PHYSICAL REVIEW E 87, 012506 (2013)

Antagonistic flexoelectric response in liquid crystal mixtures of bent-core and rodlike molecules
P. Sathyanarayana and Surajit Dhara*
School of Physics, University of Hyderabad, Hyderabad-500046, India(Received 20 October 2012; published 24 January 2013)
We report the measurements of the temperature variations of the flexoelastic coefficient (e∗ /K) of a hostcalamitic liquid crystal (RO) and its mixture with two guest bent-core (BC-120 and BC-60) liquid crystals.
The bent-core (BC) molecules have different core structures and bend angles; namely, θ " 120◦ and " 60◦ ,respectively. We find that e∗ /K is independent of temperature and decreases rapidly with increasing concentrationof BC-120 molecules and changes sign from positive to negative. In mixtures with BC-60, e∗ /K is always positiveand its concentration-dependent variation is not unique. At 7M% it is significantly large (three times) near thenematic-isotropic transition and decreases strongly with reducing temperature. Dielectric measurement suggests
antagonistic orientation of the dipole axes (arrow axes) of the two BC molecules in the host liquid crystal, andbased on this, the opposite sign of e∗ /K is explained.
DOI: 10.1103/PhysRevE.87.012506

PACS number(s): 61.30.Gd, 77.84.Nh

I. INTRODUCTION[15–18]. There are also some reports on the flexoelectricstudies in bimesogenic liquid crystals [4,19–21] with cis
form. In most of these studies, a significant enhancement offlexoelectric effect has been observed and it is expected thatapart from the bistable device it has the potential to be used insensors and microelectric power generators.

The average orientational direction of the molecules inliquid crystals is called director and is denoted by n. In nematic
liquid crystals the director is apolar; i.e., n and −n are physically equivalent. About 40 years ago, Meyer predicted that thenematic liquid crystals can exhibit microscope polarization
due to the distortions in the director field [1]. This is known as
flexoelectric effect. It was shown that the distortion-induced
polarization is given by
P = e1 (∇ · n)n + e3 (∇ × n) × n,(1)

where e1 and e3 are the flexoelectric coefficients connectedto the splay and bend distortions, respectively. Since thena large number of experimental investigations have beenreported and continuous efforts are being made to enhanceand understand this effect in various liquid crystalline systems,
such as palladium-containing nematic [2], chiral nematics[3,4], blue phase liquid crystals [5,6], and lipid bilayers[7]. Flexoelectricity can be demonstrated easily in compounds with asymmetric shape, such as seen in bent-coreor wedge-shaped molecules. Nematic liquid crystals withwedge-shaped molecules and longitudinal dipole moments
can induce flexoelectric polarization when splayed; similarly,
bent-core molecules with transverse dipole moments can
induce the flexoelectric polarization when it is subjected to abend deformation. The flexoelectro-optic effect is linear withapplied field and exploited to make switchable and bistabledevice with submillisecond response time [8]. However, theirapplication is limited due to the small flexoelectric polarizationin conventional liquid crystals with rod-like molecules. It wastheoretically shown by Helfrich [9] that in liquid crystals
with bent-core molecules, e3 ∝ "(b/a)2/3 µ, where µ is thetransverse dipole moment, " is the bend angle, and a andb are the length and breadth of the molecule, respectively.
Recently, a giant flexoelectricity in pure bent-core liquid
crystal was reported by Harden et al. [10]. This triggered
various flexoelectric studies on pure molecules [11–14] as wellas on the binary mixture of rod-like and bent-core molecules*

