Effects of Oscillatory Shear on the Orientation of the Inverse

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Effects of Oscillatory Shear on the Orientation of the Inverse Bicontinuous Cubic Phase in a Nonionic Surfactant/Water System Mutsumi Yamanoi, Youhei Kawabata, and Tadashi Kato* Department of Chemistry, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan S Supporting Information *

ABSTRACT: The bicontinuous inverse cubic phase (V2 phase) formed in amphiphilic systems consists of bilayer networks with a long-range order. We have investigated effects of oscillatory shear on the orientation of the V2 phase with space group Ia3d formed in a nonionic surfactant (C12E2)/water system by using simultaneous measurements of rheology/ small-angle X-ray scattering. It is shown that grain refining occurs by applying the large amplitude oscillatory shear (LAOS) with a strain amplitude (γ0) of ∼20, which gives the ratio of the loss modulus (G″) to the storage modulus (G′) (G″/G′ = tan δ) of ∼100. On the other hand, orientation of the cubic lattice occurs when the small amplitude (γ0 ≈ 0.0004) oscillatory shear (SAOS) in the linear regime is applied to the sample just after the LAOS. Interestingly, the orientation is strongly enhanced by the “medium amplitude” (γ0 ≈ 0.05) oscillatory shear (“MAOS”) after the SAOS. When the MAOS is applied before applying the LAOS, orientation to a particular direction is not observed, indicating that the grain refining process by the LAOS is necessary for the orientation during the MAOS. The results of additional experiments show that the shear sequence “LAOS−MAOS” is effective for the orientation of the cubic lattice. When the LAOS and MAOS are applied to the sample alternatively, grain refining and orientation occur during the LAOS and MAOS, respectively, indicating reversibility of the orientation. It is shown that (i) the degree of the orientation is dependent on γ0 and the frequency (ω) of the MAOS and (ii) relatively higher orientation can be obtained for the combination of γ0 and ω, which gives tan δ = 2−3. The lattice constant does not change throughout all the shearing processes and is equal to that before shearing within the experimental errors, indicating that the shear melting does not occur. These results suggest a possibility to control the orientation of the cubic lattice only by changing the conditions of oscillatory shear without using the epitaxial transition from other anisotropic phases, such as the hexagonal and lamellar phases.

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INTRODUCTION The effects of shear flow are important for amphiphilic systems including surfactants, lipids, and block copolymers, because the time scale in the structural fluctuations is relatively slow, compared to simple liquids, which leads to the possibility of shearinduced structural changes. Shear effects are also important in the sample preparations of these systems, because the samples are exposed to shear stress in the mixing processes. In the recent 20 years, there have been reported a large amount of studies concerning shear effects in the amphiphilic systems.1,2 However, these studies have been performed mainly on the micellar, lamellar, sponge, and hexagonal phases. Some aqueous systems of amphiphiles form a bicontinuous cubic phase, which can be classified as the normal phase (V1) and the inverse phase (V2).3−6 Both phases include the infinite periodic minimal surface (IPMS). In the V1 phase, IPMS consists of water and locates between two hydrophilic shells of different “rodlike” micelles. In the V2 phase, on the other hand, IPMS consists of hydrocarbon and locates between two hydrophobic layers in the same bilayers. The symmetry of most of the V1 phases is classified as Ia3d, whereas three forms © XXXX American Chemical Society

of symmetry are reported for the V2 phase (i.e., Ia3d, Pn3m, and Im3m). For these V1 and V2 phases, only a few studies have been reported for the shear effects. One reason may be that orientation of the sample and/or dramatic changes, such as onion formation in the lamellar phase,1,7−9 cannot be expected, because their symmetries are much higher than other phases, such as the lamellar and hexagonal phases. Olsson and Mortensen10 have measured small-angle neutron scattering (SANS) under steady-shear flow in the V1 phase formed in a ternary system of nonionic surfactant C12E5 (CnEm is an abbreviation for CnH2n+1(OC2H4)mOH), tetradecane, and water. They have found that (i) the cubic crystalline order “melts” and is transformed to the L3 (sponge) phase composed of randomly connected bilayers and (ii) after stopping shear, the cubic phase recrystallizes with a preferred orientation. Imai et al.11 have also measured SANS on the V1 phase in a binary Received: November 30, 2015 Revised: February 18, 2016

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DOI: 10.1021/acs.langmuir.5b04372 Langmuir XXXX, XXX, XXX−XXX

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Langmuir

First, we have measured the storage modulus (G′) and the loss modulus (G″), as a function of the strain amplitude (γ0) at different frequencies and also as a function of the frequency in the linear regime, because no rheology data are available for this system. Then, we have performed rheo-SAXS experiments with a stepwise variation of the stress amplitude (σ0) and the angular frequency (ω), mainly in the nonlinear regime, to survey the conditions that give substantial change in the structures. During this first series of experiments, we have found that grain refining occurs by applying the LAOS with γ0 ≈ 20 to the sample and that the cubic lattice is oriented by applying the smallamplitude (γ0 ≈ 0.0004) oscillatory shear (SAOS) in the linear regime to the sample just after the LAOS. Interestingly, the orientation is strongly enhanced when the “medium amplitude” (γ0 ≈ 0.05) oscillatory shear (here, we will call it “MAOS”) is applied after the SAOS. Because such effects of oscillatory shear have not been reported so far, we have performed two more series of rheo-SAXS experiments. In the second series of experiments, we have varied the stress amplitude of the MAOS at constant frequency. We have also examined effects of the shear sequence. In the third series of experiments, on the other hand, the frequency of the MAOS has been varied at constant amplitude. From these experiments, it has been concluded that the shear sequence “LAOS−MAOS” is effective for orientation of the cubic lattice. The present results suggest a possibility to control orientation of the cubic lattice only by changing the conditions of oscillatory shear without using the epitaxial transition from other anisotropic phases such as the hexagonal and lamellar phases.

