Viscoelasticity, dielectric anisotropy, and birefringence in the nematic phase of three four-ring bent-core liquid crystals with an L-shaped molecular frame

Article abstract of DOI:10.1039/c2sm26448j

Molecular shape is an important factor in determining the material properties of thermotropic liquid crystals (LCs). We synthesized and investigated several LC compounds formed by asymmetrically bent molecules with a rigid four-ring core in the shape of t

Full text of DOI:10.1039/c2sm26448j

Soft Matter
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Viscoelasticity, dielectric anisotropy, and birefringence
in the nematic phase of three four-ring bent-core liquid
crystals with an L-shaped molecular frame
Cite this: Soft Matter, 2013, 9, 1066
Nejmettin Avci,ab Volodymyr Borshch,a Dipika Debnath Sarkar,c Rahul Deb,c
a
ac
Gude Venkatesh,c Taras Turiv,ad Sergij V. Shiyanovskii, Nandiraju V. S. Rao
and Oleg D. Lavrentovich
*
a
*
Molecular shape is an important factor in determining the material properties of thermotropic liquid
crystals (LCs). We synthesized and investigated several LC compounds formed by asymmetrically bent
molecules with a rigid four-ring core in the shape of the letter ‘L’. We measured the temperature
dependencies of dielectric permittivities, birefringence, splay K1 and bend K3 elastic constants, splay
viscosity hsplay and flow viscosities h|| and ht. The bend–splay anisotropy dK31 ¼ K3 ꢀ K1 is negative,
similar to the case of nematic LCs formed by symmetrically bent molecules of V-shape. The dielectric
anisotropy D3 and birefringence are positive in the entire nematic range. The splay viscosity hsplay and
the flow viscosities h|| and ht are smaller than the viscosities measured for the symmetric V-shaped
bent-core materials at similar temperatures. The ratio G ¼ hsplay/h||,t is in the range 5–4 that is typical
for rod-like LCs. The reported L-shaped bent-core nematic LCs combine the useful features of bent-core
LCs (such as a negative dK31, suitable for formulation of broad-range blue phases) with the relatively
low viscosities, a property typical for rod-like LCs and beneficial for electro-optic switching applications.
Received 21st June 2012
Accepted 30th October 2012
DOI: 10.1039/c2sm26448j
www.rsc.org/softmatter
polarization contributing to the electro-optic response.18
Furthermore, the BC LCs have a relatively large rotational
1 Introduction
viscosity19–21 which makes it difficult to use them in fast-
switching electrooptic devices. It is thus of interest to explore
whether the molecular shape might be tuned to preserve the
distinctive features of BC mesogens but at the very same time, to
reduce the rotational viscosity of the materials.
In a nematic liquid crystal (LC), the anisometric molecules align
1,2
^
along a single direction called the director n. The details of
molecular shape affect the phase diagrams of LCs and macro-
scopic properties. The so-called bent-core (BC) materials
demonstrate especially intriguing new features as compared to
LCs formed by conventional rod-like or disk-like molecules.3,4
For example, BC LCs have been reported to exhibit a thermo-
dynamically stable biaxial nematic phase,5,6 giant exo-electric
response,7 and rather unusual negative values of the bend–splay
anisotropy8–10 dened as the difference between the elastic
constants of bend and splay, dK31 ¼ K3 ꢀ K1. Characterization of
their material properties is oen not so straightforward as in
the case of regular LCs, as the complex molecular shape might
facilitate smectic clustering,11–15 lead to surface anchoring
transitions and director variations along the normal to the
bounding substrates16,17 that result in optical features
mimicking those of a biaxial order, or facilitate a surface electric
Typical bent-core molecules are based on a ve-ring rigid
core in which the central ring represents the bend unit, usually
a 1,3 substituted benzene. The angle between two attached arms
is 120ꢁ. Other forms, such as a ve-membered heterocycle,
either a 2,5-disubstituted 1,3,4-oxadiazole or a 3,5-disubstituted
1,2,4-oxadiazole that yield a somewhat larger angle of 134ꢁ–
140ꢁ, are also reported.22 In most cases, the bent-core structure
is symmetric, resembling the widely open letter ‘V’. For
example, in the case of ve-ring structures, there are two rings
on both sides of the central bent unit. Recently, Sathyanarayana
et al.20 characterized a different ve-ring structure, with the
bend unit connected to three rings on one side and to one ring
on the other side. Both arms ended in alkoxy chains. It was
found that the material properties are close to those of classic V-
shaped BC nematic LCs; in particular, the splay viscosity was
slightly larger than the viscosity of BC nematics and signi-
cantly higher than the viscosity of nematic LCs based on rod-
like molecules. The high splay viscosity was attributed to either
the role of molecular weight or the formation of uctuative
clusters.
