Soft Matter
PAPER

Cite this: Soft Matter, 2016,12, 6812Eﬀect of temperature and electric field on 2D
nematic colloidal crystals stabilised by vortex-like
topological defects†
K. P. Zuhail and Surajit Dhara*
We report experimental studies on 2D colloidal crystals of dimers stabilized by vortex-like defects inplanar nematic and p/2 twisted nematic cells. The dimers are prepared and self-assembled using a laser
tweezer. We study the eﬀect of temperature and electric field on the lattice parameters of the colloidal

Received 30th May 2016,
Accepted 15th July 2016
DOI: 10.1039/c6sm01244b

crystals. The lattice parameters vary with the temperature in the nematic phase and a discontinuous
structural change is observed at the nematic to smectic-A phase transition. In the nematic phase, we
observed a large change in the lattice parameters (C30%) by applying an external electric field
perpendicular to the plane of the 2D crystals. The idea and the active control of the lattice parameters

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could be useful for designing tunable colloidal crystals.

I. Introduction
There has been growing interest in developing photonic crystals
using self-assembled colloidal particles and tuning their opticalproperties by several means. Tuning has been attempted in various
ways, such as by chemical methods,1,2 field eﬀects3,4 and temperature variation.5,6 In this context, self-assembled structuresof colloidal particles in nematic liquid crystals appeared to havepotential for making a tunable colloidal assembly.7,8 The
particles in nematic liquid crystals induce topological defects
and particle–defect combinations are known as elastic dipolesor quadrupoles depending on the symmetry of the transverse
components of the far-field director.9–15 These dipoles have anatural tendency to self-assemble due to anisotropic elastic
forces. The self-assembly of these colloids can be guided andcontrolled using laser tweezers to form several spectacular 1D,
2D and 3D structures, which are stabilized by singulardefects.8,9,16–18 An unusual defect structure in which a nonsingular disclination loop with a vortex-like defect is formed
when two collinear anti-parallel elastic dipoles are pushed.19–21
This structure is named an escaped hyperbolic defect ring
(EHDR) with a topological strength of 2. The loop encircles
the line connecting two particles and forms dimers which aremetastable in planar nematic (PN) cells (see in Fig. 1(b)).
However, in twisted nematic (TN) cells, chirality escalates the
spontaneous formation of non-singular colloidal dimers fromanti-parallel dipoles.22 In this paper, we for the first time show

Fig. 1 Optical micrograph of a colloidal dimer with a vortex-like defect in
the PN cell under crossed polarizers in the 8CB liquid crystal. (a) A dimer in
the N phase, (b) schematic diagram of director orientation around theparticles (adapted from ref. 21). (c) Transformation of defect at the N–SmA
phase transition. (d) A dimer in the SmA phase. See ESI† (Video 1). Particle
size 5.2 mm and cell thickness 8.5 mm.

the effect of temperature and an external electric field on the2D crystals formed by colloidal dimers (stabilised by nonsingular defects) used as building blocks. We show that thelattice parameters vary with temperature in the nematic phasefollowed by a structural change at the nematic to smectic-A
phase transition. Above the Freedericksz threshold field weshow a large decrease of the lattice constants with increasing
electric field.

II. Experimental
School of Physics, University of Hyderabad, Hyderabad, India.
E-mail: sdsp@uohyd.ernet.in† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sm01244b

6812 | Soft Matter, 2016, 12, 6812--6816

Experiments were performed in glass cells which were spincoated with polyimide (AL-1254) and cured at 100 1C for 1 h.

