Soft Matter
PAPER

Cite this: Soft Matter, 2016,12, 2960

Unusual temperature dependence of elastic
constants of an ambient-temperature discotic
nematic liquid crystal†
D. Venkata Sai,a G. Mirri,bc P. H. J. Kouwer,b R. Sahoo,a I. Musevicc and
Surajit Dhara*a
We report the first experimental studies on the temperature dependence of viscoelastic properties of a

Received 11th January 2016,
Accepted 4th February 2016
DOI: 10.1039/c6sm00065g

room temperature discotic nematic liquid crystal. The splay elastic constant is greater than the bendelastic constant and both show unusual temperature and order parameter dependence. The rotational
viscosity is remarkably larger than conventional calamitic liquid crystals. We provide a simple physicalexplanation based on the columnar short-range order to account for the the unusual temperaturewww.rsc.org/softmatter

dependence of the elastic constants.

I. Introduction
Discotic liquid crystals (DLCs) consist of disc-like molecules inwhich the cores are surrounded by flexible alkyl side chains.1,2
Discotic nematic LCs are very useful for wide and symmetricalviewing angles of LCDs3 and optical compensating films.4
They mostly exhibit columnar and nematic phases and relatively
a few are known to exhibit the lamellar phase.5–7 The physicalstudies on discotic nematic LCs are meagre compared to thenumber of compounds synthesized. So far physical propertiesof a few discotic nematic liquid crystals have been reported.
For example, Heppke et al. have measured the dielectric andelastic properties of hexakis((4-alkylphenyl)ethynyl)benzene.8,9Raghunathan et al. and Warmardam et al. measured the elastic
properties of truxene ester compounds.10,11 Mourey et al. havereported various physical measurements on the triphenylenehexa(alkoxybenzoate) nematic discotic compounds.12 In allthese compounds the nematic phase appears much above theambient temperature. In 2000, Kumar et al. reported the first
synthesis of room temperature discotic nematic LCs.13,14
The range of the nematic phase is very wide and the nematic toglass transition occurs much below the ambient temperature.
However, so far there has been no report on the viscoelastic
properties of these compounds. In this paper we report the firstaSchool of Physics, University of Hyderabad, Hyderabad-500046, India.
E-mail: sdsp@uohyd.ernet.inbInstitute for Molecules and Materials, Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ, Nijmegen, The NetherlandscSoft Matter Materials Lab, Solid State Physics Department, Jožef Stefan Institute,Jamova cesta 39, 1000, Ljubljana, Slovenia and Faculty of Mathematics andPhysics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sm00065g

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studies on the birefringence, dielectric and viscoelastic propertiesof a room temperature discotic nematic LC. We show that thecompound exhibits unusual viscoelastic properties, pointing to
the existence of a temperature dependent short-range columnar
order in the nematic phase.

II. Experimental
The liquid crystal cells were made of two indium-tin-oxide (ITO)
coated glass plates with patterned electrodes. These plates werespin coated with polyimide AL-1254 and cured at 180 1C for 1 hourand rubbed in an antiparallel way. It gives the homeotropicalignment of the discotic nematic liquid crystal. It may bementioned that AL-1254 is usually used for the planar alignment of
rod-like molecules. A typical cell thickness used in the experiment
was about 8 mm and measured within 1% accuracy. The empty
cell was heated and the sample was filled in the isotropic phase.
The alignment of the sample was observed using a polarising
optical microscope (Olympus BX51) and a temperature controller(Mettler FP 90). The birefringence was obtained by measuring thetransmitted intensity with the help of two crossed Glan–Thompson
polarizers, a He-Ne laser source and a photodetector. The dielectric
constant was measured using a LCR meter (Agilent, E4980A).
The parallel component of the dielectric constant (parallel to thedirector, i.e., perpendicular to the plane of disc-molecules) was
measured at an applied voltage of 0.5 V (below the Freedericksz
threshold voltage). The homogeneous alignment of the director in
the cells could not be obtained by using standard alignment layers.
Hence, to measure the perpendicular component of the dielectric
constant (i.e., parallel to the disc-molecules), we have taken the
homeotropic cell and used a lock-in-amplifier (LIA) together with aThis journal is © The Royal Society of Chemistry 2016

