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Transition between two orthogonal polar phases in symmetric bent-core liquid
crystals
Lingfeng Guo,a Kinga Gomola,a Ewa Gorecka,b Damian Pociecha,b Surajit Dhara,ac Fumito Araoka,aKen Ishikawaa and Hideo Takezoe*a
Received 30th October 2010, Accepted 14th December 2010
DOI: 10.1039/c0sm01233e
A unique phase transition between a uniaxial orthogonal phase with random polar order SmAPR andorthogonal antiferroelectric phase SmAPA is found in a series of symmetric achiral bent-core liquid
crystals. The phase transition is weakly first order or continuous. The X-ray diffraction, electro-optical,
optical second harmonic generation and dielectric methods, confirmed that the phase transition occurs
from a locally polar ordered phase to a macroscopically antiferroelectrically ordered phase.

1. Introduction
Achiral liquid crystals made of bent-core molecules belong to
a new class of materials for which the polar order is independentof molecular tilt. A number of new phases, that were not known
for rod-like molecules, were discovered for these mesogens.1–3
The bending of the molecular core causes a strong steric effect:
the free rotation of molecules is hindered, leading to ordering ofdipole moments. Either ferroelectric or antiferroelectric phases
are possible depending on polar correlation between adjacentlayers. However, it is rare for bent-core molecules to exhibit nontilted phases. The compound showing both the conventional
SmA phase and the polar ‘‘banana phase’’ B2 was first reported
by Kovalenko et al.4 and later on, a number of materials with
non-polar uniaxial SmA phase were investigated.5,6 Two othertypes of orthogonal non-polar smectic phase, composed of bentcore molecules, are the biaxial phase SmAb7 and the SmAd phase(interdigitated layer structure).8 Nevertheless, the non-tilted
biaxial smectic A phase with antiferroelectric behaviour, socalled the SmAPA phase, was not experimentally proved until
2001 by Eremin et al.9 In the following years, bent shaped
compounds showing distinct polar orthogonal phases such as
SmAdPA (interdigitated layer structure and antiferroelectricorder),10–12 SmAPR (randomly distributed polar domains),13,14
and SmAPAR (randomly distributed antiferroelectric domains)15
were synthesised and investigated.
The SmAPR phase is interesting since it appears as uniaxial
and non-polar, but the polar order can be easily induced by an
external electric field. Because of the fast response under anelectric field, the SmAPR phase was confirmed to be a promisingaDepartment of Organic and Polymeric Materials, Tokyo Institute ofTechnology, O-okayama, Meguro-ku, 152-8552, Tokyo, Japan. Fax: +81
3 5734 2876; Tel: +81 3 5734 2436b
Chemistry Department, Warsaw University, Al. Zwirki i Wigury 101,
02-089 Warsaw, PolandcSchool of Physics, University of Hyderabad, 500046, India

This journal is ª The Royal Society of Chemistry 2011

candidate for a new-generation fast switching liquid crystal
display.16 Although a few compounds showing a SmAPR phasehave been obtained,17 the narrow temperature range of this phaseis still a major limitation of utilizing this material in industry.
Besides, not much is known about the polar order developmentin the orthogonal systems composed of bent-core molecules.
In this paper, we report a new phase sequence exhibited bya homologous series of bent shaped mesogens with 1,3-dihydroxyacetophenone as the central unit. These compounds are thefirst symmetric ones showing the SmAPR phase.18 Distinct fromso far reported SmAPR materials, which have a B1RevTilted phase(a columnar phase made of layer fragments with 2D density
modulation) as a lower temperature phase, this series ofmaterials shows the antiferroelectric orthogonal phase (SmAPA)
below the SmAPR phase. Furthermore, the SmAPA phase ismaintained down to room temperature. It should be mentionedthat recently Keith et al.19 reported another series of compounds
showing a similar phase sequence.

2. Experimental
The compounds were obtained according to the procedurereported in our previous paper.18 Phase transition temperatures
and associated enthalpy changes were determined by differential
scanning calorimetry (DSC, Pyris Diamond Perkin-Elmer) andtexture observation under a polarizing optical microscope(Nikon, Optiphot-pol) equipped with a heating stage (Mettler
Toledo FP82). The DSC measurements were operated at a rate
10–20  C min1 on both heating and cooling runs. The X-ray
diffraction patterns were recorded using Bruker D8 Discover and
GADDS systems, for samples with homeotropic alignment,
obtained by slow cooling of a drop of the isotropic liquid below
the clearing temperature. The X-ray beam was directed almost
parallel to the substrate surface.
The electro-optical and switching behaviours were obtainedusing a function generator (HP 3245A) connected with a highSoft Matter, 2011, 7, 2895–2899 | 2895

