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Published paper
:
Robles-Hernández, B., Sebastián, N., De La Fuente, MR., López, D.,
Díez-Berart, S., Salud, J., Ros, MB., Dunmur, D., Luckhurst, G. and
Timimi, Bakir A. (2015)
Twist, tilt, and orientational order at the
nematic to twist-bend nematic phase transition of 1,9-bis(4-
cyanobiphenyl-4-yl) nonane: A dielectric, H 2 NMR, and calorimetric
study
Physical Review E - Statistical, Nonlinear, and Soft Matter
Physics, 92. 6. 062505. DOI 10.1103/PhysRevE.92.062505
1
Substituir per la citació bibliogràfica corresponent
PHYSICAL REVIEW E 00, 002500 (2015)1
Twist, tilt, and orientational order at the nematic to twist-bend nematic phase transition of
1
,9
-bis(4-cyanobiphenyl-4
-yl) nonane: A dielectric,
2
H
NMR, and calorimetric study
2
3
Beatriz Robles-Hern
´
andez,
1
Nerea Sebasti
´
an,
1,2
M. Rosario de la Fuente,
1,*
David O. L
´
opez,
3
Sergio Diez-Berart,
3
Josep Salud,
3
M. Blanca Ros,
4
David A. Dunmur,
5,†
Geoffrey R. Luckhurst,
5
and Bakir A. Timimi
5
4
5
1
Departamento de F
´
ısica Aplicada II, Facultad de Ciencia y Tecnolog
´
ıa, Universidad del Pa
´
ıs Vasco, Apartado 644, E-48080 Bilbao, Spain6
2
Otto-von-Guericke Universitat Magdeburg, Institute for Experimental Physics, ANP, 39106 Magdeburg, Germany7
3
Grup de Propietas F
´
ısiques dels Materials (GRPFM), Departament de F
´
ısica i Enginyeria Nuclear, E.T.S.E.I.B. Universitat Polit
`
ecnica de
Catalunya, Diagonal 647, E- 08028 Barcelona, Spain
8
9
4
Departamento de Qu
´
ımica Org
´
anica, Facultad de Ciencias–Instituto de Ciencia de Materiales de Arag
´
on, Universidad de Zaragoza-CSIC,
E-50009 Zaragoza, Spain
10
11
5
Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom12
(Received 6 October 2015; published xxxxxx)13
The nature of the nematic-nematic phase transition in the liquid crystal dimer 1
,9
-bis(4-cyanobiphenyl-
4
-yl) nonane (CB9CB) has been investigated using techniques of calorimetry, dynamic dielectric response
measurements, and
2
H
NMR spectroscopy. The experimental results for CB9CB show that, like the shorter
homologue CB7CB, the studied material exhibits a normal nematic phase, which on cooling undergoes a transition
to the twist-bend nematic phase (N
TB
), a uniaxial nematic phase, promoted by the average bent molecular shape,
in which the director tilts and precesses describing a conical helix. Modulated differential scanning calorimetry
has been used to analyze the nature of the N
TB
-N phase transition, which is found to be weakly first order, but close
to tricritical. Additionally broadband dielectric spectroscopy and
2
H
magnetic resonance studies have revealed
information on the structural characteristics of the recently discovered twist-bend nematic phase. Analysis of the
dynamic dielectric response in both nematic phases has provided an estimate of the conical angle of the heliconical
structure for the N
TB
phase. Capacitance measurements of the electric-field realignment of the director in initially
planar aligned cells have yielded values for the splay and bend elastic constants in the high temperature nematic
phase. The bend elastic constant is small and decreases with decreasing temperature as the twist-bend phase is
approached. This behavior is expected theoretically and has been observed in materials that form the twist-bend
nematic phase.
2
H
NMR measurements characterize the chiral helical twist identified in the twist-bend nematic
phase and also allow the determination of the temperature dependence of the conical angle and the orientational
order parameter with respect to the director.