aChemical Physics Interdisciplinary Program, Liquid Crystal Institute, Kent State
University, Kent, OH, 44242, USA. E-mail: olavrent@kent.edu; Fax: +1 (330) 672-
2796; Tel: +1 (330) 672-4844
b
˘
˘
¨
Faculty of Science, Department of Physics, Mugla University, 48000 Kotekli Mugla,
Turkey
cChemistry Department, Assam University, Silchar-788011, Assam, India. E-mail:
drnvsrao@gmail.com; Tel: +91 9435522541
dInstitute of Physics, Kyiv, 03039, Ukraine
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There are currently dozens of ve-ring BC molecules synthe-
sized and explored as mesomorphic materials, but only a few
reports on BC mesogens with a four-ring frame.23–31 The rst
realization was based on asymmetric biphenyls.23–25 Fergusson
and Hird reported a four-ring system that forms chiral smectic A
and C phases but no nematic phase.27 Weissog et al.29 also
reported only smectic phases in four-ring systems and concluded
that most of the four-ring compounds are not able to form the so-
called “banana” mesophases encountered in the V-shaped ve-
ring BC compounds. Recently, the banana phases (B1, B7) were
reported in the four-ring systems.30,31 A rare example of a nematic
phase in a four-ring system has been presented by Kang et al.,28
but the range of the nematic phase was small, only 4 ꢁC.
In this work, we report on the synthesis and characterization
of three LCs, named 12-F, 5-F, and 5-Cl, based on a four-ring
bent-core molecular frame, Fig. 1 and 2. In the four-ring core,
the central six-membered toluene unit is attached to two
different arms. These molecules resemble the letter ‘L’. All three
compounds show a wide temperature range of a uniaxial
nematic phase with promising material properties. First, their
bent–splay anisotropy dK31 is negative, which can be used in
expanding the temperature range of the blue phase mixtures.32
Second, their viscosities are lower than those reported for
Fig. 1 (a) Synthesis details of the compound 12-F. Reagents and conditions: (i) classic BC materials with ve-ring V-shaped molecules.10,19,21,33,34
HCl, NaNO2, 0–5 ꢁC, phenol, NaOH; (ii) dry acetone, KHCO3, C12H25Br, KI; (iii)10%
Pd/C, H2, EtOAc, stirring 48 h; (iv) abs. EtOH, AcOH, D, 6 h; (v) DCC, DMAP, DCM,
2 Experimental
2.1 Synthesis
stirring 48 h. (b) Energy optimized molecular structure of 12-F using density
functional theory (DFT) studies. (c) The phase transition temperatures for 12-F.
Two materials, 5-F and 5-Cl, have been synthesized previously.35
The higher homologue (40-uoro phenyl azo) phenyl-4-yl 3-[N-
(40-n-dodecyloxy
2-hydroxybenzylidene)amino]-2-methyl
benzoate, here aer abbreviated as 12-F, was synthesized
following the procedure outlined in Fig. 1(a).
4-HYDROXY 40-FLUORO AZOBENZENE 2. 4-Hydroxy 40-uoro
azobenzene was synthesized by the diazocoupling reaction of 4-
uoroaniline with phenol. To 4-uoroaniline (1.11 g, 10 mmol)
were added 10 ml of distilled water containing hydrochloric
acid (12 M, 2.5 ml, 30 mmol) and the mixture was heated to
dissolve the contents. The solution was then cooled to 0 ꢁC. To
the resulting stirred mixture cooled at 0 ꢁC was added, drop-
wise, a solution of sodium nitrite (0.76 g, 11 mmol) in 10 ml of
water. The resulting diazonium chloride was consecutively
coupled with an alkaline solution of phenol (0.94 g, 10 mmol) in
10 ml of water containing 0.80 g (20 mmol) of sodium hydroxide
with constant stirring. The azo-dye which formed immediately
as a yellow precipitate was ltered, washed several times with
water and dissolved in diethyl ether and the resulting organic
solution dried over anhydrous sodium sulphate.
The crude product obtained aer removal of the solvent
under reduced pressure was puried by recrystallization from
cold hexane, the precipitate was ltered and washed with water
and methanol and dried in vacuum. Yield 1.62 g (75%).
IR nmax in cmꢀ1: 1450 (nN]N, azo); 3374 (nO–H); 1H NMR
(CDCl3, 400 MHz): d ¼ 5.56 (s, 1H, –OH); 7.83 (d, 2H, J ¼ 8.4 Hz,
ArH); 7.72 (d, 2H, J ¼ 8.0 Hz, ArH); 7.61 (d, 2H, J ¼ 7.8 Hz, ArH);
6.76 (d, 2H, J ¼ 7.8 Hz, ArH). Elemental analysis calculated for
Fig.
2
Molecular structures and phase transition temperatures for the
compounds (a) 5-F and (b) 5-Cl.
C
12H9FN2O: C, 66.6; H, 4.20%; found. C, 66.5; H, 4.13%.
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The intermediate compounds 4 and 6 were prepared
following the procedure reported in ref. 35.
