Full Paper
www.advopticalmat.de

Orientation Dependent Interaction and Self-Assemblyof Cubic Magnetic Colloids in a Nematic Liquid Crystal
Devika Venkuzhy Sudhakaran, Ravi Kumar Pujala, and Surajit Dhara*
with their electric counterparts.[5,19] The
defect mediated elastic interaction gives
rise to 2D and 3D colloidal structures andsuperstructures, bearing strong potential
for photonic applications such as photonic
bandgap crystals.[10,20–22]
Research on nematic colloids ismostly concentrated so far on sphericalparticles.[19] Due to the advancement ofsynthesis and fabrication techniques,
recently a surge has been observed in
the number of investigations on nonspherical colloids, such as micro- andnanorods,[14,15] ellipsoids,[23] peanuts,[24]microbullets,[25] circular and polygonalplatelets,[16,17,26] handle-bodies of varying
genus,[7] and Mobius strips.[27] These
investigations have provided ample of new
results on the topological defects and ensuing self-assembled
structures. However, experimental studies on faceted colloids
such as cubes with flat faces are largely unexplored. There
are of course a few simulation studies on microcubes in NLC
showing the sharp edges act as pinning sites of Saturn ring
defect.[28,29] The cube is modeled using a special case of thesuperellipsoid equation: (x)2m + (y)2m + (z)2m = a2m, where mis a shape parameter, defining the roundedness of the corners.
It represents a sphere of radius a for m = 1, and a cube of side
length L = 2a for m → ∞ as shown in Figure 1. As m interpolates the shape between a sphere and a cube, the defect loop
evolves from a circular to distorted ring that wraps around thecolloid while following only the edges.[28]In this paper, we for the first time report experimental studies
on magnetic microcubes dispersed in a thin film of nematic
liquid crystal. We study spontaneous orientation, elastic interaction and laser tweezer assisted colloidal assembly. We showthat the cubic colloids stabilize diverse assemblies, which are
not viable in spherical colloids. The cubic particles are made ofhematite and hence respond to external magnetic fields, thereby
enabling us to determine the magnetic moment from the competing effects of magnetic and elastic torques. The magnetic
response provides an additional degree of freedom for manipulation and controlled assembly of colloids in liquid crystals.

Spherical microparticles dispersed in nematic liquid crystals have been
extensively investigated in the past years. Here, experimental studies arereported on the elastic deformation, colloidal interaction, and self-assembly ofhematite microcubes with homeotropic surface anchoring in a nematic liquid
crystal. It is demonstrated that the colloidal interaction and self-assemblyof cubic colloids are orientation dependent. In a notable departure from theconventional microspheres, the microcubes stabilize diverse structures, suchas bent chains, branches, kinks, and closed-loops. The microcubes reorient
under external rotating magnetic field, thereby experiencing an elastic
torque in the medium, which allows us to measure the magnetic moment
through competition between elastic and magnetic torques. The findings
envisage that the faceted magnetic colloids in liquid crystals are potential fordeveloping new functional magnetic materials with specific morphologies.

1. Introduction
Self-assembly of colloidal particles into large ordered structures is a subject of immense interest in the field of soft
matter, owing to the fundamental science and technologicalapplications.[1–4] In aqueous suspensions, the colloidal interaction is mostly driven by entropic or electrostatic forces, which
are short-range and isotropic, thus limiting the diversity in the
resulting colloidal structures. Colloidal dispersions in nematic
liquid crystals (NLCs) are very promising as they induce variety
of topological defects and interact via long-range elastic forcesof the medium.[5–13] They are especially interesting because
the interaction is anisotropic and shape dependent, thereby
providing a route to targeted colloidal assemblies.[14–17] Spherically symmetric particles with homeotropic surface anchoring
nucleates either a point defect (hedgehog) or a disclination ring
(Saturn ring)[5,18] in their vicinity. The colloids with accompanying point and ring defects are referred to as elastic dipolesand quadrupoles, based on the similarities of the director fields
D. Venkuzhy Sudhakaran, Prof. S. Dhara
School of Physics
University of Hyderabad
Hyderabad 500046, India
E-mail: sdsp@uohyd.ernet.in
Dr. Ravi Kumar Pujala
Soft and Active Matter Group
Department of Physics
Indian Institute of Science Education and Research (IISER)
Tirupati, Andhra Pradesh 517507, India
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adom.201901585.

