Dielectric, calorimetric and mesophase properties of 1′′-(2′,4-difluorobiphenyl-4′-yloxy)-9′′-(4-cyanobiphenyl-4′-yloxy) nonane: An odd liquid crystal dimer with a monotropic mesophase having the characteristics of a twist-bend nematic phase

Article abstract of DOI:10.1039/c4cp03462g

This paper reports a novel liquid crystal phase having the characteristics of a twist-bend nematic phase formed by a non-symmetric ether-linked liquid crystal dimer. The dimer 1′′-(2′,4-difluorobiphenyl-4′-yloxy)-9′′-(4-cyanobiphenyl-4′-yloxy) nonane (FFO9OCB) exhibits two liquid-crystalline phases on cooling at a sufficiently high rate from the isotropic phase. The high temperature mesophase has been reported in the literature as nematic and confirmed in this study. The other mesophase is metastable and can be supercooled giving rise to a glassy state. Its identification and characterization are based on optical textures, broadband dielectric spectroscopy, calorimetry, measurements of both splay and bend elastic constants in the nematic phase and miscibility studies. It is concluded that the low temperature mesophase exhibits the characteristics of a twist-bend nematic phase. Dielectric measurements enable us to obtain the static permittivity and information about the molecular dynamics in the isotropic phase, in the nematic mesophase and across the isotropic-to-nematic phase transition. Two orientations, parallel and perpendicular to the director, have been investigated. In the high temperature nematic mesophase, the dielectric anisotropy is found to be positive. Measurements of the parallel component of the dielectric permittivity are well-explained by the molecular theory of dielectric relaxation in nematic dimers (M. Stocchero, A. Ferrarini, G. J. Moro, D. A. Dunmur and G. R. Luckhurst, J. Chem. Phys., 2004, 121, 8079). The dimer is modelled as a mixture of cis and trans conformers and the model allows an estimate of their relative populations at each temperature. The nematic-to-isotropic phase transition has been exhaustively studied from the accurate evolution of the heat capacity and the static dielectric permittivity data. It has been concluded that the transition is first order in nature, but close to tricritical. The nature of the nematic-to-the novel liquid crystal phase transition is difficult to analyze to the same extent because of insufficient precision. Only observations at cooling rates of 10 K min^-1 or higher were possible because on heating from the glassy state, the twist-bend nematic mesophase crystallizes at temperatures far below the nematic-nematic phase transition. This journal is

Full text of DOI:10.1039/c4cp03462g

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PAPER
Dielectric, calorimetric and mesophase properties
of 100-(20,4-difluorobiphenyl-40-yloxy)-900-(4-cyano-
biphenyl-40-yloxy) nonane: an odd liquid crystal
dimer with a monotropic mesophase having the
characteristics of a twist-bend nematic phase
Cite this: Phys.Chem.Chem.Phys.,
2014, 16, 21391
N. Sebastian,a D. O. Lopez,*b B. Robles-Hernandez,ab M. R. de la Fuente,a J. Salud,b
´
´
´
M. A. Perez-Jubindo,a D. A. Dunmur,c G. R. Luckhurstc and D. J. B. Jacksonc
´
This paper reports a novel liquid crystal phase having the characteristics of a twist-bend nematic phase
formed by a non-symmetric ether-linked liquid crystal dimer. The dimer 100-(20,4-difluorobiphenyl-
40-yloxy)-900-(4-cyanobiphenyl-40-yloxy) nonane (FFO9OCB) exhibits two liquid-crystalline phases on
cooling at a sufficiently high rate from the isotropic phase. The high temperature mesophase has been
reported in the literature as nematic and confirmed in this study. The other mesophase is metastable
and can be supercooled giving rise to a glassy state. Its identification and characterization are based on
optical textures, broadband dielectric spectroscopy, calorimetry, measurements of both splay and bend
elastic constants in the nematic phase and miscibility studies. It is concluded that the low temperature
mesophase exhibits the characteristics of a twist-bend nematic phase. Dielectric measurements enable
us to obtain the static permittivity and information about the molecular dynamics in the isotropic phase,
in the nematic mesophase and across the isotropic-to-nematic phase transition. Two orientations,
parallel and perpendicular to the director, have been investigated. In the high temperature nematic
mesophase, the dielectric anisotropy is found to be positive. Measurements of the parallel component
of the dielectric permittivity are well-explained by the molecular theory of dielectric relaxation in
nematic dimers (M. Stocchero, A. Ferrarini, G. J. Moro, D. A. Dunmur and G. R. Luckhurst, J. Chem.
Phys., 2004, 121, 8079). The dimer is modelled as a mixture of cis and trans conformers and the model
allows an estimate of their relative populations at each temperature. The nematic-to-isotropic phase
transition has been exhaustively studied from the accurate evolution of the heat capacity and the static
dielectric permittivity data. It has been concluded that the transition is first order in nature, but close
to tricritical. The nature of the nematic-to-the novel liquid crystal phase transition is difficult to analyze
to the same extent because of insufficient precision. Only observations at cooling rates of 10 K minꢀ1 or
higher were possible because on heating from the glassy state, the twist-bend nematic mesophase
crystallizes at temperatures far below the nematic–nematic phase transition.
Received 2nd January 2014,
Accepted 15th August 2014
DOI: 10.1039/c4cp03462g
www.rsc.org/pccp
Molecular flexibility is one of the most important structural
aspects which may influence the average molecular shape. In
1 Introduction
Liquid crystals are molecular materials in which the type and most liquid crystals, flexible alkyl chains are attached to
stability of liquid crystalline phases or mesophases are determined anisotropic rigid or semi-rigid molecular cores. However, there
by the molecular shape and anisotropy of the constituent molecules. is a group of liquid crystal-forming molecules in which semi-
rigid pro-mesogenic or mesogenic groups are linked via flexible
a
´
´
Departamento de Fısica Aplicada II, Facultad de Ciencia y Tecnologıa,
spacers. The simplest of these compounds are the so-called
liquid crystal dimers which consist of two pro-mesogenic
groups joined by a flexible spacer (the most common spacers
are alkyl chains with an odd or even number of carbon atoms).
These compounds can be classified into two broad classes:
symmetric and non-symmetric. In a symmetric liquid crystal
´
Universidad del Paıs Vasco, Apartado 644, E-48080 Bilbao, Spain
b
´
´
Grup de Propietas Fısiques dels Materials (GRPFM), Departament de Fısica i
`
Enginyeria Nuclear, E.T.S.E.I.B. Universitat Politecnica de Catalunya, Diagonal,
647 08028 Barcelona, Spain. E-mail: david.orencio.lopez@upc.edu
c School of Chemistry, University of Southampton, Highfield, Southampton,
SO17 1BJ, UK
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dimer the two pro-mesogenic units are identical, whereas they has been reported20,23,24 for this material. However, our study
are different in a non-symmetric dimer. reveals the existence of an additional mesophase having the
Liquid crystal dimers have been revealed as a fascinating characteristics of a monotropic twist-bend nematic phase, which
group of mesogenic materials because of the discovery of unusual was not previously reported, and whose nature is an extra motiva-
properties, some of these in very recent times. It is interesting to tion for this investigation. This should be taken as understood
cite, among others, the novel alternating and modulated smectic even though throughout this paper we shall not always add the
mesophases,1,2 the new twist-bend nematics (NTB), predicted by qualifying phrase ‘having the characteristics of the twist-bend
Dozov3 and then experimentally identified,4–7 or the existence of nematic phase’. We also identify a glassy NTB phase linked to
blue phases over an unusually wide range of temperature.8 An the monotropic mesophase, which appears under some cooling
extra motivation is the current interest in liquid crystal dimers regimes.
with biaxial shapes as potential candidates for thermotropic
A further aspect reported in the present work is the N-to-I
liquid crystals presenting the elusive biaxial nematic phase phase transition of the FFO9OCB dimer. The N-to-I phase
(NB).9–13 The existence of nematic–nematic phase transitions in transition in liquid crystals attracted considerable attention
such materials has acquired a renewed interest.4,14–17
over many years because of the existing puzzle about its
One of the most exciting examples of the use of liquid crystal nature.36–38 Although the phase transition is widely considered
dimers having an odd-membered spacer18 is in flexoelectric- to be very weakly first order, some experimental data for a few
based electro-optic displays first demonstrated by Patel and liquid crystals seem to provide contradictory results and even
Lee.19 The nematic phases formed by dimers offer several advant- raise doubts about its first order character. It seems that this
ages over the use of more conventional materials, the most apparent puzzle is due to three main factors:37 fluctuations of
striking of which is the magnitude of the electro-optic response.20 the chosen order parameter, the biaxial shape of mesogenic
This is determined by the flexoelastic ratio, e/K, where e is the molecules and their flexibility. The first factor appears to be
mean flexoelectric coefficient (e1 + e3)/2 and K is the mean elastic significant in non-linear studies associated with sufficiently
constant (K1 + K3)/2,21 where K1 and K3 are the so-called splay and strong applied external fields, or for strongly polar mesogens
bend elastic constants. A large value of e/K for the odd dimers under weak external perturbations. The other two factors are
is predicted to result not only from the expected large value of relevant in liquid crystal dimers. Unfortunately, experimental
e3 but mainly from the small value of K3.22 This prediction data related to the N-to-I phase transition in such materials
has, subsequently, been confirmed by measurements of the with the required precision are very rare.12,13,15
elastic constants K1 and K3 for the odd liquid crystal dimer,
The structure of the paper is as follows. In Section 2 we
100-(20,4-difluorobiphenyl-40-yloxy)-900-(4-cyanobiphenyl-40-yloxy) describe the experimental details of our measurements. In
nonane (hereafter referred to by the acronym FFO9OCB).23,24 It Section 3, we present and discuss our results concerning the
has also been shown theoretically that large values of the overall thermal behaviour on the basis of the heat capacity
flexoelastic ratio (e/K) stabilize blue phases over large tempera- data and microscopic observations, and dielectric measure-
ture ranges in chiral doped liquid crystal dimers belonging to ments on the isotropic phase and mesophases. Particularly in
the 100-(20,4-difluorobiphenyl-40-yloxy)-900-(4-cyanobiphenyl-40-yloxy) Section 3.3, we show evidence from optical microscopy and
alkane series (FFOnOCB).25
measurements of dielectric and elastic properties for the
Liquid crystal dimers exhibit many energetically favoured formation of a twist-bend nematic phase in the ether-linked
molecular shapes (conformers), the populations of which depend non-symmetric dimer FFO9OCB. Finally in Section 3.4, very
on the parity of the flexible chain, and the population-distribution accurate heat capacity as well as static dielectric data through
of conformers is temperature-dependent. In dimers with polar the N-to-I phase transition is analysed to give information on
terminal groups this distribution can be partially characterized the nature of the phase transition. Our concluding remarks
through the dielectric permittivity. Some experimental studies are summarized in Section 4.
devoted to the dielectric properties of liquid crystal dimers have
already been published.4,5,12,26–34 Such measurements, besides
providing information on the temperature dependence of the
2 Experimental details
2.1 Materials
conformational distribution, have prompted the development of a
new theory35 for the dielectric relaxation of mesogenic dimers in a
nematic phase. It is evident that for the theory to be tested and
improved, additional experimental dielectric data for different
architectures of liquid crystal dimers are required.