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Paper

The PN cells were prepared by arranging the rubbing directionsin an anti-parallel way. The TN cells were prepared by keeping
the rubbing directions of the plates mutually perpendicular. In
both the cells, a typical gap maintained is about 8 mm. We usedsilica microspheres of (2R) 5.2 mm diameter coated with DMOAP
silane (octadecyldimethyl-3-trimethoxysilylpropyl-ammonium
chloride) to induce strong homeotropic anchoring of liquid
crystal molecules. The coated colloids are dispersed in 8CB(4 0 -n-octyl-4-cyano-biphenyl) and 5CB (4-cyano-4 0 -pentylbiphenyl)
liquid crystals. 8CB and 5CB exhibit the following phasetransitions: Cr. 21.5 1C SmA 33.5 1C N 40.5 1C I and Cr. 22 1C
N 35 1C I, respectively. The electric field is applied using afunction generator (Tektronix-AFG3102) and a voltage amplifier(TEGAM-2350). A laser tweezer was built around an inverted
microscope (Nikon eclipse Ti-U) using a CW diode pumped
solid state laser operating at 1064 nm (Aresis: Tweez 250si).
A computer interfaced acousto-optic deflector was used for thetrap movement. The temperature of the sample was controlled
by a home-built heater and a proportional-integral-derivative(PID) controller with an accuracy of 0.1 1C. The trajectories ofthe particles were video recorded using a CCD camera (iDS-UI)
at 20 frames per second. The center-to-center distance between
the particles was measured from the video analysis and particle
tracking software with a resolution of 10 nm.

III. Results and discussion
To study the eﬀect of temperature and also the N–SmA phasetransition on the 2D colloidal crystals we selected 8CB liquid
crystal. In the nematic phase, in PN cells, two collinear andparallel elastic dipoles are attracted and antiparallel dipoles are
repelled. However, if the anti-parallel collinear dipoles arestrongly pushed together using the optical tweezer it forms a
dimer, which is connected by an escaped non-singular defect.
This defect is also known as the ‘‘bubblegum defect’’.19–21
Fig. 1(a) shows an image of such a dimer in the nematic phaseof 8CB. The local frustration in the director field between thecolloids is clearly observed in the POM (polarizing optical
microscopy) images (Fig. 1(a)). The director field around the
bubblegum is known to be axially symmetric, minimally distorted
and continuous (Fig. 1(b)). Fig. 1(c) and (d) show the transformation of the bubblegum defect when the temperature changes
from the N to the SmA phase. The director distortion between thecolloids and in their surroundings expands as the SmA transition
is approached (Fig. 1(c)). In the SmA phase, the distortion shrinks
to narrow regions (the bright incomplete rings in Fig. 1(d))
around the particles except the left and right hand sides of the
dimer. The video of this transition and the temperature variationof the center to center separation between the particles acrossthe phase transition are given in the ESI.† 23 It shows that theequilibrium separation is linearly proportional to the elastic
anisotropy, DK (=K33  K11, where K33 and K11 are the bend andsplay elastic constants). Recently we have shown the transformation of dipoles,16 quadrupoles17 and boojum defects8 across the
N–SmA phase transition. The observed rings around the particles

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Soft Matter

Fig. 2 Optical micrograph of a colloidal dimer with a vortex-like defect in
the PN cell with the l-plate (green line denotes the slow axis) between theanalyzer and the sample in the CCN-47 liquid crystal. (a) A dimer in the Nphase, (b) at the N–SmA phase transition, (c) in the SmA phase,(d) schematic diagram (based on (c)) of the SmA layers around theparticles. In the SmA phase, the boundary condition is incompatible withthe layer structure above and below the particles (green regions). Particle
size 5.2 mm and cell thickness 8.5 mm.

