Influence of flexible chain, polar substitution and hydrogen bonding on phase stability in Shiff based (4)PyBD(4I)BrA-nOBA series of liquid crystals

Article abstract of DOI:10.1080/15421406.2018.1455315

Shiff based Linear Hydrogen Bonded Liquid Crystalline homologues, viz., (4)PyBD(4^I)BrA-nOBAs for n = 2,3,4,5,6,7,8,10,11 and 12 are synthesized. ¹H-NMR and ¹³C-NMR studies confirm the formation of HBLC and IR confirms the

Full text of DOI:10.1080/15421406.2018.1455315

Molecular Crystals and Liquid Crystals
ISSN: 1542-1406 (Print) 1563-5287 (Online) Journal homepage: http://www.tandfonline.com/loi/gmcl20
Influence of flexible chain, polar substitution and
hydrogen bonding on phase stability in Shiff based
(4)PyBD(4I)BrA-nOBA series of liquid crystals
A. V. S. N. Krishna Murthy, P. V. Chalapathy, M. Srinivasulu, M. L. N.
Madhumohan, Y. V. Rao & D. M. Potukuchi
To cite this article: A. V. S. N. Krishna Murthy, P. V. Chalapathy, M. Srinivasulu, M. L. N.
Madhumohan, Y. V. Rao & D. M. Potukuchi (2018) Influence of flexible chain, polar substitution and
hydrogen bonding on phase stability in Shiff based (4)PyBD(4I)BrA-nOBA series of liquid crystals,
Molecular Crystals and Liquid Crystals, 664:1, 46-68, DOI: 10.1080/15421406.2018.1455315
To link to this article: https://doi.org/10.1080/15421406.2018.1455315
Published online: 21 Jun 2018.
Submit your article to this journal
View related articles
View Crossmark data
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=gmcl20

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
, VOL. , –
https://doi.org/./..
Influence of flexible chain, polar substitution and hydrogen
bonding on phase stability in Shiff based ()PyBD(I)BrA-nOBA
series of liquid crystals
A. V. S. N. Krishna Murthya, P. V. Chalapathya, M. Srinivasulub, M. L. N. Madhumohanc,
Y. V. Raoa, and D. M. Potukuchia
aDepartment of Physics, University College of Engineering, Jawaharlal Nehru Technological University, Kakinada,
India; bDepartment of Chemistry, Manipal Institute of Technology, Manipal Academy of Higher Education,
Manipal, India; cLiquid Crystal Research Laboratory, Bannari Amman Institute of Technology, Sathyamangalam,
India
ABSTRACT
KEYWORDS
Linear hydrogen bonding;
liquid crystal phases;
longitudinal dipole;
movement; phase stability;
Shiff based
Shiff based Linear Hydrogen Bonded Liquid Crystalline homologues,
viz., (4)PyBD(4I)BrA-nOBAs for n = 2,3,4,5,6,7,8,10,11 and 12 are synthe-
1
sized. H-NMR and 13C-NMR studies confirm the formation of HBLC
and IR confirms the linear hydrogen bonding. Liquid crystal phase
abundance, transition temperatures, enthalpy and order of transition
are investigated by Polarized Optical Microscopy textural studies and
Differential Scanning Calorimetry. Nematic, Smectic-A, -D, -C, Bhexatic
,
-BCrystal, -F, -I and –G phases are identified. Large LC phase variances, viz.,
NAB FG and NACFG are exhibited by intermediate chain length with
n =h5exand 6. A-C transition exhibited unique II-order nature. II-order
nature for G-Solid transition explained. Phase diagram drawn with
flexible chain length infers INA, and ACF and CIF MultiCritical Points
and Lifshitz behaviour. NA TriCiritical Point predicted in [3+7] binary.
Influences of chain length, linear HB and end polar(-Br) substitution
for LC phase stability are is discussed. Results of Phase stability are
discussed in the wake of the body of the data and reports in other
LCs. DSC enthalpy suggests for utility of intermediate and higher
homologues for device savvy tilted Smectic LC phases.
1. Introduction
Achiral and chiral versions of liquid crystal (LC) compounds are identified as excellent
electro-optic (EO) materials [1–3] owing to the large birefringence, viewing angle and
contrast ratios in the respective phases of device interest. Among various LC phases, the
Nematic and tilted Smectic phases or their chiral analogues are characterized [1–2] for their
utility in EO displays. Although Nematic phase based devices are known to operate at milli
second speed, chiral tilted smectic phase based devices are known [3] to operate at micro
second and sub-nano second speeds. Hence, synthetic chemists pursue their research activity
for the strategic design of LC molecules capable of exhibiting EO interested phases in the
vicinity of ambient temperatures. As to meet the essential requirement of imparting certain
CONTACT PV Chalapathy
pallavajhula_vc@yahoo.com
Jawaharlal Nehru Technological University, Kakinada , India.
Department of Physics, University College of Engineering,
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gmcl.
©  Taylor & Francis Group, LLC

