PHYSICAL REVIEW E 77, 041708 共2008兲

Alternating twist structures formed by electroconvection in the nematic phaseof an achiral bent-core molecule1

Shingo Tanaka,1 Surajit Dhara,2 B. K. Sadashiva, Yoshio Shimbo,1 Yoichi Takanishi,1 Fumito Araoka,1
Ken Ishikawa,1 and Hideo Takezoe1

Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
2
School of Physics, University of Hyderabad, Hyderabad-500046, India
3
Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore-560080, India
共Received 23 January 2008; published 29 April 2008兲
We report an unusual electroconvection in the nematic phase of a bent-core liquid crystal. In a voltagefrequency diagram, two frequency regions exhibiting prewavy stripe patterns were found, as reported by Wiantet al. We found that these stripes never show extinction dark when cells were rotated under crossed polarizers.
Based on the color interchange in between neighboring stripes by the rotation of the cells or an analyzer,
twisted molecular orientation is suggested; i.e., the directors are alternately twisted from the top to the bottom
surfaces with a pretilt angle in adjacent stripes, which is an analogue of the twisted 共splayed兲 structure
observed in surface-stabilized ferroelectric liquid crystal cells. The transmittance spectra calculated using the4 ⫻ 4 matrix method from the model structure are consistent with the experimental observation.
DOI: 10.1103/PhysRevE.77.041708

PACS number共s兲: 61.30.Gd, 89.75.Kd, 61.30.Jf

I. INTRODUCTION

It is well known that electroconvection takes place in planar cells of nematic liquid crystals with negative dielectricanisotropy depending on applied voltages and frequencies
关1–3兴. Since the resultant fringe pattern was first observed byWilliams 关4兴, the pattern is called the Williams domain 关4兴.
The cause of the Williams domain was explained by Helfrich关5兴 and Carr 关6兴. Later, Penz 关7兴 considered focusing effectdue to an alignment deformation to explain the fringes observed under the polarizing microscope. Later Kondo et al.
关8兴 took into account ray deflection from wave-front distortion and succeeded in explaining the details of the fringe
characteristics. In addition to the typical Williams domains, avariety of electroconvection effects have been reported: grid
pattern and soft-mode turbulence, and so on 关9,10兴. These
patterns are related to the anisotropy of electric properties
including dielectric constant and conductivity. In the CarrHelfrich theory describing standard electroconvection
mechanism, the dielectric anisotropy and conductivity anisotropy are assumed to be negative and positive, respectively
关11兴. The researches in other situations of electric anisotropies have also been made; i.e., the case of positive dielectricanisotropy and negative conductivity anisotropy or the caseof both positive anisotropies 关12,13兴. However, most of thereported instabilities concern rodlike molecules except for aswallow-tailed molecule 关12兴.
Recently, Wiant et al. 关14兴 reported nonstandard electroconvection in the nematic 共N兲 phase of a bent-core liquid
crystal. However, the mechanism has not yet been understood completely, hence extensive investigations on the nematic phase of bent-core molecules with different molecular
structure are necessary. Liquid crystals composed of bentcore molecules have been studied actively in recent years关15,16兴 since the discovery of polar switching in achiralbent-core mesogens 关17兴. In addition to so-called banana
phases, characteristic smectic 共Sm兲 phases consisting ofbent-core molecules and being designated as B1 − B8 关15兴,
1539-3755/2008/77共4兲/041708共5兲