DOI: 10.1002/adom.201901585

Adv. Optical Mater. 2020, 8, 1901585

2. Results and Discussion
The microcubes are nearly monodispersed with slightly
round edges as seen in the scanning electron microscope(SEM) image presented in Figure 2a. The shape of our microcubes closely resembles the simulated cube with sharpness

1901585 (1 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deIn this case, the face normals of two opposite
faces are parallel to n.
There are a very few computer simulation
studies on the defects and pair interaction of
cubic colloids using Landau–de Gennes (LdG)
Q-tensor theory. Hung et al. showed that cubic
nanocolloids mostly stabilize quadrupolarstructure with a distorted disclination ring
Figure 1. Superellipsoids at various values of sharpness parameter m, showing the gradualencircling the nanocubes, where the ringchange of roundness of the corners.
bends along six of the twelve edges of the
cube.[29] Our experiments show that microcubes predominantly (≈80%) stabilize quadrupolar structure,
factor m = 3 as shown in Figure 1. The average length ofwhich is consistent with the predictions of the simulation
the face diagonal is about 1.8 mm. Figure 2b shows a polar(Figure 2i). Beller et al. predicted the polymorphism of the disizing optical microscope (POM) micrograph with a few disclination ring, showing the rewiring of the defect ring to a newpersed microcubes in 5CB liquid crystal. It is apparent thatset of edges when the cube is rotated about a vertical axis throughthe microcubes have different orientations with respect toits center.[28] They showed that all these defect configurations
the rubbing direction, which cannot be determined conspicuously due to their small size. Nevertheless, careful obserof the microcubes correspond to the degenerate states of thevation at close-up reveals that there are mainly three types
LdG free energy. However, experimentally it is difficult to rotateof orientations with distinct elastic distortions in which
the cube as described in the simulation. Hence, we looked at thethe first and second types can be identified as elastic quadBrownian motion of a quadrupolar microcube. The microcube
rupoles (Figure 2c) and dipoles (Figure 2d); the third typeexecutes rotational diffusion as a result of which the quadrupolar(Figure 2e) exhibits an intermediate structure that does
texture evolves continuously with time (Movies S1, Supporting
not resemble either of them. For a quadrupolar microcube,
Information). A few snapshots captured at different time interthe face diagonal (Figure 2f), whereas the body diagonal ofvals using polarizing optical microscope are shown in Figure 4.
a dipolar microcube (Figure 2g) is parallel to the rubbing
A movie taken with a λ-plate is also presented in Movie S2 (Supdirection. In the intermediate structure, two opposite faces
porting Information). It clearly shows the change of director withof the microcube are perpendicular to the rubbing direction
time at the vicinity of the microcube. Thus, the temporal change(Figure 2h). Microscopic investigation on a large number ofof the texture is due to the rotation of the cube which could leadmicrocubes shows that majority (≈80%) of the microcubes
to the rewiring of the disclination ring as predicted.[28] However,are quadrupolar type and about ≈15% of them are dipolar
because of small size and the roundness of the edges, it is difficulttype (Figure 2i). There are only ≈5% microcubes exhibiting
to identify the different states with reconfigured disclination ring.
intermediate type director structure and the overall result is
As a next step we study the elastic pair interaction of thealmost independent of the cell thickness.
microcubes using videomicroscopy technique. We trap two
Qualitative information about the anchoring of the LC
microcubes using laser tweezers and release them from a few
molecules and the resulting defect is obtained by inserting a
micrometers apart and record their motion. The motion of thefull waveplate (λ-plate) at an angle of 45° with respect to themicrocubes in the NLC is overdamped due to the high viscosity, hence the net force experienced by the moving microcrossed polarizers. The POM micrographs and the correcubes at any instant is zero. This means the elastic force Fel issponding images taken with λ-plate are shown in Figure 3a,d,g.
The λ-plate introduces a phase shift of exactly one wavelengthbalancedby an opposing viscous drag force, Fdrag = − ζdR/dt,(530 nm) between the ordinary and extraordinary wavefrontsi.e., F el + F drag = 0, where ζ is the drag coefficient, and R(t) is
as a result of which mainly three colors are observed. The
the interparticle separation. The interaction potential W(r) ismagenta color corresponds to either vertical or horizontal
obtained by integrating
the drag force over the trajectory, i.e.,orientation of the director, whereas the bluish and yellowish W (r ) = ∫ F drag ⋅ dr .[10] Using methods similar to those reported incolors correspond to clockwise and anticlockwise rotation of therefs. [14,15], we measure the drag coefficients ζ∥ ≃ 0.9 × 10−6 kg s−1[15,19]director, respectivelyand ζ⊥ ≃ 1.7 × 10−6 kg s−1, by measuring the anisotropic diffuas shown in Figure 3b,e,h. 3D schematic diagrams with induced defects of the microcubes are alsosion coefficients D∥ and D⊥ at room temperature (T = 298 K).
presented in Figure 3c,f,i. Figure 3c shows that two opposite
The subscripts refer in relation to the director n. The drag coefface diagonals of the microcube are parallel to n and the disficients weakly depend on the deformations hence, the averageclination ring (Saturn ring) encompasses the four vertices of adrag coefficient ζ = (ζ∥ + ζ⊥)/2 ≈ 1.3 × 10−6 kg s−1 is used inbody diagonal plane. In Figure 3f, one of the body diagonals
calculating the interaction energy. The elastic force between
is parallel to n and the microcube is accompanied by a point
two quadrupolar colloids is given by Fe = −k/R6 and the corredefect, closely resembling its spherical counterpart. The texture
sponding intercolloid separation is given by[16,17]
shown in Figure 3g evokes an interesting situation where the(1)R(t ) = {R(0)7 − 7α t}1/7
surrounding director profile as shown in Figure 3h is roughly
in agreement with the dipole, except the point defect. Thissuggests that the intermediate texture corresponds to a defectwhere α = K/ζ and R(0) is the initial separation at t = 0 s.
structure, where the defect ring wraps the four edges of a face,
Figure 5a shows the variation of R(t) of two quadrupolar microwhich is perpendicular to the director n as shown in Figure 3i.
cubes and the nonlinear least squares fit to Equation (1). The