voltage amplifier (NF 4005). The polarization reversal current
was measured across a 1 MU resistor using a standard triangularwave technique. In the birefringence measurement a Berek
compensator (Nichika No.10547) was used. Dielectric measurements were done using a frequency response analyzer (Solartron
1255B) and dielectric interface (Solartron 1296) for planar cells.
The glass substrates were coated with an indium-tin-oxide (ITO)
electrode and polyimide (AL1254). The alignment layer was
rubbed in antiparallel direction. The measuring field was 0.3 Vpp.
The real and imaginary parts of dielectric permittivity from 0.1
Hz to 1 MHz were measured under different bias fields, up to
40 V. The dielectric strength D3 and relaxation frequency fr were
found by fitting measured data to the Cole–Cole formula.
In optical second-harmonic generation (SHG) measurements,
a Nd:YAG laser (1064 nm, 8 ns duration, 10 Hz repetition) wasused. The fundamental beam was cast upon the homogeneouslyaligned cells either at 45 . The SHG signal was detected in thetransmission direction by a photomultiplier tube (R955, Hamamatsu) after blocking the fundamental light by an IR-cut filter.
The signal was accumulated by a boxcar integrator (SR-250,
Stanford Research System) for 30 s.

3. Results and discussion
The molecular structure, phase transition temperatures andrelated enthalpy changes for each compound are summarized inTable 1. Digits in the name of compound represent the number ofcarbon atoms in each terminal chain. ‘AP’ means 1,3dihydroxyacetophenone as the central bent unit and ‘N’ stands
for NO2 group at both lateral positions. All of those compounds
showed non-tilted smectic phases metastable down to room
temperature. The temperature range of the SmAPR phase wasbroader than that of previously reported materials, reachingalmost 50  C for n ¼ 18 and 20 compounds. The enthalpy change
at the SmAPR–SmAPA transition was small (0.1 kJ mol1),
indicating only weak structure difference between these two
orthogonal phases.
In all studied materials, the layer spacing, d, shows noticeable
negative thermal expansion in all temperature range of LC phases(Fig. 1(a)). Negative thermal expansion is typical for orthogonalsmectic phases. It was observed in SmAPR17 and even in SmAPAR15 of other compounds. For compounds reported here, in the
Table 1 Molecular structure of the studied compound and the phasetransition temperatures ( C). Corresponding enthalpy changes (kJ mol1)of the transitions are listed in parentheses.

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Fig. 1 (a) Layer spacing as a function of temperature measured oncooling, n denotes the length of the terminal alkyl chains. (b) Possible
molecular packing in high, intermediate and low temperature ranges of
the SmAPR phase. Because of the partially interdigitation of terminal
chains, d/L < 1.

SmAPR phase d increases on cooling more apparently than in the K1 for SmAPR, which
SmAPA phase; the slope of d vs. T is 0.2 A
is an order of magnitude larger than observed for calamitic
 K1 for SmAPA with higher
orthogonal smectics, and 0.03–0.05 A
values for longer homologues. This implies that the mechanismsof layer spacing changes in each phase are different. The spacing in
SmAPR phase is shorter than the molecular length L. The difference between L and d is in the order of magnitude of the length ofthe corresponding terminal aliphatic chain. Therefore, it isreasonable to assume that alkyl chains between adjacent layers are
partially interdigited, as was also reported in the non-polar SmA
phase composed of bent-core molecules.4,6 In such non-polarphase, individual molecules rotate freely particularly at higher
temperatures and the overall shape of rotating bent-core molecules can be regarded as bulky middle part with much thinner
flexible molecular ends (Fig. 1(b) right). Packing of such objects
into layers requires pronounced interdigitation of molecular tails
between the layers to fill the space effectively. Of course, fullinterdigitation is not possible because of gauche conformations offlexible chains and their thermal dynamic motion. We expect thatin the SmAPR phase with lowering temperature the rotation
around the long molecular axis is frozen gradually as the coherence length for polar order is growing, resulting in a lower degreeof interdigitation and thus an increase of layer thickness.
This journal is ª The Royal Society of Chemistry 2011

