Effect of the surfactant head-group size dependence of the dye-surfactant interactions on the lyotropic uniaxial to biaxial nematic phase transitions

Article abstract of DOI:10.1016/j.molliq.2021.115842

In the present study, the interactions of the anionic azo dye Sunset Yellow with dodecylalkylammonium bromide (DAABr) surfactants in lyotropic mixtures have been investigated for the stabilization of the different lyotropic nematic phases. Sunset Yellow doped mixtures of DAABr surfactants, with different head-group size, were studied by polarizing optical microscopy, laser conoscopy, and small-angle X-ray scattering. It was found that the extent of the interaction of Sunset Yellow with DAABr surfactant head groups on micelle surfaces affects the stabilization of different nematic phases, by causing the change in the micellar structural parameters. The results also indicated that the micelle surface curvature should be different in the three nematic phases.

Full text of DOI:10.1016/j.molliq.2021.115842

Journal of Molecular Liquids 332 (2021) 115842
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Effect of the surfactant head-group size dependence of the dye-surfactant
interactions on the lyotropic uniaxial to biaxial nematic phase transitions
a
a
b
b
Erol Akpinar a, , Nazli Uygur , Oznur Demir Ordu , Dennys Reis , Antônio Martins Figueiredo Neto
⁎
a
Bolu Abant Izzet Baysal University, Faculty of Arts and Sciences, Department of Chemistry, 14030 Golkoy, Bolu, Turkey
Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao, No. 1371, 05508-090, Sao Paulo, SP, Brazil
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 8 January 2021
Received in revised form 19 February 2021
Accepted 1 March 2021
Available online 4 March 2021
In the present study, the interactions of the anionic azo dye Sunset Yellow with dodecylalkylammonium bromide
(DAABr) surfactants in lyotropic mixtures have been investigated for the stabilization of the different lyotropic
nematic phases. Sunset Yellow doped mixtures of DAABr surfactants, with different head-group size, were stud-
ied by polarizing optical microscopy, laser conoscopy, and small-angle X-ray scattering. It was found that the
extent of the interaction of Sunset Yellow with DAABr surfactant head groups on micelle surfaces affects the sta-
bilization of different nematic phases, by causing the change in the micellar structural parameters. The results
also indicated that the micelle surface curvature should be different in the three nematic phases.
© 2021 Elsevier B.V. All rights reserved.
Keywords:
Lyotropic uniaxial and biaxial nematic phases
Anionic azo dye Sunset Yellow
Surfactant-dye interaction
Polarizing optical microscopy
Laser conoscopy
Small-angle X-ray scattering
1. Introduction
nematic phases and also to find the factors for obtaining the biaxial ne-
matic phase [21–25]. These factors were revealed from the perspective
Understanding the stabilization of the lyotropic uniaxial and biaxial
nematic phases is an active experimental research field. Mainly, the im-
portant feature of uniaxial lyotropic nematic phases which attracts the
attention of the researchers is the preferred alignment of their phase di-
rectors with respect to the applied magnetic field. This preferential
alignment is also an important parameter in the classification of
lyotropic nematic phases and arises from the diamagnetic susceptibility
of the surfactant alkyl chains [1–3]. Three types of lyotropic nematic
phases were identified. In the uniaxial discotic (ND) and calamitic (NC)
of choosing the suitable constituents of lyotropic mixtures by examining
inter- and intra-aggregates (i.e., micelles) interactions. The structural
units of the lyotropic nematic phases, ‘micelles’ formed by surfactants,
are very sensitive to modifications both in the micelle core and on the
micelle surfaces. For instance, the relative alkyl-chain lengths of surfac-
tants (nsurf) [25] and cosurfactants (ncosurf) [21] play a key role on the
stabilization of uniaxial and biaxial nematic phases. The biaxial nematic
phase domain in a partial phase diagram can be observed if ncosurf
=
nsurf 2, at least for the chosen surfactant/cosurfactant systems in
nematic phases, the director !n aligns perpendicular and parallel to the
magnetic field direction, respectively, in the case of the main amphi-
[21,25]. Because the alkyl chains of both surfactants and cosurfactants
have non-polar character, the ncosurf = nsurf 2 rule is mainly related
to the effect of the interactions between those alkyl chains in the
micelle core.
phile having carbonic chains. There!exist two optical axes and three or-
!
!
!
thogonal two-fold symmetry axes, l , m and !n, where !n ¼ l x m [4–8]
in the lyotropic biaxial nematic phase (NB). Furthermore, the experi-
mental studies proved that, in general, the NB phase region is located be-
tween the two uniaxial nematic phases in the phase diagrams [9–11].
Moreover, the transitions from the NB phase to the ND or NC phases
are of second order, as theoretically predicted [12,13].
The interactions on the micelle surfaces are also important, similarly
to the interactions in the interior of the micelles. In the case of the mi-
celles with ionic surfactants, there exist repulsions between the surfac-
tant head groups on the micelle surfaces. Different types of nematic
phases may be obtained by controlling the characteristics of these re-
pulsions. For instance, when an electrolyte is added to the lyotropic
mixture, its oppositely charged ions are bound to the surfactant head
groups, decreasing the micelle surface curvature strongly or loosely
[26], due to the screening of the repulsions [27–29]. In the former and
latter cases, the stabilization of the ND and NC is more favored, respec-
tively, and intermediate level of the interactions between ions and
head groups is responsible for the stabilization of the NB [11,24].
In early studies, researchers focused on whether the NB phase was a
distinct thermodynamically stable phase [10,14–20]. Recent studies
have contributed to clarify the stabilization mechanism of the different
⁎
Corresponding author.
E-mail address: akpinar_e@ibu.edu.tr (E. Akpinar).
https://doi.org/10.1016/j.molliq.2021.115842
0167-7322/© 2021 Elsevier B.V. All rights reserved.

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Surfactant-electrolyte ions interactions are also important in isotro-
pic dilute-aqueous solutions [27,30–32], which may be assumed as the
precursors of the lyotropic nematic phases [22,24]. Because both sys-
tems consist of the same structural units, i.e., ‘micelles’, information ob-
tained from one system can be useful to the other [24,33]. For instance,
the presence of the electrolyte ions causes the increase in micelle size
[34,35], leading to the packing of larger amount of the surfactant mole-
cules in the micelles, in the isotropic [7,36,37] and lyotropic [33,38,39]
solutions of surfactants. The change in micelle shape anisotropy, espe-
cially for the lyotropic nematic phases, is related to the extent of inter-
actions between ionic species, surfactant head groups and ions of the
electrolytes present in the solution. Experimental studies indicated
that the extent of those interactions is based on the “kosmotropic”
and “chaotropic” character of the ionic species [11,22–24]. Collins
et al. summarily defined these two characteristic properties of the
ionic species as the more or less hydration of the ions by surrounding
water molecules [40,41]. The ionic species with similar extent of the
kosmotropic/chaotropic characters leads to the formation of close con-
tact ion pairs [42–45].