biaxial N 关18,19兴, biaxial SmA 关20,21兴, and randomly polarly
ordered SmA 关22兴 phases were reported. Some of them exhibit conventional N and SmA phases in addition to theabove-mentioned phases 关15,16兴. A variety of interesting
phenomena observed in bent-core mesogenic systems arise
from polarity and chirality 关15兴. In this sense, unconventional electroconvection effect in the N phase of a bent-core
mesogen has to be investigated in the light of polarity and/or
chirality.
In this paper, we report electroconvection effect in a different type of a bent-core nematic liquid crystal with a very
different molecular structure. We observed a similar type of
instability as Wiant et al. 关14兴 reported: two frequency regions showing prewavy patterns with some differences. The
most important observation in our study is the alternate color
change in adjacent domains of the prewavy patterns, thecolor interchanges under the rotation of cell or analyzer, andnonexistence of extinction position upon the cell rotation. To
explain these observations, we propose a model director orientation, calculate the transmittance spectra, and compare theresults with the experimental observations. Good agreement
supports the proposed model structure, in which directors
form twisted structures from the top to the bottom surfaces.
We conclude that this structure is caused by the convection
flow and the chiral nature of bent-core molecules.
II. EXPERIMENTThe compound used is a bent-core molecule shown in Fig.
1 and synthesized as described 关23兴. As characterized by Le
et al. 关24兴, the compound shows the phase sequence, crystal
共102 °C兲 B2 共115 °C兲 N 共119.5 °C兲 isotropic 共Iso兲, where B2
is a typical banana phase and N seems to be a uniaxial nematic phase. In both liquid crystal phases, the compoundshows negative dielectric anisotropy and negative conductivity anisotropy.
Glass substrate plates with electrode made of indium tinoxide 共ITO兲 were spin coated with polyimide 共JSR, AL

041708-1©2008 The American Physical Society

PHYSICAL REVIEW E 77, 041708 共2008兲TANAKA et al.
O
CH 3

O
O

O

O

O
O

O
F

F

H

FIG. 1. Chemical structure of the compoundused. The phase sequence of this compound is
crystal 共102 °C兲 B2 共115 °C兲 N 共119.5 °C兲
isotropic.

CH 3

H

C14 H29O

OC14 H 29

1254兲 and baked at 180 °C for 1 h. The plates were rubbed
unidirectionally and assembled to 6- or 10-␮m-thick homogeneously aligned cells with antiparallel rubbing directions.
The empty cell was filled with the sample in the isotropic
共Iso兲 phase by capillary action and cooled slowly to get awell aligned N phase in a hot stage 共Mettler FP90兲.
The texture was observed under a polarizing microscope
共Nikon, OPTIPHOTO-POL兲 under the application of rectangular wave voltage of various frequencies 共10 Hz–400 kHz兲and amplitudes up to 80 V at 2 °C below the N-Iso transition
temperature. It is noted that the cells showed completely
dark in the absence of a field when the optic axis was parallel
to either of the two polarizers.

sense that the former is wavy and sometimes has branches
while the latter is more or less straight and rarely shows
branches. Figure 2共d兲 shows the electroconvection at 8 kHz.
The prewavy pattern became obscure compared with thatseen in Fig. 2共c兲. Figure 2共e兲 shows a microphotograph at 50
kHz, where a clear prewavy pattern is observed. This patternobserved at higher frequencies is called prewavy 1, although
the texture is the same as that of the prewavy 2 observed at
low frequencies. The prewavy pattern disappeared at highfrequencies such as 400 kHz under the same applied voltageof 80 V, as shown in Fig. 2共f兲. This is attributed to a dielectric heating, which is known to be serious at high frequencies
and high voltages. Namely, the N-Iso transition occurred dueto the dielectric heating.
In order to clarify the phenomenon and identify the similarities and differences between our and Wiant et al.’s results, we investigated a voltage-frequency diagram showing
the threshold voltages for the emergence of prewavy patterns. Figure 3 shows the diagram, in which threshold voltages are shown by closed diamonds as a function of frequency in a logarithmic scale. The N-Iso transitions are also
shown by closed squares. The diagram clearly distinguishes
the two prewavy patterns 1 and 2. The threshold voltage oftwo prewavy patterns is discontinuous; i.e., the thresholdvoltage increases and decreases with increasing frequency inthe prewavy 2 and 1 regions, respectively. Thus, the present
diagram and that reported by Wiant et al. 关14兴 apparently
look similar. However, there are several important differences in their detailed structures: 共1兲 In our polydomainlike
region at low frequencies, Wiant et al. observed fine parallel
stripes. 共2兲 In the frequency region in between the regions
showing prewavy 2 and prewavy 1, we observed the prewavy pattern, though it was obscure, whereas Wiant et al.
suggested the existence of nonelectroconvection region. The