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
DOI: 10.1103/PhysRevE.00.002500 PACS number(s): 61.30.Eb, 64.70.mj31
I. INTRODUCTION32
During the last few years interest in liquid crystal dimers33
has experienced an extraordinary growth due to the observation34
of nematic-nematic transitions for relatively simple materials35
where two mesogenic units are linked by methylene chains36
having odd numbers of carbon atoms [1–5]. Although the37
high temperature nematic mesophase of these materials is a38
conventional nematic phase, its elastic and dielectric properties39
are far from typical [2,6–8]. In contrast to normal low40
molecular weight nematic liquid crystals, odd dimers possess41
a bend elastic constant (K
3
) significantly smaller than the42
splay elastic constant (K
1
)[6,9,10]. Moreover, K
3
reduces43
with decreasing temperature reaching remarkably low values44
[7,9,10]. Such behavior has been successfully explained in45
terms of the effect the molecular shape exerts on elastic46
constants [11], the preferred averaged bent molecular shape47
promoted by the odd spacers being responsible for the low or48
possibly negative bend elastic constants [12]. This is especially49
the case when the spacer is linked by methylene groups to50
the mesogenic groups [13]. According to Dozov’s predictions51
[12], a negative bend elastic coefficient [14] would give rise52
*
rosario.delafuente@ehu.es
†
d.dunmur@tiscali.co.uk
to a nematic ground state where the director, instead of being 53
uniformly aligned, spontaneously bends. This state of bend 54
deformation would have to be accompanied by a splay or twist 55
deformation in order to be stabilized. In the latter case, the 56
induced twist could be left- or right-handed, and thus, even 57
though molecules are achiral, the sample would be expected 58
to form a conglomerate of domains having opposite chirality, 59
that is, a nematic phase where the directors arrange themselves 60
into a helix with the director making a constant angle with 61
respect to it [12]. Recently we have reported [15] a twist-bend 62
nematic (N
TB
) mesophase for ether-linked dimers formed at 63
low temperatures from the nematic-isotropic transition: Other 64
authors have also claimed to have observed the twist-bend 65
nematic phase with ether-linked dimers, but no results to 66
support this claim are given in their paper [16]. 67
Following a detailed investigation of the liquid crystal dimer 68
1
,7
-bis(4-cyanobiphenyl-4
-yl) heptane (CB7CB) [2]itwas 69
proposed that the low temperature nematic phase observed 70
for such odd dimers is indeed the N
TB
phase predicted 71
by Dozov [12]. This study has been followed by intense 72
research activity focused on the structure and properties of the 73
N
TB
phase. Different authors have described a characteristic 74
ropelike texture with stripes parallel to the alignment axis 75
for thin films of planar aligned samples [1,2,9,16,17]. With 76
the sample between a cover slip and microscope slide, 77
focal-conic-defect and parabolic-defect textures have been 78
1539-3755/2015/00(0)/002500(16) 002500-1 ©2015 American Physical Society
BEATRIZ ROBLES-HERN
´
ANDEZ et al. PHYSICAL REVIEW E 00, 002500 (2015)
FIG. 1. Chemical structure of the methylene-linked dimer 1
,9
-
bis(4-cyanobiphenyl-4
-yl) nonane (CB9CB).