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
47
rigidity-to-flexibility ratio the molecular body, synthetic chemists frequently consider the
following design [4, 5] features, viz.,
a) lateral polar group substitutions [6] on the end-chain
b) attaching flexible component [4, 7] as end chain whose length can be varied
c) electro-negative O-like bridging [8, 9] atom/group between flexible end chain and rigid
core to enhance lateral stacking for a possible layered smectic phases
d) conjugated environment [4, 10] through ester moieties for interaction between rigid
core and polar/chiral substitutions on flexible end-chain
e) involving [11, 12] hydrogen bonding (HB) with inclined spread over the molecular
frame and
f) varying the length of spacer [13] moiety in dimer LCs. to realize enhanced Nematic or
tilted Smectic phase stability towards room temperature.
With a perspective to realize device LC savvy phases, synthetic chemists profusely reported
work on Shiff based [7, 14, 15] LCs. Shiff based LCs of calamitic type are known to exhibit rich
diversity of smectic polymorphism. Nevertheless, polar substitutions at one end of the LC
molecule (with -CN, -OH, -OR, -R, -X/halogen etc.,) is known [6] to enhance longitudinal
dipole moment, and thereby, influence the LC phase stability. The field of LC supra-molecular
chemistry involves soft-covalent interaction [9, 10] through hydrogen bonding, i.e., by linear,
double and complementary etc., types. HBLCs are found to exhibit enhanced tilted smectic
phase stability for device utility. Design of an HBLC requires at least two chemical moieties,
viz., a moiety with proton acceptor, and the other with a proton donor group/atom. HB can
be realized in LCs by adopting either of the following three strategies for selection of chemical
moieties;
i) Both of the moieties being mesogenic to anticipate mesogenic HBLC product,
ii) Either of the mesogenic moieties to ensure probable mesogenic product and
iii) None of the mesogenic moieties on HB-interaction may form mesogenic product
The selection of both of the moieties to be mesogenic, represents the most successful route
to synthesize HBLCs. However, a variety of proton acceptor/donor moieties are selected for
the realization of HBLCs with enhanced tilted phase stability, large tilt angle in the vicinity of
room temperature. During the selection of proton acceptor/donor moieties, a pyridyl moiety
with a proton acceptor N-atom appears to be one of the frequently adopted [11, 16–23]
strategie−s.δNevertheless, selection+oδf an organic acid (-COOH) moiety comprised of carbonyl
=
(>C O ) and hydroxyl (–OH ) groups as proton acceptor and donors, respectively is
also reported frequently. In fact, selection of aromatic organic acids with alkoxy(–OR),
alkyl(–R) and polar (halogen atoms, cyno group etc.,) substitutions at para (or ortho)-
positions are profusely reported. HBLC cyclic dimers are known for considerably wide
mesomorphic phase stability.
An overview of the reports in HBLCs hints for the adoption of a hybrid strategy to enhance
tilted smectic stability. Hence, authors aim for the design of a novel series of HBLCs by a
possible involvement of a Pyridyl moiety, Shiff based central rigid core, and para-positioned
substitutions with polar atoms (Br-like halogen atom) or alkoxy flexible chain. The article
is organized in three sections. Introduction LCs, HB and device interests are presented in
Section 1. The details of the chemical moieties, solvents, synthetic route and experimental
techniques for preliminary phase characterization are presented in Section 2. The stability
cum purity of the HBLC product, spectroscopic confirmation for the formation of targeted
HBLC complex, characterization of LC phases by polarized optical microscopy (POM) and
differential scanning calorimetry (DSC) are presented in Section 3 along with the discussion
of results.

48
A. K. MURTHY ET AL.
Scheme . Three-step synthetic route for preparation of ()PyBD(I)BrA-nOBA’s.
2. Materials and experimental methods
2.1. Synthesis of PyBBr:nOBA hydrogen-bonded LC complex
The chemical ingredients, viz., 4-pyridine carboxaldehyde, 4-Bromo Aniline and 4-n-alkoxy
benzoic acids, nOBAs, for n = 3 – 8 and 10 – 12 were procured from Sigma Aldrich, (USA).
The AR grade ethanol(double distilled), Acetic acid and TetraHydroFuran (THF) were pro-
cured from CDH, India.
The three-step synthetic route adopted for the preparation of HBLCs was presented in
Scheme 1. In the 1st step, the starting materials, viz., 4-pyridine carboxaldehyde and 4-Bromo
Aniline (which are non-mesogenic) were mixed in cold conditions, in equimolar (1:1) ratio
in presence of ethanol. Since the aim is to prepare a Shiff based intermediate, it falls under
the category of condensation reaction. As such, few drops of glacial acetic acid were added
to promote the yield of Shiff based product. The intermediate product was isolated by filtra-
tion. The solvent was removed under reduced pressure. Shiff based intermediate product, viz.,
(4)-pyridyl-benzylidene-(4ꢀ)-BromoAniline, PyBDBrA appeared in white color. White colour
product initially ensured it’s purity. In the 2nd step, the naturally available dimeric form of
nOBA’s (for n = 3–8, 10–12) was converted in to their monomer form by dissolving in excess
amount of Tetrahydrofuran (THF). In the 3rd step, the monomer form of nOBA was reacted
with the intermediate product PyBDBrA, by mixing them in 1:1 molar ratio in presence of
additional amount of THF. The reactants were stirred up at room temperature for 4–6 hours.
Refluxing of the reactants was carried out for over 3 hours of time. The solvent was removed
by distillation under reduced pressure conditions. The resulting HBLC complex was isolated.
The proposed molecular formula for the HBLC product would be (4)PyBD(4I)BrA-nOBA
which was presented as final HBLC product in Scheme 1.
The presence of H-atoms and C-atoms in the targeted HBLC complex were qualitatively
1
determined by acquiring H NMR(Tetramethyl Silane as internal standard) and 13C NMR
spectra with the help of AVANCE, 300 MHz NMR spectrometer using Dueterated chloro-
form as solvent. The formation of HB-complex and its configuration on the molecular body
was confirmed with the help of Shimadzu-8701 FTIR Spectrometer by recording solid state
KBr spectra. The 1H NMR, 13C NMR and FTIR spectra were used [24–26] for the qualita-
tive confirmation of the molecular (complex) structure regarding the presence of H-atoms

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
49
and C-atoms. Purity of the sample is checked by recording the melting and clearing transi-
tion temperatures over repeated scans of heating and cooling. Invariant melting and clearing
transition temperatures were considered as signatory measures for the purity of sample. The
LC phases were characterized by textural studies with the help of an SD Tech. Optical Polariz-
ing Optical Microscope (POM equipped CCD camera and accessed to μ–master software) in
conjunction with an INSTEC 402 hot stage (Device Tech., USA) comprised of STC 200 heat-
ing system. The heating and cooling rates employed during the DSC scans were 5°C/minute.
Microscopic slides for LC samples were prepared by unidirectional rubbing technique. LC
sample is sandwiched between the glass plate and cover-slip of the slide. Further, Device Tech
(USA) made polyimide buffed thin transparent glass cells (of 4.5 µm spacing) filled with LC
sample were also used as homogeneously aligned slides. The transition temperatures (Tc) and
the enthalpy (ꢀH) associated with phase transitions involving LC phases were determined by
a Shimadzu DSC-60 instrument. The cooling and heating scans implemented during POM
measurements were 0.1°C.
3. Results and discussion
3.1. Purity and stability of HBLC
Re-crystallization followed by repeated runs of heating and cooling runs are carried out until
the transition temperatures are found to be reproducible. Melting transition temperature is
determined in the heating run, at which solid phase of LC sample melts in to the LC phase
exhibiting a characteristic POM texture. Clearing transition temperature is determined in the
heating run at which LC phase transforms in to isotropic liquid phase identified by the dis-
appearance of LC texture. Reproducibility and repeatability of melting and clearing transi-
tion temperatures for HBLC complexes reflected up on the chemical stability and prelimi-
nary purity of the sample. The chemical stability of the sample is also confirmed basing on
the observation of LC phase transition temperatures which are found to remain invariant over
a number of repeated heating and cooling scans. As the melting and clearing transition tem-
peratures remained invariant, the LC samples are confirmed to be devoid of impurities even
at trace level.
3.2. Spectroscopic confirmation for HBLC complex
The number of H-atoms and C-atoms present on the molecular body of HBLC complex are
determined by 1H NMR and 13C NMR spectra, respectively. Identification of soft-covalent
interaction between proton donor and acceptor (i.e., as HB) is carried out by with the help of
Fourier Transform Infra-Red spectra.

