Transition Processes from the Lamellar to the Onion State with

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Transition Processes from the Lamellar to the Onion State with Increasing Temperature under Shear Flow in a Nonionic Surfactant/Water System Studied by Rheo-SAXS Makiko Ito, Yuriko Kosaka, Youhei Kawabata, and Tadashi Kato* Department of Chemistry, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan

bS Supporting Information ABSTRACT: In a previous paper, we reported for the first time the lamellar-to-onion transition with increasing temperature at around 67 °C under a constant shear rate (0.3
10 s
1) in a nonionic surfactant C16E7/water system. In this study, the first temperature
shear rate diagram has been constructed in a wider range of shear rate (0.05
30 s
1) than in our previous study based on the temperature dependence of the shear stress at constant shear rate. The results suggest that the critical temperature above which the transition begins does not depend on the shear rate very much, although it takes a very shallow minimum. Then we have performed simultaneous measurements of small-angle X-ray scattering/shear stress (rheo-SAXS) with a stepwise increase in temperature of 0.1 K per 15 min at a constant shear rate of 3 s
1 near the transition temperature. When the temperature exceeds 67 °C, just before the increase in the shear stress, the intensity of the Bragg peak for the velocity gradient direction (approximately proportional to the number of lamellae with their normal along this direction) is suddenly increased. As the temperature increases by 0.2 K, the shear stress begins to increase. At the same time, the peak intensity in the velocity gradient direction rapidly decreases and instead the intensity in the neutral direction increases. As the temperature increases further, the intensities in both the neutral and gradient directions decrease whereas the intensity in the flow direction increases, corresponding to the formation of onions. We have also performed rheo-SAXS experiments with a stepwise increase in shear rate at 72 °C. The sequence of the change in the intensity in each direction is almost the same in the temperature scan experiments at constant shear rate, suggesting that the transition mechanisms along these two paths are similar. The abrupt enhancement of the lamellar orientation with the layer normal along the velocity gradient direction just before the transition is the first finding and strongly supports the coherent buckling mechanism in the lamellar-to-onion transition proposed by Zilman and Granek (Zilman, A. G.; Granek, R. Eur. Phys. J. B 1999, 11, 593).

1. INTRODUCTION The surfactant lamellar phase is one of the lyotropic liquid crystal phases and consists of stacked bilayers intercalated by aqueous layers.1 Because the size of the building block of the lamellar phase is much larger than the atomic scale, its characteristic time is much longer than that of the motion of the lowmolecular-weight molecules. This causes various effects on the structures of the lamellar phase by shear flow within the available range of shear rate for a commercial rheometer (0.1
100 s
1).2,3 Among them, the most striking result may be the transition from the lamellar phase to the “onion state” where all of the space is filled with multilamellar vesicles without excess solvent. This transition has been found for the first time by Roux and coworkers4
6 for ionic surfactants with an organic solvent. They have shown that there are three states of orientation in the _ and the volume lamellar phase depending on the shear rate (γ) fraction of membranes. At a constant volume fraction, the lamellae are transformed to onions above a critical shear rate (γ_ C). With further increases in the shear rate, however, the onions are again transformed to lamellae oriented in the velocity gradient r 2011 American Chemical Society

direction (parallel orientation). They have also shown that the critical shear rate is proportional to the third power of the volume fraction of membranes (φ) (i.e., γ_ C µ φ3) and that the radius of the onions (R) is followed by the power laws R µγ_
1/2 and R µ d
2 µ φ2, where d is the lamellar spacing. Their subsequent studies7
12 reveal the polyhedral shape of onions7 and longrange-ordered plane structures where onions are hexagonally shaped and close packed on triangular lattices8 and another ordered state made of much larger onions (10
50 μm).9 Following their studies, the shear-induced lamellar-to-onion transition has been reported for many systems.13
39 The mechanism for the lamellar-to-onion transition was first discussed by Roux co-workers.4,5 As pointed out in the study of Oswald and Kleman40 concerning the flow behavior of smectic A phases, even a perfectly oriented lamellar phase has many dislocations in order to fill up the gap in the shear apparatus Received: December 4, 2010 Revised: March 24, 2011 Published: May 16, 2011 7400

