Liquid Crystals

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Re-entrant direct hexagonal phases in a lyotropic
system of surfactant induced by an ionic liquid
Saheli Mitra, Ramesh Karri, Praveen Kumar Mylapalli, Arka Bikash Dey,
Gourav Bhattacharya, Gouriprasanna Roy, Syed Mohammed Kamil, Surajit
Dhara, Sunil Kumar Sinha & Sajal Kumar Ghosh
To cite this article: Saheli Mitra, Ramesh Karri, Praveen Kumar Mylapalli, Arka BikashDey, Gourav Bhattacharya, Gouriprasanna Roy, Syed Mohammed Kamil, Surajit Dhara,
Sunil Kumar Sinha & Sajal Kumar Ghosh (2019) Re-entrant direct hexagonal phases in alyotropic system of surfactant induced by an ionic liquid, Liquid Crystals, 46:9, 1327-1339, DOI:
10.1080/02678292.2019.1566507
To link to this article: https://doi.org/10.1080/02678292.2019.1566507

Published online: 22 Jan 2019.

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LIQUID CRYSTALS
2019, VOL. 46, NO. 9, 1327–1339
https://doi.org/10.1080/02678292.2019.1566507

Re-entrant direct hexagonal phases in a lyotropic system of surfactant induced
by an ionic liquid
Saheli Mitra a, Ramesh Karrib, Praveen Kumar Mylapallic, Arka Bikash Deyd, Gourav Bhattacharya a,
Gouriprasanna Royb, Syed Mohammed Kamila, Surajit Dhara c, Sunil Kumar Sinhae and Sajal Kumar Ghoshaa
Department of Physics, School of Natural Sciences, Shiv Nadar University, Uttar Pradesh, India; bDepartment of Chemistry, School of Natural
Sciences, Shiv Nadar University, Uttar Pradesh, India; cSchool of Physics, University of Hyderabad, Hyderabad, India; dSurface Physics andMaterial Science Division, Saha Institute of Nuclear Physics, Bidhannagar, Kolkata, India; eDepartment of Physics, University of California-San
Diego, California, USA

ABSTRACTARTICLE HISTORYIn the present study, an ionic liquid (IL), known as green solvent, 1-butyl-3-methylimidazolium
tetrafluoroborate (BMIM-BF4) with four carbons in the hydrophobic chain (C-4) has been used as
an additive to modify the self-assembled aggregates of an anionic surfactant sodium dodecyl
sulfate (SDS) and then the evolution of the liquid crystalline phases has been investigated. Small
angle synchrotron x-ray diffraction study has revealed an unprecedented phase sequence wherea hexagonal phase (HI) of direct cylindrical micelles is observed to evolve to another hexagonalphase (HII) of, again, direct cylindrical micelles with a lamellar phase (Lα ) as the intermediate. The
rheological data and the theoretical calculations have confirmed the phases. To understand sucha phase behaviour of the system, the work is extended by considering the ionic liquids with thesame head group but of shorter (C-2) and longer (C-10) hydrocarbon chains compared to BMIMBF4. While the shorter chain IL causes the hexagonal phase to form rectangular (R) phase, thelonger chain is observed to induce the lamellar phase (Lα ). The molecular mechanism of appearance of such different phases has been discussed.

Received 12 July 2018
Accepted 15 December 2018

Introduction
Surfactants are the major ingredients of laundry and cleaning products and, thus, these are used in the household.
They are also used in pharmaceutical, cosmetic and foodindustry as emulsifiers, in the plastic industry as wetting
agents, plasticizers, and foaming agents [1,2]. Because of
the vast applications along with their interesting physiochemical behaviour in solutions, both the academic andindustrial research communities have paid considerable
attention to these systems over decades. In addition, surfactants have significant importance in biological research
CONTACT Sajal Kumar Ghoshsajal.ghosh@snu.edu.in© 2019 Informa UK Limited, trading as Taylor & Francis GroupKEYWORDS

Lyotropic liquid crystal;surfactant; ionic liquids;
rheology; small angle x-ray
diffraction

as they are extensively used in mimicking the cellular
membrane, protein crystallization and protein preservation[3,4]. They are also used as nano-reactors for enzymatic
reaction and synthesizing of nanoparticles [5,6]. The extensive applications of surfactants in various fields are mainly
due to their unique properties in aqueous solution. Thesemolecules usually form various mesoscopic structures inthe solution including spherical and cylindrical micelles.
They also form vesicles depending on the shape and size ofthe molecules and the interactions among themselves.
Moreover, depending upon a specific application, the1328

