Soft Matter

PAPER

aDepartment of Chemistry, Nagaoka Univer

Nagaoka, Niigata, Japan. E-mail: sfujii@

9300; Tel: +81 258 47 9302bInstitute of Physical Chemistry, RWTH A

Aachen, Germany

Cite this: Soft Matter, 2013, 9, 5391

Received 10th December 2012Accepted 1st March 2013

DOI: 10.1039/c3sm27823a

www.rsc.org/softmatter

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Shear quench-induced disintegration of a nonionicsurfactant C10E3 onion phase

Shuji Fujii*a and Walter Richteringb

The growth kinetics of a shear-induced onion structure in the nonionic surfactant C10E3 system after the

shear quench is studied. In the small shear quench depth, the onion continuously grows up with a

ripening behavior while discontinuous growth behavior is observed when the shear quench depth

exceeds the threshold. In the discontinuous behavior, the initial onion first disintegrates into the planar

lamellae, and then rebuilding of the new onion structure is achieved by La–onion transformation. We

conclude that the driving force for the disintegration of the onion is the inhomogeneously stored

bending energy at the edge of the polyhedral onion. The slow disintegration behavior observed for the

stuffed onion with the colloidal particles indicates that the edges in the polyhedral onion are the origin

of the instability after the shear quench.

1 Introduction

The onion (multilamellar vesicle) phase has a quite fascinatingstructure organized by concentric amphiphilic bilayermembranes.1–5 Stable equilibrium onion structures of amphi-philic systems, but with polydisperse size distribution, can beprepared in a multicomponent bilayer system.6 Spontaneousformation of polydispersed onions has also been reported forionic surfactant and cosurfactant mixtures in which the modi-cation of the bending curvature of bilayer membranes inducesthe onion formation.1,5,7,8 In contrast, metastable onions can beprepared from the planar lamellar phase by shearing, whichresults in monodispersed size distribution.2–4,9–21 Among severalmethods of onion preparation, shearing the planar lamellarphase is widely applied to produce the densely packed onionphase with monodisperse size for many amphiphilic systemssuch as ionic and nonionic surfactants and block copolymers.So, the shear-induced onion phase is likely to be a genericmetastable phase. Many researchers have tried to understandthe physics underlying this shear-induced nonequilibriumstructural transition found for the layered structure, ever sincethe shear-induced onion formation was found by Roux et al.2–4

Inside the onion, bilayer membranes are spherically stackedwith a constant intermembrane distance which is the same asthe lamellar repeating distance.16 The onion radius is thereforedetermined by the number of bilayer membrane shells. It is wellknown that the onion radius decreases as the shear rate isincreased.2–4,16–18,22,23 According to the unique structure, the

sity of Technology, 1603-1 Kamitomioka,

mst.nagaokaut.ac.jp; Fax: +81 258 47

achen University, Landoltweg 2, 52056

Chemistry 2013

decrease in the onion radius under the shear ow will beconsidered to be a serial event induced by peeling off the outershell. However, it still remains unsolved how the shear-inducedonion recovers the larger size when the shear rate is reduced,although the shear rate dependence of the size and its revers-ibility against the shear rate are well established.22–27

The size growth behavior of the shear-induced onion aershear quench by decreasing the shear rate has been studied bysome groups.11,25,26 Panizza et al. reported that the size growthkinetics can be continuous or discontinuous depending on thequench depth of the shear rate. When the quench depth is largeenough, the onion grows up discontinuously, whereas acontinuous growth can be seen in the case of the small quenchdepth. In the discontinuous growth behavior, the onion is rstbroken down into the planar La phase through an La–onioncoexisting region, and an onion with a larger size appears viathe La–onion transition.25,26 The renewed onion thus containsno relic of the past.