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Langmuir (the space between the inner and outer cylinders), which is not uniform on the scale of the lamellar spacing. At low shear rates, these dislocations can move with the flow by permeation. At higher shear rates, the dislocation cannot follow the flow and so the lamellae are subjected locally to either dilational or compressive strain perpendicular to the layers, leading to the undulation instability. They consider that the onion state may arise from this instability. Wunenburger et al.11 have estimated γ_ C on the basis of this idea and the theoretical results of Oswald et al.40,41 However, the estimated γ_ C (10
4
10
3 s
1) is much smaller than the observed ones (1
10 s
1). Zilman and Granek42 have considered that the coupling of the short-wavelength membrane undulations with the shear flow generates an effective force that acts to reduce the excess area. Because the geometry of the macroscopic lamella is fixed, this force translates into an effective lateral pressure (σ). Above a critical shear rate, the lamella buckles into a harmonic shape modulation with the wavenumber qC. Assuming that the lamella breaks up into onions at this limit of stability, the critical shear rate for the formation of onions is predicted to scale as γ_ C µ d
5/2D
1/2, where D is the gap spacing. They have also predicted the scaling relation of the wavenumber as qC µ ~, ~σ/d)1/6(KD)
1/3 with the relation σ µ kd4η2γ_ 2, where B (B k, and η are the compression modulus at constant chemical potential, the single-bilayer bending modulus, and the viscosity of the solvent, respectively, and K = k/d. By using the relation ~ µ k
1d
3, the scaling relation of the wavenumber becomes B · qC µ (γd/D)1/3. This power law has been confirmed experimentally by Courbin et al.,35,36 assuming that qC is inversely proportional to the onion size that can be determined from smallangle light scattering. However, the absolute value of the critical shear rate γ_ C predicted by Zilman and Granek is about 3 103 s
1 for typical parameter values (D = 1 mm, d = 10 nm, η = 3 mPa s, and k = kBT (kB and T are Boltzmann’s constant and the absolute temperature, respectively), which is about 103 times larger than the observed values. Mallow and Olmsted43 have studied the suppression of undulations in shear flow by modeling the flow as an effective anisotropic tension, which decreases the compression modulus. They consider two cases: if new layers can be generated by permeation or defects, a decrease in lamellar spacing occurs. If the system cannot change the number of layers or the process is very slow, then an instability is induced for tension greater than σC µ (dD)
1 and this instability produces either cylinders or onions. Using the relation σC = ηγ_ Cd, they predicted the critical shear rate to be γ_ C µ d
2D
1 µ φ2D
1, which is a slightly different power law from that obtained by Zilman and Granek. However, the absolute values are about 2  104 s
1 for the same parameter values as described earlier, which is again 104 times larger than the experimental values. Thus, despite these intensive theoretical efforts, the mechanism of the lamellar-to-onion transition is still unclear and so more experimental studies are necessary. Binary systems of water and polyoxyethylene surfactants CnH2nþ1(OC2H4)mOH, abbreviated as CnEm, may be useful in investigating the transition mechanism because it has been known that a variety of phase behaviors can be observed at rest just by changing the temperature without any additives such as cosurfactants and salt.44 Richtering and co-workers15
24 have extensively studied the lamellar-to-onion transition in C10E3/water and C12E4/water systems by using small-angle neutron scattering (SANS) and simultaneous measurements of small-angle light scattering/shear stress

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(rheo-SALS). They have found that an intermediate structure oriented in the flow direction exists during the lamellar-to-onion transition in the C10E3 system, corresponding to long multilamellar cylinders before the formation of spherical onions (see also the later discussion).16
18 They have also found a discontinuous size growth in addition to the continuous size growth.21,22 In the discontinuous growth, first lamellar domains are formed, which afterward transform into larger onions. Olsson and co-workers16
19,24
29,31 have reported that the lamellae are transformed into onions with decreasing temperature under constant shear rate for the C10E3 and C12E4 systems. They explain these results in terms of the elastic properties of bilyers. In nonionic surfactant systems, the spontaneous curvature increases with decreasing temperature,45,46 which leads to a decrease in the saddle splay modulus of bilayers47,48 and thus a decrease in the stability of flat bilayers relative to that of vesicles.49 Medronho et al.28 have studied the transition processes in the C10E3 system by using deuterium NMR spectroscopy under shear as a function of time at several temperatures and shear rates. They have shown that the transition is continuous when onions are formed, starting from the oriented lamellar phase. When the onions are transformed into an oriented lamellar phase, a discontinuous nucleation-and-growth process with a coexistence region is observed. Very recently, they have measured deuterium NMR in the range of temperature and shear rate where onions are not formed even under shear.29 They have shown that a decrease in the quadrupolar splitting and an increase in the average line width are observed with increasing shear rate at a constant temperature. They have also shown that the storage modulus after preshearing increases with increasing preshear rate, suggesting that the density of the structural defects is increased with increasing shear rate. These shear-induced defects may be regarded as a pretransition prior to the shear-induced formation of onions. However, it is still unclear how these defects are transformed into onions. We have recently reported for the first time the lamellar-toonion transition with increasing temperature under a constant shear rate in a C16E7/water system by using rheo-SALS and simultaneous measurements of small-angle X-ray scattering/shear stress (rheo-SAXS).30 As described above, onion formation with decreasing temperature in the C10E3 and C12E4 systems can be explained by the temperature dependence of the saddle-splay modulus of bilayers. However, such elastic properties of bilayers cannot explain our results, which suggests the existence of unknown factors dominating onion formation. Further investigation of this system is therefore necessary for a more general understanding of the shear-induced structural transition. In our previous rheo-SAXS experiments, most data have been obtained above the transition temperature.30 The present paper concerns itself with the transition processes based on rheo-SAXS experiments that have been performed around the transition temperature. In addition, we have performed shear-rate-scan experiments under constant temperature to investigate the path dependence of the transition processes. In both temperature-scan and shear-ratescan experiments, we have found abrupt enhancements of the lamellar orientation with the layer normal along the velocity gradient direction just before the transition, which has not been reported before for any systems. Before these experiments, we measured the temperature dependence of the shear stress over a wider range of shear rate than in our previous study to make the temperature
shear rate diagram that is necessary to show the above two transition paths. 7401