... H NMR Spectra
In the wake the molecular formula, viz., (4)PyBD(4I)BrA:nOBA presented in Section 2
(Scheme 1) for n = 12, the number of H- atoms expected to be 39. 1H NMR spectra observed
for (4)PyBD(4I)BrA:12OBA (as representative) is presented in Fig. 1. Salient features of the
observed 1H NMR spectra are:
1) A triplet at δ 0.887–0.920 ppm reflects the presence of end methyl group pertaining to
nOBA moiety of the HBLC complex infers 3-H atoms.

50
A. K. MURTHY ET AL.

Figure . H-NMR spectrum for ()PyBD(I)BrA-OBA.
2a) Multiplet in the range of δ 1.288–1.370 ppm infers the presence of 16-H atoms in the
nOBA’s side chain pertaining 8-methylene groups sans the methyline unit connected
to end methyl group and first methyline unit connected to O-atom of nOBA.
b) Multiplet in the range of δ 1.465–1.501 ppm infers the presence of 2-H atoms of
methylene unit connected to end methyl group of nOBA moiety.
c) Multiplet in the range of δ 1.807–1.844 ppm infers the presence of 2-H atoms in
the second methylene connected from O-atom side of nOBA moiety.
d) Triplet at δ 4.022–4.055 ppm infers the presence of 2-H atoms corresponding to
the first methyline unit from O-atom side of nOBA moiety.
3ai) Doublets at δ 6.938–6.960 ppm infers the presence of 2-H atoms corresponding to
each of the ortho-situated C-atoms from O-atom side of aromatic nOBA.
aii) Doublet at Aromatic Proton (Ar–H) δ 7.798–7.812 ppm infers the presence of
2-H atoms corresponding to two C-atoms which are ortho-positioned to the
aromatic C-atom on -COOH side of nOBA.
bi) Doublet at δ 8.068–8.090 ppm infers the presence of 2-H atoms of two aromatic
C-atoms of pyridyl moiety which are ortho-situated from Shiff base side.
bii) Doublet at δ 8.819–8.833 ppm infers the presence of 2-H atoms corresponding
to the C-atoms in pyridyl moiety which are situated in ortho-position to N-
atom.
ci) Doublet at δ 7.144–7.166 ppm infers the presence of 2-H atoms corresponding
to the Shiff base side of C-atoms of the Bromoaniline moiety.
cii) Doublet at δ 7.553–7.574 ppm infers the presence of 2-H atoms corresponding
to the ortho-situated C-atoms Br-substitution side of Bromoaniline moiety.
4) A singlet at δ 8.465 ppm infers the presence of 1-H atom corresponding to the C atom
of Shiff base.
5) A singlet at δ 10.20 ppm infers 1-H atom in the –COOH miety of nOBA.
6) A singlet peak at δ 7.28 ppm is due to residual protons corresponding to the impurities
of the solvent.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
51
Figure . C-NMR spectrum for ()PyBD(I)BrA-OBA.
Observed 1H-NMR data (viz., detailed by points-1 to -6) viewed over the standard NMR
data [24–26] confirms the presence of 39 H-atoms on the body of targeted HBLC com-
plex(PyBBr:12OBA). Since observed number of H-atoms in (4)PyBD(4I)BrA:12OBA agrees
with the expected number, the product formation is confirmed successful.
... C NMR spectra
As per the general molecular formula presented in Section 2 (Scheme 1) for HBLC complex,
(4)PyBD(4I)BrA:nOBA for n = 12, C-atoms are anticipated to exhibit signals pertaining to
the end-chain (-C12H23) of nOBA; Aromatic moieties (of nOBA, Br-Aniline, Pyridyl moiety);
13
13
–
= –
Acid group (–COOH of nOBA) and Shiff base ( CH N ) in their C NMR spectra. The C
NMR spectra for (4)PyBD(4I)BrA:12OBA is presented in Fig. 2 (as representative). Salient
features of the 13C NMR spectra are:
1a) Peak at δ 14.1 ppm infers presence of C-atom of end –CH3 group of nOBA.
b) Peaks in the range of δ22.69–31.92 ppm infer the presence of C-atoms in the —
[CH2]- groups of nOBA moiety.
c) Peak at δ68.27 ppm corresponds to C-atom connected to O-atom of –OC12H23
chain in nOBA.
d) Peak in the range of δ76.70–77.0 ppm corresponds to C-atom of solvent, viz.,
Deuterated Chloroform (CDCl3).
2 i) Peaks at δ114.15, 116.74, 121.95, 122.65, 132.18 and 163.44 ppm infer the presence of
aromatic carbons of the aromatic ring of nOBA.
ii) Peaks at δ122.45, 142.88 and 150.21ppm infer the presence of aromatic C-atoms
of the pyridyl moiety.
iii) Superposed peaks at δ120.69, δ122.65 and single peak at δ149.76 ppm infer the
presence of aromatic C-atoms of the bromoaniline moiety.
–
=
3) Peak at δ158.11 ppm infers the presence of C-atom of CH N group.
4) Peak at δ170.85 ppm infers the presence of C-atom corresponding to –COOH group
of the nOBA.
Observed features (i.e., 1–4) of 13C NMR spectra compared with standard NMR spec-
tra [24–26] are found to infer the presence of all the C-atoms at the expected positions on