Adv. Optical Mater. 2020, 8, 1901585

1901585 (2 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 2. a) Scanning electron microscope (SEM) micrograph of the silica coated hematite microcubes. b) Polarizing optical microscope (POM)
micrograph of dispersed microcubes in 5CB nematic liquid crystal. POM micrographs of c) quadrupolar, d) dipolar, and e) intermediate type elastic
distortions. f–h) Micrographs of the corresponding microcubes without polarizer and analyzer. i) Percentage of occurrence of three types of elastic
distortions. About 200 particles are studied in two different cells with thickness 5 mm (red) and 8 mm (blue). Double headed arrows above n denotethe director, which is parallel to the rubbing direction.

binding energy of two quadrupolar microcubes is ≈800 kBT(inset to Figure 5a). The angle dependence of interaction of the
microcubes, presented in Figure 5b, resembles to that of thespherical particles. For dipolar colloids, the interaction is given

Adv. Optical Mater. 2020, 8, 1901585

by Fe = −k/R4 and the time dependent interparticle separation
can be written as[16,17]
R(t ) = {R(0)5 − 5α t}1/5

1901585 (3 of 9)(2)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 3. a,d,g) Polarizing optical microscope (POM) and the corresponding λ-plate micrographs of three types of colloids. b,e,h) Constructed director
profiles of each colloid. c,f,i) 3D orientation of the microcubes with induced defects. Defect rings (thick red lines) are pinned on the surface of the
microcubes.

