Liquid Crystals

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Rheological studies on liquid-crystal colloids
prepared by dispersing spherical microparticles
with homeotropic surface anchoring
Rasmita Sahoo & Surajit Dhara
To cite this article: Rasmita Sahoo & Surajit Dhara (2017) Rheological studies on liquid-crystal
colloids prepared by dispersing spherical microparticles with homeotropic surface anchoring, Liquid
Crystals, 44:10, 1582-1591, DOI: 10.1080/02678292.2017.1309469
To link to this article: http://dx.doi.org/10.1080/02678292.2017.1309469

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Published online: 30 Mar 2017.

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Date: 14 September 2017, At: 04:44

LIQUID CRYSTALS, 2017VOL. 44, NO. 10, 1582–1591
https://doi.org/10.1080/02678292.2017.1309469

Rheological studies on liquid-crystal colloids prepared by dispersing sphericalmicroparticles with homeotropic surface anchoring
Rasmita Sahoo and Surajit Dhara

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School of Physics, University of Hyderabad, Hyderabad, India
ABSTRACTARTICLE HISTORY

We report rheological studies on the liquid-crystal colloids prepared by dispersing silica microparticles with homeotropic surface anchoring in 8CB liquid crystal. In nematic colloids, a shearthickening behaviour is observed in low shear rate region. The apparent yield stress of both thenematic and smectic-A (SmA) phases increases with increasing volume fraction of particles ðϕÞ.
The critical strain amplitude (γc , i.e., crossover of G0 and G00 ) in SmA colloids decreases significantlywith increasing ϕ. The frequency-dependent storage modulus of SmA colloids show a power-law
behaviour ðG0 ðωÞ,ωα Þ and the loss modulus ðG00 ðωÞÞ exhibits a shallow minimum. The opticalrheomicroscopy shows that the nematic colloids form a network structure which are stretchedand broken at high shear rate. When the temperature is decreased to SmA phase, the networks
collapse showing regions of high-density particles. The variation of storage modulus with ϕindicates that the SmA colloids response is dominated by defects.

Received 31 January 2017
Accepted 10 March 2017

1. Introduction
The colloidal dispersion in isotropic liquids like water,
oil etc. has been studied since decades due to their wide
range of applications. However, the attention towards
the dispersion of nano- and microparticles in anisotropic liquids like lyotropic and thermotropic liquid crystals (LCs) has created an immense interest in last two
decades [1–6]. These are known as LC colloids.
Usually, the nanoparticles do not create any longrange elastic distortion in the nematic liquid crystal(NLC) but the physical properties of the composites
become significantly different from that of the pureLCs and such materials are potential for several

Nematic colloids; smectic-A
colloids; rheomicroscopy;
soft glass

applications [7–9]. When microparticles are dispersedin nematic LCs, they induce topological defects andcreate elastic distortions. This results long-range forcesamong the particles in the medium. These forces haveno analogue in common colloidal systems where particles are dispersed in the isotropic liquids. Usually,
three different types of topological defects are inducedby spherical microparticles in NLCs, namely, hyperbolic hedgehog, Saturn ring and boojum dependingon the anchoring strength, the elastic properties of
the LCs and the particle size [1,4,10,11]. There havebeen many interesting experimental studies reported
on LC colloids. In most studies, the attention has

CONTACT Surajit Dhara
sdsp@uohyd.ernet.in
School of Physics, University of Hyderabad, Hyderabad 560046, India
Supplemental data for this article can be accessed here.
© 2017 Informa UK Limited, trading as Taylor & Francis GroupKEYWORDS

