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Birefringence, permittivity, elasticity and rotational
viscosity of ambient temperature, high birefringent
nematic liquid crystal mixtures
a

a

a

b

b

b

D. Venkata Sai , P. Sathyanarayana , V.S.S. Sastry , J. Herman , P. Kula , R. Dabrowski &Surajit DharaaaSchool of Physics, University of Hyderabad, Hyderabad, 560046 Indiab

Department of Advanced Technologies and Chemistry, Military University of Technology,
Warsaw, Poland
Published online: 06 Dec 2013.

To cite this article: D. Venkata Sai, P. Sathyanarayana, V.S.S. Sastry, J. Herman, P. Kula, R. Dabrowski & Surajit Dhara (2014)
Birefringence, permittivity, elasticity and rotational viscosity of ambient temperature, high birefringent nematic liquid
crystal mixtures, Liquid Crystals, 41:4, 591-596, DOI: 10.1080/02678292.2013.868052
To link to this article: http://dx.doi.org/10.1080/02678292.2013.868052

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Liquid Crystals, 2014
Vol. 41, No. 4, 591–596, http://dx.doi.org/10.1080/02678292.2013.868052

Birefringence, permittivity, elasticity and rotational viscosity of ambient temperature, highbirefringent nematic liquid crystal mixtures
D. Venkata Saia, P. Sathyanarayanaa, V.S.S. Sastrya, J. Hermanb, P. Kulab, R. Dabrowskib and Surajit Dharaa*aSchool of Physics, University of Hyderabad, Hyderabad 560046, India; bDepartment of Advanced Technologies and Chemistry,
Military University of Technology, Warsaw, Poland(Received 5 October 2013; accepted 18 November 2013)

Downloaded by [University of Hyderabad] at 05:06 19 March 2014

We prepared a few binary nematic liquid crystal mixtures with high birefringence (’ 0:4 at room temperature) andstudied the temperature variation of physical properties. All the mixtures show a small, positive dielectricanisotropy and the parallel component of dielectric constant exhibits anomalous temperature dependence.
Orientational order parameter, both splay, bend elastic constants and rotational viscosity are comparatively
larger than conventional low birefringent liquid crystal mixtures. The figure of merit (FoM) of the mixtures arealso calculated as a function of temperature and expected to be useful for various applications.
Keywords: nematic liquid crystal; high birefringence; viscoelasticity; figure of merit

1. Introduction
Liquid crystals used in flat panel display devices are
optically anisotropic, i.e., birefringent. The typicalvalues of birefringence of many commercial mixtures
are in the range of 0.05–0.2. Liquid crystals with highbirefringence have attracted attraction because of
their non-display applications. For example, they are
essential for laser beam steering,[1] tunable focus
lenses,[2] optical switches for telecommunication,
infrared special light modulators,[3] and directionalreflectors.[4] They also have significant importancefor radio frequency applications in the GHz and
THz frequency range,[5,6] broad range filters andholographic devices. Moreover, high birefringenceenhances the display brightness and contrast ratio ofpolymer-dispersed liquid crystal (PDLC), holographic
PDLC, cholesteric liquid crystal display and liquid
crystal gels.[7–9] The birefringence of a liquid crystal
strongly depends on the molecular structure andπ-electron conjugation.[10,11] Usually more linearly
conjugated liquid crystal exhibits larger birefringence.[12] The increase of conjugation length leads
to high melting temperature, decrease of nematic
range, increased viscosity and poor solubility toform eutectic mixtures. One possible way to increase
nematic range is to prepare eutectic mixture of highbirefringent liquid crystals. There are some reports on
the synthesis and optical measurement of high birefringent nematic liquid crystals.[13–23] However, thedetail physical characterisation such as dielectric andviscoelastic measurements are rare. In this paper, we
report on the preparation and detail characterisation*Corresponding author. Email: sdsp@uohyd.ernet.in© 2013 Taylor & Francis

