PHYSICAL REVIEW E 89, 022510 (2014)

Rheology of nematic liquid crystals with highly polar molecules
J. Ananthaiah, Rasmita Sahoo, M. V. Rasna, and Surajit Dhara,*
School of Physics, University of Hyderabad, Hyderabad 500046, India(Received 4 December 2013; published 24 February 2014)
We report experimental studies on the rheology of a few nematic liquid crystals with highly polar molecules(CCH-7, PCH-7, CB-7). The selected molecules have the same alkyl chain (-C7 H15 ) and cyano (-CN) end group.
In the core part of the molecule, CCH-7 has two cyclohexane rings, PCH-7 has one cyclohexane and one aromaticring, and CB-7 has two aromatic rings. Two viscosities were measured as a function of temperature, namely, η2(director parallel to the shear direction) and η1 (director perpendicular to the shear direction). The orientation of
the director was studied using small angle light scattering techniques. η2 was measured in presheared sample,
whereas the electrorheological technique was used to measure η1 . We show that both viscosities of the liquid
crystals depend on the number of aromatic rings and Kirkwood correlation factor. The temperature dependent
viscosities can be understood based on the intramolecular π -electron conjugation and intermolecular associationof highly polar molecules.
DOI: 10.1103/PhysRevE.89.022510

PACS number(s): 64.70.mj, 83.50.Ax

I. INTRODUCTION

antiparallel correlation of dipoles and π -electron conjugationof neighboring molecules on the viscosity.

The electrooptical response of liquid crystals depends ontheir physical properties, and they are related to the molecular
structures [1–5]. A large number of liquid crystal compounds
are used for various technological applications, and in many
compounds the molecules have a highly polar cyano or nitro
end group. In addition, polar molecules are more stableelectrochemically and thermally. There are also some reports
on new electrooptic effects in nematic liquid crystals withhighly polar molecules [6]. Apart from applications, thesecompounds also exhibit several unusual features such as
reentrant phase transitions, smectic-A polymorphism, nematicto nematic transition, and strong suppression of director
fluctuation by fields [7–13]. When the nematic liquid crystals
are sheared, they exhibit three different viscosities dependingon the orientation of the director (the average molecularorientation direction) with respect to the flow and velocity
gradient directions, and they are called Miesowicz viscosities[14]. A schematic representation of director orientation incalamitic nematic liquid crystals with respect to the shear
direction and the corresponding viscosities are shown in
Fig. 1. These viscosities can be expressed in terms of Leslie
coefficients (α1 to α6 ), which are used to define the nematicstress tensor [15]. If both α3 and√ α2 are negative, the directoraligns at an angle, θ = tan−1 α2 /α3 [16–20], and in thiscase the effective viscosity ηeff # η2 (Fig. 1). The temperaturedependent Miesowicz viscosities of nematic liquid crystals
depend on the molecular structures and their intermolecularinteractions [2,4,21]. There are a few studies on these viscosity
coefficients of nematic liquid crystals with polar molecules[22–24], but there is no systematic investigation of the structural correlation to the Miesowicz viscosities. In this paper,
we report on the measurement of temperature variation of
two Miesowicz viscosities (η1 and η2 ) of a few low molecularweight nematic liquid crystals with highly polar molecules anda generic chemical structure. Our results reveal the effect of the*sdsp@uohyd.ernet.in