52
A. K. MURTHY ET AL.
Figure . FTIR spectrum for ()PyBD(I)BrA-OBA.
the body of HBLC complex. Since observed 13C-NMR signals agree with those expected for
(4)PyBD(4I)BrA:12OBA, the formation of HBLC complex is confirmed successful.
... FTIR spectroscopy
It is reckoned that FTIR spectra of free nOBA’s in their dimeric form exhibited [25] FTIR
absorption of doublet at 1700 cm−1 (relevant to >C O) and a singlet at 3500 cm−1 (relevant
=
to –OH stretching of –COOH moiety). The N-atom in the free pyridyl moiety is also reported
[25] to exhibit an IR absorption at 1500 cm−1. Observed IR spectra for (4)PyBD(4I)BrA:nOBA
(for n = 7 as a representative) is presented in Fig. 3. Data of IR absorption for the HBLCs in
(4)PyBD(4I)BrA:nOBA’s is presented in Table 1.
Salient features of FTIR Spectrum for (4)PyBD(4I)BrA:7OBA are:
1) A sharp absorption is observed at 1474 cm−1. In comparison with the reported [25]
absorption by free pyridyl moiety, it is found to exhibit a bathochromic shift of 26cm−1.
Oberved IR absorption at a lower wave number than that expected for a free N-atom
of pyridyl moiety is interpreted as the participation of N-atom of pyridyl moiety in HB
interaction.
2) A strong absorption is observed at 2924 cm−1. In the wake of reported [25] IR data, it
is identified as a bathochromic shift of 76 cm−1. Observed IR absorption is interpreted
due to H-atom (of -OH group) in nOBA moiety, while it’s bathochromic shift is argued
to reveal the participation of hydroxyl group pertaining H-atom in HB interaction.
Table . IR absorption data for ()PyBD(I)BrA-nOBA’s.
IR Absorption /cm−
=
=
=
n in
>C N- stretching in
-OH (hydroxyl)
stretching in nOBA
CH N- stretching in
>C O (carbonyl)
stretching in nOBA
()PyBD(I)BrA:nOBAs
Pyridyl ring
Shiff base
2


























----













3
4
5
6
7
8
10
11
12

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
53
3) A single peak is observed at 1682 cm−1. In the wake of the standard IR reports
[25], single IR peak is argued due to the O-atom of carbonyl stretching of nOBA
moiety. Observed single absorption ∼1700 cm−1 also reveal a bathochromic shift.
Bathochromic shift and single absorption peak together confirm the participation of
O-atom in the HB interaction.
Cited experimental observations from 1 to 3, when overviewed, reflect up on the existence
of linear hydrogen bonding extending from H-atom (of –COOH moiety as proton donor) to
the N-atom (of intermediate Shiff based moieties pyridyl ring as proton acceptor).
Further, an IR absorption is also observed at 1605 cm−1. In the wake of standard reports
of IR absorption [25], this observation is attributed to the presence of free N-atom of the
–
= –
shiff-base ( CH N ) group. Thus, observed IR spectrum also infers the non-participation
of Shiff based intermediate’s N-atom and prevalence of linear HB interaction in the
HBLC.
3.2.4. Polarized optical microscopy (POM)
The POM investigations are carried out in the help of microscopic slides (prepared by
sandwiching LC between glass plate and cover-slip) for HBLCs with ensured homoge-
nous alignment. As the POM textures are accompanied with transient and minute changes
(i.e., paramorphotic textural changes) in the vicinity of boundaries of focal conic fan domains,
a meticulous POM study is also carried out over the LC filled (4.5 µm thick Device Tech)
cells. LC sample is filled in to the cell by the capillary action of the LC in its high temperature
isotropic liquid state. As the cell walls are pretreated, the LC sample is ensured with homoge-
nous alignment. The LC slide (or cell) is placed in the Instec temperature controller, and
subsequently placed on the stage of microscope. The phase transitions and transition temper-
atures are determined by comparing observed POM textures with the reported [27] textures.
Textural changes are recorded in both of the heating and cooling scans. Temperature at which
textural change occurs is identified as phase transition temperature Tc. It is also observed that
certain textures are grown by the involvement of paramorphotic changes. Paramorphotic
changes call-on for meticulous and keen observation. The data for phase transition tem-
peratures (Tc) involving LC phases (for heating and cooling scans) are presented in Table 2.
Nematic phase exhibits schlieren brush (Plate 1) and schlieren threaded (Plate 2) textures.
SmA phase is found to exhibit focal conic fan (Plate 3) texture. Growth of SmD phase is
identified by the appearance of pseudo-isotropic black-background domains (Plate 4) in
the precursor Nematic fluid. SmC phase is found to exhibit typical mosaic threaded texture
(Plate 5) with sandy surface in fan domains. SmBhex phase is found to exhibit diffused focal
conic fan texture (Plate 6) with tiled cross-lines in focal conic fans. SmBcryst phase exhibits
(Plate 7) glossy focal conic platelet texture. SmI phase is found to exhibit diffused coloured
mosaic thread (Plate 8) texture. SmF phase exhibits (Plate 10) typical mosaic threaded
(Plate 9) texture. SmG phase is found to exhibit characteristic mosaic texture.
Although X-ray investigations could give the clinching evidence for the abundance of LC
phase structures, a preliminary POM based identification of LC phases is presented in Table 2.
Preliminary identification of LC phases through POM is ranked scientific as it involves com-
parison with standard [27] experimental reports.
Details of phase sequence during heating/cooling scans and phase variance exhibited
by (4)PyBD(4I)BrA:nOBA series of HBLCs is also presented in Table 2 for their analysis.
Although most of the LC phases are found to grow in both of the heating and cooling

54
A. K. MURTHY ET AL.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
55

56
A. K. MURTHY ET AL.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
57
Plate . Nematic brushes exhibited by ()PyBD(I)BrA-OBA at °C.
Plate . Nematic schlieren threaded texture of ()PyBD(I)BrA-OBA at °C.
Plate . SmA focal conic fan texture of ()PyBD(I)BrA-OBA at °C.