In a previous study, we investigated the isotropic micellar solution and
lyotropic nematic phase properties of some tetradecylalkylammonium
bromides by changing their head-group sizes [11]. That study mainly fo-
cused on the effect of the interactions between the conventional inorganic
salt (electrolyte) ions, considering the Hofmeister series anions, and sur-
factant head groups with different sizes. The results indicated that those
interactions areveryeffectiveonthe stabilizationof differentlyotropicne-
matic phases. The information obtained from the isotropic micellar aque-
ous solutions of tetradecylalkylammonium bromides/inorganic salts
gave valuable hints for the interpretation of the interactions observed in
the lyotropic nematic phases.
Another important type of interaction in micellar solutions is the
surfactant-dyeinteractions,whicharecrucialforsomeindustrialandbio-
technological applications in the dilute isotropic micellar solutions
[46–54].Recently,theeffectofthepresenceoftheazodye‘SunsetYellow’,
which consists of polyaromatic planar core and ionic parts at the periph-
ery, has been investigated in the lyotropic mixtures of dodecyl-
trimethylammonium bromide/Sunset Yellow/1-dodecanol/water. It
wasshown that SunsetYellow can beboundto the micelle surface stron-
gerthantheconventionalinorganicelectrolyteionsandgiveslargerbiax-
ialnematicphasedomaininthephasediagrams[55].Thus,dyemolecules
may be used to stabilize different lyotropic nematic phases insteadof the
inorganic salts to obtain larger temperature range of the biaxial nematic
phase.
In 2013, Cheng et al. studied one-dimensional nano-structured aggre-
gatepropertiesofsomeanionicazodyes,includingSunsetYellow,interms
of their interactions with cationic conventional and gemini surfac-
tants [56]. In general, while those dyes, except Sunset Yellow, produced
nano-structured aggregates (nano-fibers, nano-helixes or nano-rods)
with gemini surfactants, Sunset Yellow gave block-type aggregate with
the same gemini surfactant as a result of the decrease in the inter-
actionbetweendyesandsurfactants.Inthesamestudy,authorsalsoinves-
tigated the interactions of the dyes, which formed the nano-structured
aggregates, with dodecyltrimethylammonium bromide (DTMABr),
dodecyltriethylammonium bromide (DTEABr) and dodecyltripropy-
lammonium bromide (DTPABr). They concluded that, as the surfactant
head-groupsizegetslarger,thecurvatureoftheaggregatesincreases.Sim-
ilar to the case of dye-gemini surfactant mixed systems, the interaction
between the dyes and the conventional surfactants is stronger in dyes/
DTMABr and weaker in dyes/DTPABr mixed systems. Thus, it is clear that
the interactions of dyes with surfactants depend on the size of the surfac-
tant head group.
lyotropic nematic phases, especially the biaxial one, from the surfactant
head-group size dependence of the dye-surfactant interactions point of
view. For this purpose, some dodecylalkylammonium bromide surfac-
tants with different head-group sizes were used to prepare mixtures
presenting the lyotropic nematic phases. The effects of the interaction
of Sunset Yellow with those surfactants were investigated via polarizing
optical microscopy, laser conoscopy and small-angle X-ray scattering.
The results indicated, as we will show in the further parts of the present
study, that the degree of the interactions between the surfactant head
groups and Sunset Yellow influences the stabilization of the different
lyotropic nematic phases.
2. Experimental
2.1. Materials
Dodecyltrimethylammonium bromide (DTMABr), dodecyldimethy-
lethylammonium bromide (DDMEABr), 1-bromododecane, alkylamines
(dodecylamine, N-methyldodecylamine, N,N-dimethyldodecylamine,
diethylmethylamine and triethylamine), hydrobromic acid (HBraq
)
and 1-dodecanol (DDeOH) were purchased from Sigma-Aldrich and
Merck with a purity of >98–99%. The anionic azo dye, Sunset Yellow
(SSY), was also commercially available from Sigma-Aldrich with a dye
content of 90% and it was purified three times considering the proce-
dure given in [57,58]. The purification degree of the Sunset Yellow
was confirmed from the phase transition temperatures of 30% aqueous
lyotropic chromonic solution of Sunset Yellow, as described in [55].
Ultrapure water, provided by the Millipore Direct-Q3 UV purification
system with 18.2 MΩ.cm of resistivity at 25 °C, was used for the prepa-
ration of lyotropic liquid crystalline mixtures.
2.2. Synthesis and characterization of surfactants
DTMABr and DDMEABr are commercially available surfactant mole-
cules. Dodecylammonuim bromide (DABr), dodecylmethylammonium
bromide (DMABr), dodecyldimethylammonium bromide (DDMABr)
were obtained from the reaction of dodecylamine, N-methyldodecylamine
and N,N-dimethyldodecylamine, respectively, with HBr(aq). Diethyl-
methylamine and triethylamine were reacted with 1-bromododecane for
the preparation of dodecyldiethylmethylammonium bromide (DDEMABr)
and dodecyltriethylammonium bromide (DTEABr) as follows. A two-fold
molar excess of the alkylamine was mixed with 1-bromododecane in etha-
nol and refluxed. The progress of the reactions was monitored by thin-layer
chromatography carried out on 0.25 mm silica gel plates (60F-254) using
UV light as visualizing agent, and KMnO4 solution and heat as developing
agents. After the reaction was completed, a yellow two-phase mixture was
obtained. This mixture was concentrated by rotary evaporation. After pre-
cipitation by ether and subsequent filtration a solid residue was obtained.
Sometimes the mixture had to be chilled to obtain precipitation. This solid
residue was then purified by recrystallization from chloroform-ether, and
subsequent filtration followed by drying under vacuum resulted in surfac-
tants as white solids. All dodecylalkylammonium bromide surfactants,
DAABr, (synthesized and purchased ones, Fig. 1) were characterized by 1H
nuclear magnetic resonance (1H NMR) and Fourier transform infrared
(FTIR) spectroscopy techniques. 1H NMR spectra were recorded on JEOL
NMR spectrometer (400 MHz) at ambient temperature. All chemical
shifts (δ) are reported in part per million (ppm) downfield from TMS. The
abbreviations used for NMR signals are: s = singlet, t = triplet, q = quartet,
m=multiplet,brs=broadsinglet,brm=broadmultiplet.Infraredspectra
were recorded on a Shimadzu IR prestige-21 FTIR. The NMR results, includ-
ing commercially available ones for the comparison, are given in the
following.