1539-3755/2014/89(2)/022510(6)II. EXPERIMENT

We have chosen the following compounds:
4-(n-heptyl)-4$ -cyanobiphenyl (CB-7), trans-4-(4-heptylcyclohexyl)-benzonitrile (PCH-7), and trans,trans-4-nheptyl-4$ -cyanobicyclohexane (CCH-7), which have a genericmolecular structure. The lengths and widths of all themolecules are almost the same [25]. The chemical structuresand phase transition temperatures are shown in Fig. 2. They
are low molecular weight nematic liquid crystals and have ageneric chemical structure in the sense that all the compounds
have the same alkyl chain (-C7 H15 ) and cyano end group(-CN). There is a systematic variation of structure in themolecular cores; that is, CCH-7 and CB-7 are composed ofbicyclohexane and biphenyl, respectively, whereas PCH-7
has one phenyl and one cyclohexane ring. The dielectricanisotropy of all the compounds is positive (see below),i.e., %& = &|| − &⊥ > 0, where the subscripts refer to thedirections in relation to the director. Some physical properties,
such as dielectric constants, diamagnetic susceptibility, andelastic constants, have already been studied [22,25].
Viscosity measurements were made using a rheometer(Anton Paar MCR 501). Both parallel plate and cone-platesystems induce planar alignment of the director [26], andno additional alignment layer was used. We used cone-platesystem with a diameter of 50 mm and a cone angle of 1◦ tomeasure η2 and parallel plate geometry with a plate diameterof 50 mm to measure η1 . In the latter, the cell gap was taken
as 75 µm, and an electric field was applied between thebottom and the top plates by using a low friction spring wire
[26,27]. The temperature of the sample was controlled by a
Peltier temperature controller with an accuracy of 0.1 ◦ C. The
heater and the measuring system was kept inside a protective
cover for the uniformity of the sample temperature, and nomeasurable temperature gradient was observed. Calibrationof the temperature controller was checked by measuring therheological properties of some standard liquid crystals. All
the measurements were made upon cooling the sample from

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PHYSICAL REVIEW E 89, 022510 (2014)

ANANTHAIAH, SAHOO, RASNA, AND DHARA

FIG. 1. (Color online) Schematic representation of the three fundamental director orientations of nematic liquid crystals with respect
to the shear direction. Miesowicz viscosities corresponding to eachorientations are designated by η1 , η2 , and η3 , respectively.

the isotropic phase. To measure electric field dependent
viscosity, we used a signal generator (Tektronix AFG3102)
and a high voltage amplifier (TEGAM). The frequency ofthe sinusoidal voltage was 3.11 KHz. The Fréedericksz
threshold√ voltage for the nematic liquid crystal is given by
Vth = K11 /&o %&, where K11 is the splay elastic constant[3]. Since the dielectric anisotropy for the present samples ispositive and the average molecular orientation is parallel tothe direction of the shear, the measured viscosity below Vth isη2 . When the applied voltage V > Vth , the director changes
orientation and becomes perpendicular to the shear direction,
and we essentially measure η1 . The dielectric anisotropy
and birefringence were measured by using a photoelastic

FIG. 3. (Color online) Variation of (a) birefringence %n and(b) dielectric anisotropy %& with shifted temperature of CB-7 (openstars), PCH-7 (open circles), and CCH-7 (open squares) liquid
crystals. The dielectric constants are measured at a frequency of
4.11 kHz. Cell thickness is 5 µm.

modulator, He-Ne laser, and an LCR meter [28–30]. For small
angle light scattering measurement a polarized diode laser of
658 nm was directed to the sample. An analyzer, crossed withrespect to the polarizer, and a focusing lens adjusted to observe
the scattering pattern on the screen were used. A CCD camera
was used to record the image at various shear rates [27].
III. RESULTS AND DISCUSSION

FIG. 2. (Color online) Chemical structures of CB-7, PCH-7, andCCH-7 liquid crystals and their phase transition temperatures.

First, we present and discuss some nonrheological properties such as the temperature variation of the birefringence%n and dielectric anisotropy %& of the compounds in
Fig. 3. These properties are essential for understanding therheological properties discussed in the later sections. We
observe that %n of CB-7 is larger than PCH-7 and CCH7 [Fig. 3(a)]. For example, at a fixed temperature (T −TNI = −10 ◦ C) %nCCH −7 = 0.046, %nP CH −7 = 0.086, and%nCB−7 = 0.016. Thus, merely from the molecular structure
point of view (Fig. 2), the replacement of a cyclohexane

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FIG. 4. (Color online) Variation of the effective viscosity as afunction of shear rate in the nematic phase of CB-7 in quenched(open squares) and presheared (open circles) samples at 35 ◦ C. P and
A are the polarizer and analyzer. Red arrows indicate the direction ofshear.

