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Multilamellar Vesicle Formation Probed by Rheo-NMR and Rheo-SALS under Large Amplitude Oscillatory Shear Stefan Kuczera, Luigi Gentile, Timothy Brox, Ulf Olsson, Claudia Schmidt, and Petrik Galvosas Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01510 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 20, 2018

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Multilamellar Vesicle Formation Probed by Rheo-NMR and Rheo-SALS Under Large Amplitude Oscillatory Shear Stefan Kuczera,∗,†,‡ Luigi Gentile,¶,‡ Timothy I. Brox,† Ulf Olsson,‡ Claudia Schmidt,§ and Petrik Galvosas† Victoria University of Wellington, SCPS, MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington, New Zealand, Division of Physical Chemistry, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden, Department of Biology, MEMEG unit, Lund University, Sölvegatan 35, 223 62 Lund, Sweden, and Department of Chemistry, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany E-mail: [email protected]

Abstract The formation of multilamellar vesicles (MLVs) in the lyotropic lamellar phase of the system triethylene glycol mono n-decyl ether (C10 E3 )/water is investigated under Large Amplitude Oscillatory Shear (LAOS) using spatially resolved rheo-NMR spectroscopy and a combination of rheo-small angle light scattering (rheo-SALS) and conventional rheology. Recent advances in rheo-NMR hardware development facilitated ∗

To whom correspondence should be addressed Victoria University of Wellington ‡ Division of Physical Chemistry, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden ¶ Department of Biology, MEMEG unit, Lund University, Sölvegatan 35, 223 62 Lund, Sweden § Department of Chemistry, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany †

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the application of LAOS deformations in high-field NMR magnets. For the range of investigated strain amplitudes (10–50) and frequencies (1 and 2 rad s−1 ) MLV formation is observed in all NMR and most SALS experiments. It is found that the MLV size depends on the applied frequency in contrast to previous steady shear experiments where the shear rate is the controlling parameter. The onset of MLV formation, however, is found to vary with the shear amplitude. The LAOS measurements bear no indication of the intermediate structures resembling aligned multilamellar cylinders observed in steady shear experiments. Lissajous curves of stress vs. strain reveal a transition from a visco-elastic solid material to a pseudo-plastic material.

Introduction Shear-induced changes in the structure of soft matter systems have been of great interest for many decades. 1–17 A particular example are lyotropic lamellar systems that exhibit a rich phase behaviour both in the static and the dynamic range. 18–67 For these systems a continuous application of shear can induce the formation of a defect structure consisting of multilamellar vesicles (MLVs) from the original lamellar Lα phase consisting of extended stacks of parallel surfactant bilayers. 18,19 These MLVs consist of a hierarchy of many concentric spherical bilayer shells and are thus often referred to as “onions”. The potential of encapsulating certain substances in this geometry makes them an interesting medium for drug delivery in pharmaceutical applications or for microreactors. 68–71 Therefore a thorough understanding of the MLV formation process in this nonequilibrium transition is vital with respect to usage on an industrial scale. Roux et al. 19 first investigated the transition from the Lα structure to MLVs in a sodium dodecyl sulfate/pentanol/water/decane system under steady state shear. The critical shear rate for the transition to MLVs was found to be proportional to the cube of the bilayer membrane volume fraction. 19 Furthermore, Roux et al. 19 proposed a dependence of the

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radius of the MLVs, RMLV , on the applied shear rate γ˙ as RMLV ∝ γ˙ −1/2 .

(1)

On the other hand, it has been shown that MLV formation can be controlled by stress rather than shear rate for certain systems. 72 Taking into account the non-Newtonian property of the system the scaling relationship for the MLV radius 18,19 has been rewritten as RMLV ∝ σ −1/2 where σ is the shear stress. Also, MLV formation was found to be related to the membrane bending modulus and thus the Helfrich energy. 73 An alternative theory 72 predicts RMLV ∝ σ −1 , which follows from the classical capillary number of fluid mechanics whereby viscous forces balance interfacial tension. 74 In general, however, the formation of MLVs under shear is far from being fully understood to date. Consequently many experimental studies have recently been carried out, investigating mainly the lamellar phases of the nonionic surfactants of the oligoethylene glycol monoalkyl ether, Cn Em , type with different ‘n’ and ‘m’ values that denote the number of carbon atoms in the alkyl chain and the number of CH2 CH2 O moieties in the head group, respectively, and providing insight on finer details on the MLV formation process. 62,67,75–77 However, only very few studies have considered different kinds of shear deformations, as for example flow reversal 78 or oscillatory shear (in the case of an AOT/brine system). 79 Therefore, the formation of MLVs under large amplitude oscillatory shear (LAOS) is studied for the well-known surfactant system C10 E3 /water in this work. The investigation of shear-induced transitions under LAOS has gained much attention recently. 80 The imposed strain γi in an oscillatory experiment can be written as

γi (t) = γ0 sin ωt

(2)

where γ0 is the shear amplitude and ω the shear frequency. In contrast to small amplitude oscillatory shear (SAOS) (γ0 1) where the relation between applied stress and induced shear is assumed to be linear, the large amplitude regime is characterized by a non-linear 3


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response of the system. The description of the non-linear material response has gained renewed interest recently and is subject of current research. 80 Large amplitude deformations play an important role in processing operations and thus deeper knowledge about the microscopic response of a system to the mechanical perturbation is crucial. To further facilitate this understanding recently developed high field rheo-NMR hardware allowing for LAOS deformation 81 is employed in this research. The lamellar phase of the C10 E3 /water system has been a popular subject of rheoNMR 55,56,82–85 studies in recent years. The shear diagram obtained by Oliviero et al. 86 revealed that MLVs in this system are not stable under shear above a certain temperature. Instead, the bilayers are aligned parallel to the velocity-vorticity plane providing an easy route to a well-defined initial state for investigating MLV formation. Medronho et al. 85 investigated the structural transitions between the oriented lamellar phase and MLVs using 2

H NMR spectroscopy. Whereas the planar lamellae-to-onion transition was found to be

continuous with indications of cylindrical aggregates as intermediate objects, 87 experimental data suggested that the reverse transition is discontinuous, i.e., planar lamellae and MLV coexist during the transition. Later this study was extended 84 by proposing a line shape model for the 2H NMR spectra allowing for the determination of vesicle radii which were in good agreement with SALS measurements. The same transitions were the subject of a study by Medronho et al. 83 where spatially resolved 2H NMR spectroscopy was combined with spatially resolved NMR diffusometry. The latter technique provided further evidence of intermediate cylindrical objects in the lamellae-to-onion transition. Furthermore, the spatially resolved experiments confirmed that this transition occurs homogeneously across the shear gap. In contrast, for the reverse transition it was found that the nucleation of the lamellar phase preferably started at the inner wall of the Couette shear geometry before extending over the whole gap. The findings were confirmed in a follow-up study, 82 where transient shear banding and wall slip were observed by means of NMR velocimetry. It shall be noted that all previous rheo-NMR studies on C10 E3 used steady shear.