in the SmA phase in Fig. 1(d) are somewhat similar to the onethat was observed in the case of a quadrupolar defect in the SmA
phase.17 At the transition the particles appear to be touching eachother however careful measurement shows that there is about
a 0.6 mm gap between them (see ESI,† Fig. S1) and the gap
increases with decreasing temperature in the SmA phase.
To get more insight into the defect and SmA layer orientation
around the particles we have chosen the CCN-47 (4 0 -butyl-4heptyl-bicyclohexyl-4-carbonitrile) liquid crystal. It exhibits thefollowing phase transition: Cr. 25.6 1C SmA 28.4 1C N 58.2 1C I.
It has very low birefringence (Dn C 0.03), hence it is useful forunderstanding SmA layer orientation around the particles.24–26
Fig. 2 shows the image of a dimer across the N–SmA phasetransition in a PN cell with a l-plate (red-plate). Here the redcolor corresponds to a horizontal orientation of the long axes ofthe molecules, whereas bluish and yellowish colors (Fig. 2(a)and (b)) correspond to clockwise and anti-clockwise rotation of
the director from the rubbing direction, respectively. Interestingly
in the SmA phase (Fig. 2(c)) we observe rings with opposite color
above and below each particle. In addition, above the particles therings (left and right) have opposite color. These rings are highly
confined region of SmA layers that prevents extensive layer
distortion due to incompatible boundary conditions of theparticles. It suggests that the non-singular defect disappears
at the transition and the SmA layers are nearly parallel in the
narrow region observed between the particles. Based on this we
propose a simple model of SmA layer orientation around thedimer in Fig. 2(d).
In TN cells, the director twists by 901 from the bottom to the
top substrate, and the elastic dipoles are spontaneously
attracted and finally their joining line is oriented at 451 withrespect to both the rubbing directions (Fig. 3(a)). A vortex-like
defect is formed between two particles (Fig. 3(b)) although thedirector distortion is very diﬀerent from that of the PN cell (seeFig. 1(b)). The defect ring has four fold rotational symmetry
enabling four distinct directions for the assembly mechanism.21

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Paper

Fig. 3 Optical micrograph of a colloidal dimer with a vortex-like defect in
the TN cell under crossed polarizers in the 8CB liquid crystal. (a) A dimer in
the N phase. (b) Schematic diagram of director orientation around theparticles (adapted from ref. 21). (c) Transformation of defect at the N–SmA
phase transition. (d) A dimer in the SmA phase. See ESI† (Video 2). Particle
size 5.2 mm and cell thickness 8.5 mm.

Fig. 3(c) and (d) show the transformation of the defect of acolloidal dimer across the N–SmA phase transition. Near thetransition point the director distortion increases and finally in
the SmA phase, a very complex layer distortion is observed(Fig. 3(d)). A video of this transition and the temperature
variation of the center to center separation between the particles
across the phase transition are given in the ESI.† 23 The effect oftemperature change on the colloidal dimers in both PN and TN
cells is similar. In both cases the equilibrium separation between
the particles in a dimer is governed by elastic anisotropy. The
discontinuous change of the equilibrium separation at the
N–SmA transition is due to the disappearance of non-singulardefects and this is also an indicator of discontinuity in the elastic
constants. However the temperature dependence of the equilibrium separation (D) in the SmA phase is different. In particular,
in the PN cell, D shows a critical behavior whereas in the TN cell it
is independent of temperature (see ESI†).
Using two types of dimers as building blocks, we prepared
two diﬀerently assembled 2D colloidal crystals using the opticaltweezers and studied the eﬀect of temperature and electric fieldon the lattice parameters. First we discuss the 2D crystals of
dimers made of antiparallel elastic dipoles in the PN cell.
Fig. 4(a) shows a 2D crystal made of 36 dimers (72 particles).
The equilibrium lattice parameters at 36 1C are: a = b = 10.2 
0.05 mm, D = 6.4  0.05 mm and f = 45  11 in the nematic phase.
The temperature of the sample is decreased (at 0.3 1C min1)
across the N to SmA phase transition and the lattice parameters
are measured as a function of temperature (see ESI,† Video 3).
The temperature variation of the lattice parameters a, b and D are
shown in Fig. 4(e). All the lattice parameters tend to increaseslightly followed by a discontinuous jump at the N–SmA transition. The SmA 2D crystal is more compact than that of thenematic phase. The corresponding polarizing optical microscopy