Figure 5c shows the variation of R(t) and the corresponding
least squares fit to Equation (2). The binding energy of two
dipolar microcubes is ≈5000 kBT (inset to Figure 5c), which ismuch larger than that of quadrupolar microcubes. The interparticle separation R(t) for two microcubes with intermediate
structure (see Figure 3g) is shown in Figure 5e. R(t) fits well to

Figure 4. A few snapshots of rotational Brownian motion of a microcube at different time intervals (see Movies S1 and S2 in the Supporting
Information).

Adv. Optical Mater. 2020, 8, 1901585

Equation (2) and the corresponding interaction energy is shown in
the inset. The binding energy of two such microcubes is ≈1300 kBT(inset to Figure 5e), which is much lower than the dipolar
microcubes. Moreover, the angle dependence of the interactionof microcubes with intermediate structure is markedly different
than the dipolar microcubes, where the point defects of boththe colloids are on the same side (Figure 5d). In particular, theinteraction between two intermediate microcubes is attractiveat all angles (Figure 5f), whereas for the dipolar microcubes, it
is either attractive or repulsive, depending on the approachingangles with respect to the director (Figure 5d). This unusual
behavior of the microcubes with intermediate structure could
be related to the relocation of the defect loop between the two
orthogonal (with respect to n) faces while interacting. Taking
advantage of the anisotropic interactions and the cubic shape,
we prepared several equilibrium assemblies of the microcubes

1901585 (4 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 5. Interparticle separation R(t) with time of a pair of interacting a) quadrupolar, c) dipolar microcubes, and e) the microcubes exhibiting intermediate texture. Red lines are the least squares fits corresponding to equations R(t) = {R(0)7 − 7αt}1/7 for quadrupolar and R(t) ={R(0)5 − 5αt}1/5 for dipolar interactions. Corresponding potential energies (W(r)) in units of kBT are shown in the inset. b,d,f ) Relative coordinates
and resulting color-coded trajectories as a function of time for respective colloids. By “relative coordinate” we mean relative to the starting pointof each trajectory.

Adv. Optical Mater. 2020, 8, 1901585

1901585 (5 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 6. Laser tweezers assisted assembly of microcubes witha,e,h) bent chains, b,i) branches, c,j) kinks, d) 2D crystal, and f,g) closed-loop
structures. CCD images of the same are shown in Figure S1 (Supporting
Information).

with the help of the laser tweezers. Figure 6 shows a few nonlinear chains, branches, kinks, 2D crystals, and closed-loop
structures. The assembled structures of the microcubes arediverse when compared to that of spherical colloids which primarily stabilize either linear or zigzag chains.[10] The segments
which are parallel or perpendicular to the far field director are
mostly composed of either dipolar or quadrupolar colloids,
respectively. Microcubes with intermediate structure helps informing branches, kinks, and loops. These structures are highly
stable against thermal fluctuations and respond to external
magnetic fields, hence could be useful as building blocks inmaking advanced magnetic materials with desired architecture.
It may be mentioned that in addition to elastic interaction, themicrocubes also experience magnetic dipole–dipole interaction and electrostatic repulsion due to electric double layer.