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A very recent study by Gentile et al. 76 on the C12 E5 /water system gave further insight into the formation process of MLVs. The novel rheo-small angle light scattering (rheo-SANS) setup employed by those authors allowed for the detection of the velocity-velocity gradient plane, which had not been accessible in earlier experiments where the velocity gradientvorticity plane was used. Owed to this methodical improvement, tilting of the lamellar phase in the early stage of the MLV transition could be observed. Moreover, it was found that the MLVs are stretched under the application of shear flow, which had been observed earlier for similar systems. 88 Fritz et al. 79 performed oscillatory shear experiments for an AOT/brine lamellar system and investigated the formation process of MLVs. In their contribution, the oscillatory motion was defined by the stress amplitude (“LAOStress”, in contrast to “LAOStrain” where timedependent strain with fixed amplitude is imposed). From bulk rheological measurements they could determine a critical strain amplitude necessary for onion formation that was about 14. Onion radii in the range from 0.8 µm to 5 µm were found by means of small angle light scattering (SALS). It should be noted that these oscillatory experiments were carried out starting from a polydomain lamellar phase. Another notable contribution with regards to MLV formation under non-steady shear was made by Nettesheim et al. 78 for the same C10 E3 system that is under investigation here. Instead of using a sinusoidal shear modulation, their study applied a simpler flow reversal pattern, where the sample was repetitively sheared with a constant shear rate over a certain time period until the shear direction was reversed, resulting in a zigzag strain profile. Structural information during the MLV formation process was obtained by means of SALS and small angle neutron scattering (SANS). Scattering patterns from the latter technique made it possible to identify an intermediate structure which was proposed to consist of mulitlamellar cylinders or coherently buckled lamellae. Similarly to the study by Fritz et al. 79 a minimum strain amplitude necessary to trigger onion formation was found that had a value of around 6.5 in this case.

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Finally, Yatabe et al. 89 investigated the onion formation process for a quaternary mixture consisting of water, NaCl, octanol und sodium dodecyl sulfate under a similar oscillatory shear flow as Nettesheim et al. 78 The authors found that the time evolution of the onion size is in good agreement with a stretched exponential function showing a decrease in size over time. Compared to previous results for steady shear 58 it was found that flow reversal has an effect on the relaxation time of size evolution towards the steady state value. In this contribution, the MLV formation process for a particular Cn Em system (C10 E3 ) is, for the first time, probed under large amplitude oscillatory shear, or more specifically LAOStrain. A novel rheo-NMR apparatus that was recently developed 81 made it possible to apply oscillatory shear within a wide-bore superconducting magnet. Results from onedimensional (1D) 2H spectroscopic imaging are complemented by a rheo-SALS method that allowed for simultaneous SALS and bulk rheology measurements. In the following, it will be shown that MLVs are formed under LAOS and the influence of frequency and amplitude of the oscillatory motion on their size will be discussed. Particular attention is given to the structural evolution during the lamellae-to-onion transition which is compared to the case of steady shear.

Experimental Section Materials Triethylene glycol mono n-decyl ether (C10 E3 ) was purchased from Nikko Chemical Co. (Tokyo, Japan). Deuterium oxide (D2 O) with a purity of 99.9% was supplied by Sigma Chemicals. Samples were prepared by weighing 40 wt. % of surfactant and 60 wt. % of water into vials. The two components were thoroughly mixed and subsequently centrifuged in order to remove air bubbles. In the case of NMR the samples were prepared with a ratio D2 O/H2 O of 9 : 1 by weight, otherwise pure D2 O has been used. The addition of some H2 O in the NMR case, which allowed for additional 1H NMR studies (not shown here), is not 6


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considered to alter the shear behaviour of the solution.

Rheo-NMR All NMR experiments have been performed on a Bruker Avance spectrometer operating at a 2H resonance frequency of 61.4 MHz. A Micro2.5 tri-axial gradient system with a maximum magnetic field gradient of 1.45 T m−1 allowed for 1D spectroscopy imaging. The inner diameter of the dual-channel birdcage rf coil ( 1H, 2H) used was 25 mm. The rheo-NMR hardware 81,90 was built for a Bruker wide-bore magnet and utilized a concentric cylinder shear device. The cup was fixed while the bob rotated (Searle mode). The rotor of the geometry was coupled to the drive-shaft outside of the magnet and the entire assemble was installed as one part. The rigid connection between the drive system and the shear device eliminated any mechanical backlash. In combination with a servo-stepper motor, this feature allowed for oscillatory shear profiles. The drive system was comprised of a stepper motor, motor driver electronics and optical encoder; together the system operated in a closed feedback loop facilitating user defined motion profiles and precise motion control. The shear device had an inner radius of R = 8 mm and a gap size of d = 1 mm. A schematic of the Couette geometry along with the definition of the axis directions is shown in Fig. 1a and b. The procedure for the NMR experiments was as follows. The sample was sheared at a rate of γ˙ = 10 s−1 at T = 42 ◦C for at least an hour to create a well aligned lamellar phase with the layer normal parallel to the velocity gradient, that is, perpendicular to the magnetic field. Subsequently, the shear was stopped and a bulk NMR spectrum was taken in order to confirm the alignment. Then the temperature was ramped down at 0.5 ◦C/ min to 25 ◦C over a period of about 30 min using the ramp functionality of the Bruker temperature control kit. The same procedure was applied by Medronho et al. 83 and helps to avoid temperature gradients that could influence the subsequent LAOS measurement. To this end, the temperature of the gradient cooler water bath was also adjusted accordingly (no ramp). 7


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(a)

(b)

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(c)

fluid gap diameter

Rf.:

y z (vorticity) z

x

x (gradient)

x:

y (velocity)

y:

Figure 1: (a,b) Schematic of Couette geometry in horizontal (a) and vertical cuts (b). Dashed lines indicate the selected slice for the NMR imaging experiment. In (a), the velocity, velocity gradient and vorticity directions are indicated. (c) Pulse sequence for the 1D spatially resolved 2H NMR experiments. After the desired temperature was reached, the LAOS experiment was performed in a start-stop fashion similar to Nettesheim et al. 78 . In this scheme the sample was first exposed to oscillatory shear for a certain number of periods depending on the applied amplitude and frequency. Then NMR spectra with spatial resolution in one dimension (1D resolved spectra) were recorded at rest within about 4 min. Iterating this process made it possible to follow the transition from an aligned lamellar phase to an MLV phase while obtaining spatially resolved spectroscopic NMR data. Due to the metastability of the shear-induced phase structure at rest 83 it is assumed that the start-stop procedure does not alter the solution’s behaviour compared to a continuous LAOS experiment, as employed in the rheoSALS technique described later. Values probed for the shear amplitude, γ0 , were 10, 20 and 50, with angular frequencies, ω, of 1 and 2 rad s−1 . The NMR pulse sequence allowing for 1D resolved spectra to be recorded is depicted in Fig. 1c. The difference to the work of Medronho et al. 83 is the application of a selective soft pulse that restricts the region yielding the NMR signal to the 2 mm slice indicated in Fig. 1a,b. As an advantage of this technique (at the cost of a reduced signal-to-noise ratio) the recorded data can directly be Fourier transformed to yield spatially resolved spectra; no Hankel transform as employed by Medronho et al. 83 is necessary. A change of the initial

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phase of the NMR signal was observed experimentally and accounted for by a zeroth order phase correction. In terms of spatial resolution, a value of about 200 µm per pixel was found to be a good compromise between acquisition time (4 min per image) and resolution. This leads to an effective resolution of about 5 points across the gap. All spectra shown here are taken from a single position in the gap. (See Fig. S1 in supporting information (SI) for sample resolved spectra along with the pixel position chosen.) Spatial variations over the gap and their origin are subject of current research and beyond the scope of this work. Line broadening was applied to the spectra of the initial lamellar structure to compensate for an incomplete FID due to the chosen acquisition time. Finally, it shall be stated that the spectral splitting in the lamellar phase (around 500 Hz) was much smaller than the frequency variation imposed by the slice selective gradient (around 5000 Hz) and is thus not regarded a complication for the slice selection process.

Rheo-SALS Rheological measurements were performed simultaneously to small angle light scattering on an Anton Paar Physica MCR 301 rheometer equipped with a quartz cone-plate geometry (diameter: 43 mm, cone angle: α = 2.01◦ ). Steady shear flow or LAOStrain were applied to the sample. LAOS measurements were performed using the real-time position control based on the Direct Strain Oscillation (DSO) method of the rotational rheometer in order to generate an accurate sinusoidal strain input, by applying a fixed angular frequency and a fixed strain amplitude value. The LAOS strain amplitude, γ0 , was set to 10, 20, 30 or 50, while the angular frequency, ω, was fixed to 1 or 2 rad s−1 . The total experimental time for a single run was restricted by the acceptable amount of evaporation in the sample and was about 3 h. The rheo-SALS tool is a complete SALS system directly attached to the rheometer. A schematic of the setup is found in Fig. 2. In all measurements a 10 mW laser diode operating at a wavelength of 658 nm was used as the light source. Depolarized SALS patterns were 9


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captured using a CCD camera (Lumenera Corporation, Ottawa, Canada) located below the screen on which the scattered light was directed. The incoming beam travelled along the velocity gradient direction and the scattering pattern was detected in the plane of velocity and vorticity (neutral) direction. Scattering patterns presented here are either taken from single snapshots with an image resolution of 1, 392 × 1, 040 pixels or from a movie (4 fps) recorded simultaneously to the experiment with a resolution of 348 × 260 pixels. gradient

Laser Class 1

gradient velocity

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vorticity

CCD Camera

Figure 2: Schematic of the rheo-SALS setup. The velocity, velocity gradient and vorticity directions are indicated.

Prior to each LAOS experiment, in order to erase any thermal or mechanical history, the sample was heated (41◦ ) and then sheared at 10 s−1 for 30 min. This procedure allowed us to generate an alignment of the lamellar phase with its layer normal parallel to the velocity gradient. 83 This was the starting point of each LAOS experiment.

Results and Discussion In order to be able to compare experiments with different LAOS parameters, the evolution of the MLV formation process is followed with respect to the absolute strain Z γ(t) = 0

t

|γ˙ i (t0 )|dt0 ,

(3)

where γ = 0 coincides with the start of the oscillatory shear at t = 0. This definition is similar to the one used by Nettesheim et al. 78 . More information can be found in the 10


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supporting information.

Formation of MLVs under LAOS An aligned lamellar phase of the C10 E3 /water mixture was subjected to a LAOS deformation with a frequency of ω = 1 rad s−1 and an amplitude γ0 = 50. In Fig. 3a 2H NMR spectra right before the application of oscillatory shear (absolute shear γ = 0), for an intermediate state at γ = 15,000 and for a quasi steady state at γ = 80,000 are shown. The doublet of the γ = 0 pattern is a clear indication for an aligned lamellar phase at the beginning of the experiments. The spectral splitting results from the residual quadrupole interaction of the deuterium nuclei in the water molecules. In the anisotropic environment of the lamellar phase the molecular motion is not isotropic and hence the quadrupole interaction is not averaged to zero as in isotropic solutions. The size of the quadrupole splitting depends on the orientation of the phase axis with respect to the static magnetic field, and the line shape being a simple doublet (instead of a Pake pattern) is proof of the shear-induced uniform orientation of the lamellar phase. The layer normal is perpendicular to the magnetic field consistent with its orientation known to be parallel to the velocity gradient axis. The shape of the spectra clearly changes to a broad single peak at γ = 15,000 which is associated with the formation of MLVs. In MLVs the bilayers are bent and the diffusive motion of the water molecules parallel to the bilayer shells has a rotational component, which leads to additional motional narrowing. If reorientation of the water molecules due to diffusion is fast enough the quadrupolar doublet collapses to a single line whose width still depends on the radius of curvature. The superposed spectra from all bilayer shells yield the characteristic broad peaks observed for MLVs. The quasi-steady state spectrum obtained at γ = 80,000 is similar to the previous one, however, exhibiting a smaller width at half height and a slightly higher intensity maximum. From the evolution of the line shapes it can be concluded that the main MLV formation process has taken place between γ = 0 and γ = 15,000. Subsequent changes for higher absolute shear values can then be related to finer 11


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structural changes of the MLVs, e.g. the size distribution. The temporal evolution of the MLV formation shall be discussed in more detail in section ”Evolution of Structure during MLV Formation.”

