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Cite this:Phys.Chem.Chem.Phys.,

2018, 20, 26621

Ion fluctuations and intermembrane interactionsin the aqueous dispersions of a dialkylchaincationic surfactant studied using dielectricrelaxation spectroscopy and small- andwide-angle X-ray scattering†

Keiichi Yanase,a Miku Obikane,a Taku Ogura,*b Richard Buchner, c

Akinori Igarashib and Takaaki Sato *a

A dialkylchain cationic surfactant forms the so-called a-gel in water showing virtually no fluidity, which

is transformed into a highly fluidic dispersion upon addition of a small amount of salt. This intriguing

phenomenon is utilized in household industries. However, the underlying mechanisms remain unclear.

Here, we use dielectric relaxation spectroscopy (DRS) and simultaneous small- and wide-angle X-ray

scattering (SWAXS) to shed light on this issue. We find that an excess amount of CaCl2 induces an a-gel-

to-multi-lamellar vesicle (MLV) transition accompanied by a marked increase of the reservoir volume

fraction. This resembles an unbound lamellar-to-bound lamellar transition that cannot be explained

without invoking a weak long-ranged electrostatic attraction. The DRS data provide evidence that the

counterions fluctuate both vertically and laterally at the interface, whose relaxation amplitudes sharply

depend on a percolating state of an aqueous phase. The strikingly small bulk-water amplitude is likely to

reflect depolarizing electric fields induced by the MLV architecture, along with genuine hydration effects.

The modified Caille approach to the SAXS intensities reveals sensitive salt-concentration dependent

membrane–membrane interactions. The least undulating membranes are formed at a salt concentration

of ca. 10 mmol L�1. Above 25 mmol L�1, where small surface separation (o2.5 nm) is attained, far more

undulating membranes than those predicted by the Helfrich interaction are produced. This suggests that

the hydration forces, generally believed to induce strong short-range repulsion, do not suppress the

membrane undulation fluctuations.

1 Introduction

Understanding interactions between membranes is central tocomprehending a wide range of physical, chemical and bio-logical phenomena. It has long been believed that as classicalDerjaguin–Landau–Verwey–Overbeek (DLVO) theory predicted,

fundamental interactions between membranes are to a largeextent determined by a balance between attractive van derWaals and repulsive electric double-layer forces.1–4 It has beenrecognized that non-DLVO forces also play a significant role.3–14

The Helfrich undulation interaction, arising from the sterichindrance of the out-of-plane fluctuations of flexible mem-branes, leads to a long range repulsive force.7 For a double-chain surfactant, the bending modulus kc E kBT seems to be anecessary condition for spontaneous vesicles to be equilibriumstructures, where kB is the Boltzmann constant and T is thetemperature, because the induced Helfrich-type repulsion betweenbilayers can dominate the van der Waals attraction.15 Water layersand hydrated ions adjacent to the interface induce a strongrepulsive potential at a small separation of less than B20 Å, whosedecay is empirically described by an exponential function having acharacteristic length of about 5 Å.3,4,6,13 This notable short rangerepulsive force is called the hydration force, which efficientlyprevents direct contact of the membranes embedded in water.

a Department of Chemistry and Materials, Faculty of Textile Science and

Technology, Shinshu University, Ueda, Nagano 386-8567, Japan.

E-mail: takaakis@shinshu-u.ac.jp; Tel: +81 268 21 5586b Research & Development Headquarters, LION Corporation, Tokyo 132-0035,

Japan. E-mail: t-ogura@lion.co.jp; Tel: +81 3 3616 3646c Institut fur Physikalische und Theoretische Chemie, Universitat Regensburg, 93040,

Regensburg, Germany

† Electronic supplementary information (ESI) available: Density and viscositydata; simulated relaxation amplitudes of ion fluctuation processes based onGrosse theory; interaction potential calculations based on DLVO theory, Sogami–Ise theory, and the modified DLVO theory of Hishida; SAXS experimentsperformed with a pinhole camera; microscope observations. See DOI: 10.1039/c8cp05575k

Received 3rd September 2018,Accepted 21st September 2018

DOI: 10.1039/c8cp05575k

rsc.li/pccp

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Batista et al.14 indicated that a clear decomposition of the inter-action potential into individual contributions often becomes diffi-cult due to the coupled structural dynamics of neighboringcolloidal particles and surrounding media.

An alternative description of the fundamental forces to thatof the classical DLVO theory was given by Langmuir in 1938,5

which involved a long-range electrostatic attraction. Althoughthis idea was not widely accepted for a long time, it wasrestored by Sogami in his electrostatic interaction theory in1983.8 Sogami and Ise9 argued that order formation observedin a dispersion of highly charged macroions is unable to beexplained without invoking a weak long-range electrostaticattraction mediated by the intermediate counterions. Lukatskyand Safran12 also pointed out that counterion fluctuationsinduce attraction between interfaces. Using dielectric relaxationspectroscopy (DRS), Buchner and co-workers unambiguouslyshowed that multidimensional fluctuations of the counterionsoccur in aqueous micellar solutions of ionic surfactants,such as sodium dodecyl sulfate (SDS)16 and alkyltrimethyl-ammonium salts.17,18 These micelle-specific ion fluctuationscan be detected as two well-defined relaxation modes havingnanosecond timescales.

Interactions between bilayer membranes in a variety ofsystems have been studied by using a direct force measurementtechnique3,4,13,19,20 originally developed by Israelachvili.3,4 Thistechnique allowed a variety of interactions between surfaces inliquids to be revealed depending on the nature of the surfacesas well as mediating liquids at sub nanometer resolution.Quantitative information about the interactions occurring in

a stack of bilayer membranes is accessible by means of small-angle scattering of X-rays or neutrons.15,21–28 In the pioneeringstudies of Safinya and Roux,21,22 they demonstrated that inter-actions between negatively charged membranes composed ofSDS and pentanol monitored along two dilution paths withwater and brine are almost solely dominated by electrostaticand undulation forces, respectively.