The situation is illustrated in Fig. 1(b). At higher temperatures,the size of the polar domains is very small, so that the molecules
rotate almost freely, as mentioned above (Fig. 1(b) right). This is
supported by SHG measurements (see Fig. 5 later); i.e., SmAPR
is SHG inactive under a certain field strength at higher temperatures. Since macroscopic polar order is induced via the Langevin process, i.e., competition between polar interaction andthermal agitation, SHG does not emerge if the polar domain is
too small to be oriented. The evolution of polar domains
proceeds with decreasing temperature, since molecular packing
becomes tight at lower temperatures. In the vicinity of thetransition to the SmAPA phase, the adjacent layer correlation
shown in Fig. 1(b) (left) is realized. For non-rotating molecules
the efficient packing does not require strong interdigitation, since
the cross section of the middle part of molecule is not muchdifferent than its end parts. In the intermediate temperature
range, a situation shown in the middle of Fig. 1(b) may occur,
since the evolution of the polar domain occurs dynamically. Thus
the negative thermal expansion in SmAPR can be interpreted by
the continuous variation of the ratio of the three typical situations shown in Fig. 1(b). In the SmAPA phase molecular rotation
is frozen and layer spacing is larger than in the SmAPR phase,
although it is still much smaller compared with the molecularlength with fully extended chains. Moreover, the d value still
increases with decreasing temperature. These facts suggest thatthe increase of layer spacing with decreasing temperature mainly
originates from the increase of orientational order of longmolecular axes and the change of the chain conformation(decreasing number of gauche conformations on cooling). These
effects are also valid for the SmAPR phase.
If we compare the X-ray diffraction patterns of homeotropically aligned sample of AP-20-NN-20 in both phases (Fig. 2(a)and (b)) it is quite clear that although both have liquid like orderinside the layer, the layers are much better defined for the SmAPA
phase, as indicated by larger number of harmonics of the main
signal. The diffuse character of wide-angle scattering, found evenat ambient temperature, signifies a liquid-like disorder withinlayers. But it should be noticed that in the low temperature phase
SmAPA, the wide angle signal is slightly sharper than in the
SmAPR phase, indicating larger correlation length of in-plane
molecular ordering (Fig. 2(c)). The in-plane correlation lengths,

Fig. 2 Two dimensional X-ray patterns for compound AP-20-NN-20:(a) in the SmAPR phase at 130  C, (b) in the SmAPA phase at 25  C.
Slight up/down asymmetry in the pattern is due to shadowing by sample
heating stage. (c) Intensity vs. 2q obtained by integration of 2D patterns
over azimuthal angle at 130  C and 25  C, respectively.

This journal is ª The Royal Society of Chemistry 2011

obtained by fitting wide angle signal to Lorentz formula, in and 4.8 A,
 respectively.
SmAPR and SmAPA are 2.4 A
Texture observation is always useful to identify the phasebehaviour. In the homeotropic cells, aligned by polyimide
SE1211, a uniform dark image was observed in the SmAPR phaseindicating macroscopic uniaxiality. On cooling birefringent
texture slowly appears indicating the transition from uniaxial(SmAPR) to biaxial (SmAPA) phase.18 Fig. 3 shows focal conic
textures of both phases, being characteristic to lamellar structures. By comparing Fig. 3(a) and (c), it can be clearly seen thatthe phase transition causes only a birefringence change in the
texture. The extinction directions in both phases were parallel tothe layer normal, certifying the orthogonal smectic phase. Under
applying an electric field (20 Vpp/mm) (Fig. 3(b) and (d)) thebirefringence slightly increases from 0.094 to 0.101 in the SmAPR
and from 0.117 to 0.122 in the SmAPA phase. The higher value ofthe SmAPA compared to SmAPR in the field-on state, where allmolecules are oriented with their dipole moments along theelectric field, is caused by slightly higher orientational order oflong molecular axes in the SmAPA phase. The reorientation ofmolecules under the field in both phases occurs without changing
the optical extinction directions, which is also consistent with theorthogonal nature of the two phases.
Switching current was recorded on applying a triangular wave
electric field to a planar cell at various temperatures. In the
SmAPR phase, one broad peak for each half cycle was obtained
as shown in Fig. 4(a). Such a peak can be attributed to the fieldinduced reorientation of local polar domains from random
distribution to the field direction through a Langvin process,which is a typical behavior of the SmAPR phase.14 In the lower
temperature phase, SmAPA, two current peaks per half cycle
were detected (Fig. 4(b)), indicating that the ground-state
structure of the mesophase is antiferroelectric. The spontaneouspolarization (PS) values calculated from the switching current in

Fig. 3 Homogeneous textures of AP-18NN-18. (a) Field off state, Dn ¼
0.094, and (b) field-on state, Dn ¼ 0.101 in the SmAPR phase at 103  C.
(c) Field off state, Dn ¼ 0.117, and (d) field-on state Dn ¼ 0.122, in the
SmAPA phase at 85  C. Cell thickness was 4.6 mm.