(a)

γ0 = 50 ω = 1

γ/103 = 0

(b)

γ/103 = 15

101

γ/103 = 80

100 G0 , G00 [Pa]

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10−1 G00 G0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 f [kHz]

0.4

0.6

10−2 0

0.8

0.0

15.3

20

40 60 3 γ [10 ]

80

100

78.3

Figure 3: Formation of multilamellar vesicles under LAOS deformation (ω = 1 rad s−1 , γ0 = 50) observed with different techniques. (a) 2H NMR spectra for different γ values (solid lines). Dashed lines are fits assuming either a double Lorentzian (for γ = 0) or a single Lorentzian. (b) Storage and loss modulus from bulk rheology recorded with a cone-plate geometry. (c) Small angle light scattering patterns at selected γ/103 values (indicated in the upper right hand corner) collected simultaneously with the bulk rheology results of (b). The NMR findings are well supported by bulk rheology results that are depicted in Fig. 3b. A simple analysis as in linear rheology was applied to obtain approximate values for the elastic and the loss modulus, G0 and G00 , respectively. Between γ = 0 and γ = 10,000 an increase in both G0 and G00 can be observed indicating major structural changes in the sample. The transition to a more viscous solution, as expressed by the increase of G00 , can be explained by the development of MLVs that are known to be more viscous than the 12


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normal lamellar phase. 19,86 At higher absolute strains γ > 10,000 a more strongly fluctuating pattern is observed. This might be explained by minor structural changes in the sample, e.g. in the size distribution, but also may arise from effects due to the evaporation of sample as mentioned in section ”Rheo-SALS”. Finally, MLV formation under LAOS is also observed in the SALS patterns shown in Fig. 3c. In agreement with the previous techniques, we observe a significant change between the state at the start of the oscillatory shear and the intermediate state at γ = 15,000, in this case evidenced by the scattering pattern. The emergence of the clover leaf pattern, which is typical for MLVs, clearly shows that onions are formed. Furthermore, the evolution of the scattering pattern towards γ = 78,300 hints towards minor structural changes in the MLVs, as the maximum intensity peak becomes more clearly defined, in agreement with the previous observations by NMR. The rather sharp intensity peak indicates that the MLVs have a very small polydispersity. To conclude this section, different experimental methods provide evidence that LAOS can lead to formation of multilamellar vesicles. This observation is in agreement with similar studies on other lyotropic lamellar systems, in which either LAOStress 79 or a simpler flow reversal pattern 78,89 was employed.

Parameter Dependence of MLV Size After having established the formation of MLVs under LAOS, this section aims to characterize the size of the onion-like aggregates in dependence on the frequency and amplitude of the oscillatory motion. To this end, structural information on the MLVs is extracted from both the NMR spectra and the SALS patterns in the quasi steady state. An overview of all probed parameter sets is given in table 1. Let us first concentrate on the NMR results that are depicted in Fig. 4. Looking at the shape of the spectral lines, it can be inferred that the spectra for ω = 1 rad s−1 are broader as compared to the ω = 2 rad s−1 case, irrespective of the amplitude γ0 . Line widths, w1 , 13


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Table 1: Overview of all NMR and SALS experiments with respective onion sizes. Maximum shear rate is given by γ˙ max = γ0 ω. The maximum stress σm in a shear cycle has been taken at γ ≈ 60,000. RMLV,NMR was computed using the line shape model described in the text. w1 is the line width extracted from Lorentzian fits to the NMR spectra. RMLV,SALS is calculated from the maximum of the radially averaged scattering intensities. Entries with ”−” mean that no experiment for this parameter set has been performed in the NMR case or that no MLV pattern was observed in the SALS case. # 1 2 3 4 5 6 7

ω [rad s−1 ] 1 1 1 1 2 2 2

γ0 [] 10 20 30 50 10 20 30

γ˙ max [s−1 ] 10 20 30 50 20 40 60

σm [Pa] 3.6 155 133 89 6.2 243 109

RMLV,SALS [µm] − 2.4 ± 0.2 1.9 ± 0.2 1.9 ± 0.2 − 1.6 ± 0.2 2.0 ± 0.2

w1 [Hz] 140.0 ± 0.6 152.2 ± 0.8 − 128.2 ± 0.6 96.8 ± 0.4 94.7 ± 0.4 −

RMLV,NMR [µm] 3.3 3.5 − 3.0 2.2 2.2 −

obtained by single Lorentzian fits are given in table 1. From steady shear experiments on the same system 84 it is known that broader peaks correspond to larger onions, i.e., a higher number of concentric bilayer shells. Assuming that this finding from steady shear experiments can directly be transferred to the oscillatory case would mean that the size of the onions is more sensitive to the applied frequency, rather than the amplitude or the maximum shear rate in each cycle, given by γ˙ max = γ0 ω.

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RMLV [µm]

ω[rad s−1 ], γ0

2.19

2, 20

2.23

2, 10

2.95

1, 50

3.51

1, 20

3.29

1, 10

−0.2

−0.1

0.0 f [kHz]

0.1

0.2

Figure 4: 2H NMR spectra at γ = 100,000 (for γ0 = 50) and γ = 200,000 (all other amplitudes) for various LAOS experiments with parameters indicated to the right of each plot. Dashed lines are fits using the line shape model described in the text. For a quantitative determination of the vesicle radius, Medronho et al. 84 established a model for the NMR spectral line shape, which includes RMLV as a parameter. The following assumptions are made in this model. Firstly, exchange of water between adjacent shells via penetration through the hydrophobic barrier formed by the interior of the bilayers is negligibly slow so that water molecules do not leave a certain layer during the acquisition of the spectra. Secondly, the MLVs are sufficiently small so the NMR spectrum is in the isotropic motional narrowing regime, i.e., each water molecule travels far enough within a layer during the acquisition time to experience a sufficient range of orientations. Thirdly, a mono-disperse distribution of MLV sizes is assumed. Under these conditions each shell yields a separate Lorentzian with the line width and signal intensity corresponding to its curvature radius and volume, respectively. The total signal, i.e., the recorded spectrum, is then given by a sum over all vesicle layers. In Medronho et al. 84 the best fit of the model was judged by eye. In this contribution, the model function has been slightly adjusted so it is suitable for a simplex fitting algorithm. 15