58
A. K. MURTHY ET AL.
Plate . SmD psuedo-isotropic domains in Nematic of ()PyBD(I)BrA-OBA at °C
Plate . Coloured mosaic texture of SmC of ()PyBD(I)BrA-OBA at °C
Plate . SmBhex smeared focal conic fans of ()PyBD(I)BrA-OBA at °C

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
59
Plate . SmBcry focal conic platelet texture of ()PyBD(I)BrA-OBA at °C
scans (i.e., enantiotropic), certain phases are found occur in either of the scans only. The
latter type of LC phase growth is known as monotropic occurrence. The details of LC phase
occurrence and their nature whether as enantiotropic or monotropic is detailed in Table 3.
Enantiotropic LC phase occurrence is found to prevail for over sixteen times in even num-
bered (of C-atoms in flexible chain) homologues. Monotropic occurrence of LC phases is
found to prevail over nine times in even homologues and four times in odd homologues.
Nematic phase is found to exhibit enantiotropic abundance. Hence, its enantiotropic occur-
rence is attributed to the underlying 1D-order (viz., orientational order parameter) of the
phase structure. Nematic phase stability in HBLCs is found to be larger than that reported
[11, 12] for pure nOBAs. Enhanced Nematic stability is attributed to the substitution of
electronegative Br-atom at the para-position of Shiff based moiety on the body of calamitic
Plate . Diffused mosaic texture of SmI of ()PyBD(I)BrA-OBA at °C

60
A. K. MURTHY ET AL.
Plate . Mosaic threaded texture of SmF of ()PyBD(I)BrA-OBA at °C
HBLC’s molecular body. Rarely appearing SmBhex, SmD and SmI phases are also found to
exhibit monotropic occurrence. SmG is found to exhibit monotropic occurrence for over
4-times. Monotropic occurrence of SmC is observed for even numbered (n = 8 and 12)
higher homologues only. SmD and SmBhex phases are found grow in cooling runs.
It is found that intermediate homologues, viz., for n = 5 and 6 exhibited largest LC phase
variances., i.e., as penta-variant NABhexFG and NACFG sequences, respectively. Largest LC
phase variance for intermediate homologues infers their predominant viability in fundamen-
tal and application aspects of HBLCs. Observed LC phase sequence (in heating or cooling
scans) is found to agree with the standard [27] thermal order to underline the systematic
growth of LC structural order.
Plate . SmG mosaic texture of ()PyBD(I)BrA-OBA at °C

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
61
Table . LC monotropic/enantiotropic phases for )PyBD(I)BrA-nOBA’s.
n in ()PyBD(I)BrA-nOBAs
LC Phase
Enantiotropic
Monotropic
N
, , , 
, , ,,
—
(c), (c)
(c)
(H),(H)
(c)
(H)
(H)
SmA
SmD
SmC
SmBHex
SmBCry
SmI
—
, , , ,
—


SmF
SmG
, , , , ,,
, , , ,,
(c)
(H), (H), (c),(H)
(H) in heating; (C) in cooling
3.3. Differential scanning calorimetry (DSC)
DSC thermograms reflecting the heat flow envisaged across LC structural phase transitions,
i.e., during the heating and cooling scans in (4)PyBD(4I)BrA-nOBA series of HBLCs are pre-
sented in Fig. 4 (for n = 7 as representative). The Temperature at which thermogram exhibits
a dip in heating scan, or a peak in cooling scan is identified as transition temperature Tc.
The area (under the peak/dip wrt to the base line) mechanically estimated by the instrument
represents the heat (enthalpy ꢀH) of transition. The peaks and dips in thermograms and
the area under the peaks/dips reflect the underlying change of structural order across the
phase transition involving LC phases. The data for phase transition temperatures (Tc) and
enthalpy (ꢀH) involved with the transitions involving LC phases are presented in Table 2.
The LC phase transition temperatures (Tc) are found to agree with the results of POM
textures.
As ꢀH of DSC reflects change in structural order, data relevant to various LC phase with
characteristic order is also presented in Table 4 for its further analysis. As all observed transi-
tions across the isotropic phase and LC phase involve the growth of LC characteristic orien-
tational order from the disordered liquid, they are anticipated to accompany with finite non-
zero enthalpy. Such, transitions are labeled as first order natured transitions. The I-SmBcryst
;
Figure . DSC thermogram for ()PyBD(I)BrA-OBA.

