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Structure–property correlation of bicyclohexane
nematic liquid crystalsaabD. Venkata Sai , K. P. Zuhail , Rudraditya Sarkar & Surajit DharaaaSchool of Physics, University of Hyderabad, Hyderabad, Indiab

School of Chemistry, University of Hyderabad, Hyderabad, India
Published online: 13 Jan 2015.

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To cite this article: D. Venkata Sai, K. P. Zuhail, Rudraditya Sarkar & Surajit Dhara (2015) Structure–property correlation of
bicyclohexane nematic liquid crystals, Liquid Crystals, 42:3, 328-333, DOI: 10.1080/02678292.2014.987708
To link to this article: http://dx.doi.org/10.1080/02678292.2014.987708

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Liquid Crystals, 2015
Vol. 42, No. 3, 328–333, http://dx.doi.org/10.1080/02678292.2014.987708

Structure–property correlation of bicyclohexane nematic liquid crystals
D. Venkata Saia, K. P. Zuhaila, Rudraditya Sarkarb and Surajit Dharaa*aSchool of Physics, University of Hyderabad, Hyderabad, India; bSchool of Chemistry, University of Hyderabad, Hyderabad,
India(Received 7 October 2014; accepted 11 November 2014)
We report measurements of birefringence, dielectric anisotropy, splay and bend elastic constants of a homologous
series of bicyclohexane nematic liquid crystals. These liquid crystals exhibit low birefringence and high negative
dielectric anisotropy. In the nematic phase, the ratio of bend to splay elastic constant is less than 1(K33 =K11 ’ 0:7). The low birefringence, high negative dielectric anisotropy and low elastic constant ratio are
discussed based on the optimised molecular structure obtained from density functional calculations.

Downloaded by [University of Hyderabad] at 07:19 05 April 2015

Keywords: bicyclohexane nematic liquid crystals; birefringence; elastic constants; density functional theory

1. Introduction
The physical properties of liquid crystals such as
optical, dielectric and viscoelastic properties strongly
depend on the molecular structure. The electroopticalresponse of the liquid crystal displays (LCDs)
depends on the physical properties. Usually calamitic
liquid crystals (made of rod-like molecules) are usedfor LCD applications. In order to improve the performance of LCDs, efforts have always been made tosynthesise new molecules. This led to the discovery ofmany liquid crystals with new phases and physicalproperties. A class of such liquid crystals are known
as bent-core liquid crystals. The effective shapes of
the constituent molecules are bent type. Occasionallythe bent-shaped molecules also show nematic phaseand mostly they exhibit negative dielectric anisotropy,
lower bend elastic constant, large rotational viscosityand flexo-electric coefficients. It has been establishedthat the molecular shape has a significant role on theabove mentioned physical properties.[1–7]Recently, a nematic liquid crystal with bicyclohexane core (CCN-47) has been reported to show a
discontinuous anchoring transition with a large thermal hysteresis on perfluoropolymer-treated cells.[8]Subsequently, several physical phenomena and new
applications of this transition have been reported. For
example, it has been exploited to demonstrate rewritable memory device,[9–11] microflow-induced bistable alignment,[12] and photothermal switching ofconductivity in liquid crystal conducting polymer–
nanofibre composites.[13] The heat capacity and thermal diffusivity change of discontinuous anchoringtransition have also been reported.[14,15] Veryrecently, the origin of the anchoring transition has*Corresponding author. Email: sdsp@uohyd.ernet.in© 2015 Taylor & Francis

been explained both experimentally and theoretically.
[16] The molecular structure of this liquid crystal isvery different from conventional liquid crystals madeof one or more phenyl rings. These interesting results
and optical effects encouraged us to measure the physical properties and understand the structure–property
correlation of these bicyclohexane liquid crystals. In
this paper, we report on the measurements of somephysical properties such as birefringence, dielectric anisotropy, splay and bend elastic constants as a functionof temperature. The results are discussed based on the
optimised molecular structure obtained from the density functional theory (DFT).

