Dielectric Constants o C, 1kHz) *Mixture Application     BL038PDLCs MLC-6292TN AMLCDs ZLI-4792TN AMLCDs TL205AM PDLCs Fiber-Optics  material MaterialsDielectric Constant Vacuum Air Polystyrene2.56 Polyethylene2.30 Nylon3.5 Water78.54 *EM Materials

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  for directions  to aromatic ring plane.  is usually positive since:

Magnetic Anisotropy: Diamagnetism Compound

Optical Anisotropy: Birefringence ordinary ray (n o, ordinary index of refraction) extraordinary ray (n e, extraordinary index of refraction)

Optical Anisotropy: Birefringence ordinary wave  extraordinary wave For propagation along the optic axis, both modes are n o optic axis

Optical Anisotropy: Phase Shift analyzer polarizer liquid crystal light  = 2  dn o,e /  e   =2  d  n/  n = n e - n o 0 <  n < 0.2 depending on deformation 380 nm < < 780 nm visible light

Birefringence (20 o 589 nm) EM Industry  n n e n o Application Mixture BL PDLC TL PDLC TL AM PDLC ZLI STN ZLI TN ZLI AM TN LCDs MLC AM TN LCDs ZLI AN TN LCDs MLC ECB  devices MLC IPS MLC IPS Fiber Optics ZLI  device

Birefringence: Temperature Dependence Average Index Temperature Dependence

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

Nematic Elasticity: Frank Elastic Theory 11 Splay, K Twist, K 22 Bend, K 33

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

Surface Anchoring   N n polar anchoring W  azimuthal anchoring W  surface Strong anchoring J/m 2 Weak anchoring J/m 2 W ,  is energy needed to move director n from its easy axis

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

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

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

Magnitudes of Elastic Constants EM Industry K 11 K 22 K 33 Mixture(pN)(pN)(pN)Application BL PDLC TL AM PDLC ZLI TN AM LCD ZLI TN ZLI AM LCD Order of magnitude estimate of elastic constant U: intermolecular interaction energy  : molecule distance

Elastic Constant K 22 : Temperature Dependence

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

x   y E n  Effects of an Electric Field Electric Free Energy Density Electric Torque Density Using  = 5 and E=0.5 V/  m

x   y B n  Effects of an Magnetic Field Magnetic free energy density Magnetic torque density Using  = m 3 kg -1 and B= 2 T = 20,000 G

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

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

Surface  d x Coherence Length: Electric or Magnetic E Balance torque Find distance d Coherence length  Using E = 0.5 V/  m and  = 20

Viscosity: Shear Flow Viscosity Coefficient n  nn n n        Typically   >   >   n n n

Viscosity: Flow Viscosity Coefficient Dynamic Viscosity  1 kg/m·s = 1 Pa·s 0.1 kg/m·s = 1 poise Kinematic Viscosity  1 m 2 /s LC specification sheets give kinematic viscosity in mm 2 /s Approximate density

Viscosity: Flow Viscosity Coefficient Typical Conversion Density Conversion Flow  0.1 kg/ms = 1 poise Viscosity EM Industry Kinematic ( ) Dynamic (  ) MIXTURECONFIGURATION (mm 2 /s) (Poise) ZLI-4792TN AM LCDs ZLI-2293STN MLC-6610ECB MLC-6292TN AM LCDs (T c =120 o C) Fiber Optics (n o =1.4599) TL205PDLC AM LCD BL038PDLCs (  n=0.28)

Viscosity: Temperature Dependence For isotropic liquids E is the activation energy for diffusion of molecular motion. H 3 CO N C4H9C4H9

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

n Viscosity: Rotational Viscosity Coefficient n n EM IndustryViscosityViscosity MIXTURE CONFIGURATION (mPa  s) (Poise) ZLI-5400TN LCDs ZLI-4792 TN AM LCDs ZLI-2293STN  Applications MLC-6608TN AM LCD

Viscosity: Comparisons MaterialViscosity (poise) Air10 -7 Water10 -3 Light Oil10 -1 Glycerin1.5 LC-Rotational (  1 )1<  1 < 2 LC-Flow (  ii )0.2<  ii <1.0

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

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

Freedericksz Transition - The Threshold I EcEc z y E x At some critical E field, the director rotates, before E c nothing happens  n y x n E 0 0 d

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

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

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

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 k B  T c. Let M be the molecular mass, N Avogadadro’s number and  the density of the liquid crystal.

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

A X Y Z Z’ Aromatic or saturated ring core X & Y are terminal groups A is linkage between ring systems Z and Z’ are lateral substituents CH 3 - (CH 2 ) 4 C N 4-pentyl-4’-cyanobiphenyl (5CB) General Structure

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

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

Terminal Groups (one terminal group is typically an alkyl chain) CH 3 CH 2 CH 3 CH 2 C*H CH 2 CH 3 straight chain branched chain (chiral) Attachment to mesogenic ring structure Direct - alkyl (butyl) Ether -O- alkoxy (butoxy)

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

Second Terminal Group and Lateral Substituents (Y & Z) H - Fflouro Clchloro Brbromo Iiodo CH 3 methyl CH 3 (CH 2 ) n alkyl CNcyano NH 2 amino N(CH 3 )dimethylamino NO 2 nitro phenyl cyclohexyl

Odd-Even Effect Clearing point versus alkyl chain length carbons in alkyl chain (n) clearing point CH 3 -(CH 2 ) n -OO-(CH 2 ) n -CH 3 C-O O

CH 3 -(CH 2 ) 4 C N CH 3 -(CH 2 ) 4 -O C N 4’-pentyl-4-cyanobiphenyl 4’-pentoxy-4-cyanobiphenyl Nomenclature Common molecules which exhibit a LC phase

Structure - Property N N CH 3 -(CH 2 ) 4 C N vary mesogenic core A AC-N ( o C)N-I( o C)  n 

Structure - Property CH 3 -(CH 2 ) 4 COO vary end group X XC-N ( o C)N-I ( o C) H F Br CN CH 3 C 6 H

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

E Solid Liquid Crystal Isotropic Liquid Concentration (  2 ), % Why Liquid Crystal Mixtures Melt Temperature: Liquid Crystal-Solid ln  i =  H i (T eu -1 - T mi -1 )/R  H: enthalpies T eu : eutectic temperature T mi : melt temperature R: constant Nematic-Isotropic Temperature: T NI T NI =   i T NI i Temperature eutectic point

S-N <-40 Csolid nematic transition (< means supercools) Clearing +92 Cnematic-isotropic transition temperature Viscosity (mm 2 /s)flow viscosity, some materials may stipulate the +20 C 15rotational viscosity also. May or may not give 0 C 40a few temperatures K 33 /K ratio of the bend-to-splay elastic constant  5.2dielectric anisotropy  n optical birefringence (may or may not give n e, n o ) d  n (  m) 0.5product of d  n (essentially the optical path length) dV/dT (mV/ o C) 2.55how drive voltage changes as temperature varies V(10,0,20) 2.14 V(50,0,20) 2.56threshold voltage (% transmission, viewing angle, V(90,0,20) 3.21temperature) EM Industry Mixtures

PropertyZLI 4792 MLC 6292/000 MLC 6292/100 S-N <-40 C<-30 C <-40 C Clearing +92 C+120 C+120 C Viscosity (mm 2 /s) +20 C C C C K 33 /K   n d  n (  m) dV/dT (mV/C) V(10,0,20) V(50,0,20) V(90,0,20) EM Industry Mixtures

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