Adv. Optical Mater. 2020, 8, 1901585

Since the conductivity of the liquid crystal is very small, theelectrostatic repulsion is expected to be negligibly small. The
maximum magnetic dipole–dipole interaction (for parallel orientation) is estimated to be U d ≈ 100 kBT,[30] which is smaller
than the elastic interaction potential energy. Hence, the selfassembly of the microcubes is dominated by elastic interactions.
The microcubes possess a permanent magnetic moment
along a direction which is nearly parallel to the body diagonal.[30]In water, Earth’s magnetic field helps in forming linear chains,which are parallel to the field direction.[31,37] However, in NLC,
the orientation of the microcubes is mainly governed by thesurface anchoring and the ensuing energy of the elastic distortion and is unaffected by the Earth’s magnetic field. To study theeffect of applied magnetic field, we used two disc-shaped magnets and positioned them diametrically opposite on a circular
track around the plane of the sample as shown in Figure S2(Supporting Information). This arrangement provides an inplane magnetic field which can be rotated around the cell bysimultaneously rotating the two magnets. The strength of the
field at the sample position measured by a magnetometer is
300 G. Although the individual microcubes respond to therotating magnetic field, it is difficult to determine the angle ofrotation conspicuously. Hence, we assembled dipolar and quadrupolar pairs of the microcubes using the laser tweezers andstudied their magnetic response. Figure 7a shows a pair of quadrupolar microcubes, oriented perpendicular to n in the absenceof applied magnetic field. When the magnetic field is rotatedfrom −90° to +90° around the director, the body diagonal of thepair tends to follow the field direction as shown in Figure 7b.
This means  the direction of the resultant magnetic moment( µ eff = µ 1 + µ 2 ) is approximately parallel to the body diagonalof the pair as shown in Figure 7c. For a dipolar pair, the long
body axis is parallel to the director in the absence of magnetic
field as shown in Figure 8a. When the magnetic field is rotated,
the short body axis of the pair tends to follow the field direction (Figure
 8b). This suggests that the direction of the resultant
moment µeff is along the short body axis of the pair as shown in
Figure 8c.
The rotation of the microcube-pair increases the elastic
energy, which opposes the effect of the magnetic torqueµ eff × B. In both cases, µeff and the magnetic field B makeangle θ and φ with respect to the director n. At equilibrium,
the magnetic torque μeffB sin (φ − θ) is balanced by the gradientof the elastic energy −∂U/∂θ and the torque balance equation
can be written as[32,33]− ∂U / ∂θ + µ eff B sin(φ − θ ) = 0(3)

The enhancement in the elastic energy due to the rotation
by an angle θ, in analogy with the electrostatic energy of a rod
at a fixed potential is given by U = 2πCKθ2,[32] where K is theeffective Frank elastic constant and C = L/[2log(L/d)], where L
and d are the length and diameter of the assembled pair. The
magnetic moments of both the pairs are determined from theslope of the equation Bsin (φ − θ) = (4πCK/μeff)θ. Figures 7d
and 8d shows that Bsin (φ − θ) is linearly proportional to θ withslopes 143 and 106 G rad−1 for quadrupolar and dipolar pairs,
respectively. Taking C = 4.0 × 10−6 m and K = 5 × 10−12 N, theestimated magnetic moments for quadrupolar and dipolar

1901585 (6 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 7. a) POM micrograph of a pair of assembled quadrupolar cubes in the absence of magnetic field (B = 0 ). b) The direction of B is changed
from −90° to +90° as shown by the red-arrow, keeping the field strength fixed at 300micrographs of the reoriented pair at equilibrium
are also G. POM
shown. The pair flips the orientation at θ = 0. c) Individual magnetic moments µ 1 and µ 2 of the microcubes and the resultant moment µ eff of the pair.
θ and φ are the angles subtended by µ eff and B with respect to n. d) Variation of Bsin (φ − θ) with θ. The red lines are the linear least squares fits to theequation: Bsin (φ − θ) = (4πCK/μeff )θ with an average slope of 143 G rad−1.

pairs are given by μeff ≃ 18 × 10−15 and 24 × 10−15 A m2, respectively. Assuming that both the magnitudes are identical, themagnetic moment of a single microcube in quadrupolar pairis given by μ1 = μ2 = μeff/2 ≃ 9 × 10−15 A m2. For the dipolar
pair, the magnetic moment along the body diagonal makes anangle of 35° with respect to the face diagonal and hence themagnetic moment is given by μ1 = μ2 = μeff/2 cos (35°) ≃ 14 ×
10−15 A m2. The average magnetic moment obtained fromtwo differently assembled pairs of microcubes are given byμ ≈ 11.5 × 10−15 A m2. This result is very close to the theoretically calculated and experimentally measured value of the bulk
sample composed of similar microcubes by an alternating current gradient magnetometer.[30] However, our method is very
simple and provides measurement at microscopic level thanthe conventional method used for bulk sample composed of avery large number of microcubes.

