PHYSICAL REVIEW E 85, 011702 (2012)

Viscoelasticity of ambient-temperature nematic binary mixtures of bent-core and rodlike molecules
P. Sathyanarayana,1 V. S. R. Jampani,2 M. Skarabot,2 I. Musevic,2 K. V. Le,3 H. Takezoe,3 and S. Dhara1,*
1

School of Physics, University of Hyderabad, Hyderabad 500046, India
2
J. Stefan Institute, Jamova 39, SLO-1000 Ljubljana, Slovenia
3
Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1-S8-42 O-okayama,
Meguro-ku, Tokyo 152-8552, Japan(Received 21 October 2011; published 11 January 2012)
We report measurements of the temperature variations of physical parameters in ambient-temperature nematic
liquid crystal mixtures of bent-core (BC) and rodlike molecules (5CB): birefringence n; static dielectric
constants || and ⊥ ; splay K11 and bend K33 elastic constants; rotational viscosity γ1 ; and diffusion coefficients
D|| and D⊥ of a microsphere. Both n and || decreases rapidly with increasing BC concentration, whereas ⊥
remains almost constant. At a shifted temperature (e.g., T − TNI = −10 ◦ C), K11 increases by ∼50% and K33
decreases by ∼80% compared to pure 5CB when the BC concentration is increased to ∼43 mol % in the mixture.
Viscosities parallel and perpendicular to the director, η|| , η⊥ , which are nearly equal to the Miesowicz viscosities
η2 and η3 , respectively, were obtained by D|| and D⊥ using the Stokes-Einstein relation. Both the viscosities atroom temperature increase by 60 and 50 times, respectively, whereas γ1 increases by 180 times (at ∼43 mol %)compared to the corresponding values of pure 5CB. The stiffening of K11 and exorbitantly large enhancement
in all the viscosities at a higher mol % of BC indicate that the viscoelastic properties are highly impacted by
the presence of smectic clusters of BC molecules that results from the restricted free rotation of the moleculesalong the bow axis in the nematic phase. A possible attachment model of smectic type clusters of BC molecules
surrounding the microparticle is presented.
DOI: 10.1103/PhysRevE.85.011702

PACS number(s): 61.30.Eb, 61.30.Gd

I. INTRODUCTION

mixtures of rodlike and BC molecules [20–26]. Dodge et al.
showed that the addition of a small concentration of BC
liquid crystals into a calamitic compound system reduces K33
by a factor of 2 or more [22,23], and they also developeda theoretical model. However theoretical predictions underestimated the experimental results. Kundu et al. reported
anomalous trends in the temperature dependence of K11
and K33 in the nematic phase of mixtures of 4-n-octyloxy4-cyanobiphenyl (8OCB) and a BC compound that does notexhibit nematic phase. The results were understood on the basisof their mutual orientations [20] in the presence of short-range
smectic fluctuations. They also reported the evidence of polar
clusters of BC molecules in the nematic phase of a binary
mixture of rodlike and BC molecules [26]. Very recently we
showed that K33 decreases significantly, whereas n and K11
remains invariant in binary mixtures due to the structuralsimilarity of the rod molecule with one-half of the BC
molecule [24].
All the experiments reported so far on BC nematic compounds exhibit the nematic phase much above the ambient
temperature. Thus, studies on ambient-temperature BC NLCsor their mixtures with a calamitic compound could be rewarding from both the fundamental and application points of view.
In this paper we report the measurement of birefringence n;static dielectric constants || and ⊥ ; splay K11 and bend K33
elastic constants; rotational viscosity γ1 ; diffusion coefficients
D|| , D⊥ of a microsphere; and the corresponding viscosities
η|| , η⊥ of ambient-temperature liquid crystal mixtures of BC
and rodlike molecules. We show that the results are distinctly
different than in previously studied mixtures. We find that theaddition of BC to rodlike NLCs significantly increases theviscosities. High viscosities are disadvantageous and a matterof concern for room-temperature BC compounds to be usefulfor applications.

Low molecular weight liquid crystals made of rodlike
molecules are commonly used for liquid crystal displays(LCDs). Usually multicomponent liquid crystal mixtures thatexhibit a wide temperature range of the nematic phase areprepared to achieve optimum physical properties. Continuous
effort over the decades to improve physical properties thatenhances the display performance led to the discovery ofmany new liquid crystals with different molecular shapes andstructures. In this context bent-core (BC) liquid crystals havecreated worldwide interests after the discovery of electrooptical switching in achiral BC compounds [1]. Many newphases of the so-called B phases and several new results
based on the polarity and chirality are summarized in some
excellent reviews [2–4]. To bring out just the effect ofmolecular shape on the physical properties, the BC nematichas been chosen for its simplicity, and consequently various
new experimental results have been reported. For example,
it is reported that BC nematic liquid crystals (NLCs) exhibit
an opposite magnitude relation in splay-bend elastic constants[5,6], unusual electroconvection [7–9], giant flexoelectricity[10,11], large flow viscosity [12,13], the Kerr coefficient [14],and induced [15] and spontaneous biaxiality [16,17]. However,there are unresolved issues related to the alignment of thedirector in conventional liquid crystal cells [18] or phasebiaxiality of pure BC NLCs [19]. Hence BC molecules havebeen added as dopants in some well characterized uniaxial
rodlike compounds, and the effect of molecular shape on thephysical properties of the mixtures is investigated. There aresome interesting reports on the curvature elasticity of binary*

sdsp@uohyd.ernet.in

1539-3755/2012/85(1)/011702(9)011702-1©2012 American Physical Society

P. SATHYANARAYANA et al.

PHYSICAL REVIEW E 85, 011702 (2012)

