1. LIQUID CRYSTALS Introduction Introduction LC mesophases LCs in the bulk and in confined geometries optical properties of LCs fluctuations and light scattering applications of LCs

2. AGGREGATION STATES OF MATTER Solid phase (crystal) Liquid phase heating cooling Example: H 2 O molekule

3. THERMOTROPIC LIQUID CRYSTALS heating cooling Solid phase (crystal)Liquid phase Liquid crytalline phase Rod-like molecules (calamatic LCs) example: alkhyl-cianobiphenyls Synthetic materials Texture of the LC phase observed by polarization optical microscopy Disc-shape molecules (discotic LCs) example: triphenylene derivatives

4. LIOTROPIC LIQUID CRYSTALS decreasing concentration increasing concentration Solid phase (crystal)Liquid phase Liquid crystalline phase Examples: soaps, lipids, viruses, DNA... MolecularsolutionsMolecularsolutions 100 nm TM virus Natural materials

5. POLYMER LIQUID CRYSTALS main chain polymer LCs Examples: Kevlar (du Pont), solutions of biopolymers side chain polymer LCs Kevlar

6. GENERAL PROPERTIES OF LC-MESOPHASES 1)They flow and form surface level (similar to liquids) 2) They exhibit anisotropic material properties (similar to crystals) 3) In some cases they can transmitt mechanical stress (similar to crystals) Example: optical birefringence n1n1n1n1 n1n1n1n1 n2n2n2n2 n2n2n2n2 Example: bend strain

7. THERMOTROPIC LIQUID CRYSTAL PHASES Parameters describing the liquid crystalline phase: Orientational order Positional order Bond orientational order smectic A phase (SmA) nematic phase (N) smectic C phase (SmC) columnar phase (2D lattice) of achiral molecules

8. NEMATIC LC PHASE – theoretical description Basic thermodynamic argument for the I-N phase transition: Although orientational alignment of the molecules results in the loss of the entropy S, this loss is compensated by a decrease of the interaction energy U (because Van der Waals attractive forces are increased, molecular packing is optimized,...) n=director ˆ Microscopic description: f(  ) angular distribution function f(  )d  = fraction of the molecules pointing into a solid angle  head to tail invariance of the nematic phase requires f(  )=f(  -  )!! F = U – TS nematic order paramer S N = = Maier-Saupe theory: U= –u S N 2, Isotropic phase: S N = 0, totally aligned N phase S N = 1.

9. NEMATIC - ISOTROPIC PHASE TRANSITION S N can be measured via anisotropy of the material properties. example: diamagnetic susceptibility x z y  z = n(  II +   ) = n(  +( 2/3 )  a S N )  x =  y = n(  –( 1/3 )  a S N ) S N =(  z –  x )/(n  a )  =(  II +2   )/3,  a = (  II -   ), n=N/V where molecular parameters should be known from other measurements.

10. ELASTIC DEFORMATIONS IN NEMATICS Nematic phase can transmit forces in cases in which the corresponding deformation perturbs the long-range orientational order. For example: shear stress will produce usual viscous liquid flow, F F while splay, twist and bend deformations will produce elastic response. Elastic energy density of distortion (continuum theory): Frank elastic constants: K i  10 -12 N

11. EFFECT OF INTERFACE INTERACTIONS Nematic phase between two planar surfaces. Surface forces generally induce bulk aligment in some preferential direction (easy axis). Approximation of infinitely strong anchoring (B =  ) is often reasonable. F surface =f 0 +Bsin 2  Surface anchoring energy coefficients: B   B   10 -5 N/m Rapini-Papoular approximation Nematic phase cofined to spherical droplets. F=F surface +F d =MIN  easy axis n ^  = angle between n and the easy axis ^

12. glass LC Polymer surface is melted due to applied force and melted polymer molecules align in the direction of the rubbing. STANDARD TECHNIQUE TO ACHIEVE PLANAR SURFACE ANCHORING ACHIEVE PLANAR SURFACE ANCHORING STANDARD TECHNIQUE TO ACHIEVE PLANAR SURFACE ANCHORING ACHIEVE PLANAR SURFACE ANCHORINGPolyimide glass Unidirectional rubbing

13. ALIGNMENT OF LIQUID CRYSTALS ON RUBBED POLYMER SURFACE ALIGNMENT OF LIQUID CRYSTALS ON RUBBED POLYMER SURFACE Anisotropic interaction between the polymer substrate and the rod-shape liquid crystal molecules induces orientational ordering of the LC layer. 1 mm Nematic LC texture in a cell without and with the alignment layer.

