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

C
12
H
25
O
C
12
H
25
O
C
12
H
25
O
CH
2
O
CH
2
O
CH
2
O
CO
2
CO
2
OC
12
H
25
C
6
H
13
O
C
6
H
13
O
OC
6
H
13
O H O
O H O
OC
6
H
13
C
6
H
13
O
C
6
H
13
O
O
O
O
O
O
O
O
Praefcke, Kohne, Singer, Demus, Pelzl, Diele,
Liq. Cryst., 1990, 7, 589
OC
2
H
5
C
10
H
21
H
O
O
Cu
O
O
H
C
10
H
21
OC
2
H
5
H
25
C
12
O
H
25
C
12
O
OC
12
H
25
O
Li, Percec and Rosenblatt, Phys. Rev. E, 1993, 48, R1
H
25
C
12
O
OC
12
H
25
OC
12
H
25

V-shaped molecules: X-ray scattering
B. R. Acharya, A. Primak, and S. Kumar Phys. Rev. Lett. 2004, 92, 145506
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
● 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).
C
7
H
15
O
O
N N
O
ODBP-Ph-C
7
O
O
C
7
H
15
Features:
● core with high bisecting dipole
● rigid bent-core molecule (~140 ° )
● biaxiality revealed in 2D powder
2 H NMR and X-ray diffraction
C
12
H
25
O
Iso 222 N 173 SmX 166 SmY 148 Cr
O
O
N N
O
ODBP-Ph-OC
12
O
O
OC
12
H
25
Iso 204 N 193 SmC 184 SmX 148 SmY 141 SmZ 104 Cr
Drawbacks:
● core with high dipole
● bend molecule with rigid core
● i.e. nematic at inexpediently high temperatures
● materials degrade at these high temperatures

BnO
O
OH
F
HO F
F F
F
EDAC, DMAP,
DCM
BnO
Synthesis of Oxadiazoles
F
O
F
O
1
F
F
F
O
NHNH
2
HO anhydr. DMF
BnO
O
N
H
H
N
O
2
OH
SOCl
2 pyridine
BnO
R
3
R
2
R
4
O
OH
HO O
O
N N
O
6 R
1
= C
12
H
25
O
7 R
1
= C
7
H
15
EDAC, DMAP
R
1
R
2
R
3
R
4
O
O
Pd/(C), H
2
,
THF / EtOH
O
N N
BnO
O
O
O
N N
O
O
4 R
1
= C
12
H
25
O
5 R
1
= C
7
H
15
R
1
R
1
8a - h
EDAC, DMAP
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
8h C
7
H
15
C
5
H
11
8d C
12
H
25
O C
5
H
11
H H Iso 222 N 173 SmX 151 Cr
H H Iso 232 N 164 SmX 149 Cr
H H Iso 215 N 160 SmX 91 Cr
R
1
O
N N
3
OH
O
OH

C
7
H
15
Textures of the Biaxial Nematic Phase
O
O
N N
O
O
O
C
7
H
15
ODBP-P-C
7
Iso 222 N 173 SmX 151 Cr
schlieren texture of the nematic phase at 202 ° C texture of the nematic phase between slide and coverslip at 222 ° C observed by rotating the analyser (a) anticlockwise (b) clockwise despite the achiral molecular structure chiral domains in the nematic phase!

Textures of the Nematic Phase
O
O
N N
O
O
O
C
9
H
19
O
OC
12
H
25
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
● G. Pelzl, A.Eremin, S.Diele, H. Kresse, W. Weissflog, J.Mat.Chem. 12,2591 (2002).
O
Cl
O
O O O O
O O
C
12
H
25
O
Cr 98 °C (X 80 °C N 95 °C) I
OC
12
H
25
● P19: M. Hird, K.M. Fergusson, Synthesis and Mesomorphic Properties of Novel
Unsymmetrical Banana-shaped Esters.
F
F
O
F
O
O O O O
O O
C
8
H
17
O OC
12
H
25
Cr 78.6 °C (B
1
59.2 °C) N 97.2 °C I

C
5
H
11 nematic phase in an uncovered region on a glass slide at 173 ° C
O
O
Textures of the Nematic Phase
N N
O
O
C
5
-P-ODBP-P-C
7
Iso 232 N 164 SmX 149 Cr
O
C
7
H
15 nematic phase in an uncovered region on a glass slide at 167 ° C, thinner preparation
O
N N
O
C
12
H
25
O
O
O
O
OC
12
H
25
ODBP-P-OC
12
Iso 203 N 192 SmC 184 SmX 143 SmY 138 SmZ
104 Cr
F
F
O
N N
O
C
9
H
19
O
O
O
O
OC
12
H
25
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 189 ° C 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 Explanations: Suggestion II
R
O
O
N N
O
O
O
R possible twisted chiral conformer 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

• 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

• 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?

• 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, 145506

Orientational Order Parameters
XYZ phase principal axes xyz molecular principal axes
Z z x y
X
Major order parameter
S
 ZZ
S zz
Y
D
 ZZ
S xx
 ZZ
S yy
Molecular biaxiality
P
 XX
S zz
 YY
S zz
C
 XX
( S xx
 XX
S yy
)
 YY
( S xx

S
YY yy
)
Phase biaxiality
Molecular and phase biaxiality

S
 ZZ
S zz
D
 ZZ
S xx
 ZZ
S yy
P

S zz
XX  YY
S zz
C
 XX
( S xx
 XX
S yy
)
 YY
( S xx

S
YY yy
)

S
Order Parameters
D/
√6
P/ √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, 107802

Molecular structure and organisation

NMR studies



( xx
 yy
)
( S
XX zz
 YY
S zz
) zz
ZZ
S zz

Molecular field theory of biaxial nematics: Relation to molecular structure

Potential of mean torque
Uniaxial molecule – uniaxial phase z
Z phase director z molecular symmetry axis
β Z
U
Derivation:
(

)
  u
200
P
2
P
2
(cos

) a) Truncated expansion of the pair potential b) Variational analysis via dominant order parameter

Potential of mean torque
Biaxial molecule – uniaxial phase z
Z phase director xyz molecular symmetry axes
β Z y
U (

)
 x
 m

, n u
2 mn
C
2 m
C
2 n
(

) u
200 u
220
(
 u
202
) u
222
Molecular biaxiality u
220 u
200 or u
222 u
200

Potential of mean torque
Biaxial molecule – biaxial phase z
X
XYZ phase directors xyz molecular symmetry axes
β Z y
U (

)
 x
Y
 m ,
 p n , u
2 pm
2
D nm
D
2
 np
(

)
No new parameters

Parameters and molecular structure
Straley, Phys.Rev.A, 1974, 10, 1881
B
W
L 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.

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 u
20
22
= (2u
= (u xx zz
– u
– u yy xx
– u
)/2 yy
)/√6
Analogy to dispersion forces contrast to excluded volume
(Luckhurst, Zannoni, Nordio and Segre, Mol Phys., 1975, 30, 1345)

Segmental interactions z

Segmental anisotropy u a u u
20
22
Biaxiality parameter
= u a
(1 – 3cos

)/2
= (3/8)
½ u a
(1 + cos

)/2

= u
22
/u
= (3/2)
20
½ x
(1 + cos

)/(1 – 3cos

)
General
Uniaxial segments u
2 m
  i
C
2 m
(
 i i
) u
20
Biaxial segments u
2 m
 i ,
 n
2
D nm
(
 i i
) u
2 n y

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

Acknowledgements
John Goodby
Verena Görtz
Mark Wilson
Daniel Jackson