It has been proposed that such breakdown and growth of theonion structure is driven by the diffusion of solvent andsurfactant monomers, referred to as permeation,27,28 coupledwith a stored stress inside the onion originating from a smecticfree energy.11 On the basis of the smectic free energy,3,29 thestored stress will be the maximum at the onion core anddecreases with the number of layers. The stress gradient insidethe onion associated with the elastic energy of the membranecan be relaxed down by the permeation of surfactant monomersfrom the core to the outside. Strong curvature in the core regioncan thus be identied as the origin of the instability causing thebreakdown of the onion. It has been proposed that the perme-ation of monomers driven by the elastic stress gradient insidethe onion causes the breakdown. However, it has also beenrecognized that once the onion phase is prepared by shearing, it

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remains for a few weeks (or months in some cases) in spite ofthe fact that the onion structure is in a nonequilibrium stateand is mechanically unstable at the quiescent state. Theobservation of the stable onion is inconsistent with such apotential instability. Even in nonequilibrium swelling anddissociation experiments carried out by Buchanan et al., theyfound that the onion core persists quite a long time without thebreakdown.30 One of the reasons for the metastability is a quiteslow behavior of the permeation.31 Observation of the stableonion core suggests that the breakdown of the onion in ourexperimental time scale is driven not only by the permeationfrom the onion core but also by other mechanisms.

A fundamental issue remaining is thus the origin of thebreakdown of the shear-induced onion and its kinetics. Addi-tionally, it has not been argued how the continuous anddiscontinuous growth process is chosen aer the shear quench.In the present study, we mainly focus our attention on abreakdown and a discontinuous onion growth behavior.Intensive studies on the ionically charged lamellar systems byHoffmann and coworkers indicate the irreversible property ofthe vesicle structures, which were formed spontaneously or byshearing.1,5,7,8 We limit our discussion on the shear-inducedonion phase with a reversibility against shear. We conclude thatan inhomogeneous distribution of the localized elastic stress atthe edge of the onion with a polyhedral shape will cause adefect-mediated permeation and results in the disintegration.Finally, we will compare the kinetic behavior of the disintegra-tion of the onion with that of a stuffed onion via particles inwhich the polyhedral shape is cancelled because of theanchoring effect of the membrane on the surface of thecolloidal particle. Our results suggest that the disintegration ofthe onion is driven by the inhomogeneous elastic energy asso-ciated with the polyhedral shape of the onion.

Fig. 1 (A) Steady state viscosity and radius of the onion as a function of shearrate. Shear rate regions I, II and III correspond to the Newtonian, the shear-thickening and the shear-thinning region, respectively. Onion radius follows thepower law, R � _g�0.5, as represented by the solid line. (B) Polarized microscopyimages in the steady state at several shear rates. Scale bar corresponds to 100 mm.

2 Experimental

In this study, we use a nonionic surfactant, tri-ethylene glycolmono-decylether (C10E3), purchased from Nikko chemicals Co.,Ltd. The surfactant was used without further purication. Thesurfactant lamellar phase was prepared by dissolving thenonionic surfactant C10E3 into distilled water H2O with a weightfraction of 40% and was gently stirred using a magnetic stirrer.The same system is oen used for studying the shear-inducedonion formation mechanism as a model system.15,16 Theobtained onion structure at the surfactant concentration of 40wt% shows a polyhedral shape because of the dense packing with ahigh volume fraction of the onion. At a lower surfactantconcentration, unperturbed spherical onion formationmight beexpected as Hoffmann and coworkers observed for charged,dilute lamellar phases.7,8,32 However, in the nonionic surfactantC12E4 system prepared at a lower surfactant concentration,which is similar to the sample in this study, inhomogeneousdistribution of the onions suspended in the lamellar matrix wasobserved.17 In order to perform the experiment with the homo-geneous onion phase, the surfactant concentration was xed at40 wt%. Stirring the lamellar solution yields the onion phase.Fromaprevious report, we know that a thermal treatmentmakes

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sure to create a well controlled initial state of the planar lamellarphase.16 Before measurements, the solution was always shearedwith a shear rate of 10 s�1 at 42 �Cuntil the onions formedduringthe sample preparation disappeared. At this temperature andshear rate, the steady state structure under shear corresponds toplanar lamellae oriented by the ow with their bilayer normalalong the velocity gradient direction (La phase with “C”-orien-tation).Disappearanceof theonionwasmonitoredbymeasuringthe viscosity. Aer the onions disappeared, the temperature wascooled down to 25 �C at the quiescent state. The homogeneousonion phase was prepared by pre-shearing the aligned-La phaseat each shear rate. It is well known that the onion radius can becontrolled by the shear rate.2,3

