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Diﬀerent modulated structures of topological defects
stabilized by adaptive targeting nanoparticles
George Cordoyiannis,*abcd Venkata Subba Rao Jampani,b Samo Kralj,beSurajit Dhara,f Vassilios Tzitzios,g Georgia Basina,g George Nounesis,hZdravko Kutnjak,bi Chandra Shekhar Pati Tripathi,a Patricia Losada-Pérez,aDalija Jesenek,b Christ Glorieux,a Igor Muševič,b Aleksander Zidanšek,bei
Heinz Ameinitschj and Jan Thoena
It is demonstrated that interactions between nanoparticles and topological defects induce a twist-grainboundary phase in a chiral liquid crystal. The occurrence of this phase, the analogue of the Shubnikov
phase in type-II superconductors, is driven by direct interactions between surface-functionalized CdSequantum dots and screw dislocations. It is shown that, within an adaptive-defect-core-targeting

Received 16th November 2012
Accepted 30th January 2013mechanism, nanoparticles of appropriate size and functionalization adapt to qualitatively diﬀerent coresof topological defects such as disclination lines and screw dislocations. This mechanism enables theeﬀective reduction of the energetically costly, singular defect core volume, while the surrounding phaseordering remains relatively weakly aﬀected. The ﬁndings suggest new pathways towards the controlled

DOI: 10.1039/c3sm27644a

assembly of superstructures in diverse, symmetry-broken, condensed-matter systems, ranging fromwww.rsc.org/softmatter

nanoparticle-decorated liquid crystals to superconductors.

I

Introduction

In the past few years there has been a rapidly increasing interestin the interactions of colloidal particles with topological defects
in uid matrices.1–6 These added particles can induce chirality,7increase the dielectric anisotropy8,9 and the electro-opticalresponse of liquid crystals (LCs),10 explore pathways towards
tunable metamaterials,4 enable self-healing mechanisms,11 etc.
The complexity of possible behaviors is large in the case ofanisotropic liquids such as the LC phases. Inside the LC
matrices the Goldstone excitation modes of a symmetrybreaking eld introduce soness,12 i.e., a strong susceptibility toeven weak local perturbations. The LC structures could be disrupted by the immersed particles,1 giving rise to long-range
Departement Natuurkunde en Sterrenkunde, KU Leuven, 3001 Leuven, Belgium.
E-mail: george.cordoyiannis@ijs.siaCondensed Matter Physics Department, Jožef Stefan Institute, 1000 Ljubljana,
Sloveniabc

Department of Physics, University of Athens, 15784 Athens, Greece
EN FIST Center of Excellence, 1000 Ljubljana, SloveniadeDepartment of Physics, University of Maribor, 2000 Maribor, Slovenia

School of Physics, University of Hyderabad, Hyderabad 500046, Andhra Pradesh,
India

f

Institute of Materials Science, National Centre for Scientic Research “Demokritos”,
15310 Aghia Paraskevi, Greeceg

Biomolecular Physics Laboratory, National Centre for Scientic Research“Demokritos”, 15310 Aghia Paraskevi, GreecehJožef Stefan International Postgraduate School, 1000 Ljubljana, Slovenia

ijforces and strong interactions with topological defects. The
particles are attracted to locally elastically distorted LC regions
and, thus, to topological defects.3,13,14 The resulting elastic
forces are exploited to trigger ordering or self-organization ofparticles into regular templates.15–18
Recently, a new family of nanoparticles (NPs) has been reported, capable of forming stable suspensions in LCs.14 These NPs arespherical 3.5 nm diameter CdSe quantum dots, surface-treatedwith oleyl-amine (OA) and tri-octyl-phosphine (TOP). They significantly extend the stability range of blue phases (BPs) of chiral LCs.
The stabilization eﬀect was originally proposed by Kikuchi et al.13
It is based on the reduction of the free energy penalty for forming
defects via a partial replacement of their essentially isotropic core
volume by captured polymers13 or nanoparticles.14
In addition to BPs characterized by topological line defects
in the orientational order, chiral LCs can also exhibit twist-grainboundary phases (TGBs) with topological line defects in thetranslational order. TGBs consist of a one-dimensional lattice ofscrew dislocations residing in planar grain boundaries that
separate smectic blocks. They represent the LC analogue of the
Shubnikov phase exhibiting Abrikosov ux-vortex congurations in type-II superconductors. Long aer their prediction19,20
and experimental discovery,21,22 TGBA (smectic-A blocks) andvarious types of TGBC (smectic-C blocks) phases have been
observed in pure compounds and mixtures of LCs and chiraldopants.23,24 They exhibit particular thermal signatures,25 X-ray
patterns,26 nuclear magnetic resonance spectra27 and optical
microscopy textures.28