by an aromatic ring increases %n by an amount of #0.04.
This is expected as the intramolecular conjugation length
increases from CCH-7 to CB-7. The temperature variationof dielectric anisotropy %& is shown in Fig. 3(b). We observe
similar behavior in the sense that %& also increases as wego from CCH-7 to CB-7. For example, at a fixed temperature (T − TNI = −10 ◦ C) %&CCH −7 = 4, %&P CH −7 = 8.7,
and %&CB−7 = 9.9. However, the relative difference of thedielectric anisotropy between two successive compounds is
not regular. For example, at the same temperature, %&P CH −7 −%&CCH −7 = 4.7 and %&CB−7 − %&P CH −7 = 1.2. Although
the dipolar group is the same (-CN), the contribution of thepolarizability anisotropy is very different due to the different
intramolecular conjugation lengths.
To show the effect of shear on the nematic phase, we provide
representative rheology plus small angle light scattering (rheoSALS) data for CB-7. We measured the effective viscosity as afunction of the shear rate γ̇ in the quenched (isotropic to 35 ◦ C)
and in the presheared samples (Fig. 4). It is observed that in
the quenched sample, viscosity is high at lower shear rates(<10 s−1 ) and shows strong shear thinning behavior at higher
shear rates. When the sample is presheared at 500 s−1 forabout 10 min, the viscosity is constant and does not dependon the shear rate. In fact, beyond γ̇ = 50 s−1 , the effective
viscosities are almost comparable. The light scattering patterns
in two cases in the low shear range are slightly different. For
example, in the quenched sample, at γ̇ = 0.1 s−1 , the scattering
pattern is almost circular. This indicates that in the quenchedsample, at the low shear rate, there is a spatial variationof the director which gives polydomain textures. At higher
shear rates the circular patterns get elongated perpendicular
to the shear direction, and the viscosity shows shear thinningbehavior. Since SALS measures the image in the q space.
The scattering pattern suggests that the polydomain textures
are elongated parallel to the shear direction. This enforces
realignment of the director along the shear direction. In the

FIG. 5. (Color online) (a) Variation of η2 as a function of shifted
temperature at a fixed shear rate, γ̇ = 50 s−1 . The inset shows thevariation of the logarithm of η2 with the inverse of temperature in
the isotropic phase. The solid lines are the best fit to the Arrhenius
equation. (b) Comparison (ratio) of η2 of CB-7 and PCH-7 withrespect to that of CCH-7.

presheared sample the scattering pattern at γ̇ = 0.1 s−1 isslightly elongated, suggesting that the director is alreadyaligned along the shear direction. The scattering patterns inboth cases are almost similar beyond γ̇ = 10 s−1 , suggestingthat the effective viscosity at a higher shear rate is equal to η2(i.e., ηeff # η2 ).
In Fig. 5(a), the variation of η2 of CB-7, PCH-7, and CCH-7
is shown as a function of temperature. The isotropic viscosityηiso of CB-7 is much larger than that of PCH-7 and CCH-7,
CB−7
P CH −7and they vary in the increasing order, ηiso
> ηiso>
CCH −7. In addition, ηiso increases as the temperature isηiso
reduced, and an abrupt decrease is observed at the nematicisotropic (NI) transition temperature. The temperature dependent ηiso of all the compounds increase linearly, and we fitted
to the Arrhenius equation, ηiso = ηo exp(−Ea /kT ), where ηo isthe preexponential factor and Ea is the activation energy of theisotropic viscosity. The logarithm of viscosity is plotted against
inverse temperature in the inset of Fig. 5(a), and the activation

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ANANTHAIAH, SAHOO, RASNA, AND DHARA
TABLE I. Molecular weight M, birefringence %n, dielectricanisotropy %&, activation energy Ea , dipole moment µ, and Kirkwood
correlation factor g [25]. Both %n and %& are taken from Fig. 3 at
T − TNI = −10 ◦ C.
CompoundM%n%&Ea (eV)
µ (D)
g

