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Eur. Phys. J. E (2011) 34: 74

DOI: 10.1140/epje/i2011-11074-y

Eﬀect of electric ﬁeld on the rheological and dielectric properties of a liquid crystal exhibiting
nematic–to–smectic-A phase transition
J. Ananthaiah, M. Rajeswari, V.S.S. Sastry, R. Dabrowski and S. DharaEur. Phys. J. E (2011) 34: 74
DOI 10.1140/epje/i2011-11074-y

THE EUROPEAN
PHYSICAL JOURNAL E

Regular Article

Eﬀect of electric ﬁeld on the rheological and dielectric propertiesof a liquid crystal exhibiting nematic–to–smectic-A phasetransition
J. Ananthaiah1 , M. Rajeswari1 , V.S.S. Sastry1 , R. Dabrowski2 , and S. Dhara1,a1
2School of Physics, University of Hyderabad, Hyderabad-500046, India
Military University of Technology, Warsaw, Poland
Received 25 March 2011 and Received in ﬁnal form 8 May 2011c EDP Sciences / Società Italiana di Fisica / Springer-Verlag 2011
Published online: 3 August 2011 – 
Abstract. We report simultaneous measurements of shear viscosity (η) and dielectric constant (ǫ) of octyloxy cyanobiphenyl (8OCB) in the nematic (N) and smectic-A (SmA) phases as functions of temperatureand electric ﬁeld. With increasing electric ﬁeld η increases in the N phase whereas it decreases in the SmA
phase and saturates beyond a particular ﬁeld in both the phases. The ﬂow curves in the intermediate-ﬁeld
range show two Newtonian regimes in the N phase. The temperature-dependent behavior of η and ǫ atzero or at small electric ﬁeld suggests the occurrence of several structures that results from precessionalmotion of the director along the neutral direction as reported in similar other system. We show thatthe precessional motions are gradually suppressed with increasing electric ﬁeld and the eﬀective viscosity
resembles with the Miesowicz viscosity η1 at high enough electric ﬁeld. In the intermediate ﬁeld range
the temperature-dependent η exhibits anomalous behavior across the N-SmA phase transition which is
attributed to the large contribution of Leslie coeﬃcient α1 .

1 Introduction
Structure property relation, phase transitions and electrooptic properties of low-molecular-weight thermotropic liquid crystals have always been the main interest of scientists and technologists working in this area with the goalto achieve better liquid-crystal display (LCDs) properties.
Flow behavior of such materials has not been studied so
rigorously as it is not directly related to the device properties. Nevertheless some signiﬁcant progress is made in understanding the ﬂow behavior of low-molecular-weight liquid crystals both theoretically and experimentally [1–35].
Among them there are many reports on the measurement of Miesowicz viscosities or Leslie coeﬃcients in thenematic phase as a function of temperature using various experimental techniques and the results are discussed
on the basis of Leslie [1] and Ericksen [2] theories. However, the temperature-dependent shear viscosity is very
diﬀerent and complex in compounds exhibiting N-SmA
phase transition. In a pioneering work Saﬁnya et al. [14]have shown several steady-state structures that resultsfrom the interplay between the viscous frictional forcesand ﬂow-induced ﬂuctuation forces by synchrotron X-ray
radiation. They showed various shear-induced structuralchanges and precessional motions of nematic director inae-mail: sdsp@uohyd.ernet.in