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This has been achieved by scaling the total signal intensity with a generic factor and the number of layers N (see supportive information for more details). The model fits are given by the dashed lines in Fig. 4. The deviations of the fits from the experimental spectra show that the model fits better for ω = 2 rad s−1 than in the lower frequency case. The extracted vesicle radii RMLV are listed in Fig. 4 on the left hand side of each spectrum. In the higher frequency case, the similar shape of the spectra is also reflected in an almost equivalent value for the vesicle radius of around 2.2 µm. In contrast, the radii in the lower frequency case vary from about 3.0 µm to 3.5 µm. Generally, it can be concluded that the MLVs in the latter case are larger as also found for the Lorentzian fit line widths. The discrepancy of experimental line shape and the model in the lower frequency case, might stem from a broader MLV size distribution, as the first two assumptions in the model (no water exchange and isotropic motional narrowing) should affect both frequency cases in the same way. Including polydispersity in the model could lead to estimates of the MLV shape distribution, but is beyond the scope of this study. Another route for the size determination of the onion-like vesicles is provided by SALS. In Fig. 5 the radially averaged scattering intensities are plotted for all experiments, where a clover leaf pattern could be observed within the accessible experimental time (max. 3 h). A q value of around 2 µm−1 at the intensity maxima is found for most of the curves with exceptions in the 1, 20 case were qmax is around 1.6 µm−1 and the 2, 20 case were qmax is around 2.5 µm−1 . For a densely packed MLV state, the maximum intensity corresponds to a structure factor peak. Kosaka et al. 91 suggested an FCC packing of the MLVs, where the observed structure factor peak would correspond to the 111 reflection. With that we obtain RMLV = 3.9/qmax . The radii calculated by using the structure peak equation are reported in Table 1. It appears that the size of the onions varies only slightly with the input parameters. For γ0 = 20, the radius is significantly larger in the ω = 1 rad s−1 case whereas it is significantly smaller in ω = 2 rad s−1 case.

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1,20 1,30 1,50 2,20 2,30

0.5

1.0

1.5

2.0 2.5 q [µm−1]

3.0

3.5

4.0

Figure 5: Comparison of the radial intensity distribution of the scattering patterns recorded in depolarized SALS for different LAOS experiments for γ/103 ≈ 60. The corresponding parameters are given as (ω,γ0 ) tuples on the right hand side. In addition, maximum stress values, σm , from the rheo-SALS experiments, are also reported in Table 1. σm is the maximum stress in a cycle, here taken at an accumulated strain of about 60,000 for all runs. The stress is related to the viscosity of the samples and indicates MLV size as well. Steady-shear experiments have shown a strong increase in viscosity, when onions are formed from the normal lamellar phase, and a decrease of viscosity as MLVs become smaller with increasing shear rate. 34,86 Therefore, in the cases where MLV formation is observed by Rheo-SALS, σm values suggest a decrease of the MLV radius upon increasing γ0 and upon increasing ω. With the exception of the case ω = 2 rad s−1 and γ0 = 30 (in which RMLV,SALS appears too large), the overall trends of the radii obtained by SALS are in agreement with the results obtained from the stress values and with the NMR results. For γ0 = 10 no cloverleaf pattern is observed in both frequency cases. This could either mean that no onions are forming during the experimental time of around 3 h or that the onion size is not accessible within the tested q range. Additionally, the small values of σm observed for the two experiments at the lowest strain amplitude indicate that no MLVs are 17


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formed. On first sight this contradicts the NMR results, where onion formation is observed with a radius of around 2 µm to 3 µm. However, as shall be discussed in section ”Evolution of Structure during MLV Formation”, this onion formation starts at γ ≈ 50,000, which in turn corresponds to 2 h and 1 h of shear for ω = 1 rad s−1 and ω = 2 rad s−1 , respectively. During this lag time the onion formation process might be influenced or even impeded by evaporation not avoidable for the cone-and-plate geometry used for SALS. This could explain the divergence from the NMR results which were performed in a cylindrical Couette geometry. Furthermore, it shall be pointed out that Nettesheim et al. 78 found a minimum amplitude of 6.5 to induce onion formation for the same solution. Even though the deformation in their flow reversal experiments was different from the LAOS experiment described here, this value gives an indication were the limit would be expected in the sinusoidal deformation case. The MLV formation process may be very sensitive to small differences in the experimental setups for amplitudes around that value of 6.5. Additionally, the actual minimum amplitude for onion formation might be even higher for sinusoidal shear modulation. In the case of the AOT/brine system studied by Fritz et al. 79 , for example, the minimum value was found to be 14. In conclusion, SALS and NMR determine onion diameters which are in the same range. In both cases, the largest radii are found at the lower oscillation frequency and at small oscillation amplitude. The lack of a clover leaf pattern impeding size determination for γ0 = 10 in the SALS case is ascribed to specificities of the SALS setup. The onion sizes determined for ω = 1 rad s−1 in SALS are about 30% smaller than in the NMR case, which might be explained by the stronger deviations of the NMR fit model to the spectral data and the different shear geometries used for the two techniques. It shall be mentioned that an offset of about 30% between NMR and SALS data has also been observed by Medronho et al. 84 for the same system, however, with the sizes determined by SALS being larger. Furthermore, from the NMR results in particular, it seems that the onion size is mainly a function of the applied frequency and not a function of the amplitude or the maximal

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shear rate which might be expected on the basis of the steady shear results. 84 For the SALS experiments this trend is not as clear, however, the onion radii are about 15% smaller on average for the higher frequency. Only the stress values σm , which indicate a decrease in onion size with both increasing γ0 and increasing ω, are consistent with the expectation based on the steady-shear results. Although the results on onion size are not quite conclusive, the SALS patterns give an indication that the onion formation process is altered in the oscillatory experiment, which shall be further discussed in the next section.