Viscosity measurements were performed using an ARES-LSstrain-controlled rheometer of TA Instrument Co., Ltd., with aCouette shear geometry (radius of inner bob, 16.5 mm; gap size,250 mm). Microscopy observation under shear was performedusing the Linkam CSS450 shear cell, which has a plate–plateshear geometry. The shear cell was attached onto the polarizedmicroscope (Olympus BX-50) and positioned between twopolarizers. The sample thickness between upper and lowerplates was xed at 250 mm in order to t the experimentalconditions with the rheometry. Using the same sample thick-ness, we can study the size change process of the onion texturewithout any spatial connement effects.33 All measurementswere performed at 25 �C.

3 Results and discussion3.1 Steady state under shear

Fig. 1 shows shear rate dependences of a steady state viscosityand radius of the onion. The radius of the onion was estimated

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Paper Soft Matter

by the fast Fourier transformation of polarized microscopyimages. The ow curve in this system can be classied intothree regions. Region I corresponds to a planar lamellarphase with the Newtonian behavior in the low shear rate region1–3 s�1. In the microscopy image at 2 s�1, one can see a typicaloily streak defect characteristic of the La phase.34 At a criticalshear rate ( _gc x 3 s�1), the La phase undergoes the onionformation associated with a shear-thickening behavior (regionII). At 5 s�1, a tile-like pattern consisting of a connected Maltesecross characteristic of the densely packed onion phase appears.The same tile-like pattern for the densely packed onion phaseswas also observed by Roux et al. and Courbin et al.2,35 Furtherincrease in the shear rate caused the shear-thinning behavior(region III), where the densely packed onion phase is observedin the images. Shear rate dependence of the onion radiusfollows a power law relation, R � _g�0.5, as proposed by Rouxet al.2,3 Regions II and III correspond to the shear-induced onionphase. In the following, the growth kinetics of the onionstructure aer the shear quench is investigated by viscometryand microscope observation.

3.2 Onion growth aer the shear quench

Fig. 2 shows a time evolution of a transient viscosity aer theshear rate is quenched from _gi ¼ 100 s�1 to different nal shear

Fig. 2 Time evolution of the transient viscosity after the shear quench from thefixed initial shear rate _gi ¼ 100 s�1 to different final shear rates _gf. Data in panel A,B and C correspond to the shear quench into the La phase (region I) and the onionphase (regions II and III), respectively.

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rates _gf. Here, subscripts i and f indicate initial and nal shearrates, respectively. When the shear rate was quenched into theLa phase (region I), the transient viscosity decayed down. Thedecay curves could not be tted with a single exponentialfunction. Aer t ¼ 1000 s, the transient viscosity reached theplateau with the same viscosity as that of the Newtonian regionin the La phase.

For the comparison with viscometry, typical polarizedmicroscopy images aer the shear quench are shown in Fig. 3.At t ¼ 0, the tile-like pattern, which is blurred because of theresolution of the microscope objective, indicates the denselypacked onion phase at 100 s�1. Aer the shear quench from _gi¼100 s�1 to _gf ¼ 1.5 s�1, a bright band oriented along the owdirection gradually appeared at about t ¼ 250 s. In Fig. 3A, theimage at t ¼ 500 s is shown. In these polarized microscopyimages, the brightness corresponds to the birefringence inten-sity. The densely packed onion phase shows a relatively weakbirefringence intensity because of the concentric layer orienta-tion inside the onion. The bright band will thus correspond tothe La-rich region where onions are actively broken down intoplanar lamellae. This stripe pattern will be referred to as avorticity shear band which can be observed for the viscoelasticinhomogeneous complex uid systems.36–38 Appearance of theshear band has also been observed in the shear-induced oniontransition process.39,40 A coexisting phase of the onion andplanar lamellae aer the shear quench has been actually sug-gested via rheo-NMR measurements by Medronho et al.25 Theyhave also shown that the onion structure completely transformsback into the planar La aer the coexisting phase disappeared.As the disintegration of the onion proceeded, the La phasedomain appeared from the bright band region as can be seen att ¼ 1000 s. In the La phase domain, one can recognize the oilystreak networks. The La domain developed with time andeventually occupied the whole space at t ¼ 3000 s. It is wellrecognized that the densely packed onion phase is quite stableat the quiescent state and they stay for a few weeks withoutexternal agitation. It is surprising that the disintegration of theonion into the La phase is easily achieved by applying a lowshear rate. The onion disintegration process was slightlyaccelerated with _gf.