S. MITRA ET AL.

property of a surfactant in solution can be altered by controlling the physical conditions, such as temperature, or byadding suitable chemical reagents into the solution [7,8].
Various co-surfactants, organic solvents and electrolytes
have been employed to tune the inter-surfactant interactions to form desirable mesoscopic structures towards
achieving the intended properties of the system [9,10].
Recently, ionic liquids (ILs) are considered as better
additives over the conventional organic solvents becauseof their various striking features. These IL molecules arenonexplosive, nonflammable and have high thermal stability and good ionic conductivity. More importantly, they
are environmentlly benign [11]. In addition, ILs are ina liquid state [12,13] and have a negligible vapour pressure
at room temperature which inhibits evaporation into theopen atmosphere and allows simple recycling and reuses[14]. Miskolczy et al. have shown in their pioneer work thatthe imidazole-based ionic liquids possessing n-octyl moiety
in the anion and 1-butyl-3-methylimidazolium octyl sulfate
behave as a surfactant and form micelle above the critical
micellarconcentration(CMC).
Whereas,1-methyl-3-octylimidazolium chloride produced an inhomogeneous solution of larger aggregates in aqueous solution through self-assembly [15]. Moreover, they
demonstrated that these ionic liquids can be used to modify
the properties of the conventional micelles, in a controlled
fashion. The small amount (<10 mM) of ionic liquids could
markedly reduce the polarity of the Stern layer of sodium
dodecyl sulfate (SDS) micelle. Addition of low concentration of an ionic liquid 1-butyl-3-methylimidazolium tetra
fluoroborate (BMIM-BF4) into the aqueous solution of
SDS has shown to decrease the critical micellar concentration (CMC) of SDS while it increases the aggregation
number and micellar size [16]. The long-chain imidazolium IL, 1-dodecyl-3-methylimidazolium bromide, isreported to alter the geometric packing and charge densityof SDS in an aqueous aggregate [17]. In contrast, Pal et al.
have shown the increase of CMC upon addition of
3-methyl-1-pentylimidazolium hexafluorophosphate inan aqueous solution of SDS [18]. Formation of thermodynamically stable vesicles in the solution of a pure cationicdouble tail surfactant (didodecyldimethylammonium bromide) in a protic IL (ethyl ammonium nitrate) has also
been reported in the literature [19]. However, all theseprevious investigations, mentioned above, are confined toa low concentration of surfactant in water (≤5 weight %), in
which the individual self-assembled aggregates are distributed isotropically. There are very few reports on the effects
of ILs on the hierarchical lyotropic liquid crystalline (LLC)
phases formed by these surfactant aggregates [20].
Understanding the structural evolution in LLC system is
extremely important as it decides the complex rheologicalbehaviour of the system, which is one of the main interestsof the soft matter industry. Along with the effect of intermolecular interactions, ILs can influence the interaction
among the self-assembled aggregates and can exhibit modified LLC structures formed by these surfactant aggregates.
Among others, the most known structures of lyotropic
liquid crystalline phases are the hexagonal phase formed bycylindrical micelles with positive interfacial curvature andthe lamellar phase of flat bilayers with zero interfacial
curvature [21,22]. In aqueous solutions of surfactants, thetransition among these phases is reported as a function of
surfactant concentrations [23,24]. In these cases, the interfacial curvatures are modified by adding more surfactantsin the binary mixtures of surfactant and water. Instead ofchanging the surfactant concentrations, the local curvatureof an aggregate can be changed by tuning the electrostaticinteractions among the surfactant molecules. In the present study, imidazolium-based ionic liquids witha different number of carbon atoms in their single hydrocarbon chains were used as the third component in thesolution of water and the anionic surfactant SDS. At a fixed
concentration of total non-aqueous components (SDS andIL) in water, the molar ratio of these components waschanged which, effectively, altered the electrostatic interactions between the surfactant aggregates. As a result, thelocal curvature is expected to be modified, and correspondingly, the structure of the lyotropic hexagonal liquid
crystalline phases are likely to be altered.
The small angle synchrotron x-ray diffraction study has
indicated the changes in the pristine hexagonal phase,formed by cylindrical micelles of SDS in aqueous solution,
due to the addition of the ILs. The rheological studies haveshed lights on how these phases differ in their viscoelastic
behaviour. Finally, the packing parameters, calculated forthese phases, have explained the structure of selfassembled aggregates that formed these phases.

Experiment
Materials
The surfactant sodium dodecyl sulfate (SDS) (purity99%), and the ionic liquids (ILs) 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF4), 1-butyl3-methylimidazolium tetrafluoroborate (BMIM-BF4)
and 1-decyl-3-methylimidazolium tetrafluoroborate(DMIM-BF4) (purity 98%) were purchased from SigmaAldrich (USA) and were used without any purification.
The molecular structures of all these chemicals areshown in Figure 1. To prepare solutions, an appropriate
amount of de-ionized water (Millipore, 18 MΩ cm) was
added to the mixture of an ionic liquid (IL) and SDS
was taken in a glass vial. The total surfactant weightfraction (φ = (SDS + IL)/(SDS + IL + water) was kept

LIQUID CRYSTALS

(a)

(b)

1329

(c)

(d)

Figure 1. Chemical structure of (a) sodium dodecyl sulfate (SDS), (b) 1-ethyl-3-methylimidazolium tetrafluroborate (EMIM-BF4), (c)1-butyl-3-methylimidazolium tetrafluroborate (BMIM-BF4) and (d) 1-decyl-3-methylimidazolium tetrafluroborate (DMIM-BF4).

constant (0.4) and IL to SDS molar ratio (α = [IL]/[SDS]) was varied. To attain equilibrium, the prepared
solution was kept in an oven at 50°C for one week. For
the production of uniform and homogeneous mixture,
the solution was then vortexed and stored at the same
temperature for another week.

regime, the storage (G0 ) and loss (G00 ) moduli were measured as a function of strain amplitude. After establishing
the linear viscoelastic regime, the frequency sweep measurements were performed over four orders of magnitudeof angular frequency (ω) (0.05–500 s1 Þ. The sample temperature was maintained at 30°C by a constant flow ofwater from a bath (JULABO GmbH, Germany).