II. EXPERIMENTAL

The experimental cells were made of two indium tin oxide(ITO) coated glass plates with circularly patterned electrodes.
The plates were spin coated with polyimide (AL-1254), cured
at 180 ◦ C for 1 h, and rubbed antiparallely using a rubbing
machine for planar or homogeneous alignment of the sample.
In order to get homeotropic alignment, ITO plates were spincoated with polyimide (JALS-204) and cured at 200 ◦ C.
Glass-bead spacers with diameter ∼5 μm were mixed witha UV curable adhesive. The cell thickness was measured byusing a fibre optic spectrometer (Ocean Optics, HR-4000)
with an accuracy of ±1%. The empty cell was heated andfilled with the sample in the isotropic phase. The textures wereobserved, and the phase transition temperatures of the mixtures
were measured using a polarizing optical microscope (Nikon,
LV100 POL) and a temperature controller (Instec, HCS 402).
The perpendicular component of the static dielectric constant
was measured in a planar cell using an impedance analyzer(Novocontrol, Alpha-A). In the case of a parallel componentof dielectric constant (|| ), the effective dielectric constant
was measured from 0.01 to 20 V in steps of 0.02 V using
an LCR meter (Agilent, 4980A). The experimental variationof a voltage dependent dielectric constant tends to saturate
at high voltages. The linear part of the dielectric constantis plotted against 1/V and extrapolated to 1/V = 0 to
obtain || at various temperatures. The measured values agree
well with the measurements made in an independent cell.
The voltage dependent optical retardation in the planar cell
was measured simultaneously by a polarization modulation
technique [27] using a photoelastic modulator (PEM-100,
Hinds Instruments), a helium-neon laser (HT PS-Ec-1, Thor
Labs), and a lock-in amplifier (Ametek, SR-7265). The
modulation frequency was set to 50 kHz. K11 is obtained
directly from the Freedericksz threshold voltage Vth and isgiven by K11 = o (Vth /π )2 , where  = || − ⊥ is thedielectric anisotropy. At strong surface anchoring condition,
for voltages V above the threshold voltage Vth , the retardation
φ is given by the parametric equations [28]:

 π
2
V
1 + κ sin2 (φm ) sin2 (ψ)
2dψ,=
1 + γ sin2 (φm )Vthπ[1 + γ sin2 (φm ) sin2 (ψ)][1 − sin2 (φm ) sin2 (ψ)]
0⎞⎛ π 
[1+γ sin2 (φm ) sin2 (ψ)][1+κ sin2 (φm ) sin2 (ψ)]
2dψne d ⎝ 0no ⎠[1−sin2 (φm ) sin2 (ψ)][1+ν sin2 (φm ) sin2 (ψ)]
φ = 2π−, π2  [1+γ sin2 (φm ) sin2 (ψ)][1+κ sin2 (φm ) sin2 (ψ)]
λ
ne
dψ
0

(1)

(2)

1−sin2 (φm ) sin2 (ψ)

where d is the cell thickness, and the other terms of the
reduced quantities are γ = (|| /⊥ ) − 1, κ = (K33 /K11 ) − 1,and ν = (n2e /n2o ) − 1. φ is the z-dependent tilt angle, and φmis the maximum tilt angle at the middle of the cell (z = d/2)
and is substituted with sin(φ) = sin(φm ) sin(ψ). The sample
retardation at higher voltage is fitted to the above equations
by an iterative procedure to get the bend elastic constant
K33 [20,29]. Experimentally measured K11 and K33 of pure
5CB agrees well with the previously reported values [30]. To
verify the anchoring condition, we put the lower limit of theintegration as a fit parameter α in Eqs. (1) and (2) during
fitting. α was found to be less than 1◦ at all temperatures,
implying the strong anchoring at the surfaces. Moreover weestimated the anchoring energy using the high electric fieldtechnique [31] in pure 5CB as well as in one mixture (20 mol%). The estimated anchoring energy is ∼ 0.5 × 10−4 J/m2 inboth the samples, suggesting the surface anchoring condition is
sufficiently strong. It may be mentioned that the flexoelectriceffect in unconventional liquid crystals could be significant
and can influence K33 measurements. From voltage dependent
dielectric measurements, it was shown by Brown et al. that it
can slightly underestimate K33 when the flexoelectric effectis neglected [32]. Usually in voltage dependent dielectricmeasurement, the sample area is large (>100 × 10−6 m2 ),the measured data is the average response over the wholesample area, and the accuracy in the measurement is somewhat
less. In our electro-optic experiment we measured retardation
over a small region (<1 × 10−6 m2 ) using the photoelastic
modulator and expected that such effect is minimal. Further