While the effect of the dye-surfactant interactions depending on the
surfactant head groups was reported in the literature in isotropic micel-
lar solutions, this effect has not been systematically studied in the ne-
matic phases of lyotropic liquid crystals to obtain biaxial nematic
phase. In the present study we examine the stabilization of different
2

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
R1
N
Small-angle X-ray scattering (SAXS) was employed to measure and
calculate, in the framework of a model-based analysis, the structural pa-
rameters of the samples in their respective nematic phases. The exper-
imental setup, measurements' procedures, data treatment, and model
used for data analysis were detailed described in the Supporting Infor-
mation of [55].
Br
R2
R3
Fig. 1. Molecular structures of DAABr: R1 = R2 = R3 = –H for DABr; R1 = R2 = –H and
R3 = –CH3 for DMABr; R1 = –H and R2 = R3 = –CH3 for DDMABr; R1 = R2 = R3
–CH3 for DTMABr; R1 = R2 = –CH3 and R3 = –CH2CH3 for DDMEABr; R1 = –CH3 and
2 = R3 = –CH2CH3 for DDEMABr; R1 = R2 = R3 = –CH2CH3 for DTEABr.
=
3. Results and discussions
R
Itisknownthattheinteractionsbetweenionicspeciesonthemicelles'
surfaces affect the stabilization of different lyotropic nematic phases by
modifyingthepackingofthesurfactantmoleculesinthemicelles,thesur-
face curvature of the micelles, and the micellar shape anisotropy [11,33].
By modifying those interactions, the stabilization of different nematic
phases becomes possible. Moreover, the temperature range of the NB
phase in the partial phase diagrams can be controlled. This can be done
mainly in two ways, by considering the kosmotropic and the chaotropic
(preferencetobemoreorlesshydratedbywatermolecules,respectively)
properties of thesurfactant headgroupsand of the counterionsorionsof
the electrolytes present in the lyotropic mixtures: (a) using a surfactant
andchoosingionswithdifferentdegreeofthekosmotropic orchaotropic
characterwithrespecttoit[22,24];or(b)usingsurfactantswithdifferent
head-group sizes to change the degree of the kosmotropic or chaotropic
character of the surfactant head group and known electrolyte ion [11].
The latter way was followed in the present study. Thus, the interactions
between the SSY, which has chaotropic character with two ionic groups
at its periphery, and dodecylalkylammonium bromide surfactants with
different head group character will be investigated.
2.2.1. 1H NMR (400 MHz)
Dodecylammonium bromide(DABr), δ (ppm, CDCl3): 0.86(CH3, 3H, t),
1.23–1.30 (CH2, 16H, br m), 1.34–1.41 (CH2, 2H, m), 1.75–1.83 (CH2, 2H,
m), 3.02 (N+CH2, 2H, t), 7.92 (N+H3, 3H, br s).
Dodecylmethylammonium bromide (DMABr), δ (ppm, CDCl3): 0.84
(CH3, 3H, t), 1.21–1.28 (CH2, 16H, br m), 1.31–1.41 (CH2, 2H, m),
1.81–1.89 (CH2, 2H, m), 2.65 (N+CH3, 3H, t), 2.93 (N+CH2, 2H, br t),
8.92 (N+H2, 2H, br s).
Dodecyldimethylammonium bromide (DDMABr), δ (ppm, CDCl3): 0.83
(CH3, 3H, t), 1.20–1.29 (CH2, 18H, br m), 1.78–1.86 (CH2, 2H, m), 2.79
(N+CH3, 6H, t), 2.99 (N+CH2, 2H, t), 11.17 (N+H, 1H, br s).
Dodecyltrimethylammonium bromide (DTMABr), δ (ppm, CDCl3): 0.83
(CH3, 3H, t), 1.20 (CH2, 14H, br m), 1.30 (CH2, 4H, br m), 1.70 (CH2, 2H,
br m), 3.40 (N+CH3, 9H, s), 3.55 (N+CH2, 2H, t).
Dodecyldimethylethylammonium bromide (DDMEABr), δ (ppm,
CDCl3): 0.81 (CH3, 3H, t), 1.18 (CH2, 14H, br m), 1.29 (CH2, 2H,br m),
1.34 (CH3, 3H, t), 1.65 (CH2, 2H, br m), 3.33 (N+CH3, 6H, s), 3.45
(N+CH2, 2H, t), 3.66 (N+CH2, 2H, q).
The host mixture DTMABr/SSY/1-dodecanol/water (s4) was chosen
[55] and its composition is given in Table 1. As it is known, the head
group of DTMABr, –N(CH3)+3 , has a chaotropic character [61]. From
DTMABr to DABr, the head groups turn into less chaotropic, while the
head groups turn into more chaotropic from DTMABr to DTEABr. When
DTMABr was completely replaced by other surfactants (e.g., DTEABr/
SSY/1-dodecanol/water), their mixtures could not stabilize three ne-
matic phases. Considering the concentrations of substances in sample
s4, with DABr or DMABr, we did not get any homogeneous mixture.
WithDDMABr,alamellarphase(L)wasobtained(Fig.2a).DDMEABrsta-
bilized only the NC phase (Fig. 2b), while a hexagonal phase (H) was ob-
servedinthemixturesofDDEMABrandDTEABr(Fig.2candd).Becausea
completereplacementofDTMABrwithothersurfactantsdidnotstabilize
the three nematic phases, mixtures with twomainsurfactantswere pre-
pared by replacing 2.5% portions of DTMABr, in mole fraction, with other
dodecylalkylammonium bromides (DAABr), at total constant surfactant
concentrations.Inthisway,weallowedthemicellesurfacestobecovered
bylargerorsmallernumberof thechaotropic surfactantheads. Thefron-
tiers of the nematic phases' regions in the partial phase diagrams for
DTMABr/DAABr binary mixtures were determined from their texture
analysis by polarizing optical microscopy. The lyotropic nematic phases
exhibited the characteristic “schlieren” textures. At lower temperatures,
approximately below 13 °C, a gel-like phase was observed in all samples
[55]. At higher temperatures, first a nematic to nematic-isotropic phase
coexistence(2P)transitionwasobserved,andthen,byfurtherincreasing
the temperature, a 2P to isotropic phase (I) transition was observed. The
2P regions were rich in isotropic phase. The nematic to nematic phase
transition temperatures were determined by laser conoscopy and the
temperature ranges of the NB phase are given in Table 1.
Dodecyldiethylmethylammonium bromide (DDEMABr), δ (ppm,
CDCl3): 0.82 (CH3, 3H, t), 1.19–1.30 (CH2, 18H, br m), 1.34 (CH3, 6H, t),
1.60–1.67 (CH2, 2H, m), 3.22 (CH3, 3H, s), 3.34 (N+CH2, 2H, t), 3.57
(N+CH2, 4H, q).