Polarizing optical microscopy
For the microscopy, samples were placed in between
a glass slide and a coverslip. To achieve a constant temperature of 30°C, these samples were placed in a hotstage (Linkam, LTS120, UK) attached to a polarizing
microscope (Nikon H 600L, Japan).
Small angle X-ray diffraction
Small angle x-ray diffraction measurements were performed at the Indian Beamline (BL-18B), Photon Factory,
Tsukuba, Japan with the x-ray photons of wavelength
0.855Å. For these measurements, the samples were filledin glass capillaries (Hampton Research, USA, 1.5 mm diameter) and further flame sealed. The scattered photons
from the sample solutions were collected at a fixed temperature of 30°C by a 100K Pilatus detector placed at
350 mm away from the sample cell. The typical exposure
time was 100 s. DPDAK software was used to extract thediffraction data.
Rheology
A stress-controlled rheometer (MCR 501, Anton Paar) wasused for rheological measurements with a sample cell of
cone-plate geometry (cone diameter 50 mm, cone angle
0.5° and true gap 49 µm). To obtain the linear viscoelastic

Results
Polarizing optical microscopy
The polarizing optical microscope is the fundamental tool used to check the existence of crystalline
phases in the sample of birefringent materials. The
different textures in the surfactant solution in thepresence of the medium chain length IL (C-4)
BMIM-BF4 were investigated at a fixed value of
φ = 0.4 and T = 30°C with varying values of α.
For α = 0, the characteristic texture of the hexagonalphase is observed [24,25]. For intermediate values ofα (0.05–0.1), the oily streak textures are seen [25],which indicates the presence of lamellar phase in thesample. For higher values of α, the texture is foundto be different from that of low and intermediate
values of α. In the case of low chain length IL (C-2)
EMIM-BF4, at low values of α, the texture of thehexagonal phase was observed, while at higher
values of α, a distinct texture was observed. For
the long chain IL (C-10) DMIM-BF4, the texturesof hexagonal and lamellar phases were seen at low
and high values of α, respectively. The representative
textures of different phases observed in these systems are shown in Figure 2. It is quite hard toconclude the exact structures of the phases from

1330

S. MITRA ET AL.

Figure 2. (Colour online) Textures of lyotropic liquid crystalline phases in ternary mixtures of surfactant SDS, ionic liquids and water,
observed under crossed polarisers in an optical microscope. (a) α = 0 (pure SDS solution), corresponds to hexagonal phase (HI), (b)α = 0.1 (added BMIM-BF4), corresponds to lamellar phase (Lα ), (c) α = 0.2 (added BMIM-BF4) corresponds to hexagonal phase (HII)
and (d) α = 0.1 (added EMIM-BF4) corresponds to rectangular phase (R). All the images were captured at 30°C.

these micrographs; hence, small angle x-ray diffraction experiments were performed.

Structural evolution of hexagonal phase
The microstructures of lyotropic liquid crystalline samplesof SDS and the IL with four carbon atoms (C-4) in chain(BMIM-BF4), were investigated by small angle x-ray diffraction. Figure 3 shows the diffraction patterns obtained
from the samples at various compositions. At φ = 0.4 andα = 0, two Bragg peaks are observed withpthe
ﬃﬃﬃ corresponding
wave vector transfer (q) in the ratio 1: 3 (Figure 3(a)). It
confirms the existence of a two-dimensional hexagonalphase (HI) of cylindrical micelles which has been reported
in the study of the phase diagram of the SDS/water system
by Kekicheff et al. [26]. The lattice constant (a) of thehexagonal phase can be calculated from, a ¼ p2ﬃﬃ3 d10 ,where d10 ¼2π
q10 , q10

being the position of first Bragg

peak. The value of the lattice constant at this concentration
is 54.4 ± 1.5Å. Such a cylindrical aggregate is expected by
the self-assembly of a truncated cone-shaped molecule inan aqueous solution [27]. This is decided by the packing
parameter, p ¼ av0 l , where v, a0 and l are the volume,
effective cross-sectional surface area of the head groupand the length of the molecule, respectively [27]. At thisconcentration of φ = 0.4, the effective shape of the SDS
molecule becomes a truncated cone with the value of p in
the range of 1/3 to 1/2. As a result, the molecules form thecylindrical micelles. However, keeping the surfactant concentration fixed, the interfacial curvature of the cylindricalsurface can be altered by changing the interactions between
the molecules. Here, at a fixed value of φ = 0.4, the ionicliquid BMIM-BF4 was added gradually. At α = 0.1, thediffraction pattern shows, again, two peaks but theq values are in the ratio of 1:2 (Figure 3(c)). It confirms
the presence of lamellar phase (Lα ) in the sample witha periodicity of 34.69 ± 0.38 Å. The first order phasetransition from the hexagonal (HI) to lamellar is evident
from the diffraction pattern shown in Figure 3(b). At thisintermediate value of α = 0.025, the co-existence of hexagonal (HI) and lamellar (Lα ) phases with the respective
lattice constants 54.4 ± 1.5 Å and 34.7 ± 0.4 Å are observed.
On further increasing of the IL concentration, theLIQUID CRYSTALS