14. EFFECT OF EXTERNAL FIELDS Due to head-tail invariance of the molecular arrangement, the nematic phase has no spontaneous macroscopic electric polarization P and magnetization M. External electric and magnetic fields produce induced polarization/magnetization (P=  0  e E, M=  m H). For dielectric polarization local field corrections are quite important!! P z =  o n(  +( 2/3 )  a S N )fhE z =  o (  II -1 ) E z P x =  o n(  –( 1/3 )  a S N ) fhE x =  o (   -1 ) E x x z y h=3  /(2  +1) cavity field factor f reaction field factor Dielectric tensor in case of z II n: ^  =  , 0, 0 0,  , 0 0, 0,  II in general :  =   1+  a (n  n), where  a =(  II -   ) is dielectric anisotropy. ^ ^ D=  o (   E+  a (n·E)n) ^ ^

15. DIELECTRIC ANISOTROPY 203040 5070 60 Temperature dependence of the dielectric constant and the DSC response of the liquid crystal 5CB.  (T) DSC

16. + – FREEDERICKSZ EFFECT Electrostatic free energy density: For  a >0 electric field tends to align the LC director n along the field direction. In confined geometries this tendency is opposed by surface anchoring. Competition results in the threshold behaviour. Example: nematic cell with planar anchoring: z x E<E th E>E th + – U U Reorientation : n=n 0 +  n(z), n 0 =e x,,  n II e z, approximation:  n(z)= (  n)sin(  z/d) Total free energy density: F t =F e +F d = critical field ~ 1V/  m ^ ^ 

17. THERMOTROPIC LIQUID CRYSTAL PHASES Via intramolecular interactions chirality is transmitted from the microscopic to the macroscopic scale. Chiral smectic A phase (SmA*) Similar to achiral SmA, but exhibits optical activity Chiral nematic phase (N*), known also as cholesteric phase (Ch) Spontaneously twisted Chiral smectic C phase (SmC*) Tilted and spontaneously twisted (exhibits ferroelectricity) of chiral molecules p/2

18. Example: LC phases of DNA in aqueous solutions spherulite of the cholesteric phase c>10 wt % hexagonal LC phase segment of DNA

19. OPTICAL PROPERTIES

20. OPTICAL PROPERTIES OF THE NEMATIC PHASE n  -n  =  n  0.2 LC phases have very large birefringence:  =   1+  a (n  n),  a =(   –   )=nS N (   –   )fh Dielectric tensor at optical frequencies (~10 15 Hz), refractive index n=(  ) 1/2 n ^ Optical axis is parallel to the nematic director n. ^ birefringent medium  n ^ (k/k)(k/k) extraordinary polarization ordinary polarization Ordinary beam : n o = n  Extraordinary beam : k=(  /c)n sEsE

21. OPTICAL BIREFRINGENCE N I Nematic liquid crystals are strongly birefringent “liquids”!!! (n e -n o )  S N  n)d ) /  = ( 2  n)d ) / Phase retardation between ordinary and extraordinary ray in d=4 thick LC layer is 2  Phase retardation can be mediated by relatively low external voltages (Freedericksz effect). Liquid crystal have large electrooptic response!!!