Kundu et al. [33] reported that the mixture of BC and rodlike
compounds exhibit only homeotropic alignment because of alarge positive self-energy due to a high flexoelectric coefficient
at a higher concentration of BC molecules. In their study theindividual compounds as well as the mixtures show smectic
phases at lower temperature. In our samples no smectic phases
are present, and we observe both homeotropic and planaralignment. Hence the flexoelectric contribution is expected tobe negligibly small, and it can only affect the absolute accuracy
in the measurements particularly at a very high concentrationof BC molecules.
The rotational viscosity γ1 was measured in a planar cellby using a phase-decay-time measurement technique [34]. An
arbitrary signal generator (Tektronix, AFG3102) was used toapply a sinusoidal voltage at a frequency of 4.111 kHz, anda photomultiplier tube (Hamamatsu, H6780-01) was used tomeasure the time dependent transmitted intensity. A small
voltage Vb corresponding to the first maxima or minima wasapplied depending on transmission intensity such that the total
phase retardation of the sample was nπ , where n is an integer.
At time t = 0, the bias voltage Vb was switched off and therelaxation transmission intensity change of the liquid crystal
cell was measured with an oscilloscope (Tektronix, TDS
2012B). This procedure was repeated at various temperatures.
The time dependent transmittance at a particular temperature
in a planar cell is given by [34]011702-2

I (t) = Io sin2 {[tot − δ(t)]/2},(3)

VISCOELASTICITY OF AMBIENT-TEMPERATURE . . .

PHYSICAL REVIEW E 85, 011702 (2012)

where Io is the maximum intensity change and tot is
the total phase difference. The optical phase difference
δ(t) for small director distortion can be approximated as
δ(t) = δo exp(−2t/τo ), where δo is total phase difference ofa liquid crystal under bias voltage Vb that is not far fromthe Freedericksz threshold voltage Vth . In case δo is close
to nπ , δ(t) becomes δ(t) = δo exp(−4t/τo ). The slope of thevariation ln[δo /δ(t)] with time t yields the relaxation timeτo . The rotational viscosity of liquid crystals is given by
γ1 = τo K11 π 2 /d 2 , where d is the thickness of liquid crystal
sample.
To measure the diffusion coefficients D|| , D⊥ , we used
a videomicroscopy technique where the Brownian motionof a tiny silica microsphere was tracked. The silica microspheres of diameter 0.98 μm (Bangs Laboratories) weredispersed in a 0.5% water solution of octadecyldimethyl(3-trimethoxysilylpropyl) ammonium chloride (DMOAP) andmixed for several minutes. The microspheres were then rinsed
with distilled water several times and dried for 30 min at
120 ◦ C. The dried microspheres were dispersed in the liquid
crystal mixtures with an approximate concentration of 0.1%.
Uniform colloidal dispersion was obtained by mechanicalmeans like vortexing and sonication. The particles wereobserved under an inverted polarizing microscope (Nikon
Eclipse, TE2000-U) with a water immersion microscope
objective lens (100×). The Brownian motion of an isolated
microsphere was video recorded for at least 300 s, and theposition was determined with the help of an appropriatecomputer program with an accuracy of ±3 nm. The histogramof the microparticle displacements is Gaussian, and theprobability P that the particle would diffuse a certain distances in the time interval τ is given by
P = P0 exp−s 2,
2 (τ )

(4)

where (τ ) is the width of the Gaussian distribution and P0 is
the normalization constant. The diffusion coefficients paralleland perpendicular to the director (D|| and D⊥ ) of the thermal
motion are obtained using the relation D||,⊥ = ||,⊥ /4τ .
III. RESULTS AND DISCUSSION
A. Samples and phase behavior

We studied various mixtures of the BC nematic compound3-[4-(4-dodecyloxybenzylideneamino)benzoyloxy]-4hexylphenyl 4-(4-dodecyloxybenzylideneamino)-benzoate
and the calamitic nematic compound pentacyanobiphenyl(5CB). The chemical structures and the phase transition
temperatures of the compounds are shown in Fig. 1(a).
The synthesis and some preliminary characterization of
the BC compound have already been reported [35]. Boththe compounds exhibited the nematic phase at ambient
temperature and antagonistically oriented resultant dipoles
with respect to their long axes. The phase diagram of thebinary mixtures is shown in Fig. 1(b). It is interesting to notethat initially nematic-isotropic transition temperature TNI is
increasing with increasing mol % of the BC compound andreaches to a maximum at ∼30 mol % of the BC compound
before it decreases at a much higher mol %. Thus, theFIG. 1. (Color online) (a) Chemical structures of the compounds
and the phase transition temperatures. (b) Phase diagram of the binary
mixture.

nematic stability in the intermediate region of concentrations
is enhanced in the mixture.
B. Optical and static dielectric constant measurements