The schematic molecular structure of FFO9OCB is
The dielectric behaviour of the FFO9OCB dimer is one of
the main aspects on which the present paper will be focused.
In order to interpret such dielectric results, the theory35 will
be adapted to the example here, which was not considered
previously.
It consists of two mesogenic groups having almost the
same shape and size but different chemical structures (named
Additionally, the mesomorphic properties of FFO9OCB are A and B in the schematic) attached by an ether-linked spacer
presented. Previously, only one enantiotropic nematic mesophase of 9 carbons (O[CH2]9O). The terminal group B has two
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identical dipole moments of about 1.5 D associated with the washed with DCM (3 ꢁ 50 ml). The organic extracts were
C–F bond (indicated in the schematic by two thin arrows) combined and dried over anhydrous magnesium sulphate. This
leading to a longitudinal component of about 2.25 D and a was then removed by filtration and the filtrate solvent was
transverse component of about 1.3 D. The terminal group A removed in vacuo leaving a white crude product which was
has a larger dipole moment (B4 D) along its long axis purified by column chromatography (silica gel, 40 mm ꢁ
associated with the nitrile group (indicated in the schematic 70 mm; 50–100% DCM/40–60 petroleum) to yield FFO9OCB
by a thick arrow).
as a white microcrystalline solid, in a typical yield of 85%.
The structure of FFO9OCB and its purity were determined
The non-symmetric liquid crystal dimer, FFO9OCB, was
synthesised using the methodology previously used to prepare with a range of analytical techniques. These involved NMR
1
analogous dimers.39 The reaction comprises just two steps both spectroscopy, both H and 13C. The product gave clean spectra
of which involve alkylation of a phenol. The first is the prepara- in the sense that only peaks other than those from CHCl3 and
tion of 1-(4-cyanobiphenyloxy)-9-bromononane (CBO9Br). This DOH were from the target dimer. The assignment of the
involves a Williamson alkylation of 4-cyano-40-hydroxybiphenyl spectral lines, listed subsequently, was made on the basis of
(CBOH) with 1,9-dibromononane (Br9Br) but differs from the literature data for analogous compounds. They confirmed the
standard conditions in that Br9Br is in a tenfold excess. This molecular structure and the purity of the sample. The IR bands
allows the preparation of CBO9Br without its contamination given are consistent with those expected for this non-symmetric
by the symmetric dimer CBO9OCB. The second step is the dimer. It did not prove possible to use electrospray (ES) to
alkylation of 3,40-difluoro-4-hydroxybiphenyl (FFOH) with CBO9Br obtain the mass spectrum of FFO9OCB because there are no
but now in stoichiometric amounts.
protons of sufficient acidity or basicity. Consequently the
The details of the synthesis of CBO9Br are as follows. To a spectrum contained peaks other than those from the parent
stirred solution of CBOH (21 mmol, 1 eq.) in freshly distilled ion which masked the purity of the sample. The use of the
acetone (40 ml) solid potassium carbonate (37 mmol, 1.8 eq.) harder technique of electron impact (EI) resulted in more
was added in a single portion. The stirred mixture was heated complex fragmentation patterns. However, the isotope pattern
to reflux for 1 h under nitrogen and subsequently allowed to of bromine should be clear and so would allow the presence of
cool to room temperature before Br9Br (204 mmol, 10 eq.) was CBO9Br which is a likely impurity to be detected; it was not.
added in a single portion. The mixture was then heated at Thin layer chromatography based on Merck Kieselgel silica gel
reflux for 18 h, cooled, and was subsequently filtered to remove 60 F254 using DCM as the mobile phase gave a retardation
the inorganic salts; these were later washed with DCM. The factor of 0.66. More importantly there was just a single spot
combined filtrate and washings were concentrated in vacuo to consistent with an estimated sample purity of 499%. An
give a crude yellow oil. This was purified by column chromato- additional and complementary indication of the purity of the
graphy (silica gel, 40 mm ꢁ 100 mm; 10–40% DCM/40–60 liquid crystal dimer FFO9OCB was provided by the nematic–
petroleum), to give a white powder which was crystallised from isotropic transition. First, the sharpness of the transition
ethanol to afford CBO9Br with a typical yield of 87%. This found, as we shall see in Section 3.4.1, suggests that the dimer
sample of CBO9Br was then used in the second stage for the is pure. Second, comparison of the N–I transition temperature
preparation of FFO9OCB.
with values reported in the literature should provide another
To a stirred solution of FFOH (1.1 mmol, 1.1 eq.) in dry indication of purity. In fact there are four values of TNI for
butanone (40 ml) potassium carbonate (2.2 mmol, 2.2 eq.) was FFO9OCB reported in the literature by other workers;20,23,24,40
added in one portion and the suspension was heated to reflux surprisingly these vary with time from 388 K,40 to 385 K20
for about 20 min under nitrogen. The mixture was allowed to through 382 K23 to 381 K.24 No comment is made on this,
cool prior to the addition of CBO9Br (1 mmol, 1 eq.) in one although the uncertainty in the nematic to isotropic transition
portion and a catalytic quantity of sodium iodide (80 mg). The temperature seems to be of the order of ꢂ1 K. The agree-
reaction mixture was then heated back to reflux for three days, ment of our measured transition temperature of 385.5 K with
cooled and the solvent was removed in vacuo. The off-white these seems to be reasonable, especially given the differences
solid was partitioned between DCM (50 ml) and water (50 ml). in the methods used to measure the transition temperature
The organic layer was separated and the aqueous layer was (see Table 1).
Table 1 Transition temperatures (TCrN, TN
and TNI) and associated latent heats (DHCrN and DHNI)
N
TB
TCrN (K)
DHCrN (kJ molꢀ1
)
Tg (K)
TN
(K)
TNI (K)
DHNI (kJ molꢀ1
)
Ref.
TBN
323.2a
—
—
—
—
262.2
—
—
—
385.2a
382.2a
381.2b
385.5 ꢂ 0.5
20
23
24
333.2a
—
—
315.4b
17.7b,c
1.8b,c
345.6 ꢂ 0.5e
31.4 ꢂ 0.2e
B323d
0.44 ꢂ 0.05
This work
a
b
Data from optical measurements at 1 K minꢀ1
.
Measurements were performed using a Mettler-Toledo DSC823 from DSC traces at 5 K minꢀ1
.
c
From Table 1 of ref. 24 it is said that enthalpies are given in mJ gꢀ1. We believe that this is not possible and it has been interpreted as given in
J gꢀ1
.
From heat capacity measurements under a cooling regime at 10 K minꢀ1
.
Data corresponding to the crystal phase obtained by slow cooling.
d
e
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The details are as follows:
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Measurements of the complex dielectric permittivity defined
1H NMR (300 MHz, CDCl3): dH/ppm 7.61 (2H, d, J = 8.6 Hz, as e*( f ) = e0( f ) ꢀ ie00( f ) were performed over the range 103–
C4H, C6H), 7.55 (2H, d, J = 8.6 Hz, C3H, C7H), 7.44 (2H, d, J = 1.8 ꢁ 109 Hz using two impedance analysers: the HP4192A and
9.0 Hz, C9H, C13H), 7.33–7.41 (2H, m, C40H, C42H), 7.21 (1H, t, 4291A. The cell consists of two gold-plated brass electrodes
J = 9.2 Hz, C49H), 7.02 (2H, t, J = 8.8 Hz, C39H, C43H), 6.91 (2H, d, (diameter 5 mm) separated by 50 mm thick silica spacers.
J = 8.8 Hz, C10H, C12H), 6.67 (1H, dd, (J = 8.6 Hz, 2.6 Hz), C48H2), A modified HP16091A coaxial test fixture was used as the sample
6.62 (1H, dd, (J = 12.3 Hz, 2.6 Hz), C46H2), 3.93 (2H, t, 6.4 Hz, holder. It was held in a cryostat from Novocontrol and both temper-
O-C14H2), 3.90 (2H, t, 6.4 Hz, O-C22H2), 1.63–1.82 (4H, m, C15H2, ature and dielectric measurements were computer-controlled.
C
21H2), 1.24–1.50 (10H, m, C16H2, C17H2, C18H2, C19H2, C20H2). Additional details of the experimental technique can be found
13C NMR (75 MHz, CDCl3): dC/ppm 163.7 (q, C45-F(Ar)), 161.9 elsewhere.12,29,33,34,37
(q, C38-F(Ar)), 159.8 (q, C11(Ar)), 158.5 (q, C47(Ar)), 145.3
Dielectric measurements were performed on heating and
(q, C5(Ar)), 132.6 (t, C3(Ar), C7(Ar)), 131.3 (q, C8(Ar)), 130.8 on cooling with different temperature steps being stabilized
(q, C44(Ar)), 130.4 (t, C40/C42(Ar)), 128.3 (t, C4(Ar), C6(Ar)), 127.1 to ꢂ20 mK.
(t, C9(Ar), C13(Ar)), 119.1 (q, C41(Ar)), 115.4 (t, C46/C48(Ar)), 115.2
Optical textures were studied with an Olympus polarising
(t, C46/C48(Ar)), 115.1 (t, C10(Ar), C12(Ar)), 110.9 (t, C49(Ar)), 110.7 microscope equipped with a Linkam THMSG-600 hot stage and
(q, C2(Ar)), 102.7 (t, C43/C39(Ar)), 102.4 (t, C43/C39(Ar)), 68.4 a Linkam TMS-94 temperature controller.