observed [2,16], both indicative of a periodic modulation of
79
the refractive indices. However, the possibility of smecticlike80
order was initially excluded by careful x-ray experiments,81
which showed no Bragg reflections [2,4,7,9]. This observation82
rules out long-range translational order in the phase, but83
does not exclude the possibility of other structural order84
characterized by appropriate order parameters. Through
2
H
85
NMR investigations, the chiral character of this nematic86
phase has been unambiguously confirmed in agreement with87
Dozov’s predictions [18–21]. Recently, nanoscale helix pitch88
periodicities of 8−10 nm have been measured in the N
TB
89
phase using freeze fracture transmission electron microscopy90
(FFTEM), and similar values have been obtained from a91
theoretical analysis of quadrupolar splittings measured for92
8CB-d
2
dissolved in CB7CB [7,21,22]. Interestingly, although93
composed of nonchiral molecules, electroclinic effects typical94
of chiral systems have been also reported [23–25]. Broadband95
dielectric studies of this compound [2,8] show that both96
nematic mesophases have a very similar dielectric behavior. An97
interesting question concerns the character or the N
TB
-N phase98
transition. Although some theoretical approaches [12,26] seem99
to predict a second-order phase transition, calorimetric results100
point to a first-order phase transition although with a strength101
that changes with the molecular structure, such as the spacer102
length [2,8].103
The current paper focuses on the liquid crystal dimer104
1
,9
-bis(4-cyanobiphenyl-4
-yl) nonane (hereafter referred to105
as CB9CB; see Fig. 1) that belongs to the same homologous106
series of methylene-linked cyanobiphenyl-alkane dimers as107
the first reported [2] example of a twist-bend nematic phase,108
CB7CB. High-resolution adiabatic scanning calorimetry mea-109
surements, miscibility studies, and x-ray investigations of110
CB9CB by Tripathi et al. [4] have demonstrated that, similar111
to its shorter-chain homologue CB7CB, CB9CB exhibits two112
nematic phases. However, in that study no mention is made113
concerning the nature of the low temperature nematic phase.114
In this paper we present a comprehensive experimental study115
of both nematic phases of CB9CB that allows us to identify the116
low temperature nematic phase as a twist-bend nematic phase.117
The static dielectric permittivity measurements presented here118
constitute direct evidence of changes in the conformational dis-119
tribution in the mesophases, while studies of the dynamics of120
the dipolar groups at the N-N
TB
transition provide clear proof121
of the tilt of the director in the lower temperature mesophase.122
Since it has been proposed that elastic constants contribute123
to the stability of the N
TB
phase [12], K
1
and K
3
have124
been determined using Fr
´
eedericksz-transition experiments.125
The chiral structure associated with the heliconical twist-bend126
nematic phase is established by
2
H
NMR experiments using
127
CB7CB-d
4
as a spin probe which allows a measure of the phase128
chirality to be established, together with the orientational order129
and the director tilt. Additionally, by means of high-resolution130
calorimetry experiments we present a detailed description131
of the N-I and N
TB
-N phase transitions. Finally, our study 132
reveals the existence of a glassy state linked to the twist-bend 133
nematic phase. 134
The layout of the paper is as follows. In Sec. II we describe 135
the experimental details. In Sec. III we present and discuss our 136
results concerning the heat capacity data, optical microscopy, 137
dielectric permittivity, splay and bend elastic constants, and 138
the quadrupolar splittings from
2
H
NMR spectroscopy. Our
139
concluding remarks are summarized in Sec. IV. 140
II. EXPERIMENTAL DETAILS 141
A. Material 142
The symmetric liquid crystal dimer CB9CB was synthe- 143
sized using the methodology previously reported for CB7CB 144
[13]. The liquid crystalline behavior was characterized us- 145
ing its optical textures and modulated differential scanning 146
calorimetry (MDSC). The phase sequence obtained (as de- 147
tailed in Sec. III A) is in good agreement with earlier studies 148
that noted a nematic-nematic phase transition in CB9CB 149
[4], but did not identify the low-temperature phase or give 150
any indications of its structure. Recently, Hoffmann et al. 151
[27]haveused
2
H
NMR to study CB9CB and found that