In our physical measurements we restricted the mixing ratioof the BC up to ∼43 mol % beyond which the dielectricanisotropy tends to change the sign and the viscosity is so highthat the Brownian motion of the microparticle appears to be
seized.
All the mixtures were studied carefully under the opticalpolarizing microscope, and it was found that all of them exhibit
the uniaxial nematic phase. The temperature variation of nof the mixtures is shown in Fig. 2(a). In each mixture, n
is increasing with decreasing temperature. At a fixed shifted
temperature (i.e., T − TNI ), n is decreasing and tends tosaturate at a much higher mol % of the BC compound. The
temperature variation of n can be approximated by the Haller
extrapolation formula [36], n = n0 (1 − T /T ∗∗ )β , whereβ, T ∗∗ , and the birefringence of the perfectly aligned sample,
n0 , are the fit parameters. The fit parameters are listed inTable I. T ∗∗ is slightly higher than TNI , and β is of theorder of ∼0.2 instead of 0.5 as predicted by the mean field
theory [37]. Similar values of β were also reported in manyother calamitics [38] and in binary mixtures of calamitics
and BC compounds [26]. The order parameter S of the longmolecular axis was estimated using the relation S = n/n0 .
The temperature variation of S of the mixtures are shown in
Fig. 2(b). S increases in the nematic phase as the temperatureis reduced. S decreases slightly from ∼0.54 to ∼0.5 whenthe mol % is increased to 5.9 and finally tends to saturate
beyond it.
The variations of static dielectric constants as a functionof shifted temperature are shown in Fig. 3. It is observed

011702-3

P. SATHYANARAYANA et al.

PHYSICAL REVIEW E 85, 011702 (2012)

FIG. 3. (Color online) Temperature variations of dielectric constants || (closed symbols) and ⊥ (open symbols). Continuous lines
are drawn as a guide to the eye.

about their long axes, so that the effect of transverse dipole
moment is suppressed; as a result ⊥ remains constant. The
longitudinal component of dipole moment of the BC molecule
is much less than the 5CB molecule, and hence the longitudinal
dipole moment per unit volume decreases with increasing mol% of BC molecules; as a result || can decrease.
C. Splay and bend elastic constant measurements
FIG. 2. (Color online) Temperature variation of (a) birefringencen and (b) estimated orientational order parameter S of the mixtures.

that the parallel component of dielectric constant || decreases
rapidly with increasing mol % of the BC compound, whereas
the perpendicular component ⊥ remains almost constant.
The dielectric anisotropy is positive ( > 0) and reduces
significantly with increasing mol % of the BC compound.
Since both the molecules have large dipole moments which
are presumably oriented antagonistically in the nematic phase,i.e., in case of 5CB the dipole moment is parallel to the long
axis, and in case of the BC molecule it is almost perpendicular
to the bow axis. In the isotropic phases of the mixtures, it is fair
to assume that the isotropic dielectric constant iso ∝ μ2 , where
μ is the mean-square effective molecular dipole moment [39].
The reduction in iso with increasing mol % of BC as observed
indicates that the effective dipole moments in the isotropic
phase is reduced. In the nematic phase the bow axis is assumed
to be parallel to the director, and the molecules rotate freely

The splay and bend elastic constants (K11 , K33 ) were
measured from the voltage dependent retardation in theplanar cell as described earlier. Variations of the normalized
retardation as a function of the applied voltage for a few
mixtures are shown in Fig. 4. It is noticed that the Freedericksz
threshold voltage increases with increasing mol % of the
BC compound. The temperature variations of both K11 andK33 are shown in Fig. 5. In each mixture, K11 increases
as the temperature is reduced [Fig. 5(a)], and at a shifted
temperature, K11 increases with increasing mol % of the
BC compound. In the case of K33 it is noticed that at a
shifted temperature, K33 decreases rapidly [Fig. 5(b)] withincreasing mol % of the BC compound. At 20 mol % of
the BC compound, K33 is almost independent of temperature
except very close to TNI . Further, at ∼43 mol % of the BCcompound, K33 increases initially and then decreases slightly
as the temperature is reduced, showing a broad maximum

TABLE I. Fit parameters n0 , T ∗∗ , and β obtained from Haller’s
extrapolation formula for the mixtures.
Mol %TNI (K)T ∗∗ (K)

n0

β

0
2.7
5.9
11.9
20
42.9

308.2
311.8
315.2
319.2
322.4
321.8

308.9
312.2
315.6
319.5
322.6
322.1

0.33
0.33
0.31
0.30
0.29
0.27

0.18
0.19
0.20
0.20
0.20
0.18

FIG. 4. (Color online) Voltage dependent normalized optical
retardation φ for the various mol % of the BC compound.

011702-4

VISCOELASTICITY OF AMBIENT-TEMPERATURE . . .

K33 (pN)

K11 (pN)
K33 (pN)

0

− 15

− 10
T-TNI (°C)

0

10

2

00.0 M
02.7 M
05.9 M
11.9 M
20.0 M
42.9 M− 20

TNI -T=1.5 °C
TNI -T=3.0 °C
TNI -T=6.0 °C
TNI -T=10 °C

5

0

−5

− 15

− 10
T-TNI (°C)

40

(b)

1

0

−5

20
30
Mol % of BC

6

TNI -T=1.5 °C
TNI -T=3.0 °C
TNI -T=6.0 °C
TNI -T=10 °C

(b)
K33
K11

8

TNI -T=10 °C

K11 (pN)5(a)00.0 M
02.7 M
05.9 M
11.9 M
20.0 M
42.9 M

− 20
10

10

(a)

10

5

PHYSICAL REVIEW E 85, 011702 (2012)

0

10

20
30
Mol % of BC

40

FIG. 5. (Color online) (a) Temperature variations of (a) splay K11and (b) bend K33 elastic constants at the various mol % of the BCcompound. Continuous lines are drawn as a guide to the eye.