of a few high birefringent mixtures containing quarterphenyl and phenylethynyltolane cores.
2. Experimental
The experimental cells were made of two indium tinoxide (ITO)- coated glass plates with circularly patterned electrodes. The plates were spin coated withpolyimide (AL-1254) and cured at 180°C for 1 h
and rubbed antiparallel way for planar or homogeneous alignment of the sample. For homeotropicalignment, ITO plates were spin coated with polyimide (JALS-204) and cured at 200°C for 1 h. Cells
were made by placing the two plates together,ensuring that the active electrode area overlaps.
The separation was controlled by glass-bead spacers
with diameter 5 μm. The thickness of the empty cell
was measured with 1% accuracy by an interferometric technique using spectrometer (Ocean Optics,
HR-4000). Alignment of the sample was observed
using a polarising optical microscope (Nikon,
LV100 POL) and a temperature controller (Instec,
mk1000). The dielectric constants are measured byusing a LCR metre (Agilent 4980). The perpendicular component of the dielectric constant was measured in planar cell below the Freedericksz
threshold voltage. To measure the parallel component of dielectric constant, the effective dielectric
constant was measured as a function of voltage(0.02–20 V) at a fixed temperature. The experimental variation of the voltage dependent dielectric
constant tends to saturate at high voltages. The
linear part of the dielectric constant is plottedDownloaded by [University of Hyderabad] at 05:06 19 March 2014

592

D. Venkata Sai et al.

against 1/V and extrapolated to 1/V = 0 to obtainjj at various temperatures. The measured value is ingood agreement with the measurement made in an
independent cell.
The optical retardation was measured by using aphase modulation technique with the help of a
Helium–Neon laser (633 nm), a photoelastic modulator (PEM-100) and a lock-in amplifier (DSP-7265). A
sinusoidal voltage of frequency 4111 Hz and an
amplitude up to 20 V at steps of 0.02 V were used
for the measurements of dielectric constant by using
the LCR meter. The dielectric dispersion was measured by an impedance analyser (Novocontrol,
Alpha-A). The retardation and also the sample capacitance were measured simultaneously as a functionof temperature and voltage. The splay elastic constantðK11 ) is obtained from the Freedericksz thresholdvoltage (Vth ) and is given by K11 ¼ 0 ΔðVth =πÞ2 ,where Δ ¼ jj  ? is the dielectric anisotropy. K33
was estimated from the fitting of the voltagedependent optical retardation with the theoretical
calculations.[24–27] Rotational viscosity ðγ1 Þ was
measured using the phase-decay-time measurement
technique.[28–31]

3. Results and discussion
3.1 Birefringence and orientational order parameter
We prepared and studied three different mixtures using
four different nematic liquid crystals. The chemical
structure of the individual compounds and the phasetransition temperatures of the mixtures are shown in
Figure 1. At room temperature, they are nematic andhighly turbid. In each mixture, one compound is common and non-polar with larger wt%. The second compound is polar with isothiocyanate terminal groupcontaining laterally alkyl, fluorine and chlorine substituted and less in wt%. The polar compounds are
mixed with the non-polar host with maximum solubility. All the mixtures have high clearing point and wide
nematic range. The synthesis and phase transition
temperatures of the individual compounds are recently
reported.[11] The temperature variation of birefringence (Δn) of the mixtures are shown in Figure 2. Δnjumps to about ’ 0:22 from 0 at the nematic–isotropic(NI) transition in all the mixtures and reaches to a highvalue of Δn , 0:4 at room temperature. The birefringence of the mixtures increases as follows:
ΔnMix1 > ΔnMix2 > ΔnMix3 . This can be understoodbased on the molecular structure of the individual

Mix-1: SmA 5°C N 121°C I

Mix-2: N 121.9°C I

Mix-3: N 118.3°C I
Figure 1. (colour online) Molecular structure and wt% of the individual compounds and the phase transition temperature of
the mixtures (in cooling). Nematic ! N and Smectic-A ! SmA. The physical appearance of the samples in the bottles atroom temperature are also shown.

Liquid Crystals

0.3
0.2
0.1

Order parameter

0.8
0.6
0.4
0.2
0.0

0.0

–100 –80

–100

–80

–60 –40 –20
T – TNI (°C)

–60

0

–40

20

–20

0

20

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T – T NI (°C)

Figure 2. (colour online) Variation of birefringence (Δn)
and (inset) orientational order parameter ðSÞ of the mixtures
as a function of shifted temperature.

components in the mixture. In all the compounds, asignificant contribution to the Δn is due to the presenceof –C;C– bonds and phenyl rings. Usually, –C;C–
contributes more to Δn than phenyl rings.[11] As weproceed from Mix-3 to Mix-1, we notice that apartfrom a small variation in the lateral groups, the number of phenyl rings decreases and –C;C– groups
increases. Thus the effective conjugation length andhence Δn of the mixture increases.
To estimate order parameter, the temperature variation of Δn can be approximated by the Hallar extrapolation formula.[32] Δn ¼ Δn0 ð1  T =T1 Þβ , where β,T1 are the adjustable parameters, and Δn0 is the birefringence of the perfectly aligned sample. The fit
parameters are listed in Table 1. T1 is slightly higher
than TNI , and β is about ’ 0:18. Similar value of βwas also reported in many other liquid crystals.[33]The order parameter S of the long molecular axis wasestimated using the relation S  Δn=Δno . The temperature variation of S is shown in Figure 2. The
value of S increases with decreasing temperature andat room temperature it is quite high (about S ’ 0.8)
and larger than that of many common liquid crystals.
Similar large order parameter in high birefringent
nematic liquid crystals were also reported by Sekine
et al.[34]The variation of parallel (jj ) and perpendicular (? )components of dielectric constants and the average,ð¼ ðjj þ 2? Þ=3Þ; as a function of temperature isshown in Figure 3(a). The dielectric anisotropy is
positive, i.e., Δð¼ jj  ? Þ > 0 and almost the samein all the mixtures. jj increases up to a certain value
and then decreases significantly near the room temperature. Similar unusual behaviour of jj wasobserved in many compounds showing nematic tosmectic phase transition.[25,35] In addition, in thosecompounds, it was found that ? also tend to increaseat the same temperature and eventually Δ can changesign. It was shown that due to the presmectic order,
the antiparallel correlation of the dipoles parallel tothe director increases and as a result the effective
dipole moment reduces in the nematic phase leading
to the decrease of jj . Similar argument was given forincrease of ? . However, in the present mixtures only
Mix-1 exhibits N – SmA transition around 5 C and
5

Mix-1
Mix-2
Mix-3

(a)
Dielectric constants

0.4
Birefriengence

3.2 Dielectric constants

Mix-1
Mix-2
Mix-3

ε
4

ε
3

ε
–100

–80

–60

–40

–20

0

20

T – TNI (°C)
5.6

(b)

118°C

Mix-2

110°C

Dielectric Constant

0.5

593

90°C

ε

70°C
58°C

4.2

50°C

2.8

ε

38°C
30°C
26°C

103

Table 1. Fit parameters of different mixtures.
MixtureΔnoT1 (°C)TNI (°C)

β

Mix-1
Mix-2
Mix-3

0.55
0.53
0.49

125
125.4
120

121
121.9
118.3

0.18
0.18
0.17

104
105
Frequency (Hz)106

Figure 3. (colour online) (a) Variation of parallel (jj ), perpendicular (? ) components of dielectric constant and ¼ ðjj þ 2? Þ=3 as a function of shifted temperature. (b)The frequency dispersion of real part of the dielectric constants, i.e., jj ðf Þ and ? ðf Þ at various temperatures of Mix2. Solid lines are drawn as guides to the eye.

D. Venkata Sai et al.

Mix-2 and Mix-3 do not show any smectic phase but
some kind of solidification was noted around thistemperature. In addition, ? does not show any
increasing tendency at the same temperature. Thus,
the unusual temperature dependence of jj of the mixtures can not be understood based on the antiparallelcorrelation of dipoles. To understand this, we measured the frequency dispersion of both jj ðf Þ and ? ðf Þ
in one sample (e.g. Mix-2) in the frequency range of
100 Hz – 10 MHz (Figure 3(b)). We note that in boththe components, one relaxation is common (beyond
1 MHz) which comes from the finite resistance of the
ITO electrodes. ? ðf Þ is almost independent of temperature and does not show any dielectric relaxation.
On the other hand jj ðf Þ exhibits another dielectricrelaxation below 1 MHz and the relaxation frequency
decreases rapidly with decreasing temperature. For
example, relaxation frequency at 90°C is about
237 kHz and reduces to 1 kHz at room temperature(26°C). The temperature-dependent dielectric constant was measured at a fixed frequency 4.11 kHz
and the relaxation frequency decreases below thisvalue around 50°C. Hence the unusual decrease ofjj near room temperature is due to the decrease ofrelaxation frequency below the measuring frequency.
The detailed dielectric dispersion measurements of all
the samples will be reported elsewhere.

3.3 Elastic constants
The variation of splay (K11 ) and bend (K33 ) elastic
constants as a function of temperature is shown in
Figure 4. Though K11 is almost the same within theexperimental accuracy, K33 appears to be slightly different in the three mixtures. Both K11 and K33 increase
with decrease of temperature and these values are