Institute of Inorganic Chemistry, Graz University of Technology, 8010 Graz, Austria

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Paper
In the present work we experimentally prove the existence ofan adaptive-defect-core-targeting (ADCT) mechanism eﬃciently
stabilizing even qualitatively diﬀerent defect lattices insymmetry-breaking phases by using the same kind of NPs. It isdemonstrated that CdSe quantum dots of appropriate size andsurface functionalization exhibit the ADCT mechanism. In
addition to BPs,14 these NPs eﬀectively stabilize TGBs.
The plan of the paper is as follows. The measured samples
and experimental methods are described in Section II. In
Section III we introduce a simple phenomenological model thatis later used to interpret the measurements. The experimental
results are presented in Section IV, followed by mean-eldestimates focusing on NP-driven TGBA stabilization in Section
V. The results and basic principles of the ADCT mechanism are
discussed in Section VI and summarized in Section VII.

II

Materials and methods

Several mixtures of the chiral liquid crystal S-(+)-4-(2-methylbutyl)
phenyl-4-decyloxybenzoate (CE6) with NPs have been investigated using high-resolution adiabatic scanning calorimetry,small-angle X-ray scattering and polarizing optical microscopy.
CE6 exhibits all three BPs, and a cholesteric to smectic-A (N*–
SmA) transition at 314.5 K. The preparation of mixtures with
diﬀerent NP concentrations c (dened as the mass of NPs over
the total sample mass) has been described elsewhere.29
A

High-resolution adiabatic scanning calorimetry (ASC)The heat capacity (Cp) measurements were performed in a homemade, fully computerized adiabatic scanning calorimeter consisting of four stages (i.e., sample and cell are surrounded bythree shields). The air among them is being vacuum-pumped toachieve maximum insulation from the environment. The capability of adiabatic scanning calorimetry for the simultaneous andaccurate determination of heat capacity and enthalpy enables
high-resolution studies of phase transitions and criticalphenomena.30 The exceptional temperature stability of !50 mK
and the slow scanning rates bring the sample close to the real
thermal equilibrium, allowing the precise determination ofphase diagrams. For the present experiments sample quantitiesof 1.7 g were placed in a 22 g tantalum cell. The heat capacity ofthe empty cell was measured in a separate control experimentand it was subtracted in order to derive the net Cp of the sample.
B Small-angle X-ray scattering (SAXS)The X-ray measurements were performed in the Austrian
Beamline,31 located at ELETTRA Synchrotron (Trieste, Italy). An
asymmetric-cut, double-crystal monochromator and a doublefocusing toroidal mirror were used to produce a focused X-ray
beam of 8 keV. The setup has a very high resolution, better than
0.001 Å"1 (half-width at half-maximum). The samples aremounted in capillary tubes (Hingelberg Mark capillaries, no. 14)
and the temperature is controlled by an in-house-built heatingstage combined with a water bath (Huber Unistat). The
temperature stability is in the order of !10 mK. No orientation
has been imposed on the sample for X-ray measurements.

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Soft Matter
C

Polarizing optical microscopy (POM)

For observation under the microscope, the samples wereplaced between 1 cm # 1 cm glass slides. For homeotropic
cells, the glass surfaces were coated with octadecyl dimethyl (3trimethoxysilylpropyl)ammonium chloride (ABCR GmbH), in
order to obtain strong perpendicular surface-anchoring of theliquid-crystalline molecules on a chemisorbed DMOAP monolayer. For planar cells, a thin layer of polyimide (PI-2555,
NISSAN Chemicals) was spin-coated on the surface of theglasses. A velvet cloth was used for unidirectional rubbing on
polyimide for achieving a planar alignment on the glasses. A
uniform cell thickness of 5 mm was obtained by using mylar
spacers and the thickness was determined through transmission spectra using a ber optic spectrometer (Ocean Optic,
USB-2000). The cells were heated to 325 K, corresponding to
the isotropic phase of CE6, and lled with the sample. The
temperature was slowly changed by means of an Instec, STC
200 controller. The textures were observed under a polarizing
optical microscope (Nikon, Eclipse E600 POL), using a color
camera (PL-A742, Pixelink).