1331

Figure 3. (Colour online) Small angle x-ray diffraction pattern of the different phases at φ = 0.4 at different values of α: (a) 0, (b) 0.025, (c)0.1 and (d) 0.2, exhibiting the hexagonal (HI), coexistence of hexagonal and lamellar ((HI + Lα ), lamellar (Lα ) and second hexagonal (HII)
phases, respectively. The two-dimensional (2-D) images of the diffraction patterns are shown on the right panel of the figure.

Figure 4. (Colour online) The variation lattice parameter of the first hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases obtained
as a function of added BMIM-BF4 into the aqueous solution of SDS. The results correspond to the constant value of φ = 0.4 and T = 30°C.

diffraction pattern showing two peaks with their q values inpﬃﬃﬃ
the ratio 1: 3 that confirms the presence of hexagonalphase. As shown in Figure 4, the lattice constant of

this second hexagonal phase (HII) obtained at this higher
value of α = 0.2 is slightly greater than the lattice constant of
the first hexagonal phase (HI) observed at other side of the1332

S. MITRA ET AL.

Table 1. Lattice parameters of hexagonal (HI), lamellar (L)and second hexagonal (HII) phases obtained from the small
angle x-ray diffraction study of SDS solution in the presence of
BMIM-BF4 at varying sample compositions α.
φ
0.4

α
0
0.015
0.050
0.075
0.100
0.150
0.175
0.200

Lattice constant (Å)
54.4 ± 1.5
54.3 ± 1.4
34.3 ± 0.4
34.3 ± 0.4
34.7 ± 0.4
34.3 ± 0.4
34.7 ± 0.4
55.5 ± 0.6

Phases
HI
HI
Lα
Lα
Lα
Lα
Lα
HII

lamellar phase (lower value of α). These lattice parametersof different phases observed at different chemical compositions are given in Table 1 and plotted in Figure 4.
The small angle x-ray diffraction data obtained from theaqueous solution of SDS and the shorter chain (C-2) IL
EMIM-BF4 are shown in Figure 5(a). Here, again the total
surfactant concentration (φ = 0.4) was kept fixed and the
IL to surfactant molar ratio was varied. At α = 0.075, thefirst Bragg peak corresponding to (1 0) reflection of thetwo-dimensional hexagonal phase (HI) of pure SDS solution is found to shift to a lower value of q. Also, the (1 1)peak of the HI phase is not observed. Instead of that, a new
Bragg peak appears at 0.182 Å−1. At α = 0.1, along withthese two peaks, a third peak is observed at q = 0.226 Å−1.
All these three peaks then are best indexed as the reflections from (1 0), (0 1) and (1 1) planes of a rectangular(a)lattice (R) with the corresponding lattice constants
47.0 ± 1.3 and 34.5 ± 0.9 Å. On further increasing of the
IL (higher value of α), only a single broad peak appears
indicating an isotropic phase (I). In case of longer chain(C-10) IL DMIM-BF4, hexagonal phase (HI) is observed totransform to a lamellar phase (Lα ) on the addition of the IL(Figure 5(b)). This lamellar phase is not found to form
another hexagonal phase on further addition of the IL.
Instead of that, a broad peak of an isotropic phase (I) is
observed. In this context, note that in case of the medium
chain (C-4) IL BMIM-BF4, the HI phase was transformed
to another hexagonal phase (HII) at a higher value of α. The
lattice parameters of different phases observed for theseshorter and longer chain ILs are shown in Table 2.

Rheological behaviour of re-entrant hexagonalphases
The appearance of re-entrant hexagonal phases in thepresence of the medium chain (C-4) IL BMIM-BF4 in
the SDS solution is the most interesting observation in
the present study. To shed more light on the unusualphase sequence, the rheological measurements on the
SDS–BMIM-BF4 complexes have been done.
As the evolution of these phases is expected to exhibit
distinct rheological behaviour, three samples with α = 0,
0.1 and 0.2 were considered for the measurements as they(b)

Figure 5. (Colour online) Small angle x-ray diffraction patterns of the different phases at φ = 0.4. (a) The pattern for shorter chain(C-2) IL EMIM-BF4 at different values of α: (i) 0.015, (ii) 0.025, (iii) 0.075, (iv) 0.1, (v) 0.125 and (vi) 0.175 exhibiting the hexagonal (HI),rectangular (R) and isotropic (I) phases. (b) The pattern for longer chain (C-10) IL DMIM-BF4 at different values of (i) 0.015, (ii) 0.025,(iii) 0.15 and (iv) 0.175 exhibiting the hexagonal (HI), lamellar (L) and isotropic (I) phases.