62
A. K. MURTHY ET AL.
Table . Order of LC transitions in ()PyBD(I)BrA-nOBA’s.
Order of transition and enthalpy /ꢀH in J/gm
st order
n in ()PyBD(I)BrA-nOBA
Scan
nd order
2
H
C
H
C
H
C
H
C
H
C
H
C
H
C
H
G–Bcrst[.]; BCry–Iso[.]
Sld–G
—
Iso– BCry[.]; BCry–F[.]; F–Sld[.]
G–F[.]; F–N[.]; N–Iso[.]
3
Sld–G
—
Iso–N[.]; N–F[.]; F–Sld[.]
4
5
G–C[.]; C–N[.]; N–Iso[.]
Sld–G
G–Sld
Sld–G
—
Iso–N[.]; N–D[.];D–C[.]; C–G[.]
G–F[.]; F–A[.]; A–N[.]; N–Iso[.]
Iso–N[.]; N–A–Bhex–F[—.—]; F– G[.]; G–Sld[.]
G–F[.]; F–C[.]; A–N–Iso[–.–]
Iso–N[.]; N–A[.]; C–F[.]; F–G[.]
Sld–F[.]; F–C[.]; A–Iso[.]
6
7
Sld–G, C–A
A–C, G–Sld
C–A
Iso–A[.]; C–F[.]; F–G[.]
A–C, G–Sld
—
8
10
Sld–G[.];G–F[.]; F–Bcrst[.]; Bcrst–C[.]; C–Iso[.]
Iso–A[.]; A–F[.]; F–G[.]; G–Sld[.]
G–F[.]; F–I[.]; I–C[.]; A–Iso[.]
—
Sld–G, C–A
C
H
C
H
C
Iso–A[.]; C–I–F[–.–]; F-Sld#
G–F[.]; F–C[.]; A–Iso[.]
Iso–A[.]; C–F[.]; F–G–Sld[.]
Sld–G[.]; G–C[.]; C–Iso[.]
Iso–A[.]; A–G[.]; G–Sld[.]
A–C
Sld–G, C–A
A–C
11
12
—
—
#from POM
I-N and I-SmA transitions (Table 2) are observed to accompany with finite ꢀH. Hence, I-
SmBcryst; I-N and I-SmA transitions are attributed with first order nature. Certain DSC ther-
mograms are observed to accompany with shoulders on one (or either) side of the DSC
peak/dip. Observed shoulders are interpreted as un-resolved DSC peaks/dips superposed over
the main peak due to the fast scanning rate. Hence, the enthalpy corresponding to such transi-
tions is presented (as extended solid line over two Tc in Tables 2 and 4) as spread between two
braces demarcating transitions. Observed larger ꢀH across certain first order transitions is
argued due to the underlying greater structural change. But, certain transitions are accompa-
nied with very small ꢀH value. They are labled as weak first order transitions involving small
structural change. Weak first order transitions are also argued to occur due to the very small
thermal span for the pre-cursor phase. The weak first order nature of transition with smallꢀH
in these HBLCs witness the growth of minute structural order at the interface. Therefore, the
observed transitions, viz., SmF-SmG transition (for n = 7 in cooling); SmG-solid transition
(for n = 5 and 8 in cooling) and SmF-SmI transition (for n = 10 in cooling) are argued to be
of weak-first order nature in these series of HBLCs. It is also noticed that some of the transi-
tions are not accompanied with any enthalpy. Observation of null enthalpy involvement sug-
gests for the continuous nature of transtion. SmA–SmC transitions in n = 6, 7, 10 and 11 are
observed to accompany with zero ꢀH value. Growth of long range tilt order parameter across
SmA-SmC phase transition is found [28] to be analogous to suppression of second harmonic
sound and to exemplify a classical second order transition. Thus, observed second order
nature the SmA–SmC transition in these HBLCs is found to agree [28] with the theoretical
prediction.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
63
It is noticed from POM and DSC that these series of HBLCs exhibit a total number of 90 LC
phase transitions. A large number of 72 first order (i.e., including the weak-first order) tran-
sitions are observed to involve finite enthalpy. But, SmA-SmC transition is found to uniquely
exhibit second order nature. Other distinct observation is regarding the occurrence of second
order nature for some SmG-Solid phase transitions. SmG represents a 3D analogue of tilted
Smectic phase. SmG-Solid transformation involves a change of 3D tilted LC structure to 3D
orthogonal crystalline Solid. Thus, SmG-solid transition is argued to represent a metamor-
phosis, possibly without the involvement of any enthalpy. As, the crystalline dimensionality
would not undergo any change across this transition, II-order nature witnessed across SmG-
solid transition would be argued to augment the expectation.
Although LC monotropic phase occurrence remained an enigma, observed prevalence of
monotropic abundance in (4)PyBD(4I)BrA-nOBA series hints for its analysis in terms of
the total enthalpy involved with their change of room temperature abundant solid form to
isotropic liquid form. As such, the so estimated total enthalpy and it being conservation dur-
ing the cyclic heating (from room temperature to isotropic liquid state) followed by cooling
(back and down to room temperature) processes need to be analyzed for a possible clue to
resolve monotropic occurrence. The total enthalpies, viz., ꢁꢀHheat and ꢁꢀHcool are esti-
mated by adding the enthalpy (Table 4) values observed in heating and cooling scans, respec-
tively. ꢀHheat reflects the input of heat energy and ꢀHcool reflects the evolved heat energy.
Hence, their difference, viz., [ꢁꢀHheat−ꢁꢀHcool] is argued to reveal the thermal efficiency
of the LC system to realize smectic phases of device relevance. Care is taken to include the
enthalpy of transitions involving monotropic LC phases also. Analysis of ꢁꢀH is anticipated
to reveal the aspect of heat energy conservation in terms of absentee LC phases and underlying
structural variance. Differential total enthalpy [ꢁꢀHheat−ꢁꢀHcool] in a cyclic heating-cum-
cooling scans is also estimated. Further, the estimates of ꢁꢀH and [ꢁꢀHheat−ꢁꢀHcool] are
analyzed in the domain of varied chain length (n) in the HBLC series. Enthalpy analysis as a
function of n is supposed to reveal the influence of flexibility component for polymorphism
and monotropic occurrence. As such, the data of ꢁꢀH, ꢁꢀH and [ꢁꢀHheat−ꢁꢀHcool] are
individually plotted (Fig. 5) against variation in chain (n) length.
From Fig. 5, it is observed that:
i) ꢁꢀH in both of heating and cooling scans exhibit odd-even effect.
Figure . Integrated and differential enthalpy for ()PyBD(I)BrA-nOBAs.