the octyl cyanobiphenyl (8CB) compound as the SmA
phase is approached.
In the nematic phase under shear there are mainly
three diﬀerent director orientations, namely a, b, c with respect to the ﬂow (velocity) direction, and the corresponding Miesowicz viscosities [4] are represented by η3 , η2 andη1 , respectively in ﬁg. 1. In case of compounds having SmA
phase the molecules form layered structures and the corresponding layer orientations are indicated as a′ , b′ and c′ inﬁg. 1. For all nematic liquid crystals α2 < 0 and the director orientation under ﬂow depends on the sign of α3 . Normally near nematic-to-isotropic transition (TN I ) α3 < 0
and the ratio of Leslie coeﬃcients α2 /α3 is positive andthe director tends to align along the ﬂow direction with
the orientation angle θ = tan−1
α2 /α3 with respect
to the velocity direction. On the other hand α3 is renormalized (α3R > 0) in compounds exhibiting N-SmA transition due to the pretransitional smectic ﬂuctuations andthe ﬂow alignment of the director is prohibited that leads
to several structures namely am , as , a(b) and ac depending on the temperature and shear rate [14]. These structures arise because of precessional motion of the director
along the neutral direction (x-axis) that can be describedby the equation of an ellipse: n2y (t)/n2y0 + n2z (t)/n2z0 = 1,
where ny (t) = ny0 cos(ω0 t) and nz (t) = nz0 sin(ω0 t) arecomponents of the director n(t) = (nx (t), ny (t), nz (t)).
Thus the director is precessing with an angular frequency

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Fig. 2. (Color online) Schematic representation of the parallelplate setup for simultaneous measurement of rheological anddielectric properties.

Fig. 1. Schematic representation of the three fundamental director orientations in the N and SmA phase under shear. The
director orientations are along the x (neutral), y (velocity) andz (velocity gradient) directions in a, b, c, respectively. Layer orientations in the SmA phase are parallel to the zy, xz, and xy
planes in a′ , b′ , and c′ , respectively. Miesowicz viscosities corresponding to each orientations in the N phase are designatedby η3 , η2 and η1 , respectively.

ω0 = γ˙2 (−α2 α3R )/γ12 where α3R is the renormalized viscosity coeﬃcient, γ̇ is the shear rate and γ1 = α3 −α2 [14].
The above-mentioned structures are described as follows.
In am structure: the precessional motion is anisotropic
with larger amplitude in the y-direction than in the zdirection (ny0 > nz0 ); as structure: isotropic precession
with equal amplitude in both the directions (ny0 = nz0 );a(b) structure: anisotropic precession with lesser amplitude in the y-direction than in the z-direction (ny0 < nz0 )and in ac structure: anisotropic precession with very large
amplitude in the z-direction (ny0 ≪ nz0 ). The eﬀect ofthese precessional motions are also reﬂected in the rheodielectric measurements [19]. In this paper we present electrorheological and rheodielectric studies on 8OCB and report the following experimental results: i) in the nematic
phase the shear viscosity increases with increasing electricﬁeld in the low-shear-rate region and saturates at higher
ﬁelds, ii) in the SmA phase the shear viscosity decreases
with increasing electric ﬁeld, iii) the precessional motionsof the director just above the N-SmA transition under zero
electric ﬁeld appears to be similar as reported in 8CB [19]and in addition the precessional motions are suppressed at
higher ﬁelds, iv) an anomalous peak appears in the shear
viscosity under moderate electric ﬁeld across the N-SmA
transition that is suppressed at further higher ﬁelds.

2 Experimental
The compound 4′ -octyloxy-4-cyanobiphenyl (8OCB) was
synthesized in our laboratory, and exhibits the following phase sequences as observed in polarising optical microscope on cooling: I 79.5 ◦ C N 66.6 ◦ C SmA 54.5 ◦ C