FIG. 6. (Color online) (a) Variation of K11 (closed circles) andK33 (open symbols) with the mol % of the BC compound at various
shifted temperatures and (b) variation of K33 /K11 with the mol % of
the BC compound.

approximately at T − TNI  −6 ◦ C. In Fig. 6(a) variationsof K11 and K33 at some shifted temperatures are presented
with the mol % of the BC compound. It is observed that K11
increases by 50% with respect to pure 5CB at T − TNI =−10 ◦ C, whereas K33 decreases almost exponentially before
it reaches to a minimum value when the mol % of the BCcompound is increased to ∼43%. At a shifted temperature,e.g., T − TNI = −10 ◦ C, the reduction is ∼80% compared topure 5CB. The ratio of K33 /K11 as a function of the mol % at a
few temperatures is shown in Fig. 6(b). The ratio reduces below
1 at ∼5 mol % of the BC compound and reaches to ∼0.2 at∼43 mol %. Similar crossover was also reported in polymeric
nematic liquid crystals, and it was shown that the ratio reducesto 0.83 when the effective chain length to diameter ratio
increases by a factor of 3 [40]. In the present binary system theratio is significantly smaller (∼0.2 at ∼43 mol %) and mainly
due to the low K33 of the BC compound as seen in pure BC
NLCs [5].
There have been a few reports on the measurements of K11
and K33 in binary mixtures of rodlike and BC molecules asmentioned earlier. In these studies it was found that both K11
and K33 decrease with increasing mol % of the BC compound,and the rate of decrement of K33 with the mol % of BC isseveral times faster than K11 . Very recently we found that K33
shows similar behavior, i.e., it decreases significantly, whereas
K11 remains almost constant in the binary mixtures due to thestructural similarity of the rod molecule with one-half of the
BC molecule [24]. The increase of K11 with increasing mol %of BC was reported recently [41], as observed in the present
study. The reduction in K33 is explained due to the coupling of
the bent shape of the molecules with the bend distortion which
results in reduction of bend stress. The anomalous temperaturedependence of K33 at ∼43 mol % (i.e., it decreases withdecreasing temperature) is due to the enhanced orientational
order S of the BC molecules. A similar observation at a higher
mol % of BC was also reported by Kundu et al. [20]. It suggeststhat the coupling of the bent shape of the molecule with the bent
distortion is stronger at higher S. To gain more insight on therelationship between the order parameter and elastic constants,
we plotted the variations of K11 and K33 as a function of nin Fig. 7. The experimental data are fitted with Kii ∝ nx ,where x is a fit parameter. The fit parameters are listed inTable II. It is observed that the exponent x for K11 is 2 up
to 11.9 mol % and is consistent with the prediction of mean
field theory (K11 ∝ S 2 ). It increases to 2.8 at ∼43 mol %. A
similar value of x (2.9) was reported in the case of pure BC
NLC [5]. On the other hand the exponent x for K33 is ∼2 up
to 5.9 mol % and starts decreasing beyond this concentration(Table II). It clearly indicates that the coupling of bent shapewith the bent distortion is significant beyond 5.9 mol % of the
BC compound. At a higher concentration (particularly at 20
and ∼43 mol %), K33 initially increases and finally decreases
with increasing n showing a maxima at n ∼ 0.14. The
initial increase is due to the increasing orientational order S as
expected. However with increasing S the coupling with bend
distortion also gets stronger; as a result K33 starts to decrease.

011702-5

P. SATHYANARAYANA et al.

PHYSICAL REVIEW E 85, 011702 (2012)

FIG. 7. (Color online) (a) Variations of K11 and K33 with n at
the various mol % of the BC compound. Continuous lines are fit to
the equation Kii ∝ nx .

For the enhancement of K11 , at least two considerations
can be made. K11 can increase in the mixture due to anincrease in S as predicted in the mean field theory (K11 ∝ S 2 ).
On the contrary, we observe [Fig. 2(b)] that S decreases
slightly with increasing mol % of the BC compound. Thus
the stiffening of K11 can not be attributed to the enhancementof S. Another possible explanation is based on the evolutionof the transverse correlation (i.e., along the short axis) of
two or more BC molecules that is developed due to therestricted free rotation along the long axis. This can leadto the formation of smectic cybotactic clusters of a few BC
molecules. The larger exponent (i.e., x > 2) for K11 at ahigher mol % of BC may be a pointer to the existence ofa short axis correlation. There are several reports suggesting
the formation of smectic clusters in BC NLCs or in binary
mixtures of rod and BC molecules [26,42,43]. It is possiblethat the enhancement of K11 is due to the presence of suchclusters whose corresponding elastic constants are expected tobe larger. The number density and size of these clusters canincrease with an increasing concentration of BC molecules.
D. Viscosity measurements