64
A. K. MURTHY ET AL.
ii) ꢁꢀH in cooling scan is higher than that in heating scan for intermediate and higher
(n > 6) homologues.
iii) ꢁꢀH for lower homologues in heating scan is larger than for HBLCs for n ࣘ 6 (except
for n = 3).
iv) [ꢁꢀHheat−ꢁꢀHcool] is accompanied with negative values for n = 3, 7, 8, 10, 11 and
12.
iv) [ꢁꢀHheat−ꢁꢀHcool] exhibits an overall descending trend from a higher positive value
to a lower negative value.
vi) descent for [ꢁꢀHheat−ꢁꢀHcool] and its lower values indicate the involvement lower
heat supply (exchange) for Smectic polymorphs to get realized by increasing chain
length.
Overview of enthalpy and its comparative analysis did not yield any rational argument for
monotropic occurrence as a function of flexible component. However, the cited i- to vi-factors
considered together defends to opt for higher homologues (with large flexible component) to
realize device savvy smectic polymorphism.
3.4. Phase diagram and tricritical and multicritical points
A phase diagram (Fig. 6) is drawn to analyse the LC phase abundance with increasing length
(n-value) of flexible chain. The data of Tc relevant to cooling scan in Table 2 is used. All the
LC compounds are found to exhibit marginal odd-even effect at the clearing temperature, viz.,
Isotropic to Nematic, Isotropic to SmA and Isotropic to SmBcry transition interfaces. But, odd-
even effect in the transition temperatures in the vicinity of melting transition (i.e., Smectic-F to
Solid; Smectic-G- to solid transitions) is observed to be more rigorous. Solid phase represents
the most condensed 3D structure and the particle separation would be minimum. As such, the
Coulumbic interaction between them would be strong to influence the solid phase stability.
Interaction strength would be manifested through solid to LC phase transition temperatures
(i.e., melting temperatures). The axial polarizabilities [29] are anticipated to an alternating
magnitude with each of the increment of methyline group. Further, as they are docked to the
rigid core at the para-position, they are argued to play a dominant role to stabilize LC phases,
especially towards lower temperature phases involving condensed solid phases.
Figure . LC phase diagram for ()PyBD(I)BrA-nOBAs.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
65
The phase diagram (Fig. 6) drawn in these HBLCs reflects up on the occurrence of diversi-
fied smectic polymorphism and Nematic phases with varying length of flexible end chain.
Occurrence of Nematic phase (with orientational order only) and rich diversity of Smec-
tic phases (orientational order with additional intra-layer and inter-layer ordering) infers a
strong influence of flexible component. Observed influence of flexible component in HBLCs
is found to be analogous to the reports [30] of NA interface in binary mixtures of mesogenic
7CB and n-Heptane with equivalent flexible chain length. Increasing flexibility in a series is
found to result for the deviation from 3D-XY universality class for NA transition. It is of com-
parative interest to refer [31] to the effective chain length (where n∗ reflects the flexibility of
strongly polar LC binaries, viz., nOCB/mOCB) could tune the growth of re-entrant Nematic
(RN) phase from inter-digitated SmA phase. In view of the observed wide ranged and diversi-
fied smectic polymorphism in HBLCs, a meticulous analysis of phase diagram is carried out.
Phase diagram indicates a possibility for the realization of TriCritical Points (TCP) and of
MultiCirtical Points (MCP) in these series of HBLCs. Critical points, where exotic crystalline
symmetries [32, 33] involving 1D and Quasi-2D crystalline orders converge to represent a
fundamental aspect of interest. Careful study of Fig. 6 infers three such MCPTs, viz.,
i) an INA
ii) an ACF and
iii) a CIF
demarcated by coloured squares for n = 7, 8 and 11 compounds. Hence, the HBLCs for
n = 7 and 8 are identified to exhibit INA and ACF and CIF MultiCritical Points. AC interface
is found to exhibit (Table 2) second order nature and is found to agree (28) theoretical pre-
diction. IF transition involves change of quasi-2D [27] crystal’s tilt direction, viz., from apex
to the side of a hexagon, to usher a second order transition. But, the point, where two second
order transition interfaces meet with one first order transition interface is known as Lifshitz
point [32, 34] with its fundamental aspects of interest. Out of the three identified MCPTs in
the phase diagram (Fig. 6), a Lifshitz behavior is expected in the vicinity of ACF and CIF
points, owing to the fact that AC and IF interfaces are classical second order interfaces.
LC NA and AC interfaces are known to exhibit Tricritical [35] behavior, where the order
of the transition changes from second order to first order nature. It may be reckoned [35] that
NA interface can be realized in the binary by varying the component of flexible component.
Presently, HBLC for n = 3 is witnessed by wide Nematic range to usher a possible second order
NA transition. HBLC with n = 7 does not exhibit Nematic phase. For NA transition, N-phase
is a precursor phase in cooling scan. As one approaches the binary [3+7] by increasing the
component of n = 7, at a sumptuously small range of precursor N-phase, the NA transition’s
order is expected to trigger to first order nature from second order nature. As such, at a pos-
sible composition, the [3+7] binary is predicted to exhibit TriCiritical behavior. A clear way
of navigation towards TCP is illustrated by a set of hypothetical blue coloured NA interfacial
lines along with its possible direction by arrow head line in Fig. 6.
3.5. Influence of flexible chain and linear hydrogen bonding for abundance of device
savvy tilted smectic LC phases
In order to study the influence of linear HB and flexibility component in calamitic HBLCs with
a perspective of their device viability, the overall LC phase stability ꢀTLC, Nematic phase sta-
bility ꢀTN and tilted Smectic phase stability ꢀTtilt are estimated from the data of Tc in Table 2.
However, as one of the ingredients used to prepare Linear HBLCs are inherently mesogenic

