Liquid Crystal Materials

Broad Classification Lyotropics Thermotropics + - hydrophobic amphiphilic molecules, polar and non-polar parts form liquid crystal phases over certain concentration ranges when mixed with a solvent molecules consisting of a rigid core and flexible tail(s) form liquid crystal phases over certain temperature ranges. hydrophobic non-polar tail flexible tail + - hydrophilic polar head rigid core

The Lyotropic Phases micelle cross section reverse micelle

The molecule above (5CB) is ~2 nm × 0.5 nm The Thermotropic Liquid Crystal Molecule Chemist’s View Physicist’s Engineer’s View CN Shape Anisotropy Length > Width The molecule above (5CB) is ~2 nm × 0.5 nm

( ) ( ) Geometrical Structures of Mesogenic Molecules Low Molecular Weight High Molecular Weight (polymers) ( ) disk-like rod-like n ( ) n most practical applications

Crystal Nematic LC Isotropic Temperature The Liquid Crystal Phase n Crystal Nematic LC Isotropic Temperature

The Nematic Director n n The local average axis of the long molecular axis

Smectic C Smectic A Nematic Temperature Other Liquid Crystal Phases n z n n q Smectic C Smectic A Nematic Temperature

Chirality left-handed right-handed mirror images H-C-C-C-C-C C N The methyl group on the 2nd carbon atom on the alkyl chain of the molecules extends out 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 of as a right or left handed coordinate system left-handed right-handed H H H H H mirror images H-C-C-C-C-C C N H H H H H non-chiral H H H H H H-C-C-C-C-C C N CH3 non-superimposable H H H H chiral (RH)

The Chiral Nematic Ordinary Nematic Chiral Nematic n P CN CN director pitch P

The Chiral Doped Nematic You can create a cholesteric material by doping a conventional nematic with a chiral dopant. For dilute solutions Chiral Dopant HTP (mm)-1 S-811 -14 IS-4651 -13.6 - indicates left twist sense For a 10% doping of S-811

The Chiral Smectic C: Ferroelectrics q m Eye- dipole moment m fin - chiral ferroelectric LC has a dipole moment perp- endicular to its long axis, and is chiral.

The Chiral Smectic: TGB Twisted Grain Boundary (TGB) A twisted grain boundary smectic A phase (frustrated) - TGBA*

Discotic Liquid Crystal example: R=OCOC11H23 C R O R

Discotics Liquid Crystals n n Nematic discotic phase Columnar, columns of molecules in hexagonal lattice

Polymer Liquid Crystals Combining the properties of liquid crystals and polymers Main Chain Side Chain mesogenic moieties attached as side chains on the polymer backbone mesogenic moieties are connected head-to-tail rigid semi-flexible

Polymer Liquid Crystals forming nematic liquid crystal phases n side-chain main-chain

Example of Side-Chain Polymer LCs -(-CH2-C-)X- O O C-O-(CH2)n-O C-O R2 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)

The Order Parameter n q n no order perfect order perfect crystal isotropic fluid

Maier-Saupe Theory - Mean Field Approach Interactions between individual molecules are represented by a potential of average force n y q {V: minimum} when phase is ordered (-P2(cosq)) {V: V=0} when phase is disordered (<P2(cosq)>) factor for intermolecular strength ( n) f From Statistical Mechanics (Self Consistency) b=(kT)-1

n n Temperature Maier-Saupe Theory - Mean Field Approach Isotropic 1.0 Isotropic Fluid Nematic Liquid Crystal Order Parameter, S 0.0 n -0.6 Temperature

Landau-de Gennes Theory a=ao(T-T*), ao, b, c, T*, L are phenomenological constants G is a surface interaction strength Good near NI transition surface Order Parameter, S Predicts order near surface Temperature

How does it affects display performance ? The Order Parameter: How does it affects display performance ? The order parameter, S, is proportional to a number of important parameters which dictate display performance. proportional to Parameter Nomenclature  Elastic Constant Kii S2 Birefringence Dn S Dielectric Anisotropy De S Magnetic Anisotropy Dc S Viscosity Anisotropy Dh S Example: Does the threshold switching voltage for a TN increase or decrease as the operating temperature increases. Scales as the square root of S therefore lowers with increasing temperature

Anisotropy: Dielectric Constant Off-axis dipole moment, angle b with molecular axis b N: number density h,f: reaction field, reaction cavity parameters S: order parameter Da: anisotropy in polarizability m: molecular dipole moment kB: Boltzman constant T: Temperature For values of the angle b<54.7o, the dipolar term is positive, and for values b>54.7o, the dipolar term is negative, and may result in a materials with an overall -De.

