PHYSICAL REVIEW E 81, 011703 共2010兲

Polar switching in the smectic-AdPA phase composed of asymmetric bent-core molecules

1

Lingfeng Guo,1 Surajit Dhara,2,*,† B. K. Sadashiva,3 S. Radhika,3 R. Pratibha,3 Yoshio Shimbo,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, Bangalore 560080, India
共Received 22 October 2009; published 20 January 2010兲
We have studied mesogenic properties in the smectic-Ad PA phase of an asymmetric bent-core liquid crystal
by means of polarizing optical microscopy, second-harmonic generation 共SHG兲, electro-optical 共EO兲, anddielectric measurements. In homeotropically aligned cells, EO switching is clearly observed from a schlieren
texture with both four- and two-brush defects to a uniform bright domain under the application of very low
in-plane electric field below 1 V / ␮m. The phase is SHG active under an electric field, i.e., SHG gradually
increases without a threshold and saturates with the increasing field. In homogeneous cells, by applying
triangular wave field at saturated voltage, the splitting of the polarization switching current peak is observed,
indicating that the mesophase is antiferroelectric. The dielectric studies indicate a Debye-type relaxation of thetransverse dipoles associated with the rotation of the molecules about their long axis. The dc bias-dependent
dielectric relaxation time and the dielectric strength suggest that a field-induced antiferroelectric-ferroelectricphase transition occurs continuously beyond 1.2 V / ␮m and is reversible. The field-dependent texture observation is consistent with the dielectric measurements. Two possible models are proposed to interpret thecontinuous phase transition.
DOI: 10.1103/PhysRevE.81.011703

PACS number共s兲: 61.30.Gd, 42.65.Ky, 77.84.Nh

I. INTRODUCTION

Thermotropic liquid crystals composed of bent-shaped
共banana-shaped兲 molecules exhibit a rich variety of phasestructures and phase transitions 关1,2兴. Major attention has
been paid to the polarity and chirality, i.e., polar layer structure due to the packing of bent-shape molecules and theirswitchability, and macroscopic chiral domains consisting of
achiral molecules. In this paper, we focus on polar order andswitching. As for phase structures, in addition to conventional banana phases such as B1-B8 关1兴, some smectic-A
共Sm-A兲 family phases 共orthogonal smectic phases兲 and biaxial nematic phase have been reported. Some of these phases
show unique electro-optical 共EO兲 and dielectric properties
owing to the bent shape and their arrangement in the layer.
Among them, the most extensively studied phase is the B2phase. In this phase, molecules are tilted from the smectic
layer normal, so that two types of switching are possible, i.e.,
共1兲 conventional switching around cone preserving the layer
chirality and 共2兲 switching about molecular long axis 关3,4兴.
The switching of type 共2兲 is possible even in polar Sm-A
共Sm-AP兲 phases, where layer polar order exists. We will focus on one of such phases in the present work.
Some bent-core molecules exhibit the conventional nonpolar uniaxial Sm-A phase. Another nonpolar but biaxial
Sm-Ad phase, where molecules are interdigited in a smectic
layer, has been reported 关5–9兴. Polar orthogonal phases,
Sm-AP, were first reported by Eremin et al. 关10兴. They
showed antiferroelectric switching, ascribed it to a bilayer*Corresponding author.
†

sdsp@uohyd.ernet.intakezoe.h.aa@m.titech.ac.jp‡1539-3755/2010/81共1兲/011703共6兲

antiferroelectric Sm-APA structure, where the free rotation
about the longitudinal axis of molecules is hindered by thepacking of bent-core molecules and neighboring layers have
opposite bending 共polarization兲 directions. Some other
Sm-APA materials showing polar switching have also beenreported 关11–13兴. Ferroelectric analog Sm-APF has also beenreported 关14兴. Another interesting polar Sm-AP phase is theSm-APR phase 关15兴. In this phase, dipoles form small polar
domains, so that the phase is apparently uniaxial but exhibitspolar switching. Considerable attention has been paid as apossible candidate for next-generation fast response display
devices 关16–18兴. Here, we focus on the switchable Sm-Ad PA
phase which has an interdigited layer structure. The switching behavior in this phase has been reported earlier关7,11–13兴. In the present study, we used a different compound, which shows the Sm-Ad PA phase, and found electricfield-induced thresholdless antiferroelectric-ferroelectrictransition. Similar continuous transition has ever been observed in tilted smectic phases previously 关19,20兴, but not in
the nontilted phase. Further, in this phase chiral domains
were also observed in an orthogonal system composed ofachiral molecules. A variety of experimental results and possible switching models is described.
II. EXPERIMENTAL

The sample used in this study was an asymmetricbent-core molecule with a longitudinal strong dipole 共C
w N兲 and a flexible alkyl chain at one end, as shown in Fig.
1共a兲. The details of the synthetic scheme and chemical properties will be reported elsewhere. This compound shows thefollowing phase sequence: crystal 共Cr兲-134.8 ° C-Sm-Ad PA149.0 ° C-Sm-Ad-150.2 ° C-Isotropic 共Iso兲 on heating andon
Iso-149.5 ° C-Sm-Ad-148.3 ° C-Sm-Ad PA-112.6 ° C-Cr

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PHYSICAL REVIEW E 81, 011703 共2010兲

GUO et al.

