Applied Physics Express 3 (2010) 091702

Rotational Viscosity of a Bent-Core Nematic Liquid Crystal
Paladugu Sathyanarayana, Tatipamula Arun Kumar, Vanka Srinivasa Suryanarayana Sastry,Manoj Mathews1 , Quan Li1 , Hideo Takezoe2 , and Surajit Dhara
School of Physics, University of Hyderabad, Hyderabad 500046, India
1
Liquid Crystal Institute, Kent State University, Kent, OH 44242, U.S.A.
2
Department of Organic and Polymeric Materials, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan
Received July 29, 2010; accepted August 21, 2010; published online September 10, 2010
We report the detailed measurements of the rotational viscosity ( 1 ) of a bent-core nematic liquid crystal exhibiting positive dielectric anisotropy bymeasuring the decay time of the optical phase retardation of the sample. In the nematic phase,  1 ’ 0:25 Pa s (e.g., at T =TNI ’ 0:92, where TNI isnematic to isotropic phase transition temperature.), which is only slightly larger than the values known for several conventional calamitic nematic
liquid crystals.  1 starts to increase rapidly below a reduced temperature T =TNI ’ 0:9 showing the effect of short-range smectic fluctuations. Thetemperature dependence of  1 far from the nematic to smectic-C transition temperature is fitted well with the Osipov–Terentjev theory.
# 2010 The Japan Society of Applied Physics
DOI: 10.1143/APEX.3.091702

he several physical properties of thermotropic
liquid crystals are optimized for practical applications. Among them, rotational viscosity  1 is a very
important parameter that governs the response time of liquid
crystal devices (LCDs). It depends upon the molecularstructures, intermolecular interactions, and temperature.
There are several experimental and theoretical studies1–6)
on the rotational viscosity of nematic liquid crystals withrod-shaped molecules (calamitic liquid crystals). Theinterest in studying and understanding the structure-property
relation in bent-core liquid crystals has increased recently.
Various physical properties, such as ﬂexoelectric coeﬃcient,7) electroconvection,8,9) Kerr eﬀect,10) and elastic
constants,11) have been measured and reported to besigniﬁcantly diﬀerent from those of known conventionalcalamitic liquid crystals. A signiﬁcant contribution of thebent shape and the intermolecular association is revealed inmany of these physical properties. Recently, the rotational
viscosity and ﬂow viscosity of a bent-core nematic liquid
crystal with negative dielectric anisotropy have beenmeasured by Dorjgotov et al.12) by using pulsed magnetic
ﬁeld and electrorotation, respectively. They reported thatthe rotational viscosity  1 is almost 10 times and the ﬂow
viscosity is 100 times larger than those of the conventionalcalamitic liquid crystals. In this paper, we report themeasurement of  1 of a bent-core nematic liquid crystal
with positive dielectric anisotropy as a function oftemperature by using the decay time measurement of thephase retardation of liquid crystal cells. We show that therotational viscosity for the present compound is only
slightly larger than that for the calamitic nematic, and theeﬀect of strong short-range smectic ﬂuctuations arises as thetemperature is reduced. The temperature-dependent data canbe ﬁtted well with the Osipov–Terentjev4) theory that gives
rise to the activation energy similar to the values of calamitic
liquid crystals.
We used phase-decay-time measurement of a parallelaligned liquid crystal (LC) cell under small excitation
voltage. Two indium–tin-oxide-coated glass plates werespin-coated with alignment layer AL-1254 and cured for one
hour at 180  C and rubbed antiparallel to make planar cells.
The thickness was measured with a spectrometer by theTE-mail address: sdsp@uohyd.ernet.in

Fig. 1. Chemical structure of the bent-core molecule used in theexperiment.

interferometric method, and the typical cell thickness used inthe experiment was 10.3 m. The cell was ﬁlled with thesample in the isotropic phase by using capillary action, andgood alignment was observed. The chemical structure of thecompound used in the experiment is shown in Fig. 1. It
exhibits the following phase transitions: Sm-C 118.5  C N
176.5  C I. The Instec (mK1000) temperature controller wasused for controlling the temperature of the LC cell with anaccuracy of less than 0.1  C. A He–Ne laser ( ¼ 632:8 nm)
was used as a light source. The cell was kept between twocrossed Glan–Thompson polarizers, and the rubbing direction was made 45 to both the polarizer and analyzer.5) A
signal generator (Tektronix AFG3102) was used to apply avoltage at a frequency 4.111 kHz, and a photomultiplier tube
(Hamamatsu H6780-01) was used as a detector to measure
the time-dependent transmitted intensity. A small voltage(Vb ) corresponding to the ﬁrst maxima or minima wasapplied depending on the transmission intensity, such thatthe total phase retardation of the sample was n. At timet ¼ 0, the bias voltage (Vb ) was removed and the relaxationtransmission intensity change of the liquid crystal cell wasmeasured with an oscilloscope (Tektronix TDS 2012B). This
procedure was repeated for several temperatures in the entire
nematic phase. The time-dependent intensity at a particulartemperature is expressed as3)
tot  ðtÞIðtÞ ¼ I0 sin2;
ð1Þ
2
where I0 is the maximum intensity change and tot is thetotal phase diﬀerence. The phase diﬀerence ðtÞ for small
director deformation can be approximated as2tðtÞ ¼ 0 exp ;
ð2Þ
0091702-1# 2010 The Japan Society of Applied Physics

Appl. Phys. Express 3 (2010) 091702

P. Sathyanarayana et al.
0.5
0.4

τo

τo s

0.3
0.2
0.1
0.0

0.88

0.90

0.92

0.94
T TNI

0.96

0.98

1.00

Fig. 2. Time dependent transmission intensity after the removal of thebias voltage Vb at some temperatures.

Fig. 4. Variation of the measured relaxation time  0 (squares) as afunctions of temperature.

Fig. 3. Linear variation of ln½0 =ðtÞ with time (t) at various temperatures. Solid lines are theoretical fits to the experimental data.

Fig. 5. Variation of measured rotational viscosity (circles) and splay
elastic constant K11 (squares) obtained from ref. 11 as a function oftemperature. Solid line is a fit to the theoretical eq. (5).

where 0 is the total phase diﬀerence of the liquid crystal
under bias voltage (Vb ), which is not far from theFreedericksz threshold voltage (Vth ). In case 0 is close ton, ðtÞ becomes4tðtÞ ¼ 0 exp :ð3Þ0and gradually increases with decreasing temperature, andtends to diverge as the smectic-C (Sm-C) phase isapproached. The temperature-dependent splay elastic constant (K11 ) data were collected from our previous measurements ref. 11 to estimate the rotational viscosity ( 1 ) atvarious temperatures. It may be pointed out that we alsomeasured the pretilt angle (p ) in the nematic phase at a few
temperatures by crystal rotational method (CRM).13) The
pretilt angle is very small for example; p ’ 1 at TNI  T ¼
10 . Similar values were also reported by Le et al. on otherbent-core nematic liquid crystals.14) This suggests that thesurface anchoring is suﬃciently strong and the present
rotational viscosity measurements are not aﬀected by thepretilt angle.
The temperature-dependent variation of  1 is shown inFig. 5. It is noted that the value of  1 is about 0.1 Pa s or lessnear the NI transition and increases superlinearly to 0.35 Pa s
with decreasing temperature until the reduced temperature
T =TNI  0:9, and then tends to diverge before the N-toSm-C transition occurs. The measurement of  1 of a bentcore nematic liquid crystal with negative dielectric anisotropy by pulsed magnetic ﬁeld was reported by Dorjgotov
et al.12) According to their report, the rotational viscosity
is almost 10 times larger than those of calamitic liquid
crystals. Such larger rotational viscosity was attributed to theformation of temporary clusters owing to the bent shape ofthe molecules in the sense that the bent shape and transverse

The slope of the plot ln½0 =ðtÞ with time (t) yields therelaxation time (0 ). The rotational viscosity ( 1 ) of theliquid crystal is obtained as
1 ¼

0 K11 2;d2

ð4Þ

where d is the thickness of the liquid crystal sample andK11 is the splay elastic constant. K11 is obtained from theFreedericksz transition given by K11 ¼ 0 ðVth =Þ2 , where
Vth is threshold voltage and  is the dielectric anisotropy.
The time-dependent transmission intensity at various
temperatures is shown in Fig. 2. The phase diﬀerence ðtÞis estimated by using eq. (1). Some representative variationsof ln½0 =ðtÞ with time (t) at various temperatures areshown in Fig. 3. The variation is linear as predicted usingeq. (2). The slope (2= 0 ) is obtained as a ﬁt parameter. Therelaxation time 0 is measured in the entire nematic phase atvarious temperature. The variation of relaxation time 0 as
a function of temperature is shown in Fig. 4. It is observedthat near the NI transition, the relaxation time  0 is ’0:22 s

091702-2# 2010 The Japan Society of Applied Physics

Appl. Phys. Express 3 (2010) 091702

P. Sathyanarayana et al.

dipole moment of the molecules together facilitate theformation of clusters. On the other hand, the present
compound exhibits positive dielectric anisotropy, and thevalue of  1 is slightly larger by a factor of two or three (farfrom the NI transition) compared with that in many calamitic
liquid crystals, suggesting that the formation of temporary
clusters is not signiﬁcant in the present bent-core compound.
Furthermore, the close proximity in the values andtemperature dependencies of  1 data of the present bentcore compound with those of the calamitic materials urges
us to consider and compare the experimental results withthe known theories. For example, in the case of rod likemolecules in the uniaxial nematic phase according to Osipovand Terentjev,4) the rotational viscosity is given by 4  TE1 3 J0 S 1=2
E 1 þ J0 S
 1 ¼ g0
exp; ð5Þ
Tc
kB T ckB T
KB Tc
where g0 is a constant, J0 ¼ BkB Tc , E1 is the activationenergy, and S is the order parameter. The temperaturedependent  1 can be well ﬁtted to the above equation up toT =TNI ¼ 0:88 with the ﬁt parameters g0 ¼ 1:9  104 Pa s,J0 ¼ 48:5 meV, and E1 ¼ 0:525 eV. The ﬁtting of the experimental data with the above equation is shown in Fig. 5,
showing a very good ﬁt. The ﬁt parameters are comparable tothe values known for many calamitic liquid crystals.5)
Finally, we want to brieﬂy comment on the temperaturedependence of  1 . Prasad et al.15) had reported a uniaxialto-biaxial nematic transition at T =TNI  0:93, though later
on, Le et al.16) showed that the medium is uniaxial. Again,
recently, Yoon et al.17) have claimed the existence of thetransition. It is clear, however, that there is no indicationof the transition at the temperature T =TNI  0:93. Moreover, the temperature dependence of the rotational viscosity
was well ﬁtted to the Osipov–Terentjev theory4) over awide temperature range, including the suggested transition
temperature T =TNI  0:93. An upward deviation from theOsipov–Terentjev theory at lower temperature was also
observed in calamitic liquid crystals,5) and was explainedby the pretransitional eﬀect when approaching the crystal
phase. We can also attribute the deviation below (T =TNI 0:9) to the eﬀect of short-range smectic ﬂuctuations. Thus, arapid increase in  0 and, hence, the  1 is due to the onset ofthe smectic short-range ﬂuctuations in the nematic phase.
In conclusion, we showed that the values and temperaturedependence of rotational viscosity in a bent-core nematic

liquid crystal with positive dielectric anisotropy near theNI transition are comparable to those in calamitic liquid
crystals. The temperature dependence of rotational viscosity
shows a strong eﬀect of smectic short-range-order ﬂuctuations. The temperature-dependent viscosity data prior to theonset of smectic ﬂuctuations can be ﬁtted well with the
Osipov–Terentjev theory. Such bent-core compounds may
be useful as a component in the calamitic nematic mixturesto access partially some of the extraordinary physicalproperties of pure bent-core materials, such as the large
ﬂexoelectric coeﬃcient, Kerr coeﬃcient, and negative
elastic anisotropy (K33  K11 ), to optimize for practicalapplication.
Acknowledgments One of the authors Surajit Dhara gratefully
acknowledges the support from Department of Science and Technology,
Government of India for the project number SR/FTP/PS-48/2006 and UGCCentre for Advanced Studies, School of Physics. Paladugu Sathayanarayana
acknowledges Council of Scientiﬁc and Industrial Research–UniversityGrants Commission, India for the fellowship.

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# 2010 The Japan Society of Applied Physics