Finally we discuss the measurements of diffusion coefficients D|| and D⊥ of the microsphere, where the subscripts
refer to the direction in relation to the director and rotational
viscosity γ1 of the mixtures. The microparticle undergoes
TABLE II. Fit parameters obtained from Kii ∝ nx for the
mixtures.
Mol % x for K11

 x for K33

0
2.7
5.9
11.9
20
42.9

2.0
2.0
2.0
2.0
2.2
2.8

2.2
2.2
2.1
1.7

FIG. 8. (Color online) (a) Typical histograms of the displacements of a microsphere of diameter 0.98 μm in direction paralleland perpendicular to the nematic director at room temperature for the
mixture with 10 mol % of the BC compound. Dotted lines are fit
Eq. (4) to the corresponding data. (b) Variations of diffusion
coefficients parallel D|| and perpendicular D⊥ to the director with the
mol % of the BC compound at 25 ◦ C (open symbols) and TNI + 5 ◦ C(closed symbol). (c) Estimated viscosities using the Stokes-Einstein
relation. Continuous lines are drawn as a guide to the eye.

Brownian motion and the histogram of the displacement has
a Gaussian shape. Typical histograms, i.e., the variation of
the displacement of a colloid in a particular interval overa specified time (counts) along and perpendicular to thedirector in a planar aligned cell, are shown in Fig. 8(a). The
variations of diffusion coefficients D|| and D⊥ with the mol% of the BC compound are shown in Fig. 8(b). The isotropic
diffusion coefficient Diso is significantly higher than D|| andD⊥ of the nematic phase, and all of them decrease as the
mol % of the BC compound is increased. The corresponding

011702-6

VISCOELASTICITY OF AMBIENT-TEMPERATURE . . .

PHYSICAL REVIEW E 85, 011702 (2012)viscosities can be obtained from the Stokes-Einstein equation η||,⊥ = kB T /(6π rD||,⊥ ), where r is the radius of the
microparticle. From the experimental arrangement we can
expect the relationship η||  η2 and η⊥  η3 , where η2 , η3
are the Miesowicz viscosities with flow direction parallel andperpendicular to the director, respectively.
It may be pointed out that a dipole defect is associated witheach microparticle. Hence the effective hydrodynamic radiusof the microparticle could be slightly larger than the actual
size. However, it appears not to affect the measurements,
since the estimated values of η|| and η⊥ for pure 5CB atroom temperature in a planar cell agree well with Miesowicz
viscosities η2 and η3 , respectively. The estimated viscosities
against the mol % of BC are shown in Fig. 8(c). It is noticed thatthe isotropic viscosity ηiso increases only slightly with the mol% of the BC compound. This is perhaps due to the molecularsize effect of BC molecules in the mixtures. In all the mixtures
η|| < η⊥ as expected, and both of them increase relatively
more rapidly than ηiso with the mol % of the BC compound[Fig. 8(c)]. For example, η|| /ηiso  12 and η⊥ /ηiso  9 at ∼43
mol % of the BC compound at ambient temperature. Such alarge enhancement in Miesowicz viscosities with increasing
mol % of the BC compound indicates the existence of clusters
as mentioned earlier. Experimental evidence on the existenceof such clusters has been revealed in various other experiments[26,42–47].

FIG. 9. (Color online) (a) Variation of the rotational viscosity
γ1 of various mixtures as a function of the shifted temperature.
(b) Variation of the γ1 with the mol % of the BC compound at a
few shifted temperatures. Ratio of γ1 /η||,⊥ with the mol % of the BCcompound is also shown in the inset. Continuous lines are drawn asa guide to the eye.

We measured the rotational viscosity γ1 of the mixtures atvarious temperatures which is also expected to be influenced
by the presence of cybotactic clusters. The variation of γ1
for the mixtures are shown in Fig. 9; Fig. 9(a) shows theshifted-temperature dependence of γ1 for a few mixtures of thedifferent mol % of the BC compound, and Fig. 9(b) shows the
BC concentration dependence at a few shifted temperatures.
It is found that γ1 increases rapidly with the mol % of the BCcompound. For example, at T − TNI = −10 ◦ C, it increases
almost by a factor of 180 when the mol % of the BC compoundis increased to ∼43 in the mixtures. Measurement of γ1 withthe phase-decay technique and flow viscosities using a pulsed
magnetic field of a few pure BC NLCs have been reported
recently [13,48,49]. It was reported that the ratio  = γ1 /η
is significantly less for the BC compound ( ∼ 0.02) thanthe calamitic liquid crystals mainly due to the large value offlow viscosity [48]. On the contrary, in the present study weobserve that  increases remarkably with the mol % of the
BC compound compared to pure 5CB. For example, in pure
5CB, ⊥ = γ1 /η⊥ ∼ 1 and || = γ1 /η|| ∼ 1.5 and increase to
12 and 16, respectively [Fig. 9(b), inset] when the mol % of
the BC compound is increased to ∼43 in the mixture. It may
be noted that all viscosities γ1 , η2 , and η3 increase with the
mol % of the BC compound, but the rate of increment of γ1 ismuch faster than the other two.
Such exorbitantly large increase in γ1 can not be accounted
for by the increase of the mol % of BC molecules with large
molecular weight alone in the mixtures. The relatively fasterenhancement of γ1 with respect to the Miesowicz viscosities
can be attributed to the presence of smectic clusters of BC
molecules. In the present mixtures both the compounds do
not have any smectic phases. Nevertheless the smectic clusters
are formed inherently due to the highly restricted free rotationof the BC molecules along the bow axis. Further, the BC
molecules presumably align perpendicularly on the surfaceof the microparticle due to the DMOAP coating. In that casethe steric barrier and partial pinning of the molecules on
the microsphere’s surface prevent free rotation of the BC
molecules along the bow axes, and a few BC molecules

FIG. 10. (Color online) Schematic representations of the director
orientation around a microparticle with a dipole defect (a) in
rodlike molecules and (b) in the mixture. The small dot above themicroparticle is the center of the dipole defect. Note the attachmentof a few clusters of BC molecules surrounding the microparticle.