FIG. 1. 共Color online兲 共a兲 Chemical structure
and phase sequence of the compound used in theexperiment. 共b兲–共e兲 Planar texture of a
12.8-␮m-thick cell at 145 ° C under various vertical dc fields. 共f兲–共i兲 Homeotropic texture of a
5.6-␮m-thick cell at 138 ° C under various inplane dc fields.

cooling. For preparing planar cells, glass plates coated withindium tin oxide were spin coated with polyimide 共JSR, AL1254兲 and cured at 180 ° C for 1 h. The plates were rubbed
antiparallel to obtain homogeneous alignment of the director.
In homeotropic cells, polyimide 共Nissan Chemical, SE-1211兲
was used as an alignment layer. A uv curable adhesive mixed
with spacer was used to make cells of typical thickness. The
sample was filled in empty cells in the isotropic phase bycapillary action and cooled slowly.
Texture observations were made by using a polarizing optical microscope 共Nikon, Optiphot-pol兲 equipped with a hot
stage and temperature controller 共Mettler Toledo FP 82兲. A
function generator connected with a high voltage amplifier
was used to study the electro-optical switching behavior. The
polarization reversal current was measured across a 1 M⍀
resistor using a standard triangular wave technique. The
second-harmonic generation 共SHG兲 measurements were also
conducted using a planar cell. The light intensity of the fundamental light, Nd:YAG laser 共1064 nm, 8 ns duration, and
10 Hz repetition兲, was reduced down to 6 mJ/ mm2 and wasincident into the sample at 45° incidence. The SHG signal
was detected in the transmission direction by a photomultiplier tube 共Hamamatsu, R955兲 after blocking the fundamental light by IR cut and interference filters. The signal was
accumulated for 30 s with a boxcar integrator 共Stanford Research Systems, SR-250兲. A frequency response analyzer
共Solartron 1255B兲 with a dielectric interface 共Solartron
1296兲 was used to measure the dielectric properties in a homogeneously aligned cell. The measuring field was 0.3 Vppand a dc biased field up to 40 V was applied. The real andimaginary parts of the dielectric permittivity from 1 Hz to 1
MHz were measured under different bias fields.

III. RESULTS

Let us show texture changes upon electric field application in the Sm-Ad PA phase under crossed polarizers. Figures

1共b兲–1共i兲 show the results for homogeneous 共at 145 ° C兲 andhomeotropic 共at 138 ° C兲 cells, respectively. Homogeneouslyaligned samples show a fan-shaped texture. A few stripes
existed in the absence of a field 关Fig. 1共b兲兴, disappeared byapplying a small field 关Figs. 1共c兲 and 1共d兲兴, and obvious
birefringence change was followed under a higher field like
4.5 V / ␮m 关Fig. 1共e兲兴. We found that birefringence color
change was continuous, and the textural change was reversible. We also conducted x-ray diffraction experiments under
an applied field and no noticeable change in the layer spacing was observed, indicating that the antiferroelectric toferroelectric transition occurs keeping the layer spacing unchanged. In homeotropically aligned cells, a schlieren texture
with both four- and two-brush defects were observed 关Fig.
1共f兲兴. An in-plane electric field was applied across a gap of
50 ␮m, where the electric field was 45° to crossed polarizers, and the temperature was fixed at 138 ° C. By applying afield, the texture changed continuously 关Figs. 1共g兲 and 1共h兲兴and became uniformly bright 关Fig. 1共i兲兴 even under very low
voltage 共below 1 V / ␮m兲. During the whole process, nothreshold could be observed.
We now show SHG results as a function of temperatureand electric field. In the absence of an electric field, no SHG
signal was observed in the whole temperature range, implying that this phase has no macroscopic polar domains. On theother hand, by applying a rectangular wave field to planarcells, comparatively strong SH signal was detected in the
Sm-Ad PA phase both in heating and cooling runs. The
electric-field-dependent SHG signal is shown in Fig. 2共a兲.
The measurement was carried out at 140 ° C in a coolingprocess in an 8.9 ␮m cell. The SH signal gradually increased with increasing field and saturated above 120 Vpp.
Note that no distinct threshold voltage could be observed in
the SHG intensity change. Figure 2共b兲 shows the temperaturedependence of the SH signal under a rectangular wave voltage of 80 Vpp. In the cooling process, the SH signal emerged
quickly from zero and showed a maximum value when thetransition to the Sm-Ad PA occurred. Then the signal gradu-