III

Brief theoretical background

In order to qualitatively explain the observed key features, arather simple phenomenological model can be used in terms ofthe nematic director eld ~n and the smectic-A complex orderparameter
j ¼ heif.

(1)

The unit vector ~n denes the local average uniaxial LC
orientation, the translational order parameter h reveals thedegree of smectic ordering and the phase factor f determines
the position of smectic layers.
In the free energy density expression f ¼ fe(n) + fc(s) + fe(s) we
include only the essential terms that are needed for the
results discussion. The nematic elastic free energy penalty isgiven by12feðnÞ ¼

#2
"2 K 3 #"2 K2 ! !
"
K1 !
~
V$~
n þ
n$ V # ~n " qch þ #~
n#V#~
n# ;
2
2
2

(2)

where K1, K2 and K3 are the Frank nematic elastic constants, andqch stands for the chirality-enforced wave vector.
The smectic condensation and elastic free energy contributions are approximated by12,32bfcðsÞ ¼ a0 tjjj2 þ jjj4 ;(3)2

n$V " iq0)j|2 + Ct|(~n # V)j|2.
fe(s) ¼ Ck|(~(4)

The quantities a0 and b are positive Landau expansion
coeﬃcients, and
T " T*t¼(5)
T*
is the reduced temperature. Ck and Ct stand for the smectic
compressibility and the bend elastic constant, respectively.

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These constants are positive and enforce a SmA ordering with alayer thickness of d ¼ 2p/q0. Therefore, the smectic ordering
minimizing the term fc(s) + fe(s) below T* could be expressed as
jeq ¼ hseiq0x, where it is assumed that the smectic layers arealigned along the x-axis andrffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffi"ta0¼ h0 "t:
(6)
hs ¼
b

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The corresponding value of the smectic condensation term
equalsfcðsÞ ¼ "a0 jtjhs 2
a0 jtj2 h0 2
¼"
:
2
2

For the sake of simplicity it is henceforth assumed that C ¼
Ck ( Ct. Apart from the smectic layer thickness and the chiralpitch length, there are additional important material-dependent lengths,12 such as the smectic order parameter correlation
length x and the nematic twist penetration length l. Below T*
their values are roughly determined bysffiffiffiffiffiffiffiffiffi
Cxx¼¼ p0ffiffiffiffi ;(7)
a0 jtjjtj
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K2
l0
l¼¼ pffiffiffiffi :2
2
q0 Chs
jtj

IV

(8)

Experimental results

The phase transition behaviors of pure CE6 and three mixturesof CdSe NPs, c ¼ 0.0005, 0.005 and 0.02, were measured using
ASC. The temperature dependence of Cp, obtained upon slow
cooling at an average rate of 1.6 mK min"1, is shown in Fig. 1.
CE6 exhibits a single, sharp, rst-order anomaly corresponding
to a direct N*–SmA transition, with a coexistence region of 52 !
2 mK. Note that the presence of any TGBA order would bereected in a signicant broadening of the transition andchanges in the Cp pre-transitional wings.25 Such a characteristicfeature was not found for pure CE6.
However, a dramatically diﬀerent phase transition behavior
is observed in the Cp data for CE6 + NP mixtures. A wider,double-peak anomaly has been observed for all NP concentrations, marking the presence of a thermodynamically stable
TGBA order between the N* and SmA phases. Note that theanomaly appearing on the high-temperature wing is the BPI–N*
transition, shied downwards as a result of the BP
stabilization.29
The inset in Fig. 1 shows the dual feature of the lowest
temperature Cp anomaly. This feature is indicative of a SmA–TGBA and a subsequent TGBA–N*L transition, where N*L denotes a
TGBA structure of shorter range order referred to as the chiralline liquid phase.33 This double feature, together with a broad
Cp anomaly related to the continuous conversion of the N*L to N*phase, is a typical TGBA ngerprint.25 This is additionallyconrmed by SAXS measurements presented in Fig. 2. The
temperature evolution of the full-width at half-maximum