Dialkyl dimethyl ammonium salts are an important class ofcationic surfactants. Since the discovery of a totally syntheticbilayer membrane composed of didodecyl dimethyl ammoniumbromide by Kunitake et al.,29 pseudo-spontaneous vesicle for-mation in ionic30–32 and nonionic33 systems has been extensivelydiscussed.19,26,28–30,32,34 In household industries, an inorganic saltsuch as CaCl2 is used as a viscosity modifier of aqueous double-chain cationic surfactant-based materials in the productionof a wide range of home and personal products. Dihardenedtallow dimethyl ammonium chloride (DTDAC; 2HT) forms theso-called a-gel in water, i.e., a lamellar gel having partiallyfrozen hydrocarbon chains showing virtually no fluidity(Fig. 1). Upon addition of a small amount of salt, a stiff a-gelis transformed into a highly fluidic milky dispersion. To clarifythe underlying mechanisms of this intriguing phenomenon, weinvestigate the effects of CaCl2 concentration on the inter-actions between the bilayer membranes formed by 2HT. Weevaluate the extent of the bilayer undulation fluctuation dis-order by means of simultaneous small- and wide-angle X-rayscattering (SWAXS). To monitor counterion fluctuations andthe cooperative dynamics of solvent water, we use dielectricrelaxation spectroscopy (DRS).16–18,35–41

Fig. 1 Effects of CaCl2 concentration, csalt, on the fluidity of 10 wt% 2HT dispersions: (A) a visual inspection, (B) low shear rate viscosities at a shearrate of 0.01 s�1, and (C) representative images using phase-contrast microscopy (scale bar = 100 mm). For the sake of clarity, a bright-field micro-graph of a 2HT dispersion without CaCl2 salt, whose observation condition is identical to that of the image at the right top corner, is also displayed.The open and filled symbols in (B) represent the data for the a-gel and MLVs, respectively. Most plausible structures are schematically depicted in theupper part of panel (B). Light blue and red areas highlight the salt concentration regions, in which the dispersions exhibit high and low fluidity,respectively.

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2 Experimental section2.1 Materials

Dialkyl chain cationic surfactant, dihardened tallow dimethyl-ammonium chloride (2HT), was supplied by Research & Devel-opment Headquarters, LION Corporation, Japan, and calciumchloride (CaCl2) was purchased from Wako Pure ChemicalIndustries Ltd, Japan. These materials were used as received.Gas chromatography analysis indicated C16H33C16H33N(CH3)2Cl :C16H33C18H37N(CH3)2Cl : C18H37C18H37N(CH3)2Cl = 16 : 42 : 42,according to which the average molecular mass was evaluated tobe 565 g mol�1. The melted 2HT surfactant was thoroughly mixedwith hot water at 60 1C under reduced pressure. Aqueous CaCl2solution was added to the 2HT/water mixtures to adjust the saltconcentration and the samples were gently stirred for 30 minuteswhilst being kept at 60 1C. The formulated dispersions wereequilibrated at 25 1C for several days. The surfactant concentrationwas fixed to 10 wt% and the CaCl2 concentration, csalt, was variedin the range of 0 r csalt/mmol L�1 r 44.5.

2.2 Dielectric relaxation spectroscopy (DRS)

Dielectric relaxation spectroscopy monitors the response ofdipolar liquids to an applied time-dependent electric field offrequency, n. For a solution exhibiting non-negligible dc con-ductivity, k, the response is described in terms of the totalcomplex permittivity, Z*(n) = e*(n) � ik/2pne0, where e*(n) is thecomplex permittivity and e0 is the permittivity of a vacuum.An additional second term denotes an Ohmic loss contributioncaused by charge transport. We determined the complex dielectricspectra, e*(n) = e0(n) � ie00(n), of the aqueous dispersions of 2HT at25 1C in 0.5 MHz r nr 20 GHz by measuring the total complexpermittivity, Z*(n), where e0(n) and e00(n) are the relative dielectricpermittivity and the dielectric loss, respectively. We employed timedomain reflectometry (TDR) comprising the Hewlett–Packardinstruments HP54121A and HP54120B. All time-domain measure-ments and the transformation of the time-dependent reflectedpulse waveforms to the frequency-domain spectra were performedaccording to a previously reported procedure.38 The conductivity ofthe samples can be evaluated from the reflected waveform mea-surements in the TDR experiment.

To give a quantitative description of the experimental e*(n)spectra, a series of conceivable relaxation models based on asuperposition of n Havriliak–Negami equations42

e�ðnÞ ¼ e1 þXnj¼1

Dej

1þ i2pntj� �bjh iaj (1)

or its counterparts, such as Debye, Cole–Cole, and Davidson–Cole equations, were tested using a non-linear least-squaresfitting procedure. A jth dispersion step ( j = 1, 2,. . . and n) isdefined according to the magnitude of its relaxation time,tj (tj 4 tj+1). n is the number of dispersion steps, eN is theinfinite frequency permittivity and aj and bj are the shapeparameters representing asymmetric43 and symmetric44 broad-ening of the spectrum shape, respectively.

2.3 Small- and wide-angle X-ray scattering (SWAXS)

Simultaneous small- and wide-angle X-ray scattering (SWAXS)experiments were carried out using a SAXSess camera (AntonPaar, Graz, Austria) in the extended q-range between 0.06 and27 nm�1, where q is the magnitude of the scattering vector. Theapparatus was equipped with an X-ray generator with a longfine focus sealed glass X-ray tube (GE Inspection Technologies,Germany), a focusing multilayer optics, and a block collimator.The system provided a line-shaped monochromatic primarybeam (Cu Ka radiation, a wavelength l = 0.154 nm). Thegenerator was operated at 40 kV and 50 mA. The scatteringintensity was recorded using an imaging-plate detector having apixel size of 45 mm� 45 mm and the sample to detector distancewas 265 mm, corresponding to Dq E 0.007 nm�1. The two-dimensional scattered intensities were integrated into a one-dimensional scattering curve. We used a vacuum-tight quartzcapillary cell with a 1 mm diameter that can be repeatedly used.The background contributions from a capillary cell and thesolvent were subtracted. The absolute intensity calibration was madeusing water as a secondary standard.45 A model-independentcollimation correction procedure (desmearing) was appliedrelying on the Lake algorithm46 to obtain the scattering curvesequivalent to those measured by an ideal point focus system.

To confirm the isotropic scattering patterns of the 2HTdispersion, SAXS experiments were performed using a pinholecamera, a SmartLab instrument (Rigaku, Japan). This instru-ment provides a point collimated primary beam of Cu Ka

radiation. The diameters of the first and second pinholes are50 and 80 mm, respectively. The covered q-range is between0.16 and 1.21 nm�1.