Evolution of Structure during MLV Formation The mechanism of the shear-induced formation of MLVs is still under debate. This mechanism shall now be discussed in the light of the LAOS experiments. In previous studies 76,78,83 considerable effort was put into characterizing intermediate structures in the formation process, such as bent and tilted lamellae or cylindrical objects. The techniques applied here do not give as detailed information on these transient structures. Still the onset of MLV formation is reflected in the experimental data for all applied techniques as well as some signatures of possible intermediate structures that can be compared to the case of steady shear. 76,78,83 This onset should roughly correspond to a structure showing a broad size distribution of MLVs, as suggested by Gentile et al. 76 (see Fig. 7 in that reference, where the corresponding regime has been labelled “stage IV”). As in the previous sections, the results from the different techniques shall be first discussed individually, starting with NMR, before a comparison is made. NMR The evolution of the NMR spectra at ω = 1 rad s−1 and γ0 = 20 is shown in Fig. 6a. (Additional NMR data for other combinations of ω and γ0 can be found in the SI.) As a first observation the doublet of the aligned lamellar phase at γ = 0 completely disappears after around γ = 10,000. In the region between 10,000 and 20,000 absolute strain units the NMR signal is basically lost impeding any structural characterization of the sample in this region.

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From γ = 20,000 to γ = 40,000 the MLV peak develops, as can be seen in Fig. 6b where selected spectra are plotted. For higher γ values the height of the MLV peak continuously increases, however, changes in the overall shape are small. This observation is also reflected in the peak widths extracted from single Lorentzian fits shown in Fig. 6c. In the case of ω = 1 rad s−1 and γ0 = 20 a single Lorentzian is apparent only for γ/103 > 20. After a steep decrease from γ = 20,000 to γ = 40,000 the change in line width per absolute shear is relatively small up to values of around γ = 175,000. For even higher γ-values the line width is plateauing and thus it can be assumed that a steady state value has been reached. (b)

(a)

γ0 = 20, ω = 1 rad s−1 γ/103 = 20

(c) 300

3

γ/10 = 28 250

1,20 1,10 1,50 2,10 2,20

γ/103 = 40

0.7

γ/103 = 60 γ/103 = 200 250

0.6

γ/103 = 252

200

0.4 0.3

intensity [a.u.]

150

peak width [Hz]

0.5 γ[103]

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100

200

150

0.2 50

100 0.1 0.0

0 −0.4−0.3−0.2−0.1 0.0 0.1 0.2 0.3 0.4 freq [kHZ]

−0.4 −0.3 −0.2 −0.1 0.0 0.1 freq [kHz]

0.2

0.3

0.4

50 0

50

100 150 γ/103

200

250

Figure 6: (a) Evolution of the NMR spectra for ω = 1 rad s−1 and γ0 = 20. (b) Selected NMR spectra from (a) for γ values as indicated by horizontal lines in (a). Dashed lines are Lorentzian fits. (c) Widths of the Lorentzian fits as a function of the absolute strain for all NMR LAOS experiments. Corresponding parameters for each experiment are given by a γ0 , ω [rad s−1 ] tuple on the right hand side. Missing data points for lower γ values mean that no clear MLV peak was present in the spectra. From the evolution of the NMR spectra one can conclude that the onset of MLV formation happens around 20,000 strain units for ω = 1 rad s−1 and γ0 = 20 with major structural changes taking place until 40,000 strain units. These structural changes are most likely linked to a narrowing of the MLV size distribution starting from a very polydisperse state 20


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at the onset of MLV formation. For higher γ values the line width becomes only slightly narrower until reaching a final state at around γ = 175,000. The slow decrease in line width can be explained by a decrease in the size of the onions as also observed by Yatabe et al. 89 for a quaternary system under a zigzag oscillatory flow pattern. A similar functional dependence of the line width is found in the ω = 2 rad s−1 , γ0 = 20 and ω = 1 rad s−1 , γ0 = 50 cases (Fig. 6c). Whereas in the former case, the transition happens in the same γ range as for ω = 1 rad s−1 , the main transition in the latter case takes place at smaller γ values. For γ0 = 10 the situation is slightly different, as the transition is first characterized by an increase in line width after the appearance of the MLV peak at about 50,000 absolute strain units. At around 75,000 strain units a clear kink is found in both frequency cases followed by a more gentle decrease in line width, as observed for the higher amplitude experiments. This range of line width increase might indicate some intermediate state in the formation process of potentially smaller MLVs, that is not present for higher amplitudes. In summary, the transition strain/time is set by the shear amplitude but not by the frequency. The latter, however, seems to be important for the final line width of the spectra, which is an indicator for the size of the MLV aggregates, as discussed in the previous section ”Parameter Dependence of MLV Size”. SALS In Fig. 7 a series of SALS patterns at different γ values for ω = 1 rad s−1 and γ0 = 20 are depicted. (Further SALS patterns are shown in the SI.) Before the start of oscillatory shear a diffuse pattern is observed which can be attributed to a state of aligned parallel lamellae with a small amount of texture defects. 88 From 0 to 15,000 absolute strain units a pattern with two-fold symmetry and an elongation in the velocity direction develops that seems to overlap with a four-lobe pattern. This is interesting as in previous studies by Nettesheim et al. a pattern elongated in the vorticity direction was observed both under steady shear 88 and under flow reversal. 78 This pattern was ascribed to multilamellar cylinders aligned in the velocity direction and/or a buckling of the lamellar phase with reference to

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previous studies. 87,92 With respect to the present work one could speculate that the potential intermediate objects are not oriented along the velocity but along the vorticity direction. A reason might be the continuous alteration of flow velocity according to the induced sinusoidal motion which could make an orientation along the vorticity direction preferential, as opposed to flow reversal or steady shear experiments. 0

5

10

15

20

25

30

40

50

60

velocity

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vorticity

Figure 7: Evolution of the SALS pattern for ω = 1 rad s−1 and γ0 = 20 with absolute strain (γ/103 indicated in each plot). All patterns were recorded at the same oscillatory phase with maximum shear rate (γ(γ) ˙ = γ˙ max ). The cloverleaf pattern, typical for MLVs, becomes clearly visible between 20,000 and 25,000 absolute strain units indicating the appearance of MLVs. As found in previous studies 76,88 the pattern is stretched in the vorticity direction during the onset of MLV formation at γ = 25,000 meaning that the developing MLVs are slightly elongated in the velocity direction. For increasing strain values the pattern gets symmetric and more defined with a clear radial intensity maximum developed at γ = 60,000. This observation is also reflected in the radial averages of these scattering patterns, as shown in Fig. 8a. For γ = 30,000 a broad maximum is found that becomes narrower with increased absolute shear indicating a decreasing degree of polydispersity. At γ = 60,000 one finds a relatively sharp maximum around 1.6 µm−1 .