III. EXPERIMENTAL RESULTS

Let us first show the texture caused by electroconvection
observed in a 10-␮m-thick cell. Figure 2 shows photomicrographs taken at various frequencies. At 10 Hz 共a兲, the texture
is polydomainlike, as observed in the isotropic electroconvection. A wavy stripe pattern due to anisotropic electroconvection gradually appeared at 60 Hz 共b兲. At such low frequencies around 60 Hz, the direction of the stripes was notstable and not pinned in one direction, i.e., thin transversewavy stripes were observed in addition to the longitudinalwavy stripes. Namely, the anisotropy of the electroconvection is low at this frequency region. The electroconvection
pattern became distinct at 1 kHz, as shown in Fig. 2共c兲. The
period of the patterns is about 20 ␮m, approximately double
the cell thickness. This is the same pattern observed by
Wiant et al. 关14兴. Thus isotropic electroconvection was vanished and anisotropic electroconvection called prewavy 2grew at around 1 kHz. The prewavy pattern is different fromthe conventional electroconvection 共Williams domain兲 in the

(a)

(b)

(c)

(e)

(f)

P
rubbing
direction

(d)

A

100m
041708-2

FIG. 2. 共Color online兲 Photomicrographs showing the electroconvection under crossed polarizers 共crossed white arrows兲 in thenematic phase 共2 °C below the
N-Iso transition兲 of the bent-coreliquid crystal. The cell thickness
was 10 ␮m. The cell was homogeneously aligned and the rubbing
direction was 10° from a polarizer. The applied voltage was arectangular wave of 80 V and thefrequency was: 共a兲 10 Hz, 共b兲 60
Hz, 共c兲 1 kHz, 共d兲 8 kHz, 共e兲 50
kHz, and 共f兲 400 kHz.

ALTERNATING TWIST STRUCTURES FROMED BY …

PHYSICAL REVIEW E 77, 041708 共2008兲
(a) 0o(b) 20o(c) 40o(d) 60o(e) 80o(f) 100o(g) 120o(h) 140o

20m

FIG. 3. 共Color online兲 V-f diagram. Two regions showing prewavy patterns, prewavy 1 共PW1兲 and prewavy 2 共PW2兲 are locatedat high and low frequency regions, respectively, and are borderedby the region showing obscure prewavy patterns. Closed diamonds
stand for the threshold voltage to show the prewavy patterns. The
transition to the Iso phase caused by dielectric heating is also shownby closed squares.

applied voltage of 80 V at 8 kHz is near the threshold voltage
for the emergence of the prewavy pattern, as shown in Fig. 3.
共3兲 The effect of dielectric heating is clearly observed in ourcase, but not in Wiant et al. 关14兴. 共4兲 We could find no extinction positions under sample rotation between crossed polarizers, whereas Wiant et al. mentioned nothing about thisobservation.
The most important feature we observed but was not described by Wiant et al. is the nonexistence of extinction conditions; we observed no extinction position for the stripes
when the cell was rotated between crossed polarizers. This

FIG. 5. 共Color online兲 Photomicrographs showing color changes
with analyzer rotation angle under crossed polarizers in the nematic
phase 共2 °C below the N-Iso transition兲 of the bent-core liquid crystal. The cell thickness was 6.0 ␮m. The applied voltage was arectangular wave of 80 V and the frequency was 1 kHz. Rubbing
directions is along the vertical direction in these photographs. The
angle of analyzer is 共a兲 0°, 共b兲 20°, 共c兲 40°, 共d兲 60°, 共e兲 80°, 共f兲100°, 共g兲 120°, and 共h兲 140° from the polarizer direction.