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Switching current (arb. units)

PHYSICAL REVIEW E 81, 011703 共2010兲

(a)

1.2
0.8
0.4
0.0

1.6

0

30

60
90
120
Voltage (Vpp)150

CoolingHeating(b)

Ps (nC/cm2)

1.2
0.8
0.4

-45

-30 -15
T-TI-Sm (oC)

0

(a)

0.5

+60V

0.0
-0.5

-60V

-1.0

-0.04

FIG. 2. 共a兲 SHG intensity as a function of applied voltage at
140 ° C. 共b兲 SHG intensity as a function of temperature in bothcooling 共squares兲 and heating 共open circles兲 runs in a homogeneous
sample at an applied rectangular voltage of 80 Vpp and at a frequency of 10 Hz. Cell thickness is 8.9 ␮m.

ally decreased with reducing temperature. The gradual decrease could be explained by the increase in scattering
caused by rigid boundaries of local domains on cooling. The
SHG intensity drops to zero upon crystallization. Similar tendency was also observed in the heating procedure. We note,however, that the temperature-dependent behavior changes
with an applied field since the saturation field depends on
temperature. Figure 2共b兲 is one of the typical examples.
We measured the polarization reversal current in a
4.8-␮m-thick planar cell at various temperatures to identify
the switching behavior. The applied field was a triangularwave voltage of 120 Vpp and frequency of 9 Hz. At 138 ° C,
double switching current peaks were detected, as shown in
Fig. 3共a兲, indicating that the ground-state structure of themesophase is antiferroelectric. Two current peaks are closely
located at about 0 V. This behavior is consistent to the quasicontinuous ferroelectric transition shown by the SHG measurement 关Fig. 2共a兲兴. Similar continuous field-induced
antiferroelectric-ferroelectric transitions were detected intilted smectic phases by applying simple and modified triangular wave fields 关19,20兴. However, such a continuous
antiferroelectric-ferroelectric transition has never been observed in the orthogonal smectic phase such as the Sm-Ad PA
phase. The variation of spontaneous polarization 共Ps兲 as afunction of temperature is shown in Fig. 3共b兲. The Ps value
increases rapidly from ⬃60 nC/ cm2 to around 260 nC/ cm2
after the transition to the polar phase and drops sharply tozero at crystallization.
The dielectric properties were measured as a function of
frequency from 1 Hz to 1 MHz at various temperatures. The

0.00
0.04
Time (s)0.08-10
T-TI-Sm (oC)

0

(b)

200
100
0

15

-20

FIG. 3. 共a兲 Switching current in the Sm-Ad PA phase by applying
a triangular wave voltage of 120 Vpp and with the frequency of 9
Hz at 138 ° C. 共b兲 Spontaneous polarization 共Ps兲 as a function oftemperature. Cell thickness is 4.8 ␮m.

real part 共␧⬘兲 and imaginary part 共␧⬙兲 are given in Figs. 4共a兲and 4共b兲, respectively. It is noticed that in the isotropic phase
共T − TI−Sm = +1兲 only one low-frequency ionic relaxation isobserved near 20 Hz. In the Sm-Ad PA phase there is anotherrelaxation near 100 kHz and it is temperature dependent. In
order to confirm that the low-frequency relaxation is due tothe ionic relaxation, we increased the dc bias voltage up to

ε'

-60

ε"

0.0

1.0

300

ε'

SH intensity (arb. units)

SH intensity (arb. units)

POLAR SWITCHING IN THE SMECTIC-Ad PA…

400
300
200
100
0
160
120
80
40
0
400

o

-1 ( C )
-4
-7
-15
15
-19
-24
o

-1 ( C )
-4
-7
-15
-19
-24

300
100
0

1

10

2

3

4

10
10
10
Frequency (Hz)

(b)

(c)

0V
5V
10 V
15 V
20 V
30 V
40 V

200

(a)

5

10

6

10

FIG. 4. Dielectric permittivity in the Sm-Ad PA phase. 共a兲 Realpart 共␧⬘兲 and 共b兲 imaginary part 共␧⬙兲 as functions of frequency at
various relative temperatures 共T − TI−Sm兲. 共c兲 The effect of dc bias
field on the dielectric constant 共␧⬘兲 at T − TI−Sm = −10 ° C. Cell thickness is 12.8 ␮m.

