Liquid Crystal Materials

1. Liquid Crystal Materials

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

3. The Lyotropic Phases micelle cross section reverse micelle cross section

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

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

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

7. The Nematic Director n n director The local average axis of the long molecular axis

8. Other Liquid Crystal Phases n z n n q Smectic C Smectic ANematic Temperature

9. Chirality 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 C N H-C-C-C-C-C H H H H H non-chiral H H H H H C N H-C-C-C-C-C CH3 non-superimposable chiral (RH) H H H H

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

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

12. 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.

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

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

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

16. 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

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

18. Example of Side-Chain Polymer LCs R1 -(-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)

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

20. 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

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

22. 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

23. 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 ConstantKiiS2 BirefringenceDnS 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

24. 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.

25. Anisotropy: Dielectric Constant E ++ 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

26. 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

27. Materials Dielectric Constant Vacuum 1.0000 Air 1.0005 Polystyrene 2.56 Polyethylene 2.30 Nylon 3.5 Water 78.54 Dielectric Constants (@20oC, 1kHz) *Mixture Application Dee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

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

29. 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:

30. Magnetic Anisotropy: Diamagnetism Compound

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

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

33. 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

34. 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

35. Birefringence: Temperature Dependence Average Index Temperature Dependence

36. 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

37. 1 ò = Ñ × + × Ñ ´ + ´ Ñ ´ 2 2 2 F { K ( n ) K ( n n ) K ( n n ) } dV 11 22 33 d 2 V 1 ò - Ñ × × Ñ ´ Ñ × + Ñ × Ñ × { K ( n n + n n ) K ( n n )} dV 24 13 2 V D c 1 1 ò ò = - e D e × - × 2 2 F ( E n ) dV ( B n ) dV c e o o 2 2 o V V Nematic Elasticity: Frank Elastic Theory Bend, K Twist, K Splay, K 33 22 11

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

39. Surface Anchoring N polar anchoring Wq q n surface f azimuthal anchoring 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

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

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

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

43. 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

44. Elastic Constant K22: Temperature Dependence

45. 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

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

47. 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

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

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

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