fact indicates that the director deformation does not occur
within a single plane but the director orientation out of theplane is induced by the electroconvection. To clarify the phenomenon, texture observation was made by rotating a
6-␮m-thick cell between crossed polarizers. Figure 4 shows
the result observed under the condition of 80 V and 1 kHz.
The period of the stripes is around 12 ␮m, about double thecell thickness. In the figure, the cell rotation angles between
the rubbing direction 共white arrow兲 and one of the polarizer
directions are shown in the figure. Asterisks are added to
identify the same striped domain. The following characteristics should be noticed: 共1兲 Colors change alternately in adjacent striped domains, and these colors interchange at 0° and
45°, more explicitly, 0 ° + 90° n and 45° + 90° n, where n is
integer numbers. 共2兲 The two domains never become dark at
any angles. 共3兲 The boundaries between the two domains
become dark at 0 ° + 90° n and bright at 45° + 90° n. The texture observation was also made with the rotation of the analyzer. As shown in Fig. 5 关see, for example, 共d兲 and 共g兲兴, wefind the following characteristic: 共4兲 The colors of two domains also interchanged against the opposite rotations of theanalyzer with respect to the parallel and crossed position,
90° n. The characteristic 共3兲 suggests that the director is parallel to the rubbing direction in the boundaries between two
domains. By contrast, the characteristic 共2兲 suggests that thedirector orientation is out of a plane perpendicular to the cellsurface including the rubbing direction. The inversion of theiiFIG. 4. 共Color online兲 Photomicrographs showing color changes
with cell rotation angle 共rubbing direction with respect to polarizers兲 under crossed polarizers in the nematic phase 共2 °C below the
N-Iso transition兲 of the bent-core liquid crystal. The cell thickness
was 6.0 ␮m. The applied voltage was a rectangular wave of 80 V
and the frequency was 1 kHz. Rubbing direction is 共a兲 −50°, 共b兲
−40°, 共c兲 −30°, 共d兲 −20°, 共e兲 −10°, 共f兲 0°, 共g兲 10°, 共h兲 20°, 共i兲 30°,
共j兲 40°, 共k兲 50°, and 共l兲 60° from a polarizer direction.

ii

(a)

iii

iv

i and ii

ii

iii

iv

iv and iii

(b)

(c)

FIG. 6. 共Color online兲 The proposed model structure. 共a兲 Model
structures proposed for left-handed and right-handed twisted
共splayed兲 structures in SSFLC cells. 共b兲 Electroconvection modelwith twisted structure. 共c兲 C-director maps in twisted structures associated with surface pretilt.

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PHYSICAL REVIEW E 77, 041708 共2008兲TANAKA et al.
1.0

1.0

TransmittanceTransmittancei, iii: 50, ii, iv: 40i, iii: 60, ii, iv: 30
i, iii: 70, ii, iv: 20i, iii: 40, ii, iv: 50

0.5i, iii: 30, ii, iv: 60
i, iii: 80, ii, iv: 10i, iii: 20, ii, iv: 70
i, iii: 10, ii, iv: 80
i, ii, iii, iv: 0, 90

0
350

450

550

650

Yellowish green domain

0.5

0
350

550
Wavelength (nm)

750

750

Wavelength (nm)20oFIG. 7. 共Color online兲 Calculated transmittance spectra by using
the 4 ⫻ 4 matrix method. The parameters used are as follows: Refractive index of the substrate is 1.52, and those of the liquid crystal
for ordinary and extraordinary light are 1.49 and 1.63, respectively.
The azimuthal angle rotation of the c director from the surface
plane is 30° and the ratio of height to radius of a tilt cone is 3 to 1.
The spectra of two structures of i and iii and those of ii and iv are
identical for all the sample rotation angles. The spectra at angles of
opposite rotations from 45°, for instance 30° and 60°, and 20° and
70°, are the same for the former and the latter structures, consistent
with the experimental observations.

1.0
Dark red domain

Transmittancecolors of the two domains mentioned in the characteristics
共1兲 and 共4兲 may result from oppositely twisted director orientations from the top to the bottom surfaces in each domain.
IV. DISCUSSIONAs mentioned in the previous section, the experimental
observation suggests twisted director orientation with alternate change of the twist sense in adjacent domains. To confirm the structure we calculated transmittance spectra using
the 4 ⫻ 4 matrix method 关25兴. For this purpose we need someprobable models of director orientations in the prewavy pattern. Simple twisted nematic liquid crystal structures are denied, since the transmittance is identical in two oppositely
twisted structures. Clear observation of periodic pattern
共shadowgraph兲 is evidence of director modulation within aplane perpendicular to the substrates 关8,26兴. Therefore weneed to propose a model with twist or modulation extended
both in and out of a plane. A good example of such modulation is observed in surface-stabilized ferroelectric liquid
crystal 共SSFLC兲 structures, twisted or splayed orientation, as
shown in Fig. 6共a兲 关27兴. We propose the corresponding
twisted structures under electroconvection, as shown in Fig.
6共b兲. This model can be constructed by introducing twist
structures to a conventional electroconvection model structure, and has director modulation both in and out of a plane.
The role of a tilt cone on which the director rotates as shownin Fig. 6共a兲 is played by the electroconvection flow, which
induces the in-plane tilt of the director in the middle of theconvection flow and the rotation of the director at surfaces.
The rotation would be possible by taking into account thechiral nature of bent-core molecules 关28兴.
Since the cause of the twisted structure in the present
electroconvection is different from that of SSFLC, the cone