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(a)

γ/103 = 10

ω = 1 rad s−1, γ0 = 20

(b) 101

γ/103 = 20 γ/103 = 30 γ/103 = 40 γ/103 = 50 γ/103 = 60

0.5

1.0

1.5

2.0 2.5 q [µm−1]

3.0

3.5

4.0

100 G0 , G00 [Pa]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10−1 G00 G0 10−2 0

10

20

30 γ [103]

40

50

60

Figure 8: Radial averages of the SALS patterns from Fig. 7 (a) and recorded elastic and loss moduli (b).

In the other cases where onion formation is observed a similar behaviour is found in the rheo-SALS measurements (see SI). However, the two-fold scattering pattern with elongation in the velocity direction is only observed in the case of ω = 1 rad s−1 and γ0 = 20. In the other cases, the diffuse pattern is more or less directly transferred into one with a four-fold symmetry, without a sign of anisotropic intermediates. The lack of an elongated two-fold symmetry pattern might be explained by a higher maximum shear rate for these experiments. Rheology The rheology data recorded simultaneously with SALS (Fig. 8b) are in agreement with the scattering experiment. Both moduli significantly increase until a value of 30,000 absolute strain units and then level off. This increase is a signature for the development of MLVs, which lead to a more viscous solution. The subsequent region after 30,000 is associated with a change in MLV size distribution, which does not seem to have a strong effect on the bulk rheological properties of the solution. Higher values for γ were not accessible due to evaporation effects. In linear rheology materials are characterized by the storage (G0 ) and loss (G00 ) moduli as determined from the components of the time-dependent stress σ(t) in phase with time-dependent strain and in phase with the time-dependent applied strain rate, respec23


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tively. However, the linear moduli are only uniquely defined in the linear viscoelastic regime, i.e., at low strain values. Once the material response becomes nonlinear 80 the response is not a single-harmonic sinusoid anymore. In general there are two methods for data treatment in LAOS experiments: Fourier transform 93 and Lissajous-Bowditch curves. 94 LissajousBowditch curves consist of σ(t) plotted against γi (t). The latter approach will be used in the following. For a linear viscoelastic response the curve will appear as an ellipse that contains two mirror planes whereas a nonlinear viscoelastic response is characterized by a deviation from ellipticity. Fig. 9 shows Lissajous-Bowditch curves for the oscillatory experiment performed at ω = 1 rad s−1 and γ0 = 20. For a perfectly elastic material the response would appear as a straight line, while the corresponding perfect plastic reference response is a rectangle. Here high strain deformations are discussed since our focus was to observe the lamellae to MLV transition under such conditions. First of all it shall be mentioned that the small amplitude response of the lamellar phase is linearly viscoelastic and therefore the trajectory is elliptical (see supporting information Fig. S10). However, as the strain amplitude is increased a nonlinear viscoelastic response can be detected by looking at the shapes of the Lissajous curves. This rheological test highlights the distinguishing features of the MLV state. Firstly, the energy dissipated per unit volume in a single LAOS cycle, Ed =

H

σdγ, is

visualized by the area enclosed by the Lissajous-Bowditch curve of stress vs. strain. Notice that the loops in Fig. 9 are normalized to different values of maximum stress. At small strains the sample behaves like a viscoelastic solid. The area within the loop of the stress/strain plot is small, i.e., the dissipated energy is small, while with increasing strain the dissipated energy gets larger. Secondly, a gradual softening (decreasing storage modulus) with increasing strain-amplitude is indicated by the change of the curve shapes. Thirdly, a departure from the linear viscoelastic response of the lamellar phase (cf. Fig. S10 in SI) is already obvious at low absolute strain. A comparison with the SALS patterns depicted in Figure 7 shows that the rounded square-like Lissajous shapes occur when the vesicles are fully developed

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as indicated by the appearance of the clover-leaf-shaped scattering pattern. Decreasing polydispersity, inferred from the sharpening of the SALS reflections, leads to an increase of the dissipated energy but has little affect on the shape of the Lissajous pattern. 1.0

normalized Stress []

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γ/103 = 0; σm = 4.8Pa

0.5

γ/103 = 2; σm = 5.1Pa γ/103 = 10; σm = 15.5Pa γ/103 = 20; σm = 55.8Pa

0.0

γ/103 = 30; σm = 137.5Pa γ/103 = 40; σm = 164.3Pa

−0.5

γ/103 = 50; σm = 164.1Pa

−1.0 −20

−10

0 Strain [ ]

10

20

Figure 9: Lissajous curves (normalized stress σ/σm vs. strain) as a function of the absolute strain recorded during the oscillatory experiments at ω = 1 rad s−1 and γ0 = 20 by using a cone-and-plate geometry. The maximum stress σm is indicated for each absolute strain γ.

Inter-Techniques Comparison Comparing the SALS results to the NMR case, one finds that the lamellae to onion transition occurs around the same values of γ in each of the cases where onion formation is observed with both techniques. Moreover, SALS data suggest that no cylindrical intermediate structures are formed when planar lamellae undergo the transition to onions. However, SALS experiments do detect cylindrical intermediate structures for steady shear (cf. Fig. S9 in SI) similar to SALS observations for the system C16 E4 by Gentile et al. 95 . A comparison of the NMR line shapes of the intermediate structures with those observed under steady shear by Medronho et al. 85 is not possible because a significant NMR signal loss and line shape distortions were observed for the transition state between lamellae and MLVs. However, the lack of a well-defined intermediate state, like the aligned cylinders observed during the transition under steady shear, is supported by the bulk rheology data which do not show a (narrow) plateau before the onset of onion formation as observed under

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steady shear. 85 We therefore infer that LAOS (as opposed to steady shear) causes the sample to take a different path from lamellae to onions.