152
the deuterium quadrupolar tensor in the twist-bend nematic 153
phase was uniaxial which is in accord with the global 154
symmetry of the phase. Their results are consistent with earlier 155
measurements made on CB7CB-d
4
[2]. Hoffmann et al. [27] 156
argue that the lack of local biaxiality shows that the phase does 157
not have the structure proposed for the twist-bend nematic. 158
However, it has been pointed out [28] that sufficiently rapid 159
translational diffusion along the helix axis will average out the 160
local biaxiality, as happens with conventional chiral nematic 161
phases. Proton NMR measurements have indeed shown that 162
translational diffusion parallel to the helix axis is fast enough 163
to remove the biaxiality of the quadrupolar tensor, which as a 164
result appears to be uniaxial [28]. 165
The
2
H
NMR studies were performed on a sample of the
166
dimer CB9CB doped with 2 wt% of CB7CB-d
4
[2]. This 167
particular spin probe was chosen as the deuterium source 168
because of its structural similarity to the host, CB9CB; the 169
transition temperatures of CB7CB are just a few degrees lower 170
than those of CB9CB; as a result the transition temperatures of 171
the doped samples are depressed by about 1 K by the addition 172
of the probe. 173
B. Experimental techniques 174
Heat capacity measurements at atmospheric pressure were 175
made using a commercial differential scanning calorimeter 176
DSC-Q2000 from TA Instruments working in the modulated 177
mode (MDSC). Like an alternating current (ac) calorimeter, the 178
MDSC technique, besides providing heat capacity data, simul- 179
taneously gives phase shift data that allow the determination of 180
the two-phase coexistence region for weakly first-order phase 181
transitions. In our work, experimental conditions were adjusted 182
in such a way that the imaginary part of the complex heat 183
capacity data vanished. The MDSC technique is also suitable 184
for quantitative measurements of latent heats for first-order 185
transitions, even if they are weak. A more detailed description 186
of the MDSC technique can be found elsewhere [29]. 187
002500-2
TWIST, TILT, AND ORIENTATIONAL ORDER AT THE . . . PHYSICAL REVIEW E 00, 002500 (2015)
The MDSC measurements were made following different188
procedures. For a standard study of the overall thermal189
behavior of the sample, heating runs at 1 K min
−1
from room190
temperature up to the isotropic phase and cooling runs at191
several cooling rates were performed. Additionally, in order to192
study the nature of the N
TB
-N and N-I phase transitions, high-193
resolution heating and cooling runs at a rate of 0.01 K min
−1
194
were performed in a temperature interval of about 5 K around195
the transition. Modulation parameters (temperature amplitude196
and oscillation period) were ±0.5 K and 60 s in the standard197
mode and ±0.07 K and 23 s in the high-resolution mode.198
Sample masses (between 2 and 3 mg) were selected to ensure199
a uniform thin layer within the aluminum pans.200
Static dielectric permittivity measurements at 5 kHz were201
performed on an Instec cell of 8 μm thickness with antiparallel202
planar rubbing and a pretilt of between 1° and 3° (specified by203
Instec). The empty cell capacity was carefully calibrated before204
filling, and sealed afterward to prevent bubble formation. The205
experiment includes an Agilent Precision LRC meter E4890A206
that allows for the application of ac fields from 20 Hz to207
2 MHz with probe voltages up to 20 V
rms
. Samples were208
held on a hot stage (TMSG-600) with a temperature controller209
(TMS-93), both from Linkam. The hot stage was placed on210
a polarizing microscope (BH2 Olympus) equipped with a211
camera (Olympus C5050) for the observation and recording212
of optical textures. This setup was also employed for the213
measurement of the splay and bend elastic constants from214
the voltage dependence of the capacitance of the sample215
through the Fr
´
eedericksz transition. The electric-field strength216
was varied from 0.1to16V
rms
, with a waiting time of 30 s217
between the application of the field and the acquisition of218
the capacitance value to guarantee the achievement of the219
equilibrium director distribution. Details of the data analysis220
are given in Sec. III B 1.221
The complex dielectric permittivity ε
∗
(ω) = ε
(ω) −222
iε
(ω) was measured over the frequency range 10
3
−1.8 ×223
10
9
Hz by combining two impedance analyzers: HP4192A and224