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PHYSICAL REVIEW E 81, 011703 共2010兲

Relax
xation tim
me τ (µs
s)

30
25

ε''

20
15
10
5
0

0

10

20

30

40

FIG. 5. Cole-Cole plot of the dielectric permittivity at
138 ° C.

40 V and found that the low-frequency dielectric constant
reduced and the ionic relaxation could be suppressed almost
completely as the ions were swept away from the bulk underdc bias fields as seen in Fig. 4共c兲. On the contrary, anotherrelaxation at about 100 kHz was enhanced by increasing thebias voltage 共see Fig. 7 later兲. The Cole-Cole plot of real 共␧⬘兲and imaginary 共␧⬙兲 parts of the dielectric constants at thetemperature of 138 ° C is shown in Fig. 5. As we mentionedthat the low-frequency dielectric relaxation is due to the ion,
we used data from 100 Hz to 1 MHz to describe the dielectric relaxation. Single semicircular arc clearly suggests that
there is only one relaxation and further it is Debye type as
the data are well fitted with the Debye equation. Thus, we
use the Debye equation to analyze the frequency-dependent

Dielectriic strength
h ∆ε

(a)

30
20
10
0

Relaxatioon time τ (µs)

1.5

-20

-10
o
T-TI-Sm ( C )

52
48
44

1.4

40
1.2
0

ε'

40

∆ε
τ

1.6

1
2
dc bias field (V/µm)

3Dielecctric stre
ength ∆εGUO et al.

36

FIG. 7. Variation of relaxation time ␶ 共squares兲 and the dielectricstrength ⌬␧ 共open circles兲 as a function of dc bias field.

dielectric data at various temperatures and dc bias fields. The
dielectric strength 共⌬␧兲 and the dielectric relaxation time 共␶兲were obtained as fitting parameters.
The variation of the dielectric strength as a function oftemperature is shown in Fig. 6共a兲. It is seen that the dielectricstrength increases rapidly from 4 in the isotropic phase andattain a maximum at the Sm-Ad to Sm-Ad PA transition. The
value of ⌬␧ decreases slightly as the temperature is lowered
due to the gradual increase in viscosity in the cooling process. From Fig. 6共b兲 it is noticed that the relaxation time 共␶兲also rapidly increases from 0.6 ␮s to about 1.3 ␮s in thevicinity of Sm-Ad – Sm-Ad PA phase transition and in the
Sm-Ad PA phase it is almost independent of temperature.
Such a rapid increase of ␶ in Sm-Ad PA phase is due to therapid growth of the polar order. The average polarization
direction is along the bending direction and is parallel to thelayer. The relaxation at about 100 kHz is attributed to that of
the molecular motion associated with this polarization response. Figure 7 shows the effect of dc bias field on thisrelaxation mode. It is discerned that relaxation strength andrelaxation time are almost constant up to 1.2 V / ␮m. Whenthe voltage continues to rise, both of them progressively
increase with the electric field. It can be explained as follows: by applying a dc field, macroscopic polarization
emerges by distorting the antiferroelectric structure to theferroelectric one, so that the dielectric strength increases.

0
E=0

(b)

1.2
0.9

E

E

0.6
0.3
00
0.0

-20

-10
o

0

T-TI -Sm ( C )FIG. 6. Variation of 共a兲 dielectric strength 共⌬␧兲 and 共b兲 relaxation time 共␶兲 as a function of relative temperatures.

FIG. 8. Simple model of the field-induced antiferroelectricferroelectric transition. Black arrows connected to the arms of bentcores stand for the stronger dipole of C w N.

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POLAR SWITCHING IN THE SMECTIC-Ad PA…

PHYSICAL REVIEW E 81, 011703 共2010兲



100µm



100µm
FIG. 9. 共Color online兲 共a兲 and 共b兲 Homeotropic textures underpolarizers decrossed in the opposite direction. White arrows represent polarizer and analyzer. The dark regions with their brightness
interchanged by rotating the analyzer clockwise or counterclockwise are chiral domains.