sdsp@uohyd.ernet.in

1539-3755/2013/87(1)/012506(4)II. EXPERIMENTAL

We used a hybrid aligned nematic (HAN) cell as proposedby Dosov et al. [22] to measure the flexoelastic ratio e∗ /K,
where K is the average elastic constant of the nematic
liquid crystal and e∗ = e1 − e3 . The splay-bend distortion,and hence the polarization, is produced by treating the plateswith appropriate planar and homeotropic alignment layers(Fig. 1). The inplane electric field was applied by using thinand parallel aluminum strips, which also acts as spacers. The
polarization is coupled to the electric field (E) and generates
twist distortion along the perpendicular direction of the cell
(y axis), which is given by φ = −e∗ Ed/πK, where d is thecell thickness. In the present experiment, d = 20 µm, and thegap between the electrodes is 850 µm. We used a motorized
and computer controlled analyzer to measure φ as a functionof applied electric field and e∗ /K was estimated from thebest fit in the linear region. The error in the measurement isabout 7%, considering the errors from both the cell thickness
measurement and the gradient of φ with electric field. It may
be mentioned that we did not observe any domain formationin the cell within the range of applied field.
In this paper, we report the measurement of e∗ /K as
a function of temperature of a calamitic liquid crystal RO
and its mixture with two bent-core liquid crystals (BC-120
and BC-60) having different molecular structures and bend
angles. We found that e∗ /K is almost temperature independent
and, moreover, it decreases rapidly and changes sign withincreasing concentration of BC-120 molecules. In mixtureswith BC-60 molecules, it is positive and increases withconcentration, except at lower concentration. We present aphysical model on the orientation of the arrow axes of the two
bent-core molecules that explains the experimental results.

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PHYSICAL REVIEW E 87, 012506 (2013)

P. SATHYANARAYANA AND SURAJIT DHARA

Angle (radians)

0.2
⊕
ˆ

FIG. 1. (Color online) (a) Geometry of the HAN cell used in themeasurement of e∗ /K. (b) Twist deformation produced by an inplanedc electric field along the y axis. The top plate is coated with ahomeotropic alignment layer (θh " 0◦ ) and the bottom plate is coatedwith a planar alignment layer (θp " 90◦ ).
III. RESULTS AND DISCUSSION

We prepared two mixtures with different concentrations,
namely 4.5M% and 7M% of bent-core compounds with thecalamitic compound, RO (Fig. 2). The phase diagram of thebinary mixture of BC-120 with RO has already been reported[23]. The core of BC-120 is a resorcinol derivative substituted
at the 1,3 position and the bent angle is about 120◦ . There
are some reports on the measurements of various physicalproperties of these mixtures [24,25]. The compound BC-60
has a naphthalene core in which Schiff’s based side wings aresubstitutes on 1,2 positions. The synthesis and characterizationof this compound was reported by Lee et al. [26]. It exhibits
only the liquid crystalline SmA phase and it was suggested
from the x-ray studies that the arrow axis of the molecule isaligned perpendicular to the SmA layer. We found that thebinary mixture of BC-60 and RO exhibits nematic phase in the
low concentration range (<10M%).
We measured the azimuthal twist angle (φ) as a functionof applied field for all the mixtures and the host compound.
A representative variation of φ with the applied dc electricfield in the mixtures with BC-120 molecule is shown in
Fig. 3. It is noticed that the slope decreases and changes
sign from positive to negative with increasing concentration

0.0 M
4.5 M
7.0 M

0

−0.2
−40

−20

0
Voltage (V)20

40

FIG. 3. (Color online) Variation of field-induced azimuthal twist
angle as a function of voltage in binary mixture of RO and BC120 molecules. Solid lines represent the best fit to the equation
φ = −e∗ Ed/π K.

of BC-120 molecules. The temperature variation of e∗ /Kis shown in Fig. 4. It is noticed that e∗ /K decreases
and changes sign with increasing concentration of BC-120
molecules [Fig. 4(a)]. For example, in the host compound(RO), at a shifted temperature T − TNI = −5◦ C, e∗ /K "1.7 Cm−1 N−1 , and it reduces to " −0.48 Cm−1 N−1 when
the concentration of BC-120 molecules is 4.5M%. It further
reduces to about −1.9 Cm−1 N−1 when the concentration isincreased to 7M%. Assuming a linear variation, e∗ /K ofpure BC-120 liquid crystal is expected to be 30 times larger(negative) than the host compound. The temperature variationof e∗ /K in the binary mixture of BC-120 and 8OCB (octyloxy
cyanobiphenyl) was reported by Kundu et al. [17]. They foundthat e∗ /K is negative and the magnitude increases significantlywith increasing concentration of BC-120 molecules. Theysuggested that e∗ /K in pure BC-120 compound could be 20
times larger than that of 8OCB. Thus, in the present mixture
the enhancement is significantly more than they reported. The
compound RO has relatively larger transverse component ofe*(Cm -1N -1)
K2