66
A. K. MURTHY ET AL.
Figure . LC phase stability for ()PyBD(I)BrA-nOBAs and nOBAs.
nOBA, the corresponding overall LC phase stability and Nematic/tilted Smectic phase stabil-
ity are estimated for pure nOBAs and presented through a histogram in Fig. 7. Salient features
of Fig. 7 reflect that:
i) a maximum overall LC phase stability (ꢀTLC) by HBLC with n = 10. ꢀTLC is found to
be enhanced by involving HB interaction and specific chain length.
ii) approach of ꢀTLC towards its maximum for intermediate homologues in HBLCs and
nOBAs. Approach of maximum value infers an optimal flexibility to rigidity ratio in
series of calamitic type of HBLCs.
iii) lower homologues (for n ࣘ 7) exhibit Nematic phase. Realization of Nematic phases in
calamitic linear HBLCs emphasize lower flexiblity-to-rigidity ratio in liner HBLCs.
iv) HBLC with n = 7 get induced with maximum tilted smectic polymorphism (ꢀTtilt),
while homologues with n = 2, 7 and 8 resulted for its effluence.
v) even homologues (i.e., for n = 2, 6, 8 and 10) also exhibited large tilted smectic stabil-
ity ꢀTtilt. Although ꢀTtilt is known to be exhibited by odd-homologues only, possible
inclination of linear HB interaction might have resulted for out-board projection of
transverse dipole moment to infer large ꢀTtilt.
4. Conclusions
Overview of experimental observations in (4)PyBD(4I)BrA-nOBA series of calamitic linear
HBLCs infer:
r
Largest phase variance for intermediate homologues.
Prevalent monotropic LC phase abundance in Shiff based calamitic linear HBLCs.
Rich Smectic polymorphism results by including Shiff based moieties in HBLCs.
Overall LC phase stability can be enhanced by involving HB interaction.
Higher heat energy intake is involved for lower homologues of linear HBLCs.
Higher heat energy is evolved by higher homologues of linear HBLCs.
Difference between heating scan enthalpy and cooling scan enthalpy exhibits decreasing
trend with flexible component (n).
r
r
r
r
r
r
r
Device savvy tilted smectic polymorphism would be realized in higher homologues.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
67
r
r
r
r
Even members witness enhanced tilted smectic polymorphism due to inclined spread of
linear HB.
Intermediate and higher homologues predominantly exhibit tilted smectic polymor-
phism.
INA, ACF and CIF MultiCritical Points and Lifshitz points can be realized in linear
HBLCs.
Large Nematic range for n = 3 and quenched Nematic phase for n = 7 predicts existence
of an NA TriCrtical Point in the [3+7] binary.
References
[1] Maier, G., Sackmann, E., & Grabmaier, J. G. (1975). Applications of Liquid Crystals; Spinger-Verlag:
Berlin, Germany.
[2] Demus, D. (1976). in Non Emissive Electro-optic Displays; 94, Ed: A. R. Knetz & F. K. Von Willison,
Plenum Press: New York; Mosley. (1993). Displays; 14(2), 67.
[3] Goodby, J. W., Blink, R., Clark, N. A., Lagerwall, S. T., Osipov, S. A., Pikin, S. A., Sakurai, T.,
Yushino, & Zeks, B. (1991). in Ferro-Electric Liquid Crystals, Principles, Properties and Applica-
tions; Gordon and Breach, (Eds.) Philadelphia.
[4] Demus, D., Demus, H., & Zaschke, H. (1974). Flussgie Kristalle in Tabellen; VEB Deutcher Verlag
fur Grundestoffindustrie: Liepzig.
[5] Luckhurst, G. R., & Gray, G. W. (1979). in Molecular Physics of Liquid Crystals; Academic Press:
New York.
[6] Ashok Kumar, A. V. N., Sridevi, B., Srinivasulu, M., Chalapathy, P. V., & Potukuchi, D. M. (2014).
J. Mol. Liqd., 41, 184 and the references there in.
[7] Pisipati, V. G. K. M. (2003). Z. Naturforsch., 58a, 661.
[8] Coates, D. (1987). Liq. Cryst., 2(4), 423.
[9] Bhagavath, P., Mahabaleswara, S., Bhatt, S. G., Potukuchi, D. M., Chalapathy, P. V., & Srinivasulu,
M. (2013). J. Mol. Liq., 186, 56.
[10] Kumar, P. A., & Pisipati, V. G. K. M. (1998). Adv. Mater., 12, 1617.
[11] Kato, T., & Frechet, J. M. J. (1989). J. Am. Soc., 111, 8533–8534; Frechet, J. M. J., & Kato, T. (1992)
US Patent No. 5139, 696.
[12] Paleos, C. M., & Tsiourvas, D. (1995). Angew. Chem., Int. Ed. Engl., 34, 1696; ibid. (2001). Liq.
Cryst., 28, 1127; Sideratou, Z., Tsiourvas, D., Paleos, C. M., & Skoulios, A. (1997). Liq. Cryst.,
22, 51.
[13] Ashok Kumar, A. V. N., Chalapathy, P. V., Srinivasulu, M., Muniprasad, M., & Potukuchi, D. M.
(2015). J. Mol. Struct., 1079, 94 and the references there in.
[14] Godzwon, J., Sienkowska, M. J., & Galewski, Z. (2008). Act. Phys. Pol. A., 113, 1145.
[15] Rananavare, S. B., & Pisipati, V. G. K. M. (2011). in Trans World Research Network; 19–52, ISBN:
978-81-7895-523-0.
[16] Tian, Y., Xu, X., Zhao, Y., Tang, X., & Li, T. (1997). Liq. Cryst., 22, 87.
[17] Kihara, H., Kato, T., Uryu, T., Ujhe, S., Kumar, U., Frechet, M., Bruce, W. D., & Price, J. D. (1996).
Liq. Cryst., 21, 25.
[18] Srinivasulu, M., Satyanarayana, P. V. V., Kumar, P. A., & Pisipati, V. G. K. M. (2001). Mol. Mater.,
14, 215.
[19] Swathi, P., Kumar, P. A., & Pisipati, V. G. K. M. (2000). Liq. Cryst., 28 , 1163; ibid. (2001). Liqd.
Cryst., 27, 665.
[20] Srinivasulu, M., Satyanarayana, P. V. V., Kumar, P. A., & Pisipati, V. G. K. M. (2001). Liq. Cryst.,
28, 1321; ibid (2001). Z. Naturf., 56a, 685.
[21] Srinivasulu, M., Satyanarayana, P. V. V., Kumar, P. A., & Pisipati, V. G. K. M. (2001). Liq. Cryst.,
28, 1321.
[22] Swathi, P., Sastry, S. S., Kumar, P. A., & Pisipati, V. G. K. M. (2001). Mol. Cryst., Liq. Cryst., 365,
523.
[23] Biligi, G., & Koen, B. (2000). Liq. Cryst., 27, 851.

68
A. K. MURTHY ET AL.
[24] Silverstein, R. M., & Webster, F. X. (2004). in Spectroscopic Identification of Organic Compounds
(6th Ed.); John Wiley & Sons, Inc.: New York.
[25] Nakamoto, K. (1978). Infra-Red and Raman Spectra of Inorganic and Co- ordination Compounds
(4th ed.); Inter-Science Publishers: New York.
[26] William, K. (2008). Organic Spectroscopy; Replika Press Pvt. Ltd.: Haryana, India.
[27] Gray, G. W., & Goodby, J. W. (1984). in Smectic Liquid Crystals – Textures and Structures; Leonard
Hill: London.
[28] de Gennes, P. G. (1993). in The Physics of Liquid Crystals; Ed: W., Marshall & D. H., Wilkinson,
Clarendon Press: Oxford, UK.
[29] Marcelja, S. (1974). J. Chem. Phys., 60, 3599.
[30] Yamamura, Y., Taniguchi, y., Yasuzuka, S., Yamamura, Y., & Saito, K. (2011). J. Chem. Phys., 135,
044705; doi:10.1063/1.3615491.
[31] Yamamaoka, Y., Tsuchiya, R., Fuzimura, S., Hishida, M., & Saito, K. (2017). J. Phys. Chem. B., 1438;
doi:10.1021/acs.jpcb.6b12977.
[32] Stanley, H. (1971). in Introduction to Phase Transitions and Critical Phenomena; Clarendon press,
p.10; Lawrie, I. D., & Sarbach, S. (1984). in Introduction to Phase Transitions and Critical Phenom-
ena; No.9, Ed: C. Domb & M. S. Green, Academic Press.
[33] Litster, J. D., Birgeneau, R. J., Pershan, P. E. (1982). Physics Today, May; Brock, J. D., Birgeneau, R.
J., Litster, J. D., & Aharany. (1989). Physics Today, 52, July.
[34] Rananavare, S. B., Pisipati, V. G. K. M., & Wong, E. W. (1994). Phys. Rev. Lett., 72, 3558 and the
references there in.
[35] Ocko, B. M., Birgeneau, R. J., & Litster, J. D. (1986). Z. Cond. Mater. Phys. B., 62, 487.