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Fig. 4 Optical photomicrograph of a 2D colloidal crystal in the N phase(36 1C) and in the SmA phase (32.6 1C) of the 8CB liquid crystal in the PN
cell made of antiparallel dipoles (a and b) without polarizers; (c and d)
between crossed polarizers. (e) Temperature variation of the lattice parameters a, b and D across the N–SmA transition. See ESI† (Video 3). Cell
thickness 8.5 mm.

images are also shown in Fig. 4(c) and (d). In the N phase,
between two neighboring dimers there are periodic voids of uniform
nematic region. In the SmA phase strong distortion of layers isobserved and the director distortion surrounding the particles is
extended up to a few micrometer distance. In the SmA phase(32.6 1C) the lattice parameters are: a = b = 8.6  0.05 mm,
D = 5.9  0.05 mm and f = 42  11. Thus lattice constants in the
SmA phase (a and b) are lower by B16% and D is lower by B7%
with respect to the nematic phase. Consequently the area of the2D crystal decreases from 2650 mm2 (nematic phase) to 2100 mm2(SmA phase), which is about 21% reduction.
Fig. 5(a) shows a 2D crystal made of dimers in the TN cell of
the 8CB liquid crystal. The temperature of the sample isdecreased (0.3 1C min1) across the N to SmA phase transition
and the lattice parameters are measured as a function oftemperature (see ESI,† Video 4). Fig. 5(b) shows a more compact
structure in the SmA phase than in the nematic phase. The
corresponding polarizing optical microscopy images are shownin Fig. 5(c) and (d). The structure of the SmA 2D crystal in the
TN cell is very diﬀerent from that of the PN cell. In particular,
two neighboring dimers are connected by a cross-type texture in
TN cells (Fig. 5(d)). The variation of the lattice parameters a, b
and D as a function of temperature is shown in Fig. 5(e). In the
N phase at 36 1C, the equilibrium lattice parameters are:This journal is © The Royal Society of Chemistry 2016

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Fig. 6 Optical photomicrograph of a 2D colloidal crystal in a PN cell of
the 5CB liquid crystal at (a) zero field and at (b) 1 V mm1. (c) Variation of thelattice parameters a, b and D as a function of the applied electric field at afrequency of 1 kHz. See ESI† (Video 5). Cell thickness 8.5 mm.

Fig. 5 Optical photomicrograph of a 2D colloidal crystal in the N phase(36 1C) and in the SmA phase (32.6 1C) in the TN cell of the 8CB liquid
crystal (a and b) without polarizers and (c and d) between crossed
polarizers. (e) Temperature variation of the lattice parameters; a, b and D
across the N–SmA transition. See ESI† (Video 4). Cell thickness 8.5 mm.

a = b = 10.5  0.05 mm, D = 6.5  0.05 mm and f = 45  11
(Fig. 5(a)). In the SmA phase at 32.6 1C, the lattice parameters
are reduced, for example, at the highest field: a = b = 8.5 
0.05 mm, D = 5.9  0.05 mm and f = 45  11 (Fig. 5(b)). The SmA
lattice constants, a and b, are lower by 19% and D is lower by
9% with respect to the nematic phase. The area of the colloidal
crystal decreases from 3050 mm2 (nematic phase) to 2150 mm2(SmA phase), which is about 29% reduction. The process ofcontrolling the lattice parameters by temperature in the TN cellis completely reversible while in the case of the PN cell it ismostly irreversible.
Finally we discuss the eﬀect of an electric field on the 2D
crystals in both PN and TN cells in the 5CB liquid crystal atroom temperature (see ESI,† Video 5). The equilibrium lattice
parameters are measured as a function of the applied electricfield. Fig. 6(a) shows an image of a 2D crystal in the PN cell atzero field and Fig. 6(b) shows the image taken at the highest
field (1 V mm1) above which the lattice constants do notdecrease. It is observed that the lattice constants tend toincrease slightly up to the Freedericksz threshold field(C00.4 V mm1) and then decrease with increasing field(Fig. 6(c)). For example, at room temperature and zero field,
a = b = 10.2  0.05 mm and D = 6.4 mm and it decreases toa = b = 7.3  0.05 mm and D = 5.7 mm at a field of 1 V mm1.