011702-7

P. SATHYANARAYANA et al.

PHYSICAL REVIEW E 85, 011702 (2012)

can form smectic clusters or permanent layers at the surface
which in principal can reduce the Brownian motion of the
microparticle and can increase the Miesowicz viscosities.
Schematic representations of such clusters surrounding the
microparticle with dipole defects are shown in Fig. 10. It may
be mentioned that no Brownian motion was observed in thepure BC compound at room temperature. This is perhaps dueto the very large viscosities and presence of a few smectic
layers surrounding the microparticle.
IV. CONCLUSIONS

the Miesowicz viscosities; and (4) a two order of magnitudeenhancement in the rotational viscosity with increasing mol %of the BC compound. The stiffening of K11 and extraordinarily
large viscosities are attributed to the presence of smectic
clusters of BC molecules in the mixtures. Present studies
suggest that an ambient-temperature BC nematic could be
advantageous as a dopant for optimizing the birefringence,dielectric constants, and elastic properties of low molecularweight liquid crystals, but the enhanced viscosities in the
mixtures are highly disadvantageous as well as a matter ofconcern and have to be reduced for practical application.

In conclusion, measurements of optical, dielectric, andviscoelastic properties of room temperature nematic liquid
crystals with rodlike and BC molecules have shown thefollowing interesting results: (1) a mutual alignment of thebow axis in 5CB is such that the effective dipole moment in
the isotropic and in the nematic phases parallel to the director
is reduced; (2) a significant stiffening of splay and large
softening of bend elastic constants; (3) a large reduction inboth the diffusion coefficients in the nematic phase comparedto the isotropic phase and hence an unprecedented increase in

S.D. gratefully acknowledges the support from UGC-CAS
School of Physics and DST, Government of India, Project No.
SR/NM/NS-134/2010 for financial support. P.S. acknowledges
support through a CSIR-UGC fellowship. V.S.R.J acknowledges (EC)7OP Marie Curie ITN Project HIERARCHY Grant
No. PITN-GA-2008-215851 and the Slovenian Research
Agency (ARRS) Contract No. P1-0099. We thank Professor J.
Mieczkowski for the BC compound.

[1] T. Niori, T. Sekine, J. Watanabe, T. Furukawa, and H. Takezoe,
J. Mater. Chem. 6, 1231 (1996).
[2] H. Takezoe and Y. Takanishi, Jpn. J. Appl. Phys. 45, 597 (2006).
[3] J. Etxebarria and M. B. Ros, J. Mater. Chem. 18, 2919 (2008).
[4] R. A. Reddy and C. Tschierske, J. Mater. Chem. 16, 907 (2006).
[5] P. Sathyanarayana, M. Mathew, Q. Li, V. S. S. Sastry, B. Kundu,
K. V. Le, H. Takezoe, and S. Dhara, Phys. Rev. E 81, 010702(R)(2010).
[6] M. Majumdar, P. Salamon, A. Jakli, J. T. Gleeson, and S. Sprunt,
Phys. Rev. E 83, 031701 (2011).
[7] D. Wiant, J. T. Gleeson, N. Eber, K. Fodor-Csorba, A. Jakli, andT. Toth-Katona, Phys. Rev. E 72, 041712 (2005).
[8] S. Tanaka, S. Dhara, B. K. Sadashiva, Y. Shimbo, Y. Takanishi,
F. Araoka, K. Ishikawa, and H. Takezoe, Phys. Rev. E 77, 041708(2008).
[9] S. Tanaka, H. Takezoe, N. Eber, K. Fodor-Csorba, A. Vajda, and
A. Buka, Phys. Rev. E 80, 021702 (2009).
[10] J. Harden, B. Mbanga, N. Eber, K. Fodor-Csorba, S. Sprunt,
J. T. Gleeson, and A. Jakli, Phys. Rev. Lett. 97, 157802 (2006).
[11] K. V. Le, F. Araoka, K. F. Csorba, K. Ishikawa, and H. Takezoe,
Liq. Cryst. 36, 1119 (2009).
[12] E. Dorjgotov, K. Fodor-Csorba, J. T. Gleeson, S. Sprunt, andA. Jakli, Liq. Cryst. 35, 149 (2008).
[13] P. Sathyanarayana, T. Arun Kumar, V. S. S. Sastry, M. Mathews,
Q. Li, H. Takezoe, and S. Dhara, Appl. Phys. Express. 3, 091702(2010).
[14] S. Dhara, F. Araoka, M. Lee, K. V. Le, L. Guo, B. K. Sadashiva,
K. Song, K. Ishikawa, and H. Takezoe, Phys. Rev. E 78,
050701(R) (2008).
[15] J. A. Olivares, S. Stojadinovic, T. Dingemans, S. Sprunt, andA. Jakli, Phys. Rev. E 68, 041704 (2003).
[16] B. R. Acharya, A. Primak, and S. Kumar, Phys. Rev. Lett. 92,145506 (2004).