Anisotropy: Dielectric Constant ++ e + ++ positive - - - - - e De = e - e > 0 E + E - negative all angles in the plane  to E are possible for the -De materials De = e - e < 0

Anisotropy: Duel Frequency high frequency, De<0 low frequency, De>0 MLC-2048 (EM Industries), Duel Frequency Material Frequency (kHz) 0.1 1.0 10 50 100 Dielectric Anisotropy (De) 3.28 3.22 0.72 -3.0 -3.4

Dielectric Constants (@20oC, 1kHz) *Mixture Application De e e BL038 PDLCs 16.7 21.7 5.3 MLC-6292 TN AMLCDs 7.4 11.1 3.7 ZLI-4792 TN AMLCDs 5.2 8.3 3.1 TL205 AM PDLCs 5 9.1 4.1 18523 Fiber-Optics 2.7 7 4.3 95-465 -De material -4.2 3.6 7.8 *EM Materials Materials Dielectric Constant Vacuum 1.0000 Air 1.0005 Polystyrene 2.56 Polyethylene 2.30 Nylon 3.5 Water 78.54

Dielectric Constants: Temperature Dependence 4’-pentyl-4-cyanobiphenyl Temperature Dependence Average Dielectric Anistropy

Magnetic Anisotropy: Diamagnetism Diamagnetism: induction of a magnetic moment in opposition to an applied magnetic field. LCs are diamagnetic due to the dispersed electron distribution associated with the electron structure. Delocalized charge makes the major contribution to diamagnetism. Ring currents associated with aromatic units give a large negative component to c for directions  to aromatic ring plane. Dc is usually positive since:

Magnetic Anisotropy: Diamagnetism Compound

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

Optical Anisotropy: Birefringence ordinary wave extraordinary wave optic axis q For propagation along the optic axis, both modes are no

Optical Anisotropy: Phase Shift f = 2pdno,e/l Df = fe - fo=2pdDn/l Dn = ne - no 0 < Dn < 0.2 depending on deformation 380 nm < l < 780 nm visible light analyzer liquid crystal polarizer light

Birefringence (20oC @ 589 nm) EM Industry Dn ne no Application Mixture BL038 0.2720 1.7990 1.5270 PDLC TL213 0.2390 1.7660 1.5270 PDLC TL205 0.2175 1.7455 1.5270 AM PDLC ZLI 5400 0.1063 1.5918 1.4855 STN ZLI 3771 0.1045 1.5965 1.4920 TN ZLI 4792 0.0969 1.5763 1.4794 AM TN LCDs MLC-6292 0.0903 1.5608 1.4705 AM TN LCDs ZLI 6009 0.0859 1.5555 1.4696 AN TN LCDs MLC-6608 0.0830 1.5578 1.4748 ECB 95-465 0.0827 1.5584 1.4752 -De devices MLC-6614 0.0770 --------- --------- IPS MLC-6601 0.0763 --------- --------- IPS 18523 0.0490 1.5089 1.4599 Fiber Optics ZLI 2806 0.0437 1.5183 1.4746 -De device

Birefringence: Temperature Dependence Average Index Temperature Dependence

Birefringence Example: 1/4 Wave Plate circular polarized What is minimum d for liquid crystal 1/4 wave plate ? linear polarized Unpolarized d LC: Dn=0.05 polarizer Takes greater number of e-waves than o-waves to span d, use Dn=0.05

ò Nematic Elasticity: Frank Elastic Theory Splay, K Twist, K Bend, K F dV d V e o = Ñ × + ´ - ò 1 2 11 22 33 24 13 { ( ) } )} n E B c D Splay, K Twist, K Bend, K 22 33 11

Surface Anchoring Alignment at surfaces propagates over macroscopic distances microgrooved surface - homogeneous alignment (//) rubbed polyimide ensemble of chains - homeotropic alignment () surfactant or silane

Surface Anchoring q f N polar anchoring Wq n surface azimuthal Wf Wq,f is energy needed to move director n from its easy axis Strong anchoring 10-4 J/m2 Weak anchoring 10-7 J/m2

E or B Creating Deformations with a Field and Surface - Bend Deformation E or B

E or B Creating Deformations with a Field and Surface - Splay Deformation E or B

E or B Creating Deformations with a Field and Surface - Twist Deformation E or B

Magnitudes of Elastic Constants EM Industry K11 K22 K33 Mixture (pN) (pN) (pN) Application BL038 13.7 ------ 27.7 PDLC TL205 17.3 ------ 20.4 AM PDLC ZLI 4792 13.2 6.5 18.3 TN AM LCD ZLI 5400 10 5.4 19.9 TN ZLI-6009 11.5 5.4 16.0 AM LCD Order of magnitude estimate of elastic constant U: intermolecular interaction energy a: molecule distance