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2. EXPERIMENTAL SECTION Materials and Sample Preparation. C16E7 was purchased from Nikko Chemicals, Inc. in crystalline form (>98%) and used without further purification. Deuterium oxide purchased from ISOTEC, Inc. (99.9%) was used after being degassed by bubbling nitrogen to avoid the oxidation of the ethylene oxide group of the surfactants. (We used D2O as the solvent instead of H2O following our previous study where 2H NMR is used to determine the phase diagram.50) Samples containing the desired amount of surfactant and water (∼10 g) were sealed in an Erlenmeyer flask. For homogenization, we annealed samples for 3 h at about 55 °C with occasional shaking and then held them at room temperature for 21 h. This treatment was repeated for about 1 week. In the rheo-SAXS experiments, we first sheared the sample with a shear rate of 1 s
1 for 10 min at 48 °C corresponding to the bicontinuous cubic (V1) phase. Then the shear was stopped and the sample was heated to the initial temperature in the lamellar phase without shear. All of the measurements were made for the sample containing 48 wt % C16E7. Rheo-SAXS. The apparatus for rheo-SAXS experiments is the same one reported previously.30 We used a cuvette cell made of polycarbonate consisting of two concentric cylinders whose diameters are 27 and 29 mm. The thicknesses of the inner cylinder at the X-ray beam position and the outer cylinder are both 0.5 mm, and the height of the inner cylinder is 23 mm. The outer cylinder is fixed, and the inner cylinder is attached to the AR550 rheometer (TA Instruments). The temperature of the cell is controlled to (0.1 °C by Peltier elements attached to the rheometer through the copper block surrounding the outer cylinder. To prevent sample evaporation, a vapor seal is incorporated into the cell. The experiments were conducted on beamline 15A at the photon factory (PF) of the High Energy Accelerator Research Organization (KEK), Tsukuba, Japan. The scattered X-rays were detected using the CCD area detector. The exposure time was 30 s. The approximate q range is from 0.3 to 3 nm
1. Two scattering configurations were used: one is the so-called radial configuration where the X-ray beam is directed through the center of the cell (along the velocity gradient direction), and the other is the tangential configuration where the beam is directed through the end of the cell (along the flow direction). The 2D SAXS pattern in the flow-neutral (vorticity) plane is obtained in the radial configuration, and that in the velocity gradient-neutral plane is obtained in the tangential configuration. For the lamellar structure, there are three principal orientations: perpendicular (or A
), transverse (or B
), and parallel (or C
), with the layer normal along the neutral, flow, and velocity gradient directions, respectively. These three orientations can be detected by using both radial and tangential configurations. In our apparatus, the configuration can be changed within 10 s by using an automatic stage.

3. RESULTS Temperature Dependence of Shear Stress at a Constant Shear Rate. Figure 1 shows the temperature dependence of the

shear stress at a constant shear rate in the range of shear rate from 0.1 to 30 s
1 for the sample containing 48 wt % C16E7. According to the phase diagram at rest reported previously, the lamellar phase exists above 50.0 °C up to at least 75 °C at this concentration. The shear stress first slightly decreases as the temperature is increased up to a specific temperature (hereafter referred to as T*, which is around 66
68 °C depending on the shear rate). When the temperature exceeds T*, the shear stress begins to increase. At shear rates larger than or equal to 1 s
1, the shear stress takes a maximum at a certain temperature hereafter referred to T** and then slightly decreases with further increases in the temperature.

Figure 1. Evolution of the shear stress with increasing temperature at different shear rates (as indicated). See also Figure 1 in the Supporting Information. The open and closed symbols at 3 s
1 correspond to different runs (Figures 3 and 4 in the Supporting Information). The vertical line indicates the temperature where the shear stress is measured for a long time at a constant temperature and shear rate (Figure 3).

Figure 2. Temperature
shear rate diagram for the sample containing 48 wt % C16E7 in D2O constructed from Figure 1. The circles and crosses indicate the onion and lamellar states, respectively, and the triangles indicate the transition region. (See the text.) The upward and rightward arrows indicate the temperature scan and shear rate scan experiments using rheo-SAXS, respectively.

In our previous study,30 we found that the SALS intensity at a particular azimuthal angle begins to increase above T* and that a four-lobed pattern is observed above T**. In general, 2D depolarized light scattering spectra from optically anisotropic spheres such as polymer spherulites with a radius of R give a four-lobed pattern that has an intensity maximum at the scattering vector qmax given by qmax = 4.1/R.51,52 The same holds true for multilamellar vesicles, so the four-lobed pattern is regarded as evidence of the onion formation.13
19,21,22,24 It has also been reported that the lamellar-to-onion transition accompanies a substantial increase in the shear stress.2
4,6,16,17,19
23,26 Therefore, the results in Figure 2 strongly suggest that the lamellar-toonion transition begins at T* and is completed at T**. In Figure 2, T* and T**are plotted as a function of the shear rate. In the temperature range between T* and T**, not all the lamellae are transformed to onions, so this range is referred to as the transition region. In these experiments, the temperature was increased stepwise. At the temperatures between T* and T**, the shear stress does not become constant at each temperature, suggesting that the system does not reach a steady state (Figure 1 in the Supporting Information). Therefore, we have also measured the shear stress as a function of time at a constant temperature and shear rate. 7402

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Figure 3. Time evolution of the shear stress after applying shear flow at 72 °C and different shear rates.

Figure 4. Time evolution of the shear stress after applying shear flow at 3 s
1 and at different temperatures.