2.4 Density measurements

Using a high precision densimeter, DMA4500 (Anton Paar, Austria),which is based on a conventional mechanical oscillator method,density measurements were carried out on aqueous dispersions of2HT at 25 1C at different salt concentrations. The density data wereused for calculating the molar concentration of the 2HT surfactant,c2HT [mol L�1], as well as the analytical water concentration, cw(c)[mol L�1], from the surfactant weight fraction, w2HT. The data aresummarized in Table S1 of the ESI.†

2.5 Viscosity curve measurements

Shear viscosities of the 2HT dispersions at different salt concen-trations were measured on an MCR92 rheometer (Anton Paar)equipped with a cone-plate measuring device in the shear raterange of 0.01–1000 s�1 at 25 1C. Viscosity curves are shown inFig. S1 of the ESI.†

2.6 Optical microscopy observation

Microscopy observations were performed using an invertedmicroscope Eclipse Ts2 (Nikon, Japan). A drop of the 2HTdispersion was placed onto a 1 mm thick microscope slide,and the specimen was covered by a thin cover glass to avoidsolvent evaporation.

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3 Results and discussion3.1 Dielectric properties of the aqueous dispersions of 2HT

In Fig. 2, we show the complex dielectric spectra, e*(n), of theaqueous dispersions of 2HT at 25 1C as a function of CaCl2

concentration, csalt. Upon addition of 2HT to water, broad low-frequency dispersions emerge. At high salt concentrations(csalt \ 10 mmol L�1), these contributions become morepronounced and far exceed the solvent contribution in termsof their amplitudes. The high frequency process centered atB19 GHz always appears without a notable shift in the losspeak frequency of pure water. By fitting the experimental e*(n)spectra to eqn (1), we find that a superposition of four Debyerelaxation functions gives the best and most consistent descrip-tion of the dielectric response of the 2HT dispersions, which isconveniently written as

e�ðnÞ ¼ e1 þDeMW

1þ i2pntMWð Þ þDe1

1þ i2pnt1ð Þ

þ De21þ i2pnt2ð Þ þ

De31þ i2pnt3ð Þ

(2)

The results of the fitting procedure are shown in Fig. 2B–E.The lowest-frequency process centered at about 3 MHz isassigned to the so-called Maxwell–Wagner (MW) relaxationarising from interfacial polarization effects. This emerges whenthe transportation of ions is blocked by the interface, whichcannot be seen for aqueous solutions of ionic surfactants,such as SDS16 or alkyl trimethyl ammonium bromide (TAB) orchloride (TAC).17 Apart from the MW relaxation, we observe twoadditional solute relaxation processes ( j = 1 and 2) in the MHzfrequency region, whose relaxation times are rather similarto those observed in a variety of ionic micellar solutions.16–18

They can be assigned to counterion fluctuations despite the

fairly different surfactant self-assembly structures. By compar-ing the spectrum of pure water,40 the high-frequency process( j = 3) is clearly attributed to the cooperative relaxation of bulkwater. In Fig. 3, the relaxation times, tj, and amplitudes, Dej, arepresented.

3.2 Solute relaxation and ion fluctuations

We analyzed the salt concentration dependence of the spectra.Two solute-modes for ionic surfactant solutions are generallywell described by the Grosse model for a dispersion of chargedspherical colloidal particles.16–18,47 The Grosse model predictsthat the relaxation times, tj, and amplitudes, Dej, of the ion-cloudrelaxation ( j = 1) and of the surface-hopping mode of the adsorbed

Fig. 2 Spectra of (A) dielectric dispersion, e0(n), and dielectric loss, e00(n), of 10 wt% 2HT dispersions at 25 1C in a CaCl2 concentration range between0 and 44.5 mmol L�1. Solid lines represent the pure water spectrum40 for comparison. The e*(n) spectra at CaCl2 molar concentrations of (B) 0 mmol L�1,(C) 5.3 mmol L�1, (D) 13.3 mmol L�1, and (E) 44.5 mmol L�1.

Fig. 3 (A) Dielectric relaxation times, tj, and (B) amplitudes, Dej, of theaqueous dispersions of 2HT at 25 1C (a Maxwell–Wagner (MW) relaxationand j = 1, 2 and 3) as a function of added salt (CaCl2) concentration. Theopen and filled symbols represent the data for the a-gel and MLVs,respectively. The blue area highlights the highly fluidic region. Cross marksindicate the predicted De2 (eqn (6)) values from lS determined from theexperimental t2 values.

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but still mobile counterions ( j = 2) are defined by the followingfour equations,17,47

t1 �RG

2

D(3)

De1 ¼9fem

2wlSk

� �4

162wlSk

2lSRGk

þ 1

� �þ 2

� �2 (4)

t2 ¼e0em

epemþ 2

� �

k2lSRGk

þ 2

� � (5)

De2 ¼9fem

2lSRGk

� epem

� �2

epemþ 2

� �2lSRGk

þ 2

� �� �2 (6)

where D is the diffusion coefficient of free counterions, RG is theGrosse radius describing the location of the adsorbed counterionsfrom the center of mass of the particles, f is the volume fraction ofthe particles, ep and em are the static permittivities of the particle’score and the medium, respectively, w�1 is the Debye length, k is thedc conductivity of the dispersion, and lS is the surface con-ductivity. Strictly speaking, the Grosse model can be validlyapplied to spherical particle systems in the limit of RG c w�1.Nevertheless, we apply it to the present MLV systems in anextended manner. Note that, obviously, the 2HT bilayermembrane is not a homogeneous spherical particle, but itssmall curvature gives a better situation for applying the Grossemodel to the charged bilayers than to charged spherical-likemicelles. Using eqn (3)–(6), RG, lS, De2, and w�1 can be evaluatedusing the experimentally determined parameters of t1, De1, t2,De2, and k (Fig. 3 and 4). We fix f to 0.11 and assume the valuesof ep = 2 and em = 78.4, whereas D of Cl� (2.03 � 10�9 m2 s�1) istaken from the literature.48

The RG value can solely be determined from t1 (eqn (3)),assuming that the constant diffusion coefficient D =2.03 �10�9 m2 s�1. From t1 E 6.4 ns, RG E 3.6 nm is obtained,which is virtually independent of csalt. Since the salt-added 2HTdispersions show the formation of sub-micron to micron-sizedspherical-like particles, it is obvious that RG E 3.6 nm cannotbe correlated with the radii of the MLVs. Instead, the value is nicelycoupled to the thickness of the 2HT bilayer, d (ca. 4.8–5 nm) (seeFig. 8B and C). Indeed, RG E 3.6 nm is comparable to the distanceof d/2 + 4r(H2O) + r(Cl�) E 3.3 nm estimated by accounting for thehydration layers of the interface and chloride ion, where r(H2O)and r(Cl�) are the radii of a water molecule and chloride ion,respectively. Therefore, the value of RG can be practically inter-preted as the location of the center of the condensed counterionsrelative to the center of the 2HT membrane around which thecounterions fluctuate.