2. Experimental
For measuring physical properties, cells were preparedby two indium tin oxide (ITO)-coated glass plates withcircularly patterned electrodes. The plates were spincoated with polyimides (AL-1254 and JALS-204) andcured at 180°C and 200°C, respectively, for 1 h andrubbed antiparallel way for planar and homeotropicalignment of the director (the average alignment direction of the molecules). Cells were made by placing thetwo plates together, ensuring that the electrode area
overlaps. The separation was controlled by glass-beadspacers with diameters 8–13.5 μm for various measurements. The thickness of the empty cell was measured
with ! 1% accuracy by an interferometric techniqueusing a spectrometer (Ocean Optics, HR-4000). The
empty cell was heated and filled with the sample in theisotropic phase. The alignment of the sample wasobserved using a polarising optical microscope(Nikon, LV100 POL) and a temperature controllerDownloaded by [University of Hyderabad] at 07:19 05 April 2015

Liquid Crystals(Instec, mK 1000). The temperature-dependent birefringence in a planar cell was measured by using aphase modulation technique [17] with the help of ahelium–neon laser, photoelastic modulator (PEM100) and a lock-in amplifier. The dielectric constants
are measured by using an LCR meter (Agilent
E4980A). The parallel component of the dielectric
constant was measured in a homeotropic cell at an
applied voltage of 0.2 V below the Freedericksz threshold voltage. To measure the perpendicular componentof dielectric constant, the effective dielectric constant
was measured as a function of applied voltage (from0.02 V to 15 V in steps of 0.02 V) at various temperatures. The experimental variation of the voltage-dependent dielectric constant tends to saturate at highvoltages. The linear part of the dielectric constant isplotted against 1/V and extrapolated to 1/V = 0 to
obtain !? at various temperatures. The measured
value is in good agreement with the measurement
made in planar cells. The bend elastic constant (K33 )is obtained from the electric field-induced Freedericksz
transition [18] and is given by K33 ¼ !0 j!!jðVth =πÞ2 ,where Vth is the Freedericksz threshold voltage and!! ¼ ð!k % !? Þ is the dielectric anisotropy. K11 wasestimated from the fitting of the voltage-dependent
dielectric constant with the theoretical equations [19]:V
2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiffiffiffiffiffiffiffiffiffi¼
1 þ γ sin ðϕm Þ (Vth π

3. Results and discussion
The phase transition temperatures of the com0
0
pounds 4; 4 -dialkyl-(1α; 1 α-bicyclohexyl)-4 β-carbonitrile (CCN-mn) are shown in Table 1. All thecompounds have the same core with varying alkyl
chain length on both sides (Figure 2). The compound
CCN-35 exhibits only nematic (N) phase. CCN-38
and CCN-47 exhibit nematic and smectic-A (SmA)
phases. The remaining compounds CCN-46, CCN-55
and CCN-73 exhibit nematic and smectic-B (SmB)
phases. Some physical characterisations such as
X-ray, NMR and dielectric relaxation studies on someof these compounds have been reported.[21–27]
The variation of dielectric anisotropy (!!)
with shifted temperature is shown in Figure 1. The
dielectric anisotropy is negative (!! < 0) in all thecompounds and exhibits a typical behaviour, that is,!! increases with decreasing temperature. At a relative temperature, the dielectric anisotropy is largest
for CCN-35 and lowest for CCN-47. The variation ofbirefringence (!n) of the compounds with shifted
temperature is shown in the inset of Figure 1. The
birefringence is very low in all the compounds, forexample, near the room temperature !n & 0:03. It
may be mentioned that !n is more than five times
lower than the very well-known liquid crystal, forð ¼π sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
1 þ κ sin ðϕm Þ sin ð Þ
#
$#
$d
2
1 þ γ sin ðϕm Þ sin2 ð Þ 1 % sin2 ðϕm Þ sin2 ð Þ
¼0

0ð

329

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
ð1þκ sin2 ðϕm Þ sin2 ð ÞÞð1þγ sin2 ðϕm Þ sin2 ð ÞÞ
d C
B
B ¼0
C
ð1%sin2 ðϕm Þ sin2 ð ÞÞ
BC!eff ðV Þ ¼ !jj ( B ð ¼π sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C
B
C
2
2
2
ð1þκ sin ðϕm Þ sin ð ÞÞ@Adð1þγ sin2 ðϕm Þ sin2 ð ÞÞð1%sin2 ðϕm Þ sin2 ð ÞÞ
¼0