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Thus, the lattice parameters a and b decrease by B28% and D
decreases by B11% at the highest field. The area of the 2D
crystal decreases from 3000 mm2 (0 V mm1) to 1600 mm2 which
is about 46% smaller compared to the area at zero field.
Fig. 7 shows the eﬀect of electric field on the 2D crystal in
the TN cell in the 5CB liquid crystal (see ESI,† Video 6). The
lattice constants are measured as a function of field in the same
way as we discussed. It is observed that the lattice parameters
tend to increase slightly up to the threshold field (C00.6 V mm1)

Fig. 7 Optical photomicrograph of a 2D colloidal crystal in a TN cell of the
5CB liquid crystal under the field, (a) 0 V mm1 and (b) 1.5 V mm1. (c) Variationof the lattice parameters a, b and D as a function of the applied electric field ata frequency of 1 kHz. See ESI† (Video 6). Cell thickness 8.5 mm.

Soft Matter, 2016, 12, 6812--6816 | 6815

Soft Matterand then continuously decrease with increasing electric field up to
1.15 V mm1 (Fig. 7(c)). For example, the lattice constants at zero
field and at room temperature are: a = b = 10.4  0.05 mm andD = 6.5 mm. At the highest field (1.5 V mm1), it decreases toa = b = 7.1  0.05 mm and D = 5.71 mm. Thus a and b show
B31% and D shows B21% decrease at the highest field. The
area of the 2D crystal also decreases from 3000 mm2 (0 V mm1)
to 1650 mm2 (1.5 V mm1) which is about a 45% reduction
compared to the crystal area measured at zero field. The
process of controlling the lattice parameters by field in boththe cells is completely reversible.
The temperature variation of the lattice parameters is mainly
due to the variation of elastic constants. In particular, theincrease of the lattice parameters with decreasing temperatureis due to the rapid increase of the bend elastic constant comparedto the splay elastic constant. The discontinuity of the elastic
constants at the N–SmA transition is marked by a discontinuouschange of the lattice parameters. The effect of an electric field on
the colloidal crystals can be expected due to the combined effect ofnematic elasticity, the response of the nematic to the external
electric field and the field-induced dipole–dipole interaction (electric)
between the colloids.7 In the low field range of the present experiment, the latter effect may not have a significant contribution. The
director is highly nonuniform throughout the 2D crystals and hence
there is no sharp threshold field of elastic deformation; consequently
there are small deformations inside the 2D crystals which try to push
the particles apart. On the other hand the nematic deformation
outside the 2D crystal region, above the Freedericksz threshold field,
exerts pressure on the crystal and its volume shrinks.

IV. Conclusion
In conclusion, we have shown a structural response of 2D colloidal
crystals (stabilized by bubblegum defects in planar and twisted
nematic cells) to temperature variation and an external electricfield. In the nematic phase the equilibrium separation between theparticles weakly depends on temperature followed by a discontinuous structural change at the N–SmA phase transition. In the SmA
phase the surrounding liquid crystal compresses the 2D crystals
and the area of the crystals decreases significantly in both planar
and twisted cells. The electric field response was studied only inthe nematic phase as the 2D crystals in the SmA phase do notrespond to the applied field. Above the Freedericksz thresholdfield, the surrounding medium compresses the 2D crystals. Theinter-dimer spacing decreases by about 30% due to the applied
electric field and consequently the areas of the 2D crystals decreasesignificantly. Based on this concept large electrically and thermallytunable colloidal crystals could be designed which may be usefulfor tunable photonic crystals.