Papervoltage amplifier.15,16 At sufficiently high voltage the director wascompletely reorientated to the homogeneous state. The bendelastic constant (K33) was obtained from the electric field induced
Freedericksz transition and is given by K33 = e0|De|(Vth/p)2, where
De = e||  e> is the dielectric anisotropy and Vth is the thresholdvoltage. The splay elastic constant (K11) was estimated from thenumerical fitting of the voltage dependent dielectric constant withthe theoretical variation.17,18 The rotational viscosity (g1) was
measured using the phase-decay-time measurement technique.19
The LCR meter was used to apply voltage at a frequency of 1000 Hz
and a photodetector was used to measure the time dependenttransmitted intensity. A small voltage (Vb) corresponding to thefirst maxima was applied depending on the transmission intensity
such that the total change of the phase retardation of the sample
was np, where n is an integer. At time t = 0, the bias voltage (Vb) wasremoved and the transmission intensity change of the liquid
crystal cell was measured using an oscilloscope (Tektronix, TDS
2012B). The time dependent intensity at a particular temperatureis given by:19 I(t) = I0 sin2[Dtot  d(t)]/2, where I0 is the maximum
intensity change and Dtot is the total phase difference. The timedependent optical phase difference d(t) for small director distortion can be approximated as d(t) = d0 exp(2t/t0), where d0 is thetotal phase difference of the liquid crystal under bias voltage (Vb)that is not far from the Freedericksz threshold voltage (Vth).
The slope of the plot ln[d0/d(t)] with time (t) gives the relaxation
t0 K33 p2time (t0). The rotational viscosity (g1) is given by g1 ¼,
d2
where d is the thickness of the sample. This procedure wasrepeated in the entire nematic range at different temperatures.

III. Results and discussion
The chemical structure and the phase transition temperatures of
the compound are shown in Fig. 1. It is a pentaalkynylbenzene
derivative having a combination of branched alkoxy chains and awide nematic range. The compound was synthesized as per thereported procedure.13,14

Fig. 1 Chemical structure and phase transition temperatures of the discotic
compound used in the experiment.

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Soft Matter

Fig. 2 Photomicrographs obtained in the homeotropic cell at various
voltages under a polarising optical microscope. White arrows indicate
the rubbing direction.

The alignment of the sample was checked using a polarising
optical microscope at various applied voltages and temperatures.
Fig. 2(a) shows a dark texture where the short axes of the discs arealigned perpendicular to the plane of the substrate (homeotropicalignment). When the applied voltage is greater than Freedericksz
threshold voltage, the field of view becomes brighter and the color
change indicates increasing retardation with applied voltage(Fig. 2(a)–(d)). This suggests that the director is continuously
tilting from homeotropic to the planar state with increasing
voltage. It may be mentioned that no electroconvection wasobserved in the applied voltage and frequency range.
To measure the birefringence (Dn) of the nematic phase(ND), we first measured the voltage dependent birefringence atroom temperature. Beyond the Freedericksz threshold voltage,
Dn increases and saturates above 20 V. The saturation of
Dn indicates the planar state of the director. We applied 25 V(higher than the saturation voltage) to measure the temperature dependent birefringence. The temperature variation of Dn
is shown in Fig. 3. The birefringence is negative i.e., (ne  n0) o 0
and Dn jumped to C0.13 from zero at the nematic–isotropic

Fig. 3 Variation of birefringence (Dn) as a function of temperature (measured
at l = 632.8 nm). (inset) Variation of dielectric anisotropy (De) as a function oftemperature. Frequency of measurement: 411 Hz.