3. Conclusion
Microcubes with homeotropic surface anchoring exhibit
mainly three different orientations in a nematic liquid crystal.
For majority of the microcubes, the face diagonals of a pair ofAdv. Optical Mater. 2020, 8, 1901585

opposite faces are parallel to the rubbing direction and exhibit
quadrupolar interaction. Dipolar structure with a point defectis exhibited by a small number of microcubes for which oneof the body diagonals is nearly parallel to the rubbing direction. In a very small fraction of microcubes, two opposite faces
are oriented perpendicular to the rubbing direction in which
the disclination ring wraps around the four edges of eitherof the faces. The angle dependence of the elastic interactions
is markedly different for all three distinct orientations of the
microcubes. Our experiments provide an evidence of defectpolymorphism of the microcubes, which was predicted earlier
by the computer simulation. With the help of the laser tweezers, we assembled microcubes into various structures, such as
highly bent chains, branches, kinks, closed loops, which are notachievable in spherical colloids. The combined effects of particle-shape, anisotropic interaction, and magnetic properties ofthe microcubes in liquid crystals are effectively used to design
diverse building blocks which could be useful for assembling
complex, programmable, and magnetically responsive colloidal structures. Our investigations have focused on cubic
particles; however, the plethora of faceted colloids accessible
promises a wide range of as yet unexplored phenomena andtheir applications.

1901585 (7 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.deFigure 8. a) POM micrograph of a pair of assembled dipolar microcubes in the absence of magnetic field (B = 0). b) B is changed from −90° to +90° as
shown by the red arrow, keeping the strength fixed at 300 G. POM micrographs of thepair are also shown. The pair flips the orientationat reoriented
θ = 0.c) Schematic
representation of the direction of individual magnetic moments µ 1 and µ 2 of the microcubes and the resultant moment µ eff of thepair. µ eff and B make angle θ and φ with respect to n. d) Variation of Bsin (φ − θ) with θ. The red lines are the linear least squares fits to the equation:
Bsin (φ − θ) = (4πCK/μeff )θ with an average slope of 106 G rad−1.

4. Experimental Section
Cubic hematite particles (α-Fe2O3) were synthesized using sol–gel
method.[34,35] In the synthesis, NaOH solution (100 mL, 6 m) was slowly
added to 2.0 m FeCl3 solution (100 mL) in a Pyrex bottle and agitated for
15 min. The entire solution was aged for 8 days at 100 °C and washedwith milliQ water to obtain the hematite cubes. A thin layer (60 nm) of
Silica (SiO2) coating on the cubes was made via an adaption of the Stöber
method.[36,37] A smooth layer of silica was grown on to the hematite cube
by functionalizing it with polymer polyvinylpyrrolidone (PVP, 40 kg mol−1).
PVP is a nonionic and amphiphilic polymer that readily adsorbs on a variety
of materials. In this study, PVP got adsorbed onto the hematite surface andacted as a coupling agent between the seed particle and the silica coating.
PVP also acted as a stabilizing polymer on the silica-coated hematite cube.
Approximately 0.5 g of hematite cubes was dispersed in 5 mL of waterand the resulting dispersion was mixed with 50 mL of PVP solution. The
mixture was stirred for 8 h and then sonicated to ensure the complete
dissolution of PVP. Later, ethanol, water, and tetramethylammoniumhydroxide (TMAH, 25 wt%) solution were added, followed by dropwise
addition of tetraethoxysilane (TEOS). TMAH is a strong base which is used
to catalyze the hydrolysis and condensation of TEOS. The resulting solution
was washed several times by centrifugation and redispersed in ethanol
to obtain silica coated hematite microcubes. Further, the silica coatedmicrocubes were treated with N,N-dimetyl-N-octadecyl-3 aminopropyltrimethoxysilyl chloride (DMOAP) to ensure perpendicular or homeotropic
anchoring of the liquid crystal molecules on the surface.