Different behavior was observed when the shear rate isquenched into regions II and III. The time evolution of thetransient viscosity showed double decays followed by anincrease (Fig. 2B). Similar to the observations in Fig. 2A and 3A,the disintegration from the densely packed-onions into the Laphase proceeds through the La domain formation from theshear band in Fig. 3B. The appearance of the shear band at acharacteristic time tSB always corresponds to the beginning ofthe second decay. The second decay mode accompanies theincrease in the La domain, and the viscosity approached to theminimum hm. In the shear band state, the planar La phase withdifferent orientations, powder La, was previously conrmed viarheo-SANS measurements by Koschoreck et al.26 Equivalent hmto the Newtonian thus indicates that the onion phase trans-formed back into the planar lamellar structure. Actually, the oilystreak defects typical for the La phase can be seen in themicroscopy image at t ¼ 1500 s where the viscosity almost

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Fig. 3 Polarized microscopy images obtained after the shear quench at t ¼ 0 from _gi ¼ 100 s�1 to _gf ¼ 1.5 s�1 (A), to _gf ¼ 5 s�1 (B) and to _gf ¼ 70 s�1 (C), respectively.The inset in the image at t ¼ 5000 s in panel B is a magnified one. Scale bar in each image corresponds to 100 mm. Arrow indicates the flow direction.

Fig. 4 Comparison of the time evolution of the viscosity after the shear quenchfrom _gi ¼ 100 s�1 to _gf ¼ 10 s�1 (triangles) with the shear induced La–oniontransition after a start up shear of 10 s�1 (circles). (A) Transient viscosities arecompared against the elapsed time. (B) The onion reformation process after theshear quench is compared with the shear induced La–onion transition behavior.tind indicates the induction time from where the onion reformation starts.

Soft Matter Paper

corresponds to hm. Immediately aer reaching hm, the onionphase reformation started at an induction time tind and a newonion with a larger size was achieved (t¼ 5000 s). The inductiontime tind for the onion reformation is also shortened with _gf

as well as the onion disintegration. In Fig. 4, the shear-inducedLa–onion transformation process at _g¼ 10 s�1 was compared tothe shear quench behavior from _gi ¼ 100 s�1 to _gf ¼ 10 s�1. Theonion reformation process aer the shear quench seems not tocoincide with the shear-induced La–onion transformationprocess (Fig. 4A). However, by subtracting an induction timetind, the onion reformation process well agrees with the shear-induced onion formation process (Fig. 4B). While the disinte-gration of the onion appears inhomogeneously such as anucleation, the onion reformation aer the disintegration islikely to occur homogeneously.

In our previous study, the rst decay mode was assigned tothe uctuation of the positional order of the onion.26 Such auctuation of the positional order might be caused by realign-ment of the onion due to the planar lamellar layers generatedvia the disintegration. Non-single exponential like decay inFig. 2A will reect the appearance of a weak intensity of the slowmode. Above results indicate that the onion growth kinetics is adiscontinuous one. As can be seen in Fig. 2B, discontinuouskinetics depends on _gf. In contrast to these results, when theshear quench gap is small enough, no signicant time devel-opment of the viscosity and no shear band formation areobserved as shown in Fig. 2C and 3C. One can always nd thetypical tile-like pattern for the onion phase. Fig. 5 shows thetime development of the volume of the onion when the shear

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Fig. 5 Time evolution of the radius of the onion after the shear quench from _gi¼40 or 20 s�1 to _gf ¼ 20 or 10 s�1. Experimental data obtained from ref. 24 wereused. R0 is the radius of the onion at the initial state before quenching shear rate.