Soft Matter, 2016, 12, 2960--2964 | 2961

Soft Matter(NI) transition and gradually decreased as the temperature islowered. At room temperature (T  TNI = 55 1C) it reaches
approximately 0.2. This is comparable to the other discotic
nematic compounds having similar molecular structures.8
We measured the dielectric dispersion at various temperaturesand observed that the parallel component (e||) does not show any
dielectric relaxation whereas the perpendicular component (e>)
exhibits dielectric relaxation and the relaxation frequency vary withthe temperature in the range of 1 kHz–100 kHz (see the ESI,†ref. 20). The temperature variation of the dielectric anisotropy(De = e||  e>) at a fixed frequency (411 Hz) is also shown in
Fig. 3. The dielectric anisotropy of the ND phase, is very small
and negative (De C 0.18 at T  TNI = 60 1C). This is expected
as the permanent dipoles are mostly confined in the plane ofthe disc.
To obtain splay (K11) and bend (K33) elastic constants, wemeasured the voltage dependent dielectric constant, eeﬀ (V)at various temperatures in the ND phase. The variation of
the normalised dielectric constant at a few representative
temperatures is shown in Fig. 4. It is clearly observed that thethreshold voltage increases with decreasing temperature.
The temperature variation of K11 and K33 is shown in Fig. 5(a).
Interestingly we observe K11 4 K33 at all temperatures and theyshow very diﬀerent temperature dependence. For example, as thetemperature is reduced from the NI transition point, boththe elastic constants increase but K11 increases more rapidly
than K33. Below T  TNI = 45 1C, K11 saturates whereas K33
shows a kind of diverging behavior. The temperature variationof K11/K33 is also shown in the inset of Fig. 5(a). It is observedthat the ratio increases as the temperature decreases andreaches a maximum around T  TNI = 40 1C. Below thistemperature it reduces rapidly as the ambient temperature isapproached. To gain insight into the relationship between theorder parameter and the elastic constants, we plotted thevariation of K33 and K11 with Dn (near NI transition) according

Fig. 4 (a) Variation of the normalised dielectric constant (eeﬀ  e||)/De at a
few representative temperatures. The continuous line is the best fit withthe theoretical variation. Schematic representation of splay and bend
distortions of the discotic nematic liquid crystal.

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Paper

Fig. 5 (a) Variation of splay (K11) and bend (K33) elastic constants as a functionof temperature. (inset) Variation of the ratio of K11/K33 with temperature.
(b) Variation of K11 and K33 with Dn. Corresponding temperature range isalso shown in the upper abscissa (green colour). Continuous lines are best
fits to the equation, Kii p Dnx.

to the mean-field, Kii p S2 p Dn2, where S is the orderparameter.21 Interestingly we observed that K33 p Dn1.1 andK11 p Dn4.1 respectively (Fig. 5(b)). Thus both K33 and K11
exhibit significant deviations from the mean-field behavior.
There are a very few reports on the temperature dependenceof splay and bend elastic constants of the ND phase. Sokalski
et al. theoretically predicted that for discotic nematic with along-range orientational order, K11/K33 4 1.22 This has been
experimentally verified by a couple of experiments. For example,
Heppke et al., measured both the splay and bend elastic
constants of a homologous series of non-polar nematic discotic
compounds showing I to ND transition.8,9 They reported that inmost of the compounds, K11/K33 4 1. Warmardam et al.
measured the elastic constants of two discotic compoundswith a polar molecule.11 In addition to the ND phase thesecompounds also exhibit two columnar phases. They reported
that in the ND phase, K11/K33 4 1. Raghunathan et al., measured
the elastic properties of truxene compounds and found that
K11/K33 o 1.10 In their compounds the nematic phase appeared
between two discotic columnar phases and it was attributed toThis journal is © The Royal Society of Chemistry 2016

Paperthe short-range columnar order. Phillips et al., studied the elastic
properties of triphenylene discotic nematic liquid crystals.23
These compounds exhibit I to ND phase transition much above theambient temperature. They found that the ratio, K11/K33 is very high(C5) and decreases (C3) as the temperature is decreased.23 It has
been reported that three types of discotic nematic can be envisaged
based on the local organization of the disc-like molecules andthey are known as ND, Ncol and NL. In the Ncol and NL phases
there is a short-range columnar order and a short-range 2D latticerespectively.24 The eﬀect of a short-range columnar order in the
discotic nematic has also been studied by computer simulation.25
It was reported that the onset of growth in the orientational orderin the parent phase is found to induce the translational order,
arising from short-range columnar structures. We attribute thisunusual temperature dependence of elastic constants to the shortrange columnar order. We provide a simple physical explanationthat accounts for the eﬀect of short-range columnar order on the
splay and bend distortion (Fig. 6). A short-range columnar orderdoes not hinder the splay distortion hence the splay elastic
constant is not significantly aﬀected. On the other hand theshort-range columnar order can increase the bend stress as it isenergetically unfavorable to bend the columns. This leads to a
rapid increase of K33 than K11 and possibly a cross-over may takeplace at a much lower temperature with the growth of orientational
order. Thus the elastic properties at a higher temperature are dueto the long-range orientational order. The short-range columnar
order increases as the temperature is decreased and the elastic
constants show unusual temperature dependence.
We further measured the rotational viscosity (g1) of the ND
phase as a function of temperature. It may be mentioned thatthe direct value of g1 of discotic nematic has not been reported
so far. The normalized transmission intensity at some representative temperatures are shown in Fig. 7(a). It is observed thatat lower temperature (e.g., T  TNI =  57.4 1C) it (intensity)
takes about 200 s to decay to the zero value. Linear variationof ln[do/d(t)] with time is shown in the inset of Fig. 7(a).
The rotational viscosity g1 increases very rapidly with decreasing
temperature (Fig. 7(b)). For example, near the NI transition
g1 = 0.1 Pa s and it increases to C200 Pa s at room temperature.
Warmerdam et al. directly measured the temperature dependenceof g1/Dw, where Dw is the diamagnetic susceptibility anisotropy.26
Assuming a typical value of Dw they estimated that g1 for discotic

Soft Matter

Fig. 7 (a) Time dependent normalised transmitted intensity after theremoval of bias voltage (Vb) for various temperatures. (inset) Variation ofln[do/d(t)] with time at T  TNI = 41.5 1C. (b) Variation of rotational
viscosity (g1) as a function of temperature. Continuous line is the best fit.
(inset) A linear variation of ln(g1/Dn) with 1/T.

nematic is about 10 to 100 times larger compared to the rod-like
mesogens. In our compound it is about three orders of magnitudelarger than conventional calamitic liquid crystals and this could
be attributed to the eﬀect of the short-range columnar order. In
addition, such a large rotational viscosity could be due to theeﬀect of glass transition below the room temperature. In thissample the glass transition temperature is reported to beat 35 1C.13 The rotational viscosity can be written as
g1 B S exp(W/kT), where S is the order parameter and k is theBoltzmann constant.27 Since S p Dn, we show the variation ofln(g1/Dn) with 1/T in the inset of Fig. 7(b). The estimatedactivation energy is about 837 meV, which is about double
compared to the values known in conventional calamitic liquid
crystals.28 It may be mentioned that theoretically it has beenshown that the microscopic friction coeﬃcient of discotic
nematic shows an exponential temperature dependence witha large activation energy.29

IV. Conclusion
Fig. 6 Schematic representation of (a) splay and (b) bend distortion in a
discotic nematic liquid crystal. Columnar short-range order is shown using
dotted red lines.

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In conclusion, we measured birefringence, dielectric and curvatureelastic properties of an ambient-temperature discotic nematicSoft Matter, 2016, 12, 2960--2964 | 2963

Soft Matter

liquid crystal with a wide temperature range. Both the birefringenceand the dielectric anisotropy are negative. Near the NI transition,
K11 and K33 exhibit quartic and linear variation with birefringence
respectively. This is not in accordance with the prediction ofmean-field. As the ambient temperature is approached the elastic
constants show unusual temperature dependence. The rotational
viscosity is three orders of magnitude high at room temperatureand the corresponding activation energy is more than double
compared to conventional calamitic mesogens. These results
suggest that viscoelastic properties near the ambient temperature
are dominated by the eﬀect of the short-range columnar order.
Further experiments are underway to quantify the temperaturedependent columnar order from the X-ray scattering studies.

Acknowledgements
We gratefully acknowledge support from the DST PURSE.
Venkata Sai D acknowledges UGC for fellowship and thankK. Sravan, Department of Electronics, UoH for helping in the
dielectric measurements. G. M. acknowledges the European
Commission for a Marie Curie Intra European Fellowship(Nemcode IEF-2012-331350), G. M., I. M. and P. K. acknowledge
a Marie Curie ITN (Hierarchy ITN-2007-215851) both the projects
were funded within the 7th European Community Framework
Program. We thank Dr Krishna Prasad from CeNS, Bangalore for
useful discussion.

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