Adv. Optical Mater. 2020, 8, 1901585

In the next step, the microcubes were dispersed (1 wt%) in a roomtemperature nematic liquid crystal, pentyl cyanobiphenyl (5CB) by using
a vortex mixture and ultra sonicator. The nematic colloid was filledin cells prepared by two parallel glass plates, which were polyimide(AL-1254) coated and baked at 180 °C, followed by a unidirectional
rubbing. The nematic director n (mean molecular orientation) wasaligned along the rubbing direction. The cell gap (≃5–8 mm) was
maintained by spherical silica spacers mixed with a UV curable
optical adhesive (NOA-81). An inverted polarizing optical microscope(Nikon eclipse Ti-U) with a 60× water immersion objective and a color
camera (Nikon DS-Ri2) was used for texture observation and video
recording. A first-order waveplate, so-called λ-plate (530 nm) was used
for constructing director field (n) surrounding the particles. A laser
tweezer operating at 1064 nm (Tweez 250si) was built on the inverted
microscope. An acousto-optic deflector (AOD) was used for optical trap
and hence the particle manipulation. A charge-coupled device (iDs-UI)
was used for the video recording of the particle trajectories. A particle
tracking program was used off-line for tracking the centers of theparticles with an accuracy of 20 nm.

Supporting Information
Supporting Information is available from the Wiley Online Library orfrom the author.

1901585 (8 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.com

www.advopticalmat.de

Acknowledgements
S.D. acknowledges the support from DST (DST/SJF/PSA-02/20142015) and DST-PURSE. D.V.S. acknowledges DST for INSPIRE
fellowship. R.K.P. acknowledges DST for INSPIRE Faculty award grant(DST/INSPIRE/04/2016/002370). We greatly acknowledge the help ofRamakrishna Kotni and Prof. Alfons van Blaaderen at Utrecht University,
Netherlands, during the synthesis of hematite cubes.

Conflict of Interest
The authors declare no conflict of interest.

Keywords
cubic hematite colloids, magnetic moments, self-assembly, topologicaldefects
Received: September 19, 2019
Revised: December 13, 2019
Published online: January 22, 2020

[1] G. M. Whitesides, B. Grzybowski, Science 2002, 295, 2418.
[2] S. Noda, T. Baba, in Roadmap on Photonic Crystals (Eds: S. Noda,
T. Baba), Springer, Boston, MA 2003, pp. 243–249.
[3] V. W. A. de Villeneuve, R. P. A. Dullens, D. G. A. L. Aarts,
E. Groeneveld, J. H. Scherff, W. K. Kegel, H. N. W. Lekkerkerker,
Science 2005, 309, 1231.
[4] A. van Blaaderen, R. Ruel, P. Wiltzius, Nature 1997, 385, 321.
[5] H. Stark, Phys. Rep. 2001, 351, 387.
[6] P. Poulin, H. Stark, T. C. Lubensky, D.A. Weitz, Science 1997, 275, 1770.
[7] B. Senyuk, Q. Liu, S. He, R. D. Kamien, R. B. Kusner, T. C. Lubensky,
I. I. Smalyukh, Nature 2013, 493, 200.
[8] K. P. Zuhail, S. Dhara, Appl. Phys. Lett. 2015, 106, 211901.
[9] I. I. Smalyukh, O. D. Lavrentovich, A. N. Kuzmin, A. V. Kachynski,
P. N. Prasad, Phys. Rev. Lett. 2005, 95, 157801.
[10] I. Muševič, M. Škarabot, U. Tkalec, M. Ravnik, S. Žumer, Science
2006, 313, 954.
[11] I. Muševič, M. Škarabot, Soft Matter 2008, 4, 195.
[12] K. P. Zuhail, S. Čopar, I. Muševič, S. Dhara, Phys. Rev. E 2015, 92,052501.