Mix-1
Mix-2

30
Elastic constants (pN)

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594

Mix-3

K33

comparatively larger than that of many common(low birefringent) nematic liquid crystals. For
instance, in 5CB, K11 ¼ 5 pN and K33 ¼ 9 pN whereas
in the present mixture (Mix-1), these numbers are 10
and 30 pN, respectively at room temperature. Since
Kii / S 2 ,[36] the large elastic constant could be due tothe large orientational order of the mixtures. It is also
noticed that K33 tends to decrease slightly near theroom temperature at which jj shows anomalous
dependence. This is due to the decrease of the dielectric anisotropy.
3.4 Rotational viscosity
Finally, we discuss the rotational viscosity ðγ1 Þ of the
mixtures in the nematic phase. The intensity of thetransient response of various mixtures are measured.
A representative variation of ln½δo =δðtÞ with time (t)is shown in Figure 5(a). γ1 was calculated from themeasurement of relaxation time (τ o ) and K11 of the
mixtures. The variation of γ1 as a function oftemperature is shown in Figure 5(b). γ1 increases
very rapidly with decrease of temperature. For
instance, at room temperature, this is ’ 1 Pa s
(Mix-2) which is about two orders of magnitudelarger than conventional (low birefringent) nematic
liquid crystals. The rotation viscosity can be written
as γ1 , S expðW =kT Þ, W being the activation energy,
S the order parameter and k the Boltzmann
constant.[35] Since S / Δn, we plotted lnðγ1 =ΔnÞwith 1=T in Figure 5(b) (inset). The estimated activation energy for the three mixtures are 330, 350 and
380 meV respectively and these are comparable to thevalues reported for many low birefringent nematic
liquid crystals.[30]To characterise the performance of the liquid crystal materials, we estimated figure of merit (FoM)
using the formula, FoM ¼ K11 Δn2 =γ1 as a functionof temperature. Figure 6 shows the temperature variation of the FoM. Since, K11 / S 2 / Δn2 , the temperature dependence of FoM can be written as
follows:
FoM ¼ Að1  T =T1 Þ3β expðW =kT Þ:

20

K11

10

–100

–80

–60

–40

–20

0

20

T – TNI (°C)

Figure 4. (colour online) Variation of splay (K11 ) and bend
(K33 ) elastic elastic constants as a function of shifted temperature. Solid lines are drawn as guides to the eye.

(1)

FoM is largest for Mix-1 and reduced in Mix-2 andMix-3. At higher temperature, the FoM of all the
mixtures are reasonably larger than conventional
low birefringent nematic liquid crystals but it
decreases at room temperature. For instance, for
Mix-1, at 95 C, FoM is 15 μm2 /s and decreases to
1.5 μm2 /s near room temperature. The reports on
FoM at room temperature, high birefringent nematic
liquid crystal is rare hence not available for comparative discussion. Though the birefringence is large at

Liquid Crystals(a)room temperature, high viscosity is disadvantageous
especially where fast switching is needed.

120°C

In[δο/δ(t)]

1.5

90°C

4. Conclusion

1.0

0.5
50°C

0.0
0

5

10

20

15

1

(b)

Mix-1, W = 330 meV
Mix-2, W = 350 meV
Mix-3, W = 380 meV

In(γ1/Δn)00.8γ1(Pa s)

–1

0.6

–2

In conclusion, we prepared and measured various
physical properties of three high birefringent room
temperature nematic liquid crystal mixtures. The
orientational order parameter, both splay and bent
elastic constants are comparatively larger than thatof many common liquid crystal mixtures. The unusual temperature dependence of parallel componentof dielectric constant near the room temperature isdue to the rapid decrease of dielectric relaxation frequency with decreasing temperature. The FoM athigher temperature is reasonably large but reduces
at room temperature due to the very high viscosity.
Thus elastic and dielectric properties of high birefringent materials are suitable but high viscosity is amatter of concern for application and hence needs tobe reduced.

–3

0.4

2.6

2.8

3.0

3.2

3.4

–1

(1000/T) K

0.2

Funding

Mix-1
Mix-2
Mix-3

0.0

–100

–80

We gratefully acknowledge support from the DST (SR/NM/
NS-134/2010) and CSIR (03(1207)/12/EMR-II) and DSTPURSE. V. D acknowledges UGC for fellowship.
–60

–40

–20

0

T – TNI (°C)

Figure 5. (colour online) (a) Linear variation of ln½δo =δðtÞwith time(t) at various temperatures of Mix-1. Solid lines
are theoretical fits to the experimental data. (b)Variation ofrotational viscosity γ1 of different mixtures as a function ofshifted temperature (inset). Linear variation of lnðγ1 =ΔnÞwith 1=T . Solid lines are theoretical fits to the corresponding
equations as described in the text.

15

Mix-1
Mix-2
Mix-3

12
FoM (μm2/s)

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Time (ms)
1.0

595

9
6
3

27

57

87

117

Temparature (°C)

Figure 6. (colour online) Temperature variation of figure of
merit (FoM). Solid lines are theoretical fits of the experimental data to Equation (1).

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