3958 | Soft Matter, 2013, 9, 3956–3964

Fig. 1 The temperature proﬁles of Cp obtained by ASC upon cooling (rate of
1.6 mK min"1) are shown for the pure CE6 and the mixtures with c ¼ 0.0005, 0.005
and 0.02. CE6 exhibits a sharp, direct N*–SmA transition, while all mixtures exhibit
an essentially wider double-peak anomaly, marking the presence of the TGBA order.
The inset shows that the low-temperature anomaly also consists of a dual peak,identiﬁed as the unique pattern of a SmA–TGBA–N*L phase sequence.25(FWHM) and the maximum scattered intensity (Io) clearlysupport the presence of TGBA and N*L phases. Io and FWHM,
plotted on the same temperature scale with Cp data for c ¼ 0.02,
demonstrate the gradual loss of the quasi-long-range smectic
order along the N*L phase, exactly as observed in the pioneeringexperiments on TGBs by Navailles et al.34
Additional evidence related to the presence of the TGBA
order is provided by POM textures. Both homeotropic andplanar anchoring conditions were imposed on the samples.
Textures observed under POM for homeotropic cells are shownin Fig. 3(a). The images corresponding to pure CE6 are presented in the le-hand column. In the SmA phase (top row) the
director is parallel to the direction of the light propagation
resulting in dark images between crossed polarizers. A typicalchiral nematic N* texture is also found at higher temperatures(bottom row). Of particular interest is the texture appearing in
the coexistence region of the rst-order N*–SmA transition.
Here N* islands or stripes evolve and supersede the dark SmA
phase on heating. However, a completely diﬀerent texture isobserved for the CE6 + CdSe c ¼ 0.02 mixture (central column).
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Paper

Soft Matter
Note that the textures specied as TGBA in Fig. 3 are obtainedon the edge between TGBA and N*L phases for the c ¼ 0.02
sample. No diﬀerence was observed in textures slightly above or
below the specied temperature, i.e., at temperatures belonging
to TGBA and N*L phases according to ASC data. Since both thesephases exhibit exactly the same kind of order (being long-range
for TGBA and progressively changing to short-range for N*L),
their distinction based on POM might be unattainable. Moreover, the imposed anchoring conditions (planar or homeotropic) in the sample–glass interfaces can additionally obstruct
such a distinction.
Finally, the phase diagram of the system CE6 + NPs isdepicted in Fig. 4. The inset shows the temperature window
DTTGBA þN*L of the stable TGBA order, i.e., the joined range of
TGBA and N*L phases. The phase transition lines are drawn
based on the ASC data that are the most reliable in terms oftemperature precision.

V

Fig. 2 The FWHM (a) and Io proﬁles (b), obtained by SAXS, are shown on thesame temperature scale with the Cp data (c) for the c ¼ 0.02 sample. The FWHM
evolution demonstrates the gradual loss of the quasi-long range order along the
N*L phase range. The signiﬁcant change of the scattered intensity along thediﬀerent LC phases is visualized in the insets. Although FWHM changes only
slightly along the region of the established TGBA order, Io decreases substantially,
displaying the ﬁngerprint of the N*L phase34 between TGBA and N*. Note that qo
refers to the q value corresponding to the maximum intensity Io.

from the dark SmA phase, growing into an immaculate lament
network (middle row) characteristic of the TGBA structure.28
Similar diﬀerences between the textures of pure CE6 and the
mixture with c ¼ 0.02 are observed in the planar cells, shown in
Fig. 3(b). In the SmA phase of both CE6 (le column) and c ¼
0.02 mixture (central column), the characteristic focal conic
texture is observed, exhibiting only a color diﬀerence due to thepresence or absence of NPs. The textures in the N* phase arealso similar (bottom row). However, they are quite diﬀerent atintermediate temperatures, corresponding to the N*, SmA
phase-coexistence region of CE6 (le) and the stable TGBA
structure of the c ¼ 0.02 mixture (center). For the TGBA phase
diﬀerent color regions evidence the continuous twist of thesmectic slabs, resulting in a helical and birefringent structure
perpendicular to the glass plates. From the POM images weconclude that in the c ¼ 0.02 mixture a stable TGBA structure isobserved upon heating from SmA or cooling from the N* phase.