Elastic Constant K22: Temperature Dependence

The Flexoelectric Effect - + - + Undeformed state of banana and pear shaped molecules Polar structure corresponds to closer packing of pear and banana molecules Bend Polar Axis Splay

Effects of an Electric Field y E x q e e Electric Free Energy Density Electric Torque Density Using De = 5 and E=0.5 V/mm

Effects of an Magnetic Field y n B x q c c Magnetic free energy density Magnetic torque density Using Dc = 10-7 m3kg-1 and B= 2 T = 20,000 G

Deformation Torque x q Surface Orientation of molecules obeys this eq. Free energy density from elastic theory Torque density

Deformation Torque x q Surface Material Shear Modulus Steel 100 GPa Silica 40 GPa Nylon 1 GPa Shear modulus  Young’s modulus

x Coherence Length: Electric or Magnetic q E Surface Balance torque d x E Balance torque Find distance d Coherence length x Using E = 0.5 V/mm and De = 20

n n  n  n  Viscosity: Shear Flow Viscosity Coefficient h11 h33 Typically h22 > h33 >h11

Viscosity: Flow Viscosity Coefficient LC specification sheets give kinematic viscosity in mm2/s Kinematic Viscosity (n) 1 m2/s Dynamic Viscosity (h) 1 kg/m·s = 1 Pa·s 0.1 kg/m·s = 1 poise Approximate density

Viscosity: Flow Viscosity Coefficient Typical Conversion Density Conversion Flow r 0.1 kg/ms = 1 poise Viscosity EM Industry Kinematic (n) Dynamic (h) MIXTURE CONFIGURATION (mm2/s) (Poise) ZLI-4792 TN AM LCDs 15 0.15 ZLI-2293 STN 20 0.20 MLC-6610 ECB 21 0.21 MLC-6292 TN AM LCDs (Tc=120oC) 28 0.28 18523 Fiber Optics (no=1.4599) 29 0.29 TL205 PDLC AM LCD 45 0.45 BL038 PDLCs (Dn=0.28) 72 0.72

Viscosity: Temperature Dependence C4H9 H3CO For isotropic liquids E is the activation energy for diffusion of molecular motion.

Viscosity: Rotational Viscosity Coefficient Rotation of the director n bv external fields (rotating fields or static). Viscous torque's Gv are exerted on a liquid crystal during rotation of the director n and by shear flow. n Time n g1: rotational viscosity coefficient

Viscosity: Rotational Viscosity Coefficient EM Industry Viscosity Viscosity MIXTURE CONFIGURATION (mPas) (Poise) ZLI-5400 TN LCDs 109 1.09 ZLI-4792 TN AM LCDs 123 1.23 ZLI-2293 STN 149 1.49 95-465 -De Applications 185 1.85 MLC-6608 TN AM LCD 186 1.86

Viscosity: Comparisons Material Viscosity (poise) Air 10-7 Water 10-3 Light Oil 10-1 Glycerin 1.5 LC-Rotational (g1) 1< g1 < 2 LC-Flow (hii) 0.2< hii<1.0

Relaxation from Deformation field on state Surface x Relaxation when field is turned off Relaxation time t Surface zero field state x

Relaxation from Deformation Balance viscous/deformation torque Assume small deformations Solution For 100 mm cell For 5 mm cell

Freedericksz Transition - The Threshold I y E n z E Ec q x y x d n At some critical E field, the director rotates, before Ec nothing happens

Freedericksz Transition - The Threshold II E-field free energy total free energy Minimize free energy with ‘Euler’ Equation

Freedericksz Transition - The Threshold III differential equation soln. small q threshold mid-layer tilt (deg) 1.0 E/Ec

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

Estimate Defect Size The simplest hypothesis is that the core or defect or disclination is an isotropic liquid, therefore the core energy is proportional to kBDTc. Let M be the molecular mass, N Avogadadro’s number and r the density of the liquid crystal.