Adv. Optical Mater. 2020, 8, 1901585[13] K. P. Zuhail, P. Sathyanarayana, D. Šec, S. Čopar, M. Škarabot,
I. Muševič, S. Dhara, Phys. Rev. E 2015, 91, 030501.
[14] M. Rasi M, R. K. Pujala, S. Dhara, Sci. Rep. 2019, 9, 4652.
[15] U. Tkalec, M. Škarabot, I. Muševič, Soft Matter 2008, 4,
2402.
[16] C. P. Lapointe, T. G. Mason, I. I. Smalyukh, Science 2009, 326, 1083.
[17] M. V. Rasna, K. P. Zuhail, U. V. Ramudu, R. Chandrasekar,
J. Dontabhaktuni, S. Dhara, Soft Matter 2015, 11, 7674.
[18] S. Ramaswamy, R. Nityananda, V. A. Raghunathan, J. Prost, Mol.
Cryst. Liq. Cryst. 1996, 288, 175.
[19] I. Muševič, Liquid Crystal Colloids, Springer, Cham, Switzerland
2017.
[20] M. Ravnik, M. Škarabot, S. Žumer, U. Tkalec, I. Poberaj, D. Babič,N. Osterman, I. Muševič, Phys. Rev. Lett. 2007, 99, 247801.
[21] U. Tkalec, M. Ravnik, S. Čopar, S. Žumer, I. Muševič, Science 2011,
333, 62.
[22] A. Martinez, L. Hermosillo, M. Tasinkevych, I. I Smalyukh, Proc.
Natl. Acad. Sci. USA 2015, 112, 4546.
[23] M. Tasinkevych, F. Mondiot, O. Mondain-Monval, J.-C. Loudet, Soft
Matter 2014, 10, 2047.
[24] D. K. Sahu, T. G. Anjali, M. G. Basavaraj, J. Aplinc, S. Copar,
Surajit Dhara, Sci. Rep. 2019, 9, 81.
[25] M. A. Gharbi, M. Cavallaro Jr., G. Wu, D. A. Beller, R. D. Kamien,
S. Yang, K. J. Stebe, Liq. Cryst. 2013, 40, 1619.
[26] J. Dontabhaktuni, M. Ravnik, S. Žumer, Soft Matter 2012, 8,
1657.
[27] T. Machon, G. P. Alexander, Proc. Natl. Acad. Sci. USA 2013, 110,
14174.
[28] D. A. Beller, M. A. Gharbi, I. B. Liu, Soft Matter 2015, 11, 1078.
[29] F. R. Hung, S. Bale, Mol. Simul. 2009, 35, 822.
[30] L. Rossi, J. G. Donaldson, J. M. Meijer, A. V. Petukhov, D. Kleckner,
S. S. Kantorovich, W. T. M. Irvine, A. P. Philipse, S. Sacanna, Soft
Matter 2018, 14, 1080.
[31] L. Rossi, S. Sacanna, W. T. M. Irvine, P. M. Chaikin, D. J. Pine,
A. P. Philipse, Soft Matter 2011, 7, 4139.
[32] F. Brochard, P.G. de Gennes, J. Phys. 1970, 31, 691.
[33] C. Lapointe, A. Hultgren, D. M. Silevitch, E. J. Felton, D. H. Reich,R. L. Leheny, Science 2004, 303, 652.
[34] T. Sugimoto, K. Sakata, J. Colloid Interface Sci. 1992, 152, 587.
[35] T. Sugimoto, K. Sakata, A. Muramatsu, J. Colloid Interface Sci. 1993,
159, 372.
[36] C. Graf, D. L. J. Vossen, A. Imhof, A. van Blaaderen, Langmuir 2003,
19, 6693.
[37] J. M. Meijer, D. V. Byelov, L. Rossi, A. Snigirev, I. Snigireva,
A. P. Philipse, A. V. Petukhov, Soft Matter 2013, 9, 10729.

1901585 (9 of 9)© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim