PHYSICAL REVIEW E 95, 012710 (2017)

Propelling and spinning of microsheets in nematic liquid crystals driven by ac electric field
M. V. Rasna,1 U. V. Ramudu,2 R. Chandrasekar,2 and Surajit Dhara1,*
2

1
School of Physics, University of Hyderabad, Hyderabad-500046, India
School of Chemistry, University of Hyderabad, Hyderabad-500046, India(Received 23 November 2016; published 30 January 2017)

Dynamics of microparticles in isotropic liquids by transducing the energy of an applied electric field havebeen studied for decades. Recently, such studies in anisotropic media like liquid crystals have opened up new
perspectives in colloid science. Here, we report studies on ac-electric-field-driven dynamics of microsheets innematic liquid crystals. In planar aligned liquid crystals, with negative dielectric anisotropy, the microsheets arepropelled parallel to the director. A steady spinning of the microsheets is observed in homeotropic cells withpositive dielectric anisotropy liquid crystals. The velocity of propelling and the angular frequency of spinningdepends on the amplitude and the frequency of the applied electric field. The electrokinetic studies of anisotropic
microparticles are important as they are potential for applications in microfluidics and in areas where the controlled
transport or rotation is required.
DOI: 10.1103/PhysRevE.95.012710
I. INTRODUCTION

Study on the externally driven dynamics of colloidal
particles is an active research field in soft matter science.
Most commonly used media for dispersing colloidal particles are the isotropic liquids, like water, and the common
driving force for particle dynamics is the electric field.
The electrokinetic phenomena are exploited in microfluidic
devices and electrophoretic displays [1–3]. They are mostly
described by induced charge electrophoresis (ICEP) and
induced charge electroosmosis (ICEO). The ICEP is assigned
to the particle motion driven by the ICEO flow around theparticle. The ICEP leads to the transport and rotation of
freely suspended colloidal particles [4–11]. In the isotropic
medium, for the particle to be electrokinetically active, it
must be charged or asymmetric [6,7]. However, in anisotropic
medium like liquid crystals some interesting phenomena withspherically symmetric and neutral microparticles are reported.
This includes nonlinear electrophoresis of dielectric andmetal microspheres, backflow-induced transport of particles
associated with the director realignment, linear and nonlinear
electrophoresis, Quincke rotation etc. [12–16]. In addition,some new mechanisms have been reported, which are known
as liquid crystal enabled electroosmosis (LCEEO) and liquid
crystal enabled electrophoresis (LCEEP). In the case of
LCEEO, the asymmetric ion flow leads to the pumping of
liquid crystal around static particles, whereas in LCEEP theparticles are free to be transported [17–23]. In all theseeffects the anisotropic physical properties of the medium,the director orientation as well as the induced defects play a
crucial role. It has been shown that no electrophoretic mobility
is observed for spherical microparticles with quadrupolar
director configuration such as Saturn ring and Boojum defects
due to the symmetric ion flow [17]. However, the ion flow
becomes asymmetric for spherical microparticles with dipolar
configuration. Although there are a few studies reported on theorientation, interaction, and induced defects by nonsphericalparticles, the electrokinetic studies of anisotropic microparti-*

sdsp@uohyd.ernet.in

2470-0045/2017/95(1)/012710(6)cles in the nematic liquid crystals are rare [23]. In this paper,
we report the electrokinetics of birefringent microsheets innematic liquid crystals. We show that the microsheets propel
along the director and spin around its long axis under ac electricfields. The velocity of propelling and the angular frequency ofspinning is controlled by the amplitude and frequency of theapplied electric field.
II. EXPERIMENTThe organic microsheets were prepared as per the reported
procedure [24]. It grows either in rectangular or hexagonal
shape. We have used 5,10,15,20-tetra(p-tolyl) porphyrin as abuilding block to prepare nearly monodispersed microsheets.
Figure 1 shows the optical microscopy image of a few
number of microsheets on the glass slide. The microsheets are
crystallized in tetrahydrofuran (THF) or THF/H2 O solvents.
The microsheets lengths and widths are in the range of 9 to
10 μm and 4 to 5 μm, respectively. The average thicknessof the microsheet is about 500 nm. The microsheets have amonoclinic crystal structure [24] and are optically birefringent[25]. They are emitting fluorescence light at wavelengths 719
and 653 nm upon excitation at 488 nm.
The microsheets are dispersed in liquid crystal by physicalmixing. In the present study we used 5CB liquid crystal having
positive dielectric anisotropy ( = 9.6) [26] and MLC-6608
exhibiting negative dielectric anisotropy ( = −4.2). The
experimental cells with required spacing were fabricated byusing indium-tin-oxide (ITO)-coated glass plates that are spincoated with polyimide AL-1254 and cured at 180◦ C for
1 h. They were rubbed antiparallel way for homogeneousalignment of the nematic director. For homeotropic alignment,
we used JALS-204 and cured at 200◦ C for 1 h. Sinusoidal
voltage was applied across the ITO electrodes of the cell using
a function generator (Tektronix-AFG 3102) and a voltage
amplifier (TEGAM-2350). The direction of the applied field
was perpendicular to the cell substrates. All the experiments
are done using ac electric field. The sample was observed
using an inverted microscope (Nikon eclipse Ti-U). The
trajectories of the particles were video recorded using a CCD
camera (Pixelink PLB 741F) and an appropriate computer

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RASNA, RAMUDU, CHANDRASEKAR, AND DHARA

PHYSICAL REVIEW E 95, 012710 (2017)

FIG. 1. Optical microscopy image of hexagonal single crystal
microsheets.

program was used to track the trajectories of the microsheets.
The orientation, interaction, and laser-assisted self-assemblyof the microsheets in nematic liquid crystal is reported in
our previous studies [25]. The microsheets induce tangential
anchoring (without any coating) of liquid crystal moleculeson the surface. Experimentally, it is difficult to identify theeffective shape of the defects such as being points or loops
around the microsheets. Dontabaktuni et al. have shown by
Landau de Gennes Q-tensor modeling that in the case ofplatelet-shaped particles, for strong anchoring, the defect cores
are at the edges of the platelets and for weak anchoring
the defects virtually sink inside the platelets [27]. In fact,
they showed that for the weak anchoring the defect are
spread as quasidefect line along the edges. In the present
case the anchoring is weak and similar defect structure isconsistent with the experimental observation. We also studied
the multiaxis rotations of the microsheets in both the isotropic
and nematic phase of liquid crystals recently [28].
III. RESULT AND DISCUSSION
A. Electric-field-driven propellingFirst, we discuss the electric-field-driven propelling of the
microsheets in a negative dielectric anisotropy nematic liquid
crystal (MLC-6608). In this case a planar cell was chosen
and the direction of the applied field is perpendicular tothe substrates. At zero field the plane of the microsheet isparallel to the cell substrates [Fig. 2(a)]. The long axes ofthe microsheets makes about 30◦ angle with respect to therubbing direction. This was supported by Landau de Gennes
Q-tensor modeling and reported in our previous studies [25].
When the electric field strength is increased the microsheet
first rotates about the long body axis beyond a field amplitudeof 0.2 V/μm [Fig. 2(b)]. The short axis of the microsheet
is now along the field direction. This rotation is due to theelectric-field-induced torque [28]. When the field is increased
beyond 1 V/μm, it starts to move along the x axis [Figs. 2(c)and 2(d)]. The long axis of the moving microsheet is tilted withrespect to the substrates. A video clip of the particle transport
is provided in the Supplemental Material (S1: video 1) [29].

FIG. 2. (Top view) Electric-field-driven propelling of a microsheet in a planar nematic cell with negative dielectric anisotropy
liquid crystal (MLC 6608) (see Supplemental Material S1: video 1[29]). (a–d) Sequence of CCD images of the microsheet taken at
different times and at applied field, E= 2.8 V/μm and frequency,
f = 1 kHz. Cell thickness d = 15 μm. Double-headed arrow at theright corner indicates the director and the electric field direction isout of plane.

The transport properties of the microsheet is characterized
by measuring the linear velocity as a function of applied
electric field and the driving frequency. Figure 3(a) shows
the time-dependent position. The linear variation suggests thatit moves with a uniform velocity. We measured the velocity(v) at various applied electric fields. Figure 3(b) shows thatbeyond a threshold field (1 V/μm), v varies quadratically withthe applied field. It may be mentioned that no transport isobserved in the isotropic phase. Similar behavior was observedin the case of spherical water microdroplets with a point defect(dipolar configuration) in a negative dielectric anisotropy
nematic liquid crystal [22,23]. It has been shown that theanisotropic character of the liquid crystal and the spatiallyvarying director distortion around the spherical microparticle
with hyperbolic hedgehog leads to liquid crystal enabledelectrophoresis (LCEEP) [13,17,18,21]. In that case the mobileions of liquid crystal move in opposite directions due to the
Coulomb force and the ionic mobility parallel to the local
director is different from that of the perpendicular direction.
The associated electro-osmotic flows are different in the two
opposite sides of the particle and the mirror symmetry ofelectro-osmotic flow is broken. Therefore, the flow is stronger
on one side of the microsphere and consequently it moves
toward the opposite side with a velocity given by: |v| =α◦ ¯ R[| σ− |]E 2 , where α is a constant and depends onησ̄¯
the director configuration, R is the size of the particle, ηis the average viscosity, σ̄ is the average conductivity, and¯ the average dielectric constant [17,20,21]. It should be
noted that for microparticles with Saturn ring and Boojum
defects, the director configuration is quadrupolar, which
preserves the fore-aft symmetry of the ion flow and resultsin zero electrophoretic mobility.
We further studied the frequency dependence of the liquid
crystal enabled electrophoretic velocity of the microsheets.

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PROPELLING AND SPINNING OF MICROSHEETS IN . . .

PHYSICAL REVIEW E 95, 012710 (2017)ceases to exist at both higher and lower frequencies. In
particular, the velocity is zero below 450 Hz and above
2.5 kHz. The frequency dependence of the induced charge electrophoretic flow has been studied for spherical microdropletsand microparticles [21,22]. The flow is described byω2 τe2,v(ω) = vo 
1 + ω2 τp2 1 + ω2 τe2FIG. 3. (a) The time-dependent position of a microsheet at a fixed
field strength E = 3.4 V/μm. (b) Electrophoretic velocity v as afunction of the applied electric field at a fixed frequency f = 1 kHz.
Cell thickness d = 15 μm. The red line is the best fit to v ∝ E 2 .
(Inset) The linear variation of v with E 2 .

Figure 4 shows the frequency dependence of transport velocities for two different field amplitudes namely, E = 3.2 V/μm
and 4 V/μm. They exhibit broad maxima and the propulsion

FIG. 4. Variation of velocity as a function of applied frequency
at two different fixed field strengths, E = 3.2 V/μm (green open
circles) and E = 4 V/μm (filled blue circles), respectively. Cell
thickness d = 15 μm. The continuous red lines are the best fits to
Eq. (1).

(1)where ω = 2πf , τp = λD L/2D is the particle charging timeand τe = λD d/2D is the electrode charging time. λD is the
Debye screening length, D is the diffusion coefficient of theions, and L is the particle size. The frequency dependence ofthe microsheets shows a generic behavior, i.e., similar to thatof spherical particles [22]. Therefore, it may be legitimate touse the same model for analysis. The experimental data is fittedwith Eq. (1), and the continuous red lines in Fig. 4 show thebest fits to the data. At higher frequency a small discrepancy inthe fitting may be partially due to the change in values of and σ of the liquid crystal with frequency. The fit parametersare τp = 5 × 10−4 s and τe = 2 × 10−3 s. The corresponding
lower and upper cutoff frequencies are given by fl = τe−1 ≈450 Hz and fu = τp−1 ≈ 2 kHz. These cutoff frequencies arevery close to the experimental values despite the very different
shape of the particle. One quantitative difference with theprevious studies on spherical microparticles is that here thefrequency range is much larger.
The quadratic variation of velocity with the electric field
and their frequency dependence clearly suggests that the
microsheets propel due to symmetry breaking ion flow. We
propose a possible mechanism by which the symmetric ion
flow around the microsheets can be broken. From our previous
studies we know that the director distribution has an asymmetry along the y axis (perpendicular to the rubbing direction)
as shown in Fig. 5(a) [25]. In particular, the distortion isstronger on the right side of the microsheet than the left side.
Figure 5(b) shows the schematic side view (after the rotation)of the microsheet when the electric field is applied (>1 V/μm).
In this case the microsheet is tilted with respect to the substrate
and one corner is closer to the bottom substrate than the other.
The strongest distortions of director are at the corners and

FIG. 5. (a) Schematic top view of a microsheet in a planar aligned
nematic at E = 0. Here the plane of the microsheet is parallel to x-yplane. The director field surrounding the microsheet is shown withdotted lines. (b) Schematic side view when the field is applied along
the z axis and E > 1 V/μm, the microsheet rotates along the x axis
and its plane becomes parallel to x-z. The black arrow indicates thetransport direction of the microsheet.

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PHYSICAL REVIEW E 95, 012710 (2017)

FIG. 6. Electric field response of microsheet at higher frequency(f = 100 kHz). Applied field amplitude E = 3.5 V/μm. (b) The
microsheet first rotates and the short axis of the sheet is now along thefield direction. (c) The microsheet moves toward the bottom substrate
and goes out of focus (see Supplemental Material S2: video 2). (d–f)
Returning back to the previous position after switching off the field.

these regions are enriched with positive and negative ions. The
applied electric field exerts a bulk force on the charge cloud,which leads to the flow of ions in the opposite directions andthe flow pattern follows the director structure. The flow ofions is stronger at the right side of the microsheet, which
pushes the particle in the left side [black arrow in Fig. 5(b)].
The microsheet is propelled along the negative direction of
the x axis when it is tilted counterclockwise with respect tothe director. Similarly, it moves along the positive x direction
when tilted in the clockwise direction. Thus, tilting of the
microsheet and the asymmetric director orientation can breakthe symmetry of the ion flow.
At much higher frequencies of the electric field [larger thanthe upper cutoff frequency, fu  2.5 kHz (see Fig. 4)], we
observed a change in the vertical position of the microsheetwith respect to the bottom substrate. In this case we applied anelectric field of amplitude 3.5 V/μm and frequency 100 kHz
and observed the response of a microsheet with time afterswitching on and switching off the field. Figure 6 shows thatwhen the field is switched on the microsheet first rotates
and tend to align the short axis along the field direction[Fig. 6(b)] and then goes down toward the bottom substratewith increasing time [Fig. 6(c)]. A video clip of the particles
movement showing that it goes out of focus toward thebottom surface is provided in the Supplemental Material (S2:video 2) [29]. Once the field is switched off, the microsheet
comes back to its original position due to the liquid-crystalenabled levitation [Figs. 6(d)–6(f)] [13]. A similar kind of
net displacement was observed for colloidal fullerenes in anematic liquid crystal [3]. It is suggested that if the frequencyof the electric field is greater than the frequency corresponding
to the particle charging time, a net dipole moment is induced
and the particles can get attracted toward the electrodes. In thepresent experiment it always move toward the bottom substrate
and this is probably due to the fact that the microsheets arecloser to the bottom substrate.

FIG. 7. Electric-field-driven spinning of a microsheet in a homoetropic cell with 5CB nematic liquid crystal (see Supplemental
Material S3: video 3). (a–f) Sequence of CCD images of the
microsheet taken at different times at field amplitude E = 0.85 V/μm
and frequency, f = 1 kHz. n̂ is the director and the field direction isout of the plane. White arrows indicate the direction of rotation. Cell
thickness d = 20 μm.

B. Electric-field-driven spinning

Further, we studied the electric-field response of the
microsheets in homeotropic cells with positive dielectricanisotropy nematic liquid crystal (5CB). The microsheet isstanding with respect to the substrate surface. From thecomputer simulation in our previous studies we found that thelong axis of the microsheet is tilted with respect to the verticaldirection by an angle of 22◦ [25]. When the ac electric field
is applied we observed that the microsheet becomes verticaland continuously spins about the field direction. The spinning
direction could be either clockwise or counterclockwise. Somesequence of images at different times of a microsheet is shownin Fig. 7. A video clip showing the spinning of three microsheets in both clockwise and counterclockwise directions
is provided in the Supplemental Material (S3: video 3) [29].
We measured the angular frequency of spinning at various
fields at a fixed frequency of the electric field. Figure 8(a)shows that the angular frequency varies quadratically withthe electric field beyond a threshold field (0.2 V/μm). We
also measured the dependence of the spinning frequency
on the driving frequency of the electric field at a fixedvalue (E = 1.5 V/μm). Figure 8(b) shows that the spinningfrequency decreases rapidly with increasing the driving (field)
frequency and finally becomes zero. It varies almost inverselywith the driving frequency (i.e., ω ∝ 1/f ) up to 2 kHz and thenchanges slope at 2.5 kHz and finally goes to zero at 3 kHz. Herethe upper cutoff frequency (3 kHz) is connected to the particle
charging time and this is almost comparable to the upper cutoff
frequency for the linear transport. When the field is switchedon in the isotropic phase, no sustained spinning was observed,
although it shows a tendency to spin but stops immediately (seeSupplemental Material, S4: video 4 [29]). This could be due tothe sedimentation of the microsheets. In the nematic phase therotation is sustained because the microsheets are pushed awayfrom both the plates due to the antagonistic director alignment

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PHYSICAL REVIEW E 95, 012710 (2017)of microparticles under ac field in isotropic fluids [6,8–10,30].
Bazant and coworkers have shown theoretically that breaking
spatial symmetry generically leads to an ICEO pumping flowthat can give rise to either directional motion or steady rotationof free particles in isotropic fluids [4,5,11]. They have studiedin great details on objects with various shapes and surface
properties, and the angular frequency of colloidal rotationshows quadratic field dependence [6,30]. Subsequently, there
have been some experimental studies showing the rotation ofJanus doublets, microvalves, microrod, etc., under ac electricfield [6,8,31]. From the field and frequency dependence ofspinning the microsheets it is clear that the spinning is dueto the ICEO as described by Bazant and coworkers. Although
the shape of our particle is very different than those usedin previous theoretical and experimental studies the basic
mechanism (ICEO) appears to be the same. Further studies
are needed to understand the system quantitatively.
IV. CONCLUSION

FIG. 8. (a) Variation of angular frequency of spinning of a
microsheet as a function of the applied electric field. The driving
frequency is f = 1 kHz. The solid red line is the best fit to ω ∝ E 2 .
(Inset) Linear variation of ω with E 2 . (b) Variation of angularfrequency of spinning as a function of driving frequency of the field(E = 1.5 V/μm). Red line shows the best fit to ω ∝ 1/f .

at the top and bottom sides of the microsheet with respect tothe plates [13]. It may be mentioned that this rotation is very
different than the Quincke rotation, which is observed underdc field, where the axis of rotation is perpendicular to the field
direction [14].
Under normal condition a uniform ac electric field cannot
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In conclusion, we have studied the electric-field-induced
propelling and spinning of microsheets in nematic liquid
crystals. These microsheets are optically anisotropic. In planaraligned liquid crystals with negative dielectric anisotropy, theelectric field does not reorient the director but the microsheet
propels parallel to the director. The propelling velocity varies
quadratically with the electric field. The frequency dependenceof the microsheet’s velocity exhibits a maximum and the
propulsion ceases above a particular frequency. We proposeda mechanism of asymmetric ion flow around the microsheetsthat accounts for the observed propulsion. We observed
sustained spinning of microsheets driven by ac electric field
in homeotropic cells with positive dielectric anisotropy liquid
crystals. The angular frequency of spinning is proportional
to the square of the applied field and decreases rapidly withincreasing frequency of the electric field and finally ceases
beyond a particular frequency. The diversity and complexityof electrokinetics of colloids are interesting and promising andwe hope this study will invoke more studies on highly shapeanisotropic microparticles.
ACKNOWLEDGMENTS

We gratefully acknowledge the support from the Department of Science and Technology (Grant No. DST/SJF/PSA02/2014-2015), and DST-PURSE. M.V.R. acknowledges
UGC-BSR for support through a fellowship grant.

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