Dodecyltriethylammonium bromide (DTEABr), δ (ppm, CDCl3): 0.82
(CH3, 3H, t), 1.19 (CH2, 18H, br m), 1.33 (CH3, 9H, t), 1.59–1.67 (CH2,
2H, m), 3.21 (N+CH2, 2H, t), 3.46 (N+CH2, 6H, q).
2.3. Preparation of lyotropic liquid crystal samples
Lyotropic liquid crystalline mixtures were prepared into well-closed
glass test tubes and then well-homogenized by applying vortex and
centrifuging at 25 °C with a temperature-controlled centrifuge. A
small amount of water-based ferrofluid (Ferrotec) was added into the
samples, at a concentration of 1 μL per 1 g of the mixture, to obtain
well-oriented nematic samples in the presence of an external magnetic
field for the measurements of polarizing optical microscopy, laser
conoscopy and small-angle X-ray scattering.
2.4. Experimental techniques
Polarizing optical microscopy was used to observe the textures and
measure the transition temperatures of the different lyotropic liquid
crystalline phases, using a microscope Eclipse E200POL (Nikon, Japan).
The usual procedure is described elsewhere [11].
Laser conoscopy was employed to measure the two optical birefrin-
gences Δn and δn as functions of temperature in the three nematic
phases of well-oriented samples in an external magnetic field. The opti-
cal birefringences are written as by Δn = n2 − n1 and δn = n3 − n2,
where n1, n2 and n3 are the principal refractive indices of the medium
along the 1, 2 and 3 axes of the laboratory frame. This technique was
used to unambiguously identify each nematic phase, to determine the
nematic uniaxial to biaxial phase transition temperatures and the
order of these transitions. The experimental setup and procedures, as
well as the samples' alignment procedure in the magnetic field, were
previously described [11,59,60].
Table1andFig.3clearlyshowthat,asthenumberofthe–CH2groupsin
the surfactant head groups from samples s1 to s7 increases, the ND-NB and
NB-NC phase transition temperatures shift to the higher values. Further-
more, the NC phase stabilization is favored while the ND and NB phase do-
mains get narrow, within the working-temperature range. Some models
were proposed in the literature to explain the stabilization mechanism of
the lyotropic nematic phases [15,62,63], but one of them seems to be
more appropriate to explain how the different nematic phases are stabi-
lized. This model, so-called ‘Intrinsically Biaxial Micelles’, or IBM, model
3

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Table 1
Mixtures' identifications, second main surfactant identifications, compositions in percent molar fraction (X), nematic to nematic phase transition temperatures, temperature range of the
B phase in °C (ΔTNB), and the average number of –CH2 groups in the head groups – see Eq. 1 - (navg).
N
Mixture
DAABr
XDTMABr
XDAABr
XSSY
XDDeOH
Xwater
Phase transitions
ΔTN
navg
B
14:95ꢀ
C
s1
s2
s3
s4
s5
s6
s7
DABr
4.856
4.856
4.856
4.981
4.856
4.856
4.856
0.125
0.125
0.125
0.000
0.125
0.125
0.125
0.132
0.132
0.132
0.132
0.132
0.132
0.132
1.792
1.792
1.792
1.792
1.792
1.792
1.792
93.095
93.095
93.095
93.095
93.095
93.095
93.095
–
–
–
2.93
2.95
2.98
3.00
3.03
3.05
3.08
ND
ND
ND
ND
ND
ND
ND
N
N
N
N
N
N
N
ƒƒƒƒ!
B
B
B
B
B
B
B
15:70ꢀ
C
DMABr
DDMABr
–
ƒƒƒƒ!
17:35ꢀ
C
ƒƒƒƒ!
21:15ꢀ
C
17:05ꢀ
C
4.10
3.70
3.20
2.75
N
N
N
N
ƒƒƒƒ!
ƒƒƒƒ!
C
C
C
C
21:35ꢀ
C
17:65ꢀ
C
DDMEABr
DDEMABr
DTEABr
ƒƒƒƒ!
ƒƒƒƒ!
21:85ꢀ
C
18:65ꢀ
C
ƒƒƒƒ!
ƒƒƒƒ!
23:05ꢀ
C
20:30ꢀ
C
ƒƒƒƒ!
ƒƒƒƒ!
[62,63] assumes the micelles have orthorhombic symmetry in the three
nematic phases and different orientational fluctuations are responsible
for stabilizing the different nematic phases. In the IBM model, the micelles
aresketched, ina firstorderapproximation, asrectangularparallelepipeds
(or a flatted prolate ellipsoid), with average dimensions A′, B′ and C′,
whereC′representsthemicellebilayerthickness. Theorientationalfluctu-
ations around the axis perpendicular to the A′ × B′ plane lead to the stabi-
lization of the ND phase, and those around the axis parallel to the
dimension A′ favor the stabilization of the NC phase. The NB phase is stabi-
lized when only small-amplitude orientational fluctuations exist around
the three orthogonal symmetry axes of the micelles. Considering the IBM
model and the results of samples s1 to s7, by increasing the head-group
size of the dodecylalkylammonium bromide surfactants, the orientational
fluctuations responsible for the stabilization of the NC phaseovercomethe
orientational fluctuations for the stabilization of the ND phase. Further-
more, the temperature range of the NB phase (ΔTNB) gets smaller, as
showninFig. 4.InFig. 4,ΔTNB wasplottedasafunctionoftheaveragenum-
ber of –CH2 groups in the head groups (navg), calculated from Eq. 1:
The micelle surface curvature is expected to increase in the sequence
from lamellar to ND, NB, NC, hexagonal and isotropic phases [64–66]. This
may be attributed to the increase in the repulsions between the head
groups and/or increase in the head-group size of the surfactant. Two fac-
tors are important to obtain different lyotropic structures, the tempera-
ture and the relative concentrations of the constituents of the mixture.
In our case, constituents' concentrations were kept constant. When tem-
perature increases, the phase sequence is NC, NB and ND for the mixtures
s4 to s7. It means that, as the temperature increases, the micelle surface
curvature gets flatter due to charge screening between the ionic head
groups of the surfactants on the micelle surfaces. This screening can
only be provided by binding larger number of ionic species, counterions
of the surfactants and/or ions of electrolytes present in the mixture.
However, it was reported for the isotropic micellar solutions of
DTMABr/water that the degree of counterion binding to the micelle de-
creases with the increase in the temperature [67,68]. Because the struc-
tural units of lyotropic systems are micelles, similar to the isotropic
micellar solutions, experimental studies indicated that the information
obtained from latter one can be applied to the former [23,24,33–37,69].
Our results can be interpreted as follows. When the temperature in-
creases, a fewer number of counterions, Br−, is bound to the micelle sur-
face. Assuming that, at least, some number of SSY anionic part is bound
instead of Br−, the dye-surfactant interactions get stronger to stabilize
the ND phase. This happens by screening of repulsions between the
head groups of the dodecylalkylammonium bromides rather than Br−
XDTMABr
Xtotal
XDAABr
Xtotal
navg
¼
nDTMABr
þ
nDAABr
ð1Þ
where nDTMABr and nDAABr are the numbers of the –CH2 groups in the
head groups of DTMABr and other dodecylalkylammonium bromides,
respectively. navg for all samples are shown in Tables 1 and 3.