Figure 3 shows the time evolution of the shear stress at 72.0 °C at different shear rates of 0.3, 1, 3, and 30 s
1 (evolution versus strain shown in Figure 2 of the Supporting Information). One can see that the shear stress becomes almost constant after a long time (>104 s) and close to the value at the corresponding shear rate at 72 °C in the temperature-scan experiments shown in Figure 1. Figure 4 illustrates the time evolution of the shear stress at 3 s
1 and different temperatures of 66.7, 67.8, and 72.0 °C. At 66.7 and 72.0 °C, the shear stresses after a long time are again nearly equal to those obtained from the temperature scan experiments. At 67.8 °C, however, the shear stress oscillates irregularly and does not become constant within 2  104 s. This may result from the fact that this temperature is between T* and T** and so it takes a very long time until the system reaches a steady state. We have also performed the temperature scan experiments at 3 s
1 for different heating rates and confirmed that T* does not depend on the heating rate very much but T** slightly decreases with a decreasing heating rate (Figures 3 and 4 in the Supporting Information). Rheo-SAXS Experiments: Temperature Scan at Constant Shear Rate. Figure 5a
c shows the evolution of 2D SAXS patterns for the (a) radial and (b) tangential configurations and the shear stress with increasing temperature at a constant shear rate of 3 s
1. The pattern for the tangential configuration is not symmetric about the neutral direction (i.e., the intensity on the left-hand side is greater than that on the right-hand side). This is due to the path differences of the scattered X-ray. The radial pattern at 66 °C indicates that the intensity in the neutral direction is much larger than that in the flow direction as expected. However, the tangential pattern indicates that the intensity in the velocity gradient direction is much larger than that in the neutral direction. Therefore, the number of lamellae with the layer normal to the three principal directions follows the order of velocity gradient direction > neutral direction > flow direction. When the temperature exceeds 67 °C, the shear stress increases more than 1 order of magnitude. At the same time, the

Figure 5. Evolution of 2D SAXS patterns for the (a) radial and (b) tangential configurations, (c) the shear stress, and the intensities of the Bragg peak for the (d) radial and (e) tangential configurations with increasing temperature at a constant shear rate of 3 s
1. The circles, squares, and closed triangles in d and e indicate the intensities for the neutral, flow, and velocity gradient directions, respectively. The numbers below the SAXS pattern indicate q values in nm
1. The temperature is raised 0.1 K every 15 min, corresponding to the average heating rate of 0.007 K/min. The schematic pictures at the bottom show possible transition processes consistent with the SAXS intensities and the theoretical model proposed by Zilman and Granek.42

scattering intensities for both neutral and velocity gradient directions are substantially changed. As the temperature increases further, the SAXS patterns become almost isotropic, consistent with onion formation because the orientation of lamellae is isotropic in the onion state. It should be noted that powder samples of the lamellar phase also give an isotropic diffraction ring. However, the substantial increase in the shear stress and our previous SALS results cannot be explained by the change from oriented to powder lamellae. The isotropic diffraction ring has been regarded as evidence of onion formation in the nanometer scale.5,8,15
17,24,25 These 2D SAXS patterns were reduced to 1D patterns in the directions of μ = 0, 90, 180, and 270° by integrating the scattering intensity over a segment of width Δμ = (10° where μ is the 7403

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Figure 6. Evolution of 1D SAXS patterns with increasing temperature (as indicated) for the (a) neutral and (b) flow directions in the radial configuration and (c) the velocity gradient direction in the tangential configuration at 3 s
1. The ordinate is shifted in order to separate each pattern. The temperature is raised 0.1 K every 15 min, corresponding to the average heating rate of 0.007 K/min.

azimuthal angle (flow direction set to 0°). Figure 6 shows typical results for the neutral (average of the intensities for μ = 90 and 270°) and the flow (average of the intensities for μ = 0 and 180°) directions in the radial configuration and those for the velocity gradient directions (μ = 180°) in the tangential configuration. It can be seen from this Figure that only first- and second-order diffractions are observed, indicating that the system is still in the lamellar phase under shear and that a transition to other phases does not occur. It should be noted that the peak position is slightly shifted to the lower angle above 67 °C, indicating an increase in the lamellar spacing. Most studies in the past revealed that the lamellar spacing does not change in the lamellar-toonion transition, although a decrease in lamellar spacing has been reported in the transition from disordered onions to ordered onions.8 More systematic studies concerning the change in the lamellar spacing are in progress and will be reported elsewhere. In Figure 5, the evolution of the peak intensities for neutral, flow, and velocity gradient directions is also included. At 66 °C, as described before, the most lamellae are oriented with the layer normal to the velocity gradient direction. At 67.2 °C, just before the increase in the shear stress, the intensity in the velocity gradient direction increases suddenly. As the temperature increases by 0.2 K, the intensity in the gradient direction rapidly decreases and instead the intensity in the neutral direction increases. As the temperature increases further, the intensities for the neutral and velocity gradient directions decrease whereas the intensity in the flow direction increases, corresponding to the formation of onions. It should be noted, however, that the intensity in the neutral direction is still slightly larger than that in the flow direction, suggesting that the transition to the onions is not complete at 69 °C. In these experiments, the temperature is raised 0.1 K every 15 min, corresponding to the average heating rate of 0.007 K/min. In spite of such a slow heating rate, the shear stress does not become constant at each temperature between T* and T**. Therefore, it may be more desirable to plot the shear stress and the peak intensities against time or shear strain. These plots are shown in Figure 5 of the Supporting Information. The results