system of a nonionic surfactant (C16E7) and water under steady shear and reported transformation to the Lα phase. In recent years, much interest has been devoted to the V2 phase of lipid systems, because of the utility as a matrix in the crystallization of membrane proteins,12 especially after the success of the crystallization of G-protein.13 A few years ago, Seddon et al.14,15 performed small-angle X-ray scattering (SAXS) measurements in a ternary system of monoolein, 1,4-butanediol, and water. They have shown that an oriented V2 (Pn3m) phase can be obtained by applying the largeamplitude oscillatory shear (LAOS) to the L3 (sponge) phase during addition of water to transform the L3 phase to the V2 phase. The gyroid phase of block copolymer systems has the same symmetry (Ia3d) as that of the V1 phase and one of the V2 phases.2 It has been known that the oriented sample of the gyroid phase can be obtained by using the epitaxial phase transition from other phases adjacent to the gyroid phase; first, the LAOS is applied to the perforated lamellar phase16,17 or cylinder phase18 to align the building blocks (bilayers or cylinders). The temperature then is changed without shear to transform them into the gyroid phase. It has also been shown that the aligned gyroid sample can be obtained by applying LAOS during the lamellar-to-gyroid phase transition induced by temperature increment.19 To the authors’ knowledge, however, no one has succeeded in aligning the gyroid phase by shear flow alone (see the review of Sakurai20), except for the very recent paper by Vukovic et al.21 for supramolecular block copolymer-based complexes of polystyrene-block (4-vinylpyridine) (pentadecylphenol) (PS-b-P4VP(PDP). In this system, PDP molecules make hydrogen bonds with the pyridine group of a P4VP repeating unit and form a comblike block P4VP(PDP)x (where x denotes the ratio between PDP molecules and P4VP repeat units). The double gyroid phase is formed at temperatures between 60 °C and 120 °C when the weight fraction of the comblike block in the supramolecular PS-b-P4VP(PDP)x is 0.62.22,23 Above 120 °C, PDP is resolved in both PDP blocks, which results in the order−disorder transition within the comblike block. Vukovic et al. have found that the sample is oriented after only several seconds of LAOS. However, the degree of orientation is not good, compared to those obtained by using the epitaxial phase transition. This may be due to the fact that (i) the measurements have been made at 120 °C, which is very close to the order−disorder temperature, and (ii) the structure of the block copolymer is designed to use it as templates for the preparation of metal nanofoams. Moreover, rheology data have not been shown. Thus, effects of shear flow on the structure and/or alignment (i.e., grain size) of the bicontinuous cubic phase are still unclear. In the present study, we have performed simultaneous measurements of rheology and SAXS (rheo-SAXS) on the V2 phase of a binary system of C12E2 and water. In our previous study, we have investigated effects of shear flow as well as equilibrium structures in the lamellar phase of C16E7/water24−26 and C14E5/water27 systems. The C12E2/water system can be regarded as one of these nonionic surfactant systems, but exhibits the Pn3m and Ia3d phases,28−30 in addition to the Lα and L3 phases, which is similar to the lipid systems. This may be due to the relatively short length of the ethylene oxide chain. We have chosen the Ia3d phase, because it extends to much wider temperature and concentration ranges than the Pn3m phase does.

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EXPERIMENTAL SECTION

Materials and Sample Preparation. C12E2 was purchased from Nikko Chemicals, Inc. in crystalline form (>98%) and used without further purification. Water was purified by using the Milli-Q system (Millipore) and degassed by bubbling of nitrogen to avoid oxidation of the ethylene oxide group of surfactants. Samples containing desired amount of surfactant and water (∼8 g) were sealed in an Erlenmeyer flask. For homogenization, we annealed samples at 20 °C, corresponding to the lamellar phase with occasional shaking for ∼1 week. At this temperature, shear-induced lamellar-to-onion transition does not occur. Identification of the Phase. Phase diagram of the C12E2/water system has been reported by Conroy et al.28 and Lynchi et al.30 According to the latter phase diagram, which is more detailed than the former, the lower and upper temperature limits of the Ia3d phase are 26 °C at 55 wt % and 30 °C at 72 wt %, respectively. Funari and Rapp29 have performed time-resolved SAXS measurements during a temperature scan in the concentration range of 48−70 wt %. According to their results, the Ia3d phase is observed in the temperature range of 27.0−30.5 °C at 60 wt % and 28.3−34.6 °C at 67 wt %. So, first, we have prepared samples containing 60 and 66 wt % C12E2 and measured SAXS at 30 °C by using Rigaku NANOViewer. We observed two diffraction peaks, corresponding to the (211) and (220) reflections, and also a weak peak corresponding to the (332) reflection, which are characteristic of the Ia3d phase (see Figure S1 in the Supporting Information). In the 66 wt % sample, the (420) and (432) reflections are also observed. These results indicate that the Ia3d phase exists at least in the concentration range 60−66 wt % at 30 °C. Because the concentration range of the Ia3d phase is much narrower than of other phases such as the lamellar phase (see refs 28 and 30), all the rheo-SAXS measurements in the present study have been performed at the intermediate concentration between 60 wt % and 66 wt % (i.e., 63 wt % at 30 °C). In Figure S1(a), we have shown the 1D-SAXS pattern at 63 wt % and 30 °C in the rheo-SAXS cell before applying the LAOS. The peak positions are consistent with the results at 60 wt % and 66 wt %, as can be seen B

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Langmuir from Figure S1(b). The lattice constants for these concentrations are summarized in Table S1 in the Supporting Information, together with the half-thickness of the hydrophobic layers. Rheology and Rheo-SAXS. The rheological measurements have been made by using a stress-controlled rheometer (Model AR550, TA Instruments). The apparatus for the rheo-SAXS experiments is the same one reported previously. In these experiments, we used a Couette cell that was composed of polycarbonate consisting of two concentric cylinders with diameters of 27 mm and 29 mm. The outer cylinder is fixed, and the inner cylinder is attached to the AR550 rheometer. To prevent sample evaporation, a vapor seal is incorporated in the cell. The Rheo-SAXS experiments were made on the BL 6A at the photon factory (PF) of the High Energy Accelerator Research Organization (KEK), Tsukuba. The scattered X-rays were detected using the CCD area detector (Hamamatsu, Model C7300, with a 9 in. image intensifier). The exposure time was 30 s. The approximate q-range is from 0.3 nm−1 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 two-dimensional (2-D) SAXS pattern in the flow-neutral (vorticity) plane is obtained in the radial configuration, while that in the velocity gradient-neutral plane is obtained in the tangential configuration. Initial Conditions of the Sample. In all of the experiments, we first sheared the sample with a shear rate of 0.05 s−1 for 30 min at 25 °C, corresponding to the Lα phase. The shear then was stopped and the sample was heated to 30 °C (Ia3d) without shear. The SAXS pattern was changed to one characteristic of the Ia3d phase within 200 s. To confirm that the sample reaches equilibrium, we measured the storage modulus (G′) and the loss modulus (G″), as a function of time, after the temperature becomes 30 °C at an angular frequency of 0.1 rad s−1 and a stress amplitude of 20 Pa, corresponding to the linear regime (the strain amplitude is ∼0.0004; see the next section). We confirmed that G′ and G″ become almost constant after ∼3000 s. So we waited 3600 s before we started the experiments that are described in the next section. Time evolutions of the lattice constant and G′ and G″ during this waiting time are shown in Figure S2 in the Supporting Information, together with 2-D SAXS patterns. The lattice constant averaged in the last 800 s (12.80 ± 0.02 nm) is also included in Table S1, together with the half-thickness of the hydrophobic layers.

Figure 1. Storage modulus (G′, dark symbols) and loss modulus (G″, pale symbols), each plotted as a function of the strain amplitude (γ0) at the angular frequency (ω) of 0.1 (circles, ●), 1 rad s−1 (triangles, ▲), 6.28 rad s−1 (squares, ■), and 15 rad s−1 (diamonds, ◆).