Cr 98.5 °C SmA2 109.5 °C N 125.0 °C I

(a)
0

−2

0.0 M
4.5 M
7.0 M

120°

e*
(Cm -1N -1)
K

Cr 114 °C B2 128.5 °C I

60°

5

0
−15
Cr 84.4 °C SmA 151.6 °C I

FIG. 2. (Color online) Chemical structures and phase transition
temperatures of the compounds. The first, second, and third compounds are designated as RO, BC-120, and BC-60, respectively. The
phase transition temperatures are indicated below each compound.

0.0 M
4.5 M
7.0 M

(b)

−10

T-T NI (°C)

−50FIG. 4. (Color online) Temperature variation of flexoelastic ratioe∗ /K for (a) mixtures with BC-120 and (b) mixtures with BC-60
molecules for three different concentrations, 0, 4.5, and 7M%.
Continuous lines are drawn as guides to the eye.

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PHYSICAL REVIEW E 87, 012506 (2013)

0.6

(a)
n

0.4
0.0 M
4.5 M
7.0 M

0.2
0

Dielectric anisotropy (∆ε)

dipole moment than 8OCB and appears to be a good hostfor BC-120 molecules for large flexoelastic response, perhaps
due to its partial structural similarity; i.e., the aromatic andaliphatic parts of the rod are matched with one arm of the
BC-120 molecule. Further, it is observed that e∗ /K is almost
independent of temperature [Fig. 4(a)]. It is expected, as
both e∗ and K are proportional to the square of the orderparameter (S 2 ). e∗ in the host compound RO is positive; i.e.,e1 > e3 . Since the dopant molecule (BC-120) has a large
dipole moment along the arrow axis (i.e., transverse dipole),
the bend distortion of the medium gives rise to a large e3
with increasing concentration of BC-120 molecules, and as aresult e∗ /K changes sign beyond a particular concentration.
In Fig. 4(b), we show the temperature variation of e∗ /K forthe mixtures with BC-60 molecules. It remains positive but
reduces slightly in the mixture (4.5M%) compared to the hostcompound (RO) and also exhibits weak temperature dependence. Interestingly, it increases significantly in the mixture with 7M%. For example, at a shifted temperature
T − TNI = −2◦ C, e∗ /K " 1.5 Cm−1 N−1 in host compoundRO, and in the mixture it is " 5.8 Cm−1 N−1 , i.e., about fourtimes larger, and decreases rapidly with reducing temperature.
Thus, in the mixture (with BC-60), the sign of e∗ /K is
antagonistic in the sense that e∗ /K is largely positive comparedto the largely negative value at the same concentration with
BC-120 molecules. Hence, it is possible to tune significantly
the magnitude and sign of flexoelastic coefficient by adding
appropriate bent-core molecules.
To get an idea about the orientation of BC-60 and BC120 molecules in the mixture, we measured the dielectricanisotropy (%& = &|| − &⊥ ) as a function of temperature ata frequency of 4111 Hz. The perpendicular component ofdielectric constant (&⊥ ) was measured by using a LCR meter(Agilent 4980A) below the Freedericksz threshold voltage asa function of temperature. To estimate the parallel component(&|| ), we measured dielectric constant in the same cell as afunction of voltage. Since the dielectric anisotropy is positive,
it increases with voltage and saturates at higher voltages.
The linear part is plotted against 1/V and fitted to a straightline. The extrapolated value of dielectric constant at 1/V = 0
provides &|| . The temperature variation of %& of all the samples
is shown in Fig. 5. Measurement of viscoelastic properties and%& of the mixtures with BC-120 was reported earlier [24]. It
is observed that %& is small and positive [Fig. 5(a)]. At any
shifted temperature it decreases with increasing concentrationof BC-120 molecules. This indicates that the arrow axes areorientated perpendicular to the director as shown schematicallyin Fig. 5(a). With increasing concentration, two or more
BC-120 molecules can form pairs or clusters; as a result,quadrupolar contribution to the flexoelastic properties can also
be significant. The temperature variation of %& of mixtureswith BC-60 is not unique, in the sense that it decreases at
4.5M% and then tends to increase at 7M% [Fig. 5(b)]. The
increase of %& at 7M% suggests that the effective dipole
moment along the director is increased; i.e., the arrow axisof the molecule is orientated parallel to the director as the
direction of large dipole moment of the molecule is along
the arrow axis. On the other hand, the decrease of %& at
4M% cannot be understood based on this model. However,it may be noted that the terminal units of BC-60 molecules