Fig. 2. Textures of (a) lamellar phase of DDMABr; (b) NC phase of DDMEABr; and 2D-hexagonal phases of (c) DDEMABr and (d) DTEABr. A and P show the directions of the analyzer and the
polarizer, respectively. The long axis of the flat capillary was at 45° to both A and P. The white bar corresponds to 200 μm. The sample thicknesses are 200 μm.
4

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Fig. 3. Birefringences Δn = n2 – n1 (●) and δn = n3 – n2 (○) as functions of the temperature for mixtures given in Table 1.
counterions. This is an expected result because in our very recent study it
was shown that SSY has bigger chaotropic character than Br−, and the in-
teractions between SSY and DTMA+ head groups are stronger than those
between Br− and DTMA+ [55]. Thus, the laser conoscopy results shown
in Fig. 3 show that the dye-surfactant interactions control the stabiliza-
tion of different nematic phases better than the conventional inorganic
ions considering their chaotropic character. Furthermore, according to
the IBM model, as the temperature increases, the SSY-binding to the mi-
celle surface causes the micelle growth in the A′ × B′ plane, which favors
the orientational fluctuations around the axis perpendicular to that
plane, and the ND phase was observed.
chaotropic going from s1 to s7, i.e. from DABr to DTEABr. Indeed,
chaotropic or kosmotropic character is directly related to the ratio of
charge/diameter or charge per surface area of the ionic species [44]. As
expected, the apparent charge on the micelles [70] decreases from
DABr to DTEABr. For instance, it was reported that the values of the ap-
parent charges on the micelles are 15 1 and 6 1 for DTMABr and
DTEABr under same conditions, respectively [71]. At 14 °C, the samples
s1 to s3 stabilized the ND and NB phases but not the NC. From s4 to s7, the
samples exhibited the NC phase in addition to the ND and NB. At constant
temperature and relative concentrations, while the surfactant head-
group size of dodecylalkylammonium bromides gets larger (smaller),
the NC (ND/NB) phase stabilization is favored due to weakening
(strengthening) of the dye-surfactant interaction between the head
In the case of constant temperature and relative concentration of the
substances, for instance, at about 14 °C, the micelle surfaces are more
5

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
constructed considering the average number of the –CH2 group in the
head groups, Fig. 6. Furthermore, the change in ΔTNB is plotted in Fig. 7.
The partial phase diagram clearly shows that the extent of
surfactant-dye interactions is one of the factors that affects the stabiliza-
tion of different nematic phases. Remember that the strong (weak) in-
teractions between ionic species with similar (opposite) characters, in
terms of kosmotropic and chaotropic, favor the stabilization of lyotropic
ND (NC) phase [24].
The structural parameters of the samples given in Table 3 were also
evaluated from the SAXS measurements (Table 4). The results are sim-
ilar to those observed for other samples (Table 2). At a constant temper-
ature (Fig. 6), as the head-group size of dodecylalkylammonium
bromide increases, the shape anisotropy of the micelles decreases
(Table 4) and the NC phase is stabilized.
Fig. 4. Temperature range of the NB phase (ΔTN ) as a function of the average number of –
CH2 groups in the head groups (navg) for the binary main surfactant mixtures of
dodecylalkylammonium bromides. Solid line represents a linear fit.
B
To interpret the effect of the head-group size dependence of the dye-
surfactant interactions on obtaining different lyotropic nematic phases,
a complete comparison considering the SAXS results of all mixtures
studied according to the navg values is necessary and will be made in
the following. The structural parameters were plotted as a function of
the navg values of dodecylalkylammonium bromides, Fig. 8. The meth-
odology used to obtain these parameters was described in Ref. [55].
Within the experimental error, the change in the structural parameters
fits, in a first approach, to a linear behavior. The volume of surfactant
chain (v) values in the calculation of the average surfactant packing pa-
rameter, v/a0l, are obtained from Tanford's equation[72], v =
27.4 + 26.9 nc in Å3, where nc is the number of carbon atoms in the
alkyl chain of a surfactant molecule and its value is taken as 11 for all
dodecylalkylammonium bromides, because one –CH2 group is present
in the head groups. Furthermore, the length of the alkyl chain, l, corre-
sponds to half the micelle's core average bilayer thickness C′. The aver-
age a0 was calculated in the model-based analysis of the SAXS results
(Tables 2 and 4).
groups and the anionic parts of SSY molecules on the micelle surfaces.
This also shows that the chaotropic character of the SSY molecule is sim-
ilar to that of DDMABr rather than DTMABr because, as the surfactants
and ions have similar character, the ND and/or NB phases stabilization
are highly possible [24]. Considering the IBM model, the SSY/DAABr in-
teractions play a crucial role depending on the surfactant head-group
sizes to control the orientational fluctuations responsible to obtain dif-
ferent nematic phases. The interactions between the smaller surfactant
head groups than DTMABr and SSY dominantly favor the micelle
growth in the A′ × B′ plane. This situation is confirmed by SAXS data
given in Table 2. The dimension in the A′ × B′ plane decreases in the se-
quence DABr>DMABr>DDMABr>DTMABr. However, in the case of the
surfactants which have higher chaotropic character with respect to
DTMABr, the dimension of the A′ × B′ plane is almost unchanged. This
may be attributed to the relatively weakly SSY-binding to the micelle
surfaces, which favors the orientational fluctuations along the axis par-
allel to the A′ direction, to give the larger NC phase domain.
Ifwecomparethehostmixture,s4,withothersfromTable 1,theaddi-
tion or removal of the same number of –CH2 group in the head group of
DTMABr affects the nematic phase properties differently, e.g., nematic-
nematic phase transitions and the nematic-phase domains in the phase
diagrams. For instance, when 2.5% of DTMABr was replaced by DDMABr
at constant total mixture’ concentration, i.e., removal of one –CH2 group
in the head group, the ND-NB phase transition temperature changed
~3.8 °C and the NC phase was not observed anymore. However, when
same amount of DTMABr was replaced by DDMEABr, i.e., addition of
one –CH2 group in the head group, the ND-NB and NB-NC transitions
were shifted only 0.2 °C and 0.6 °C, respectively. Similar situation can be
seen for other mixtures. To clarify the reason why the removal of –CH2
group from the head group affects the nematic phase properties more
than the addition of –CH2 group to the head group, additional samples
were studied by preparing binary-surfactant mixtures of DTMABr/
DDMABr and DTMABr/DDMEABr, where the relative concentrations of
thesetwosubstanceswerechanged, keepingthetotalsurfactantconcen-
tration constant (Table 3). Fig. 5 shows the birefringences asa functionof
the temperature for these mixtures. The partial phase diagram was
It is interesting to note that, although samples s2 and s9 consisted of
different binary surfactants, DTMABr/DMABr with XDMABr/Xtotal = 2.5%
and DTMABr/DDMABr with XDDMABr/Xtotal = 5.0%, respectively, they
have similar nematic to nematic phase transition temperatures, ND–NB
is 15.70 °C for s2 and 15.05 °C for s9, and similar values of the structural
parameters (Fig. 8), within the experimental error (navg = 2.95 for both
samples). The samples s6 and s10 (XDDEMABr/Xtotal = 2.5% and XDDMEABr
/
Xtotal = 5.0%) exhibited the same behavior (navg = 3.05). Furthermore,
samples s6 and s10 gave very similar ΔTNB, 3.20 °C for s6 and 3.60 °C
for s10.