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been paid on the topological defects induced by avariety of particles or the laser assisted self-assembly,
manipulation of defects by optical tweezers [3,4,12–14].
However, a few studies have been reported on thebulk and rheological properties of LC colloids. For
example, Oswald et al. studied the rheology of a lyotropic lamellar phase, where they showed under shear
flow how the dislocation loops cross and connect thelayers and disturb the flow [15]. Meeker et al. havefound an unusual soft–solid state in 5CB (pentyl cyanobiphenyl) LC colloids prepared by dispersing
PMMA(polymethylmethacrylate)
nanoparticles(250 nm) [16]. Petrov et al. showed that solid cellular
structures are formed in these systems [17]. Anderson
et al. studied the details of the morphology of thecellular microstructures [18]. Subsequently, they studied the mechanical properties of the nematic matrix
with the cellular morphology [19]. The origin of cellular structure was studied and discussed by Vollmer
et al. [20,21]. Raghunathan et al. studied the elastic
properties (splay and bend) of lyotropic LC colloids
and found no substantial change in the elastic constants in the low particle concentrations (<2%) [22].
Poulin et al. have studied the phase separation andmorphology of lyotropic colloidal systems made ofsmall particles (60–120 nm latex polyballs) [23].
Zapotocky et al. investigated the effect of bigger silica
particles (about 1 μm) in cholesteric LCs. From therheological studies, they showed the effect of networkof disclinations connecting the bigger clusters of particles [24]. Wood et al. dispersed nearly a micron-sizedparticle in 5CB and showed that the elasticity of the LC
colloids increases beyond a certain concentration. They
showed that it was due to the formation of percolating
network structure of disclination lines. These lines areentangled with the particles giving a self-quencheddefect glass state of line defects [25].
Bandyopadhyay et al. studied the rheology of LC–
aerosil (7 nm) composites of smectic-A (SmA) LC(8CB) and reported a soft glassy behaviour of thecomposites with increasing particle density [26].
Recently, Kulkarni et al. have reported on the effectof particle loading, particle shape on the rheology andthe phase-transition kinetics of lyotropic hexagonalLCs [27]. In all the above experiments, topologicaldefects induced by the particles play a crucial roleand these defects were induced mostly due to thespontaneous anchoring of the molecules on the particle’s surface. In the present study, we investigate therheological properties of LC colloids prepared by dispersing silica microparticles in 8CB LC. The particles
are treated for homeotropic alignment of the LC molecules at the surface that usually induce hyperbolic

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hedgehog, Saturn ring or escaped defects (bubblegum defects) depending on the surface anchoring andconfinement. We performed rheomicroscopy studies
that reveal shear-dependent microstructural change ofthe nematic colloid that gives shear thickening. Our
study suggests that with increasing volume fraction, the
SmA colloids tend to emerge from soft glass to shear
induced ordered state of colloids.

2 Experimental
In the experiment, we used monodisperse silica microspheres (average diameter 5 μm), coated with octadecyldimethyl (3-trimethoxysilylpropyl) ammonium
chloride (DMOAP) to obtain perpendicular (homeotropic) alignment of LC molecules on the surface.
Relatively larger size of the particle was chosen (thanpreviously reported) for the purpose of simultaneous
optical rheomicroscopy studies. The microspheres withdifferent volume fractions ðϕÞ namely 1–20% weredispersed in the nematic phase of 8CB LC by using avortex mixture and ultrasonication. Rheological measurements were made by using a controlled strainrheometer (Anton Paar MCR-501). The optical rheomicroscopy setup consists of a CCD colour camera(model: Lumenera), a microscope tube and a long
working-distance objective (NA = 0.4, 20×, Nikon)[28]. A polariser and an analyser were kept crossed
and placed in the tube in appropriate places. We used
parallel plate geometry of diameter 43 mm provided byAnton Paar for rheomiscroscopy studies. The thicknessof the bottom glass plate is 6 mm. The sample was
illuminated by light source through the objective fromthe bottom and the images were taken in the reflection
mode. The microscope tube is adjustable in both thehorizontal and vertical directions for the focusing purpose. The gap maintained between two parallel glass
plates was 0.075 mm. The temperature of the sample
was controlled by a Peltier temperature controller. The
compound 4-cyano-4′octylbiphenyl (8CB) was
obtained from Sigma-Aldrich and exhibits the following phase sequence: I 39.7°C N 32.4°C SmA. Thesetemperatures are measured by the Peltier temperature
controller of the rheometer. All the experiments were
performed in cooling the sample from the nematic to
SmA phase.

3. Results and discussion
3.1. Nematic colloids
First, we observed the textures and the phase-transition
temperatures of sample using polarising opticalDownloaded by [University of Hyderabad] at 04:44 14 September 2017

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Figure 1. Rheomicroscopy image taken under crossed without shear for ϕ ¼ 1% in the nematic phase (35°C). Four bright lobes showing
the director distortion due to the Saturn ring defects associated with the particles.

