3 NUMERICAL RESULTS FOR SYMMETRIC DIMERS

1
The molecular origin of the unusual flexoelectric
properties of cyanobiphenyl liquid crystal
dimers Alberta Ferrarini,a Cristina Greco,a
Daniel Jackson,b Geoffrey R. Luckhurst b a
Dipartimento di Scienze Chimiche, Università di
Padova, Italy b School of Chemistry, University
of Southampton, UK
-1- INTRODUCTION -1.1- LIQUID CRYSTAL DIMERS In
these novel mesogens1 the molecular flexibility
is confined to the core of the molecule which
links the two mesogenic groups together. The
shape of the molecule depends critically on the
parity of the spacer for an odd number of atoms
when the chain is in its all-trans form the shape
is bent whereas when the spacer has an even
number of atoms the shape is elongated. This
difference in shape is often invoked to explain
the odd-even variation in, say, the transition
temperatures and transitional entropies which are
both larger for the even dimers. However, the
coupling between the orientational order and the
conformational order plays a major role in
creating this unusual effect. -1.2-
FLEXOELECTRIC COEFFICIENTS FOR LIQUID CRYSTAL
DIMERS The different shapes and associated
polarities of odd and even dimers suggests that
they might have different flexoelectric
coefficients and should also show a strong
odd-even effect. Detailed measurements of the
flexoelectric coefficients of liquid crystal
dimers have been made by Coles and his
colleagues.2-4 Their measurements provide the
flexoelastic ratio, e /K, where e (e1 e3) /2
and K (K1 K3) /2 that is the means of the
splay and bend flexoelectric coefficients and
elastic constants, respectively. Measurements
for symmetric dimers were restricted to the even
member CBO8OCB 2 which exhibits an unexpectedly
high value of e namely ? 8pCm-1 in contrast e
for the analogous monomer, 7OCB, is just ?2pCm-1.
A more extensive investigation was carried out
for non-symmetric dimers 4, the results for
which are summarized in the following two
figures. The results for the series of
non-symmetric dimers do indeed exhibit a strong
odd-even alternation as had been expected the
odd dimers have much larger values than their
even homologues. Part of this difference in the
behaviour of e/K results from the smaller values
of the elastic constants found for the odd  in
comparison with even dimers. Using partially
estimated values for K reveals that the mean, e,
also exhibits an odd-even effect but now the
difference between odd and even dimers is
somewhat reduced.

-2.3 - FLEXOELECTRIC COEFFICIENTS
-2- THEORETICAL MODEL AND CALCULATION METHODS 5
??0 orientational average with respect to f0(W)
(orientational distribution function in an
undeformed nematic)
- 2.2 - MOLECULAR MODEL THE SURFACE
INTERACTION MODEL
Dipolar Contribution 6
Quadrupolar Contribution 7
Surface parametrisation of the molecular-field
potential U(R0, O) acting on a molecule located
at R0 and with an orientation, O, in a deformed
nematic
each surface element dS tends to orient its
normal s perpendicular to the local director n(R)

• 2.4 - CONFORMATIONAL ANALYSIS AND
• DETERMINATION OF MOLECULAR STRUCTURE

• S molecular surface
• x orienting strength
• director field, n(R), in a deformed nematic
• n(R) n(R0) ?I,J eJ (?IR0 nJ)(RI-R0,I)

CBO8OCB
long flexible spacer several different
conformers different molecular shapes and
electrical properties different contributions
to the flexoelectric coefficients
CBO7OCB
-3- NUMERICAL RESULTS FOR SYMMETRIC DIMERS
- 3.1 - ODD DIMER CBO7OCB
- 3.2 - EVEN DIMER CBO8OCB

• RIS approximation 5
• selection of the most stable conformers

• the all-trans conformer

• all the conformers with a single
• gauche state in the spacer

• geometry optimization DFT (B3LYP/6-31G) 8
• atomic charges Merz-Singh-Kollman scheme 8
• molecular surface MSMS algorithm

• -5- CONCLUSIONS
• The model rationalises the experimental findings
  
• High, positive values of e3 and vanishingly
  small values of e1 (giving high e) have been
  obtained not only for the odd dimer CBO7OCB, but
  also for the even dimer CBO8OCB.
• In comparison, negligible flexoelectric
  coefficients are predicted for 7OCB.
• Important molecular features can be identified
  dimers possess
• an elongated structure, providing high
  orientational order.
• conformations with a bent shape, which,
  together with a significant transverse dipole,
  allows an effective coupling with bend
  deformations in the director.
• Essential to these molecular features is the
  presence of a long spacer between the mesogenic
  units and strong terminal dipoles.
• In general, strong flexoelectric coupling is
  expected for systems possessing the features
  described. Indeed, high flexoelectric
  coefficients have been measured for CBOnOBF2
  dimers preliminary calculations give an average
  value of e 13 pCm-1 for the
  g1 conformers of CBO8OBF2.
• The theoretical results show the strong
  dependence of the flexoelectric effect upon the
  molecular details. We need models to be able to
  account for the flexoelectric coefficients. This
  can be accomplished by the surface interaction
  model, at low computational cost given the
  molecular geometry and charges, calculations for
  properly selected conformers, sufficient to give
  the magnitude and sign of the flexoelectric
  coefficients, can be performed in a few minutes
  on a desktop PC. More accurate predictions could
  be obtained by an integrated approach, combining
  the present model with a conformational sampling
  technique.

1. The flexoelectric coefficients are reported in
units of pCm-1. e (e1 e3 ) /2 2. The symbols
(d) and (q) denote the dipolar and the
quadrupolar contributions, respectively 6,7.
The relation e3 (q)-e1(q) holds. 3. The green
arrows show the magnitude and direction of the
electric dipole moment.
-4- COMPARISON WITH THE MONOMER 7OCB
g
t

• Selected conformers
• the all-trans conformer
• the O-C1 gauche conformer
• (the most bent conformer)

e1(d) 1
e3(d) -1 e1(q) 14
e 0
e1(d) -1
e3(d) 5 e1(q)
8 e 2
REFERENCES 1 C. T. Imrie and G. R. Luckhurst,
in Handbook of Liquid Crystals, eds. D. Demus et
al. (Wiley-VCH, Weinheim,1999) Vol 2B, Chapt.
X. 2 H. J. Coles, B. Musgrave, M. J. Coles, J.
Willmott, J. Mater. Chem., 11, 2709 (2001). 3
H. J. Coles, M. J. Clarke, S. M. Morris, B. J.
Broughton, A. E. Blatch, J. Appl. Phys. 99,
034104 (2006). 4 M J Clarke, PhD Thesis,
Southampton 2004.5 A. Ferrarini, Phys. Rev.
E 64, 021710 (2000). 6 R.B. Meyer, Phys. Rev.
Lett., 22, 918 (1979). 7 J. Prost, J. P.
Marceroux, J. Phys. (Paris), 38, 315 (1977). 8
M. J. Frisch et al., Gaussian03 (Gaussian, Inc.,
Wallingford, CT, 2004).