Where are we with the discovery and design of biaxial nematics? Geoffrey Luckhurst School of Chemistry, University of Southampton, UK

Praefcke, Kohne, Singer, Demus, Pelzl, Diele, Liq. Cryst., 1990, 7, 589 Li, Percec and Rosenblatt, Phys. Rev. E, 1993, 48, R1

V-shaped molecules: X-ray scattering B. R. Acharya, A. Primak, and S. Kumar Phys. Rev. Lett. 2004, 92, B. R. Acharya, A. Primak, T. J. Dingemans, E. T. Samulski, S. Kumar, Pramana, 2003, 61, 231

The molecules

The scattering patterns

Calculated scattering patterns

V-shaped molecules: structure and optical studies V. Görtz and J.W. Goodby BLCS, Exeter March 2005

Thermotropic Biaxial Nematic Liquid Crystals Features: ● core with high bisecting dipole ● rigid bent-core molecule (~140°) ● biaxiality revealed in 2D powder 2 H NMR and X-ray diffraction Drawbacks: ● core with high dipole ● bend molecule with rigid core ● i.e. nematic at inexpediently high temperatures ● materials degrade at these high temperatures ● L.A. Madsen, T.J. Dingemans, M. Nakata, E.T. Samulski, Phys. Rev. Lett. 92, (2004). ● B.R. Acharya, A. Primak, S. Kumar, Phys. Rev. Lett. 92, (2004).

Synthesis of Oxadiazoles No R1 R2 R3 R4 Phase Transitions [°C] 8a C 12 H 25 O C 12 H 25 O H H Iso 203 N 192 SmC 184 SmX 143 SmY 138 SmZ 104 Cr 8b C 12 H 25 O C 9 H 19 O H H Iso 210 N 182 SmX 157 SmY 149 SmZ 91 Cr 8c C 12 H 25 O C 8 H 17 O H H Iso 213 N 176 SmX 162 SmY 152 SmZ 77 Cr 8e C 12 H 25 O C 9 H 19 O H F Iso 205 N 168 SmX 135 SmY 125 SmZ 72 Cr 8f C 12 H 25 O C 9 H 19 O F F Iso 210 N 197 SmC 186 SmX 155 SmY 150 SmZ 100 Cr 8g C 7 H 15 C 7 H 15 H H Iso 222 N 173 SmX 151 Cr 8h C 7 H 15 C 5 H 11 H H Iso 232 N 164 SmX 149 Cr 8d C 12 H 25 O C 5 H 11 H H Iso 215 N 160 SmX 91 Cr

Textures of the Biaxial Nematic Phase despite the achiral molecular structure chiral domains in the nematic phase! texture of the nematic phase between slide and coverslip at 222 °C observed by rotating the analyser (a) anticlockwise (b) clockwise ODBP-P-C 7 Iso 222 N 173 SmX 151 Cr schlieren texture of the nematic phase at 202 °C

Textures of the Nematic Phase C 9 O-P-ODBP-P-OC 12 Iso 210 N 182 SmX 157 SmY 149 SmZ 91 Cr texture of the nematic phase between slide and coverslip at 202 °C observed by rotating the analyser (a) anticlockwise (b) clockwise Cr 98 °C (X 80 °C N 95 °C) I ● G. Pelzl, A.Eremin, S.Diele, H. Kresse, W. Weissflog, J.Mat.Chem. 12,2591 (2002). ● P19: M. Hird, K.M. Fergusson, Synthesis and Mesomorphic Properties of Novel Unsymmetrical Banana-shaped Esters.

Textures of the Nematic Phase nematic phase in an uncovered region on a glass slide at 173 °C C 5 -P-ODBP-P-C 7 Iso 232 N 164 SmX 149 Cr C 9 O-2F3FP-ODBP-P-OC 12 Iso 210 N 197 SmC 186 SmX 155 SmY 150 SmZ 100 Cr nematic phase in an uncovered region on a glass slide at 167 °C, thinner preparation nematic phase in an uncovered region on a glass slide at 189 °C ODBP-P-OC 12 Iso 203 N 192 SmC 184 SmX 143 SmY 138 SmZ 104 Cr nematic phase in an uncovered region on a glass slide at 189 °C

Possible Explanations: Suggestion I ● G. Pelzl, A.Eremin, S.Diele, H. Kresse, W. Weissflog, J. Mat. Chem. 12, 2591 (2002). R. Memmer, Liq. Cryst. 29, 483 (2002). helical superstructure in a nematic phase of an achiral bent-core molecule can occur due to conical twist-bend deformations

possible twisted chiral conformer Possible Explanations: Suggestion II helix-formation via self-assembly of twisted conformers

Questions ● Are pitch lines really observed in the nematic? ● Are similar effects to be expected for all achiral bent-core materials that have a nematic phase? ● Is there a connection between these observations and the biaxiality of a nematic phase?