Figure 7. The same as for Figure 5 but for a faster heating rate; the temperature is raised every 15 min by 0.5 K (corresponding to the average heating rate of 0.03 K/min) and 1 K (corresponding to the average heating rate of 0.07 K/min) below and above 69 °C, respectively.

indicate that as time evolves, first the intensity in the velocity gradient direction takes a maximum and then the intensity in the neutral direction does. Therefore, the sequence for the change in intensity in each direction is the same as in Figure 5. We have also performed rheo-SAXS experiments at the same shear rate with a faster heating rate; the temperature is raised every 15 min by 0.5 K (corresponding to the average heating rate of 0.03 K/min) and 1 K (corresponding to the average heating rate of 0.07 K/min) below and above 69 °C, respectively. The results are shown in Figure 7. When comparing Figure 7 with Figure 5, it is obvious that the variation in the peak intensities with temperature is similar, although the transition occurs over narrower temperature range for the slower heating rate, as expected. Rheo-SAXS Experiments: Shear Rate Scan at Constant Temperature. Figure 8 shows the evolution of the 2D SAXS pattern, the shear stress, the viscosity, and the peak intensities with increasing shear rate at 72 °C. At shear rates lower than 0.1 s
1, the viscosity decreases with increasing shear rate. The slope of the double logarithmic plot of the viscosity is close to
0.5 (straight line in the Figure), which was theoretically predicted by Lu et al.53 It should be noted that another theoretical value proposed by Mayer et al.54,55 (
0.4) may also be consistent with our results, taking into account that the number of data 7404

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Figure 9. (a) Evolution of viscosity (dots) and the peak intensities for the (b) radial and (c) tangential configurations vs strain at 72 °C with a stepwise increase in shear rate (the line in a). The circles, squares, and closed triangles in b and c indicate the intensities in the neutral, flow, and velocity gradient directions, respectively. The vertical lines indicate the strain where the 2D SAXS patterns shown in Figure 8 are observed.

temperature-scan experiments (Figure 5 in the Supporting Information).

4. DISCUSSION Temperature
Shear Rate Diagram. In our previous study,30 Figure 8. Evolution of 2D SAXS patterns for the (a) radial and (b) tangential configurations and (c) the shear stress (open circles) and the viscosity (closed circles) and the peak intensities for the (d) radial and (e) tangential configurations with increasing shear rate at 72 °C. The circles, squares, and closed triangles in d and e indicate the intensities in the neutral, flow, and velocity gradient directions, respectively. (b) The numbers below the SAXS pattern indicate q values in nm
1. The shear rate is raised stepwise every 15 min. (See Figure 9.)

points here is too small. As the shear rate increases from 0.1 to 0.2 s
1, the viscosity begins to increase. At the same time, the intensities for the neutral and velocity gradient directions abruptly increase and the latter takes a sharp maximum. When the shear rate increases from 0.2 to 0.3 s
1, the intensity in the velocity gradient direction decreases and the intensity in the neutral direction takes a maximum. As the shear rate increases further, the intensities for the neutral and velocity gradient directions decrease whereas the intensity in the flow direction increases, corresponding to the formation of onions. In these experiments, the shear rate is raised every 15 min. In Figure 9, the viscosity and the peak intensities are plotted against the logarithm of shear strain. As can be seen from panel a, the viscosity does not become constant at each shear rate, indicating that the system is not in the steady state. However, it is clear that first the intensity in the velocity gradient direction takes a sharp maximum (at around 1.2  104 strain units) and then the peak intensity in the neutral directions takes a broad maximum (at around 2  104 strain units). Therefore, the sequence in the change in the intensity in each direction is almost the same in the

we constructed a temperature
shear-rate diagram based on the rheo-SALS experiments in the shear-rate range of 0.3
10 s
1. In the present study, such a dynamic phase diagram has been constructed over a wider shear-rate range (0.05
30 s
1) on the basis of the temperature dependence of the shear stress under a constant shear rate. These two results are consistent with each other in the same range of shear rate (0.3
10 s
1). The present results over a wider shear-rate range suggest that the transition temperature T* does not depend on the shear rate very much but takes a very shallow minimum at around 0.3
3 s
1. However, T** rapidly decreases with increasing shear rate up to about 3 s
1 and then levels off. Oliviero et al.26 made the temperature
shear-rate diagram in the C10E3
D2O system (40 wt % C10E3) in the range of shear rate of 0.1
100 s
1 on the basis of the measurements of the shear stress in the steady state at several temperatures and temperature-scan experiments of SANS at 10 and 100 s
1. Their results indicate that the transition temperature rapidly increases with increasing shear rate (or the critical shear rate slightly increases with increasing temperature) up to about 10 s
1. In our previous paper,30 we predicted the existence of a system where onions can be formed over a limited range of temperature under a constant shear rate. In other words, only the upper transition is observed in the C10E3 system whereas the C16E7 system exhibits only the lower transition. In such a system, the onion region may be surrounded by the lamellar region in the temperature
shear-rate diagram. The existence of the minimum in Figure 2 may be consistent with this prediction. Transition Processes from Lamellar to Onion State. Zipfel et al.16 and Nettsheim et al.17 performed SANS under shear and 7405