Figure 2. (a) Shear rate-dependent shear stress (σ) and (b) yield stress (σ y ) at various volume fractions at a fixed temperature(T = 35°C).

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LIQUID CRYSTALS

microscope. There was no appreciable change in thenematic–isotropic and nematic–SmA phase-transition
temperatures. This was further confirmed by differential scanning calorimetry studies (see Supplementary
Information) [29]. The sample was mounted on therheometer’s plate in the nematic phase.
Figure 1 shows the texture observed under rheomicroscope after mounting (without shear). Most of theparticles are agglomerated in smaller domains and only
a few of them are dispersed individually. The isolatedparticles in Figure 1 show four visible-coloured lobes of
director distortion suggesting they have quadrupolar
director configuration [25].
The sample was presheared at a low shear rate
(γ_ ¼ 10 s1 ) for 5 min before starting the measurements. Figure 2(a) shows the shear rate-dependentshear stress at different concentrations of particles in
the nematic phase (35°C). The apparent yield stress(σ y ) is increasing with increasing volume fraction ofparticles. Above shear rate 10 s–1, the stress is proportional to the shear rate and this behaviour is typical fornematics at high shear rate. Figure 2(b) shows thevariation of yield stress (σ y ) as a function of volume
fraction (ϕ). Up to ϕ ¼ 5%, it shows a small but linear
increase and beyond this σ y changes slope andincreases rapidly. For example, σ y at ϕ ¼ 20% isapproximately 200 times larger than that of the pure
8CB (Figure 2(b)). The linear increase of stress is
expected in dilute colloidal systems (Einstein’s relation). The rapid increase in the σ y suggests that there
are some collective response of the particles.
To get more insight into the dilute systems, we
looked at the textures in the rheomicroscope and measured the shear rate dependent viscosity at various temperatures. The sample was presheared at a high shear
rate (_γ ¼ 500 s1 ) for 5 min to disperse the particles.

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Figure 3 shows the variation of apparent viscosity at ϕ ¼
1% in the nematic phase at various temperatures. A
clear shear-thickening behaviour is observed in thenematic phase (with particles) at all temperatures in
the low shear rate range. This behaviour is significantly
different than the shear-thinning behaviour of nematicwithout particles (open circles in Figure 3).
Figure 4 shows some representative images taken at
different shear rates at temperature 33:5 C for ϕ ¼ 1%.
With increasing shear rate, different microstructures ofthe particles are observed. In the low shear rate range(0.01–0.4 s–1), the colloidal chains are bridged to forma network structure. The increase of the yield stress(Figure 2(b)) with volume fraction of particles is due tothese network structures. In the shear-thickening
region, the network is stretched, accompanied bydeformation of the bridging chains. Increasing theshear rate increases the stress on the network structuresand once the critical force is exceeded (about
γ_ ¼ 0:6 s1 ), they begin to break into smaller chainsshowing a shear-thinning behaviour. The shear thinning continues as long as the breaking process continues. At higher shear rate (γ_ ¼ 39:8 s1 ), the chains
start to break and forms relatively shorter chains. This
shear-thickening mechanism is somewhat similar to
those reported in micelle forming associating polymers
in water [30]. At much higher shear rate γ_ ¼ 100 s1 ,many chains tend to align normal to the shear direction. At the same time, many long disinclination lines
are appeared (Figure 4, γ_ ¼ 100  150 s1 ). These line
defects could be similar to those observed in microchannels by Sengupta et al.[31]. With increasing shear,
the nematic director is orientated more uniformly andthe nearly perpendicular orientation of the chains is
consistent with the quadrupolar defect structure. In
particular, in aligned cells, the quadrupolar chains

Figure 3. (Colour online) Variation of apparent viscosity η at a few temperatures at concentration ϕ ¼ 1%.