[3-(4-N-DODECYLOXY-2-HYDROXYBENZYLIDENE
AMINO)-2-
METHYLBENZOIC ACID] 7. An ethanolic solution of 2-methyl-3-
aminobenzoic acid (0.5 g, 33 mmol) was added to an ethanolic
solution (20 ml) of 4-n-dodecyloxy 2-hydroxy benzaldehyde
(1.01 g, 33 mmol). The mixture was reuxed with few drops of
glacial acetic acid as the catalyst for 4 hours to yield the pale
yellow colored Schiff’s base. The precipitate was collected by
ltration from the hot solution and recrystallized several times
from absolute ethanol to produce a pure compound. Yield ¼
1.2 g (82.7%).
IR nmax in cmꢀ1: 1624 (nCH]N, imine); 1726 (nC]O, acid); 3440
(nO–H, H-bonded); 1H NMR (CDCl3, 400 MHz): d ¼ 13.51 (s, 1H,
–OH); 10.18 (s, 1H, –COOH); 8.33 (s, 1H, –CH]N–); 7.88 (d, 1H,
J ¼ 8.4 Hz, ArH); 7.33 (t, 1H, J ¼ 8.0 Hz, ArH); 7.46 (d, 1H, J ¼ 8.4
Hz, ArH); 2.44 (s, 3H, Ar–CH3); 7.23 (d, J ¼ 7.8 Hz, 1H, ArH); 6.98
(d, 1H, J ¼ 8.4 Hz, ArH); 6.43 (s, 1H, ArH); 4.04 (t, 2H, J ¼ 7.8 Hz,
–O–CH2–); 1.61 (q, 2H, –O–CH2–CH2–); 1.29–1.18 (m, 18H, –O–
(CH2)2–(CH2)9–); 0.90 (t, 3H, J ¼ 7.8 Hz, –O–(CH2)11–CH3).
Elemental analysis calculated for C27H37NO4: C, 73.7; H, 8.48%;
found. C, 73.5; H, 8.33%.
Fig. 3 (a) DSC spectrum of 12-F obtained in the second heating and cooling
cycle at 5 ꢁC minꢀ1 with insets showing the Iso–N and N–SmA phase transitions;
(b) Schlieren texture of the nematic phase at 130.0 ꢁC; (c) homeotropic texture of
the SmA phase at 105.0 ꢁC.
(40-FLUORO PHENYL AZO) PHENYL-4-YL 3-[N-(40-N-DODECYLOXY
2-HYDROXYBENZYLIDENE)AMINO]-2-METHYL BENZOATE, 12-F. The
compound 4-hydroxy 40-uoroazobenzene 2 (0.22 g, 1 mmol)
and 2-methyl 3-[N-(4-n-dodecyloxysalicylidene)amino]benzoic
acid 7 (0.44 g, 1 mmol) and 4-dimethylamino pyridine (DMAP)
(2 mg, 0.01 mmol) were dissolved in dry dichloromethane 134.0 ꢁC (0.245, 0.60) N 112.9 ꢁC (0.136, 0.35) SmA 84.4 ꢁC (36.3,
(DCM) (50 ml) under inert atmosphere. A solution of N,N0- 101.8) Cr. For 5-F the values for heating: Cr 149.6 ꢁC (38.2, 90.5)
dicyclohexylcarbodiimide (DCC) (0.25 g, 1.2 mmol) in DCM N 159.3 ꢁC (0.224, 0.52) Iso, and for cooling: Iso 156.7 ꢁC (0.262,
(20 ml) was added to the above mixture and the mixture was 0.61) N 71.4 ꢁC (19.1, 55.5) Cr. For 5-Cl the values for heating: Cr
stirred at room temperature for 48 h. The white precipitate N,N0- 138.6 ꢁC (51.2, 124.6) N 179.6 ꢁC (0.197, 0.43) Iso, and for
ꢁ
ꢁ
dicyclohexylurea was removed by ltration and the solvent DCM cooling: Iso 174.9 C (0.205, 0.46) N 90.8 C (18.3, 50.3) Cr.
was evaporated to get the residue from the ltrate. The solid
residue was puried by column chromatography on silica gel
using hexane/chloroform (9/1) as the eluent followed by recrys-
2.2 Material characterization techniques
tallization from absolute ethanol to afford the pure product as a For dielectric and electrooptical measurements we prepared
yellowish solid in more than 70% yield. The yellow product was cells in the following fashion. First, glass plates with a trans-
then recrystallized several times from absolute ethanol to get the parent indium tin oxide (ITO) layer were cleaned in an ultra-
pure product and dried in vacuum. Yield ¼ 0.46 g (72%).