(1)

¼π2

where !eff is the effective dielectric constant, φm is thetilt angle at the middle of the cell and the other termsof the reduced quantities are γ ¼ ð!? =!jj Þ % 1,
κ ¼ ðK11 =K33 Þ % 1. φ is the z-dependent tilt angle
and φm is the maximum tilt angle at the middleof the cell (z ¼ d=2) and substituted with
sinðϕÞ ¼ sinðϕm Þsinð Þ. The dielectric constant at
higher voltage are fitted to the above equations by
an iterative procedure to get the splay elastic constant
K11 .[20](2)

Table 1. Phase transition temperatures of the compounds.
Compounds
CCN-35
CCN-38
CCN-46
CCN-47
CCN-55
CCN-73Phase transition temperatures (°C)
Cr 38.4 N 49.3 I
Cr 41 SmA (23) N 49.5 I
Cr 30 SmB (26) N 54.7 I
Cr 25.6 SmA 28.2 N 57.3 I
Cr 25 SmB 30 N 66.4 I
Cr 38.6 SmB (38) N 50.2 I

Note: Cr, crystal; N, nematic; SmA, smectic-A; SmB, smectic-B.

Downloaded by [University of Hyderabad] at 07:19 05 April 2015

330

D.V. Sai et al.

Figure 1. (colour online) Variation of dielectric anisotropy(!!) of the compounds as a function of shifted temperature.
Frequency for the dielectric measurement is 4111 Hz. (Inset)
Temperature variation of birefringence (!n) measured at
λ ¼ 632:8 nm.

example, 5CB (pentyl cyanobiphenyl). The birefringence of bicyclohexane compounds with longitudinal
cyano group such as nCCH (trans, trans-4’-n-alkylbicyclohexyl-4-carbonitriles) has been reported by several authors.[28] It appears that the birefringence ofCCN-mn homologues is somewhat lower (about 25%)
than that of nCCH compounds.
In order to understand the structure–property correlation, we performed ground state electronic structure calculations of all the molecules with the help of
the DFT by using GAUSSIAN-09 suite programming
package. All the calculations are performed in the gas
phase and optimisation of the structures is done by
B3LYP level of theory using cc-pVDZ basis set.[29]Figure 2 shows the two-dimensional (2D) projectionof optimised structures of the molecules. It is observedthat the molecules are not linear and their 2D projections (keeping the cyano group along the y-axis andbicyclohexane along the x-axis) are bent-shaped. The
principal components of the dipole moments andFigure 2. (colour online) Two-dimensional projection of the energy-minimised molecular structures obtained by DFT
calculations in the gas phase.

Liquid Crystals

331

Table 2. Components of dipole moment and principal polarisabilities obtained from DFT calculations.

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Dipole moment (D)Polarisability (a.u.)

