>TNI = S ciTNIi </p><p>Temperatureeutecticpoint</p></li><li>S-N </li><li>PropertyZLI 4792 MLC 6292/000 MLC 6292/100S-N </li><li><p> Thermotropic Liquid Crystal Anisotropy Nematic phase Chirality Order parameters Dielectric Anisotropy Diamagnetism Birefringence Elastic constants Surface Anchoring Viscosity Threshold Defects Eutectic MixtureSummary of Fundamentals</p></li></ul>