sonic bath lled with a water solution of a detergent. Then the
IR nmax in cmꢀ1: 1624 (nCH]N, imine); 1747 (nC]O, ester); plates were rinsed with deionized water, and cleaned by meth-
3194 (nO–H, H-bonded); 1H NMR (CDCl3, 500 MHz): d ¼ 13.51 (s, anol and ethanol several times, rinsed with isopropanol, and
1H, –OH); 8.45 (s, 1H, –CH]N–); 8.02–7.99 (m, 5H, ArH); 7.40– dried at 60 ꢁC. The dried substrates were irradiated with UV
7.26 (m, 7H, ArH); 6.52 (d, 2H, J ¼ 6.4, ArH); 4.01 (t, 2H, J ¼ 6.8 light for ve minutes in order to remove organic contamina-
Hz, –O–CH2–); 2.68 (s, 3H, Ar–CH3); 1.82–1.26 (m, 20H, tions. Using photolithography, we etched ITO electrodes in a
–(CH2)10–); 0.86 (t, 3H, –CH3). Elemental analysis calculated for square shape of area 25 mm2. The substrates were spin-coated
C
39H44FN3O4: C, 73.4; H, 6.95%; found C, 73.2; H, 6.86%.
with a 1 : 4 solution of the alignment agent PI2555 (HD
The phase diagrams were characterized by differential Microsystems) in T9039 solvent (HD Microsystems), baked at
scanning calorimetry (DSC) and polarizing microscopy (Fig. 3). 90 ꢁC for one minute, and then additionally baked at 275 ꢁC for
12-F exhibits a uniaxial nematic phase in the heating cycle and 1 hour. To achieve a uniform planar alignment, the PI2555-
uniaxial nematic and smectic A (SmA) phases in the cooling coated plates were rubbed with a clean velvet cloth and
cycle. 5-F and 5-Cl demonstrate only a uniaxial nematic phase assembled in an ‘antiparallel’ fashion. The cells were glued with
on both heating and cooling. The phase transition temperatures a UV-curable Norland adhesive NOA-65 containing glass beads
with enthalpy (kJ molꢀ1) and entropy (J molꢀ1 Kꢀ1) values in as spacers. The cell thickness d was measured by the standard
parentheses obtained during second heating and cooling cycles interferometric method. The temperature was controlled by a
at 5 ꢁC minꢀ1 are as follows. For 12-F during heating: Cr Linkam hot stage LTS350 and a controller TMS94 with an
116.6 ꢁC (40.5, 103) N 134.6 ꢁC (0.231, 0.56) Iso, and cooling: Iso accuracy of ꢂ0.1 C.
ꢁ
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For dielectric characterization, we used an impedance gain
Soft Matter
For the setting shown in Fig. 4, the transmitted light inten-
analyser HP4284A that measures complex values of impedance sity is determined by the voltage-dependent optical phase
Z ¼ Re(Z) + iIm(Z). The effective dielectric permittivity across retardation F(V) of the cell,
the planar cell of thickness d was calculated as 3 ¼ (CeuIm(Z))ꢀ1
,
FðVÞ
IðVÞ ¼ I0 sin2
;
(2)
where Ce is the capacitance of the empty cell and u is the
angular frequency of the applied electric eld. For these
measurements we used a cell of thickness d ¼ 3.5 mm for 12-F
and d ¼ 3.9 mm for 5-F and 5-Cl. A signal generator (Keithley
3390) was used to apply an AC voltage with frequency 25 kHz
(u z 1.57 ꢃ 105 sꢀ1). We ramped the voltage V from 0.01 V to
2 V in 0.01 V steps and from 2 V to 20 V in 0.1 V increment. The
dielectric permittivity for the direction perpendicular to the
director, 3t, was determined from the capacitance measured
for low voltages, below the Frederiks threshold Vth of dielectric
reorientation. The parallel component 3|| was measured by
extrapolating the voltage dependency of capacitance in the high
voltage range, 10–20 V, to V / N. The data yield the dielectric
anisotropy D3 ¼ 3|| ꢀ 3t.
2
where I0 is the maximum light intensity. By measuring I(V) in
the broad range of voltages, from 0 to 20 V, and calculating the
interference maxima, we determined the total phase retardation
Ftot ¼ 2pdDn/l of a cell which provides the value of birefrin-
gence Dn ¼ ne ꢀ no, where ne and no are the extraordinary and
ordinary refractive indices of the LC, respectively.41
The splay viscosity is determined by monitoring light
intensity changes caused by director relaxation from the state
slightly above the Frederiks threshold V > Vth to the zero-voltage
planar state. As a function of time t elapsed aer the voltage is
switched off, the light intensity is
Ftot ꢀ dðtÞ
IðtÞ ¼ I0 sin2
;
(3)
To determine the elastic constants of splay K1 and bend K3,
we followed the Saupe technique,36–38 in which one uses a single
planar cell and determines the voltage dependence of its
capacitance C. The splay constant is obtained by measuring the
Frederiks threshold, K1 ¼ 30D3Vth2/p2. For strong surface
anchoring, K3 is extracted by tting the experimental data well
above Vth with the expression:39
2
where the time-dependent small correction to the total phase
retardation shows an exponential decay42
d(t) ¼ d0eꢀ2t/s
;
(4)
0
from its maximum value d0 (at t ¼ 0) to 0, with a characteristic
decay time s0. The slope of dependence ln(d0/d(t)) (obtained
experimentally with the help of eqn (3)) versus time is equal to
2/s0. The splay viscosity of the LC is then calculated as:43
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
ð
pffiffiffiffiffiffiffiffiffiffi
C ꢀ C0
C|| ꢀ C0
2
Vth
V
1 þ kx2
1 þ xx2
¼ 1 ꢀ
1 þ x
dx;
(1)
p
0
hsplay ¼ p2s0K1/d2.