Acknowledgements
S. D. acknowledge support from DST-PURSE and a Swarnajayanti
fellowship (DST/SJF/PSA-02/2014-2015). K. P. Z. acknowledges
UGC for a fellowship.

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References
1 J. H. Holtz and S. A. Asher, Nature, 1997, 389, 829.
2 Y. Kang, J. J. Walish, T. Gorishny and E. Thomas, Nat.
Mater., 2007, 6, 957.
3 J. Xia, Y. Ying and S. H. Foulger, Adv. Mater., 2005, 17, 2463.
4 M. Aschwanden and A. Stemmer, Opt. Lett., 2006, 31, 2610.
5 J. M. Weissman, H. B. Sunkara, A. S. Tse and S. A. Asher,
Science, 1996, 274, 959.
6 B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand and
C. J. M. Smith, Appl. Phys. Lett., 2004, 84, 846.
7 M. Humar, M. Skarabot, M. Ravnik, S. Zumer, I. Poberaj,
D. Babic and I. Musevic, Eur. Phys. J. E: Soft Matter Biol.
Phys., 2008, 27, 73.
8 K. P. Zuhail and S. Dhara, Appl. Phys. Lett., 2015, 106,
211901.
9 P. Poulin, H. Stark, T. C. Lubensky and D. A. Weitz, Science,
1997, 275, 1770.
10 I. Muševič, M. Škarabot, U. Tkalec, M. Ravnik and S. Žumer,
Science, 2006, 313, 954.
11 T. C. Lubensky, D. Pettey, N. Currier and H. Stark, Phys. Rev.
E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1998,
57, 610.
12 H. Stark, Phys. Rep., 2001, 351, 387.
13 Y. Gu and N. L. Abbott, Phys. Rev. Lett., 2000, 85, 4719.
14 R. W. Ruhwandl and E. M. Terentjev, Phys. Rev. E: Stat.
Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1997, 55, 2958.
15 H. Stark, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.,
2002, 66, 032701.
16 K. P. Zuhail, P. Sathyanarayana, D. Seč, M. Škarbot,
I. Muševič and S. Dhara, Phys. Rev. E: Stat., Nonlinear, Soft
Matter Phys., 2015, 91, 030501(R).
17 K. P. Zuhail, S. Čopar, I. Muševič and S. Dhara, Phys. Rev. E:
Stat., Nonlinear, Soft Matter Phys., 2015, 92, 052501.
18 A. Nych, U. Ognysta, M. Škarabot, M. Ravnik, S. Žumer andI. Muševicš, Nat. Commun., 2013, 4, 1489.
19 P. Poulin, V. Cabuil and D. A. Weitz, Phys. Rev. Lett., 1997,
79, 4862.
20 J. Fukuda and H. Yokoyama, Phys. Rev. Lett., 2005, 94,
148301.
21 U. Tkalec and I. Muševič, Soft Matter, 2013, 9, 8140.
22 U. Tkalec, M. Ravnik, S. Žumer and I. Muševič, Phys. Rev.
Lett., 2009, 103, 127801.
23 See ESI† for temperature variation of interparticle separationin dimers in PN and TN cells across the N–SmA phasetransition in the 8CB liquid crystal. Several video clips showing
transformation of defects across the phase transition and theeffect of the electric field on the lattice parameters of 2D
colloidal crystals in the 5CB liquid crystal.
24 S. Dhara and N. V. Madhusudana, Europhys. Lett., 2004,
67, 411.
25 S. Dhara and N. V. Madhusudana, Phase Transitions, 2008,
81, 561.
26 T. A. Kumar, P. Sathyanarayana, V. S. S. Sastry, H. Takezoe,
N. V. Madhusudana and S. Dhara, Phys. Rev. E: Stat., Nonlinear,
Soft Matter Phys., 2010, 81, 011701.

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