Cr. Rheological measurements were performed using a
Rheometer (Anton Paar MCR 501) in parallel-plate geometry with plate diameter of 50 mm. The parallel-plate conﬁguration was chosen for the simultaneous measurementsof the rheological and dielectric properties. The cell gap
was taken to be 75 μm as we experimentally veriﬁed thatthe eﬀect of surface anchoring is observed below 50 μm. A
similar observation was also reported by Cidade et al. [36].
In addition, we ﬁnd that the zero-ﬁeld viscosity in theisotropic and nematic phases of the same compound agrees
well with the values reported in the literature in which themeasurements are made by using other geometries [19,22].
A schematic setup for measuring the rheological and dielectric properties is shown in ﬁg. 2. The electric ﬁeld wasapplied between the bottom and the top plates by using a
low-friction spring wire (ﬁg. 2). The “air correction” i.e.,
contribution due to the small friction in the absence of thesample was subtracted from the measured viscosity withthe sample at various temperatures and ﬁelds. The dielectric constant was measured by measuring the ratio of thesample capacitance with that of the empty capacitance(i.e., without sample). The temperature of the sample wascontrolled within an accuracy of 0.1 ◦ C by a Peltier temperature controller ﬁtted with a hood (protection cover)for the uniformity of the sample temperature. Calibrationof the temperature controller was checked by measuring
the phase transition temperatures of some standard liquid
crystalline materials. All the measurements were made on
cooling the sample from the isotropic phase. The dielectric
properties were measured as a function of temperature up
to 20 V with the help of a LCR meter (Agilent E4980A).
To apply a voltage beyond 20 V we used a signal generator(Tektronix AFG3102) and a voltage ampliﬁer (TEGAM).
The frequency of the sinusoidal voltage was 3.11 kHz.

3 Results and discussion
The ﬂow curve i.e. the variation of shear viscosity (η)
as a function of shear rate (γ̇) at various applied electric ﬁelds in the nematic phase (72 ◦ C) is shown in ﬁg. 3.
The electric ﬁeld is perpendicular (z-axis) to the ﬂow ﬁeld
direction (y-axis in ﬁg. 1). At zero ﬁeld the viscosity islow (∼ 10.5 mPa s) and is comparable to the shear viscosity η3 [22]. It does not depend on the shear rate thus

J. Ananthaiah et al.: Electro and rheodielectric studies on a liquid crystal exhibiting N-SmA transition

Fig. 3. (Color online) Variation of (a) shear viscosity (η) and(b) dielectric constant (ǫ) as a function of shear rate (γ̇) atvarious applied ac electric ﬁelds. Dotted lines are drawn as a
guide to the eye.

shows Newtonian ﬂow behavior. With increasing electricﬁeld the director tends to align along the ﬁeld direction
beyond a threshold ﬁeld as the dielectric anisotropy is positive (Δǫ = ǫ −ǫ⊥ > 0). Both η (ﬁg. 3(a)) and ǫ (ﬁg. 3(b))
increase with increasing ﬁeld up to ∼ 27 × 104 V/m in the
low-shear-rate region. At higher shear rate the ﬂow ﬁeld
is strong and tends to align the director parallel to thexy-plane (ﬁg. 1) as a result both η and ǫ decrease. In theintermediate shear rate a non-Newtonian ﬂow behavior isobserved where the director makes an angle with respect
to the xy-plane due to the competition between the electric and the ﬂow ﬁelds. Further beyond ∼ 6.6 × 104 V/mviscosity shows two Newtonian regimes within the measured shear rate range. In the low-shear-rate region (upto γ̇ ∼ 100 s−1 ) there is no signiﬁcant increase in η and ǫ
beyond ∼ 27×104 V/m suggesting that the director orientation is almost parallel to the electric ﬁeld (z-axis). Furthermore, the shear rate at which the director orientation
deviates from the electric ﬁeld direction increases almost
linearly with increasing ﬁeld as seen in ﬁg. 1 demonstrating the opposite and competing orientating eﬀect of theﬂow ﬁeld and electric ﬁeld.
Variation of the shear viscosity with the applied electric ﬁeld at diﬀerent shear rates is shown in ﬁg. 4(a). At

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Fig. 4. (Color online) (a) Variation of the shear viscosity (η)
as a function of applied electric ﬁeld at various shear rates γ̇ at
72 ◦ C. (b) Variation of the dielectric constant (ǫ) as a functionof applied electric ﬁeld at shear rates γ̇ = 0 and 50 s−1 at thesame temperature. Dotted lines are drawn as a guide to the eye.