Conclusions and Outlook The combination of three methods, namely rheo-NMR, rheo-SALS and bulk rheology, has been used to observe, for the first time, the formation of multilamellar vesicles under large amplitude oscillatory shear (LAOS) for a lyotropic lamellar system (C10 E3 /water). A novel rheo-NMR apparatus 81 allowed for oscillatory shear deformations of the studied sample in a superconducting NMR magnet. For the range of investigated strain amplitudes (10–50) and frequencies (1 and 2 rad s−1 ) MLV formation was observed for all experiments with amplitudes greater than 10. From the results it can be concluded that the size of the formed multilamellar vesicles depends mainly on the applied frequency and not on the amplitude or the maximum shear rate of the oscillatory cycle. This is surprising as the shear rate is the controlling parameter for steady shear experiments. On the other hand, it was found that the type of transition state and the absolute strain at which the transition occurs rather depend on the amplitude of the imposed sinoidal strain. This is in contrast to the case of steady shear, in which the transition process scales with the absolute strain. 85 Also, there is no clear signature of intermediate objects in the MLV formation process, such as multilamellar cylinders, indicating that the formation mechanism is altered compared to the steady shear case. The Lissajous curves recorded simultaneously to the light scattering experiments reveal a transition from a viscoelastic solid material to a pseudo-plastic material. For future studies it would be worthwhile to explore the formation process in a larger range of frequencies and amplitudes to see if the observations in this work hold a more general validity. Finally, we hope that the present study can spark theoretical studies on the MLV formation process under LAOS.

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Acknowledgement The authors thank Bruno Medronho for useful discussion.

Supporting Information Available Explanation on the line shape model and Lorentzian fitting. Example of a 1D NMR spectroscopy image. Detailed explanation of absolute strain γ. NMR and SALS MLV evolution for other parameter sets not shown in article. SALS of intermediate state under steady shear. Lissajous pattern under SAOS. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Larson, R. The Structure and Rheology of Complex Fluids; Topics in Chemical Engineering; Oxford University Press, 1999. (2) van Egmond, J. W. Shear-thickening in suspensions, associating polymers, worm-like micelles, and poor polymer solutions. Current Opinion in Colloid & Interface Science 1998, 3, 385–390. (3) Butler, P. Shear Induced Structures and Transformations in Complex Fluids. Current Opinion in Colloid and Interface Science 1999, 4, 214–221. (4) Richtering, W. Rheology and shear induced structures in surfactant solutions. Curr. Opin. Colloid Interface Sci. 2001, 6, 446–450. (5) Gradzielski, M. Vesicles and vesicle gels—structure and dynamics of formation. J. Phys.: Condens. Matter 2003, 15, R655–R697. (6) Gradzielski, M. The rheology of vesicle and disk systems—relations between macroscopic behaviour and microstructure. Current Opinion in Colloid and Interface Science 2011, 16, 13–17. 27


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(7) Mortensen, K. Structural Studies of Lamellar Surfactant Systems Under Shear. Curr. Opin. Colloid Interface Sci. 2000, 6, 140–145. (8) Berni, M. G.; Lawrence, C. J.; Machin, D. A review of the rheology of the lamellar phase in surfactant systems. Advances in Colloid and Interface Science 2002, 98, 217–243. (9) Dreiss, C. A. Wormlike micelles: where do we stand? Recent developments, linear rheology and scattering techniques. Soft Matter 2007, 3, 956–970. (10) Lerouge, S.; Berret, J. In Polymer Characterization; Dusek, K., Joanny, J., Eds.; Advances in Polymer Science 230; Springer Berlin Heidelberg, 2010; pp 1–71. (11) Fielding, S. M. Complex dynamics of shear banded flows. Soft Matter 2007, 3, 1262– 1279. (12) Manneville, S. Recent experimental probes of shear banding. Rheologica Acta 2008, 47, 301–318. (13) Dhont, J. K. G.; Briels, W. J. Gradient and vorticity banding. Rheologica Acta 2008, 47, 257–281. (14) Callaghan, P. T. Rheo-NMR: nuclear magnetic resonance and the rheology of complex fluids. Reports on Progress in Physics 1999, 62, 599–670. (15) Callaghan, P. T. Rheo-NMR: A new window on the rheology of complex fluids. Encyclopedia of Magnetic Resonance 2002, 9, 739–750. (16) Eberle, A. P. R.; Porcar, L. Flow-SANS and rheo-SANS applied to soft matter. Current Opinion in Colloid and Interface Science 2012, 17, 33–43. (17) Svenˇsek, D.; Brand, H. Layered systems under shear flow. Advances in Polymer Science 2010, 227, 101–143.

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(18) Diat, O.; Roux, D.; Nallet, F. Effect of shear on a lyotropic lamellar phase. Journal de Physique II 1993, 3, 1427–1452. (19) Roux, D.; Nallet, F.; Diat, O. Rheology of Lyotropic Lamellar Phases. EPL (Europhysics Letters) 1993, 24, 53. (20) Soubiran, L.; Staples, E. T., I.; Penfold, J.; Creeth, A. Effects of Shear on the Lamellar Phase of a Dialkyl Cationic Surfactant. Langmuir 2001, 17, 7988–7994. (21) Soubiran, L.; Coulon, C.; Sierro, P.; Roux, D. Conductivity and Dielectric Measurements of a Lyotropic Lamellar Phase under Shear Flow. EPL (Europhysics Letters) 1995, 31, 243–248. (22) Gulik-Krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. FreezeFracture Electron Microscopy of Sheared Lamellar Phase. Langmuir 1996, 12, 4668– 4671. (23) Lukaschek, M.; M¨ uller, S.; Hasenhindl, A.; Grabowski, D. A.; Schmidt, C. Lamellar lyomesophases under shear as studied by deuterium nuclear magnetic resonance. Colloid Polym. Sci. 1996, 274, 1–7. (24) Läuger, J.; Weigel, R.; Berger, K.; Hiltrop, K.; Richtering, W. Rheo-small-Angle-LightScattering Investigation of Shear-Induced Structural Changes in a Lyotropic Lamellar Phase. Journal of Colloid and Interface Science 1996, 181, 521–529. (25) Weigel, R.; Läuger, J.; Richtering, W.; Lindner, P. Anisotropic Small Angle Light and Neutron Scattering from a Lyotropic Lamellar Phase under Shear. Journal de Physique II 1996, 6, 529–542. (26) Auguste, F.; Douliez, J.; Bellocq, A.; Dufourc, E. J.; Gulik-Krzywicki, T. Evidence for Multilamellar Vesicles in the Lamellar Phase of an Electrostatic Lyotropic Ternary Sys-

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Large Amplitude Oscillatory Shear (LAOS)

Shear-induced multilamellar vesicles

Lyotropic lamellar phase


Multilamellar Vesicle Formation Probed by Rheo ... - ACS Publications

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