0.5

350

550
Wavelength (nm)750

FIG. 8. 共Color online兲 Preliminary result of transmittance spectra from adjacent stripes of a prewavy pattern.

is not defined, so that the in-plane tilt angle is not necessarily
the same as the angle of the director at the surface withrespect to the rubbing direction. For simplicity, however, wetested the twisted state of SSFLC. It is known in the twisted
state of SSFLC cells that two twisted structures with thesame twist sense give different transmittance spectra, only
when surface pretilt is introduced 关29兴. Figure 6共c兲 is themodel showing the c-director map in which pretilt 共c-director
rotation at surfaces兲 is added to the model shown in Fig. 6共a兲.
The calculation was made using this model.
Figure 7 shows the transmittance spectra calculated undercrossed polarizers during the sample rotation using the fourmodels shown in Fig. 6共c兲. The parameters we used are azimuthal angle rotation of the c director from the surface plane
being 30° and height to radius of tilt cone being 3 to 1,
ordinary and extraordinary refractive indices of the liquid
crystal being 1.49 and 1.63, respectively, and 1.52 for therefractive index of the substrate. The results for i and iii, andthose for ii and iv in Fig. 6共c兲 are shown in Fig. 7. When therotation sense of the c director is the same such as in i and iii
and in ii and iv, the spectra are identical to each other. When

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ALTERNATING TWIST STRUCTURES FROMED BY …

PHYSICAL REVIEW E 77, 041708 共2008兲

Thus, the electroconvection in the N phase of bent-core molecules provides a type of chirality-related phenomenon.

the rotation angle is 0° and 90°, namely, the tilt-cone axis isalong the polarizer direction, all the spectra are the same, as
experimentally observed; i.e., the colors of the two domains
are the same. It is obvious that the spectra for i and iii andthose for ii and iv interchange with respect to the angles at
0°, 45°, and 90° under sample rotation. The calculated results
also agree with texture observations. The transmittance spectra under the rotation of the analyzer were also calculated.
We obtained qualitative agreement with the experiments,
though the calculated results are not shown.
Preliminary experimental measurements of the transmittance spectra from adjacent domains were conducted. The
results are shown in Fig. 8, where spectra from yellowish
and reddish domains at a cell rotation angle of 20° areshown. Although quantitative agreement was not possible,
we can suggest that the unique electroconvection effect in
the N phase of a bent-core molecule is due to alternate twist
molecular orientations. Further careful experiments andsimulation using various parameters may give quantitative
agreement, leading to a detailed director orientational model
structure. We tentatively used a model structure, which is theanalogue of static twisted structures of SSFLC cells 关27兴. It
is noted, however, that the origin of the structure is totallydifferent: Tilt of the director with respect to the layer normal
in the middle of the cell corresponds to the in-plane tilt by
the electroconvection flow. Twisted structures in SSFLC are
caused by the surface polar interactions, whereas those between both surfaces in the present cells are caused by themolecular chirality characteristic to bent-core molecules.

We observed unique electroconvections in the nematic
phase of a bent-core liquid crystal. The voltage-frequency
diagram for the emergence of the prewavy patterns is quite
similar to the one reported by Wiant et al., although a few
distinct differences exist. We found that neighboring domainsof the prewavy patterns show different colors and no extinction by rotating cells under crossed polarizers. Moreover, thecolors interchange by oppositely rotating cells with respect
to the angles 0° and 45° or an analyzer with respect to theparallel and crossed positions. These observations clearlysuggest oppositely twisted director orientations from the top
to the bottom surfaces in adjacent domains in the prewavy
pattern. We propose a possible model director orientation
analogous to the twisted 共splayed兲 structure in SSFLC cells
and calculated the transmittance spectra using the 4 ⫻ 4 matrix method. The calculated transmittance spectra are consistent with the experimental observations. Thus, the unique
textural characteristics observed in the prewavy patterns are
explained by introducing the chiral nature of bent-core molecules. Further detailed spectral measurements are necessaryfor quantitative comparison with the calculation. Direct observations of the structure by means of freeze fracture transmission electron microscopy and tomograms using confocal
microscopy are important and are under investigation.

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V. CONCLUSION

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