Figure 2. Storage modulus (G′, dark circles), loss modulus (G″, pale circles), and the strain amplitude (γ0, dots) as a function of the angular frequency (ω) obtained for σ0 = 20 Pa, corresponding to the linear regime. The dashed line indicates the frequency used in the rheoSAXS experiments.

processes above the crossing frequency. These features are similar to the viscoelastic spectra for the monoolein/water system reported by Mezzenga et al.32 Evolution of 2-D and 1-D SAXS Patterns in the First Series of Experiments. As described in the Experimental Section, we waited more than 3600 s after the temperature was set to 30 °C. During this waiting time, SAXS was measured every 60 s. The 2-D SAXS patterns are always spotty patterns whose positions are irregular along the azimuthal angle (see Figure S2). This indicates that the grain size is much larger than the so-called powder sample but much smaller than the single crystal. Then, as a first series of experiments, we have observed 2-D SAXS patterns with a stepwise variation of the stress amplitude σ0 and the angular frequency ω mainly in the nonlinear regime of the strain−stress relationship (see Figure S3). Figure 3a shows time evolution of the strain amplitude γ0 with the variations of σ0 and ω, where each step is numbered from 1 to 9. First, we increased σ0 stepwise every 1800 s from 200 Pa to 1400 Pa for ω = 1 rad s−1 (from step 1 to step 5), which increased γ0 from 0.004 to 2. Because the upper limit of our rheometer is 2000 Pa, the upper limit of γ0 at ω = 1 rad s−1 is ∼4, whereas the upper limit at ω = 0.1 rad s−1 is ∼100. To increase γ0 further, therefore, we changed ω from 1 rad s−1 to 0.1 rad s−1, keeping σ0 to 1400 Pa (step 6). The decrease of ω from 1 rad s−1 to 0.1 rad s−1 enabled us to increase γ0 from 2 to 20. Then, we changed σ0 from 1400 Pa to 20 Pa, keeping ω at 0.1 rad s−1 (step 7), which led to the rapid relaxation of γ0 from 20 to ∼0.002, followed by the slow relaxation to the steady state (γ0 ≈ 0.0004). After we continued to step 7 for 5400 s, we changed σ0 from 20 Pa to 800 Pa and ω from

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RESULTS AND DISCUSSION Basic Rheological Properties. Because no rheology data are available for the C12E2/water system, first we have measured the relationship between the strain amplitude (γ0) and the stress amplitude (σ0) at different frequencies. In Figure S3 in the Supporting Information, the results at the angular frequency (ω) of 0.1, 1, 6.28, and 15 rad s−1 are shown, together with typical examples of stress and strain waveforms. Nonlinear behaviors are observed when the σ0 exceeds about 100, 200, 400, and 800 Pa at ω = 0.1, 1, 6.28, and 15 rad s−1, respectively. Figure 1 shows plots of the storage modulus (G′) and loss modulus (G″) at these frequencies against γ0. Note that the strain wave in the nonlinear regime is not sinusoidal (see the photographs given in Figure S3), so the G′ and G″ values in this regime correspond to the leading order terms.31 Figure 1 demonstrates that G′ and G″ are almost constant for γ0 < 10−3, which can also be expected from the behaviors shown in Figure 3 in the Supporting Information. Figure 2 shows the frequency dependences of G′ and G″ for σ0 = 20 Pa, corresponding to the linear regime. The crossing of G′ and G″ occurs at ω ≈ 0.025 rad s−1, which gives the longest relaxation time of ∼40 s. As can be seen from Figure 2, the frequency dependence of G′ and G″ cannot be fitted to the Maxwell model, because of the existence of the many relaxation C

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Figure 5. Evolution of 1-D SAXS patterns obtained by circularly averaging the 2-D patterns in Figure 4 for the (a) radial and (b) tangential configurations with the variations in the stress amplitude and the frequency of the oscillatory shear shown in Figure 3. The symbols “A”, “D”, “G”, “J”, and “L” on the right-hand side are the same as in Figure 3; these indicate the times when the SAXS patterns are obtained. The ordinate is shifted in order to separate each pattern. In panel (a), the intensities (magnified by a factor of 10) are also shown in order to demonstrate the diffractions at higher angles.

Figure 3. Time evolutions of (a) the strain amplitude γ0 (pale line, right axis) of the oscillatory shear with the variations in the stress amplitude σ0 (dark line, left axis) and the angular frequency ω (indicated by the numbers (ω (rad s−1)) in panel (b)), (b) the storage modulus G′ (dark line) and the loss modulus G″ (pale line), (c) the lattice constant ac, (d) the degree of orientation α calculated from eq 1, (e) standard deviation σα calculated from eq 2, and (f) the full width at half-maximum (fwhm) of the (211) reflection in the first series of experiments. The dotted line in panel (f) indicates the instrumental resolution (see the text). The arrows in the top of the figure indicate the times when the 2-D SAXS patterns in Figure 4 are obtained.

The symbols “A”−“L” in these figures are the same as those in Figure 3. For all the 1-D SAXS patterns, we observed diffraction peaks from (211), (220), and (332) reflections in the radial configuration, which are characteristic of the Ia3d symmetry.2,17,33 In the tangential configuration, on the other hand, only (211) and (220) reflections can be observed due to the weak intensity, compared to that in the radial configuration. It can be seen from the figure that the peak position is almost independent of the time, which indicates that the structure of the cubic lattice is hardly influenced by oscillatory shear in the range of σ0 and ω studied. In fact, the lattice constant obtained from the 211 and 220 reflections (12.82 ± 0.03 nm) does not change very much during shear steps 1−9 and is equal to that

0.1 rad s−1 to 6.28 rad s−1 (1 Hz) (step 8). Finally, σ0 was increased from 800 Pa to 1000 Pa, keeping ω at 6.28 rad s−1 (step 9). The γ0 values in the last two steps are ∼0.05, which is almost intermediate between the maximum value (20) and the minimum value (0.004) of γ0 in the logarithmic scale. Figures 4 and 5 show the evolutions of the 2-D SAXS patterns and the 1-D SAXS patterns obtained by circularly averaging the 2-D patterns, respectively, during steps 1−9.