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Figure 10. Evolution of 2D SAXS patterns for the (a) radial and (b) tangential configurations, (c) the shear stress, and the intensities of Bragg peak for the (d) radial and (e) tangential configurations at a constant temperature of 73 °C and a constant shear rate of 1 s
1. The circles, squares, and closed triangles in d and e indicate the intensities for the neutral, flow, and velocity gradient directions, respectively. (b) The numbers below the SAXS pattern indicate q values in nm
1. (e) The open triangles are the same as the closed triangles but are multiplied by 4.

rheo-SALS as a function of time at a constant shear rate and temperature in the C10E3
D2O system (40 wt % C10E3). They have found that the SANS intensity at the lamellar Bragg peak in the neutral direction first increases with time and reaches a maximum at about 3000 strain units for shear rates of 1
100 s
1. They have also observed SANS in the tangential configuration at 1 and 10 s
1. At 1 s
1, the intensity in the velocity gradient direction decreases monotonously. At 10 s
1, however, the intensity in the gradient direction first decreases and takes a minimum at about 3000 strain units where the intensity in the neutral direction takes a maximum. The 2D pattern in the tangential configuration at this stage is almost isotropic. Then the intensity in the gradient direction increases and takes a maximum at about 6000 strain units. After about 104 strain units, the SANS pattern in the tangential configuration again becomes isotropic. From these results, they have proposed the existence of multilamellar cylinders (MLCs) at about 3000 strain units whose symmetric axes are along the flow direction as intermediate structures between lamellae and onions. They have also considered

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the possibility of coherent stripe buckling with the wave vector of the undulation in the neutral direction proposed by Zilman and Granek42 because both models give the same SAXS pattern. The deuterium NMR spectra under shear reported by Medronho et al.28 are also consistent with the formation of MLCs and/or coherent stripe buckling at about 3000 strain units. Although our results have been obtained under varying temperature or shear rate, it is worth comparing them with the results of Nettsheim et al.17 As can be seen in Figures 5 and 7
9, we have also observed an intensity maximum in the neutral direction before the formation of onions. However, there is a significant difference between our results and theirs. In our system, the intensity in the gradient direction takes a maximum before the maximum of the intensity in the neutral direction both in the temperature-scan and shear-rate-scan experiments. In the experiments of Nettsheim et al.,17 however, the maximum of the intensity in the gradient direction is not observed at 1 s
1 or after the maximum of the intensity in the neutral direction at 10 s
1. To make it clear whether this difference is due to the difference in the system or in the transition path, we have performed rheoSAXS experiments as a function of time at a constant temperature and shear rate above T**. Figure 10 shows the strain dependence of the shear stress and the peak intensities at 73 °C and at a shear rate of 1 s
1. In this experiment, after the preshearing of the sample at 48 °C (in the same manner as described in the Experimental Section), the sample was heated to 62 °C without shear. Then we presheared the sample again at 1 s
1 for 10 min at 62 °C where the onion cannot be formed even at higher shear rates. This process was added to give reproducible starting conditions following Nettsheim et al.17 After that, the temperature was raised to 73 °C without shear and the rheo-SAXS experiment was started. As can be seen from Figure 10b,c, the most lamellae are oriented with the layer normal along the velocity gradient direction at zero strain as a result of the preshearing. After applying shear flow at 73 °C, the shear stress increases immediately and levels off at about 1000 strain units. Above about 3000 strain units, the shear stress increases again and become almost constant above about 10000 strain units. The SAXS intensity in the neutral direction increases rapidly after shearing and takes a maximum at about 500 strain units. Above this strain-unit level, the intensity in the neutral direction decreases whereas the intensity in the flow direction increases. The intensities in these two directions are close to each other above about 3000 strain units. However, the intensity in the gradient direction decreases rapidly and becomes close to those in the other two directions. It should be noted that the maximum in the gradient direction is observed neither before nor after the maximum in the neutral direction. These results are similar to the SANS experiments of Nettsheim et al.17 in the C10E3 system at 1 s
1. Therefore, the difference in the evolution of the peak intensities between our results in the temperature-scan and the shear-rate-scan experiments and those of Nettsheim et al. is not due to the difference in the system but is due to the difference in the transition path. We performed the experiments under constant temperature at a shear rate of 1 s
1 instead of 3 s
1. Nevertheless, the maximum in the neutral directions is observed after only 500 s (500 strain units), which is much shorter than in the temperature-scan and the shear-rate-scan experiments (see Figure 5 in the Supporting Information and Figure 9, respectively) (i.e., after about 3000 s (∼10 000 strain units)). Therefore, it may be difficult to observe the intensity maximum in the velocity gradient direction before 7406