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Mean-ﬁeld estimates

In the following we estimate the impact of NPs on the TGBA
phase stability range using the phenomenological freeenergy expression introduced in Section III. We illustrate
the impact of NPs on the temperature stability width
DTTGBA þN*L ðcÞ ¼ TN " TTGB-SmA of LC structures dominated byscrew dislocations. Here TTGB–SmA stands for the TGBA–SmA
phase transition and TN estimates the temperature of the N*–N*L
phase transformation. The TGBA structure is characterized by awell-dened, one-dimensional lattice of screw dislocations. On
the contrary, in the N*L phase the dislocations strongly oscillate.35 Within a mean-eld-type approach the diﬀerences
between the TGBA and N*L structures are neglected and, henceforth, we use the former conguration as the representative
defect structure.
The main characteristic geometric features needed for thederivation are shown in Fig. 5(a). The TGBA phase consists ofslabs of length lb exhibiting essentially bulk SmA ordering. The
slabs are separated by grain boundaries (GBs) of width given
roughly by the nematic twist penetration length l. Parallel screw
dislocations reside within each GB, separated by a distance23 ld( lb. Globally, the system exhibits a helical structure due to thetilt between the adjacent slabs, which is enabled by screw
dislocations. The volume of a representative TGBA unit cell,consisting of a SmA slab and a GB, is given by Vu ( lbl2, where
the grain boundary surface is set to be equal to l2. The averagedislocation length is approximated by l. Hence, the number Ndefof defects within a GB is Ndef ( l/ld ( l/lb.
AFree energy costs of competing phases

Here the free energy costs DF(phase) related to the N*, SmA and
TGBA order formation are estimated within a unit cell Vu.
The ordering within the N* phase is described using theCartesian frame (x, y, z) by hs ¼ 0, ~n ¼ (sin q, cos q, 0) where q ¼
qchz. The corresponding spatially averaged free energy densityf (phase) ¼ DF(phase)/Vu equals*f (N ) ¼ 0.

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Fig. 3 (a) Homeotropic cells: textures of pure CE6 (left column) and c ¼ 0.02 mixture (central column). The dark textures at the top correspond to SmA phase, while
the images at the bottom to the N* phase. In the middle, mixed textures of coexisting N*, SmA domains are depicted for CE6, while a TGBA ﬁlament structure is revealed
for c ¼ 0.02. (b) Planar cells: textures of pure CE6 (left column) and c ¼ 0.02 mixture (central column). The textures at the bottom and top correspond to N* and SmA
phases, respectively. In the middle, mixed N*, SmA domains are observed for CE6 and a more colorful TGBA texture for c ¼ 0.02, resulting from the continuous twist of
the smectic slabs. A scheme of the ideal molecular orientation for each structure is depicted in the right-hand columns of both (a) and (b).

ðlb
0

"2 Dq2! !
"" 2qch Dq þ qch 2 lb :dz ~n$ V # ~n " qch (lWithin the cores of screw dislocations SmA ordering isessentially melted. The resulting average smectic condensation
free energy within a volume Vu readsFcðTGBÞ ¼ "Fig. 4 The temperature versus concentration (T–c) phase diagram of the system
CE6 + NPs constructed from ASC, SAXS and POM measurements. The inset shows
the range DTTGBA þN* of the induced TGBA order as a function of c. This order is ofL
long-range (TGBA) and it progressively changes to a shorter range (N*L ) uponincreasing T.