Figure 4. Evolutions of 2-D SAXS patterns for the (a) radial and (b) tangential configurations with the variations in the stress amplitude and the frequency of the oscillatory shear shown in Figure 3. The symbols “A”−“L” above the patterns are the same as in Figure 3; these indicate the times when the 2-D SAXS patterns are obtained. D

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Langmuir before shearing within experimental errors (see Table S1 and SAXS pattern A in Figure 4). On the other hand, the 2-D SAXS pattern is strongly dependent on the conditions of the oscillatory shear. During the increase of σ0 from 200 Pa to 1400 Pa at ω = 1 rad s−1 (corresponding to the increase of γ0 from 0.003 to 2), the 2-D SAXS pattern was changed from the spotty pattern to the powder pattern, as can be seen from patterns B−F in Figure 4. When γ0 is increased from 2 to 20 by decreasing ω from 1 rad s−1 to 0.1 rad s−1 at σ0 = 1400 Pa, the diffraction pattern becomes completely powderlike (see pattern G in Figure 4). These results indicate that the cubic grain is refined during steps 1−6. Immediately after the decrease of σ0 from 1400 Pa to 20 Pa at ω = 0.1 rad s−1 in step 7 (corresponding to the decrease of γ0 from 20 to 0.0004), the spotty pattern reappeared. With the elapse of time, the peak intensity at a particular azimuthal angle increases, suggesting orientation of the sample (see patterns H−J in Figure 4). When σ0 is again increased from 20 Pa to 1000 Pa via 800 Pa, together with the increase of ω from 0.1 rad s−1 to 6.28 rad s−1 in steps 8 and 9 (corresponding to an increase of γ0 from 0.0004 to 0.05), the 2-D SAXS pattern in the tangential configuration becomes more symmetric, indicating enhancement of the orientation. Orientation of Cubic Lattice. The relationship between 2-D SAXS pattern and the orientation of the Ia3d lattice has already been reported for the V1 phase of a C12E6/water system33−35 and the gyroid phase of the block copolymer systems. Schulz18 et al. have reported 2-D SAXS patterns in the radial and tangential configurations for the gyroid phase of polystyrene−poly(1,2-vinylpyridine) diblock copolymer mixture aligned by using the epitaxial phase transition from the hexagonal phase. They have observed the (211) reflection at the azimuthal angles (ϕ) of nπ/3 (where n = 0, 1, 2, ...) and the (220) reflection at ϕ = (2n + 1)π/6, where ϕ is defined so that ϕ = 0 indicates the velocity gradient direction. These results indicate that the [111] axis is directed to the flow direction and the normal vector of the (211) plane is directed to the neutral direction (see Figure S4(a) in the Supporting Information). Vigild et al.17 have shown diffraction patterns in the radial configuration expected for single crystals of the Ia3d phase encountered as the gyroid structure is rotated around the [111] direction. It has been known that, in the radial configuration, the oriented gyroid phase gives 8 diffraction spots in the 211 reflection and 2 diffraction spots in the 220 reflection. Vigild et al. have shown that such a “10 spot pattern” is observed when the orientation of the gyroid lattice is random around the [111] direction. Figures 6 and 7 show azimuthal plots of the (211) and (220) reflections, respectively, in the radial (Figures 6a and 7a) and tangential (Figures 6b and 7b) configurations in the first series of experiments. It can be seen from the azimuthal plots L in Figures 6b and 7b obtained at the end of step 9 that the 211 and 220 reflections are observed in the tangential configuration at ϕ (deg) = 60n and ϕ (deg) = 30 + 60n (where n = 0, 1, 2, 3, 4, 5) for the 211 and 220 reflections (indicated by the dashed lines), respectively. These results indicate that (i) the cubic lattice is oriented so that the [111] axis is directed to the flow direction and (ii) the normal vector of one of the (211) plane is directed to the velocity gradient direction, as shown in Figure S4(b) in the Supporting Information. According to Vigild et al., such an orientation does not give any (211) reflection and only a pair of (220) reflections is observed

Figure 6. Azimuthal plots of the (211) reflection in the (a) radial and (b) tangential configurations. The symbols “A”, “D”, “G”, “J”, and “L” in the right-hand side are the same as in Figure 3 and so indicate the time when the 2-D SAXS patterns are obtained. The dotted lines in the panel (b) indicate the azimuthal angles expected for the orientation shown in Figure S4(b), i.e., ϕ (deg) = 60 n (where n is an integer). The pair of lines with two arrows (top right of panel (b)) indicate the angle range (±5°) used for the calculation of the degree of orientation α (see eq 1).

Figure 7. Azimuthal plots of the (220) reflection in the (a) radial and (b) tangential configurations. The symbols “A”, “D”, “G”, “J”, and “L” in the right-hand side are the same as in Figure 3; these indicate the time when the SAXS patterns are obtained. The dotted lines indicate the azimuthal angles expected for the orientation shown in Figure S4(b), i.e., ϕ (deg) = 30 + 60n (where n is an integer).

at ϕ = 90° and 270° in the radial configuration. As can be seen from the L plots in Figures 6a and 7a, we have observed the (211) reflections at several angles and the (220) reflections at ϕ = 90° and 270°. These results suggest that the orientations of the most grains in steps 8 and 9 are those shown in Figure S4(b), although some grains with other orientations still exist. The azimuthal J plots in Figures 6b and 7b (tangential configuration) shows that the diffraction peaks are observed at almost the same angles as the L plots, i.e., ϕ (deg) = 60n and ϕ (deg) = 30 + 60n for the 211 and 220 reflections, respectively. However, the peak intensities for n = 0, 1, 5 for the 211 reflections and those for n = 2, 3, 5 for the 220 reflections are rather weak. These results indicate that the degree of orientation is less than that observed in step 9. Evolution of Degree of Orientation in the First Series of Experiments. To discuss the time development of the degree of the orientation, we have calculated the fractions of the diffraction intensity observed for the azimuthal angles of nπ/3 ± δϕ (for n = 0−5) to that for all the azimuthal angles E

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Langmuir (0−2π) (αn) and their sum (α) over n = 0−5 for the (211) reflection, expressed as