Table 5 summarizes the structural parameters' variations from
navg = 2.90 to navg = 3.15. As the head-group size of the dodecyl-
alkylammonium bromide increases the micellar dimensions A′ and B′
decrease about 16% and 12%, respectively, accompanying with the de-
crease in the Nagg (23%) and the SA (37%). This result seems to be due
to the weakening of the surfactant-dye interactions on the micelle sur-
faces. Furthermore, the water layer around micelles gets thinner due to
the hydration of the surfactant by less amount of water molecules
which arises from the existence of the larger amount of chaotropic
head groups at the micelle surfaces. Interestingly, although the decrease
Table 2
Structural parameters from SAXS measurements' results for samples given in Table 1. Mixture identification, micelle's core average dimensions (A′, B′, C′), average polar layer thickness
(w), average aggregation number (Nagg), average area per polar head (a0), average surfactant molecular packing parameter (v/a0l), and shape anisotropy, SA = {[(A ' + B')/2 – C']/
[(A ' + B')/2]}.
Mixture
A′ (Å)
B′ (Å)
C′ (Å)
w (Å)
Nagg
a0 (Å2)
v/a0l
SA
s1
s2
s3
s4
s5
s6
s7
53.9
51.4
50.5
46.9
48.1
48.4
48.5
2.3
2.7
2.6
1.5
2.1
2.2
2.5
38.3
35.8
35.4
35.2
34.8
34.7
34.4
1.6
1.8
1.6
1.1
1.6
1.4
1.6
28.1
28.7
29.0
29.4
29.3
29.2
29.1
1.4
1.6
1.5
0.9
1.3
1.3
1.5
15.2
14.9
14.7
14.4
14.5
14.6
14.5
1.4
1.6
1.5
0.9
1.3
1.3
1.4
181
165
161
150
152
153
151
6
6
6
3
5
5
5
51.6
52.6
53.0
54.0
53.8
53.7
54.0
3.1
3.8
3.5
2.4
3.3
3.2
3.6
0.446
0.428
0.420
0.407
0.410
0.412
0.412
0.035
0.039
0.035
0.022
0.031
0.031
0.035
0.39
0.34
0.33
0.28
0.29
0.30
0.30
0.04
0.04
0.04
0.03
0.04
0.04
0.04
6

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Table 3
Binary surfactant mixtures' compositions of DTMABr/DDMABr and DTMABr/DDMEABr in percent molar fraction (X), nematic-to-nematic phase transition temperatures, temperature
range of the NB phase in °C (ΔTNB), and the average number of –CH2 groups in the head groups (navg).
Mixture
XDTMABr
XDDMABr
XDDMEABr
XSSY
XDDeOH
Xwater
Phase transitions
ΔTNB
navg
s8
s9
4.482
4.731
0.499
0.250
–
–
0.132
0.132
1.792
1.792
93.095
93.095
ND
–
–
2.90
2.95
15:05ꢀ
C
ND
ND
ND
ND
ND
N
N
N
N
N
ƒƒƒƒ!
B
B
B
B
B
17:35ꢀ
C
s3
4.856
4.981
4.856
4.731
4.482
4.233
3.984
3.734
3.484
0.125
–
0.132
0.132
0.132
0.132
0.132
0.132
0.132
0.132
0.132
1.792
1.792
1.792
1.792
1.792
1.792
1.792
1.792
1.792
93.095
93.095
93.095
93.095
93.095
93.095
93.095
93.095
93.095
–
2.98
3.00
3.03
3.05
3.10
3.15
3.20
3.25
3.30
ƒƒƒƒ!
21:15ꢀ
C
17:05ꢀ
C
s4
–
–
–
–
–
–
–
–
–
4.10
3.70
3.60
2.40
1.45
1.10
0.45
–
N
N
N
ƒƒƒƒ!
ƒƒƒƒ!
C
C
C
21:35ꢀ
C
17:65ꢀ
C
s5
0.125
0.250
0.499
0.748
0.997
1.247
1.497
ƒƒƒƒ!
ƒƒƒƒ!
22:15ꢀ
C
18:55ꢀ
C
s10
s11
s12
s13
s14
s15
ƒƒƒƒ!
ƒƒƒƒ!
22:85ꢀ
C
20:45ꢀ
C
ND ƒƒƒƒ! NB ƒƒƒƒ! NC
24:20ꢀ
C
22:75ꢀ
C
ND ƒƒƒƒ! NB ƒƒƒƒ! NC
24:45ꢀ
C
23:35ꢀ
C
ND ƒƒƒƒ! NB ƒƒƒƒ! NC
25:95ꢀ
C
25:50ꢀ
C
ND ƒƒƒƒ! NB ƒƒƒƒ! NC
NC
in the thickness of the water layer (Fig. 8d) is observed, the micelle bi-
layer thickness (Fig. 8c) increases. It may be attributed to the increase
in the average area per surfactant head group, a0 (Fig. 8f). Mitchel and
co-workers [65] discussed the relationship between the micelle shape,
or lyotropic structure, and a0: if a0 < 47 Å2 the lamellar structure is sta-
bilized; if 70 Å2 > a0 ≥ 47 Å2, the nematic phase (rod or disc-like
Fig. 5. Birefringences Δn = n2 – n1 (●) and δn = n3 – n2 (○) as a function of the temperature for mixtures given in Table 3.