As for ionic spherical-like micelles, such as SDS16 andC8TAB, C12TAB, C16TAB and C12TAC17 micelles, the amplitude

of the surface-hopping (the lateral mode), De2, is always domi-nant over that of the ion-cloud fluctuation (the vertical mode),De1. However, we find that in the 2HT dispersions, the ampli-tudes of the lateral and vertical modes are inverted (De1 4 De2).Furthermore, De1 shows approximately one order of magnitudegreater values than that observed for ionic micellar solutions.16,17

These phenomena can be understood based on simple simulationusing eqn (4) and (6). Although the Grosse model does notexplicitly involve ion concentration or ionic strength, the effect isimplicitly expressed in the Debye length, w�1, and the relativesurface conductivity against the bulk conductivity, lS/k. The simu-lated De1 and De2 as a function of lS/k are shown in Fig. S2 (ESI†),in which the Debye length w�1 is fixed as 2, 2.5, and 3 nm forsimplicity although in a strict sense, w�1 and k are not indepen-dent. At higher csalt, the shorter w�1 leads to greater values of De1.De1 shows an upturn increase with lS/k, while De2 exhibits arelatively moderate upward-convex increase. Thereby, a high lS/kvalue, i.e., a high surface conductivity lS relative to the bulkconductivity k, results not only in greater relaxation amplitudesof the ion fluctuations, but also in the inversion of De1 and De2,yielding a greater value of De1 than De2.

It is known that membranes and vesicle architectures serveas an insulator of electric conduction. The conductivity in thevesicle dispersions can be approximated to be in inverseproportion to the diameter of the MLVs.26,49 Indeed, themeasured conductivities of the 2HT dispersions are one orderof magnitude smaller than those of the C12TAC solutions withno added salt.17 Furthermore, ions dissolved in an inneraqueous phase of the vesicles may not practically contributeto the conductivity of the dispersion.

Fig. 4 (A) The Grosse radius, RG, (B) the bulk conductivity, k, (C) the Debyelength, w�1, and (D) the relative surface conductivity against the bulkconductivity, lS/k, as a function of added salt (CaCl2) concentration. Theopen and filled symbols represent the data for the a-gel and MLVs,respectively. The blue area highlights the highly fluidic region. Crosssymbols in (C) represent the Debye length calculated in a conventional

manner from w�1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieme0kBT2NAe2I

r.

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Importantly, we observe that the amplitude of the diffuseion cloud (De1) exhibits an eccentric behavior, a minimum atcsalt E 5 mmol L�1 and a most abrupt increase in the range of10 o csalt/mmol L�1 o 20. In Fig. 4D, we present the evaluatedlS/k from t2 applying eqn (5) using the measured k and thereadily determined RG. In Fig. 3B, the predicted De2 values fromlS determined from the experimental t2 values are shown.Despite a successive increase of the ion concentration, lS/kshows a minimum at csalt E 10 mmol L�1. This causes thecharacteristic behavior of De1 shown in Fig. 3B. As shown inFig. 1, the viscosity of the 2HT dispersions drastically decreasesupon addition of a small amount of salt (csalt o 3 mmol L�1),but with a further increase of the salt concentration (csalt 410 mmol L�1), it rapidly increases. Therefore, the minimum oflS/k and the resulting marked change of De1 in the range of10 o csalt/mmol L�1 o 20 can be attributed to the a-gel-to-vesicle transition accompanied by a drastic increase of thereservoir volume fraction due to expelled solvent water. A sharpminimum of lS/k mainly reflects a macroscopically permeablestate of an aqueous phase.

As shown in Fig. 4C, the w�1 values resulting from the DRSanalysis based on the Grosse model show a similar decreasingtrend to those obtained by conventional calculations. Althoughthe discrepancy between them is far less than one order ofmagnitude, this may be caused by non-ideal application con-ditions of the Grosse theory to the MLVs or a-gel. A simpleassumption for the degree of counterion dissociation E0.1 forthe conventional calculation may also be an error source.

3.3 Hydration effects of 2HT

The dielectric spectrum of pure water in the microwave regionis governed by a single Debye relaxation attributed to thecollective reorientation of water molecules, which is associatedwith the cooperative rearrangement of the hydrogen-bond net-work of water.40 In the 2HT dispersions, the amplitude of bulkwater, De3, is strikingly smaller than those predicted by amixture model and the analytical (actual) water concentration,it is reduced to about 65% or less than that of pure water atw2HT = 0.1. This seems to be in part due to the manifestation ofthe strong water binding capability of 2HT and may imply thatan enormous number of water molecules are strongly bound bythe surfactants and ions in a cooperative manner. However,such a marked reduction of the bulk water amplitude is notobserved for the nonionic and ionic micellar solutions,16,18,36,41

but the situation is rather similar to those observed for aqueousdispersions of zwitterionic phospholipids in a pioneering workof Pottel et al.35 Here, we attempt to quantify the hydrationeffects. Relying on the generalized Cavell equation,39,50 therelaxation amplitude of the jth relaxation process, Dej, is con-nected to the concentration of the relaxation species, cj, by

Dej ¼e

3 eþ 1� eð ÞAj

NA

kBTe0

gjmGj2

1� aj fj� �2cj (7)

where e is the static permittivity, Aj is the shape parameter, NA isAvogadro’s number, kB is the Boltzmann constant, e0 is the

vacuum permittivity, mGj is the gas-phase dipole moment, gj isthe dipole–dipole correlation factor, aj is the polarizability andfj is the field factor. By normalizing eqn (7) to that of pure water(solute concentration c = 0), the apparent water concentration,cw(c)app, at solute molar concentration c is written as

cw cð Þapp ¼ gwðcÞgwð0Þ

cw cð Þ

¼ eð0Þ 2eðcÞ þ 1½ �eðcÞ 2eð0Þ þ 1½ �

1� awfwðcÞ½ �2

1� awfwð0Þ½ �2DewðcÞDewð0Þ

cwð0Þ(8)

where Dew(0) = 72.5 and Dew(c) = De3(c). Assuming a sphericalwater molecule (Aj = 1/3) having a radius r = 0.1425 nm and apolarizability aw = 1.607 � 10�40 C m2 V�1, the apparentconcentration of bulk water, cw(c)app, can be calculated(Fig. 5A). Generally, cw(c)app is understood as the concentrationof water molecules that are not affected by the presence ofsolute molecules and/or ions, and thus they still retain theirdynamic properties identical to those of bulk-water. We furtherdefine the effective hydration number of a 2HT molecule, Zhyd,involving counterion hydration effects as

Zhyd ¼cwðcÞ � cwðcÞapp

c(9)

where c is the molar concentration of the surfactant (=c2HT).From eqn (9), Zhyd gives the number of water molecules thatcannot contribute to the bulk-water relaxation process ( j = 3)due to hydration effects.