observed linewidth. Therefore, it is difficult to discuss the linewidth quantitatively. Relationships between SAXS and Rheological Behaviors in the First Series of Experiments. Figure 3b shows the time evolution of the storage modulus (G′) and the loss modulus (G″) simultaneously obtained with SAXS. In step 1, G′ is larger than G″ (i.e., elasticity dominated). Note that G′ and G″ take almost the same values as those in the frequencysweep experiments (see Figure 2), because γ0 is still in the linear regime (γ0 ≈ 0.004) (see Figure 1). In step 2, corresponding to the nonlinear regime (γ0 ≈ 0.02), G″ becomes larger than G′. As γ0 increases (steps 3−6), both G′ and G″ decreases, but G′ decreases more rapidly than G″. In step 6 (γ0 ≈ 20), G″ becomes much larger than G′ (G″/G′ = tan δ ≈ 100) (i.e., viscosity dominated). In step 7, both G′ and G″ increase with time, but G′ increases more rapidly than G″. After ∼500 s, G′ becomes larger than G″ (tan δ ≈ 0.3) (i.e., elasticity dominated). Note that α begins to increase just after the crossing of G′ and G″. In steps 8 and 9, G′ decreases and G″ increases, which results in a viscosity-dominated regime (tan δ ≈ 3). These results suggest that the grain refining occurs in the viscosity-dominated regime, whereas the orientation of the cubic lattice accompanies the rapid increases of G′ and G″, as well as changing from the viscosity-dominated regime to the elasticity-dominated regime. Note that we have applied the oscillatory shear in the linear regime (σ0 = 20 Pa, ω = 0.1 rad s−1) for 60 min before step 1. During this waiting time, however, the orientation occurs only slightly, as can be seen from SAXS pattern A in Figure 4 (and Figure S2). We have also obtained the fraction α setting δϕ in eq 1 to 10° (instead of 5°) and confirmed that α changes with time irregularly around the limiting value for the “ideal” powder sample (α = 1/3 for δϕ = 10°) (see Figure S2(d)). This indicates that the grainrefining process in steps 1−6 is necessary for the orientation of the cubic lattice. When the orientation occurs, the adjacent grains should rotate to adjust the lattice directions. Such a rotation can occur more easily for smaller grains. This may be a reason why the orientation occurs in step 7 after the LAOS. It is not clear why the grain growth is enhanced in steps 8 and 9, where G″ is slightly larger than G′. Because the γ0 values in these steps are almost the same as those in steps 2 and 3 (see Figure 4), not only γ0 but also the sequence of applied shear may be important. Effects of Shear-Sequence and Stress Amplitude of the “MAOS”: Results of the Second Series of Experiments. The foregoing results show that (1) grain refining occurs by applying the LAOS with a strain amplitude (γ0) of ∼20 to the sample, (2) orientation of the cubic lattice occurs when small amplitude (γ0 ≈ 0.0004) oscillatory shear (SAOS) in the linear regime is applied just after the LAOS, and (3) the orientation of the cubic lattice is strongly enhanced by the “medium amplitude” (γ0 ≈ 0.05) oscillatory shear (hereafter, we refer to this condition as “MAOS”) after the SAOS. However, the following questions may arise:

(nπ /3) + δϕ

αn ≡

∫(nπ /3) − δϕ I(ϕ) dϕ 2π

∫0 I(ϕ) dϕ

(1a)

5

α≡

∑ αn

(1b)

n=0

where I(ϕ) is the diffraction intensity at the azimuthal angle ϕ. We also have calculated the standard deviation of αn (σα), defined as σα ≡

⟨[αn − ⟨αn⟩]2 ⟩

⟨αn⟩ ≡

1 6

(2a)

5

∑ αn n=0

(2b)

For the “ideal” powder sample, I(ϕ) is independent of ϕ; therefore, α should be given as α=

12δϕ 6δϕ = 2π π

Since the fwhm for each peak in the azimuthal plot is a few degrees, we set δϕ = π/36 (5°). So α = 1/6 ≈ 0.17 for an “ideal” powder sample. On the other hand, when the orientations of all the grains are those shown in Figure S4(b), α becomes unity. In both limits, σα should be 0. Figures 3c−e show time evolutions of the lattice constant (ac) obtained from the (211) and (220) reflections and α and σα obtained from the (211) reflection in the tangential configuration. Figure 3 shows that, in steps 1 and 2, both α and σα strongly oscillate, but the amplitude of oscillation decreases with increasing γ0. In step 6, where γ0 ≈ 20, α is converged to 1/6, corresponding to the “ideal” powder sample. The standard deviation σα also oscillates in steps 1 and 2, but becomes almost 0 during steps 3−6. In step 7, ∼100 s after the decrease of σ0 from 1400 Pa to 20 Pa at ω = 0.1 rad s−1, α increases rapidly up to ∼0.6 and levels off. After the small oscillation, α once again decreases and increases. The evolution of σα is similar to that of α. In step 8, α keeps its value (∼0.5) whereas σα suddenly decreases and takes much smaller values than those in step 7. In step 9, α gradually increases while σα maintains low values. These results quantitatively support the grain refining in steps 1−6, the orientation of the cubic lattice in step 7, and the enhancement of the orientation in steps 8 and 9. Note that the lattice constant is almost constant during steps 1−9. Figure 3f shows the time evolution of the fwhm (Δq1/2) of the diffraction peak in the tangential configuration obtained by least-squares fitting of the circularly averaged 1D-SAXS patterns using the double Lorentzian function. The fitting results are shown in Figure S5 in the Supporting Information. As can be seen from Figure 3f, Δq1/2 increases/decreases as α and σα decrease/increase, which suggest that the orientation of the cubic lattice accompanies the grain growth as expected. Unfortunately, however, the instrumental resolution (Δqresol) calculated from the beam diameter (∼0.8 mm), the sample thickness (∼7 mm in the tangential configuration), and the detector resolution (0.35 mm) is ∼0.026 nm−1 (indicated by the dotted line in Figure 3f), which is the same order with the

(i) Does the orientation of the cubic lattice occur if only the MAOS is applied to the sample without applying the LAOS? (ii) Does the grain refining occur because of the stepwise increase in the strain amplitude or is it only due to the application of the LAOS with the largest γ0 value (∼20)? F

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Langmuir (iii) Does the orientation of the cubic lattice occur if the MAOS is applied just after the LAOS, instead of the shear sequence of the LAOS−SAOS−MAOS? (iv) How does the stress amplitude of the MAOS affect the orientation? (v) How does the frequency of the MAOS affect the orientation? To answer these questions, we have performed two more series of experiments. In the second series of the experiments, first, we have applied the MAOS with ω = 6.28 rad s−1 and σ0 = 820 Pa (γ0 ≈ 0.04) after waiting 6000 s at 30 °C (the initial conditions of the sample, such as preshearing, are the same as those described in the Experimental Section) to answer question (i). The time evolution of rheological properties (σ0, γ0, G′, and G″) and 2-D SAXS patterns are shown in Figure S6 in the Supporting Information. Although the grain growth occurs partly (similar to the results before the stepwise increase of σ0 in the first series of experiments shown in Figure S2), the degree of orientation is much lower than in step 8 or step 9 in the first series of experiments. These results indicate that the grain refining process is necessary for the orientation of the cubic lattice. Then, we have applied the LAOS and MAOS to the sample alternatively to answer questions (ii)−(iv). The conditions of each shear step are summarized in Table 1. The angular

Figure 8. Time evolutions of (a) the strain amplitude γ0 (pale line, right axis) of the oscillatory shear with the variations in the stress amplitude σ0 (dark line, left axis) and the angular frequency ω (indicated by the numbers (ω (rad s−1))) together with the 2-D SAXS patterns in the tangential configuration (the arrow indicate the times when each pattern is obtained), (b) the storage modulus G′ (dark line) and the loss modulus G″ (pale line), (c) the lattice constant ac, (d) the degree of orientation α calculated from eq 1, and (e) the standard deviation σα calculated from eq 2 obtained in the second series of experiments.