LIQUID CRYSTALS

Table 2. Lattice parameters of hexagonal (HI) and rectangular(R) phases of SDS solution in the presence of EMIM-BF4, andhexagonal (HI) and lamellar (Lα) phases in the presence of
DMIM-BF4 obtained from the small angle x-ray diffraction
study at varying sample compositions α.
φ
0.4

Ionic liquids

EMIM-BF4

α
0.015
0.025
0.075
0.1

DMIM-BF4

0.015
0.025
0.15

Lattice constants (Å)
52.8 ± 1.4
54.3 ± 1.5
48.4 ± 1.4
34.5 ± 0.9
47.0 ± 1.3
34.5 ± 0.9
55.9 ± 1.6
55.9 ± 1.6
56.5 ± 1.9

Phases
HI
HI
R
R
HI
HI
Lα

represent the compositions of the HI, Lα and HII phases,
respectively, keeping φ = 0.4 and T = 30°C fixed. To obtainthe linear rheology regime of the samples, the strain amplitude was varied at a constant angular frequency of 10 rad/sand the corresponding storage (G0 ) and loss (G00 ) moduli
were measured. The data are shown in Figure 6. At low
values of strain amplitude (γ) (<1%), the storage modulus(G0 ) for all the three phases is found to be higher than that1333

of the loss modulus (G00 ). The crossover value of the strain
amplitude of Lα phase (4.65%) is smaller than both the
hexagonal phases. The corresponding values for HI and HIIphases are 10.00% and 25.20%, respectively.
The frequency sweep measurements on all the samples
were carried out at a fixed strain amplitude of 0.1% that
corresponds to the linear viscoelastic regime (see Figure 6).
The frequency (ω) was varied in the range of 0.05–500 Hz.
The measured viscoelastic spectra of the moduli G0 and G00 ,again at α = 0, 0.1 and 0.2 corresponding to HI, Lα and HIIphases, respectively, are shown in Figure 7. Even though
the values of G0 and G00 are very close in the low-frequency
region, the values of G0 becomes higher compared to G00
over the wide range of the frequency. For all these samples,
Figure 8 represents the complex viscosity (η ) as a functionof angular frequency (ω). For all the phases, η decreases
monotonically with ω. Interestingly, the values of η forboth the hexagonal phases are very similar, while for thelamellar phase, it has a lower value compared to both of thehexagonal phases. This result is observed over the entire
range of the angular frequency.

Figure 6. (Colour online) Measurements of storage (G0 ) and loss (G00 ) moduli of lyotropic liquid crystalline phases: (a) α = 0, (b)α = 0.1 and (c) α = 0.2 corresponding to hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases, respectively. φ = 0.4 andT = 30°C were constants.

Figure 7. (Colour online) Frequency sweep measurements of lyotropic liquid crystalline phases: (a) α = 0, (b) α = 0.1 and (c) α = 0.2
corresponding to hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases, respectively. The strain amplitude 0.1%, φ = 0.4
and T = 30°C were constants.

1334

S. MITRA ET AL.

Figure 8. (Colour online) Complex viscosity (η Þ of lyotropic
liquid crystalline phases at α = 0 (o), 0.1 (◊) and 0.2 (Δ)
corresponding to hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases, respectively.

Discussions
Phases in surfactant solutions in the presence ofionic liquids with varying chain length
At a low concentration of surfactants in water, the physical properties of the isotropic solution of micelles arevery sensitive to additives, such as organic and inorganic
salts, alcohols and co-surfactants. In particular, ionicadditives much strongly affect the critical micellar concentration (CMC) of an ionic surfactant, its surface activity and, also the shape and size of the micelles formed by
the surfactant [28,29]. As a result, for many of the cases,
the viscoelastic properties of the solution are modified
due to the formation of long wormlike micelles [30,31].
At a higher concentration of the surfactant in water, there
are various liquid crystalline phases, which are altered byadditives due to a reshaping and reorganization of theself-assembled aggregates [32,33]. Most interesting phenomenon here is the sequential appearance of structuralphases, which is important to comprehend the phasetransition in lyotropic liquid crystalline systems.
Especially, the transition between the hexagonal phaseof cylindrical micelles of positive interfacial curvatureand lamellar phase of flat bilayers with zero interfacial
curvature has been discussed in literature over decades tounderstand the topological links between these twophases [28,32,34,35]. In the present study, the small
angle x-ray diffraction data show that the twodimensional hexagonal phase of SDS surfactant transforms into three different phases in the presence ofionic liquids (IL) with same imidazolium head groupbut of increasing hydrocarbon chain length. Note that

