Where are we with the discovery and design of biaxial

nematics?

Geoffrey Luckhurst

School of Chemistry, University of Southampton, UK

CH2C12H25O

CH2C12H25O O

O

CH2OC12H25O CO2 CO2 OC12H25

C10H21

OO

H

OC2H5

C10H21

O

O

H

OC2H5

Cu

OC12H25

OC12H25H25C12O

OC12H25

H25C12O

H25C12O

C6H13O

C6H13OOC6H13

O

O H

C6H13O

C6H13OOC6H13

O

OH

OO

OO

O

O

O

O

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, 145506B. 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

N N

OO O

C7H15

OO

C7H15

N N

OO O

OC12H25

OO

C12H25O

ODBP-Ph-C7

ODBP-Ph-OC12

Iso 204 N 193 SmC 184 SmX 148 SmY 141 SmZ 104 Cr

Iso 222 N 173 SmX 166 SmY 148 Cr

Thermotropic Biaxial Nematic Liquid Crystals

Features:● core with high bisecting

dipole

● rigid bent-core molecule

(~140°)

● biaxiality revealed in 2D

powder

2H 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, 145505 (2004).

● B.R. Acharya, A. Primak, S. Kumar, Phys. Rev. Lett. 92, 145506 (2004).

Synthesis of Oxadiazoles

OH

O

BnO

F

F

F

F

F

HO

O

O

BnO

F

F

F

F

F NHNH2

O

HONH

O

BnO

HN

O

OH

N N

OBnO OH

OH

O

R1

N N

OBnO O

R1

ON N

OHO O

R1

O

OH

O

R2N N

OO O

SOCl2

EDAC, DMAP,DCM

1

anhydr. DMF

2 3

pyridine

EDAC, DMAP

4 R1 = C12H25O5 R1 = C7H15

Pd/(C), H2,THF / EtOH

EDAC, DMAP

O OR2

R3R4

R1

R3

R4

6 R1 = C12H25O7 R1 = C7H15

8a - h

No R1 R2 R3 R4 Phase Transitions [°C]

8a C12H25O C12H25O H H Iso 203 N 192 SmC 184 SmX 143 SmY 138 SmZ 104 Cr

8b C12H25O C9H19O H H Iso 210 N 182 SmX 157 SmY 149 SmZ 91 Cr

8c C12H25O C8H17O H H Iso 213 N 176 SmX 162 SmY 152 SmZ 77 Cr

8e C12H25O C9H19O H F Iso 205 N 168 SmX 135 SmY 125 SmZ 72 Cr

8f C12H25O C9H19O F F Iso 210 N 197 SmC 186 SmX 155 SmY 150 SmZ 100 Cr

8g C7H15 C7H15 H H Iso 222 N 173 SmX 151 Cr

8h C7H15 C5H11 H H Iso 232 N 164 SmX 149 Cr

8d C12H25O C5H11 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

N N

OO O C7H15

OO

C7H15

ODBP-P-C7 Iso 222 N 173 SmX 151 Cr

schlieren texture of thenematic phase at 202 °C

Textures of the Nematic Phase N N

OO O OC12H25

OO

C9H19O

C9O-P-ODBP-P-OC12

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

FF

F

OO

O O

O O

O O

C8H17O OC12H25Cr 78.6 °C (B1 59.2 °C) N 97.2 °C I

Cl

OO

O O

O O

O O

C12H25O OC12H25

● 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 N N

OO O C7H15

OO

C5H11

nematicphasein an

uncovered

region on a

glass slide

at 173 °C

C5-P-ODBP-P-C7 Iso 232 N 164 SmX 149 Cr

N N

OO O OC12H25

OO

C9H19O

FF

C9O-2F3FP-ODBP-P-OC12 Iso 210 N 197 SmC 186 SmX 155 SmY 150 SmZ

100 Cr

nematic phasein anuncoveredregion on aglass slideat 167 °C,thinnerpreparation

nematic phasein an uncoveredregion on aglass slideat 189 °C

N N

OO O OC12H25

OO

C12H25O

ODBP-P-OC12 Iso 203 N 192 SmC 184 SmX 143 SmY 138 SmZ

104 Cr

nematic phasein an

uncoveredregion on aglass 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 achiralbent-core molecule can occur due to conical twist-bend deformations

possible twisted chiral conformer

Possible Explanations: Suggestion II

helix-formation via self-assemblyof twisted conformers

N N

OO O R

OO

R

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. WilsonBLCS, 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!

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 degBarrier 5 kJ/mol

Min 0/180 degBarrier 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. MeyerPhys. Rev. Lett. 2004, 92, 145506

Orientational Order Parameters

XYZ phase principal axes xyz molecular principal axes

Major order parameter

Molecular biaxiality

Phase biaxiality

Molecular and phase

biaxiality

ZZzzSS

ZZyy

ZZxx SSD

YYzz

XXzz SSP

)()( YYyy

YYxx

XXyy

XXxx SSSSC

Y

X

Z

x

y

z

ZZzzSS

ZZyy

ZZxx SSD

YYzz

XXzz SSP

)()( YYyy

YYxx

XXyy

XXxx SSSSC

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. MehlPhys. Rev. Lett. 2005, 94, 107802

Molecular structure and organisation

NMR studies

zzyyxx qqq ~)~~(~ ZZzz

YYzz

XXzz SSS )(

~

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

)(cos)( 22200 PPuU

Potential of mean torque

Biaxial molecule – uniaxial phase

Molecular biaxiality or

n,m

n2m2mn2 )(CCu)(U x

y

z

Z

Z phase director xyz molecular symmetry axes

β

200u )u(u 202220 222u

200220 uu 200222 uu

Potential of mean torque

Biaxial molecule – biaxial phase

No new parameters

pnm

npnmpm DDuU,,

222 )()(

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

u200 = {– 2B(W2 – L2) – 2W(L2 + B2) + L(W2 + B2) + 8WBL}/3

u220 = (L2 – BW)(B –W)/√6

u222 = – 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

u2mn = u2mu2n

Geometric mean approximationu220 = (u200u222)½

Principal axis system u20 = (2uzz – uxx – uyy)/√6u22 = (uxx – uyy)/2

Analogy to dispersion forces contrast to excluded volume

(Luckhurst, Zannoni, Nordio and Segre, Mol Phys., 1975, 30, 1345)

Segmental interactions

Segmental anisotropy ua

u20 = ua(1 – 3cos)/2u22 = (3/8)½ua(1 + cos)/2

Biaxiality parameter

= u22/u20

= (3/2)½(1 + cos)/(1 – 3cos)GeneralUniaxial segments

Biaxial segments

x

y

z

i

iimm uCu 2022 )(

ni

ininmm uDu

,2

22 )(

Surface tensor model

u20 = (2LB – B2)(1 – 3cos)/2 + B2cos(/2)(1 + sin(/2)u22 = (3/8)½ (2LB – B2)(1 + cos) – 2B2cos(/2)(1 – sin(/2))

n.b.

u200 = u20u20

u220 = u22u20

Landau point shifts from ~109º to 105º

Acknowledgements

John Goodby

Verena Görtz

Mark Wilson

Daniel Jackson