Paper Soft Matter

rate is quenched from 40 to 20 and from 20 to 10, respectively.In this plot, experimental data in ref. 24 were replotted. Withthis shear quench depth which is not as large as the discon-tinuous kinetics in Fig. 2B and 3B, the volume of the onioncontinuously increases. A linear increase with time is similar tothe Ostwald ripening. The ripening behavior of vesicle disper-sion was discussed by Olsson et al.27 They proposed that thecontinuous growth of the onion is caused by the monomerdiffusion, i.e., the permeation, attributed to the higher orderterm of the curvature energy. In the case of the small shearquench depth, the onion growth kinetics can be continuous.These observations ensure that the discontinuous and contin-uous growth kinetics can be easily distinguished by measuringthe transient viscosity.

Fig. 6 _gf dependence of the initial viscosity h0 obtained just after the shearquench (t ¼ 0 s), and the minimum viscosity hm obtained from the time evolutionof the viscosity. Filled and open symbols correspond to h0 and hm, respectively.Results of the shear quench test from _gi ¼ 100 and 30 s�1 are compared with theshear rate dependence of the steady state viscosity h (filled circle). The horizontaldashed line is the Newtonian viscosity of the La phase.

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In Fig. 6, an initial viscosity h0 obtained at t ¼ 0 s just aerthe shear quench and the minimum viscosity hm at tind arecompared with the steady state viscosity h. Here, results of theshear quench from _gi¼ 100 and 30 s�1 are shown. h0 well agreeswith h in region III in spite of _gi. However it still shows theshear-thinning behavior even in regions I and II. The shear-thinning behavior of h0 in a whole _gf range will reect therheological property of the onion phase, since the oniondisintegration slowly progresses with time and the onionremains at the beginning of the shear quench. The shear-thin-ning behavior of the onion phase in regions I and II is describedby the power law relation of h0 � _gf

�0.5. On the other hand, hmalmost coincides with the Newtonian viscosity of the planar Laphase when _gf belongs to the region I and II. As _gf approaches to_gi, hm increases from the Newtonian viscosity. At _gf approachesclose enough to _gi, h0, hm and h correspond to each otherbecause of no time development of the viscosity according tothe continuous growth of the onion.

3.3 Disintegration and reformation kinetics

Fig. 7 and 8 show the disintegration and reformation behaviorsaer the shear quench with different combination of _gi and _gf.In these gures, _gf was xed and _gi was controlled. Fig. 7 shows_gi dependence of the disintegration process from different _gi tothe La phase _gf ¼ 2 s�1. As _gi was increased, the disintegrationbehavior also quickly proceeded. _gi dependence as well as thosein the _gf dependence in Fig. 2A indicates that the onion disin-tegration process depends both on _gi and _gf. Fig. 8 shows _gi

dependence of the discontinuous kinetics. Here _gf was xed at5 s�1. A typical discontinuous property with double decaymodes followed by an increase in the viscosity can be seen.Similar to Fig. 7, the increase in _gi accelerates the oniondisintegration and thus shortens tSB, while the induction timetind is independent of _gi. The onion reformation starts at thesame tind. However, a higher hm than the La phase, for instanceat 15 s�1, indicates that the disintegration into the planar

Fig. 7 Time evolution of the viscosity after the shear quench from _gi to _gf¼ 2 s�1

corresponding to the La phase in the Newtonian region. Here, _gi was changedfrom 100 to 5 s�1. The horizontal dotted line corresponds to the viscosity of the Laphase in the Newtonian region.

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Fig. 8 Time evolution of the viscosity after the shear quench from _gi to _gf¼ 5 s�1

corresponding to the shear-thickening region. Here, _gi was changed from 100 to15 s�1. The horizontal dotted line corresponds to the viscosity of the La phase inthe Newtonian region.

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lamellae is not completed when _gi is close enough to _gf. Theonion reformation can be initiated even before the La phase isformed.