In ionic surfactant solutions, a slow water mode oftenappears as a several-times-slower relaxation process comparedto that of bulk-like water.16,18,36 This is normally assigned to thewater molecules exhibiting reduced but not rotationally immo-bilized dynamics. Importantly, we are not able to resolve anyslow water relaxation in the 2HT dispersions in the entire csalt

range. Therefore, the evaluated Zhyd based on eqn (9) is to beinterpreted as Zib, where Zib is the number of ‘irrotationally

Fig. 5 Effects of added CaCl2 on the hydration of 2HT. (A) The apparentbulk water concentration, capp

w , calculated from the bulk water relaxationamplitude and analytical water (molar) concentration, cw, and (B) theKirkwood’s dipole–dipole correlation factor of water, gw(c), in the 2HTdispersions normalized by that in pure water, gw(0), as a function of CaCl2concentration, csalt. The blue area highlights the region where the disper-sion is highly fluidic.

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bound’ water molecules per surfactant. cw(c) � cw(c)app reaches12 mol L�1 at w2HT = 0.1 (c2HT E 0.17 mol L�1) under low saltconditions, corresponding to Zib E 70. Furthermore, Zib 4100 is obtained under high salt conditions, where csalt 425 mmol L�1. There are more than a couple of factors thatmay conceivably explain the high Zib values; the 2HT bilayermembranes are covered with an extended hydrophobic surface,cations potentially have a higher impact on the rotationalmobility of water molecules than anions do (the hydrationnumber of Ca2+ was estimated to be ca. 10 at room temperatureby means of extensive measurements of the colligative proper-ties of aqueous calcium salts,51 whereas Zib = 0 was evaluatedfor Cl� by DRS37), and water molecules can be cooperativelybound by an anion and a cation, resulting in a frozen state intheir rotational dynamics.

However, we obtain Zib E 80 at csalt = 18 mmol L�1, whichalready exceeds the number of water molecules existing in a3.4 nm-thick water layer between the surfaces. Strong compres-sions of water layers and/or an extremely long-range influenceextended over more than several water layers from the surfacethat freezes the rotational mobilities of all water molecules hasbeen suggested.52

Eqn (8) yields the relative Kirkwood’s dipole–dipole correla-tion factor in solution against that in pure water, gw(c)/gw(0), asexpressed in its second term, which is a measure of theperturbation of the water dipole moments’ parallel alignment(Fig. 5B). The observed drastic reduction of the bulk wateramplitude corresponds to a decrease of the Kirkwood’s dipole–dipole correlation factor, decreasing to less than 70% of that inpure water. This finding is corroborated by the observation of

Pottel et al. in their pioneering work on aqueous dispersions ofzwitterionic phospholipids.35 The drastic effects on the bulkwater relaxation amplitude, De3, manifested in the gw(c)/gw(0)values are likely to reflect depolarizing electric fields induced bythe MLV architectures, as recently predicted by Steinhauser andco-workers,53 which should be distinctly different from those inionic micellar solutions and dispersions of homogeneousdielectric spheres. The simultaneous appearance of the maximain capp

w and gw(c) as well as the minimum in lS/k in the high-fluidityregion of csalt o 10 mmol L�1 should be closely linked with apermeable state of an outer aqueous phase.

3.4 Static structures of 2HT dispersions

It is established that liquid-like systems, e.g., a-gels, lamellarlyotropic liquid crystals,54 and MLVs,55,56 exhibit isotropicscattering patterns under static conditions. In Fig. S3 (ESI†),we compare the scattering patterns obtained by a point and aline collimated apparatus, which confirm the isotropic scatter-ing patterns of the 2HT dispersions and that the collimation-corrected I(q) measured by the line-collimation apparatuscoincides well with that measured by the point collimatedapparatus.

In Fig. 6A, we show I(q) for the 2HT dispersions on anabsolute scale as a function of csalt. The q�2 behavior asindicated by a dashed line is the so-called fractal scatteringfrom the planar object, whose fractal dimension is 2. The high-q oscillation seen in range of 2–6 nm�1 comes from the formfactor of the planar object, mainly reflecting the thickness andinternal electron-density distributions within the bilayers.The emergence of up to three reflections in the positional ratio

Fig. 6 (A) Collimation-corrected SWAXS intensity, I(q), of the aqueous dispersions of 0.174 mol L�1 2HT at 25 1C on an absolute scale as a function ofadded CaCl2 concentration from 0 to 44.5 mmol L�1, and (B) a plot of q2I(q) in 0.06 r q/nm�1 r 2.5, emphasizing the intermembrane interferencecontributions. GIFT analyses of I(q) at CaCl2 concentrations of (C) 0 mmol L�1, (D) 2.7 mmol L�1, (E) 5.3 mmol L�1, (F) 8.9 mmol L�1, (G) 17.8 mmol L�1, and(H) 44.5 mmol L�1. The green curve represents the GIFT fit to the experimental I(q). The deduced form factor, P(q), and structure factor, S(q), are shown inred and blue curves, respectively.

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of 1 : 2 : 3 in the small angle regime reflects the long-range orderof the membrane–membrane correlations. As shown in Fig. 1,the microscope images of the 2HT dispersions confirm theformation of sub-micron to micron-sized spherical-like particles inthe salt-added dispersions, whereas no particle-like objects arefound in the sample with no added salt (a-gel). We also performedmicroscope observations on the 20-fold diluted dispersions and wewere able to observe that spherical-like particles are still present(Fig. S4, ESI†). These data confirm the formation of a multi-lamellar vesicle (MLV) structure, which can be classified as alamellar gel (Lb) phase. In Fig. 6B, the SAXS intensities in theexpression of q2I(q) are shown for a better visibility of the inter-ference scattering. Importantly, even without imposing any struc-ture factor model, it is already clear that at csalt E 10–20 mmol L�1,the sharpness of the primary peak attains its maximum and thedecay of the higher-order reflections becomes slowest.