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R. SAHOO AND S. DHARA

Figure 4. (Colour online) Representative rheomicroscopy images taken during the measurement of shear rate-dependent shear
viscosity in the nematic phase at 33:5 C for ϕ = 1%. Red arrows indicate the disclination lines.

tend to align perpendicular to the nematic director. At
very high shear rate (above γ_ ¼ 200 s1 ), the shortchains further break into individual particles which
are connected by the disclination lines. This can beunderstood based on the competing effect of shear
energy and elastic interaction energy of the particles.
The approximate shear energy of a particle can be
written as E ¼ 6πηγ_ ha2 , where η is the apparent viscosity, h is the gap between the plates and a is the radiusof the particles. The estimated shear energy at γ_ ¼
20 s1 is about 106 kB T. Typical elastic interactionenergy per particle is about a few thousand kB T [4].
However, this energy is expected to be a few orders ofmagnitude larger in the network (because a large

number of particles are involved) and comparable tothe shear energy. When the shear energy exceeds theelastic interaction energy, the breaking of chains into
individual particles is expected.

3.2. SmA colloids
Induced defects and colloidal interaction in SmA LCs
are not well understood so far. There are a few studies
on the transformation of the topological defects acrossthe nematic–SmA phase transition [12–14] in uniformly aligned cells. The induced disorder by the foreign particles in the SmA phase is expected to affect themechanical properties. Hence, we carried out

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37oC (N)32.4oC (TN-SmA)

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28.5oC (SmA)

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Figure 5. (Colour online) Some representative rheomicroscopy images taken across the N–SmA phase transition (shear rate
γ_ ¼ 1 s1 ).

rheological measurements in the SmA phase. Figure 5
shows some representative rheomicroscopy images
taken across the N–SmA phase transition. We observedthat as the SmA phase is approached, the networks
tend to get compressed and in the SmA phase, theparticles are collapsed creating focal conic texture.
The regions without particles are well aligned (nofocal conic texture). Unlike the nematic phase, no
colloidal chains are observed in the SmA phase.
Isolated colloidal particles with quadrupolar defectacross the N–SmA phase transition have been studied
by us in planar-aligned cell [14]. The Saturn ring disappears at the transition and there is a boundary

condition violation at the interface, and clear layer
structure around the particles cannot be directlydeduced from the optical micrographs [14].
Figure 6(a) shows the variation of shear stress in the
SmA phase (28 C) at various volume fractions. The
apparent yield stress (σ y ) increases with increasing
volume fraction of particles. For example, σ y for pure
SmA is about 0.33 Pa and it increases to 51 Pa at
ϕ ¼ 20%; hence, this is about 150 times larger(Figure 6(b)).
Figure 7 shows the variation of storage (G0 ) and loss00
(G ) moduli, as a function of applied strain γ at different
volume fractions. Two important observations are madeFigure 6. (Colour online) (a) Shear rate-dependent shear stress in the SmA phase (28 C) at various volume fractions of particles. (b) Variationof yield stress (σ y ) with ϕ obtained from Figure 6(a).

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Figure 7. (Colour online) (a)–(e) Strain dependence of the storage G0 and loss G00 moduli with increasing volume fraction of particle
at constant angular frequency ω ¼ 1 rad=s at T ¼ 25 C. The arrows indicate the crossover. (f) The variation of critical strain
amplitude, γc (the crossover of G0 and G00 ), at different volume fractions.

[1]; both the elastic moduli (G0 and G00 ) increase and [2]the critical strain amplitude γc (crossover of G0 and G00 )decreases with increasing ϕ. For example, G0 is 300 times
larger in LC composite with ϕ ¼ 20% compared to thepure 8CB. The variation of γc (strain induced yielding)with ϕ at two different temperatures is shown in Figure 7(f). It is observed that γc is decreasing with increasing ϕ.
For example, the value of γc for 0–10% is one order ofmagnitude larger than that of ϕ ¼ 20%. This behaviour
can be explained based on the jammed domains ofparticles as seen in the rheomicroscopy (Figure 5, SmA
phase). With increasing ϕ, the number density and size ofthese jammed domains increase. As they are fragile,
under low strain amplitude, they can break and flow; asa result, the critical strain amplitude (γc ) is expected todecrease [32].
It is known that the colloidal suspension canundergo glass transition with increasing particle concentration and can crystallise under favourable

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Figure 8. (Colour online) Angular frequency dependence of storage (G0 ) and loss (G00 ) moduli at different volume fractions at constantstrain amplitude 0.03% at T ¼ 25 C. Continuous lines are the best fit to Equation (1). Vertical arrows indicate the minimum in G00 .