In Fig. 9, _gf dependences of tSB and tind are summarized. tSBshows a power law behavior of tSB � _gf

�1 and depends not onlyon _gf but also on _gi. tind also shows a power law behavior oftind � _gf

�2 but it depends only on _gf and data obtained atdifferent _gi fall on the same line. Inverse linearity of tSB against_gf seems to indicate that the shear band, thus the breakdown of

Fig. 9 tind and tSB where onion reformation starts and the shear bandingappears, respectively, as a function of _gf. Filled and open symbols correspondto tSB and tind, respectively. Each symbol in the graph legends corresponds tothe different initial shear rates _gi. tSB and tind follow the power law relations oftSB � _gf

�1 and tind � _gf�2, respectively.

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a part of the onion, appears aer the applied shear strain _gftSBapproached to a certain amount. Values of the applied strainneeded for the shear band formation are _gftSB x 3300, 1500 and600 for _gi ¼ 15, 30 and 100 s�1, respectively. The breakdown ofthe onion at constant strain indicates that the disintegration ofthe onion is a strain-controlled process as well as the La–oniontransformation process. Fig. 10 shows _gi dependence of tSB.Power law relation of tSB � _gi

�1 can be observed. Combining _gfand _gi dependences yields the relation of tSB � ( _gi _gf)

�1.Reducing tSB to the shear strain _gftSB, the shear strain subjectedto the system until the appearance of the shear band collapsesonto the same line and varies as _gi

�1. Therefore the disinte-gration of the onion depends only on the initial condition of theonion phase. Taking into account the scaling law on the shearrate dependence of the onion radius, R � _g�0.5,41 the mastercurve in the inset can be converted into _gftSB � Ri

2. This relationimplies that the larger onions are more stable against the shearquench rather than smaller ones. Similar scaling law has beenreported for the swelling behavior of the onion phase.42 Thestrain needed to break the onion seems to be proportional tothe surface area of the onion at the initial state.

Similar to tSB, the power law behavior tind � _gf�2 may also

be reduced to the applied strain aer the shear quench,tind _gf � _gf

�1. As we have seen in Fig. 8, the onion reformation isindependent of the initial condition at _gi. Coupling of the shearrate and a relaxation mode of the planar layers generated aerthe onion disintegration seems to dominate the _gf dependence.For the moment, however, we have no explanation of whatdetermines tind.

It has been reported that the shear-induced La–oniontransformation is a strain-controlled mechanism.16,18,35,43 Aprevious study performed with the C10E3/H2O system at 40 wt%

Fig. 10 tSB as a function of _gi. Solid lines show a slope of tSB � _gf�1. The inset

shows the shear strain _gftSB at which the shear band appears as a function of _gi.Filled square corresponds to tSB shown in Fig. 9.

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also suggested that the shear-induced onion formationbehavior can be scaled by a shear strain, and at least strain unitsof _gt x 30 000 are required for the onion formation at 10 s�1.16

Short tind (or _gftind x 1000–20 000) compared to the time (orstrain units of 30 000) needed for the onion formation indicatesthat the breakdown of the onion easily proceeds rather than theformation of the onion phase.

3.4 Dynamic diagram and instability of the onion phase

In the densely packed onion phase, onions are stronglydeformed and constrained by a hard sphere interaction exertedby the neighbors. Elastic force resulting from the compressionof the onion yields a pressure in the onion phase.44 The pressurearising from the repulsive contact force is mainly attributed to acurvature elastic energy and an interfacial energy. It is necessaryfor the stability of the onion that the internal pressure isbalanced with the external pressure exerted by the compressedonion Pela and the shear stress. The external pressure Pela will begiven by Pela � ~K /R2 + 2geff/R. The rst and the second terms arethe curvature elastic and the interfacial contributions, respec-tively. ~K is a spherical bending modulus given by ~K ¼ 2K + �K .34

geff is an effective interface tension of the membrane. Assumingthat the steady shear stress at _gi is always balanced with theinternal stress of the onion, the mechanical stability of theonion structure under shear thus seems to be given bybalancing the above contributions with the shear stress. Whenthe shear rate is quenched, the reduction in the applied shearstress will cause an excess pressure inside the onion. This excesspressure would be a driving force for the breakdown of the

Fig. 11 Dynamic diagram representing the kinetic process of continuous anddiscontinuous onion growth. Filled symbol shows the shear quench conditionwhere the discontinuous behavior is observed while open one corresponds to thecontinuous process determined by viscometry. The dotted line shows sf ¼ si. Thesolid line corresponds to the threshold between continuous and discontinuousgrowth.