Table 1. Conditions of Each Shear Step in the Second Series of Experiments Value parameter

step 1

step 2

step 3

step 4

step 5

step 6

ω (rad s−1) σ0 (Pa) γ0a G″/G′ = tan δa duration (s)

0.1 1400 ∼20 ∼100 3600

6.28 820 ∼0.03 ∼2.5 3600

0.1 1400 ∼20 ∼100 2400

6.28 1040 ∼0.06 ∼4 3600

0.1 1400 ∼20 ∼100 2400

6.28 620 ∼0.015 ∼1 3600

a

Values shown are the values at the end of each step.

frequency (ω) and the stress amplitude (σ0) of the LAOS have been fixed to 0.1 rad s−1 and 1400 Pa, respectively (γ0 ≈ 20). The angular frequency of the MAOS has been maintained at 6.28 rad s−1, whereas the stress amplitude has been set to 820, 1040, and 620 Pa in turn, which leads to strain amplitudes of ∼0.03, 0.06, and 0.015, respectively. The time evolution of σ0, γ0, G′, and G″ is shown in Figures 8a and 8b, together with 2-D SAXS patterns. The 2-D SAXS patterns in the radial configuration are shown in Figure S7 in the Supporting Information. Figures 8c−f show the time evolutions of the lattice constant, the degree of orientation α calculated from eq 1, and standard deviation σα calculated from eq 2, respectively. The lattice constant is again almost independent of the time. Figures 9a, 9b, and 9c shows azimuthal plots of the (211) and (220) reflections at the end of steps 2, 4, and 6, respectively. The time evolution of the azimuthal plot in each step is shown in Figure S8 in the Supporting Information. Figure 8 clearly shows that the diffraction pattern becomes completely powderlike when the LAOS is applied (steps 1, 3, and 5), whereas oriented patterns are obtained by applying the “MAOS” (steps 2, 4, and 6) after the LAOS. As can be seen from Figures 8a−c and 9a−c, the largest degree of orientation is obtained in step 2 (i.e., σ0 = 820 Pa). The orientation of the cubic lattice in this step is the same as that in Figure S4(b).

Figure 9. Azimuthal plots of the (211) (lower, red lines) and (220) (upper, blue lines) reflections in the tangential configuration at the end of (a) step 2, (b) step 4, and (c) step 6 in Figure 8 (the second series of experiments). Also shown are azimuthal plots of the (211) (lower, red lines) and (220) (upper, blue lines) reflections in the tangential configuration at the end of (d) step 2, (e) step 4, and (f) step 6 in Figure 10 (the third series of experiments), respectively. The red and blue dotted lines indicate the azimuthal angles expected for the orientation shown in Figure S4(b) in the Supporting Information, i.e., ϕ (deg) = 60n and 30 + 60n (where n is an integer).

In step 4, the sample is still oriented whereas the degree of orientation is not so large as in step 2. In step 6, the degree of orientation takes a maximum of ∼30 min after the start of the MAOS and then decreases with time. Effects of Frequency of the “MAOS”: Results of the Third Series of Experiments. To answer question (v), we have performed a third series of experiments. First, we have applied the LAOS and, in turn, the MAOS, under the same conditions as those described in steps 1 and 2 in the second series of experiments (see Figure 8). The results are shown in Figure S9 in the Supporting Information. G

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both step 2 (ω = 6.28 rad s−1) and step 4 (ω = 15 rad s−1) give relatively higher degrees of orientation. The orientation of the cubic lattice in these steps is the same as that in Figure S4(b). In step 6 (ω = 1 rad s−1), on the other hand, the degree of orientation takes a maximum of ∼30 min after the start of the MAOS and then decreases with time. Relationships between Orientation and Rheological Behaviors in the Second and Third Series of Experiments. Figures 8b and 10b show that, during the time applying the LAOS (in steps 1, 3, and 5) in the second and third series of experiments, G″ is much larger than G′ (G″/G′ = tan δ ≈ 100) (i.e., viscosity dominated). When the “MAOS” is applied to the sample after the LAOS, both G′ and G″ rapidly increase with time. Within only 10 s, tan δ becomes 1−4, depending on the stress amplitude. Among the five different conditions of the MAOS (note that the conditions of step 2 of the second and third series of experiments are the same), step 2 in the second series of experiments and steps 2 and 4 in the third series of experiments give relatively higher orientation, as can be seen from Figures 8−10. It is interesting to note that the tan δ values of these steps are similar (i.e., 2−3). In the first series of experiments, orientation of the cubic lattice has been observed under the oscillatory shear in the linear regime (step 7 in Figure 3), where tan δ ≈ 0.3. The final value of α (∼0.5) is almost equal to that under the “MAOS” (step 9 of the first series of experiments and step 2 of the second series of experiments). Under the SAOS, however, ∼15 000 s are needed to reach the maximum α value, whereas only ∼2000 s are needed in the case of the “MAOS”. It is possible that such a difference is due to the difference in the frequency of the “MAOS”. In the third series of experiments, in fact, the value of α for ω = 15 rad s−1 increases more rapidly than for ω = 6.28 rad s−1. However, it should be noted that the maximum values of α for step 2 in the second series of experiments (Figure 8d) and step 2 in the third series of experiments (Figure 10d) are slightly different (∼30%), despite the fact that the conditions of the MAOS are the same. Therefore, more systematic experiments are necessary to confirm the relationship between α and tan δ. Comparison with Previous Studies. As described in the Introduction, Olsson and Mortensen10 measured SANS under steady shear flow with a shear rate of 300 s−1 in the V1 phase of the C12E5/tetradecane/water system and found that the V1 phase is transformed into the L3 phase. They also found that after shear is stopped, the V1 phase recrystallizes. They observed the “10 spot pattern” in the radial configuration, which indicates that the [111] axis is directed to the flow direction and that the orientation of the lattice around the [111] axis is random (see the previous section), in contrast to the present results where the configurations around the [111] axis is almost fixed (see Figures 6, 7, and 9). Ramos et al.36−38 have measured SAXS from a hexagonal phase in a quaternary mixture of sodium dodecyl sulfate (SDS), pentanol, cyclohexane, and brine under steady shear with a high shear rate (typically 1200 s−1). They have shown that the 2-D polycrystalline texture is converted to a liquid of rods aligned along the flow. They have also found that, after the abrupt cessation of shear, the sample continuously evolves from liquid rods to a monocrystal rod. In these previous studies, the hexagonal or cubic structure melts under the steady shear. In our case, on the other hand, the 1-D SAXS patterns in Figure 5 clearly shows sharp diffraction peaks, indicating that the lattice structure is still

Then, similar to the second experiments, we have applied the LAOS and MAOS alternatively to the sample. The conditions of each shear step are summarized in Table 2. In the third series Table 2. Conditions of Each Shear Step in the Third Series of Experiments Value parameter

step 1

step 2

step 3

step 4

step 5

step 6

ω (rad s−1) σ0 (Pa) γ0a G″/G′ = tan δa duration (s)