(5)
where k ¼ K3/K1 ꢀ 1, x ¼ 3||/3t ꢀ 1, C0 is the capacitance for V <
Vth, and C|| is the capacitance obtained by extrapolating to 1/V ¼
0. In order to avoid trans- to cis-photoisomerization of the azo-
benzene group, all the dielectric measurements were done in a
completely darkened hot stage.40
To determine birefringence and splay viscosity, we measured
transmission of a polarized light beam through the planar cell
of thickness d z 19 mm, subject to the 25 kHz electric eld,
Fig. 4. A He–Ne laser (wavelength l ¼ 633 nm) was used as a
light source. The He–Ne beam promotes cis-to-trans isomeriza-
tion of the azobenzene group.40 The LC cell was placed between
two crossed linear polarizers with a rubbing direction at 45ꢁ to
their extinction directions. The Babinet–Soleil compensator was
used to control an additional optical phase retardation. The
transmitted light intensity was measured by a photo-detector
TIA-525 (Terahertz Technologies Inc.) connected to an oscillo-
scope Tektronix TDS-2014.
We also determined effective ow velocities in the direction
parallel and perpendicular to the director, by exploring the
Brownian motion of colloidal particles in the nematic
phase.22,44,45 We studied poly(methyl methacrylate) (PMMA)
spheres of radius R ¼ 2.7 mm that align the director tangentially
to its surface. The dynamics of isolated particles was monitored
using an inverted microscope Nikon Eclipse TE2000-E equipped
with a 60ꢃ objective and a MotionBlitz EoSens mini1 (Mikro-
tron GmbH) video camera with a frame rate of 100 fps.46 The
diffusion coefficients for the motion parallel (D||) and perpen-
dicular (Dt) to the director were obtained from the mean
square displacement (MSD) of a particle as a function of the lag
time s. A typical time evolution of a particle’s MSD at temper-
ꢁ
ature 122 C is plotted in the inset in Fig. 8. Using the Stokes–
Einstein equation, the corresponding viscosities are found as
h||,t ¼ kBT/(6pRD||,t), where kB is the Boltzmann constant and
T is the absolute temperature.
Separate experiments to explore whether the nematic phase
of 12-F, 5-F, and 5-Cl might be of a biaxial type were conducted.
For 12-F, we prepared cells with homeotropic surface
anchoring. For homeotropic alignment, we used an inorganic
passivation layer NHC AT720-A (Nissan Chemical Industries,
Ltd) as well as ITO-coated substrates covered with lecithin. Aer
slow cooling (0.3 ꢁC minꢀ1) from the isotropic phase, the
homeotropic alignment was achieved. A polarizing microscope
OptiPhot2-Pol (Nikon Instruments, Inc.) with objectives Nikon
Fig. 4 Electrooptical setup: the LC cell and the Babinet–Soleil compensator (B–S)
are placed between a crossed polarizer (P) and an analyser (A). The intensity of the
transmitted light of the He–Ne laser is measured by a photodetector (PD).
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MPlan 20ꢃ/NA ¼ 0.4 ELWD, MPlan 40ꢃ/NA ¼ 0.5 ELWD, and
CFPlan 50ꢃ/NA ¼ 0.45 SLWD, where ELWD stands for extra-
large working distance, SLWD stands for super long working
distance, and NA is the numerical aperture, was used for
orthoscopic and conoscopic observations.
To discriminate between the uniaxial and biaxial nematic
order in the studied materials, we used two approaches. For 12-
F, which can be aligned homeotropically, we used conoscopic
studies. 5-F and 5-Cl cannot be aligned homeotropically. The
test of potential biaxiality in these two materials was based on
observation of topological defects formed when small silica
spheres (diameter 10 mm, Duke Scientic) were added to the
LC16,47 and when the LC was dispersed as spherical droplets in
glycerine.48
3 Results and discussion
3.1 Dielectric permittivity
Dielectric permittivity as a function of temperature is shown for
all three compounds in Fig. 5(a)–(c). The parallel (3||) compo-
nent of dielectric permittivity of 12-F (Fig. 5(a)) increases with
the decrease in temperature and ends up slightly decreasing
near the N–SmA phase transition. The perpendicular compo-
nent (3t) increases as the temperature is lowered. This leads to
a non-monotonous behaviour of the dielectric anisotropy (D3 ¼
3|| ꢀ 3t), Fig. 5(d). The average dielectric permittivity 3¼(3||
+
23t)/3 continues the trend of the isotropic phase permittivity,
3iso, monotonously decreasing with temperature.
