A B. What s a Liquid Crystal? G = H - TS K = [B]/[A] K = e - G/RT

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1 What s a Liquid Crystal? Phases (supramolecular equilibrium configurations) and molecules (equilibrium conformations) are basically the same thing. Phases are superamolecules; a large collection of atoms caught in a well on the hypersurface with a "time average" structure and symmetry, but in this case not all of the atoms are covalently bonded. Key difference: Phases have collective relative free energy! A B slopes = -S G = H - TS More ordered molecule/phase K = [B]/[A] G A More disordered molecule/phase B K = e - G/RT T Collective Volume G = (free energy/molecule) x (some big # of molecules)

2 First rder Phase Transition G slopes = -S T B More ordered molecule/phase A At low T More disordered molecule/phase At high T Two distinct wells and a barrier allows the possibility of metastable states and domain walls between phases in first order transitions G Increasing T G B A A Configuration B Configuration

3 Second rder Phase Transition* G A T B A changes continuously to B with increasing temperature. Lack of two co-existing wells means there can be no domain walls between phases in a second order transition. At low T At high T G Increasing T G The well for A slides over to B continuously with increasing T A Configuration B Configuration *Some of us are thinking that all LC transitions have some first order-ness

4 Potpourri of LC Mesogens and SmA Cyanobiphenyls (ematics) C R R R R IAC Phenylpyrimidines (Tilted Smectics) R R Discotics (Columnar) IAC 2 o-itrophenyl-biphenylcarboxylates (Chiral Tilted Smectics for L) R R I- Bn Banana Mania!

5 ematic and Smectic LCs C 5CB (nematic) Cr I C 5 H 11 ematic Schlieren texture (Photo by Mary eubert) C 10 H 21 2 W314 (SmC* - SmA*) Cr 63.5º SmC* 93.7º SmA* 116º I Cr (20 ) SmC* 93.7 SmA* 116 I SmC SmA Smectic A focal conic texture

6 Columnar Phases R R R R R R Discotic Mesogens (columnar phases) The B1 columnar banana phase (Photo by Renfan Shao) R R Bent-core Mesogens (smectic and columnar banana phases) Long-range positional order in two dimensions

7 Some Techniques used to Study LCs Polarized optical microscopy (PM) Electrooptics Cross-polarization magic angle spinning 13 C MR (CP-MAS) X-ray diffraction (XRD) Dielectric spectroscopy Depolarized reflected light microscopy from freely suspended films (DRLM) Freeze fracture transmission electron microscopy (FFTEM) Powder XRD FFTEM Zasadzinski and Clark DRLM from freely suspended films

8 A Polarized Light Microscope C Low index Fast Axis Low index - fast axis Slow Axis C 5 H 11 High index - slow axis and optic axis High index Birefringent Specimen ptic axis An isotropic sample has only E refractive index, a uniaxial materials has TW refractive indices and is birefringent ( n).

9 Light enters a birefringent medium 45 Slow axis Pol ptical E field Slow axis + =...and splits into two orthogonal plane polarized beams - one parallel to the fast axis, and one parallel to the slow axis. The two orthogonal plane polarized beams see different refractive indices - one fast and one slow

10 Light enters a birefringent medium Slow axis (larger refractive index) vertical beam horizontal beam resultant polarization two orthogonal plane polarized beams - one parallel to the fast axis, and one parallel to the slow axis. Plane polarized in

11 Relative phase of the beams changes - at 1/4 wave... vertical beam horizontal beam resultant polarization Passing through the birefringent medium, one beam is retarded relative to the other. At the 1/4 wave thickness, the horizontal beam is 90 (1/4 * 360) behind the vertical beam, leading to circularly polarized light.

12 Relative phase of the beams changes - at 1/2 wave... vertical beam horizontal beam resultant polarization At the 1/2 wave thickness, the horizontal beam is 180 behind the vertical beam, leading to linearly polarized light rotated by 90 from the incident beam s polarization

13 ne sees rotation of the plane of polarization, and interference colors (birefringence colors) can be seen (Isaac ewton) White light in Air Reflection at both interfaces These waves interfere, colors come out il thin Water thick Since the speed of light (refractive index) in air and oil are different, a thin film of oil causes a retardation of one reflected wave with respect to the other, magnifying the path length difference. Since different colors are slowed down differently, colors come out! ewton

14 Birefringent Materials Give Interference Colors in PM All birefringent materials have something in common: They are all anisotropic Piece of stretched plastic (LC polymers are a special kind of plastic which can have very special properties, like kevlar) Mica crystal rganic crystals Liquid crystals - the only birefringent liquids The color you see is related to the birefringence ( n) and the thickness of the sample (d). Retardation (effective path difference) = n) d m 1st order purple 2nd order green

15 Electrooptics - Birefringence Changes and Brush Rotation

16 Birefringence Color and Extinction Brushes When the optic axis (slow axis) of the birefringent sample is parallel or perpendicular to the polarizer in the PLM, you see dark features known as extinction brushes

17 Calamitic Liquid Crystals Bent-Core LCs Reinitzer s Cholesteric (1888) Chiral LC Phase Gatterman/Lehmann Azoxyphenol ethers (1890) C 2 H Et H H H H H H Vorländer, D.; Apel, A. Ber. Dtsch. Chem. Ges. 1929, 62, Mauguin, C. "Sur les cristaux liquides de Lehmann," B. Soc. Franc. Miner. 1911, 34, 71. C 2 H 5 X 184 M I (Vorländer 1929) X 186 B I (Pelzl et al. 2001) Pelzl, G.; Wirth, I.; Weissflog, W. Liq. Cryst. 2001, 28, C2H5 Rotate top sheet iori, T.; Sekine, T.; Watanabe, J.; Furukawa, T.; Takezoe, H. J. Mater. Chem. 1996, 6, (7), Chiral director structure from an achiral phase... But never chiral phases from achiral molecules Banana Phases... The first fluid conglomerates 17