all these ILs have same anions (BF4−), which are expected
to dissociate in the aqueous solution leaving the cations
with a hydrocarbon chain attached to it. The cation of
C-2 IL has two hydrocarbons in the chain, which may nothave a strong effect in modifying the hydrophobic coreregion of the cylindrical micelles of SDS, which has 12hydrocarbons in the chain. However, the presence of thecations is expected to reduce the negatively charged headgroup area of the micelle. This can produce a non-circularcross-sectional micelle as the region of the more populated IL will have less curvature compared to the region ofpure SDS. This can produce either a distorted twodimensional hexagonal or a rectangular lattice[22,24,36]. The data obtained here resembles the rectangular lattice. However, as the electron density contrast
between the surfactant complex and the surrounding
aqueous medium is poor, low brilliance synchrotron
source, which is the case here in the present study, is
not good enough to conclude the type of lattice unambiguously. On the other hand, the C-10 IL is expected toinfluence both the head group and the hydrophobic
regions of a SDS micelle as this IL has a comparable
chain length. The presence of this IL may screen therepulsive force between the surfactant head groups reducing the head group area, which should reduce the local
curvature. At the same time, at higher concentration of
the IL, the long chain of the IL does not allow thesurfactant chains to come closer. This phenomenon
may end up with the transition of the hexagonal phase
to a lamellar phase. For medium chain IL (C-4), at low
concentration, the head group screening again is expected
to produce lamellar phase. However, at higher concentration, the high head group area IL molecule will increase
the effective head group area allowing the long chains of
the surfactant to come closer. This phenomenon may giverise to the reappearance of the hexagonal phase at thishigh concentration. The physical explanations given here
are the subjects to further systematic experiments andsimulation works, which are the future plans of theauthors.
The most common intermediate phase between the
hexagonal and lamellar phases is the bicontinuous cubic
phase with triply period minimal surface characterized byzero mean curvature of the surface [34]. Another wellknown phase is the lamellar phase with in-plane curvaturedefects called the mesh phase [37]. The two-dimensional
meshes are also reported to form three-dimensional rhombohedral and tetragonal phases due to the out of plane
positional correlation among the in-plane curvaturedefects of the meshes [36,37]. In all these cases, strongly
bounded anionic counterions were used in cationic surfactants to modify the morphology of the aggregates of thesurfactants. Kekicheff et al. have reported a detailed phase

LIQUID CRYSTALS

diagram of SDS-water system where the hexagonal phase
was observed to transform to lamellar phase witha number of intermediate phases between these two [26].
However, these intermediate phases were observed overa very narrow range of SDS concentration, unlike the casesin references [37]. In the ternary system of SDS–decanol–
water, nematic phases of rod-like and disc-like micelles
were reported as the intermediate phases [38,39]. Ghoshet al. have also reported the hexagonal phase of SDS totransform to lamellar phase with the sequential appearanceof the nematic phase of rod-like micelles, the isotropic
phase of spherical structure and another nematic phaseof disc-like micelles at the presence of the strongly binding
counterion p-toluidine hydrochloride (PTHC) [21]. In
none of all these cases of SDS system, the hexagonal tohexagonal transition was reported which is an interestingfinding of the present work.

Rheology'of re-entrant hexagonal phases
At high surfactant concentration in water, the viscoelastic
properties of the solution highly depend on the type ofliquid crystalline phases in the solution. This is reflectedin the cross-over values of strain amplitudes here in thethree distinct phases (Figure 6). The lowest value of strain
amplitude for lamellar phase signifies the least resistanceagainst the applied strain, which is because of the layered
structure of the lamellar phase formed by surfactant/IL
bilayer. These bilayers can easily flow compared to thecylindrical micelles in both the hexagonal phases.
In the frequency sweep measurements, the values of G0
are found to be higher compared to the values of G00 for all
three phases (Figure 7). These data suggest the samples toexhibit long relaxation time [40,41]. The values of G0 and
G00 for HI phase are 46.0 and 18.0 kPa, while these valuesfor HII phase are 63.3 and 29.6 kPa, respectively, at thefrequency 10 s−1. These values indicate the two hexagonalphases to differ in their rheological behaviour.
To distinguish between the HI and HII hexagonalphases, the magnitude of the complex modulus (jG j)
has been calculated from the values of G0 and G00 fol1lowing the equation, jG j ¼ G0 2 þ G00 2 2 . It can be
expressed in terms of angular frequency (ω)
1as,jG j ¼ AωZ , where z is the coordination number
and A is a constant that signifies the strength of interaction among the units constituting a phase [42,43].
From the fits, as shown in Figure 9, the values of z and
A for the HI phase are calculated as 10 and ~32 x 103,
respectively. The respective values for HII phase are
5.75 and ~85 × 103. It shows higher resistive natureof sample at α = 0.2 compared to the sample at α = 0.
The relaxation time (τ) for all the samples can be

1335

Figure 9. (Colour online) Magnitude of the complex shear modulus(jG j) of HI (0) and HII (Δ) hexagonal phases at α = 0 and 0.2,
respectively, as a function of angular frequency (ω).

calculated from the slope of the linear fit to the data0
as shown in Figure 10, where GG00 is plotted asa function of angular frequency (ω). As expected, thevalue of τ (~83 ms) for the lamellar phase is smaller
compared to HI (~122 ms) and HII (181 ms) phases.
These values, again, indicate the stronger cohesive
force among the units of the HII phase compared tothe one in HI phase.
It is known that the addition of salts in the aqueous
solution of micelles of charged surfactants produces
longer micelles [27]. The curvature of the end-cap of
a micelle is more compared to its surface. Hence, it ispreferable to increase the length rather than increasing
the number of micelles. However, the length cannot bevery long as it reduces the entropy of the system. The
equilibrium structure depends on both the factors ofenergy including the effective end-cap energy and theentropy of the system. The present rheological behaviour of HI and HII phases indicates the formation of
longer micelles in case of the HII phase.
In general, on increasing the surfactant concentration
in a binary mixture of surfactant-water, the lamellar
phase forms hexagonal phase with reverse micelles [44].
This is observed at a very high concentration of surfactant(>80 wt.%) which is not the case in the present study.
Here, at a much lower concentration of surfactant(~40 wt.%), the hexagonal (HII) is observed after thelamellar (Lα ) by varying the ratio between the ionic liquid
and the surfactant, keeping the wt.% constant. Even
though the x-ray diffraction confirms the hexagonal lattice in HII sample and the rheology indicates it to bemuch resistive to shear force compared to HI sample, it
is hard to conclude about the nature of micelles in the HIIphase. In the following section, the theoretical calculation
will shed light on the issue.