The ester group and the uorine atom on one of the arms of
the rigid 12-F core contribute to the transverse and longitudinal
components of the molecular permanent dipole. For 12-F, the
non-monotonous behavior of D3 with temperature can be
explained by the possible formation of smectic cybotactic
clusters in the nematic phase.49,50 In the clusters, molecular
separations are much larger in the direction perpendicular to
the smectic layers than within the smectic layers. As a result, the
longitudinal components of molecular dipoles tend to form
antiparallel arrangements within the layers thus reducing 3||.
Similarly, the transverse components between the adjacent
molecules in the same smectic layer tend to align parallel to
each other, increasing 3t. The effect explains why D3 decreases
rather dramatically for 12-F when one approaches the smectic
phase by lowering the temperature.
The dielectric permittivity of 5-F and 5-Cl shows similar
temperature behaviour, Fig. 5(b) and (c). Although these two
compounds do not exhibit the smectic phase, D3 dependence
on temperature is also non-monotonous, Fig. 5(d), suggesting
that the smectic clusters might form even without the explicit
appearance of a homogeneous smectic state. This result is in
agreement with the recent demonstration by transmission
electron microscopy of smectic clusters in a broad temperature
range (tens of degrees) of a uniaxial nematic phase for a BC
compound that does not have a stable smectic phase.51
Fig. 5 Temperature dependence of dielectric permittivities for (a) 12-F, (b) 5-F,
and (c) 5-Cl. Figure (d) shows the temperature dependence of the dielectric
anisotropy. The lines are guides to the eye.
3.2 Splay and bend elastic constants
molecules and negative for oblate molecules.52–55 Recently, it
The bend–splay anisotropy dK31 ¼ K3 ꢀ K1 in rod-like LCs is was shown that in BC LCs, dK31 < 0,8,9,20,33,56 which is a natural
typically positive when the nematic is formed by prolate result because of the bent shape of BC molecules. Our data
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3.3 Splay viscosity and ow viscosities
The splay viscosity hsplay for all three compounds, determined
from the director relaxation in the Frederiks splay transition,
shows a monotonous increase as the temperature is lowered,
with a tendency to diverge near the transition to a higher
ordered phase, Fig. 7. Its value is noticeably smaller as
compared to other BC LCs with a similar nematic temperature
range. For example, we nd that at T ¼ 120 ꢁC, hsplay ¼ 0.14 Pa s
for 12-F and hsplay ꢄ 0.3 Pa s for both 5-F and 5-Cl. For a ve-ring
hockey-stick nematic LC, the viscosity is noticeably higher:20
ꢁ
hsplay ꢄ 0.6 Pa s at the same temperature T ¼ 120 C. For the
symmetric V-shaped compound, the reported34 viscosity is
hsplay ¼ 0.2 Pa s at T ¼ 147.5 ꢁC, which is much larger than hsplay
ꢁ
measured for 12-F at temperatures above 120 C (Fig. 7).
The splay viscosity of all three studied L-shaped compounds
remains higher than that of the rod-like nematics at similar
temperatures (hsplay ¼ 5.9 mPa s for PAA at 125 ꢁC (ref. 43) and
hsplay ¼ 20 mPa s for M957 at 114 ꢁC (ref. 58)) but is comparable
to hsplay of rod-like nematics measured at room
temperature.42,58,59
The splay viscosity is expressed through the rotational
2
viscosity g1 and Leslie coefficients ai as hsplay ¼ g1 ꢀ a3 /hb ¼
2
a3 ꢀ a2 ꢀ 2a3 /(a4 + a5 ꢀ a2), where hb is the viscosity in Mie-
sowicz geometry with the ow parallel to the xed orientation of
the director60 (hb is close to the value h|| determined from the
Brownian motion experiment, see below). For the rod-like LCs,
a3 is typically very small, and thus hsplay y g1. For the BC
materials, a3 has not been reported so far, thus we keep the
notation hsplay in our discussion. We conclude that hsplay in 12-
F, 5-F, and 5-Cl is intermediate between the values typically
found in BC and rod-like LCs at comparable temperatures.
The ow viscosities h|| and ht for 12-F are shown in Fig. 8.