(s, C14(OCH2)), 29.4 (s, C15–21(CH2)), 29.3 (s, C15–21(CH2)), 29.2
(s, C15–21(CH2)), 29.1 (s, C15–21(CH2)), 29.0 (s, C15–21(CH2)).
Capacitance measurements to determine the splay K1 and
bend K3 elastic constants were carried out using 8 mm anti-
IR (solid):
n
max/cmꢀ1 2933(m) (C-H2), 2852(m) (C-H2), parallel planar aligned cells. The method consists of inducing
2223(m) (CRN), 1600(s) (Ar), 1519(s) (Ar), 1492(s) (Ar).
the planar to homeotropic Freedericksz transition in the sample
EIMS: m/z 525 ([M]+, 54%), 330 ([C23H24NO]+, 5%), 206 by applying an AC signal at a frequency of 5 kHz from an Agilent
([C15H11O]+, 100%), 195 ([C13H9NO]+, 72%), 83 ([C6H11]+, Precision LRC meter E4890A. The capacitance of the sample was
48%), 69 ([C5H9]+, 28%).
monitored as a function of the applied voltage which is varied
from 0.1 Vrms to 16 Vrms, with a delay time of 30 s between the
application of the AC signal and the acquisition of the capacitance
value. Ultimately, values of the splay and bend elastic constants
2.2 Experimental techniques
Heat capacity data at atmospheric pressure were obtained were extracted from the fitting of the entire voltage dependence of
by means of a commercial differential scanning calorimeter the capacitance to the theory.42
(DSC-Q2000) from TA-Instruments working in the modulated
mode (MDSC). It is important to realize that, like an alternating
current (ac) calorimeter, the MDSC technique, besides provid-
ing heat capacity data, simultaneously gives phase shift data (f)
that allow the determination of the two-phase coexistence
3 Results and discussion
3.1 Thermal behaviour
region for weakly first-order phase transitions. In our work, It was reported by Morris et al.20 that on cooling from the isotropic
the experimental conditions were adjusted in such a way that phase FFO9OCB exhibits a nematic mesophase followed by a solid
the imaginary part of the complex heat capacity data vanished. crystalline state (Cr). Identification of such a phase sequence was
Similarly, by means of a special calibration procedure in which made by means of their optical textures, and transition tempera-
very precise latent heat data measured for other homologues tures obtained on cooling are listed in Table 1.
through adiabatic calorimetry are considered, the MDSC
Our optical textures partially confirm the phase sequence
technique is also suitable for quantitative measurements of found by Morris et al.,20 although they reveal a more complex
latent heats of first order transitions, even if they are weak. A phase behaviour that depends strongly on the cooling rate.
more detailed description of the MDSC technique can be found Fig. 1 shows optical textures seen at different temperatures on
elsewhere.12,13,41
cooling the sample from the N-mesophase (light green texture)
The MDSC measurements were made using two different at 10 K minꢀ1 (top sequence) and at 15 K minꢀ1 (bottom sequence),
procedures. The first one was a standard study of the overall in cells (8 mm thick) with planar alignment. For the former, at about
thermal behaviour of the sample, consisting of heating runs at 315–310 K, another mesophase appears (striped texture on a
1 K minꢀ1 from room temperature up to the isotropic phase and photograph taken at about 310 K) whose identity at this stage is
cooling runs at several cooling rates to observe the glassy behaviour unknown. Subsequent experiments, to be described later, suggest
if possible. The second procedure, designed to study the nature of that this phase is the twist-bend nematic phase (the symbol NTB
the N-to-I phase transition, consisted of heating and cooling runs in will be used, subsequently, to denote this new phase), for which
a temperature interval of about 5 K around the transition at a rate of further evidence is provided by miscibility and other studies.
0.01 K minꢀ1. For both procedures, the modulation parameters At present, there is no particular texture that is identified as
(temperature amplitude and oscillation period) were ꢂ0.5 K and an unequivocal signature of the twist-bend nematic phase.
60 s in the standard and ꢂ0.07 K and 23 s in the other procedure. However a number of investigations with a variety of materials
The sample masses (chosen between 2 and 3 mg) were selected to have revealed that thin film samples of the twist-bend nematic
ensure a uniform thin layer within the aluminium pans.
phase in rubbed (planar) cells exhibit a characteristic ‘‘rope-like
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1 K minꢀ1 (red symbols) and after faster cooling at 30 K minꢀ1
(black open symbols). In the former case, the sample crystal-
lizes on cooling, at about 335 K, and the crystal phase [Cr] is
observed at low temperatures. In the second case (cooling rate
of 30 K minꢀ1), crystallization is prevented and ultimately the
mesophase vitrifies. On heating runs, the top-left inset shows
the characteristic heat capacity jump of a glass transition for
samples cooled at different rates. Cases denoted by (a) and (b)
in Fig. 2 provide comparable heat capacity jumps, proving that
a cooling rate of about 15 K minꢀ1 is fast enough to obtain the
glassy state. Taking into account the optical information sum-
marized in Fig. 1, the glassy state should correspond to this
new NTB mesophase [(NTB)gl]. On cooling, the phase transition
N-to-NTB is not observed by heat capacity experiments, neither
at rates of 30 K minꢀ1 nor 15 K minꢀ1. The bottom-right inset
of Fig. 2 shows the heat capacity measured at a cooling rate of
10 K minꢀ1 in which a small peak (assigned to the N-to-NTB phase
transition) is observed at about 323 K. It should be stressed that at
lower temperatures the sample crystallizes making it impossible to
follow the heat capacity of the NTB mesophase down to the glass
transition. Even so, subsequent heating of the sample from 250 K
at 1 K minꢀ1 reveals the characteristic heat capacity jump assigned
to a glass transition (the case denoted by (c) in the top-left inset of
Fig. 2), but smaller than the situations denoted by (a) and (b). This
apparently curious fact is understandable since the sample tends
to crystallize partially if the cooling rate is not sufficiently high
according to the top sequence of Fig. 1. So, the sample is found in
an unstable situation in which one part is becoming crystalline
and the remainder is becoming glassy. Fig. 2 clearly shows how the
Fig. 1 Optical textures of FFO9OCB obtained from 8 mm thick cells with
uniform planar alignment at some selected temperatures.
texture’’. The compound FFO9OCB which is the subject of this
paper exhibits this rope texture (see Fig. 9), and a more detailed
discussion of the texture is given in Section 3.3.1 of this paper.
This texture seemed to persist at low temperatures mixed with
what is usually found for a crystalline state. However, when the
cooling rate is high enough (bottom sequence), only textures
compatible with the NTB-mesophase are found. Irrespective of
the cooling rate of either 10 or 15 K minꢀ1, a subsequent heating
from 244 K at 1 K minꢀ1 (middle sequence) causes the sample to
crystallize between 276 and 288 K (photo recorded at 288 K).
Fig. 2 shows the heat capacity as a function of temperature
over a wide temperature range for a sample heated at 1 K minꢀ1
coming from two initial states: after cooling from the I-phase at
sample in the supercooled NTB mesophase [(NTB spc] crystallizes
)
irreversibly on heating at about 280 K (black symbols), a fact
already observed from optical measurements (see the middle
sequence of Fig. 1).
In Fig. 2, the N-to-I phase transition is observed to be identical
in both experiments (red and black symbols), but this is not the
case for the Cr-to-N phase transition. It can be observed that such a
phase transition is found to be represented by a single heat
capacity peak (at about 345 K) for (a): sample cooled slowly at
1 K minꢀ1 (red symbols). However, the sample heated from the
NTB glassy state (black symbols) which crystallizes on heating
exhibits two heat capacity peaks associated with transformation
into the nematic mesophase, one at about 345 K and the other at
about 357 K. It seems that the crystal phase obtained by slow
cooling [Cr] and that from the supercooled NTB mesophase [Cr]*
are different. In fact, we believe that [Cr]* is really a mixture of the
crystal phase obtained by slow cooling [Cr] and another metastable
crystal phase. The temperatures associated with the glass transition
and both Cr-to-N and N-to-I phase transitions, along with the values
taken from the literature, are listed in Table 1.
In general terms, the total enthalpy change associated with
Fig. 2 Heat capacity data as a function of temperature for a sample of
FFO9OCB in heating mode at 1 K minꢀ1 which has been previously cooled
from the I-phase at 30 K minꢀ1 (black symbols) and at 1 K minꢀ1 (red symbols).
The top-left inset shows in a zoom window the characteristic heat capacity
jump at the glass transition recorded in heating mode at 1 K minꢀ1 for samples
cooled at different rates ((a) 30 K minꢀ1; (b) 15 K minꢀ1; (c) 10 K minꢀ1). The
bottom-right inset shows evidence for the N–NTB phase transition through
any transition (DHTOT) can be written as
Ð
DHTOT = DH + DCp dT
(1)
where the second term on the right-hand side of eqn (1) is the
pretransitional fluctuation contribution (DCp being the difference
Cp–Cp,background due to the change of orientational order intrinsic
the heat capacity data on cooling the sample at 10 K minꢀ1
.
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to this transition) and the latent heat is DH which vanishes for
second-order transitions. In strongly first-order phase transitions,
the second term on the right-hand side of eqn (1) can be neglected
in comparison with the latent heat and the total enthalpy change
is identified with the latent heat associated with the phase
transition. The resulting latent heat for the Cr-to-N phase transi-
tion (we only consider the crystal phase formed by slow cooling) is
also listed in Table 1 together with the value taken from the
literature. It should be stressed that both TCrN and DHCrN are
clearly different from those obtained by us. Even the transition
temperatures referred to in studies published by some of the
same authors change substantially, as can be seen in Table 1.
3.2 Dielectric behaviour
3.2.1 Theoretical background. The dielectric data for con-
ventional liquid crystal monomers34,37,43,44 have been success-
fully interpreted using the theories of Maier–Meier45 for the
static permittivity and Nordio–Rigatti–Segre46 for the molecular
Fig. 3 Schematic representation of the four stable states of non-symmetric
dimers, according to Stocchero et al.’s35 theoretical model.
dynamics (both approaches assume that the constituent mole- angles (bA, bB) made by the mesogenic groups (A, B) of the dimer
cules are rigid). However, to interpret the dielectric properties with the director for different degrees of order. It is found that
of symmetric and non-symmetric liquid crystal dimers29 models the potential energy surface has four minima corresponding to
accounting for molecular flexibility are needed. To achieve this, parallel or anti-parallel orientations of the groups A, B with
Stocchero et al.35 proposed a quantitative model with which to respect to the director, and the dimer is assumed to be in one of
understand the observed dielectric properties of nematogenic the four stable states (see Fig. 3). It must be emphasized that the
liquid crystal dimers.
model of dielectric relaxation applied here makes no assumption
Calculations show how for the liquid crystal dimer, which is about the shape of the relaxing molecule, which itself is per-
considered as a mixture of trans and cis conformers, the trans- mitted to explore all possible conformations. Thus the cis and
conformer population increases with order and, in addition, trans states shown in Fig. 3 schematically represent the orienta-
the average molecular shape becomes more elongated. As a tions of the mesogenic groups undergoing rotational relaxation,
result, for symmetric dimers the mean square dipole moment and the dipoles attached to the mesogenic groups are the
decreases with order as does the value of the static permittivity, components responsible for end-over-end or flip-flop relaxation.
observed experimentally.4,29,33,34 For a non-symmetric dimer The actual geometries corresponding to these energy minima are
where only one of the mesogenic units contains a longitudinal obtained by detailed calculation over the full conformation space
dipole moment, the change of the conformation of the mole- accessible by the flexible relaxing molecules (see ref. 35 for
cule has no impact on the mean square dipole moment, and details). This equilibrium model considers that only individual
then the static permittivity is predicted to behave as for liquid end-over-end rotations of each unit are allowed. The simulta-
crystal monomers with positive dielectric anisotropy, as observed neous rotations of the two rigid units (i.e. a 2 d and b 2 c in
experimentally.12,13 For non-symmetric dimers where the two pro- Fig. 3) are excluded because they are associated with the passage
mesogenic units contain different longitudinal dipole moments, over a potential maximum with too great an activation energy to
an intermediate behaviour is expected. The change in the con- produce a relevant transition rate. The relative rates for flipping
formational distribution of the molecules with order is expected of the different rigid units (kTn-C and knC-T, n being A or B) are
to decrease the mean square dipole moment to a certain extent determined by their rotational diffusion coefficients and the
and hence the longitudinal component (the component parallel nematic potential experienced by the terminal groups. A time-
to the director) of the static permittivity. This is the case con- scale separation is assumed between the slow end-over-end
sidered in the present paper and, as far as we know, the first one rotations of the terminal groups and other faster processes, at
investigated with such characteristics for which there are still no higher frequencies. The latter are not included in the kinetic
experimental results published.
model, for example rotations around the long molecular axis or
The equilibrium properties of some odd and even symmetric the precession around the director.
dimers have been calculated using the rotational isomeric state
Calculations according to the model for symmetric dimers
(RIS) model and a model which allows for a continuous torsional predict a single relaxation time for the parallel component of
potential about the carbon–carbon bonds of the flexible spacer the dielectric permittivity with an intensity that diminishes
(see ref. 35 for details). It turns out that for flexible dimers the with decreasing temperature (or increasing orientational order)
RIS model is not satisfactory and the full torsional potential in quite good agreement with experimental determinations.29,33,34
must be used. Using the latter model, the effective potential of The results for non-symmetric dimers depend on the shape, size
mean torque for the dimer, i.e. the energy of a flexible dimer with and dipole moments of the different rigid units. Some of these
respect to the director, can be calculated as a function of the examples have already been developed in the original paper
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by Stocchero et al.35 while others must be developed ad hoc such only one mode in the isotropic phase which is believed to
as the case treated in the current study. correspond to the concerted rotation of the whole dimer, and
3.2.2 Interpretation of the dielectric relaxation data. we denote this as the m1-mode.
Dielectric results for FFO9OCB have been obtained for both
The parallel component of the permittivity in the nematic
parallel and perpendicular alignment of the director in the mesophase (Fig. 4A) shows three relaxations, one of them at
nematic and isotropic phases. In metallic cells the director high frequencies and the other two at lower frequencies whose
spontaneously aligns parallel to the surface allowing us to amplitudes seem to be correlated in a similar way to other non-
obtain the perpendicular component of the permittivity (e>). symmetric dimers.12,29 As cited previously, the latter case was
The fact that the material has a positive dielectric anisotropy considered explicitly by Stocchero et al.,35 but not the case of
(De = eJ ꢀ e>),20,23 allows the parallel component of the the dimer FFO9OCB with two different terminal units, A and B,
permittivity (eJ) to be measured by applying a dc bias voltage exhibiting different longitudinal dipole moments. In the fol-
(25 V equivalent to an electric field of 0.5 mV mꢀ1). Saturation lowing, such a case will be developed according to the model.
of the parallel alignment of the director in the nematic phase
has been confirmed by measuring the capacitance as a function moment correlation function (GJ(t)) which is deduced through
of voltage. the calculation of the temporal evolution of the population of
The starting point consists in determining the dipole
Fig. 4A and B show the imaginary part of the parallel and each of the four stable states (taken as a four-component vector
perpendicular dielectric permittivities, respectively, as a func- P(t)) of the dimer (see Fig. 3) as
X
tion of frequency and temperature in the isotropic phase and in
the nematic mesophase. The dielectric relaxation results show
G ðtÞ ¼
k
PaðtÞhm i ¼ PðtÞ ꢃ v
(2)
k
a
a
The four-component vector v represents the equilibrium
average of the longitudinal dipole moment of the dimer in
each of the four stable states. The exact analytical solution of
P(t) for non-symmetric dimers is too complicated to allow a
direct physical interpretation. Alternatively, a simplified strat-
egy is suggested in which well-separated time-scales are
assumed for the transition processes of both rigid units A
and B. A short time scale of the order of 1/kA, where kA
=
12(kTA-C + kCA-T), is specified for the independent equilibration
of the two pairs of states (a 2 c) and (b 2 d) of the rigid unit
A. For this time scale, the rigid unit B does not experience any
transition. At a time t 4 1/kA, the rigid unit B is active with an
effective time of 1/kB, where kB = 2(PeCqkCB-T) = 2(PTeqkBT-C) for
the independent equilibration of the two pairs of states (a 2 b)
and (c 2 d) (see Fig. 3). The simplified form for the long-
itudinal dipole moment correlation function (GJ(t)) is:35
GJ(t) = GJ(t*)eꢀ2k t + [GJ(0) ꢀ GJ(t*)]eꢀ2k t
(3)
B
A
where t* is a suitable time between the fast and the slow range
of time scales (1/kA o t* o 1/kCB-T). Thus, considering for
simplicity that in our case hmJiB E 1/2hmJiA and combining the
average of each dipole moment the following four-component
vector v is obtained:
ꢀ
ꢀ
ꢀ
ꢀ
1=2
3=2
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
v ¼ hm i
(4)
(5)
k
A
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ3=2
ꢀ1=2
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
leading to
GJ(t) = 4hmJiA2PeTqPeCqeꢀ2k t + hmJiA2(PTeq ꢀ 3PeTq)2eꢀ2k t
A
1
4
B
Fig. 4 Three-dimensional plot of dielectric loss versus temperature and
the logarithm of the frequency for FFO9OCB in (A) parallel and (B)
perpendicular alignments.
The correlation function given by eqn (5) is associated with
two relaxation processes in the dielectric spectra of the parallel
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component of the permittivity, due to each rigid unit of the
The perpendicular component (e>) also decreases as tem-
dimer. The relaxation at lower frequencies is a consequence perature decreases, saturating at low enough temperatures, as
of the flip-flop motion of the B-unit (denoted hereafter as the expected45 for rod-shaped mesogens.
m1,L-mode). The other relaxation, at higher frequencies, involves
3.2.4 Dynamic dielectric measurements and analysis.
a flip-flop of the A-unit (denoted hereafter as the m1,H-mode). Fig. 6 is representative of the dielectric response of the dimer
The amplitudes of the modes, m1,L and m1,H, depend on FFO9OCB for the real and imaginary parts of the permittivity in
1/4(PTeq ꢀ 3PCeq)2 and 4PeCqPeTq, respectively. The cis-to-trans inter- the parallel and perpendicular alignments as a function of
change as the temperature decreases involves a concerted frequency at two characteristic temperatures, in the I phase
change in the amplitude of the modes: that of the m1,H decreases (388 K) and in the N mesophase (353 K). The data analysis of
while the other increases.
the frequency dependence of the permittivity when the different
Let us recall Fig. 4A and the relaxation at higher frequencies relaxation modes appear partially superimposed (as observed in
with a much lower amplitude than the other two relaxations Fig. 6B or C) is made using the empirical function
described by eqn (5). Such a relaxation, denoted hereafter as the
m
X
Dek
sdc
oe0
2,J-mode, is not dealt with in the model of Stocchero et al.,35
eðoÞ ¼
þ e1 ꢀ i
(6)
bk
ak
½1 þ ðiotkÞ ꢄ
k
but is attributed to rotation around the molecular long axis.
The perpendicular component of the permittivity in the
nematic mesophase (Fig. 4B) shows, at first glance, a prominent
relaxation process, denoted as m2,>, which is believed to be due to
the superposition of the precessional motions of the semi-rigid
units and the rotation of the dimer around its long molecular axis.
3.2.3 The static dielectric permittivity. Measurements of
the static dielectric permittivities (limiting low frequency per-
mittivity) of the non-symmetric dimer FFO9OCB are shown in
Fig. 5 as a function of temperature. This figure demonstrates
that both components of the static permittivity (e> and eJ) and
the mean permittivity (emean = 1/3[eJ + 2e>]) change with
temperature as expected. The parallel component (eJ) decreases
as temperature decreases, as predicted by the equilibrium
calculations of Stocchero et al.35 referred to earlier. It is
noteworthy that such a decrease is less drastic than that
reported for symmetric dimers.4 According to the simplified
kinetic model developed in the previous section for the non-
symmetric FFO9OCB, the contribution of the low frequency
where the summation is extended over all relaxation modes, and
each is fitted according to the Havriliak–Negami (H–N) function.
In eqn (6), Dek is the dielectric strength of each relaxation mode,
tk is the relaxation time which is related to the frequency of
ꢁ
ꢂ
9
mode to eJ is proportional to
ꢀ 2PeTq while in the case of
4
symmetric dimers it is proportional to 4(1 ꢀ PeTq).35
Fig. 6 Frequency dependence of the dielectric permittivity of FFO9OCB
in the isotropic phase (T = 388 K) (A) and in the nematic phase (T = 353 K) in
both parallel (B) and perpendicular (C) director alignments. Black solid and
dashed lines are fittings according to eqn (6). Symbol-lines represent
deconvolution into elementary modes. For simplicity, the direct current
conductivity contribution (sdc) is not drawn, but is considered in the fitting
procedure.
Fig. 5 Static dielectric permittivity behaviour in the I and N phases of
FFO9OCB.
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Table 2 Fitting parameters (ak and bk) according to eqn (6) for the
different relaxation modes measured over the temperature range 340–
400 K
Modes
ak
bk
Phase
m1
0.8
1
1
0.8
0.7
0.8
1
1
1
1
I
m1,JL
m1,JH
m2,J
N
N
N
N
m2,>
maximum dielectric loss, ak and bk are the parameters which
describe the shape (symmetry and width) of the relaxation
spectra (ak = bk = 1 corresponds to Debye relaxation) and sdc is
the dc conductivity.
The dielectric results in Fig. 6A (I phase) were fitted, accord-
ing to eqn (6), to a single mode (m1-mode). The shape para-
meters am1 and bm1 were found to be temperature independent
Fig. 8 Arrhenius plot of the relaxation frequencies (fk) of the different
contributions to the dielectric relaxation for FFO9OCB.
over the temperature range of the isotropic phase analysed and director alignments. For the parallel alignment, the dielectric
are listed in Table 2.
strengths Dem1,LJ and Dem1,HJ are related, through eqn (5), with
The dielectric results shown in Fig. 6B correspond to the the change of the conformational distribution, being propor-
parallel component of the permittivity in the N mesophase at tional to 1/4(PeTq ꢀ 3PCeq 2
)
and 4PeCqPeTq, respectively. Thus, a
353 K. As already indicated in Fig. 4A, the results were fitted, decrease in temperature causes Dem1,LJ to increase, that is,
according to eqn (6), to three relaxation modes (m1,LJ, m1,HJ, m2J) PeTq increases (note that PeTq + PeCq = 1). At the same time, Dem1,HJ
and the fitted shape parameters are listed in Table 2.
decreases as the temperature decreases. The dielectric strength
Fig. 6C shows the dielectric results for the perpendicular of the m2J-mode (Dem2J) decreases on entering the N-mesophase
component of the permittivity in the N mesophase, also at 353 K. stabilizing at a nearly constant value at lower temperatures as
The fittings through eqn (6) require two relaxation modes, one at a previously reported for other dimers in which the same mode
frequency similar to that found for parallel alignment (m1,HJ, see has been identified.12,33,34 For perpendicular alignment of the
Fig. 6B) but with only a few per cent of the strength measured for director, the most prominent contribution (Dem2>) evolves with
the latter which is not perceived by the eye in Fig. 4B and 6C. We temperature, to a certain extent, similar to Dem2J, as expected.
attribute this mode to an imperfect perpendicular alignment of the
Fig. 8 shows, in an Arrhenius plot, the temperature depen-
director (for consistency we denote this mode as m1>) and it will dence of the characteristic relaxation frequencies associated
not be taken into account for further analyses. The other mode at with each mode for both N and I phases. Activation energies
high frequencies, the most prominent in the perpendicular align- for the m1,LJ (Ema 1,LJ) and m1,HJ (Eam1,HJ) relaxation modes are
ment, is denoted as the m2>-mode. The corresponding shape 90 kJ molꢀ1 and 65 kJ molꢀ1, respectively. The ratio (Eam1,HJ/Ema 1,LJ
)
parameters are listed in Table 2.
is about 0.7, a value certainly somewhat lower than that found for
Fig. 7 shows the temperature dependence of the dielectric other non-symmetric dimers (of about 0.8) with only one long-
strength for all the aforementioned relaxation modes in both itudinal dipole moment located in the smaller semi-rigid
unit.12,29,47 Regarding the so-called m2,J or m2,> relaxation modes,
the corresponding activation energies (Ema 2J or Eam2>) are close
to each other, with a value of about 35 kJ molꢀ1, a value similar
to that found for the same modes in other non-symmetric
dimers.12,47
3.2.5 Conformational distribution. The temperature
dependence of the conformational distribution of the mole-
cules in the nematic mesophase for the FFO9OCB dimer can be
estimated by applying the model of Stocchero et al.35 According
to eqn (5), the ratio of dielectric strengths for both m1,LJ and
m
1,HJ modes can be expressed as a function of the equilibrium
population of trans conformers (PeTq) as
ꢃ
ꢄ
2
Dem1;Lk
Dem1;Hk
4PeTq ꢀ 3
ꢃ
ꢄ
¼
(7)
16PeTq 1 ꢀ PeTq
From eqn (7), PeTq is obtained as a function of temperature
with values ranging from about 0.94 (94% of trans-conformers)
Fig. 7 Dielectric strength data as a function of temperature for the
different elementary contributions for FFO9OCB.
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at the N-to-I phase transition to 0.98 (98% of trans-conformers)
at temperatures 45 K lower in the nematic phase. It should be
stressed that these values have been calculated following some
simplifying assumptions detailed in Section 3.2.2. While it is
true that eqn (5) provides valuable assistance in the interpreta-
tion of our dielectric measurements, quantitative calculations
such as the conformational distribution of the molecules should be
taken with caution. By way of illustration, for the non-symmetric
dimer 100-(4-cyanobiphenyl-40-yloxy)-900-(4-decylaniline-benzylidene-
40-oxy) nonane (with the same ether-linked spacer as FFO9OCB),
the calculated PeTq ranges from 0.74 at TNI to 0.84 at 45 K
29
below TNI
.
3.3 The nature of the monotropic mesophase
It has been reported that certain liquid crystal dimers exhibit
the recently discovered twist-bend nematic phase (NTB), predicted by
Dozov.3 The first compounds to exhibit this phase were methylene-
linked odd-membered dimers,4,6,7,48–50 but recently an ether-linked
twist-bend phase has been reported.51 Our observations on
FFO9OCB, the subject of this paper, strongly suggest that it
forms a monotropic twist-bend nematic phase.
A virtual twist-bend nematic–nematic transition has been
observed for a mixture of five ether-linked odd liquid crystal
dimers; this mixture was denoted by the letters KA.52 The
Fig. 9 Phase diagram for FFO9OCB + CB7CB mixtures. Full symbols
(circles, squares, diamonds and stars) correspond to heat capacity mea-
surements recorded on heating at 1 K minꢀ1. The open diamond is related
to the monotropic NTB–N-phase transition of pure FFO9OCB from heat
capacity measurements recorded on cooling at 10 K minꢀ1 (see Table 1).
Note that the full square for pure FFO9OCB corresponds to the Cr–N
phase transition (see Table 1).
mixture was designed, in part, to produce a system of dimers order of 16 mm (2d, where d is the thickness of the cell)
with relatively low transition temperatures and so facilitate the perpendicular to the stripes direction can be observed. On cooling
experimental investigation of the twist-bend nematic phase. the sample such a periodicity is maintained but tilted bands
The nematic–isotropic transition temperature for KA is 348 K across the stripes are developed giving rise to a rope-like texture at
and the virtual NTB–N transition temperature has been located 270 K.4,14,52 It has also been observed that consecutive stripes
at 295 K.52 The shifted virtual transition temperature, TNI–TN N, is show reversed optical birefringence on opposite rotation. All these
TB
53 K which is smaller than that found for the single component features were already observed in the optical textures of the
system, FFO9OCB, explored here of 62 K. The larger value CB7CB dimer which was the first compound to be identified as
determined for the single component is consistent with its forming a twist-bend nematic phase.4
long spacer whereas for the mixture which contains odd dimers
3.3.2 Dielectric measurements. Fig. 11 shows the perpendi-
cular component of the dielectric loss at two temperatures close to
heptane as well as nonane spacers52 it is expected that TNI–TN
TBN
will be smaller. This follows from calculations of the bend elastic each other, one in the N mesophase and the other in the NTB
constants which show that for the odd dimers, FFOnOCB, the mesophase. It can be observed how the amplitude of the m1>-mode
shifted transition temperature decreases with reduction in the sharply increases in the NTB mesophase, a fact already
length of the spacer.22
reported for the NTB of the CB7CB dimer.4 This is consistent
Further evidence for the assignment of the lower tempera- with the formation of a phase in which the director tilts away
ture nematic phase of FFO9OCB as a twist-bend nematic has from the planar alignment direction defined in the precursor
been provided by miscibility studies with CB7CB.53 The latter nematic phase. In the absence of any evidence of a tilted
dimer has been extensively examined using X-ray4,6 and freeze smectic C phase, we attribute this dielectric feature to the
fracture transmission electron microscopy6,7 and its assign- formation of a twist-bend nematic phase. It should be stressed
ment as NTB is not in doubt. Our mixture phase diagram is that the amplitude of the m2>-mode abruptly decreases, in
given in Fig. 9, and the continuous mixing shown in the NTB fact much more than expected,4 which is believed to be due
phase is a consequence of this phase for FFO9OCB and CB7CB to the partial crystallization of the sample. It should be
having the same structural symmetry.
remembered that this mesophase is highly metastable and
3.3.1 Optical textures. We now consider in detail some must be obtained by using high cooling rates making dielectric
selected optical textures at three temperatures within the measurements difficult.
proposed NTB mesophase which are shown in Fig. 10. These were
3.3.3 Splay and bend elastic constants. The essence of the
obtained on cooling the sample from the I-phase at 15 K minꢀ1 in Landau or elastic model proposed by Dozov3 for the formation
cells (8 mm thick, with an anti-parallel alignment layer from of the twist-bend nematic phase is the bent shape of the
Instec) with a defined planar alignment direction. Under these constituent molecules. Under certain conditions the ground-
conditions a characteristic striped texture with the stripes parallel state remains in a state of permanent bend, and accompanying
to the surface alignment direction is obtained. A periodicity of the the bend distortion there is also a twist.
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Fig. 11 Frequency dependence of the imaginary part of the perpendicular
component of the permittivity at two temperatures, one (T = 319 K) in the
N phase and the other (T = 313 K) in the NTB phase.
For this structure there are two defining features, the tilt of
the director with respect to the helix axis, y0, and the wave
vector, k = 2p/p where p is the pitch of the helix. The main
assumption in Dozov’s model is that in the twist-bend nematic
phase the coefficient of the bend distortion in the free energy
should be negative. This assumption does not apply to the high
temperature uniform nematic phase, but it is tempting to
speculate that nematic phases with low values of the bend
elastic constant might have a predisposition to form a twist-
bend nematic phase, although for any particular example, other
factors may intervene.
We now turn to the elastic constants in the uniform nematic
phase of dimer liquid crystals. It is to be expected, and indeed
found, that for the odd dimers the splay K1 and twist K2 elastic
constants behave normally, namely K1 4 K2, and in addition
both increase with decreasing temperature and hence orienta-
tional order.22 In marked contrast, theory4,22 and experiment23,50,52
reveal that the bend K3 elastic constant is small and decreases with
decreasing temperature. The bend and splay elastic constants have
been measured for FFO9OCB23 and the results show that K1
increases with decreasing temperature while K3 is significantly
smaller than K1 and decreases slightly with decreasing tempera-
ture. They are found to be in accordance with earlier theoretical
predictions.22 The lowest reduced temperature for which the
experimental results are available is B0.93 which is significantly
higher than the monotropic NTB–N transition at B0.83.
Fig. 10 Optical textures at three temperatures obtained from 8 mm thick
cells (anti-parallel alignment from Instec). Red arrows correspond to the
direction of the rubbing and crossed arrows indicate the direction of the
polarizer axes. The width of all pictures is 144 mm and D = 2d.
We have determined the splay (K1) and bend (K3) elastic
constants for FFO9OCB over a more extended range of tem-
The twist is not spontaneous, assuming no intrinsic chirality, perature. Our results are given in Fig. 12 as a function of
but is imposed by the bend to enable topological continuity. In reduced temperature (T/TNI) along with values measured by
the theory it was assumed that the bent-core or banana meso- Atkinson et al.23 over a shorter temperature range. As regards
genic molecules had a fixed geometrical bend, but the first K1, there is a reasonable agreement between the two sets of
compound reported to form the twist-bend nematic phase was measurements over the common temperature range. As regards
the flexible odd-membered liquid crystal dimer CB7CB.4 This K3, a certain difference is observed in absolute values between
mesogen has a flexible core which can give rise to a variety the two sets of measurements. However, and despite this
of molecular shapes. The conformationally averaged shape difference, K3 is significantly smaller than K1 at temperatures
depends on the type of the phase, temperature and degree of close to the NTB–N phase transition and a similar behaviour is
order, but in general is also bent. In the twist-bend nematic observed as the temperature decreases on approaching the
phase, the director distribution is both bent and twisted. transition to the proposed NTB phase.
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Fig. 12 Temperature dependence of the splay (K1) and bend (K3) elastic
constants in the nematic phase for FFO9OCB. J – our results for K1; K –
results for K1 from ref. 23; B – our results for K3;E – results for K3 from
ref. 23.
Fig. 13 Heat capacity data (J) as a function of temperature near the
N-to-I phase transition of FFO9OCB. Phase shift angle (f) data (D) are
included to define the limits of the heat capacity coexistence region (area
delimited by the vertical dashed lines). Grey solid lines are fittings according
3.4 The nematic-to-isotropic phase transition
0
to eqn (9a) and (9b). The inset shows QN data according to eqn (11) as a
One of the simplest theoretical descriptions of the N-to-I phase
transition is that offered by the Landau-de Gennes free energy
expansion in terms of the second-rank symmetric traceless
order parameter tensor Q. In the simplest case for uniaxial
nematic phases, the tensor Q can be substituted by a scalar
order parameter QN (QN = 1/2h(3cos2 y ꢀ 1)i). In such a situation
the free energy density expansion for the nematic phase up to
sixth order can be written as
function of temperature together with the fitting curve (grey line) according
to eqn (12).
the first order character of the N-to-I phase transition and will be
used to determine the limits of the coexistence region indicated
by dashed lines in Fig. 13.
Let us consider the analysis of the heat capacity data
through the standard expressions:36–38
2
3
4
6
1
2
1
3
1
4
1
6
FN = FI + AQN ꢀ BQN + CQN + DQN
(8)
ꢀ
ꢀ
ꢀ
ꢀ
ꢀꢀa
ꢅ
ꢆ
ꢀ
ꢀ
ꢀ
T
Tꢅ
T
Tꢅ
Cp;I ¼ BC þ DC
ꢀ 1 þ AC;I
ꢀ 1
T 4 TNI ¼ Tꢅ þ DTꢅ
where A, B, C, and D are the expansion coefficients and FI is the
free energy density of the isotropic phase. It is usual to define A
as a0(T ꢀ T*) with a0 4 0 and T* the spinodal temperature
accounting for the metastable limit of the I-phase. The other
terms B, C, and D are assumed to be temperature independent
and among them, the term B, the so-called cubic invariant, is
responsible for the first-order character of the N-to-I phase
transition. If the molecules forming the uniaxial nematic phase
are flexible and/or biaxial, then the absolute value of B is
(9a)
ꢀ
ꢀꢀa
ꢅ
ꢆ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
T
Tꢅꢅ
T
Tꢅꢅ
Cp;N ¼ BC þDC
ꢀ1 þAC;N
ꢀ1
T oTNI ¼ Tꢅꢅ ꢀDTꢅꢅ
(9b)
Both eqn (9a) and (9b) are assumed to be valid in a region of
diminished.36 When B is very small and the other parameters no more than ꢂ3 K around TNI, but excluding all the points in
A and C become simultaneously zero, the N-to-I phase transi- the coexistence region. The exponent a (the same in the I and N
tion becomes strictly tricritical.36,54 In such a situation the heat phases), both spinodal temperatures T** and T*, the BC and DC
capacity critical exponent a in both N and I phases must be 1/2 terms corresponding to the so-called heat capacity background
and the QN critical exponent b must be 1/4. From an experi- and the corresponding amplitudes AC,N and AC,I are found by
mental point of view, such parameters can be obtained from fitting the experimental data of Fig. 13 according to eqn (9a)
very accurate heat capacity data combined with static dielectric and (9b). In the methodology followed, the common para-
determinations through the N-to-I phase transition. In addi- meters in both phases (BC, DC and a) have been simultaneously
tion, indications about the magnitude of B can be obtained refined after a previous independent fitting. The most signifi-
from the determination of the spinodal temperatures T* and cant parameters (AC,N/AC,I, (T** ꢀ T*) and a) that characterize
T** (T** accounts for the metastable limit of the N mesophase) the nature of the N-to-I phase transition are listed in Table 3. All
and from the magnitude of the latent heat as well.
the fitted parameters are consistent with the measured heat
3.4.1 Heat capacity measurements and the order parameter. capacity data, as indicated by the w2 values and as shown in
Fig. 13 shows the heat capacity together with the f-phase shift Fig. 13 where both eqn (9) are drawn.
data around the N-to-I phase transition. The sharp-peak in the
The latent heat associated with the N-to-I phase transition is
f-phase shift data at the transition temperature is a signature of calculated using eqn (1) over the heat capacity data of Fig. 13
21402 | Phys. Chem. Chem. Phys., 2014, 16, 21391--21406
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through a previous careful calibration.12,13,37 Our value is listed
in Table 1.
In this work, the critical behaviour of the scalar order para-
meter QN around the N-to-I phase transition has been estimated
from very precise measurements of the heat capacity shown in
Fig. 13 according to the procedure given by Iannacchione and
Finotello.55 The methodology was applied successfully by us38,56
and is based on the Landau-de Gennes approach given by
eqn (8). The square of the scalar order parameter is defined as
ꢅ
ꢆ
ð
ð
TCI
T
2r
a0
DCp DHNI
DCp
T
2
QN ðTÞ ¼
þ
þ
(10)
T
TNI
T0
TCN
where r is the density of the liquid crystal and the constant a0 is
the first coefficient in eqn (8) (A = a0(T ꢀ T*) with a0 4 0). The
integration is done numerically on cooling from T0 in the
I-phase, well above TNI, at which QN could be considered zero
down to temperature T in the N-mesophase. Both temperatures
TCI and TCN are the limiting temperatures of the coexistence
region in the isotropic and nematic phases, respectively. The
terms DHNI and DCp are the latent heat and the difference
between the heat capacity and the heat capacity background,
respectively. Assuming that the density of the liquid crystal is
Fig. 14 Behaviour of the mean static dielectric permittivity in the nematic
phase (B) and the static dielectric permittivity in the isotropic phase (J) for
FFO9OCB. Grey solid lines are fittings according to eqn (13a) and (13b). The
inset shows the derivative of the static dielectric permittivity (left y-axis and
open symbols) and heat capacity data (right y-axis and grey points) both as
a function of temperature.
e
mean = e** + aN|T ꢀ T**| + Ae,N|T ꢀ T**|1ꢀa T o TNI = T** ꢀ DT**
(13b)
0
constant in the integrated temperature range, we can write QN as
1
2
1
2
ꢅ
ꢆ
ꢅ
ꢆ
where a is the specific heat critical exponent; T* and T** have
the same meaning as in eqn (9); e* and e** are the extrapolated
values of eiso and emean at T* and T**, respectively; both aI and
aN are the static dielectric permittivity background; Ae,I and Ae,N
are the corresponding dielectric amplitudes. All these para-
meters have been obtained by fitting the dielectric data and the
most significant values (Ae,N/Ae,I, (T** ꢀ T*) and a) are listed in
Table 3. In our fitting strategy, the star symbols in Fig. 14 have
been removed from the fitting according to the scaling relation-
ship between the derivative of the static dielectric permittivity
(demean/dT and deiso/dT) and the heat capacity (see the inset of
Fig. 14) around the phase transition as was theorized earlier by
Mistura.59 It may be emphasised that both demean/dT and deiso/dT
have been obtained numerically by distortion-sensitive derivative
analysis of the static permittivity data according to the procedure
given elsewhere.12,57,58
ð
ð
TCI
T0
T
a0
DCp DHNI
DCp
T
QN0 ðTÞ ¼ QN
¼
þ
þ
(11)
2r
T
TNI
TCN
0
where QN is not strictly the scalar order parameter but is a
proportional quantity which displays the same critical behaviour
at the N-to-I phase transition. Such a critical behaviour is usually
parameterized, according to the Landau-de Gennes theory,36,57,58
as a generic expression
b
QN = QN0** + K|T ꢀ T**| T o T** ꢀ DT*
(12)
0
where T** has the same meaning as in eqn (9b). The critical
exponent b and K and QN0** are parameters obtained from fits
of the QN data calculated using eqn (11). The inset of Fig. 13
shows the calculated QN data and the fitting according to
eqn (12) (grey line). The value of the critical exponent b is listed
in Table 3 together with the fitting w2 value.
0
0
Both eqn (13a) and (13b) with the corresponding fitting
parameters portray almost perfectly our experimental data as
shown in Fig. 14 and also as indicated by the w2-value listed in
Table 3 which is indicative of the quality of the fitted results.
3.4.3 The critical behaviour. From our analysis using high-
resolution heat capacity measurements, it has been clearly
demonstrated that the N-to-I phase transition is first order in
nature. The latent heat (DHNI) (see Table 1) is estimated to be
3.4.2 Static dielectric permittivity measurements. Fig. 14
shows the static permittivity data (emean and eiso) around the
N-to-I phase transition in more detail than in Fig. 5. The data
analysis at the N-to-I phase transition has been carried out
according to the equations12,13,57
eiso = e* + aI|T ꢀ T*| + Ae,I|T ꢀ T*|1ꢀa T 4 TNI = T* + DT*
(13a)
Table 3 Results of the fittings for the N-to-I phase transition
Physical property
AN/AI
T** ꢀ T* (K)
DT**/DT*
a
b
w2 ꢁ 104
1
0.5
1
Heat capacity
2.4 ꢂ 0.1
0.59a
3.97a
—
0.83
0.46
—
0.50 ꢂ 0.05
0.5 ꢂ 0.1
—
—
—
Static permittivity
ꢀ0.6 ꢂ 0.1
0
QN
—
0.25 ꢂ 0.02
a
The error is estimated to be about 50% of the absolute magnitude of (T** ꢀ T*).
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4 times lower than the one reported by Atkinson et al.24 Such scalar orientational order parameter, has been obtained from
discrepancies are usually observed in other liquid crystals for the heat capacity data. The associated critical exponent is found
which latent heats are determined from standard DSC mea- to be 0.25, the tricritical value which supports other strong
surements at 5 or 10 K minꢀ1
.
evidence arising from calorimetric and dielectric measure-
The width of the metastable region (T** ꢀ T*), that is linked ments suggesting that the N-to-I phase transition exhibits a
with the magnitude of the cubic invariant B, has been found to tricritical behaviour.
be non-zero and positive (see Table 3). The value of (T** ꢀ T*)
In relation to the mesomorphism of the FFO9OCB the
obtained from static dielectric permittivity is higher than that main unpublished result is the discovery of a new metastable
found from heat capacity measurements, as usually occurs.12,58,60 nematic phase formed when the sample is cooled at sufficiently
It was thought that such differences are caused by a non-perfect high rates (at least 10 K minꢀ1). Evidence for identifying this
experimental scaling between the heat capacity and the derivative phase as a twist-bend nematic phase (NTB) comes from optical
of the static dielectric permittivity, as shown in the inset of Fig. 14. textures, dielectric measurements close to the N-to-NTB phase
The ratio DT**/DT* (see Table 3) ranges from 0.8 (heat capacity) transition and the temperature dependence of both K1 and K3
to about 0.5 (static dielectric permittivity). It is noteworthy that elastic constants. This assignment is confirmed by miscibility
DT**/DT* of about 0.5 agrees with the tricritical hypothesis of the studies with CB7CB. Thus, the FFO9OCB dimer constitutes an
N-to-I phase transition.60–64 In addition, the heat capacity critical example of a pure ether-linked dimer exhibiting the twist-bend
exponent a is found to be 0.5 whatever the technique used (either nematic mesophase. Additionally, the FFO9OCB dimer exhibits
heat capacity or static dielectric0data). The b-critical exponent of a glassy state when the sample is cooled at 10 K minꢀ1 or
the order parameter through QN is found to be 0.25. Both critical higher, and it has been shown that this glassy state corresponds
exponents are also compatible with the tricritical hypothesis. The to the vitrification of this new NTB mesophase. Unfortunately,
heat capacity amplitude ratio (AC,N/AC,I) and even the dielectric the fact that the NTB mesophase is metastable (it crystallizes on
amplitude ratio (Ae,N/Ae,I) (see Table 3) are in quite good agreement cooling even at high cooling rates) prevents the possibility of
with the values obtained for the tricritical behaviour in other performing a detailed investigation, by dielectric spectroscopy,
liquid crystals.12,58,61 Noteworthy is the validation of the approx- of the motions involved in the glass transition5 and to apply the
imate scaling relation Ae,N/Ae,I E 1 ꢀ 4a.61–64
most advanced procedures65,66 to characterize the glass transi-
tion in the light of critical phenomena.
Our earlier claim4 to have discovered a new liquid crystalline
phase has rightly been subjected to critical review in the
literature.67 The theoretical possibility for such a phase has
4 Conclusions
The study reported in this paper is an extensive investigation been raised in the past by a number of authors,68,69 and most
of the non-symmetric liquid crystal dimer FFO9OCB. So far, recently by Dozov.3 A conical nematic phase has been reported
our dielectric relaxation and heat capacity measurements in a lyotropic suspension of helical flagella70 and other groups
are the first measurements performed in compounds of the have reported additional examples of the twist-bend nematic
FFOnOCB series.
phase in thermotropic systems.6,7,51
In the nematic phase, the temperature dependence of the
static dielectric permittivity is qualitatively similar to that
exhibited by symmetric liquid crystal dimers,4,29,33,34 but the
parallel component decreases with temperature to a lesser
extent. Dielectric relaxation results have been obtained over a
wide range of frequencies from 103 to 109 Hz. The model of
Stocchero et al.35 has allowed us to identify and interpret the
molecular processes that are responsible for the two different
longitudinal dielectric relaxations observed at low frequencies.
Both relaxations are a consequence of flip-flop motions of the
terminal groups of the dimer. On the basis of the model, the
conformational distribution of the molecules in the N meso-
phase has been estimated as a function of temperature.
The N-to-I phase transition has been characterized as first-
order in nature from heat capacity as well as static dielectric
permittivity measurements. The measured latent heat and
transitional entropy change (DS/R = 0.14) associated with the
N-to-I phase transition is found to be much lower than the
value previously reported in the literature24 and is in agreement
with the very weakly first order character of the transition
evidenced by the small value of the width of the metastable
region. The magnitude of QN0, which is proportional to the
Acknowledgements
The authors are grateful for financial support from the MICINN
project MAT2012-38538-C03-02,03 and from the Gobierno Vasco
(GI/IT-449-10). The authors also thank the recognition from the
Generalitat de Catalunya of GRPFM as Emergent Research Group
´
(2009-SGR-1243). One of us, N. Sebastian, would like to thank the
´
Universidad del Paıs Vasco for a post-doctoral grant.
Notes and references
1 C. T. Imrie and P. A. Henderson, Chem. Soc. Rev., 2007, 36,
2096–2124.
2 M. S. Sepelj, A. Lesac, U. Baumeister, S. Diele, H. L. Nguyen
and D. W. Bruce, J. Mater. Chem., 2007, 17, 1154–1165.
3 I. Dozov, Europhys. Lett., 2001, 56, 247–253.
4 M. Cestari, S. Diez-Berart, D. A. Dunmur, A. Ferrarini,
´
M. R. de la Fuente, D. J. B. Jackson, D. O. Lopez, G. R.
´
Luckhurst, M. A. Perez-Jubindo, R. M. Richardson, J. Salud,
B. A. Timimi and H. Zimmerman, Phys. Rev. E: Stat.,
21404 | Phys. Chem. Chem. Phys., 2014, 16, 21391--21406
This journal is © the Owner Societies 2014

View Article Online
PCCP
Paper
Nonlinear, Soft Matter Phys., 2011, 84, 031704. First pre- 28 D. Bauman, E. Wolarz and E. Bialecka-Florjanczyik,
sented 23rd International Liquid Crystal Conference,
Krakow (2010), Abstract Oral 62.
Liq. Cryst., 1999, 26, 45–49.
29 D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez and
´
´
´
5 D. O. Lopez, N. Sebastian, M. R. de la Fuente, J. C. Martınez-
M. A. Perez-Jubindo, J. Chem. Phys., 2001, 115, 8681–8691.
Garcıa, J. Salud, M. A. Perez-Jubindo, S. Diez-Berart, D. A. 30 J. P. F. Lagerwall, F. Giesselmann, M. D. Wand and D. M.
Dunmur and G. R. Luckhurst, J. Chem. Phys., 2012, 137, 034502. Walba, Chem. Mater., 2004, 16, 3606–3615.
6 D. Chen, J. H. Porada, J. B. Hooper, A. Klittnick, Y. Shen, 31 M. G. Tamba, B. Kosata, K. Pelz, S. Diele, G. Pelzl,
´
´
M. R. Tuchband, E. Korblova, D. Bedrov, D. M. Walba,
M. A. Glaser, J. E. Maclennan and N. A. Clark, Proc. Natl.
Acad. Sci. U. S. A., 2013, 110, 15931.
Z. Vakhovskaya, H. Kresse and W. Weissflog, Soft Matter,
2006, 2, 60–65.
32 A. S. Pandey, R. Dhar, M. B. Pandey, A. S. Achalkumar and
C. V. Yelamaggad, Liq. Cryst., 2009, 36, 13–19.
7 V. Borshch, Y.-K. Kim, J. Xiang, M. Gao, A. Jakli, V. P. Panov,
´
´
J. K. Vij, C. T. Imrie, M. G. Tamba, G. H. Mehl and O. D. 33 M. R. de la Fuente, D. O. Lopez, M. A. Perez-Jubindo, D. A.
Lavrentovich, Nat. Commun., 2013, 4, 2635.