To obtain further insights into the interactions between thebilayer membranes, we analyzed the SAXS data by applying thegeneralized indirect Fourier transformation (GIFT) technique27,57

to the small-angle regime (0.07 r q/nm�1 r 6) of the experimentalI(q). Similarly to the case of globular particle systems, the scatter-ing intensity I(q) from a multilamellar stack of the bilayermembranes can be written as I(q) p P(q)S(q), where P(q) isthe form factor and S(q) is the structure factor.27 The structurefactor S(q) in the modified Caille model24,25,27 is given by

SðqÞ ¼ N þ 2XN�1m¼1ðN �mÞ cosðmdqÞ exp � d

2p

� �2

q2Zg

" #(

�ðpmÞ�d2p

� �2q2Z�

(10)

where d is the interlayer spacing, N is the mean number ofcorrelated bilayers, which scatter X-rays in a coherent manner,and g (=0.5772) is Euler’s constant. The Caille parameter, Z, isinterpreted as a measure for the undulation fluctuation dis-order, which is given as a function of the bending modulus K ofthe bilayers and the compression modulus B24,25,27,58

Z ¼ q12kBT

8pffiffiffiffiffiffiffiKBp (11)

where q1 = 2p/d is the scattering vector corresponding to theprimary peak position in S(q). kc = Kd is the bending modulus ofa single membrane. In our present approach, it is only possibleto evaluate the product of these two moduli, KB or kcB, from theSAXS data.

Using the thickness scattering function Pt(q), P(q) is writtenas P(q) = (2pA/q2)Pt(q),27,59 where Pt(q) is given by the cosinetransformation of the thickness distance distribution function,pt(r), as

PtðqÞ ¼ 2

ð10

ptðrÞ cosðqrÞdr (12)

The thickness of the bilayer, d, is estimated to be about4.8–5.0 nm from the distance at which pt(r) goes to zero. Theelectron density profile, Dr(r), is calculated by deconvoluting

pt(r) (Fig. 8B and C). The maximum distance read out fromDr(r) (2.4–2.5 nm) is comparable to the length of a 2HTmolecule (ca. 2.5 nm).60 The negative values of Dr(r) atr o 1.5 nm can clearly be attributed to the lower electrondensity of the hydrocarbon chains compared to that of solventwater. Dr(r) appears to become nearly zero or only slightlypositive at an intermediate distance of r = 1.5–1.8 nm and againshows negative values at larger r. We infer that this behaviorreflects the average locations of the charged ammonium (N+)group and terminal methyl groups of 2HT, respectively.

As already seen in the q2I(q) plot (Fig. 6B), the shape of thestructure factor S(q) is strongly salt concentration dependent.Interlayer spacing, d, directly linked with the first-peak posi-tion, q1, in S(q) as d E 2p/q1, decreases with an increase of csalt.As shown in Fig. 6B and 8A, the a-gel-to MLV transition inducedby adding a small amount of CaCl2 causes a broader andweaker primary peak to appear in S(q), but an increase of csalt

leads to a sharper and stronger peak. The sharpest primarypeak and the slowest decay of higher-order reflections areobserved at csalt in the range of 10–20 mmol L�1, resulting inthe minimum value of the Caille parameter Z, indicating theformation of the least undulating membranes. With a furtherincrease of csalt, the interference peaks get rapidly broaderand weaker again. The number of correlated membranes, N,shows a maximum at csalt E 20 mmol L�1, leading to a localmaximum of Nd.

3.5 Interaction potential calculations

The drastic reduction of the dispersion viscosity upon additionof salt indicates that the a-gel-to-MLV transition in the 2HTsystem is accompanied by a marked increase of the reservoirvolume fraction due to expelled (excess) solvent water. In viewof the csalt-dependent behavior of the dispersion viscosity(Fig. 1B) and the interlayer spacing d (Fig. 7A), the presenta-gel-to-MLV transition looks as if it is an unbound lamellar-to-bound lamellar transition although it is still uncertain if thea-gel can be classified as an unbound lamellar phase in a strictsense. The size of the innermost aqueous phase in a MLV mayalso largely change depending on csalt. To model the inter-actions between the 2HT membranes, we calculate the inter-action free energy per unit area for two flat surfaces usingthree different potential models based on Derjaguin–Landau–Verwey–Overbeek (DLVO) theory,1,2,4 the Sogami–Ise theory,8–10

and an extended DLVO theory.61 Details of the interactionpotential calculations are described in the ESI.† The DLVOpotential, VDLVO, accounting for the attractive van der Waals andrepulsive electric double-layer forces, is shown in Fig. 9A. Milnerand Roux discussed the transition between bound and unboundstates of surfactant bilayers, which is controlled by the strength ofattractive van der Waals interactions.11 They demonstrated thatwhen the attractive van der Waals interaction is strong enough (orthe Hamaker constant, A, is large enough), the potential may havea minimum at a finite surface separation. A bound lamellar phasecannot be infinitely diluted, as it expels excess solvent whenexceeding a certain maximal dilution. In contrast, in the unboundregime, d is simply governed by the surfactant concentration.

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With increasing A, a discontinuous phase transition from anunbound lamellar phase to a bound lamellar phase coexistingwith excess solvent occurs. However, a distinct secondary minimumcannot be seen in the calculated DLVO potentials for the 2HT MLVbilayers at all investigated csalt values, which is a typical feature of anunbound lamellar phase.11 Therefore, the DLVO potential cannotexplain the observed csalt-dependence of the d values for the2HT dispersions.

