Electric-field-dependent dielectric response in the de Vries–type smectic-A
*
phase possessing local
orientational order with nanoscale correlation length
U. Manna,
1
Jang-Kun Song,
1
J. K. Vij,
1,
*
and J. Naciri
2
1
Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
2
Center for Bio/Molecular Science and Engineering, Naval Research Laboratory, Washington, DC 20375, USA
Received 10 May 2008; revised manuscript received 18 July 2008; published 13 October 2008
The dielectric strength is shown to increase and the relaxation frequency to decrease for a large temperature
range up to a certain value of the electric field in the smectic-A* phase. This behavior contrasts to that observed
in a conventional smectic-A*, but can be explained in terms of de Vries scenerio. On assuming the reorientation
of the molecular dipoles with electric field to be of the Langevin type in the de Vries smectic-A*, we find that
around 1300 molecules, corresponding to a minimum correlation length of
45 nm in a single layer
cooperatively respond to the applied field.
DOI: 10.1103/PhysRevE.78.041705 PACS numbers: 61.30.-v, 77.22.Gm
I. INTRODUCTION
At the transition from smectic-A
*
SmA
*
to smectic-C
*
SmC
*
or smectic-C
A
*
SmC
A
*
phase, the layer shrinkage
along with the surface anchoring of the molecules lead to the
formation of chevrons. The chevrons of opposite fold direc-
tions separated by zigzag defects degrade the quality of
electro-optic devices based on ferroelectric liquid crystals
FLCs and antiferroelectric liquid crystals AFLCs1–4.
Application of the electric field in the SmA
*
phase parallel to
the smectic layers induces stripes arising from a reduction in
the smectic layer spacing due to molecular tilting and the
consequent smectic layer buckling 5,6. This has a detri-
mental effect on the contrast ratio of electro-optic devices
7,8. As a result, the materials having zero or low layer
shrinkage with decreasing temperature or increasing electric
field have drawn significant scientific interests due to their
potential for applications in display and photonic devices 9.
In de Vries’ “diffuse cone model” of these materials, the
molecular long axis and presumably the local director is
tilted through a finite angle, but azimuthally randomized with
a uniform distribution f =1 / 2 on a cone from layer to
layer as well as in a single layer 10–13, with the macro-
scopic director along the layer normal. Landau theory of
smectic phases was developed to show that de Vries behavior
occurs in materials with unusually small orientational order
14, which has been experimentally demonstrated
12,15–19. It was also shown that a decrease in the layer
shrinkage increases the soft mode strength and decreases the
Landau coefficient at the de Vries SmA
*
-SmC
*
transition
20,21. Application of an electric field parallel to the smec-
tic layers orders the azimuthal orientation, such that an aver-
age director is tilted away from the layer normal. But it has
been an issue of discussion in recent years as to how this
azimuthal ordering is achieved in these materials with the
application of electric field. It has been suggested that the de
Vries materials with sufficiently high polarization density ex-
hibit large analog optical axis rotation 30° accompanied
by increased birefringence, as found by the electro-optic
measurements. These can be modeled by Langevin theory of
field-induced director orientation on assuming the molecules
in the SmA
*
phase are confined to a tilt cone 22. Another
theoretical model predicts the dependence of the optical bi-
refringence and tilt angle on electric field and temperature
assuming the local order is slightly biaxial 23. It has also
been suggested that perhaps there is some type of modulation
or spatial periodicity in the azimuthal angles associated with
the tilt directions 24.
Here, we report that on application of an increasing field
in the SmA
*
phase, the dielectric strength increases and
the relaxation frequency f
max
decreases up to a certain
value of the field over a large temperature range 12 °C.
This behavior cannot be explained by the tilt angle fluctua-
tions of conventional SmA
*
phase undergoing first- or
second-order transition to SmC
*
phase, but can be explained
in terms of de Vries scenario by assuming the reorientation
of the molecules by rotation around the smectic cone with
the electric field as suggested in the previous models 22,23.
On assuming that the reorientation of the molecular dipoles
with the electric field is of the Langevin type, we show that
the tilted molecules in the de Vries–type SmA
*
phase possess
a local orientational order even without the electric field, and
a maximum of around 1300 molecules cooperatively respond
to the applied field corresponding to a effective dipole mo-
ment,
eff
2000 D. This value corresponds to a correlation
length,
45 nm if the local ordering occurs along a
single layer and to
22 nm if the local ordering occurs
along the layer normal as well as within a single layer.
II. RESULTS AND DISCUSSIONS
The liquid crystalline compound TSiKN65
4-3'-nitro-4'-R-1-methylhexyloxyphenyl-phenyl 4-6-
heptylmethyltrisiloxyhexyloxy, chemical structure and
phase diagram are shown in Fig. 1, used mainly for our
experiment is a recently reported prototype de Vries material
having small layer contraction with temperature and electric
field, large electroclinic effect, and small orientational order
parameter 16,23,25. For planar alignment, the conducting
inner surfaces of the liquid crystalline cell were spin coated
with a polyimide RN 1175 Nissan Chemicals, Japan align- *
jvij@tcd.ie
PHYSICAL REVIEW E 78, 041705 2008
1539-3755/2008/784/0417055 ©2008 The American Physical Society 041705-1