HP4291A. High-frequency dielectric measurements require225
the utilization of cells with untreated metal electrodes. In our226
setup the cell consists of a parallel plate capacitor made of227
two circular gold-plated brass electrodes 5 mm in diameter228
separated by 50-μm-thick silica spacers. It was placed at the229
end of a coaxial line and a modified HP16091A coaxial test230
fixture was used as the sample holder and then held in a231
Novocontrol cryostat, which screens the system. Dielectric232
measurements were performed on cooling with different233
temperature steps being stabilized to ±20 mK.234
The
2
H
NMR spectra were measured on a Varian Che-
235
magnetics CMX Infinity spectrometer which has a magnetic236
field strength of 9.40 T. In the nematic phase the director237
is aligned parallel to the field and in the twist-bend nematic238
it is the helix axis that aligns parallel to the magnetic field239
[18]. The sample was placed in a short NMR tube 5 mm in240
diameter and the tube was arranged orthogonal to the magnetic241
field. The sample temperature is controlled by a Chemagnetics242
temperature controller; it is stable to ±0.3 K during the243
spectral measurements and the transition temperatures of the244
doped mesogen were used to calibrate the controller to about245
±0.5 K. The spectra were measured using a single pulse246
sequence with a pulse width of 5 μs. The relaxation delay247
between the end of the acquisition of the free induction decay, 248
FID and the pulse was set at 0.05 s. Typically 10000 FIDs 249
were acquired into 4096 words of computer memory with a 250
spectral window of 250 kHz. 251
III. RESULTS AND DISCUSSION 252
A. Mesophase behavior and calorimetry 253
The phase sequence of CB9CB was studied in the past by 254
means of high-resolution adiabatic calorimetry and conven- 255
tional DSC [4] revealing only two mesophases. By means of 256
x-ray investigations the high temperature phase was identified 257
as a conventional uniaxial nematic phase, and a second 258
unidentified nematic phase appeared at lower temperatures [4]. 259
Our studies of CB9CB show that on cooling from the isotropic 260
phase, a nematic phase is formed at about 394 K, as can 261
be clearly identified from the characteristic uniform nematic 262
texture obtained in planar cells, and the Schlieren texture 263
formed in cells with no alignment treatment. Further cooling 264
reveals another mesophase, which propagates along the cell 265
leading to an initial quasiuniform texture [see Fig. 2(a)] that 266
develops systematically into a striped texture [see Fig. 2(b)]. 267
The stripes grow slowly parallel to the surface easy axis with a 268
periodicity of the order of twice the cell thickness as reported 269
for other twist-bend nematic forming dimers [1,17]. For slow 270
cooling rates, the stripes are totally developed showing tilted 271
bands across them, as in a ropelike texture, characteristic of a 272
FIG. 2. (Color online) Optical textures obtained in 8-μm-thick
cells (antiparallel alignment, from Instec). (a) At the N
TB
-N transi-
tion; width of the microphotograph 575 μm. (b) Ropelike texture;
width of the microphotograph 300 μm.
002500-3
BEATRIZ ROBLES-HERN
´
ANDEZ et al. PHYSICAL REVIEW E 00, 002500 (2015)
FIG. 3. (Color online) Heat capacity data as a function of tem-
perature on heating at 1 K min
−1
after cooling the sample from the I
phase at 30 K min
−1
(open symbols) and 1 K min
−1
(full symbols).
Inset shows a zoom on the N
TB
-N and N -I transitions for both
conditions.
twist-bend nematic phase [2], while for faster cooling rates a
273
less uniform texture with regions of focal conics is observed.274
When rotating the sample with respect to the crossed polarizers275
bright and dark states are revealed which suggest that there are276
optical extinction positions that make an angle with the axis277
of the stripes.278
Measurements of the heat capacity as a function of temper-279
ature over a wide temperature range are given in Fig. 3. Black280
and red symbols correspond to data recorded on heating at281
1Kmin
−1
from 260 K with the sample in two different states:282
after cooling the sample from the isotropic phase at 30 K min
−1
283
(black symbols) and after slow cooling at 1 K min
−1
(red284
symbols). The fast cooling rate of 30 K min
−1
is sufficiently285
high to prevent crystallization and the twist-bend nematic286
phase becomes a glassy state ([N
TB
]
gl
). It should be stressed287
that for slower cooling rates (for example, 20 K min