CCH-7

PCH-7

CB-7

289.5
0.046
4.0
0.17
3.5
0.70

283.45
0.086
8.7
0.2
4.4
0.60

277.40
0.161
9.9
0.24
4.7
0.50

energies are listed in the Table I. We notice that they increasein the following order: EaCB−7 > EaP CH −7 > EaCCH −7 . The
increase of activation energy is an indicator of increasing
intermolecular interaction in the isotropic phase. It should
be reemphasized that CCH-7 has no aromatic ring, PCH-7
has one aromatic ring, and CB-7 has two aromatic rings. The
increase of the number of aromatic rings can enhance the π -πinteraction of aromatic cores (π -electron conjugation) amongneighboring molecules, and hence a stronger intermolecularinteraction is expected. Thus the increase in isotropic viscosity
in compounds having phenyl rings can be attributed tothe effect of enhanced π -electron conjugation compared tocompounds with cyclohexane because in the latter there is no
π -electron at the core.
In the nematic phase, at a fixed temperature, η2 also
increases in the same order, i.e., η2CB−7 > η2P CH −7 > η2CCH −7[Fig. 5(a)]. Further, it is interesting to note that the relative
differences among the viscosities of CCH-7, PCH-7, andCB-7 are reduced in the nematic phase compared to thosein the isotropic phase. For example, at T − TNI = −1 ◦ C,
P CH −7
CCH −7CB−7
P CH −7ηiso− ηiso= 3.4 mPa s and ηiso
− ηiso=10.4 mPa s. In the nematic phase, for example, at T − TNI =−5 ◦ C, η2P CH −7 − η2CCH −7 = 2 mPa s and η2CB−7 − η2P CH −7 =9.7 mPa s. We compare η2 of CB-7 and PCH-7 withrespect to CCH-7 and show their temperature variation in
Fig. 5(b). It is noticed that η2CB−7 /η2CCH −7 is much larger than(almost double) η2P CH −7 /η2CCH −7 , and the former increases
with decreasing temperature. This suggests that the viscosity
enhancement is not linear with the number of aromatic rings(replacing cyclohexane rings), keeping the other parts of themolecule same. The molecular weights of the compounds
are slightly different (Table I) and hence are not expected tocontribute very much to the viscosity. On the other hand, the
CCH −7
NI phase transition temperatures are very different (TNI>P CH −7CB−7
TNI> TNI ), which will have a significant effect on theviscosity in the sense that the viscosity is lower at higher
temperature. Nevertheless, the large differences in η2 among
the compounds and their temperature dependence cannot be
accounted for based on this fact alone. To understand this, we
present some useful data in Table I, i.e., the birefringence %n,dielectric anisotropy %&, dipole moment µ, and Kirkwood
correlation factor g,g = (µeff /µ)2 ,(1)

where µeff is the effective dipole moment as calculated fromthe Kirkwood-Froehlich equation [31] using dielectric dataand µ is the dipole moment of a single molecule. Both %n and%& are positive and increase from CCH-7 to CB-7 as expected
because aromatic rings contribute more to the birefringencethan cyclohexanes, as discussed earlier. The dipole moment µof the molecules obtained from Ref. [25] varies in the orderµCB−7 > µP CH −7 > µCCH −7 . It should be mentioned (Fig. 2)that the charge separations of the molecules in the ground state
are very different [25]. For example, the conjugation between
the two aromatic rings in CB-7 is only partial because thetorsional angle between the planes in the ground state is about
35◦ . The cyano group is conjugated with one aromatic ring in
PCH-7 and unconjugated in the case of CCH-7; hence there
is no delocalization of the electrons, and as a result there is asystematic variation in the dipole moments (see Table I). This
gives rise to molecular association, which is usually measured
in terms of the Kirkwood correlation factor.
The Kirkwood correlation factors of these compounds were
measured by Schad and Osman just above the NI transition
temperature [25]. They are presented in Table I for comparative
discussion. g less than 1 for all compounds suggests theexistence of antiparallel correlation of the molecular dipoles
even in the isotropic phase. In addition, we notice thatg CB−7 < g P CH −7 < g CCH −7 . This suggests that the strengthof the antiparallel correlation of dipoles is stronger in CB-7
than in both PCH-7 and CCH-7. In the nematic phase thedensity increases, the decrease of intermolecular distance, andthe antiparallel correlation is even stronger, which is reflected
in terms of a reduction of the average dielectric constant[& = (&|| + 2&⊥ )/3] [25]. In addition to that causes π -electron
conjugation of the aromatic rings of neighboring molecules. In
the case of CB-7, due to the effect of intermolecular π -electron
conjugation and dipolar antiparallel correlation, the molecules
behave like a dimer because of almost complete overlap of thearomatic rings, whereas CCH-7 behaves like a monomer due
to the lack of π -electron conjugation [2]. Thus the relative
reduction of η2 in the nematic phase compared to the isotropic
viscosity ηiso can be attributed to the molecular association due
to the antiparallel correlation of dipoles and intermolecular
π -electron conjugation.
To measure η1 , first, we measured the electric fielddependent viscosity at a fixed temperature in the nematic phase[Fig. 6(a)]. It is observed that the effective viscosity increases
with applied electric field for all the samples and saturates
beyond about 80 × 104 V/m. Since the dielectric anisotropy is
positive (i.e., %& > 0), beyond the Fréedericksz threshold field
the director tends to orient along the electric field direction.
However, the shear field tends to align the director along theshear direction. Thus there is a competing effect of these twoforce fields on the director orientation. However, at a steadyshear rate, if the electric field is strong enough the director
is finally orientated along the electric field direction. As aresult the equilibrium orientation of the director is perpendicular to the shear direction. Thus, essentially, we measureη1 at high electric field (>80 × 104 V/m). In Fig. 6(b),we show the variation of η1 as a function of temperature
for all the compounds. We notice that apart from a sharp
increase at the nematic-isotropic transition, η1 increases almost
linearly as the temperature is reduced for all the compounds.