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Figure 12. SALS patterns calculated for (left) anisotropic spheres and (right, middle) prolates on the basis of the equations in ref 52. The axial ratios are (middle) 1.2 and (right) 1.5. Figure 11. Time evolution of 2D small-angle light scattering (SALS) patterns after the temperature is raised from 67 to 68 °C at a constant shear rate of 3 s
1 (the flow direction is horizontal). The numbers indicate the time (in seconds) after the temperature elevation. A 2D SALS pattern at 70 °C is shown for comparison. The last two patterns are shown in our previous paper.30

the maximum in the neutral direction in the experiments at constant temperature and shear rate. In the temperature-scan and shear-rate-scan experiments, however, we can control the transition rate, which enabled us to observe the enhancement of the orientation in the velocity gradient direction before that in the neutral direction. As described in the Introduction, Zilman and Granek assume that the coupling between the short-wavelength undulations and the shear flow produces effective lateral pressure. Because of the fixed geometry of the macroscopic lamella, this pressure induces coherent buckling. According to this model, the orientation of lamellae with respect to the velocity gradient direction should be enhanced before coherent buckling occurs. Then the scattering intensity in the velocity gradient direction should increase before the intensity in the neutral direction does. When coherent buckling occurs, the orientation of lamellae with respect to the gradient direction is immediately suppressed. Thus, the maximum of the intensity in the gradient direction should be observed before the maximum of the intensity in the neutral direction if coherent stripe buckling occurs. Our results are consistent with this prediction. In Figure 5, the correspondence between the SAXS intensities and the model of Zilman and Granek is schematically shown. It should be noted, however, that the critical shear rate γ_ C predicted by Zilman and Granek is about 103 times larger than the observed values. According to the theory of Zilman and Granek, the wavelength of the coherent buckling should be larger than the size of the onion, which is on the micrometer scale. Therefore, timeresolved small-angle light scattering (SALS) may give further information on the transition processes. Figure 11 shows the time evolution of a 2D SALS pattern after the temperature is raised from 67 to 68 °C, which was obtained in our previous study.30 For comparison, we added a SALS pattern at 70 °C (2100 s after the temperature elevation from 68 to 70 °C). The last two patterns are shown in our previous paper.30 As can be seen in Figure 11, a specific pattern appears about 600 s after the temperature elevation. It should be remarked that the symmetry of the pattern is slightly different from the usual four-lobed patterns where the scattering peak is located every azimuthal angle of 90°. As time elapses, the peak position is

shifted to higher q values and the symmetry of the pattern becomes the usual one. In Figure 12, we illustrate SALS patterns calculated for anisotropic spheres and prolates based on the equations in ref 52. As the axial ratio increases, the pattern becomes narrow in the direction of the major axis of the prolate. Comparing the observed SALS patterns in Figure 11 with the calculated ones in Figure 12, we can infer that onions are elongated along the flow direction just after the transition and that the elongated onions become spherical with the elapse of time. At the same time, the size of elongated onions is decreased. (Note that the axis in Figure 12 is qR, where R is the radius of spheres or the minor radius of prolates.) Taking into account the rheo-SAXS results in Figure 5, it can be deduced that elongated onions are formed from coherent stripe buckling. Le et al.24 have reported temperature-scan experiments (0.3 K/ min) on the C10E3 system by using SANS at a constant shear rate. They have obtained the fraction of onions in the lamellar/onion coexistence region (between 39.7 and 41.3 °C) at 100 s
1 assuming that the 2D SANS pattern in this region is a superposition of those at 39.7 °C (onions) and 41.3 °C (lamellae). They have shown that the transition is reversible for the temperature and that the fraction is monotonously changed both in the heating and cooling processes, which indicates that there is no singular change in the intensity in each direction at least at 100 s
1. They have also reported 2D SANS patterns in the radial and tangential configurations at 10 s
1 and at several temperatures. These 2D patterns also appear to be changed monotonously, although the temperature dependence of the peak intensity is not shown.

5. CONCLUSIONS In our previous study, we found for the first time the lamellarto-onion transition with increasing temperature at around 67 °C under a constant shear rate (0.3
10 s
1) in a C16E7/H2O system.30 The present results give further information on this system, which can be summarized as follows. (1) We have constructed a temperature
shear-rate diagram for the lamellar-to-onion transition over a wider range of shear rate (0.05
30 s
1) than in our previous study based on the temperature dependence of the shear stress at a constant shear rate. The critical temperature above which the transition begins (T*) does not depend on the shear rate very much, although it takes a very shallow minimum at 0.3
3 s
1. However, the temperature where the 7407

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Langmuir transition is completed (T**) rapidly decreases with increasing shear rate up to 1 s
1 and levels off. (2) Rheo-SAXS experiments have been performed with a stepwise increase in temperature of 0.1 K per 15 min at a constant shear rate of 3 s
1 near the transition temperature. When the temperature exceeds 67 °C, just before the increase in the shear stress, the intensity of the Bragg peak for the velocity gradient direction is suddenly increased. As the temperature increases by 0.2 K, the shear stress begins to increase. At the same time, the peak intensity in the velocity gradient direction rapidly decreases and instead the intensity in the neutral direction increases. As the temperature increases further, the intensities in both the neutral and gradient directions decrease whereas the orientation with respect to the flow direction increases, corresponding to the formation of onions. (3) Rheo-SAXS experiments have also been performed with a stepwise increase in the shear rate at a constant temperature of 72 °C. The sequence of the change in the intensity in each direction is the same in the temperature-scan experiments at a constant shear rate (i.e., the intensity in the gradient direction first takes a maximum, followed by the maximum of the intensity in the neutral direction). These results suggest that the transition processes are independent of the path. (4) Results 2 and 3 are consistent with the model proposed by Zilman and Granek, who assume that the coupling between the short-wavelength undulations and the shear flow produces effective lateral pressure and that this pressure induces coherent buckling due to the fixed geometry of the macroscopic lamella. The enhancement of the orientation with the layer normal along the neutral direction has already been reported by Nettsheim et al. in the C10E3 system and is explained by either coherent stripe buckling or multilamellar cylinders. However, the abrupt enhancement of the orientation in the velocity gradient direction before that in the neutral direction is the first finding and strongly supports the coherent buckling mechanism. The reason that the enhancement of the velocity gradient direction has not been reported so far may be that the transition occurs so fast that it cannot be detected. In the present study, we have performed temperature-scan and shear-rate-scan experiments, which can keep the transition as slow as possible.