[17] L. A. Madsen, T. J. Dingemans, M. Nakata, and E. T. Samulski,
Phys. Rev. Lett. 92, 145505 (2004).
[18] A. Kumar, K. V. Le, J. K. Kim, H. Takezoe, and S. Dhara, Liq.
Cryst. 38, 917 (2011).
[19] B. Senyuk, H. Wonderly, M. Mathews, Q. Li, S. V. Shiyanovskii,
and O. D. Lavrentovich, Phys. Rev. E 82, 041711 (2010).
[20] B. Kundu, R. Pratibha, and N. V. Madhusudana, Phys. Rev. Lett.
99, 247802 (2007).
[21] R. Pratibha, N. V. Madhusudana, and B. K. Sadashiva, Science
288, 2184 (2000).
[22] M. R. Dodge, C. Rosenblatt, R. G. Petschek, M. E. Neubert, andM. E. Walsh, Phys. Rev. E 62, 5056 (2000).
[23] M. R. Dodge, R. G. Petschek, C. Rosenblatt, M. E. Neubert, andM. E. Walsh, Phys. Rev. E 68, 031703 (2003).
[24] P. Sathyanarayana, B. K. Sadashiva, and S. Dhara, Soft Matter
7, 8556 (2011).
[25] P. Salamon, N. Eber, A. Buka, J. T. Gleeson, S. Sprunt, andA. Jakli, Phys. Rev. E 81, 031711 (2010).
[26] B. Kundu, R. Pratibha, and N. V. Madhusudana, Eur. Phys. J. E
31, 145 (2010).
[27] T. C. Oakberg, SPIE Proceedings 3121, 19 (1997).
[28] G. Barbero and L. R. Evangelista, An Elementary Course on
the Continuum Theory for Nematic Liquid Crystals (World
Scientific, Singapore, 2000).
[29] S. W. Morris, P. Palffy, and D. A. Balzarini, Mol. Cryst. Liq.
Cryst. 139, 263 (1986).
[30] A. Bogi and S. Faetti, Liq. Cryst. 28, 729 (2001).
[31] H. Yokoyama and H. A. Sprang, J. Appl. Phys. 57, 4520
(1985).
[32] C. V. Brown and N. J. Mottram, Phys. Rev. E 68, 031702 (2003).
[33] B. Kundu, A. Roy, R. Pratibha, and N. V. Madhusudana, Appl.
Phys. Lett. 95, 081902 (2009).
[34] S. T. Wu and C. S. Wu, Phys. Rev. A 42, 2219 (1990).

ACKNOWLEDGMENTS

011702-8

VISCOELASTICITY OF AMBIENT-TEMPERATURE . . .

PHYSICAL REVIEW E 85, 011702 (2012)[35] J. Matraszek, J. Mieczkowski, J. Szydowska, and E. Gorecka,
Liq. Cryst. 27, 429 (2000).
[36] I. Hallar, Prog. Solid-State Chem. 10, 103 (1975).
[37] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals,
2nd ed. (Clarendon Press, Oxford, 1993).
[38] S. Dhara and N. V. Madhusudana, Eur. Phys. J. E 13, 401(2004).
[39] H. Froehlich, Theory of Dielectrics, 2nd ed. (Clarendon Press,
Oxford, 1968).
[40] S. D. Lee and R. B. Meyer, Phys. Rev. Lett. 61, 2217
(1988).
[41] S. T. Hur, M. J. Gim, H. J. Yoo, S. W. Choi, and H. Takezoe,
Soft Matter 7, 8800 (2011).
[42] C. Baily, K. Fodor-Csorba, J. T. Gleeson, S. N. Sprunt, andA. Jakli, Soft Matter 5, 3618 (2009).

[43] S. Stojadinovic, A. Adorjan, S. Sprunt, H. Sawade, and A. Jakli,
Phys. Rev. E 66, 060701(R) (2002).
[44] O. Francescangeli and E. T. Samulski, Soft Matter 6, 2413
(2010).
[45] S. H. Hong, R. Verduzco, J. C. Williams, R. J. Twieg, E. DiMasi,
R. Pindak, A. Jakli, J. T. Gleeson, and S. Sprunt, Soft Matter 6,4819 (2010).
[46] O. Francescangeli, F. Vita, C. Ferrero, T. Dingemans, and E. T.
Samulski, Soft Matter 7, 895 (2011).
[47] M. Cifelli and V. Domenici, Phys. Chem. Chem. Phys. 9, 1202
(2007).
[48] E. Dorjgotov, K. Fodor-Csorba, J. T. Gleeson, S. Sprunt, andA. Jakli, Liq. Cryst. 35, 149 (2008).
[49] P. Tadapatri, U. S. Hiremath, C. V. Yelamaggad, and K. S.
Krishnamurthy, J. Phys. Chem. B 114, 1745 (2010).

011702-9