The SmA ordering within a unit cell can be determined by~n ¼ (1,0,0) and j ¼ hseiq0x. It follows
f

ðSmAÞ

a0 jtj2 h0 2 K2 qch 2
þ
:
¼"
2
2

(10)

To estimate the free energy costs for the formation of a TGBA
structure it is assumed that within the smectic blocks an ideal
SmA ordering is established and the structure exhibits on
average a twist along the z-coordinate. The presence of the twist
is enabled by the incorporation of screw line dislocations at
GBs. Across each GB (the width of which is roughly given by l)
the director eld is approximately rotated by an angle23
Dq (

d
d
( :
ld lb

(11)

Consequently, the orientational elastic penalties are given by

3960 | Soft Matter, 2013, 9, 3956–3964"
a0 jtj2 h0 2 !
Vu " Vdef ;2(12)

where Vdef ( Ndeflpx2 ( l2px2/lb is the volume occupied by the core
defects. We further neglect other elastic contributions (e.g., interactions among dislocations) that play a secondary role if lb [ l.
With this in mind we obtain!
&'
K2 Dq2 2qch Dq
a0 jtj2 h0 2
px2
f ðTGBÞ ¼
1 " 2 : (13)"
þ qch 2 "
lb
2 llb
2
lb
Next, the addition of NPs is considered with an averagevolume density
f ¼ (NNPvNP)/Vu ( c(rLC/rNPs).
Here NNP stands for the number of NPs within Vu, vNP is theaverage volume of one nanoparticle, and rNP and rLC stand forthe mass densities of NPs and LC, respectively. It is assumed
that the NPs are predominantly assembled at the dislocation
cores. Furthermore, we assume that the main impact of NPs
from the energy point of view is their eﬀect on the condensation
free energy penalty within the cores of defect.
Taking this into account, the condensation free energy
F(TGB)
within Vu readsc"a0 jtj2 h0 2 !
(14)
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Soft Matterthat would further enlarge the elastic costs. Hence, the additional smectic elastic penalty costs are given by# # # # upl 2 ld xDFeðTGBÞ ( NNP Vm # fcðsÞ # ( # fcðsÞ # f
;
(15)
r

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where Vm estimates the volume of the essentially melted region
that surrounds an eﬀectively spherical NP characterized byradius r and u ( 1.
Therefore, if NPs are present, we obtain&'
K2 Dq2 2qch Dq
f ðTGBÞ ðfÞ ("þ qch 2
2 llb
lb
(16)
&
'!
2
2
a0 jtj h0
px2
upx
1" 2 þf 1"
"
:
2
r
lb
B Phase transition behavior
The phase behavior in the absence of NPs is rst considered. If
the chirality is not strong enough then on lowering temperature
the N* phase directly transforms into the SmA order without anintermediate TGBA structure. The corresponding phase transition temperature TNA is determined by the condition f (SmA) ¼*
f (N ). Using eqn (9) and eqn (10) it follows rNA ¼ "l0x0q0qch, i.e.
TNA ¼ T*(1 " l0x0q0qch).

(17)

If the chirality is strong enough then the TGBA phase intervenes between N* and SmA ordering. The N*–TGBA transition*
temperature TN is determined by the condition f (N ) ¼ f (TGB).
Using eqn (9) and eqn (13) we obtain0
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
u
d2
2d
u
B
C
u1 þ 3 2 "Bt
llb qchqch lb 2 CC:xqq
TN ¼ T* B
1
"
l
(18)
0
0
ch
0
B
C
1 " px2 =lb 2@
A

Fig. 5 (a) CdSe nanoparticles (top left), with a core diameter of 3.5 nm, surfacetreated with OA and TOP, induce a TGBA order by stabilizing the lattice of screw
dislocations at GBs separating the twisting smectic slabs (bottom). A blow-up of
the TGBA unit cell is presented at the top right. (b and c) The adaptive character of
CdSe NPs, enabled by their size and ﬂexible surface chains, is depicted. The NPs
accommodate with the average local orientational order of the qualitatively
diﬀerent nematic disclination lines (b) and smectic screw dislocations (c). Notethat this ﬁgure serves as an illustrative picture without aiming to precisely
represent the relative sizes of the components.

The measurements suggest that the CE6 + NP system is close
to a triple point, where the onset of TGBA and SmA coincides on
decreasing temperature from the N* phase. The triple point isdetermined by the condition TN ¼ TNA. The correspondingchirality strength q(t)ch fullls the equation0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
d @
px2 A
ðtÞ
:
(19)
qch ( 2 1 " 1 "llbpx
Therefore, in the limit lb ( ld / N where SmA and TGBA
phases are almost indistinguishable, it follows q(t)ch ( 0 as it should.