shear rate γ̇ ∼ 50 s−1 , the viscosity increases monotonically and saturates at higher ﬁeld. No clear threshold is observed in the viscosity data as the director is already tilted
by a ﬁnite angle with respect to the xy-plane. At higher
shear rates (γ̇ = 100 and 199.5 s−1 ) in the intermediateﬁeld region, i.e. from ∼ 8 × 104 V/m to ∼ 30 × 104 V/m(ﬁg. 4(a)), η is always low compared to the values atγ̇ = 50 s−1 , suggesting that the tilt angle is reduced withrespect to the xy-plane at higher shear rates. Beyond∼ 30 × 104 V/m the viscosity curves tend to saturate andmerge together at higher ﬁeld. There is a slight change
in the slope of the viscosity at ∼ 8 × 104 V/m (ﬁg. 4(a))
and it can be explained as follows: The director gets partially aligned (homogeneously) due to the ﬂow ﬁeld andthe slope change indicates a threshold ﬁeld in the homogeneously aligned sample at which the director starts tilting
signiﬁcantly. Simultaneous measurement of the dielectric
constant at the same temperature (72 ◦ C) and at shear
rate γ̇ = 50 s−1 is shown in ﬁg. 4(b). In the unsheared sample (γ̇ = 0 s−1 ) the dielectric constant remains constant up
to the threshold electric ﬁeld ∼ 1.5 × 104 V/m and thenincreases rapidly to saturate beyond ∼ 7 × 104 V/m. The
dielectric constant below the threshold ﬁeld is ǫ ∼ 11 andcomparatively larger than measured in the aligned cell(ǫ⊥ ∼ 7.3 [29]) suggesting that the director orientation

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The European Physical Journal E

is random in the unsheared sample. The dielectric constant at high ﬁeld (∼ 25 × 104 V/m) is comparable toǫ ∼ 15.2 [29] (measured in the aligned cell) and suggeststhat the director is oriented almost parallel to the ﬁeld direction in the unsheared sample. At shear rate γ̇ = 50 s−1 ,the dielectric data is very diﬀerent than in the unsheared
sample (ﬁg. 4(b)). The dielectric constant is low (ǫ ∼ 7.6)
compared to the unsheared sample indicating that the director is oriented slightly out of the xy-plane. The dielectric constant increases almost linearly up to ∼ 8×104 V/mand saturates at higher ﬁeld followed by a slope change
at this ﬁeld and is consistent with the viscosity data in
ﬁg. 4(a).
The variation of temperature-dependent shear viscosity and the simultaneous measurement of the dielectric
constant at various applied electric ﬁelds is shown in ﬁg. 5.
The viscosity does not depend on the electric ﬁeld in
the isotropic phase and is comparable to the previously
reported values [22]. The rheodielectric [19] and sheardependent X-ray measurements [15] of 8CB are suggestive for understanding the present temperature-dependent
electrorheological and rheodielectric data of 8OCB. In thenematic phase the zero-ﬁeld viscosity decreases initially
up to T − TN I = −2◦ and suggests ﬂow-induced alignment of the director (similar to the b orientation in ﬁg. 1).
Below this temperature a mixed state, namely a-b orientation, occurs and the viscosity increases monotonicallyup to T − TN I = −11◦ (ﬁg. 5(a)). A slight slope change
below this temperature followed by a rapid increase of theviscosity in the SmA phase is observed. The temperaturedependent dielectric constant (ﬁg. 5(b)) together with theviscosity data between T − TN I = −11◦ and −13◦ reﬂect the various precessional motions of the director along
the neutral direction such as ac , a(b), as , am of the director that are seen in the X-ray measurements of the similar compound 8CB. In the SmA phase the viscosity ishigh due to the occurrence of the a′ -c′ orientation (ﬁg. 1).
When the ﬁeld is increased to 13.3 × 104 V/m, the viscosity increases in the nematic phase and its temperature dependence is diﬀerent than the zero-ﬁeld viscosity.
The temperature-dependent dielectric constant (ﬁg. 5(b))
at this ﬁeld in the nematic phase is higher compared to
the values measured at smaller ﬁeld (1.2 × 104 V/m) andindicates that the director is tilted with respect to theﬁeld direction. However, in the SmA phase the viscosity
at 13.3 × 104 V/m is comparable to the zero-ﬁeld viscosity, suggesting that this ﬁeld is not suﬃcient to change
the director orientation compared to the zero-ﬁeld orientation. An anomalous increase in the viscosity is also observed across the N-SmA phase transition that will be discussed later. The dielectric constant (at 13.3 × 104 V/m)is rapidly increasing across the I-N transition and thendecreases monotonically as the temperature is reduced towards the N-SmA transition. The temperature-dependent
viscosity and the dielectric constant (ﬁg. 5(a) and (b))
at this ﬁeld just above the N-SmA transition does notshow any signature of the presence of several structures
as seen at zero ﬁeld. Further, a comparatively smootherdecrease of the dielectric constant and the increase of viscosity at 13.3 × 104 V/m with temperature in the nematicFig. 5. (Color online) Variation of (a) the shear viscosity (η)
and (b) the dielectric constant (ǫ) as a function of temperature and various applied electric ﬁelds. Vertical dotted lines
are drawn considering the similarity of temperature-dependentzero-ﬁeld viscosity with that of 8CB [19] and represent theapproximate temperature regions with possible director orientations. The vertical arrow indicates the peak position in theviscosity (T − TN I = −13.8◦ ). (c) Schematic representationof the precessional motions of the director at the applied ﬁeld
13.3×104 V/m and at various temperatures as indicated bynumbers from 1 to 4 on the dielectric data in (b).