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onion. The onion growth kinetics thus might be scaled bystress.

In Fig. 11, a dynamic diagram with a threshold between thediscontinuous and continuous growth behavior as a function ofthe shear stress is shown. In most of the combinations of si andsf, quenching shear induces the discontinuous growth.However, onlywhen thequenchdepth remains in a limited rangeof si � sf < 27, the onion continuously grows up. It should benoted that the experimental condition showing the ripeningbehavior in Fig. 5 belongs to this shear stress range. Discontin-uous andcontinuous growthbehavior canbe clearly separatedbya threshold ofsfxsi� 27. Thedynamicdiagramsummarizedbythe shear stress indicates that the balance between externalshear and internal pressure determines the onion growthkinetics. This dynamic diagram is qualitatively similar to thatpresented by Panizza et al. for ionic surfactant onion systems,11

although they have made the dynamic diagram as a function ofthe shear rate instead of the shear stress. As discussed by Panizzaet al.,11 the permeation driven by the stress gradient inside theonion might be the origin of the internal pressure.

However, it is also known that the permeation in the lamellarphase is extremely slow rather than the characteristic time forthe breakdown of the onion.31 Slow kinetics attributed to thepermeation has also been reported on the swelling behavior of acompressed onion under shear by Leng et al.42 They argued thata defect formation within the onion will promote the perme-ation and results in the acceleration of the swelling behavior. Inother swelling experiments performed by Buchanan et al., theyfound that the core of the onion persists for a long time.30

Metastability of the onion core was attributed to an absence ofthe defect due to a high tension of the bilayer membranes.Signicant contribution of the dislocation to the stability of thelayered system and the shear-induced onion phase was alsopresented in detail by Dhez et al.45 It seems that the permeationis quite difficult for the defect-free onion, while it becomeseasier once the defects are produced inside the onion.

We should remind that the onion is compressed in a poly-hedral shape, and thus strongly deformed membranes withstored elastic energy are localized at edges with a width of apenetration depth l ¼ (K/B)1/2.28,46 The localization of the storedelastic energy will yield an inhomogeneous distribution of atension on the membrane which might cause the permeation.When the shear stress is reduced, the permeation driven by thedissipation of the elastic energy will split the membrane andyield the defect in order to relax the tension localized at theedges. Permeation coupled with the tension under shear alsoplays an important role in the dynamic of lipid vesiclesystems.47,48 Such a defect formation will accelerate the perme-ation. Additionally the permeation will also be signicantlyaffected by the baroclinic mode which is a characteristic slowmode of the planar La phase.49 The importance of the baroclinicmode for the rheology of the onion phase has been very recentlyproposed by Lu.41 The solvent ow between two layers excited bythe baroclinic mode will also accelerate the permeation inaddition to the material transport via the shear ow. Actually,coupling of the applied shear and the baroclinic mode has beenexperimentally conrmed.50

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It has been suggested that the onion size R is determinedby the Laplace relation with the effective surface tension,R f geff/h _g.22,23 We have previously estimated geff of the C10E3

onion phase to be 2.1 � 10�4 N m�1.33 Experimentally foundrelation on the threshold si � sf x 27 and above relation on geff

enable us to convert the dynamic diagram in a relation of theonion size. The inset in Fig. 11 shows a threshold line betweencontinuous and discontinuous growth as a function of theonion size. The upper side of the threshold line corresponds tothe discontinuous growth. As the initial onion size Ri becomessmaller, the discontinuous growth kinetics dominates thegrowth behavior. The fraction of the edge volume per volume ofthe onion lR2/R3 is increased as the onion radius is decreased.46

Dominance of the discontinuous behavior at small R would bethus attributed to the fractional increment of the edge with l.The stability of the onion structure will be enhanced by elimi-nating the edge in the polyhedral onion.