For qch ¼ q(t)ch the added NPs stabilize the TGBA structure in a

If the added NPs are adaptive with respect to the neighboring
LC order they relatively weakly disturb the latter. In this case theadditional elastic free energy costs due to NPs are negligible.
Consequently, the overall impact of NPs is a decrease in the
singular defect core volume free energy. If the NPs are notadaptive they could signicantly distort locally the LC ordering.
In order to estimate the consequent impact it is assumed that
only the smectic degree of ordering is aﬀected. This order isenforced to be melted at the surface of NPs. For simplicity weneglect the local distortions in the LC orientational ordering

This journal is ª The Royal Society of Chemistry 2013

nite temperature interval providing they are adaptive, i.e.
upx
\1 (see eqn (16)). The TGBA–SmA transition temperaturer
TTGB–SmA is determined by the condition f (TGB) ¼ f (SmA).
upx
Therefore, in the adaptive regime (\1) it holds
r
'
2 &
f lb
pux
1
"
DTTGBA þN* ðcÞ ( ðT* " TNA Þ
L
2 px2
r
'
2 &
crLC lb
pux
1"
:
(20)
( ðT* " TNA Þ
2
2rNPs pxr

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VI

Discussion

The present observations infer that surface-functionalized CdSe
NPs eﬃciently stabilize networks of screw dislocations. In thefollowing we discuss the conditions enabling the stabilizationby using the estimates derived above. We claim that the key
mechanism behind this is the defect-core replacement eﬀect, asrst discussed by Kikuchi et al.13 According to it the condensation free energy penalty due to the presence of topologicaldefects is substantially reduced if NPs replace a substantial partof their defect-core volume. This is illustrated in eqn (14) where
NPs trapped within screw dislocations reduce the total volume
where the smectic order is essentially melted due to topologicalreasons. However, this free energy gain could be wasted if NPs
apparently disrupt the defect-core structure. Such additional
penalties for specic “non-favorable” boundary conditions at
NP–LC interfaces are estimated in eqn (15) where only the
deformations in smectic ordering are considered. In our
samples NPs can adapt to a defect core structure due to theirsize and attached exible chains. One might argue that the NPdriven stabilization is most eﬀective if NPs do not interact with
LC and their impact is embodied only via the defect-corevolume replacement eﬀect. However, in this case the targetingof NPs towards topological defects would not be eﬃcient andwould be driven solely by Brownian motion. For this reason NPs
should weakly interact with the smectic phase factor f (see eqn(1)). It namely represents the gauge component of the smectic
order parameter which possesses a Goldstone mode. Consequently, the coupling between NPs and f enables the propagation of long-range interactions.12,36,37 It has been shown thathomogeneously dispersed NPs alter the average layer
spacing.37,38 Such conguration changes are relatively energetically costly and the resulting forces could be relatively large.
Note that the phase transition temperature in the SmA phaseapparently decreases on increasing c (see Fig. 4) revealingelastic distortions in the gauge component of the orderparameter.36,37 We further note that if NPs are small enough tot inside the cores of defects, their interactions with the gauge
eld are substantially reduced due to the essentially meltedorder parameter within the cores.
In Section V it has been shown that NPs could trigger the
onset of TGBA ordering although it is absent in a pure LC
sample if the chirality is not strong enough. In our theoreticalestimate the triple point conditions (eqn (19)) were considered,
where all the competing (N*, TGBA, SmA) phases coexist for c ¼
0, as suggested by the experimental results. In the case ofadaptive nanoparticles the TGBA ordering is established for c >0. In the diluted regime our estimate suggests DTTGBA þN*L ðcÞfc
(see eqn (20)), which is in line with the experimental measurements (see inset of Fig. 4).
Furthermore, previous studies have revealed that the sameNPs essentially stabilize disclination lines in BPs.14,29,39 The core
structures of nematic disclinations (see Fig. 5(b)) and smectic
screw dislocations (see Fig. 5(c)) are qualitatively diﬀerent. The
CdSe NPs are eﬃciently trapped into both defects due to theirsize and attached exible chains which enable their adaptability. Simulations have revealed that NPs tend to aggregate in