phase suggests uniform precessional motions of the director (below T − TN I = −2◦ ) about an axis (in thexz-plane) that is tilted with respect to the xy-plane. A
schematic representation of the director orientation along
a cone that is tilted with respect to the xy-plane is shownin ﬁg. 5(c). The dielectric constant at 26.7 × 104 V/min the nematic phase agrees well with ǫ [29] at the

J. Ananthaiah et al.: Electro and rheodielectric studies on a liquid crystal exhibiting N-SmA transition

same temperature and indicates that at this temperature the director orients almost along the ﬁeld direction
and goes towards an a′ -c′ orientation in the SmA phase.
At the applied ﬁeld ∼ 26.7 × 104 V/m, the temperaturedependent viscosity is almost similar with the data measured at 13.3 × 104 V/m, except for a slight increase in
the viscosity in the nematic phase and a slight increase in
the peak height of the anomalous viscosity. In the SmA
phase at ∼ 26.7 × 104 V/m the viscosity is substantially
low compared to the viscosity measured at zero ﬁeld or
13.3 × 104 V/m. On the other hand, the dielectric data in
the SmA phase at 26.7 × 104 V/m is almost comparable toǫ as measured in the aligned cell sample [29]. This indicates that under this ﬁeld the SmA layers are parallel tothe shear plane and acquire c′ orientation (ﬁg. 1). Further,at higher ﬁeld (∼ 66.7 × 104 V/m) there is no signiﬁcantchange in the viscosity in the nematic and SmA phases
compared to the values at 26.7 × 104 V/m except that theanomalous peak is suppressed completely.
At least two possible explanations can be considered
for the occurrence of the anomalous peak across the NSmA transition. The anomalous increase of shear viscosity can occur due to the eﬀect of shear on the pretransitional ﬂuctuating clusters as suggested by de Gennes [30]and Onuki [31]. When the SmA phase is approached fromthe nematic phase the relaxation time of the collective
ﬂuctuation of smectic clusters increases and the ﬂow ﬁeld
can easily distort the clusters as suggested by Saﬁna etal. [15], as a result the viscosity can increase anomalously.
However, the suppression of the viscosity peak at higher
ﬁeld cannot be understood on this basis. Another possible explanation is based on the large contribution of the
Leslie coeﬃcient α1 to the measured viscosity. When sufﬁcient electric ﬁeld is applied the director tends to alignin the ﬁeld direction (z-axis). The ﬂow alignment angle isobtained from the balance of the viscous torque and theelectric torque that is given by [16, 17]1(α3 sin2 θ − α2 cos2 θ)γ̇ − ΔǫE 2 sin 2θ = 0,2(1)where Δǫ is the dielectric anisotropy and E is the applied
electric ﬁeld. The viscosity in such condition can be calculated by using Leslie-Ericksen theory [1, 2]
1
η(θ) = α1 cos2 θ sin2 θ + (α3 + α6 ) sin2 θ2
1
12+ (α5 − α2 ) cos θ + α4 ,
2
2