−1
), the288
sample partially crystallizes giving rise to a coexistence of a289
crystalline state with a glassy state. Figure 3 clearly shows290
the characteristic heat capacity jump assigned to the glass291
transition and how the sample in the supercooled N
TB
phase292
crystallizes irreversibly on heating at about 285 K (black293
symbols). The crystalline state obtained in this way has the294
same heat capacity value as the crystalline state obtained295
by slow cooling (red symbols) but both crystalline states296
are clearly different as can be inferred from the separation297
of about 15 K of their melting points. Irrespective of the 298
initial crystalline state, once the phase transition to the lower 299
temperature nematic phase takes place, both the N
TB
-N and 300
the N-I phase transitions are observed to be identical as is 301
shown in the inset of Fig. 3. The characteristic temperatures 302
corresponding to the different phase transitions are listed in 303
Table I. 304
The MDSC technique through the heat capacity data allows 305
us to obtain the latent heat associated with the first-order phase 306
transitions. The total enthalpy change associated with any 307
transition (H
TOT
) can be written as 308
H
TOT
= H +
C
p
dT , (1)
where the second term on the right-hand side of Eq. (1)
309
is the pretransitional fluctuation contribution (C
p
being 310
the difference C
p
− C
p,background
due to the change in the 311
orientational order intrinsic to this transition) and H is 312
the latent heat which vanishes for second-order transitions. 313
In strongly first-order phase transitions, the second term of 314
the right-hand side of Eq. (1) can be neglected and the total 315
enthalpy change is identified with the latent heat associated 316
with the phase transition. This applies to the latent heat 317
obtained for the Cry-N
TB
transition (considering the crystal 318
phase formed by slow cooling), and the result is listed in 319
Table I. The results are in quite good agreement with the 320
value reported by Tripathi et al. [4]. The latent heat associated 321
with the N -I and N
TB
-N phase transitions deserves a special 322
mention and will be analyzed in the following sections: 323
Secs. III A 1 and III A 2. 324
1. The N-I phase transition 325
The theoretical description of the uniaxial N -I phase 326
transition through the Landau–de Gennes theory is similar 327
to the mean-field Landau model, but in the free energy density 328
expansion of the nematic phase in terms of the scalar order 329
parameter Q
N
, identified with the average value of the second 330
Legendre polynomial P
2
(cos θ
i
) with θ
i
the angle of the ith 331
molecule with respect to the nematic director, a cubic term B 332
is needed: 333
F
N
= F
I
+ AQ
2
N
+ BQ
3
N
+ CQ
4
N
+ DQ
6
N
+···. (2)
The B parameter is the so-called cubic invariant and is
334
responsible for the first-order character of the N-I phase 335
transition. If B is very small and the other parameters A 336
and C become simultaneously zero, the N -I phase transition 337
TABLE I. Transition temperatures (T
CryN
TB
, T
g
, T
N
TB
N
,andT
NI
) and transition entropies (S
CryN
TB
/R, S
N
TB
N
/R,andS
NI
/R).
T
CryN
TB
(K) S
CryN
TB
/R T
g
(K) T
N
TB
N
(K) S
N
TB
N
/R T
NI
(K) S
NI
/R Reference
– – – 377.22 0.037 ± 0.002 392.92 0.18 ± 0.02 Ref. [4]
a
380.45 – 395.90 – Ref. [4]
b
357.6
c
10.6
c
277.2
d
379.09 0.038 ±0.006
e
394.92 0.16 ±0.02
e
This work
a
Data from adiabatic scanning calorimetry (ASC) at 0.15 K h
−1
.
b
Data from DSC traces.
c
From MDSC data on heating at 1 K min
−1
. The sample was previously cooled at 1 K min
−1
.
d
From MDSC data on heating at 1 K min
−1
. The sample was previously cooled at 20 K min
−1
.
e
From MDSC data on heating at 0.01 K min
−1
.
002500-4
![FIG. 17. (a) The dependence of the order parameter, Sp , on the reduced temperature in the twist-bend nematic phase, both experimental (•) and calculated (—). (b) The dependence of the orientational order parameter for the para-axis of the cyanobiphenyl group, Snp , for CB7CB-d4 in CB9CB on the reduced temperature in the twist-bend nematic (indirect —) and nematic (direct ) together with comparable results for pure CB7CB-d4 (indirect —) and nematic (direct ) [45]. (c) The dependence of the conical angle, θ0, in the twist-bend nematic phase on the reduced temperature for CB7CB-d4 in CB9CB (—) and for pure CB7CB-d4 (—) [45].](/figures/fig-17-a-the-dependence-of-the-order-parameter-sp-on-the-nypoygfn.webp)