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TABLE II. Viscosity anisotropy %η (= η1 − η2 ) obtained from
Figs. 5(a) and 6(b) at T − TNI = −10 ◦ C.
Compound%η (mPa s)

CCH-7

PCH-7

CB-7

25

45

62

concerned (Fig. 2), it seems that replacing a cyclohexane by
an aromatic ring increases %η by 15 to 20 mPa s. In the caseof η2 the director is parallel, and in the case of η1 , the director
is perpendicular to the shear direction. In the rheometer, thebottom plate is fixed, and the top plate is rotating; hence
the velocity gradient decreases from top to bottom. From themicroscopic point of view this will cause a net downward flowof momentum per unit time and area which is proportional tothe viscous frictional force. The frictional force depends onmolecular associations, which are due to the intermolecular
conjugation and permanent dipole moment. Thus the molecular associations contribute not only to the dielectric and opticalproperties but also to the Miesowicz viscosities.
IV. CONCLUSIONS

FIG. 6. (Color online) (a) Variation of effective viscosity ηeff at
a fixed shear rate, γ̇ = 50 s−1 , as a function of applied field at afrequency of 3.11 kHz. At high field (beyond about 80 × 104 V/m)ηeff = η1 . (b) Variation of η1 as a function of shifted temperature anda fixed electric field of 133 × 104 V/m (γ̇ = 50 s−1 ).

At a fixed temperature, in all the compounds, η1 > η2 , as
expected. In the nematic phase, the relative differences of η1
among the compounds are almost comparable. For example,
at T − TNI = −5 ◦ C, η1P CH −7 − η1CCH −7 = 18.7 mPa s, andη1CB−7 − η1P CH −7 = 19.8 mPa s. The viscosity anisotropy %η
(= η1 − η2 ) obtained from Figs. 5(a) and 6(b) is presented inTable II. It is noticed that %η increases almost linearly with%n from CCH-7 to CB-7. As far as the molecular structure is[1] P. G. de Gennes, The Physics of Liquid Crystals, 2nd ed. (Oxford
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We have measured the temperature dependence of two
Miesowicz viscosities (η1 and η2 ) for a few highly polar
nematic liquid crystals with a systematic variation in themolecular structure. We showed that nematic compounds withmore aromatic rings and a lower Kirkwood correlation factor
have larger viscosities. A low Kirkwood correlation factor isan indication of a strong antiparallel correlation of the dipoles.
The temperature variation of η2 reveals strong intermolecularassociations that result from both the π -electron conjugationof neighboring molecules and the antiparallel correlation ofmolecular dipoles. Compared to molecular associations, theintramolecular conjugation length seems to be more significant
in determining η1 . Finally, our measurements established thatapart from the optical and dielectric properties, molecularassociations of highly polar molecules in nematic liquid
crystals significantly affect the rheological properties.
ACKNOWLEDGMENTS

S.D. gratefully acknowledges financial support from CSIR
Grant No. 03(1207)/12/EMR-II and DST PURSE, UoH. J.A.
and R.S. gratefully acknowledge CSIR-SRF and UGC-BSR,
UoH, for financial support. The authors would like to thankProf. N. V. Madhusudana for fruitful discussions.

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