Similar phenomenon has been observed in the antiferroelectric smectic-Cⴱ 共Sm-CAⴱ兲 关21兴.
IV. DISCUSSION

Now we consider a possible model of EO switching basedon x-ray, EO, and SHG studies. We believe the previous
model of molecular packing proposed by Sadashiva et al.
关6兴, as shown in Fig. 8 共middle兲. In the absence of a field, thebent cores of molecules are parallel to substrate surfaces because of an electrostatic interaction between molecules andsurfaces as well as packing entropy effect. This model isreasonable from x-ray analysis data, i.e., the calculated individual molecular length L is 46.4 Å, while the layer thickness experimentally obtained is 54.5 Å, suggesting an interdigited structure. Moreover, this arrangement satisfies
compact packing of bent cores. In this arrangement, the polarization component along the layer normal is totally cancelled, whereas macroscopic layer polarization emerges parallel to the layer. Because of the antiferroelectric orientation,
this layer polarization is also cancelled between adjacent layers, so that no macroscopic polarization can be detectedwithout applying an electric field, being consistent to nonSHG activity. However, when an external field is applied on
the sample, the layer polarization reorients toward the field
direction, as shown in Fig. 8, i.e., the paired molecules rotate
about their molecular long axis or the layer normal. It is clearthat the birefringence increases by applying an electric field,
being consistent to the texture change shown in Figs.
1共b兲–1共e兲.
Usually field-induced antiferroelectric-ferroelectric transition is associated with the threshold behavior both in classical Sm-CAⴱ 关22兴 and bent-core B2 关23兴 phases. In the present

case, however, all the measurements indicate the thresholdless behavior. We can suggest two ideas to explain this behavior. 共1兲 The potential barrier between the antiferroelectricand ferroelectric states is so low that electric-field-induced
transition occurs quasicontinuously. This idea is supported
by closely located double switching current peaks as shownin Fig. 3共a兲. 共2兲 The existence of helical structure. Actually
we observed spontaneous formation of chiral domains, as
shown in Fig. 9. In these textures of homeotropically aligned
cells under decrossed polarizers, the brightness of some areas
interchanged by slightly rotating an analyzer clockwise orcounterclockwise, indicating the existence of chiral domains.
The phenomenon is similar to the spontaneous chiral domain formation observed in the B4 关24兴 and dark conglomerate 关25兴 phases. However, the phase shown by the present
sample is a fluid phase, being quite different from B4 anddark conglomerate phases. So far, the spontaneous chiral domain formation has also been reported in nonchiral fluid
nematic phase 关26–29兴. However, these chiral domain formations were recently ascribed to surface effect 关30兴. In thepresent case, however, the situation is very different becauseof the following reasons: 共1兲 we used homeotropic cells, sothat the surface anchoring must be very weak, and 共2兲 thechiral domains are very unstable. The shape of domains iseasily changed by slightly changing temperature and lightly
touching even the oven, where our sample is located. Hence,
we can conclude that the chiral domain formation in our
sample is not caused by surfaces.
Moreover, the observed phenomenon is slightly different:
besides the chiral domains, which show brightness change in
oppositely decrossed polarizers, there exist bright areas,
which show no significant change under uncrossed polarizers. In this nontilted 共orthogonal兲 Sm-Ad PA phase, the longitudinal axis is parallel to the layer normal and the polar direction lies in the layer planes. Therefore, there are two
twofold rotation axes along the polar 共bending兲 direction andperpendicular to it at the layer boundaries. In addition bending plane is a mirror plane, so that the local structure of the
Sm-Ad PA phase has D2h symmetry. For the Sm-Ad PA phase
to be chiral, a helical structure must be formed. Therefore,
three domains, two chiral and one nonchiral, are attributed toright- and left-handed helix and nonhelical domains, respectively. By applying an electric field, helix unwinding andantiferroelectric to ferroelectric deformation take place at thesame time. This may be the reason why the threshold of the
field-induced antiferroelectric-ferroelectric is not so distinct.
Further studies are necessary to clarify the helical structure.
V. CONCLUSIONSWe characterized the Sm-Ad PA phase of an asymmetricbent-core liquid crystal by means of polarizing optical microscopy, SHG, EO, x-ray, and dielectric measurements. The
compound is SHG active under electric field and a characteristic dielectric relaxation appears at about 100 kHz attributed to the rotation of the molecules about the long axis. The
dc field enhances this dielectric relaxation, suggesting thepolar order nucleated by the dc bias effect. The field-induced
antiferroelectric-ferroelectric 共Sm-Ad PA – Sm-Ad PF兲 transi-

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PHYSICAL REVIEW E 81, 011703 共2010兲

tion occurs continuously without a distinct threshold. We
suggested two possible models to interpret this continuoustransition, i.e., very low barrier between the two phases andthe existence of helical structure. Both ideas are supportedby the present experiments.

ACKNOWLEDGMENT

One of the authors 共S.D.兲 gratefully acknowledges the
support from the DST, Government of India for Project No.
SR/FTP/PS-48/2006 under the SERC Fast Track Scheme.

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