Dielectric anisotropy (∆ε)

ANTAGONISTIC FLEXOELECTRIC RESPONSE IN A . . .

0.6

(b)

n

0.4
0.0 M
4.5 M
7.0 M

0.2
0
−15

−10

−5
T-T NI (°C)

0FIG. 5. (Color online) Variation of dielectric anisotropy (%&)
with temperature for (a) mixtures with compound BC-120 and(b) mixtures with compound BC-60. Cell thickness " 8 µm. The
orientations of the bent-core molecules in the respective mixtures
and a local domain (dotted circle) are shown schematically in theinset. Dotted lines are drawn as guides to the eye.

are alkoxy chains, which have conformational freedom. As aresult, at low concentration of BC-60 molecules, the transverse
component of the dipole moment can increase, and hence %&is reduced. Further, BC-60 can be considered wedge-shaped
molecules that can generate substantial splay distortion in thehost calamitic sample, reducing the steric interaction, and form
local domains in which a bent-core molecule is surrounded bya few rod-like molecules [Fig. 5(b)], as indicated in the recent
x-ray studies of Lee et al. [18]. In addition, these domains will
have asymmetric charge distributions as a result quadrupolar
moment contributes significantly to the flexoelectric coefficients. We conjecture that with increasing concentration,
the conformational freedom of individual B-60 molecules inthe domain is reduced and the longitudinal components ofdipole moments can also get weakly correlated; as a result,%& can again increase. Presence of such local domains in
the medium is expected to increase e1 more significantly
than e3 , as a result, e∗ /K is large and positive [Fig. 4(b)].
The effect of conformational freedom on the flexoelastic
coefficient in 8OCB liquid crystal was experimentally studied
by Dosov et al. [27]. They reported that e∗ /K decreases with
reducing temperature. Using the Landau-de Gennes theory,
Osipov [28] showed theoretically that it can be understoodbased on the average conformational degrees of freedom ofalkoxy chains. The anomalous temperature dependence ofe∗ /K in the present mixture is expected to originate fromsimilar conformational degrees of freedom of terminal alkoxy
chains. We also measured the splay elastic constant (K11 ) in
these mixtures (with BC-60), and the details will be reported
elsewhere. Interestingly, we found that in the mixture, K11012506-3

PHYSICAL REVIEW E 87, 012506 (2013)

P. SATHYANARAYANA AND SURAJIT DHARA

decreases with increasing concentration of BC-60 molecules.
For example, at a shifted temperature T − TNI = −2◦ C, inthe host compound RO, K11 " 4.2 pN and in 7M% mixture
K11 " 2.4 pN, respectively. Thus, K11 is reduced in the
mixture due to spontaneous splay deformation caused by the
BC-60 molecules as shown schematically in Fig. 5(b).

The arrow axes of the BC-120 molecules in the mixture arealigned perpendicular to the director, whereas they are aligned
parallel to the director in the case of BC-60 molecules. We
showed that the appropriate selection of bent-core moleculesin the binary mixture could provide a viable route to greatly
enhance and tune the sign of the flexoelectric properties.

IV. CONCLUSIONSACKNOWLEDGMENTS

In conclusion, we have measured the flexoelastic coefficientof a binary mixture with bent-core molecules having two
different bend angles. We showed that both the magnitude
and sign can be tuned over a large range by adding small concentration of bent-core molecules with different bend angles.

We gratefully acknowledge the support from the DST(SR/NM/NS-134/2010) and CSIR [03(1207)/12/EMR-II]. We
thank B. K. Sadashiva and S. K. Lee for the BC-120 and BC-60
compounds. P.S. acknowledges UGC for financial support
through a fellowship.

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