Next, we recall the Sogami–Ise potential, VSI,8–10 which assumes

a weak long-range electrostatic attraction mediated by intermediatecounterions in addition to an intermediate-range repulsion(Fig. 9B). The predicted interlayer spacing from the Sogami–Isepotential, dSI = hSI + d, where hSI is the surface separationscorresponding to the minimum in VSI and d E 4.8 nm is thethickness of the 2HT bilayer, eventually coincides with the experi-mentally obtained d values (Fig. 7A). We note that as shown inFig. 9B, the depth of the potential minimum in VSI becomesshallower at a higher salt concentration, which predicts a moredisordered state of the membrane’s spatial distributions at ahigher salt concentration. The observed destabilization of thelonger-ranged ordering of the membranes, as manifested by adecrease of Nd, at a higher salt concentration is in fair agreementwith the predictions of the Sogami–Ise model and can be at leastqualitatively explained by Fig. 9B. This finding may indicate that aweak long range attraction mediated by counterions is operative inthe present systems although the issue is open to debate.62

Recently, Hishida and coworkers suggested the modifiedelectric double layer interaction potential, in which additionalosmotic pressure arising from an ion concentration differencebetween the inner and outer aqueous phases separated byvesicle architecture is taken into account.61 The modified DLVOpotential, Vmod-DLVO, is thus defined by a sum of the van derWaals and the modified electric double layer potentials.According to this model, the potential minimum becomesmarkedly deeper at a higher-salt concentration, which wouldresult in a highly ordered stacking state of the membranes at ahigher salt concentration. However, We observe the smallest Nand Nd values with unexpectedly large values of Z at high saltconcentrations, typically csalt 4 25 mM, which is an indicationof the destabilization of the long-range order of the membranesat high csalt. The predicted d values from the position of thepotential minimum in Vmod-DLVO systematically overestimatethe observed d values, as shown in Fig. 7A.

Fig. 7 Structure factor parameters for the 2HT dispersions at c2HT =0.174 mol L�1. (A) Interlayer spacing, d, (B) Caille parameter, Z, (C) theproduct of the bending modulus of a single membrane and the compres-sion modulus, kcB, and (D) the number of correlated bilayers, N, and theextent of the long-range correlation, Nd, as a function of CaCl2 concen-tration, csalt. The predicted d-values from the Sogami–Ise potential, dSI

(red cross marks), and the modified DLVO potential, dmod-DLVO (bluepositive signs), are also plotted in (A). An arrow in (B) highlights a markedincrease of Z induced by addition of a small amount of excess salt and theresulting a-gel-to-MLV transition. The blue area highlights the saltconcentration region where the dispersion exhibits high fluidity.

Fig. 8 (A) Static structure factor, S(q), of the 2HT membranes in theaqueous dispersion at c2HT = 0.174 mol L�1 as a function of CaCl2concentration in the range of 0 r csalt/mmol L�1 r 44.5 deduced fromthe SAXS intensity, I(q), shown in Fig. 6C–F using the modified Caillemodel. The thickness pair-distance distribution function, pt(r), and theelectron density profile of the 2HT membranes are also displayed in (B) and(C), respectively.

Fig. 9 Interaction free energy for two charged flat surfaces per unit areain an aqueous electrolyte solution calculated based on (A) the Derjaguin–Landau–Verwey–Overbeek (DLVO) model, VDLVO, (B) the Sogami–Isemodel, VSI, and (C) the modified DLVO model, Vmod-DLVO, as a functionof surface separation of h.

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3.6 Interactions between the 2HT membranes

To further quantify the interplay between the experimentallyobtained Caille parameter, Z, and the interlayer spacing, d,we consider the electric double-layer repulsion and Helfrichundulation interaction. The Helfrich undulation interaction isamong the non-DLVO forces arising from the steric hindranceof the out-of-plane fluctuations of flexible membranes.7 Thisleads to a long range repulsive force. According to Roux andSafinya,21,22 the compression modulus for the undulationinteraction, Bund, can be calculated from the free energy perunit volume as

Bund ¼ d9p2 kBTð Þ2

64kc

1

ðd � dÞ4 (13)

For systems in which interactions between the membranesare solely governed by the Helfrich undulation interaction, theCaille parameter, Zund, is simply given by

Zund ¼4

31� d

d

� �2

(14)

On the other hand, under the assumption that the compressi-bility of the system is dominated by electrostatic interaction, thecompression modulus, Belc,

20,22,28 may be estimated as

Belc ¼p2kBTd

2Lðd � dÞ3 1� 3S

aLðd � dÞ þ 6S2

a2L2ðd � dÞ2 þ � � �� �

(15)

where S is the surface area of the surfactant molecule, a isthe dissociation ratio of counterions, and L is defined asL = pe2/(emkBT), lB = e2/(emkBT) being called the Bjerrum lengthand about 0.72 nm in water. Combining eqn (11) and (15), theCaille parameter for such electrically stabilized systems, Zelc, atlow salt concentration is given by

Zelc ¼kBTL

2kcd

� �1=2

1� dd

� �3=2

� 1� 3S

aLðd � dÞ þ 6S2

a2L2ðd � dÞ2 þ � � �� ��1=2 (16)

When using eqn (15) and (16), the bending modulus of asingle membrane, kc, has to be treated as an unknown para-meter. Soubiran et al.26 claimed that membranes of cationicsystems are far more rigid compared to the lamellar phaseconsisting of SDS, in which kc B kBT and consequently theundulation forces are thought to be dominant for the inter-actions between lamellae. If this is the case, the thermalfluctuations may not largely contribute to the stability of themembranes in a cationic lamellar phase, but they are expectedto be stabilized almost exclusively by the electrostatic double-layer repulsions, especially at low csalt values. According toMitchell and Ninham,63 when interactions between the mem-branes are exclusively dominated by electrostatic interactions,

the bending rigidity for low salt concentrations, kLSc , can be

approximated as

kLSc ¼empw

kBT

e

� �2

(17)

This gives, for instance, kLSc = 1.04kBT at csalt = 2.7 mmol L�1,

where w�1 = 2.3 nm.In Fig. 10, we present the experimentally determined Z as a

function of d, in which the theoretically predicted Zund and Zelc

are also shown. Zelc is calculated for kc = kBT, 5kBT, 10kBT, andkLS

c . The a-gel shows Z (E0.2), which is rather close to theprediction from the electric double-layer repulsion and kc BkBT. We observe that when the salt-induced transition froma-gel to MLV occurs, Z is markedly increased. The Z value (E0.35)at csalt E 3 mmol L�1, which is considerably greater than Zelc withkc = kBT but is certainly smaller than Zund, cannot be explained interms of the purely repulsive models. As pointed out in ref. 11,attractive forces efficiently reduce the compression modulus B.Thus, the presence of attraction may potentially result in anincrease of Z. Therefore, the results indicate the operation of someattractive forces in the salt-added system. An additional attractiveinteraction due to ion–ion correlation effects,4,12,14 i.e., correlationsbetween laterally mobile ions on the surfaces and those betweenions in the diffuse double layers, is predicted. Indeed, fluctuationsof both laterally mobile ions and the vertically diffusing ion cloudin the diffuse double-layers are detected by DRS. The multidimen-sional fluctuations of the counterions and their correlationsappear to induce extra attractive interactions that may cancel thedouble-layer repulsion. Note that substitution of kc = 5kBT or 10kBTgives far smaller Zelc values, which are no longer comparable withthe experimental Z (Fig. 10). As we have already shown, the least

Fig. 10 The Caille parameter, Z, plotted as a function of the interlayerspacing, d. The filled circles and the empty circle represent the experi-mental Z values for the MLVs and the a-gel, respectively. A dashed curve isdrawn as an eye guide. The theoretically predicted Z values for the electricdouble-layer repulsion, Zelc, and the Helfrich undulation interaction, Zund

(line 1), are also shown for comparison. Zelc is calculated for kc = kBT (line 3),5kBT (line 4), 10kBT (line 5), and kLS

c (line 2) using eqn (16). The vertical dashedline indicates the bilayer thickness, d. An arrow highlights a jump of Zaccompanying the salt-induced a-gel-to-MLV transition.