condition [32,33]. To see this aspect, we studied thefrequency dependence of the storage (G0 ) and loss (G00 )moduli. Figure 8 shows the angular frequency dependence of G0 and G00 at different volume fractions.
The SmA phase (without colloids) shows typicalfrequency dependence, i.e. both moduli are increasing
withfrequency.
It
is
noted
that
for
00
ϕ ¼ 1%; 5%and10%, G ðωÞ exhibits a shallow minimum. This is due to the increase in G00 ðωÞ at both
lower and at higher frequencies. The low frequency
rise is due to a very slow structural rearrangement of
the particles suggesting that there exists a relaxation
process. The high-frequency rise signifies thedomination of viscous relaxation of fluid phase[34,35]. This is also a typical characteristic of many
colloidal soft glasses. Hence, we analyse the results
based on the soft glassy rheology model. In thismodel, the real part of the storage modulus is given
by Refs [36,37]:G0 ðωÞ ¼ G0 þ βωα(1)where G0 is the plateau modulus that arises due to thestatic defects in SmA and the frequency-dependent term
results from the bulk response of the materials. β arises
from the disorientated (misaligned) parts of the sample[26,36,38]. The fit parameters are plotted with volume

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R. SAHOO AND S. DHARA

Figure 9. (Colour online) (a) Variation of α and the ratio G00 =G0 as a function of volume fraction of particles ϕ. (b) Variation of G0
and β with ϕ. The red line is the best fit result G0 ,ϕ1:80:2 .

fraction in Figure 9. It is observed that α decreases withincreasing volume fraction and tends to zero (α ! 0) up
to ϕ ¼ 10% (Figure 9(a)). Similar behaviour was also
observed in many colloidal soft glass materials [26,33].
The variation of the ratio G00 =G0 with ϕ is also shown in
Figure 9(a). We observe that G00 =G0 ,α as expected in thesoft glassy rheology model [26,37,39]. Figure 9(b) shows
the variation of G0 and β with volume fraction. The
increase of β with ϕ indicates that the contribution fromthe disoriented parts of the sample increases due to theinclusion of the particles. The increase of G0 indicatesthat the smectic line defects dominate this soft glassy
rheology. Theoretically in analogy with rubber elasticity,
the elastic response of static defect networks should vary
as G0 ,ρ2 , where ρ is the density of the particles [26,36].
In our experiment, we find that G0 ,ϕ1:80:2 (Figure 9(b)). Similar exponent was also reported in case of aerosildispersed SmA LCs (8CB) [26]. At higher concentrations(ϕ ¼ 20%), both α and the ratio G00 =G0 tend to increase
with ϕ. We conjecture that at this high-volume fraction ofparticles under oscillation, some short-range orderamong the particles is developed. However, further
study is required.

mediated by the induced defects with quadrupolar director configuration and form networks with increasing
volume fraction. We observed a shear-thickening behaviour in the low shear rate range. The rheomicroscopy
studies reveal the shear rate-dependent distinct dynamics
of the networks. The dynamic response of the SmA
colloids shows a soft glassy rheology with increasing
volume fractions up to a certain range. Finally, thisstudy shows that the rheological properties of nematicand SmA colloids are significantly contributed by theparticle-induced defects and their self-assembly.

4. Conclusion

Funding

In conclusion, we have studied the rheological propertiesof nematic and SmA LC colloids prepared by dispersing
spherical microparticles with homeotropic boundary condition in 8CB LCs. The microparticles create chains

We gratefully acknowledge the support from UPE-II, DST(Project ref.: DST/SJF/PSA-02/2014-2015), CSIR (Project ref.:03(1207)/12/EMR-II). R.S. acknowledges UGC for BSR
fellowship.

Acknowledgements
We gratefully acknowledge the support from UPE-II, DST(Project ref.: DST/SJF/PSA-02/2014-2015), CSIR (Project ref.:03(1207)/12/EMR-II). R.S. acknowledges UGC for BSR
fellowship.

Disclosure statement
No potential conflict of interest was reported by the authors.

LIQUID CRYSTALS

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