Since the data were obtained for relatively weak tangential
surface anchoring, the two quantities can be considered as
approximately equal to the Miesowicz viscosities45 measured for
the ow parallel (hb) and perpendicular (ha) to the xed director,
namely, h|| y hb ¼ (a3 + a4 + a6)/2 and ht y ha ¼ a4/2. As
expected, h|| < ht at all temperatures. The values of h|| and ht
Fig. 6 Splay (circles) and bend (squares) elastic constants vs. temperature for (a)
12-F, (b) 5-F and 5-Cl.
demonstrate that in all three L-shape BC LCs, dK31 is also
negative in a relatively broad temperature range, Fig. 6(a),(b). In
12-F dK31 becomes positive as the temperature is reduced
towards the smectic phase, Fig. 6(a). The latter is explained by a
strong pre-transitional divergence of K3 as bend deformations
are incompatible with the equidistance of smectic layers.1,2 The
compounds 5-F and 5-Cl do not exhibit the smectic phase, and
the behaviour of K3 is similar to that reported by Kaur et al.57
Fig. 8 Flow viscosities h|| and ht for 12-F as a function of temperature. The inset
shows a typical mean-square displacement (MSD) of the probe particle vs. time at
122 ꢁC.
Fig. 7 Temperature variation of the splay viscosity hsplay for 12-F (open circles),
5-F (closed black circles), and 5-Cl (grey triangles).
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ꢁ
in 12-F for the temperature range 113–135 C are very close to
those of 5CB in the range 23–35 C.61 As compared to the rod-
ꢁ
like LCs with a nematic temperature range similar to that of 12-
F, the ow viscosities in 12-F are higher. For example, the
literature data list ha and hb as 3.4 mPa s and 2.4 mPa s at 122 ꢁC
for PAA;60 14 mPa s and 9 mPa s at 133 ꢁC for ethyl p-[(p-
methoxybenzylidene)amino] cinnamate,62 respectively.
The data above allow us to estimate the splay-to-ow
viscosity ratios G|| ¼ hsplay/h|| and Gt ¼ hsplay/ht for 12-F. For
T ¼ 122 ꢁC, we nd G|| ¼ 5 and Gt ¼ 4. These values are
comparable to those for rod-like LCs, such as 5CB at 25 ꢁC (G|| ¼
3.5 and Gt ¼ 2.1)43 and PAA at 125 ꢁC (G|| ¼ 3 and Gt ¼ 2).43 Our
results are also not very different from the results of Sathya-
narayana21 (G|| ¼ 16 and Gt ¼ 12) for a 43% mixture of V-sha-
ped BC with 5CB at T z 40 ꢁC. On the other hand, our data
differ signicantly from G ¼ (0.01 – 0.02) determined for a V-
shaped BC at T ¼ 70 ꢁC by Dorjgotov et al.19 Such a drastic
difference in G’s is caused mainly by the difference in the ow
viscosities h|| and ht, as these in 12-F appear to be at least
103 times smaller than those measured19 for V-shaped BC
nematics. One of the possible reasons might be the difference
in molecular shapes (the BC molecules studied in ref. 19 have a
ve-ring rigid core and two aliphatic chains). The other possible
reason might be related to the difference in experimental
techniques used to determine ow velocities. In ref. 19, the ow
velocity was measured by the Quincke rotation technique in
which a cylindrical particle rotates in a nematic host, while in
our case, the tracked motion is a random Brownian diffusion.
Fig. 10 Conoscopic Maltese cross texture of a homeotropic 12-F cell of thickness
d ¼ 19 mm observed with 20ꢃ objective between crossed polarizers, at temper-
ature 130 ꢁC. The images (a) and (b) were taken for two orientations of the cell
that differ by 45ꢁ.
^
^ ^
phase, there are three directors usually labelled n, m, and l, that
correspond to the orientational order of all three principal axes
of the molecules. In the biaxial nematic, there are two optic axes
with an angle between them that is determined by the values of
three refractive indices. The simplest test of potential biaxiality
^
consists in preparing a homeotropic cell in which the director n
is perpendicular to the at bounding plates. If the material is
uniaxial, the single optic axis is also perpendicular to the
bounding plates. If the material is biaxial, the two optic axes
^
should be tilted away from the direction of n. The difference is
easy to establish by observing the sample in the conoscopic
mode (for more details, see ref. 16 and 17).
Fig. 10 shows the conoscopic texture of the homeotropically
aligned 12-F cell viewed between crossed polarizers. The texture
has the shape of a symmetric ‘Maltese cross’ with four dark
brushes, the so-called isogyres. The texture remains unchanged
when the sample is rotated in the plane of view, demonstrating
that there is no in-plane ordering in the homeotropic sample
and that the optic axis of the sample remains parallel to the
direction of observation. The Maltese cross texture persists in
the entire temperature range of the nematic phase of 12-F,
demonstrating that the nematic phase is of a uniaxial type. The
rate of temperature change was slow, 0.3 ꢁC minꢀ1, to avoid
director tilt and apparent optical biaxiality associated with
thermal expansion.63
3.4. Birefringence
Birefringence Dn of 12-F in the nematic phase is relatively high,
reaching a maximum value of 0.175 near the transition to the
smectic phase, Fig. 9. For 5-F and 5-Cl, the birefringence is
higher. Their temperature dependencies are standard, with Dn
monotonously increasing when the temperature is lowered.