8 H. J. Coles and M. N. Pivnenko, Nature, 2005, 436, 997–1000.
9 G. R. Luckhurst, Nature, 2004, 430, 413–414.
Dunmur, S. Diez-Berart and J. Salud, J. Phys. Chem. B, 2010,
114, 7864–7873.
´
34 D. A. Dunmur, M. R. de la Fuente, M. A. Perez-Jubindo and
10 G. R. Luckhurst, Angew. Chem., Int. Ed., 2005, 44, 2834–2836.
11 G. R. Luckhurst, Liq. Cryst., 2009, 36, 1295–1308.
S. Diez, Liq. Cryst., 2010, 37, 723–736.
35 M. Stocchero, A. Ferrarini, G. J. Moro, D. A. Dunmur and
G. R. Luckhurst, J. Chem. Phys., 2004, 121, 8079–8097.
´
´
12 N. Sebastian, M. R. de la Fuente, D. O. Lopez, M. A. Perez-
Jubindo, J. Salud, S. Diez-Berart and M. B. Ros, J. Phys. 36 M. A. Anisimov, Critical Phenomena in Liquids and Liquid
Chem. B, 2011, 115, 9766–9775.
Crystals, Gordon and Breach Science Publishers, Amsterdam,
´
´
13 N. Sebastian, D. O. Lopez, S. Diez-Berart, M. R. de la Fuente,
1991.
´
´
J. Salud, M. A. Perez-Jubindo and M. B. Ros, Materials, 2011, 37 P. Cusmin, M. R. de la Fuente, J. Salud, M. A. Perez-Jubindo,
´
4, 1632–1647.
S. Diez-Berart and D. O. Lopez, J. Phys. Chem. B, 2007, 111,
14 V. P. Panov, M. Nagaraj, J. K. Vij, Y. P. Panarin,
8974–8984.
´
A. Hohlmeier, M. G. Tamba, R. A. Lewis and G. H. Mehl, 38 J. Salud, P. Cusmin, M. R. de la Fuente, M. A. Perez-Jubindo,
´
Phys. Rev. Lett., 2010, 105, 167801.
D. O. Lopez and S. Diez-Berart, J. Phys. Chem. B, 2009, 113,
´
15 C. S. P. Tripathi, P. Losada-Perez, C. Glorieux, A. Kohlmeier,
15967–15974.
M. G. Tamba, G. H. Mehl and J. Leys, Phys. Rev. E: Stat., 39 G. S. Attard, R. W. Date, C. T. Imrie, G. R. Luckhurst,
Nonlinear, Soft Matter Phys., 2011, 84, 041707.
16 V. P. Panov, R. Balachandran, M. Nagaraj, J. K. Vij,
S. J. Roskilly, J. M. Seddon and L. Taylor, Liq. Cryst., 1994,
16, 529–581.
M. G. Tamba and A. Kohlmeier, Appl. Phys. Lett., 2011, 40 M. J. Clarke, PhD thesis, University of Southampton, 2004.
´
99, 261903.
41 M. B. Sied, J. Salud, D. O. Lopez, M. Barrio and J. Ll.
17 P. V. Panov, R. Balachandran, J. K. Vij, M. G. Tamba,
Tamarit, Phys. Chem. Chem. Phys., 2002, 4, 2587–2593.
A. Kohlmeier and G. H. Mehl, Appl. Phys. Lett., 2012, 42 S. W. Morris, P. Palffy-Muhoray and D. A. Balzarini,
101, 234106. Mol. Cryst. Liq. Cryst., 1986, 139, 263–280.
18 H. J. Coles, B. Musgrave, M. J. Coles and J. Wilmott, J. Mater. 43 S. Diez, M. A. Perez-Jubindo, M. R. de la Fuente, D. O. Lopez,
´
´
Chem., 2001, 11, 2709–2716.
J. Salud and J. Ll. Tamarit, Chem. Phys. Lett., 2006, 423,
19 J. S. Patel and L. Sin-Doo, J. Appl. Phys., 1989, 66, 1879–1881.
463–469.
´
´
20 S. M. Morris, M. J. Clarke, A. E. Blatch and H. J. Coles, Phys. 44 S. Diez, M. A. Perez-Jubindo, M. R. de la Fuente, D. O. Lopez,
Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 041701. J. Salud and J. Ll. Tamarit, Liq. Cryst., 2006, 33, 1083–1091.
21 J. S. Patel and R. B. Meyer, Phys. Rev. Lett., 1987, 58, 45 W. Maier and G. Meier, Z. Naturforsch., A: Astrophys. Phys.
1538–1540. Phys. Chem., 1961, 16, 262–267.
22 M. Cestari, E. Frezza, A. Ferrarini and G. R. Luckhurst, 46 P. L. Nordio, G. Rigatti and U. Segre, Mol. Phys., 1973, 25,
J. Mater. Chem., 2011, 21, 12303–12308. 129–136.
23 K. L. Atkinson, S. M. Morris, F. Castles, M. M. Qasim, 47 N. Sebastian, M. R. de la Fuente, D. O. Lopez, M. A. Perez-
´
´
´
D. G. Gardiner and H. J. Coles, Phys. Rev. E: Stat., Nonlinear,
Soft Matter Phys., 2012, 85, 012701.
Jubindo, J. Salud and M. B. Ros, J. Phys. Chem. B, 2013, 117,
14486–14496.
24 K. L. Atkinson, S. M. Morris, M. M. Qasim, F. Castles, 48 C. Meyer, G. R. Luckhurst and I. Dozov, Phys. Rev. Lett.,
D. G. Gardiner, P. J. H. Hands, S. S. Choi, W. S. Kim and 2013, 111, 067801.
H. J. Coles, Phys. Chem. Chem. Phys., 2012, 14, 16377–16385. 49 P. A. Henderson and C. T. Imrie, Liq. Cryst., 2011, 38,
25 F. Castles, S. M. Morris, E. M. Terentjev and H. J. Coles,
Phys. Rev. Lett., 2010, 104, 157801.
26 H. Furuya, S. Okamoto, A. Abe, G. Petekidis and G. Fytas,
J. Phys. Chem., 1995, 99, 6483–6486.
1407–1414.
50 R. Balachandran, V. P. Panov, J. K. Vij, A. Kocot, M. G.
Tamba, A. Kohlmeier and G. H. Mehl, Liq. Cryst., 2013, 40,
681–688.
27 A. Hohmuth, B. Schiewe, S. Heinemann and H. Kresse, 51 Long after the present paper was submitted for publication,
Liq. Cryst., 1997, 22, 211–215.
the following paper has appeared: R. J. Mandle, E. J. Davis,
This journal is ©the Owner Societies 2014
Phys. Chem. Chem. Phys., 2014, 16, 21391--21406 | 21405

View Article Online
Paper
PCCP
S. A. Lobato, C. C. A. Vol, S. J. Cowling and J. W. Goodby, 59 L. Mistura, J. Chem. Phys., 1973, 59, 4563–4564.
Phys. Chem. Chem. Phys., 2014, 16, 6907. 60 A. Zywozinsky, J. Phys. Chem., 2003, 107, 9491–9497.
52 K. Adlem, M. Copic, G. R. Luckhurst, A. Mertelj, O. Parri, 61 P. Barmatz, P. C. Hohenberg and B. I. A. Kornblit, Phys. Rev.
R. M. Richardson, B. D. Snow, B. A. Timimi, R. P. Tuffin and B: Solid State, 1975, 12, 1947–1968.
D. Wilkes, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 62 P. C. Hohenberg, A. Aharony, B. I. Halperin and E. D. Siggia,
2013, 88, 022503. Phys. Rev. B: Solid State, 1976, 13, 2986–2996.
53 Authors’ data for all members of the set of mixtures show 63 A. Aharony and P. C. Hohenberg, Phys. Rev. B: Solid State,
the same phase sequence on cooling as the pure CB7CB: 1976, 13, 3081–3090.
I-N-NTB-NTB,gl. Further details will be given in another 64 K. J. Stine and C. W. Garland, Phys. Rev. A: At., Mol., Opt.
ˇ
ˇ
manuscript, in preparation, devoted to these miscibility
studies.
Phys., 1989, 39, 3148–3156.
´
´
´
´
65 J. C. Martınez-Garcıa, J. Martınez-Garcıa, S. J. Rzoska and
54 P. H. Keyes and J. R. Shane, Phys. Rev. Lett., 1979, 42, 722–725.
J. Hulliger, J. Chem. Phys., 2012, 137, 064501.
´
´
55 G. S. Iannacchione and D. Finotello, Phys. Rev. E: Stat. Phys., 66 J. C. Martınez-Garcıa, S. J. Rzoska, A. Drozd-Rzoska and
´
´
Plasmas, Fluids, Relat. Interdiscip. Top., 1994, 50, 4780–4795.
J. Martınez-Garcıa, Nat. Commun., 2013, 4, 1823.
56 S. Diez, D. O. Lopez, M. R. de la Fuente, M. A. Perez-Jubindo, 67 R. J. Mandle, E. J. Davis, C. T. Archbold, S. J. Cowling and
J. Salud and J. Ll. Tamarit, J. Phys. Chem. B, 2005, 109, 23209–23217. J. W. Goodby, J. Mater. Chem. C, 2014, 2, 556–566.
57 S. J. Rzoska, J. Ziolo, W. Sulkowski, J. Jadzyn and 68 R. B. Meyer, in Molecular Fluids, Les Houches Lectures, ed.
´
´
G. Czechowski, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.,
2001, 64, 052701.
R. Balian and G. Weill, Gordon and Breach, 1976, p. 320.
69 P. G. de Gennes and J. Prost, The Physics of Liquid Crystals,
Clarendon Press, Oxford, 1993, p. 292.
´
58 S. J. Rzoska, A. Drozd-Rzoska, P. K. Mukherjee, D. O. Lopez
´
´
and J. C. Martinez-Garcıa, J. Phys.: Condens. Matter, 2013, 70 E. Barry, Z. Hensel, Z. Dogic, M. Shribak and R. Oldenbourg,
25, 245105.
Phys. Rev. Lett., 2006, 96, 018305.
21406 | Phys. Chem. Chem. Phys., 2014, 16, 21391--21406
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