0.1 1400 ∼20 ∼100 2400

6.28 820 ∼0.03 ∼2.5 3600

0.1 1400 ∼20 ∼100 2400

15 1040 ∼0.04 ∼2.3 3600

0.1 1400 ∼20 ∼100 2400

1 560 ∼0.03 ∼4 3600

a

Values shown are the values at the end of each step.

of experiments, the frequency of the MAOS, in turn, has been set to 6.28, 15, and 1 rad s−1. To keep the strain amplitude at ∼0.03, which gives the highest degree of orientation in the second series of experiments, the stress amplitude, in turn, has been set to 820, 1040, and 620 Pa, based on the strain−stress plot in Figure S3. The time evolutions of σ0, γ0, G′, and G″ are shown in Figures 10a and 10b, together with 2-D SAXS

Figure 10. Time evolutions of (a) the strain amplitude γ0 (pale line, right axis) of the oscillatory shear with the variations in the stress amplitude σ0 (dark line, left axis) and the angular frequency ω (indicated by the numbers (ω (rad s−1)) together with the 2-D SAXS patterns in the tangential configuration (the arrow indicate the times when each pattern is obtained), (b) the storage modulus G′ (dark line) and the loss modulus G″ (pale line), (c) the lattice constant ac, (d) the degree of orientation α calculated from eq 1, and (e) the standard deviation σα calculated from eq 2 obtained in the third series of experiments.

patterns. The 2-D SAXS patterns in the radial configuration are shown in Figure S10 in the Supporting Information. Figure 8c−f shows the time evolutions of the lattice constant, the degree of orientation α calculated from eq 1, and the standard deviation σα calculated from eq 2, respectively. Azimuthal plots of the (211) and (220) reflections at the end of steps 2, 4, and 6 are shown in Figures 9d, 9e, and 9f, respectively. Time evolution of the azimuthal plot in each step is shown in Figure S11 in the Supporting Information. These figures strongly confirm the results in the second series of experiments, i.e., grain refining and orientation of the cubic lattice occur by applying the LAOS and MAOS, respectively. As can be seen from Figures 9d−f and 10, H

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Langmuir maintained, even for the maximum strain amplitude of ∼20 (in step 6). Moreover, the lattice constant does not change during all the shear steps in the present study (see Figures 3c, 8c, and 10c). Therefore, the shear melting does not occur in our case. This may be due to the fact that the maximum shear rate (ωγ0) is only 2 s−1 for ω = 0.1 rad s−1 and γ0 = 20, which is much lower than the steady shear rates in the previous studies (i.e., 1200 s−1 and 300 s−1 in the studies of Ramos et al.36,37 and Olsson and Mortensen,10 respectively). However, note that the product of the maximum shear rate and the longest relaxation time (∼40 s, see the previous section) is ∼80, which is already much greater than unity. Unfortunately, the characteristic relaxation times are not available for the systems of Ramos et al. and of Olsson and Mortensen, although Ramos et al.38 have shown that stress- and strain-controlled experiments give different flow curves in the shear-rate range of 30−1000 s−1. For the micellar cubic phase of block copolymers, many studies have been reported concerning shear-induced orientation.2,39−41 Diat et al.39 have measured SAXS under shear both in the radial and tangential configurations on the micellar cubic phase of (EO)127(PO)48(EO)127 in water (35%), where EO and PO denote a poly(ethylene oxide) and poly(propylene oxide), respectively. They have found that application of steady shear with the shear rate of 100 s−1 to the “powder” sample gives a 2-D SAXS pattern where the stacking order along the velocity gradient direction is completely lost and that twinned facecentered cubic (fcc) single crystals can be obtained by applying oscillating shear with γ0 = 0.4 and ω = 10 rad s−1 after the steady shear. López-Barrón et al.41 have measured timeresolved SANS in the radial configuration during one cycle of the LAOS (γ0 = 10−150) on the (EO)106(PO)68(EO)106 in the protic ionic liquid ethylammonium nitrate. For γ0 = 100 and 150, they have found that the degree of order becomes a maximum when the shear stress reaches a plateau value, whereas shear melting is maximized slightly after the maximum shear rate is reached. These results indicate that both ordering and melting occurs during a single LAOS cycle. For γ0 = 10−50, on the other hand, the degree of order is kept constant during a cycle which is almost the same as the maximum value for γ0 = 100. In our study, the LAOS with γ0 ≈ 20 gives a powder pattern and therefore situations from their system may be different. Unfortunately, our rheometer cannot record the stress and strain waves, which makes it impossible to obtain the Lissajous plot, although the wave is displayed after each cycle (the stress and strain waves are shown in photographs taken by a camera, shown in Figure S3). In the case of micellar cubic phase, spherical micelles are separated by solvent and, therefore, it may be relatively easy to make an order. In the bicontinuous cubic phase, on the other hand, the bilayers are continuously connected. When orientation of the lattice occurs, as described previously, the adjacent grains should rotate to adjust the lattice directions.

after the LAOS. The orientation is strongly enhanced when the “MAOS” (γ0 ≈ 0.05) is applied after the SAOS. (3) The azimuthal plots of the (211) and (220) reflections during the MAOS indicate that the cubic lattice is oriented so that the [111] axis is directed to the flow direction and that the normal vector of one of the (211) plane is directed to the velocity gradient direction. (4) When the “MAOS” is applied before applying the LAOS to the sample, the oriented SAXS pattern is not observed, indicating that the grain refining process by the LAOS is necessary for the orientation of the cubic lattice. (5) The shear sequence “LAOS−MAOS” is effective for the orientation of the cubic lattice. When the LAOS and MAOS are applied to the sample alternatively, the grain refining and orientation occur during the LAOS and MAOS, respectively, indicating reversibility of the orientation. (6) The degree of the orientation is dependent on γ0 and ω of the MAOS. Relatively higher orientation has been obtained for the combination of γ0 and ω that gives tan δ = 2−3. (7) The lattice constant does not change very much throughout all the shearing processes and is equal to that before shearing within the experimental errors, indicating an absence of shear melting. As described in the Introduction, the preparation of oriented samples has been reported for the V1 and V2 phases in the amphiphilic systems and the gyroid phase of the block copolymers. In these studies, however, oriented cubic phase is obtained by using epitaxial phase transition from other anisotropic phases oriented by shear, or shear melting from the cubic to the sponge phase. The present results strongly suggest a possibility to control the degree of orientation only by changing the conditions of oscillatory shear.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b04372. One-dimensional (1-D) SAXS patterns at rest for the samples containing 60 wt % and 66 wt % C12E2 at 30 °C with the plot of the positions of the diffraction peaks vs (h2 + k2 + l2)1/2, time evolution of two-dimensional (2-D) SAXS patterns, the lattice constant ac, the degree of orientation α, and the storage modulus G′ and loss modulus G″ at ω = 0.1 rad s−1 and σ0 = 20 Pa after the temperature is set to 30 °C, the lattice parameters at rest, relationships between the strain amplitude (γ0) and the stress amplitude (σ0) at several angular frequencies, orientation of the cubic lattice, results of least-squares fitting of the 1-D SAXS patterns, time evolution of 2-D SAXS patterns, ac, α, and rheological parameters before the start of the experiments shown in Figure 8, time evolution of 2-D SAXS patterns in the radial configuration in the second series of experiments, time evolution of the azimuthal plot in the tangential configuration in the second series of experiments, time evolution of 2-D SAXS patterns, ac, α, and rheological parameters before the start of the experiments shown in Figure 10, time evolution of 2-D SAXS patterns in the radial configuration in the third series of experiments, and time evolution of the azimuthal plot in the tangential configuration in the third series of experiments (PDF)