7

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
parameter from lamellar to nematic phase and from nematic toisotropic
phase decreases. Moreover, it is known that the micelle curvature in-
creases in the sequence of lamellar → nematic → isotropic. They calcu-
lated the packing parameter, i.e., v/a0l, at the nematic to lamellar
transitionas0.55. Thus, itisclearlyseenthatthepackingparameterisin-
versely proportional to the micelle surface curvature, i.e. the higher the
packing parameter the smaller the micelle surface curvature. Table 5 in-
dicates that, from the dodecylalkylammonium bromide with the lowest
n
avg to the one with the highest navg, the packing parameter assumes
smaller values. Possible extent of curvature and the value of the packing
parameter to obtain the biaxial nematic phase, as well as some other
lyotropic structures, are summarized in Fig. 9. It is well-known that if
the packing parameter is lower than 1/3, the micelle surface has the
highest micellesurfacecurvatureandhead-grouparea, and the aggrega-
tion of the surfactants molecules in the micelles is like a cone, Fig. 9a,
i.e., the cross-section of the infinitively long micelles of the hexagonal
phase. As the surfactant head-group size decreases the surfactant-
aggregation type is a truncated cone, with smaller head-group size and
mediumextentofcurvature,Fig. 9b,e.g., nematicphases. Finally,thesur-
factant aggregates in the lamellar phase show lowest surfactant head
group and extent of curvature, Fig. 9c. Considering the classification of
the a0 values to obtain the uniaxial and biaxial nematic phases, we may
generalize the packing parameter and extent of the curvature according
tothelaserconoscopyandespeciallySAXSresults:onlyND phasewasob-
tained from the s8 and it has the value of the packing parameter slightly
smallerthan½,of0.440;Thevalueofthepackingparameterforthesam-
ple s15, which gives only NC phase, is 0.362 and this value is slightly
higher than 1/3. So, we can make an assumption for obtaining the
lyotropic biaxial nematic phase that 0.37 > v/a0l > 0.44. Consequently,
it is seen that the packing parameter of the surfactant molecules in the
micellesofthenematicphasesisanimportantparametertoobtaindiffer-
ent nematic phases. Thus, we may introduce to the IBM model that three
nematic phases are composed of same kind of orthorhombic micelles
with different micelle surface curvatures.
Fig. 6. Partial phase diagram of mixtures of Table 3 as a function of the average number of –
CH2 groups in the head groups of dodecylalkylammonium bromides. Grey region
corresponds to two-phase region, i.e., coexistence of nematic and isotropic phase.
Fig. 7. Dependence of the temperature range of the NB phase (ΔT ) in the partial phase
NB
diagram on the average number of –CH2 groups in the head groups of
dodecylalkylammonium bromides. Solid line represents a linear fit.
At this point we need to say somethings about an eventual relation
between optical anisotropies and micelle surface curvature. In the biax-
ial phase temperature range, we experimentally observed that there is a
micelles) is stabilized; if a0 > 70 Å2 isotropic micellar or hexagonal
phases are stabilized (spheres, rod or discs). The a0 values obtained in
Mitchel's et al. study is exactly in the range from 47 to 70 Å2, near the
one for the nematic phases. In addition, for the ND phase, it was reported
that the a0 is about 44–47 Å2 [66]. According to Tables 2 and 4,
52 Å2 ≥ a0 > 57 Å2 for a lyotropic mixture to show the biaxial nematic
phase. Combining our results with those from [65,66], it is most likely
to obtain only ND and only NC phases, if 52 Å2 > a0 ≥ 47 Å2 and
70 Å2 > a0 ≥ 57 Å2, respectively.
TheIBMmodel,aswedescribedintheprevioussections,assumestwo
important parameters to explain the stabilization mechanism of differ-
entnematic phases: micelle symmetryorshape anisotropy, and orienta-
tional fluctuations. Inpreviousstudies [11,24] wequalitatively proposed
that the micelle surface curvature should be different in each nematic
phase.Here,theSAXSresultsquantitativelyshowthatthemicellesurface
curvature is also an important parameter for obtaining the different ne-
matic phases. Dawin et al. [33] experimentally showed that the packing
temperature where Δn = δn. In terms of the invariants of the order pa-
̿
rameter (the tensor optical dielectric tensor ε), their invariants (σi) are
written as:
ꢀ
ꢁ
4hni
δn
2
εa1 ¼ −
Δn þ
3
2hni
εa2
εa3
¼
¼
½Δn−δnꢁ
3
ꢀ
ꢁ
4hni Δn
−δn
3
2
σ1 ¼ 0
À
Á
2
2
2
2
σ2
¼
εa1 þ εa2 þ εa3
3
σ3 ¼ 4ðεa1εa2εa3
Þ
Table 4
Structural parameters from SAXS measurements results for some samples listed in Table 3. Mixture identification, micelle's core average dimensions (A', B′, C′), average polar layer thick-
ness (w), average aggregation number (Nagg), average area per polar head (a0), average surfactant molecular packing parameter (v/a0l), and shape anisotropy (SA).
Mixture
A′ (Å)
B′ (Å)
C′ (Å)
w (Å)
Nagg
a0 (Å2)
v/a0l
SA
s8
s9
s3
s4
s5
s10
s12
51.3
51.4
50.5
46.9
48.1
46.4
43.5
1.6
2.6
2.6
1.5
2.1
1.8
1.4
39.2
37.7
35.4
5.2
34.8
35.4
34.4
1.2
1.9
1.6
28.5
28.5
29.0
29.4
29.3
29.3
29.8
1.0
1.6
1.5
0.9
1.3
1.1
0.9
15.1
15.1
14.7
14.4
14.5
14.5
14.2
1.0
1.6
1.5
0.9
1.3
1.1
0.9
178
173
161
150
152
150
139
4
6
6
3
5
4
3
51.6
52.0
53.0
54.0
53.8
54.0
55.1
2.3
3.7
3.5
2.4
3.3
2.7
2.3
0.440
0.437
0.420
0.407
0.410
0.409
0.394
0.025
0.039
0.035
0.022
0.031
0.026
0.020
0.37
0.36
0.33
0.28
0.29
0.28
0.23
0.03
0.04
0.04
0.03
0.04
0.03
0.03
1.1
1.6
1.1
1.0
8

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Fig. 8. Structural parameters of all samples as a function of navg of dodecylalkylammonium bromides. Samples s2 and s9, and s6 and s10 have the same navg values of 2.95 and 3.05,
respectively, so that the parameters of s9 and s10 are represented by open-circles. Solid lines represent linear fits.
Table 5
The laboratory frame axes are 1, 2 and 3. The orthorhombic micelle
(e.g., a flattened ellipsoid) is oriented in this reference frame with the
major radius parallel to the 1 axis, the smallest radius along the 3 axis
Change in the structural parameters, (χfinal − χinitial)/χinitial, where χinitial and χfinal are the
parameters at navg = 2.90 and navg = 3.15, respectively, from SAXS measurements for
some samples listed in Tables 1 and 3. The values are obtained from the linear fit of the ex-
perimental values. The numbers in the parentheses are non-fitted experimental values.