3.5 Biaxiality tests
^
In the uniaxial nematic phase, the director n is also the local
optic axis of the material. In the hypothetical biaxial nematic
Since the materials 5-F and 5-Cl cannot be aligned homeo-
tropically in the at cells, we used different approaches to test
their potential biaxiality, based on the features of topological
defects in conned geometries.16,17
The rst experiment is to disperse colloidal silica spheres in
the LC cell of thickness d z 50 mm with a uniform director
Fig. 11 Colloidal silica spheres in a planar 5-Cl cell at 165 ꢁC. An isolated sphere
with two boojums at poles viewed (a) between two crossed polarizers; (b)
between two parallel polarizers. (c) An aggregated chain of spheres, tilted by
Fig. 9 Temperature dependence of birefringence Dn in the nematic phase of
12-F, 5-F, and 5-Cl.
z30ꢁ with respect to the overall director n0 set by rubbing.
^
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textures with two surface point defects–boojums at the poles48
that do not change with temperature in the entire range of the
nematic phase, Fig. 12.
If it were the biaxial nematic phase, the two points should be
either connected by a linear defect or merge into a single surface
point defect of charge 2. In the biaxial nematic, the smallest
charge of the isolated surface point defect is 2.65
The above experiments demonstrate that all the studied
materials 12-F, 5-F, and 5-Cl show only a uniaxial orientation
order (as opposed to the biaxial one) in the entire range of the
nematic phase.
4 Conclusions
Fig. 12 Polarizing microscopy textures of a 5-F nematic droplet dispersed in
glycerine, viewed between two crossed polarizers (a and c) and with an additional
wavelength compensator; the slow axis orientation of the compensator is indi-
cated in the bottom right corner of parts (b and d). Images (c and d) were taken
after the sample was rotated by about 15ꢁ.
We explored the properties of the uniaxial nematic phase of
three bent-core nematic LCs: 12-F, 5-F, and 5-Cl, with four-ring
rigid molecular frames bent in the shape of the letter ‘L’. The
materials show properties intermediate between those of LCs
formed by rod-like and V-shaped ve-ring bent-core molecules.
All compounds demonstrate a relatively wide temperature range
of the uniaxial nematic phase. The elastic bend–splay anisot-
ropy, dK31 ¼ K3 ꢀ K1, is negative, which might be of interest in
formulating wide temperature range blue phase mixtures.66 The
relatively low viscosities hsplay, h||, and ht as compared to other
BC LCs might be of interest for electro-optical applications with
^
^
n ¼ n0 set by rubbing the bounding plates and to observe the
director distortions around the particles. Polarizing microscopy
shows that the director aligns parallel to the surface of spheres,
Fig. 11(a). The director eld dened at the spherical surface
must contain a certain number of point singularities with the
´
total topological charge equal to 2, according to the Poincare
a short response time. We found that the ratio G||,t ¼ hsplay
/
theorem. In a uniformly aligned uniaxial nematic, the most
energetically stable is a conguration with two point defects–
boojums located at the axis that is parallel to the overall director
h||,t is on the order of a few units, close to the values reported
on the majority of other types of nematic materials. The studied
three compounds do not display a biaxial nematic phase. The
experimental results add to a general understanding of struc-
ture–property relationships in LCs formed by molecules of
complex shapes, showing that the L-shaped molecules, being
structurally intermediate between the rod-like and V-shaped BC
mesogens, yield similarly intermediate macroscopic character-
istics of the uniaxial nematic phase.
^
n0, each of them of a topological charge equal to 1 (as the
director rotates by an angle 2p when one circumnavigates the
defect core once). The structure expected for the uniaxial
nematic is compatible with the experimental texture, in which
each sphere is accompanied by two point defects; the imaginary
line that connects the point defects is parallel to the overall
^
director n0. These textures do not change in the entire range of
the nematic phase of both 5-F and 5-Cl.
Can the textures in Fig. 11 be made compatible with the
biaxial nematic order in the surrounding LC? The answer is
negative. The reason is that the defects of topological charge 1
at a surface of a biaxial nematic cannot be isolated point
defects. They must represent the ends of singular lines (dis-
clinations) of strength 1 terminating at the surface.64 These
lines are not observable in the textures of 5-F and 5-Cl. One
might argue that their contrast is too low to allow for direct
observation under the microscope. The disclinations should
reveal themselves in particle assemblies. In the biaxial nematic,
the disclinations are expected to run along the overall director
Acknowledgements
This work was supported by DOE grant #DE-FG02-06ER 46331
(dielectric, splay viscosity, and elastic measurements), NSF
DMR 1104850 (ow viscosities) and by Samsung Electronics
Corp. N.A. acknowledges support from The Council of Higher
Education of Turkey. D.D.S., G.V. and N.V.S.R. acknowledge
nancial support from Directorate of Naval Research and
Development (DNRD) and Department of Science and Tech-
nology (India).
^
n0 and should guide the chaining of the spheres along the same
Notes and references
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^
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