1336

S. MITRA ET AL.

0

Figure 10. (Colour online) Plot of GG00 as a function of angular frequency (ω) for the lyotropic liquid crystalline phases: (a) α = 0, (b)α = 0.1 and (c) α = 0.2 corresponding to hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases, respectively.

Packing parameters of hexagonal phases
As discussed in the RESULTS section, the geometricpacking parameter p, of a molecule in an aggregate may
influence the nature of micelles in an aggregate [45,46].
In the present study, this parameter has been calculatedusing the lattice constant of a phase obtained from the
x-ray diffraction study.
For a particular sample, one could write the total
 c , where M1 andmass of the sample as, M1 þ M2 ¼ DV
M2 are the masses of amphiphilic molecules and water,
 the average mass density of the sample
respectively, D

and Vc the total volume. The volume of water (Vw ) andthe amphiphilic molecule (Vs ) then, can be written asVw ¼ 


Vc D

M1
þ
1
Dw
M2

0
Vs ¼ Vc @1  

DM1M2 þ 1

(1)

1
A



(2)

Dw

Figure 11. (Colour online) Schematics of hexagonal phases made up of direct micelles (left) and reverse micelles (right). The figure
represents only the 2D cross-section of cylinders.

LIQUID CRYSTALS

where Dw is the mass density of water. For a twodimensional (2D) phase in a homogeneous surfactant
solution, Vw =Vs ¼ Sw =Ss where Sw and Ss are the surface areas of the 2D-lattice covered by water andamphiphiles, respectively (Figure 11).
Hexagonal phase (HI) at α = 0: For the hexagonal phasewithout IL, the value of Sw =Ss is calculated using equations(1) and (2) and the value is found to be 1.91. Further, for the
hexagonal phase, the total surface area of the 2D unit cell is pﬃﬃ
calculated to be, Sw þ Ss ¼ 3 2 3 a2 ¼ 5118:37 AA2
using the value of lattice parameter, a ¼ 54:4 AA, which
was obtained from diffraction study (Table 1). From thesevalues of Sw =Ss and Sw þ Ss , one could find the value of theradius (R) of the cylindrical micelles following the relation,
Ss ¼ 3πR2 as there are effectively three cylindrical micelles
in each unit cell. The value of R is found to be 16.74 AA2
which is very close to the value mentioned in the literature[27]. Considering the average length of a cylinder as L, themass of total amphiphiles in a unit cell can be calculated
from the equation,pﬃﬃﬃ
 pﬃﬃﬃ

3 3 2 3 3 2
2a LD 
a  3πR LDw
M1 ¼
2
2

(3)

The number of the amphiphilic molecule in this mass
1
NA wherecan be calculated from NSDS ¼ mMSDS
mSDS is the molecular weight of SDS surfactant andNA the Avogadro’s number. The value of the crosssectional area of the head group of each molecule isthen, a0 ¼ A=NSDS , A being the curved surface area
(6πRL) of all the three cylinders. The value of a0 is
calculated to be 44.82AA2 . The volume of each molecule, v ¼ 3πR2 L=NSDS , is found to be 375.17AA3 . The
critical value of chain length is calculated from theequation [28], lc ¼ ð1:54 þ 1:265 nÞ AA, where n is
the number of carbon atoms in the chain. For SDS
molecule with n = 12, the value of lc = 16.72 AA.
Using the values of a0 , v and lc , the packing parameter,p ¼ av0 l , of the SDS molecule is found to be 0.50 whichcorresponds to the formation of direct cylindrical
micelles [27]. It is already known that the hexagonalphase observed in an aqueous solution of SDS at low
surfactant content is made up of direct cylindrical
micelles [26] (Figure 11). However, this result validates
our approach to calculate the value of the packing
parameter for the second hexagonal phase (HII)
which is observed on the other side of the lamellar
phase.
Hexagonal phase (HII) at α = 0.2: As is stated above,
the hexagonal phase that appears after the lamellar
phase is generally formed by reverse cylindrical
micelles as shown in the schematic in Figure 11.