V-shaped molecules: atomistic simulations M. Wilson BLCS, Exeter, March 2005

4 key dihedrals with low barriers where rotation leads to conformations with radically different structures at a cost of < 2.5 kcal/mol Bananas are not really bananas!

4 key dihedrals with low barriers were rotation leads to conformations with radically different structures at a cost of < 2.5 kcal/mol Min 90/-90 deg Barrier 5 kJ/mol Min 0/180 deg Barrier kJ/mol Min 90/-90 deg Barrier 5 kJ/mol

Bulk phase – biaxial? Fully atomistic simulation of biaxial phase at 468 K 256 molecules, 3 ns Colour coding (according to direction of dipole across central ring) (Red + along short axis director blue – along short axis director) Looks like the formation of biaxial domains but not biaxial phase?

Bulk phase – biaxial? Fully atomistic simulation of biaxial phase at 468 K 256 molecules, 3 ns Colour coding (according to direction of dipole across central ring) (Red + along short axis director blue – along short axis director) Looks like the formation of biaxial domains but not biaxial phase?

Tetrapodes: The orientational order parameters from IR spectroscopy K. Merkel, A. Kocot, J. K. Vij, R. Korlacki, G. H. Mehl and T. Meyer Phys. Rev. Lett. 2004, 92,

Orientational Order Parameters XYZ phase principal axes xyz molecular principal axes Major order parameter Molecular biaxiality Phase biaxiality Molecular and phase biaxiality Y X Z x y z

Order Parameters S P/√6 D/√6 C/6

Tetrapodes: NMR studies J. L. Figueirinhas, C. Cruz, D. Filip, G. Feio, A. C. Ribeiro, Y. Frère and T. Meyer, G. H. Mehl Phys. Rev. Lett. 2005, 94,

Molecular structure and organisation

NMR studies

~

Molecular field theory of biaxial nematics: Relation to molecular structure

Potential of mean torque Uniaxial molecule – uniaxial phase Derivation: a)Truncated expansion of the pair potential b)Variational analysis via dominant order parameter z Z Z phase director z molecular symmetry axis β

Potential of mean torque Biaxial molecule – uniaxial phase Molecular biaxiality or x y z Z Z phase director xyz molecular symmetry axes β

Potential of mean torque Biaxial molecule – biaxial phase No new parameters XYZ phase directors xyz molecular symmetry axes x y z Z Y X β

Parameters and molecular structure Straley, Phys.Rev.A, 1974, 10, 1881 u 200 = { – 2B(W 2 – L 2 ) – 2W(L 2 + B 2 ) + L(W 2 + B 2 ) + 8WBL}/3 u 220 = (L 2 – BW)(B –W)/√6 u 222 = – L(W – B) 2 /2 n.b. Does not obey the geometric mean rule. L B W

Separability: Molecular field parameters Relation to molecular properties u 2mn = u 2m u 2n Geometric mean approximation u 220 = (u 200 u 222 ) ½ Principal axis system u 20 = (2u zz – u xx – u yy )/√6 u 22 = (u xx – u yy )/2 Analogy to dispersion forces contrast to excluded volume (Luckhurst, Zannoni, Nordio and Segre, Mol Phys., 1975, 30, 1345)

Segmental interactions Segmental anisotropy u a u 20 = u a (1 – 3cos  )/2 u 22 = (3/8) ½ u a (1 + cos  )/2 Biaxiality parameter = u 22 /u 20 = (3/2) ½ (1 + cos  )/(1 – 3cos  ) General Uniaxial segments Biaxial segments  x y z

Surface tensor model u 20 = (2LB – B 2 )(1 – 3cos  )/2 + B 2 cos(  /2)(1 + sin(  /2) u 22 = (3/8) ½ (2LB – B 2 )(1 + cos  ) – 2B 2 cos(  /2)(1 – sin(  /2)) n.b. u 200 = u 20 u 20 u 220 = u 22 u 20 Landau point shifts from ~109º to 105º

Acknowledgements John Goodby Verena Görtz Mark Wilson Daniel Jackson