3.5 Stability of the stuffed onion

One of the ideas to eliminate the edges is the use of a stuffedonion including colloidal particles. Incorporation of the

Fig. 12 Disintegration behavior of silica particle stuffed onions after the shearquench from 100 to 5 s�1. Silica particles with different diameters d ¼ 45 nm,100 nm, and 200 nm were respectively mixed at concentrations of (A): 1% and(B): 5%. In each panel, particle size dependence of the disintegration behavior isshown.

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particles in the core and interstices between onions wasexperimentally conrmed by Arrault et al.51,52 In such stuffedonion systems, colloidal particles incorporated in the corecancel the unstable curvature energy inside the onion so thatthe polyhedral shape becomes rounded. Actually the sphericalonion formation is observed for the stuffed systems. Addition-ally, membranes aligned around the particle surface willsuppress the baroclinic mode by the anchoring effect on theparticle surface and thus pretend the defect formation. Fig. 12shows the disintegration behavior of the silica particle stuffedonion phases aer the shear quench from 100 to 5 s�1. Hereparticles with different diameters of 45, 100, and 200 nm wererespectively mixed at the concentration of 1 wt% and 5 wt%.Stuffed onions also show the disintegration behavior byquenching shear rate. The stuffed onion with a small particle(d ¼ 45 nm) shows almost the same disintegration kinetics asthat of the non-stuffed onion system irrespective of the particleconcentration. At 1%, the breakdown of the stuffed onion isslightly slowing down with the increase in the particle size(d ¼ 100 and 200 nm). On the other hand, the inuence of thecolloidal particle is much more emphasized at 5%, and thedecay time remarkably depends on the particle size. The largerthe particle size, the slower the disintegration of the onion.Having the large colloidal particle in the core prevents thepolyhedral shape formation due to the anchoring effect of themembranes. Stability of the stuffed onion would thus indicatethat the instability of the onion phase stems from the inho-mogeneous distribution of the elastic bending energy associ-ated with edges additionally to the stress gradient inside theonion. Rheology and detailed property of the shear quenchbehavior of the stuffed onion will be a next topic.

4 Conclusions

We have studied the growth kinetics of a shear-induced onionstructure aer the shear quench. Once the shear rate isquenched, the onion undergoes a continuous or discontinuousgrowth behavior depending on the quench depth. Thethreshold between the discontinuous and continuous kineticswas clearly distinguished on the dynamic diagram as a functionof the shear stress. As proven by microscope observation andviscometry, the discontinuous process accompanies the disin-tegration of the onion with double decay modes, while theonion grows up via the ripening behavior in the continuousprocess. In the discontinuous kinetics, the rst decay corre-sponds to the break down of the part of the onion which resultsin the shear band formation at tSB. The characteristic strain forthe shear band formation _gftSB depends only on the initialonion size at _gi. We conclude that the driving force for thedisintegration of the onion is the inhomogeneous elastic energystored at the edges of the polyhedral onion prepared at _gi. Slowdisintegration kinetics in the stuffed systems with sphericalonions will indicate that the elastic energy stored at the edgesare the driving force for the disintegration. Quenching shearwill rst create the defect inside the onion, and then thepermeation of the material coupled with the defect formationand the baroclinic mode of the membranes will accelerate the

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Paper Soft Matter

disintegration kinetics. In the preliminary investigation usingcolloidal particles, the disintegration process of the stuffedonions depends on the particle size and concentration. Slowingdown of the disintegration kinetics indicates that the elimina-tion of the edges due to the anchoring effect effectivelycontributes to the stability of the onion structure.

We should also note that there are several kinds of onionphase. The shear-induced onion phase of the nonionic surfac-tant system is one of them. As Hoffmann et al. reported, aspontaneously formed onion phase in charged lamellar systemsirreversibly changes the size and structure under shear.5,7,8 Itwould be also interesting to study the origin of the irreversibleproperty of such onion phases.

Acknowledgements

SF thanks T. Takahashi for use of the rheometer and micro-scope equipped with a shear cell. This work was supported byKAKENHI (Grant-in-Aid for Scientic Research) on PriorityAreas “So Matter Physics” grant no. 21015007 and for YoungScientists (B) grant no. 19740258 from the Ministry of Educa-tion, Culture, Sports, Science and Technology of Japan.

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