Soft Matter, 2011, 7, 2895–2899 | 2897

Fig. 4 Switching current response recorded by applying a triangularwave voltage to a 5.2 mm-thick cell. (a) SmAPR at 97  C (140 Vpp, 6 Hz)
and (b) SmAPA at 87  C (140 Vpp, 0.2 Hz). In order to resolve the double
switching current peak in SmAPA phase the frequency of the applied
voltage has to be below 1 Hz.

no signal could be obtained at any temperature, indicating thatneither of the two polar phases has macroscopic spontaneouspolarization. Upon field application, polar order is easily
induced in the SmAPR phase; i.e., SH signal gradually increasedon cooling and reached a maximum value near the SmAPR to
SmAPA phase transition. That is because molecular dipoles
cooperatively orient in the layer by the application of an electricfield and with reducing temperature the coherence length gradually increases. On the contrary, in the low temperature phase,
SmAPA, the induction of polar order is associated witha threshold for the structure change from SmAPA to SmAPF.
Since this threshold voltage increases with lowering temperature,
the SH signal under the same voltage decreases rapidly on
cooling in SmAPA phase.
The dielectric measurements were conducted in planar cells.
The overall dielectric behaviour as functions of temperature andfrequency is shown as a 3-D plot of imaginary part of dielectric
permittivity (3’’) recorded in a cooling process (Fig. 6(a)). In thewhole temperature range, two relaxation modes could be clearly
seen. The higher frequency mode can be attributed to the noncollective motion of polar molecules, its relaxation frequency
follows the Arrhenius law: fArrh ¼ f0eE/kT with activation energy
Ea ¼ 151 kJ mol1, and the dielectric strength slightly increases
with reducing temperature. The lower frequency mode shows
critical behaviour near the phase transition, thus can be attributed to collective movement of dipole moments. The relaxation

SmAPR and SmAPA are 170 nC cm2 (97  C) and 300 nC
cm2 (87  C), respectively.
The polar order in both phases was also monitored by the
SHG method. The intensity of the SHG signal as a function oftemperature with and without an applied electric field is given in
Fig. 5. When the materials were tested without an electric field,

Fig. 5 Temperature dependence of the SHG intensity in a homogeneously aligned 4.8 mm-thick cell on cooling from the isotropic phase.
Open triangles represent a zero field run and closed circles represent dataobtained under applying dc 10 V to the sample.

2898 | Soft Matter, 2011, 7, 2895–2899

Fig. 6 (a) Three-dimensional (3D) plot of imaginary part of dielectric
permittivity of AP-18NN-18 material. Two relaxation modes caused bycooperative motion and non-collective movement of dipole molecules canbe seen at low and high frequencies, respectively. (b) Relaxation
frequency fr and (c) dielectric strength D3 of the both dielectric modes asa function of temperature. Homogeneous aligned cell with the thicknessof 5.4 mm was used in the dielectric measurement.

This journal is ª The Royal Society of Chemistry 2011

4. Conclusion
The unique system showing transition from the uniaxial
orthogonal phase with local polar order (SmAPR) to the antiferroelectric non-tilted smectic phase (SmAPA) was studied.
Within the resolution of the used techniques (X-ray diffraction,dielectric and electro-optic), it seems that the transition iscontinuous or weakly first order, which is allowed for phases ofdifferent symmetry (DNv and D2h for SmAPR and SmAPA,
respectively). The correlation length of polar order increases in
the SmAPR phase gradually as well as antiferroelectric interlayer
correlations. The interlayer polar coupling is weak as indicatedby a low value of relaxation frequency of a ferroelectric mode at
the phase transition. We suggest that the ferroelectric-like
response in the SmAPR phase, identified by a single wide peak,occurs by collective reorientation of molecules in the layers.

References

Fig. 7 Frequency dependence of imaginary part of dielectric permittivity in (a) SmAPR at 100  C and (b) SmAPA at 80  C under applicationof various dc bias fields.

frequency reaches the minimum (3 Hz) and mode strength
maximum (30), at the phase transition, that indicates longliving polar fluctuation in the system on approaching phasetransition. Since fr is proportional to the strength of interlayer
polar interactions in the system (the stronger interaction thehigher relaxation frequency)20 its low value at Tc indicates thatfor studied material interlayer polar coupling is weak. The low
dielectric response in the SmAPA phase is consistent with theproposed antiferroelectric model of this phase.
The effect of dc bias on the relaxation mode was also examinedin both polar phases. In the SmAPR phase the relaxation
frequency increased, simultaneously with decreasing dielectricstrength, under increasing bias voltage (Fig. 7(a)). This is because
bias filed suppresses the collective motion of molecular dipoles.
This behaviour is consistent with the expected ferroelectric-likecharacteristic of the SmAPR phase. By contrast, in the SmAPA
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However the increase of the bias voltage above the threshold (theelectric field required to impose ferroelectric state) results innearly total suppression of the mode (Fig. 7(b)). The relaxation
originating from non-collective movement of molecular dipolesis scarcely affected by a dc bias field.

This journal is ª The Royal Society of Chemistry 2011

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