3=2
and the medium axis along the 2 axis. In the ND and NC phase σ3 ¼ σ2
and σ3 ¼ −σ23=2, respectively. In the NB phase −σ23=2<σ3<σ23=2. The
χ
navg = 2.90
navg = 3.15
Change (%)
n1þn3
temperature where Δn = δn corresponds just to σ3 = 0, i.e., n2
¼
, a
A′ (Å)
B′ (Å)
C′ (Å)
w (Å)
Nagg
52.8 (51.3)
37.6 (39.2)
28.4 (28.5)
15.0 (15.1)
176 (178)
51.8 (51.6)
0.438 (0.440)
0.372 (0.370)
44.2 (43.5)
33.2 (34.4)
29.8 (29.8)
14.1 (14.2)
136 (139)
55.1 (55.1)
0.391 (0.394)
0.233 (0.230)
–16 (−19)
– 12 (−12)
+ 5 (+ 5)
– 6 (−6)
– 23 (−22)
+ 6 (+ 7)
– 11 (−10)
– 37 (−38)
2
meanvaluebetweenn1 andn3. Inotherwords, atthistemperature,theop-
tical anisotropies (Δn and δn) between the micellar medium along axis 2
and 1 equals that of the axis 3 and 2. There is no a simple relation between
these optical anisotropies and the curvature in the micelle's surfaces and
packing parameter, since the distribution of the main surfactant and co-
surfactant is not homogeneous in the micelle (see, e.g., [73]). Our
a0 (Å2)
v/a0l
SA
9

E. Akpinar, N. Uygur, O.D. Ordu et al.
Journal of Molecular Liquids 332 (2021) 115842
Fig. 9. Relationship between the micelle surface curvature and the packing parameter (PP = v/a0l), and the expected lyotropic structures.
[2] B.J. Forrest, L.W. Reeves, New lyotropic liquid crystals composed of finite nonspher-
ical micelles, Chem. Rev. 81 (1981) 1–14.
[3] F. Fujiwara, L.W. Reeves, M. Suzuki, J.A. Vanin, Solution Chemistry of Surfactants,
Plenum Press, New York, 1979.
experimental evaluations of the micellar dimensions and packing param-
eterwere(SAXSresults)doneatafixedtemperature(~25°C). Tobeableto
discuss the relation between the optical anisotropies and the micellar
shape anisotropy and aggregation number (in particular when both bire-
fringences equals), additional SAXS measurements will need to be per-
formed, for a given sample, as a function of the temperature, and then
compare with the conoscopy results, which will be a subject of another
study.
[4] L. Nasrin, E. Kabir, M. Rahman, External magnetic field-dependent tricritical points
of uniaxial-to-biaxial nematic transition, Phase Transit. 89 (2016) 193–201.
[5] Y. Kim, B. Senyuk, S. Shin, A. Kohlmeier, G.H. Mehl, O.D. Lavrentovich, Surface align-
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Lavrentovich, Search for microscopic and macroscopic biaxiality in the cybotactic
nematic phase of new oxadiazole bent-core mesogens, Phys. Rev. E 93 (2016),
062701, .
4. Conclusions
[7] A.M.F. Neto, S.R.A. Salinas, The Physics of Lyotropic Liquid Crystals: Phase Transitions
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We studied the effect of surfactant head-group size dependence of
surfactant-dye interactions on the stabilization of different lyotropic ne-
matic phases and nematic to nematic phase transitions. All experimen-
tal studies indicated that those interactions play a role in the
stabilization of the uniaxial and biaxial nematic phases and phase tran-
sition temperatures by modifying the micellar structural parameters
such as micelle’ dimensions, average area per surfactant head group
on the micelle surfaces, and micellar shape anisotropy. Furthermore,
the surfactant packing parameter and the area per surfactant head
group should have certain values for the stabilization of the nematic
phases, especially the biaxial one. The IBM model, which explains the
formation mechanism of the different nematic phases, needs to assume
‘micelle surface curvature being different in three nematic phases' in ad-
dition to micelle symmetry and orientational fluctuations.
Author statement
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tions of sodium lauryl sulfate-1-hexadecanol-water, Langmuir 7 (1991) 630–635.
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The Authors certify that they have seen and approved the revised
version of the manuscript being submitted.
[19] A.M. Filho, A. Laverde, F.Y. Fujiwara, Observation of two biaxial nematic mesophases
in the tetradecyltrimethylammonium bromide/decanol/water system, Langmuir 19
(2003) 1127–1132.
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rod- and platelike colloids, Langmuir 16 (2000) 10144–10149.
[21] E. Akpinar, D. Reis, A.M.F. Neto, Effect of alkyl chain length of alcohols on nematic
uniaxial-to-biaxial phase transitions in a potassium laurate/alcohol/K2SO4/water
lyotropic mixture, Liq. Cryst. 39 (7) (2012) 881–888.
Declaration of Competing Interest
None.
Acknowledgements
[22] E. Akpinar, D. Reis, A.M.F. Neto, Effect of Hofmeister anions on the existence of the
biaxial nematic phase in lyotropic mixtures of dodecyltrimethylammonium bro-
mide/sodium salt/1-dodecanol/water, Liq. Cryst. 42 (7) (2015) 973–981.
[23] E. Akpinar, K. Otluoglu, M. Turkmen, C. Canioz, D. Reis, A.M.F. Neto, Effect of the
presence of strong and weak electrolytes on the existence of uniaxial and biaxial ne-
matic phases in lyotropic mixtures, Liq. Cryst. 43 (2016) 1693–1708.
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actions at micelle surfaces on the stabilization of lyotropic nematic phases, Eur.
Phys. J. E 39 (2016) 107.
[25] E. Akpinar, C. Canioz, M. Turkmen, D. Reis, A.M.F. Neto, Effect of the surfactant alkyl
chain length on the stabilization of lyotropic nematic phases, Liq. Cryst. 45 (2)
(2018) 219–229.
[26] D. Myers, Surfactant Science and Technology, John Wiley & Sons, New Jersey, 2006.
[27] B. Kumar, D. Tikariha, K.K. Ghosh, Effects of electrolytes on micellar and surface
properties of some monomeric surfactants, J. Dispers. Sci. Technol. 33 (2012)
265–271.
The authors thank the following scientific councils and agencies for
supporting this work. From Turkey, the Scientific and Technological Re-
search Council of Turkey (TÜBİTAK) [grant number: 217Z079] and Bolu
Abant Izzet Baysal University Directorate of Research Projects Commis-
sion (BAP) [grant number 2020.03.03.1459]. From Brazil, the National
Council for Scientific and Technological Development, the National In-
stitute of Science and Technology Complex Fluids (INCT-FCx: 2014/
50983-3), (NAP-FCx: 2011.1.9358.1.6) and the São Paulo Research
Foundation (FAPESP-2018/07340-5 & 2016/24531-3) for supporting
this work.
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ters of sds in the presence of some electrolytes for emulsion polymerization sys-
tems, J. Surfactant Deterg. 16 (2013) 271–278.
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