1337

Considering reverse cylindrical micelle and following
the approach above, the radius (R) of the water cylinder was calculated to be 24.34 Å. The lattice parameterfor this phase was, a ¼ 55:52 AA: Here, the expressionof the total mass of amphiphiles is composed of SDS
and BMIM-BF4 and the expression is given aspﬃﬃﬃ
3 3 2 M1 ¼ MSDS þ MIL ¼
a LD  3πR2 LDw(4)
2
The masses, MSDS and MIL of SDS and IL, respectively, canbe calculated from equation (4) and from the molar ratio,IL
α = MMSDSIL =m=mSDS where mIL and mSDS are the molecular weightof BMIM-BF4 and SDS, respectively.Taking care of contributions from SDS and the IL, the average cross-sectional
area (ao ) of the head group and the volume (v) of theamphiphilic molecule were found to be 65.9 7 AA2 and349.29 AA3 , respectively, for the sample at α = 0.2. The
volume (v) is calculated from equation (5) as given below.
pﬃﬃ
3 3 2
a  3πR2v¼ 2(5)NSDS þ NIL
where a is the lattice parameter of the hexagonal latticeand SDS and NIL are the number of SDS and BMIM-BF4
molecules, respectively. Calculating the average critical
chain length, lc ¼ 15:03 AA, with n = 12 for SDS and
4 for BMIM-BF4, the packing parameter (p) was foundto be 0.35. However, the value of p for a reverse micelleshould be ≥1. Hence, the micelle in this hexagonalphase may not be of a reverse type.
Considering the micelle as the direct one and following the approach taken for the sample at α = 0, thevalue of the radius of the cylinder was found to be
16.05 AA. The total mass M1 was calculated again from
Equation (3), however having two components MSDS
and MIL : The average cross-sectional area of headgroup (a0 ) and the volume (v) of the amphiphilicmolecule were calculated to be 43.49 AA2 and348.95AA3 , respectively. Using the calculated averagevalue of lc ¼ 15:03 AA, the packing parameter was
calculated to be 0.53. This value is close to the packing
parameter of a direct micelle. Hence, the micelle in thishexagonal phase is likely to be of the direct type. The
calculated parameters for all the phases are given in
Table 3. The presence of cations of the IL in the
micelles will screen the repulsion between the SDS
head groups, which, in turn, may reduce the effective
head group area. This is a condition to achievea reverse micelle. However, in the present case, thishead group effect is compensated due to the reductionin the effective volume of the molecule, which may be
the reason for observing the direct micelle. It is

1338

S. MITRA ET AL.

Table 3. Calculated parameters of an amphiphilic molecule in hexagonal (HI), lamellar (Lα ) and second hexagonal (HII) phases.
Weight fraction
φ
0.4

Molar ratioα0 (HI)
0.015 (HI)
0.2 (HII) (Reverse micelle)
0.2 (HII) (Direct micelle)

Head group areaa0 (Å2)44.82 ± 4.26
35.52 ± 3.37
65.97 ± 3.43
43.49 ± 4.13

reported that the IL molecules used in this study insert
their chains into the hydrocarbon region of amphiphilic molecules and reduce the effective thickness of themolecular layer [47]. In such an effect in chain length isalso evident here as shown in Table 3.

Molecular volume v (Å3)
375.17 ± 19.51
260.91 ± 13.57
349.29 ± 18.16
348.95 ± 18.14

Chain length lc (Å)
16.72 ± 0.57
16.60 ± 0.56
15.03 ± 0.51
15.03 ± 0.51

Packing parameterp
0.50 ± 0..06
0.44 ± 0.05
0.35 ± 0.04
0.53 ± 0.06

ORCID
http://orcid.org/0000-0002-5132-3526
Saheli Mitra
http://orcid.org/0000-0001-5235Gourav Bhattacharya
9240
http://orcid.org/0000-0003-3144-0300
Surajit Dhara
http://orcid.org/0000-0002-4974-7311
Sajal Kumar Ghosh

Conclusions
The hexagonal phase of direct cylindrical micelles in an
aqueous solution of sodium dodecyl sulfate has beenfound to transform to rectangular and lamellar phases
at the presence of short (two hydrocarbons in the
chain) and long (10 hydrocarbons in the chain) hydrophobic chain imidazolium-based ionic liquids, respectively. However, at the presence of a medium chain
ionic liquid (four hydrocarbons in the chain) the hexagonal phase of pure surfactant is transformed toanother hexagonal phase of direct cylindrical micelles
at the presence of few mol% of the ionic liquid,
1-butyl-3-methylimidazolium tetrafluoroborate. The
lamellar phase of stacked bilayers was the intermediateof these two phases. Even though the small angle x-ray
diffraction study has revealed the lattice parameters ofthese hexagonal phases to be comparable to each other,
their rheological behaviour has been distinctly different. Generally, the hexagonal phase after the lamellar
phase in a phase diagram of a surfactant molecule is
known to form by reverse micelle, which is not the casein the present study. Theoretical calculations haveestablished the second hexagonal phase to be made of
direct micelles also.

Acknowledgements
S. M acknowledges the financial assistance of the Department of
Science and Technology (DST), India through INSPIRE fellowship and S. K. G acknowledges the financial support received
from UGC-DAE CSR (Mumbai Centre). We also thank DST
for financial support and Saha Institute of Nuclear Physics(SINP) for facilitating the experiments at the Indian Beamline,
Photon Factory, KEK, Japan. S. M and S. K. G are thankful toProf. Rupamanjari Ghosh and Prof. Sankar Dhar for theiracademic support and encouragement.

Disclosure statement
No potential conflict of interest was reported by the authors.

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