Microscopic Fluttering and Fluctuations Characteristic time t of Fluctuations: Can see fluctuations with microscope: Responsible for opaque appearance of nematic LC Thermally induced Deformations

Z Z’ Y X A General Structure X & Y are terminal groups Aromatic or saturated ring core X & Y are terminal groups A is linkage between ring systems Z and Z’ are lateral substituents CH3 - (CH2)4 C N 4-pentyl-4’-cyanobiphenyl (5CB)

Common Groups Mesogenic Core Linking Groups Ring Groups biphenyl terphenyl diphenylethane stilbene tolane schiffs base azobenzene azoxyben- zene phenylbenzoate (ester) phenylthio- benzoate phenyl N pyrimidine N cyclohexane

Nomenclature Mesogenic Core terphenyl biphenyl phenyl benzyl benzene phenylcyclohexane (PCH) cyclohexane cyclohexyl 3’ 2’ 2 3 1’ 1 Ring Numbering Scheme 4’ 4 5’ 6’ 6 5

Terminal Groups CH2 CH2 straight chain CH2 CH3 branched chain (chiral) (one terminal group is typically an alkyl chain) CH2 CH2 straight chain branched chain (chiral) CH2 CH3 CH2 CH2 C*H CH3 CH3 Attachment to mesogenic ring structure Direct - alkyl (butyl) Ether -O- alkoxy (butoxy)

Terminal Groups CH3- methyl CH3-O- methoxy CH3-CH2- ethyl CH3-CH2-O- propyl CH3-(CH2)2-O- propoxy CH3-(CH2)3- butyl CH3-(CH2)3-O- butoxy CH3-(CH2)4- pentyl CH3-(CH2)4-O- pentoxy CH3-(CH2)5- hexyl CH3-(CH2)5-O- hexoxy CH3-(CH2)6- heptyl CH3-(CH2)6-O- heptoxy CH3-(CH2)7- octyl CH3-(CH2)7-O- octoxy

Second Terminal Group and Lateral Substituents (Y & Z) H - F flouro Cl chloro Br bromo I iodo CH3 methyl CH3(CH2)n alkyl CN cyano NH2 amino N(CH3) dimethylamino NO2 nitro phenyl cyclohexyl

Odd-Even Effect Clearing point versus alkyl chain length O CH3-(CH2)n-O C-O O-(CH2)n-CH3 18 16 14 12 10 clearing point 0 1 2 3 4 5 6 7 8 9 10 11 carbons in alkyl chain (n)

Nomenclature Common molecules which exhibit a LC phase CH3-(CH2)4 C N 4’-pentyl-4-cyanobiphenyl CH3-(CH2)4-O C N 4’-pentoxy-4-cyanobiphenyl

Structure - Property A vary mesogenic core A C-N (oC) N-I(oC) Dn De CH3-(CH2)4 C N A C-N (oC) N-I(oC) Dn De 22.5 35 0.18 11.5 N 71 52 0.18 19.7 31 55 0.10 9.7

Structure - Property X C-N (oC) N-I (oC) H F Br CN CH3 C6H5 87.5 92.0 vary end group CH3-(CH2)4 COO X X C-N (oC) N-I (oC) H F Br CN CH3 C6H5 87.5 92.0 115.5 111.0 106.0 155.0 114.0 156.0 193.0 226.0 176.0 266.0

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

Why Liquid Crystal Mixtures Melt Temperature: Liquid Crystal-Solid ln ci = DHi(Teu-1 - Tmi-1)/R DH: enthalpies Teu: eutectic temperature Tmi: melt temperature R: constant Nematic-Isotropic Temperature: TNI TNI = S ciTNIi Isotropic Liquid Liquid Crystal Temperature eutectic point Solid 0 50 100 Concentration (c2), %

EM Industry Mixtures S-N <-40 C solid nematic transition (< means supercools) Clearing +92 C nematic-isotropic transition temperature Viscosity (mm2 /s) flow viscosity, some materials may stipulate the +20 C 15 rotational viscosity also. May or may not give 0 C 40 a few temperatures K33/K11 1.39 ratio of the bend-to-splay elastic constant De 5.2 dielectric anisotropy Dn 0.0969 optical birefringence (may or may not give ne, no) dDn (mm) 0.5 product of dDn (essentially the optical path length) dV/dT (mV/oC) 2.55 how drive voltage changes as temperature varies V(10,0,20) 2.14 V(50,0,20) 2.56 threshold voltage (% transmission, viewing angle, V(90,0,20) 3.21 temperature)

EM Industry Mixtures Property ZLI 4792 MLC 6292/000 MLC 6292/100 S-N <-40 C <-30 C <-40 C Clearing +92 C +120 C +120 C Viscosity (mm2 /s) +20 C 15 28 25 0 C 40 95 85 -20 C 160 470 460 -40 C 2500 7000 7000 K33/K11 1.39 ------- ------ De 5.2 7.4 6.9 Dn 0.0969 0.0903 0.1146 dDn (mm) 0.5 0.5 0.5 dV/dT (mV/C) 2.55 1.88 1.38 V(10,0,20) 2.14 1.80 1.38 V(50,0,20) 2.56 2.24 2.25 V(90,0,20) 3.21 2.85 2.83

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