Compounds

μx

μy

μz

αxx

αyy

αzz

CCN-35
CCN-38
CCN-46
CCN-47
CCN-55
CCN-73

0.276
0.726
0.138
0.165
0.910
0.482

3.818
3.757
3.864
3.903
3.639
2.199

0.438
0.314
0.159
0.186
0.932
3.158

262.56308.70286.48304.48283.67295.61225.34259.53248.99257.39256.86224.72216.53244.50239.52249.64235.70262.47polarisabilities are listed in Table 2. The transverse
components of dipole moments (μy or μz ) are muchlarger in magnitude than that of the longitudinalcomponents (μx ). For example, in CCN-35, μx ¼
0:276 D, μy ¼ 3:818 D and μz ¼ 0:438 D, respectively.
This explains the origin of large negative dielectricanisotropy in all the compounds. The polarisabilitiesof all the compounds are larger along the long molecular axis (x-axis) compared to the components inthe y and z directions. The birefringence of thecompounds is proportional to the polarisability anisotropy (!α). In uniform sample, the polarisability anisotropy can be defined as !α & αxx %ðαyy þ αzz Þ=2. The average !α of all the compounds
is about 50 (a.u.) and it is about five times lower thanthat of 5CB [30] and consistent with five times lower
birefringence of CCN-mn compounds.
The splay and bend elastic constants (K11 and K33 )were measured from the voltage-dependent dielectric
constant data in the homeotropic cell as described in
the experimental section. The variation of splay (K11 )and bend (K33 ) elastic constants as a function oftemperature is shown in Figure 3. The variation of!eff together with the best fit of Equations (1) and (2)is also shown in the inset of Figure 3(a). Both K11 andK33 of all the compounds (except CCN-47) in thenematic phase increase with decreasing temperature.
In addition, both the elastic constants show presmectic divergence in CCN-47 compound. The ratio of
K33 =K11 is shown in the inset of Figure 3(b).
Interestingly, it is observed that K33 is lower than
K11 , that is, K33 =K11 ’ 0:7, except very close to the
SmA phase transition temperature of CCN-47.
Similar behaviour may also be expected in CCN-38
but the N-SmA transition temperature is below theambient and beyond accessible temperature range ofour temperature controller. The presmectic divergence of K11 is rare as the splay distortion is permitted
even in the smectic-A phase. However, there are a few
reports showing presmectic divergence of both K11
and K33 .[2,20] In case of bent-core nematic liquid
crystals, it has been reported that K33 < K11 andoccasionally they exhibit unusual temperature

Figure 3. (colour online) (a) Variation of splay elastic constant (K11 ) as a function of shifted temperature. (Inset)
Effective dielectric constant as a function of applied voltage.
Solid black line is a theoretical fit to the experimental data.
(b) Temperature variation of bend elastic constant (K33 ).
(Inset) Temperature variation of the ratio, K33 =K11 .

dependence.[1,4] It was suggested that the strain in
the bend distortion is partly relieved if the molecules
are curved or bent shaped and consequently K33 is
expected to be lower than K11 .[31] The energy-minimised structures of the present calamitic molecules
are bent type (Figure 2) and expected to beDownloaded by [University of Hyderabad] at 07:19 05 April 2015

332

D.V. Sai et al.

responsible for the similar results as that of bent-corenematic liquid crystals.
It may be useful to discuss and compare the elastic
constant ratio with bicyclohexane nematic compounds such as nCCH.[32] It was reported that theelastic constant ratio of nCCH is always greater than
1 (i.e. K33 =K11 > 1). This is in contrast to the observed
effect in the present compounds. The important structural difference between the two homologous series ofnCCH and CCN-mn is the position of the cyanogroup (-CN). In case of nCCH, the cyano group isat the longitudinal position, whereas in CCN-mn, it isin the lateral position. In addition, the alkyl chainsare present on both sides of bicyclohexane. The side
chains of CCN-mn increase the flexibility of the molecules. Apart from the enhanced flexibility, the transverse dipole moment of CCN-mn molecules can havea significant role on the ratio of the curvature elastic
constants. It was proposed that the effect of dipole
moment on the elastic constants is connected to the
local ordering of the dipoles in nCCH compounds.
[33] The effective molecular length could be greater in
nCCH compounds because of the antiparallel local
ordering of the molecules with the overlappedcyano group. It has been shown both experimentallyand theoretically that in nematic liquid crystals,
K33 =K11 / ðL=W Þ2 , where L is the length and W is
the width of the mesogenic molecule, respectively.[31]Thus, the lower ratio of K33 =K11 of CCN-mn compounds than nCCH compounds partially could be
due to the absence of local ordering, apart from theeffect of molecular shape.

4. Conclusion
In conclusion, we have measured the birefringence,dielectric anisotropy, splay and bend elastic constantsof homologous series of bicyclohexane nematic liquid
crystals as a function of temperature. The optimised
molecular structure obtained from the calculation of
DFT shows that the molecules are bent-shaped withlarge transverse dipole moments and low polarisability anisotropy. The low birefringence, high negative
dielectric anisotropy and low elastic constant ratio of
the compounds are explained based on the optimised
molecular properties.

Acknowledgements
We gratefully acknowledge support from the DST (SR/NM/
NS-134/2010) and CSIR (03(1207)/12/EMR-II), DSTPURSE and UPE-II. VD acknowledges UGC for fellowship. We thank Prof. W. Haase for providing CCN-mn
compounds. RS acknowledges UGC for doctoral

fellowship. We thank Prof. S. Mahapatra, School ofChemistry, UoH, for useful discussion.

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