1. Dielectric Constants (@20 o C, 1kHz) *Mixture Application     BL038PDLCs16.721.75.3 MLC-6292TN AMLCDs7.411.13.7 ZLI-4792TN AMLCDs5.28.33.1 TL205AM PDLCs59.14.1 18523Fiber-Optics2.774.3 95-465-  material-4.23.67.8 MaterialsDielectric Constant Vacuum1.0000 Air1.0005 Polystyrene2.56 Polyethylene2.30 Nylon3.5 Water78.54 *EM Materials

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

3. 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:

4. Magnetic Anisotropy: Diamagnetism Compound

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

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

7. 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

8. Birefringence (20 o C @ 589 nm) EM Industry  n n e n o Application Mixture BL0380.27201.79901.5270 PDLC TL2130.23901.76601.5270PDLC TL2050.21751.74551.5270 AM PDLC ZLI 54000.10631.59181.4855STN ZLI 37710.10451.59651.4920TN ZLI 47920.09691.57631.4794 AM TN LCDs MLC-62920.09031.56081.4705AM TN LCDs ZLI 60090.08591.55551.4696AN TN LCDs MLC-66080.08301.55781.4748ECB 95-4650.08271.55841.4752-  devices MLC-66140.0770------------------IPS MLC-66010.0763------------------IPS 185230.04901.50891.4599Fiber Optics ZLI 28060.04371.51831.4746 -  device

9. Birefringence: Temperature Dependence Average Index Temperature Dependence

10. 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

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

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

13. Surface Anchoring   N n polar anchoring W  azimuthal anchoring W  surface Strong anchoring 10 -4 J/m 2 Weak anchoring 10 -7 J/m 2 W ,  is energy needed to move director n from its easy axis

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

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

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

17. Magnitudes of Elastic Constants EM Industry K 11 K 22 K 33 Mixture(pN)(pN)(pN)Application BL03813.7------27.7PDLC TL20517.3------20.4AM PDLC ZLI 479213.26.518.3TN AM LCD ZLI 5400105.419.9TN ZLI-600911.55.416.0AM LCD Order of magnitude estimate of elastic constant U: intermolecular interaction energy  : molecule distance

18. Elastic Constant K 22 : Temperature Dependence

19. 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

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

21. x   y B n  Effects of an Magnetic Field Magnetic free energy density Magnetic torque density Using  = 10 -7 m 3 kg -1 and B= 2 T = 20,000 G

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

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

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

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

26. 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

27. 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 15 0.15 ZLI-2293STN 20 0.20 MLC-6610ECB 21 0.21 MLC-6292TN AM LCDs (T c =120 o C) 28 0.28 18523Fiber Optics (n o =1.4599) 29 0.29 TL205PDLC AM LCD 45 0.45 BL038PDLCs (  n=0.28) 72 0.72

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

29. 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

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

31. 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

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

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

34. 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

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

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

37. 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)

38. 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.

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

40. 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

41. 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

42. Nomenclature Mesogenic Core phenyl benzyl benzene biphenyl terphenyl phenylcyclohexane (PCH) cyclohexane cyclohexyl Ring Numbering Scheme 3’2’ 1’ 6’5’ 4’ 32 1 6 5 4

43. 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)

44. 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

45. 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

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

47. 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

48. Structure - Property N N CH 3 -(CH 2 ) 4 C N vary mesogenic core A AC-N ( o C)N-I( o C)  n  22.5350.1811.5 71520.1819.7 31550.109.7

49. 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 5 87.5 92.0 115.5 111.0 106.0 155.0 114.0 156.0 193.0 226.0 176.0 266.0

50. 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

51. E Solid Liquid Crystal Isotropic Liquid Concentration (  2 ), % 0 50 100 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

52. 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 11 1.39ratio of the bend-to-splay elastic constant  5.2dielectric anisotropy  n 0.0969optical 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

53. 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 15 2825 0 C 409585 -20 C 160470460 -40 C 250070007000 K 33 /K 11 1.39-------------  5.27.46.9  n 0.09690.09030.1146 d  n (  m) 0.50.50.5 dV/dT (mV/C) 2.551.881.38 V(10,0,20) 2.141.801.38 V(50,0,20) 2.562.242.25 V(90,0,20) 3.212.852.83 EM Industry Mixtures

54. 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