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undulating membranes are formed at csalt E 10 mmol L�1.A further increase of salt concentration to 425 mmol L�1 leadsto h t 3 nm, where the double-layer theory may not hold at suchsmall separations, and highly disordered and far more undulatingmembranes than those predicted by the Helfrich interaction areproduced. We suggest that the strongly undulating membraneformation at small separations should be partly related to thedynamical properties of the hydrated counterions.

The minimum in the Sogami–Ise potential appears as aconsequence of the long-ranged weak attractive forces andthe minimum becomes shallower at a higher salt concen-tration, as shown in Fig. 9B.8 Suppose that different from thisprediction, if the attractive potential becomes deeper at a high-salt concentration, the ordered structure should be morestabilized by the electrostatic attraction with a higher saltconcentration. However, this is not the case for the present2HT systems. Hachisu et al.64 studied coexisting ordered anddisordered structures in monodisperse polystyrene latexes.They showed that at a very low ion concentration, a stableiridescent (ordered) phase is formed, whose interparticle dis-tance far exceeds the range of the van der Waals attraction.However, with increasing salt concentration, the ordered struc-ture becomes unstable and the disordered phase appears as awhitish supernatant. Despite the large difference of the sys-tems, our findings that the long-range ordering of the 2HTmembranes is most efficiently stabilized at a relatively low saltconcentration (csalt E 10 mmol L�1) and is rapidly destabilizedat a higher salt concentration of csalt \ 25 mmol L�1 arepractically in line with the observation of Hachisu et al.64

When the surface separation reduces to less than 2–3 nm,hydration forces, known as an extremely strong short-rangerepulsion induced by the presence of tightly bound watermolecules to ions or surfaces,3,4,6,13 are thought to be operative.Considering the size of the hydration shell of the ions, which istypically less than but rather close to 1 nm, the water layerbetween two membranes is mostly occupied by bound watermolecules at surface separations of about 1–2 nm observed atcsalt \ 25 mmol L�1. However, in view of the sharp increase of Zwith decreasing d, hydration forces do not suppress the undu-lation fluctuation of the membranes. If the hydrating waterlayers are so strongly bound, how can they generate highlyundulating membranes, instead of making them solid-like?This is likely to come either from the mobility of the bound ionsthemselves as detected by DRS or the exchange of hydrationwater molecules between the ions/surfaces.

We will further investigate these issues using differentco-ions and counterions more strongly and weakly bound towater molecules. The results will be reported elsewhere.

4 Conclusions

The observed salt-induced a-gel-to-MLV transition in a dispersionof dialkylchain cationic surfactant (2HT), accompanied by amarked increase of the reservoir volume due to expelled solventwater, leads to a drastic decrease of the dispersion viscosity.

This transition can be viewed as a pseudo unbound lamellar-to-bound lamellar transition, which appears to be driven by acounterion-mediated weak long-range attraction between themembranes although its generality and origin still need to beclarified. The DRS results demonstrate that the counterions fluc-tuate both vertically and laterally at the interface. The interferencescattering observed in the small-angle regime was quantified bythe modified Caille model.24,25,27,58 An experimental Z value for thea-gel (E0.2) was found to be rather close to a predicted value fromthe electric double-layer repulsion. When the a-gel-to-MLV transi-tion occurs, Z is markedly increased. The Z value at a low saltconcentration cannot be explained without invoking weak long-range attractive forces. We infer that the dynamic properties ofhydrated counterions may induce extra attractive forces betweenthe membranes,4,12,14 which can lead to a reduction of B and theconsequent increase of Z. lS/k sharply depends on whether anaqueous phase is in a permeable or an impermeable state. Thisclearly correlates with a drastic decrease of the dispersion viscositywith csalt and its subsequent increase with a further increase ofcsalt. The minimum of lS/k appears at csalt E 10 mmol L�1.Furthermore, the pronounced minimum of Z and the maximumof N at csalt E 10–20 mmol L�1 demonstrate that the undulationfluctuation disorder of the MLV membranes is most efficientlysuppressed and the long-range ordering of the membranes is moststabilized under this salinity condition. At csalt 4 25 mmol L�1,where the small surface separation of less than 2.5 nm is attained,highly disordered membranes are produced with no meltingtransition, which are far more undulating than that the Helfrichinteraction model predicts. The actual interactions between thecationic membranes seem to be more complex than what ispredicted by the existing continuum models. Our data suggestthat the hydration forces, known as a very strong short-rangerepulsion caused by the presence of tightly bound water moleculesto ions or surfaces,3,4,6,13 do not suppress the undulation fluctua-tion of the membranes under the present salinity conditions. Thesignificant reduction of the bulk water relaxation amplitudecannot be entirely attributed to the irrotationally bound watermolecules to ions and/or the interface, but it seems to come fromdepolarizing electric fields induced by the MLV architectures, assuggested for phospholipid MLV dispersions.35 This should bekept in mind when hydration effects in the MLV dispersions arediscussed.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors wish to thank Mr Daisuke Sasaki (LION Corpora-tion, Japan) for sample preparation of the 2HT dispersions,Prof. Nobuyoshi Miyamoto (Fukuoka Institute of Technology,Japan) for helpful discussion, Prof. Hiroaki Yoshida (ShinshuUniversity, Japan) for supporting microscopy observations, andMr Junji Nakamura (Anton Paar Japan K. K.) for providing

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rheological measurement data. K. Y. gratefully acknowledgesthe support from the Japan Society for the Promotion of Science(JSPS) research fellowship for young scientists DC2 (grantnumber 17J06213).

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