22. COLORFULL NEMATIC TEXTURES observed between crossed polarizers COLORFULL NEMATIC TEXTURES observed between crossed polarizers A nalyser P olariser Optical polarization microscopy:  n)d ) /  = ( 2  n)d ) / Phase retardation between ordinary and extraordinary ray Transmittance  Transmittance  =  (  depends on local orientation of the director field n(r) ^

23. OPTICAL PROPERTIES OF THE CHOLESTERIC PHASE Cholesteric LCs are natural 1D photonic band-gap media !! Spatial periodicity (pitch p) of the director field n(r) is typically in the range of optical wavelengths. ImK means strong selective reflection for ~p.  n(z)=(cos(qz), sin(qz), 0) /2 z ^ Spiralling index ellipsoid. (Analytical solutions of WE for k II z and d=  ) q=2  /p x Dielectric tensor in x,y plane:  =   1+  a (n  n) = a+bcos(2qz), bsin(2qz) bsin(2qz), a-bcos(2qz) a=(   +   )/2, b=(   -   )/2 ^^

24. SELECTIVE REFLECTION and MAUGUIN LIMIT For ~p circularly polarized beam which matches the chirality of the structure is totally reflected. The width of the reflection (forbidden) band  ~  n·p. Theory versus practice. For << p the polarization plane of the linearly polarized light is rotated synchro- nously with the spontaneous twist of the structure (Mauguin limit). The material acts as a strongly optically active medium.

25. LIGHT SCATTERING

26. LIGHT SCATTERING IN THE NEMATIC PHASE One of the most profound optical manifestations of the thermal fluctuations. n0n0 q F d =(V/2)    n 1 (q)  (K 1 q  2 +K 3 q  2 ) +  n 2 (q)  (K 2 q  2 +K 3 q  2 )  12 kT dF d /dn i = -  i  n i /  t, i=1,2 Relaxation rate : (1/  )  (K/  )q 2 10 -5 cm 2 /s n(r)=n0(r)+n(r)n(r)=n0(r)+n(r)  n(r)=  n(q)e iqr 22 q kT Fluctuations of the director field n(r) produce increase of the elastic energy F d K i  10 -12 N 10 -6 –1 s  n(q,t)=  n(q,0)e -t/  d Overdamped relaxation: nnnn

27. Laser Detector ( I(t)  |E s (t) | 2 )  sample H V n(q,t). DLS provides information on  of different fluctuation modes  n(q,t). This gives the values of (K i /  ) for different types of deformations. EKSPERIMENTAL ANALYSIS Photon correlation spectroscopy (known as PCS or DLS): probing range 10 -9 –10 3 s Largest scattering cross section for  n(q= ).  n(q= q s ). g (2) (t)= / 2 we measure scattered light transmitted light

28. LIGHT SCATTERING FROM CONFINED LC STRUCTURES LIGHT SCATTERING FROM CONFINED LC STRUCTURES A)Spherical LC droplets of radius R q min  /R, (1/  ) min  (K/  )R -2 B) Thin LC film of thickness D ~. DLS gives information on cavity size (R or D) and surface anchoring koefficient B. ? q min  /D, (1/  ) min  (K/  )D -2 s

29. APPLICATIONS OF LIQUID CRYSTALS Most important comercial products based on LCs are LCDs. Other applications: optical switching devices, optical filters, temperature and stress sensors, special paints and colorants, cosmetics, etc. Present top LCD: WUXGA (wide ultra extended graphics array) 1920 x 1200 pixels.

30. Electrodes Voltage ON Polarized output light No output light Liquid Crystal Display (LCD) PRINCIPLE Picture element is white Picture element is black Polariser Analyser

31. FROM PICTURE ELEMENT to THE DISPLAY Segment-type display Active matrix display semiconductor platform composition of TFT LCD colour filter polariser liquid crystal material common electrode backlight skupna elektroda skupna elektroda segment electrode (RGB) colours

32. SWITCHABLE WINDOWS voltage off voltage on Switchable windows are made from polymer dispersed liquid crystals (PDLC)

33. OTHER APPLICATIONS LCs in ART: Art-painting made by use of the polysiloxane LC paint. left: in reflected light right: in transmitted light Car paint from chiral LCs. Temperature sensor from cholesteric LCs

34. Olenik 2001