(2)

where α1 to α6 are the Leslie coeﬃcients [16, 17]. Due tothe smallness of α1 it is neglected frequently in the nematic
phase but this can contribute signiﬁcantly to the measured
viscosity near the N-SmA phase transition as suggested by
Negita et al. [27]. Under zero ﬁeld there are several precessional motions just above the TN A which are suppressedat some ﬁnite ﬁeld (∼ 13.3 × 104 V/m) and the director orientation changes gradually via precessional motion
around a cone as shown in ﬁg. 5(c). In the nematic phase
it starts from some ﬁnite angle on the cone (ﬁg. 5(c)-1)
and rotates from some minimum angle (ﬁg. 5(c)-3) to a

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maximum angle (∼ 90◦ , ﬁg. 5(c)-4) through 45◦ at which
the ﬁrst term in eq. (2) has the maximum contribution
and can lead to the peak in the shear viscosity. Further, it
is noticed from ﬁg. 5(b) that at 13.3 × 104 V/m the minimum (mark 3 in ﬁg. 5(b)) and the maximum (mark 4 inﬁg. 5(b)) in the dielectric constant occur at temperatures
T − TN I ≃ −13.3◦ and ≃ −14.3◦ , respectively. Interestingly the anomalous peak in the viscosity data (ﬁg. 5(a))
at the same ﬁeld appears at an intermediate temperature
T − TN I ≃ −13.8◦ and indicates that the director orientation at the anomalous peak is nearly 45◦ . When the ﬁeld
is suﬃciently high the director is aligned parallel to theﬁeld direction and the precessional motions are completely
suppressed, consequently α1 does not contribute to η andthe peak is suppressed.
In conclusion, we have measured the shear viscosityof 8OCB in both the N and SmA phases as functions oftemperature and applied electric ﬁeld. The ﬂow curve atvarious applied ﬁelds shows the competing orientating effect of the ﬂow ﬁeld and electric ﬁeld. The viscosity increases with increasing electric ﬁeld in the nematic phaseand saturates to η1 . At suﬃciently high ﬁeld the SmA
exhibits c′ orientation and the corresponding viscosity issigniﬁcantly low compared to the viscosity of the a′ -c′ orientations. The shear viscosity and the dielectric data atzero or small electric ﬁeld suggest the occurrence of several
structures related to the precessional motions of the director as reported in 8CB. An anomalous peak is observed in
the viscosity across the N-SmA transition (i.e. from c toc′ orientation). Two possible explanations are discussed
for the anomalous increase in the viscosity, namely the
pretransitional smectic ﬂuctuations and the large contribution of α1 to the shear viscosity near TN A . We argue
that the second explanation is more appropriate and explains our data satisfactorily.
The authors MR, VSSS and SD gratefully acknowledge thesupport from the CAS, School of Physics.

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