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CONCLUSIONS We have performed rheological measurements and simultaneous measurements of rheology/small-angle X-ray scattering on the V2 (Ia3d) phase in the nonionic surfactant (C12E2)/ water system. The results may be summarized as follows: (1) Grain refining occurs by applying the LAOS with γ0 ≈ 20, which gives the ratio G″/G′ = tan δ ≈ 100 to the sample. (2) Orientation of the cubic lattice occurs when the SAOS (γ0 ≈ 0.0004) in the linear regime is applied to the sample just I

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(17) Vigild, M. E.; Almdal, K.; Mortensen, K.; Hamley, I. W.; Fairclough, J. P. A.; Ryan, A J. Transformations to and from the Gyroid Phase in a Diblock Copolymer. Macromolecules 1998, 31, 5702−5716. (18) Schulz, M. F.; Bates, F. S.; Almdal, K.; Mortensen, K. Epitaxial Relationship for Hexagonal-to-Cubic Phase-Transition in a BlockCopolymer Mixture. Phys. Rev. Lett. 1994, 73, 86−89. (19) Vigild, M. E.; Eskimergen, R.; Mortensen, K. SANS, SAXS, Rheology and BirefringenceStrengths and Weaknesses in Probing Phase Behaviour of a Diblock Copolymer. Phys. B 2004, 350, E885− E888. (20) Sakurai, S. Progress in Control of Microdomain Orientation in Block CopolymersEfficiencies of Various External Fields. Polymer 2008, 49, 2781−2796. (21) Vukovic, I.; Friedrich, H.; Merino, D. H.; Portale, G.; ten Brinke, G.; Loos, K. Shear-Induced Orientation of Gyroid PS-B-P4VP (PDP) Supramolecules. Macromol. Rapid Commun. 2013, 34, 1208−1212. (22) Vukovic, I.; Voortman, T. P.; Merino, D. H.; Portale, G.; Hiekkataipale, P.; Ruokolainen, J.; ten Brinke, G.; Loos, K. Double Gyroid Network Morphology in Supramolecular Diblock Copolymer Complexes. Macromolecules 2012, 45, 3503−3512. (23) Valkama, S.; Ruotsalainen, T.; Nykänen, A.; Laiho, A.; Kosonen, H.; Ten Brinke, G.; Ikkala, O.; Ruokolainen, J. Self-Assembled Structures in Diblock Copolymers with Hydrogen-Bonded Amphiphilic Plasticizing Compounds. Macromolecules 2006, 39, 9327−9336. (24) Minewaki, K.; Kato, T.; Yoshida, H.; Imai, M.; Ito, K. SmallAngle X-Ray Scattering from the Lamellar Phase Formed in a Nonionic Surfactant (C16E7)−Water System. Analysis of Peak Position and Line Shape. Langmuir 2001, 17, 1864−1871. (25) Kosaka, Y.; Ito, M.; Kawabata, Y.; Kato, T. Lamellar-to-Onion Transition with Increasing Temperature under Shear Flow in a Nonionic Surfactant/water System. Langmuir 2010, 26, 3835−3842. (26) Ito, M.; Kosaka, Y.; Kawabata, Y.; Kato, T. 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. Langmuir 2011, 27, 7400−7409. (27) Sato, D.; Obara, K.; Kawabata, Y.; Iwahashi, M.; Kato, T. ReEntrant Lamellar/Onion Transition with Varying Temperature under Shear Flow. Langmuir 2013, 29, 121−132. (28) Conroy, J. P.; Hall, C.; Leng, C. A.; Rendall, K.; Tiddy, G. J. T.; Walsh, J.; Lindblom, G. Nonionic Surfactant Phase Behavior. The Effect of CH3 Capping of the Terminal OH. Accurate Measurements of Cloud Curves. Progr. Colloid Poym. Sci. 1990, 82, 253−262. (29) Funari, S. S.; Rapp, G. X-Ray Studies on the C12EO2/Water System. J. Phys. Chem. B 1997, 101, 732−739. (30) Lynch, M. L.; Kochvar, K. A.; Burns, J. L.; Laughlin, R. G. Aqueous-Phase Behavior and Cubic Phase-Containing Emulsions in the C12E2−Water System. Langmuir 2000, 16, 3537−3542. (31) Hyun, K.; Wilhelm, M.; Klein, C. O.; Cho, K. S.; Nam, J. G.; Ahn, K. H.; Lee, S. J.; Ewoldt, R. H.; McKinley, G. H. A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS). Prog. Polym. Sci. 2011, 36, 1697−1753. (32) Mezzenga, R.; Meyer, C.; Servais, C.; Romoscanu, A. I.; Sagalowicz, L.; Hayward, R. C. Shear Rheology of Lyotropic Liquid Crystals: A Case Study. Langmuir 2005, 21, 3322−3333. (33) Rancon, Y.; Charvolin, J. Epitaxial Relationships during Phase Transformations in a Lyotropic Liquid Crystal. J. Phys. Chem. 1988, 92, 2646−2651. (34) Clerc, M.; Levelut, A. M.; Sadoc, J. F. Transitions between Mesophases Involving Cubic Phases in the Surfactant−Water Systems. Epitaxial Relations and Their Consequences in a Geometrical Framework. J. Phys. II 1991, 1, 1263−1276. (35) Clerc, M.; Levelut, A. M.; Sadoc, J. F. X-ray Study of PhaseTransitions in Amphiphilic Systems. J. Phys. (Paris) 1990, 51, C7-97− C7-104. (36) Ramos, L.; Molino, F. Shear Melting of a Hexagonal Columnar Crystal by Proliferation of Dislocations. Phys. Rev. Lett. 2004, 92, 018301.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +81-42-677-1111 (ex. 3435). Fax: +81-42-677-2525. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by JSPS KAKENHI Grant No. 23340124 (Grant-in-Aid for Scientific Research (B)). The rheoSAXS experiments have been performed on the BL-6A at Photon Factory under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2011G589). We thank Dr. Nobutaka Shimizu and Dr. Noriyuki Igarashi in PF for assistance of the experiments.

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DOI: 10.1021/acs.langmuir.5b04372 Langmuir XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.langmuir.5b04372 Langmuir XXXX, XXX, XXX−XXX