3962 | Soft Matter, 2013, 9, 3956–3964

Paperregions exhibiting congurations compatible with the conditions at the NP–LC interface.39
To our knowledge, no other study has so far revealed such aphenomenon, i.e., the simultaneous stabilization of disclination lines and screw dislocations by the same type of NPs.
The eﬃcient trapping of NPs within these qualitatively diﬀerent
networks of topological defects is enabled by a set of conditions
referred to as the ADCT mechanism. One may argue that a
critical (upper) size of NPs is expected for their adaptability to
the cores of defects. Note that in our theoretical modeling it isassumed that the radius r of NPs is smaller than the defect core
size which is roughly comparable to x. This scenario is realized
in the case of CdSe nanoparticles. In the case of r > x the NPs are
expected to disrupt the phase of smectic ordering and, hence,the energy penalties gained by the defect-core-replacement
would be reduced. The importance of the spherical NP size has
been very recently reported in the case of BP stabilization,40
where particles larger than 100 nm have been proven ineﬀectivewith respect to essentially smaller ones. Further experimental
studies are needed to conrm the validity of such an assumption in the case of screw dislocations.

VII

Conclusions

In summary, it is demonstrated that the ADCT mechanism
eﬃciently stabilizes lattices of screw dislocations using surfacefunctionalized CdSe NPs. The same NPs also stabilize thequalitatively diﬀerent line disclinations in BPs,14 proving therobustness of ADCT. Note that CdSe NPs are typicalquantum dot representatives exhibiting size-dependent
photoluminescence.10
The ADCT mechanism could be exploited for diverse applications. It could be used to enhance the stability range ofdiverse periodic structures with potential use in display orphotonic applications,41 where the periodicity and the related
desired optical properties arise due to defect lattices. In addition, the ADCT-driven trapping of appropriate NPs triggering
nucleation and stabilization of structures possessing topological defects could be exploited for designing sensitive NP
detectors, provided that the defect patterns are clearly visible bymeans of optical methods. The present as well as previous
studies14 reveal that even minute concentrations of NPs cansubstantially increase the stability of structures dominated by
topological defects. A closely related mechanism has been
recently demonstrated,42 where ppm concentrations of endotoxin were suﬃcient to trigger a structural transition in asolution of micrometer-sized LC droplets. ADCT is also of great
importance towards the controlled assembly of NPs in so,anisotropic media. The trapped NPs are exploited as functionality-conveying agents, as it has been recently demonstrated in
the case of photoluminescence of CdSe quantum dots,10 thesurface plasmon resonance of gold4,43 and the multiferroic
behavior of LC and g-Fe2O3 nano-composites.44
The direct analogy between LC screw dislocations andmagnetic vortices20,45 infers that the understanding andmastering of the universal ADCT mechanism could contributeto resolving several enigmatic phenomena in magnetism.

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Magnetic vortices exhibit a rich diversity of complex structures,45 and the impact of disorder on their static and dynamic
properties is far from being fully understood.46 The easily
accessible congurations of LCs + NPs may serve as an additional experimental testing ground to gain an insight towards
the impurity-driven pinning of vortices in superconductors.47

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Published on 22 February 2013 on http://pubs.rsc.org | doi:10.1039/C3SM27644A

Acknowledgements
This work has been supported by the Project PE3-1535 within
the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning”, conanced by the European Social Fund and the Greek State. S. D.
acknowledges the funding of Projects DST (SR/NM/NS-134/
2010(G)) and CSIR (03(1207)/12/EMR-II). S. K. acknowledges the
support of the Project P1-0099. Z. K. acknowledges the ProjectP1-0125 and the Centre of Excellence “NAMASTE”. C. G.
acknowledges the support of the FWO Research ProjectG.0492.10. S. K., G. C. and Z. K. acknowledge the nancial
support of the European Oﬃce of Aerospace Research andDevelopment Grant FA8655-12-1-2068. G. N. and V. T.
acknowledge the support of the J. S. Latsis Public BenetFoundation.

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