’ ASSOCIATED CONTENT

bS

Supporting Information. Time evolution of the shear stress at different shear rates with a stepwise increase in temperature. Evolution of shear stress versus strain at 72 °C and different shear rates, shear stress versus strain at 3 s
1 with a stepwise increase in temperature for different heating rates, shear stress versus strain at 3 s
1 for different heating rates, and shear stress and the intensities of the SAXS peak versus strain in the experiments shown in Figure 5. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel: þ81-426-77-2528. Fax: þ81-426-77-2525. E-mail: [email protected].

ARTICLE

’ ACKNOWLEDGMENT We thank Mr. Kosaku Ohno of ELQUEST, Co., Ltd. for making the rheo-SAXS cell for us.30 This work was supported by KAKENHI (a grant-in-aid for scientific research) on priority area “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The rheo-SAXS experiments have been performed under the approval of the Photon Factory Program Advisory Committee (proposal nos. 2007G566 and 2009G581). Thanks are also given to Mr. Masato Oka and Daijiro Sato for helping us to perform additional experiments and data analyses. ’ REFERENCES (1) For example, Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; Micelles, Membranes, Micro-emulsions, and Monolayers; Springer: New York, 1994. (2) Bernia, M. G.; C.J. Lawrence, C. J.; Machin, D. Adv. Colloid Interface Sci. 2002, 98, 217. (3) Richtreing, W. Curr. Opin. Colloid Interface Sci. 2001, 6, 446. (4) Roux, D. In Nonequilibrium Dynamics, Metastability and Flow; Cates, M. E., Evans, M. R., Osborne, P., Eds.; Institute of Physics Publishing: Bristol, U.K., 2000; Chapter 7. (5) Diat, O.; Roux, D.; Nallet, F. J. Phys. II 1993, 3, 1427. (6) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. (7) Gulik-krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. Langmuir 1996, 12, 4668. (8) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (9) Sierro, P.; Roux, D. Phys. Rev. Lett. 1997, 78, 1496. (10) Panizza, P.; Colin, A.; Coulon, C.; Roux, D. Eur. Phys. J. B 1998, 4, 65. (11) Wunenburger, A. S.; Colin, A.; Colin, T.; Roux, D. Eur. Phys. J. E 2000, 2, 277. (12) Leng, J.; Nallet, F.; Roux, D. Eur. Phys. J. E 2001, 4, 77. (13) Bergenholtz, J.; Wagner, N. J. Langmuir 1996, 12, 3122. (14) Muller, S.; Borschig, C.; Gronski, W.; Schmidt, C.; Roux, D. Langmuir 1999, 15, 7558. (15) Weigel, Lauger, J.; Richtering, W.; Lindner, P. J. Phys. II 1996, 6, 529. (16) Zipfel, J.; Nettesheim, F.; Lindner, P.; Le, T. D.; Olsson, U.; Richtering, W. Europhys. Lett. 2001, 53, 335. (17) Nettesheim, F.; Zipfel, J.; Olsson, U.; Renth, F.; Linder, P.; Richtering, W. Langmuir 2003, 19, 3618. (18) Nettesheim, F.; Olsson, U.; Linder, P.; Richtering, W. J. Phys. Chem. B 2004, 108, 6328. (19) Medronho, B.; Fujii, S.; Richtering, W.; Miguel, M. G.; Olsson, U. Colloid Polym. Sci. 2005, 284, 317. (20) Fujii, S.; Richtering, W. Eur. Phys. J. E 2006, 19, 139. (21) Koshobeck, S.; Fujii, S.; Richtering, W. Prog. Theor. Phys. 2008, 175, 154. (22) Koshobeck, S.; Fujii, S.; Lindner, P.; Richtering, W. Rheol. Acta 2009, 48, 231. (23) Fujii, S.; Koshobeck, S.; Lindner, P.; Richtering, W. Langmuir 2009, 25, 5476. (24) Le, T. D.; Olsson, U.; Mortensen, K.; Zipfel, J.; Richtering, W. Langmuir 2001, 17, 999. (25) Le, T. D.; Olsson, U.; Mortensen, K. Phys. Chem. Chem. Phys. 2001, 3, 1310. (26) Oliviero, C.; Coppola, L.; Gianferri, R.; Nicotera, I.; Olsson, U. Colloids Surf., A 2003, 228, 85. (27) Medronho, B.; Miguel, M. G.; Olsson, U. Langmuir 2007, 23, 5270. (28) Medronho, B.; Shafaei, S.; Szopko, R.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2008, 24, 6480. (29) Medronho, B.; Rodrigues, M.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2010, 26, 11304. 7408

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