pubs.acs.org/Langmuir © 2010 American Chemical Society
Order-Disorder Transition of Nonionic Onions under Shear Flow Yukiko Suganuma,† Masayuki Imai,*,† Tadashi Kato,‡ Ulf Olsson,§ and Tsutomu Takahashi^ †
Department of Physics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo, Tokyo 112-8610, Japan, ‡ Department of Chemistry, Tokyo Metropolitan University, 1-1 minami-Osawa, Hachioji, Tokyo 192-0397, Japan, §Chemical Physics, Lund University, P. O. Box 124, 221 00 Lund, Sweden, and ^Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japan Received December 26, 2009. Revised Manuscript Received February 26, 2010
We have investigated the shear-induced ordering of multilamellar vesicles (onions) in a nonionic surfactant (C12E4) system using a small-angle light scattering (shear-SALS) and a small-angle X-ray scattering (shear-SAXS) technique. In a narrow shear rate-temperature space, the onions form a two-dimensional (2D) hexagonally close-packed structure that shows characteristic hexagonal scattering patterns in both SALS and SAXS. In the dynamic phase diagram, the ordered onion phase is surrounded by disordered onion phase, indicating reentrant behavior against the temperature. The disorder-order transition is accompanied by a jump in onion size by a factor of 5-6. In the disordered onion phase, by applying a shear flow, the planar lamellar membranes transform to an intermediate structure, multilamellae cylinders or a coherent stripe buckling, and then the intermediate structure develops to the isotropic onions. On the other hand, in the ordered onion phase, the intermediate structure breaks to onions stretched in the shear velocity direction, and then the stretched onions aligned gradually to form the 2D hexagonal close packing.
1. Introduction Surfactants form various mesoscopical scale assemblies in water due to the amphiphilic nature of the molecules. Since the molecular assemblies are stabilized by relatively weak interactions, the assemblies easily deform their morphologies when subjected to external fields, such as a shear and an electric or a magnetic field. When we apply the shear field to the mesoscopic assemblies composed of surfactants, the assemblies often tend to align. The shear stress sometimes also causes characteristic isotropic-anisotropic morphological transitions such as a sponge to lamellar1-3 and a gyroid to lamellar transitions4 where the three-dimensional networks are torn by the shear stress and reassembled to form less stressed mesostructures against the shear flow. However, it is quite interesting to note that by applying a shear field to the anisotropic lamellar assemblies, the planar membranes often transform to the isotropic multilamellar vesicles (onions).5 Since the discovery of the shear induced lamellar-onion transition, the onions have gathered much interest from experimental and theoretical points of view. Experimentally, the onion formation is detected by a four-lobe cloverleaf pattern of
the depolarized small-angle light scattering (SALS)6-14 and a Maltese cross image of a polarized optical microscope observation.5,13-15 The details of the onion structure were directly addressed by the electron micrographs. The onions fill the space with various polyhedra having size polydispersity, and the concentric lamellar membranes are packed in the inside of onions.16 The shear field causes another characteristic onion configuration. Diat et al. observed characteristic hexagonal patterns in the SALS and a small-angle X-ray scattering (SAXS) image in the shear velocity-neutral plane, indicating formation of two-dimensional (2D) hexagonally close-packed onions.17,18 The ordered onion phase has been reported in various surfactant bilayer systems having the disordered onion phase.17-23 Especially, Le et al. have found that nonionic membranes of the C12E4-water system have 2D closely packed honeycomb-shaped onions within a certain temperature interval under shear flow, and above and below this temperature interval, the disordered onions are generated.21 Interestingly, they have observed disorder-orderdisorder transition as the temperature increases. However, the system was only characterized using small-angle neutron scattering (SANS) on the length scale of the bilayer repeat distance
*Corresponding author: Tel þ81-03-5978-5316, Fax þ81-5978-5316, e-mail
[email protected].
(12) Kosaka, Y.; Ito, M.; Kawabata, Y.; Kato, T. Langmuir 2010, 26, 3835. (13) Medronho, B.; Fujii, S.; Richtering, W.; Miguel, M. G.; Olsson, U. Colloid Polym. Sci. 2005, 284, 317. (14) Koschoreck, S.; Fujii, S.; Lindner, P.; Richtering, W. Rheol. Acta 2009, 48, 231. (15) Fujii, S.; Richtering, W. Eur. Phys. J. E 2006, 19, 138. (16) Gulik-Krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. Langmuir 1996, 12, 4668. (17) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (18) Sierro, P.; Roux, D. Phys. Rev. Lett. 1997, 78, 1496. (19) Wunenburger, A. S.; Colin, A.; Leng, J.; Arna˚Leodo, A.; Roux, D. Phys. Rev. Lett. 2001, 86, 1347. (20) Leng, J.; Nallet, F.; Roux, D. Eur. Phys. J. E 2001, 4, 337. (21) Le, T. D.; Olsson, U.; Mortensen, K. Phys. Chem. Chem. Phys. 2001, 3, 1310. (22) Courbin, L.; Cristobal, G.; Rouch, J.; Panizza, P. Europys. Lett. 2001, 55, 880. (23) Courbin, L.; Panizza, P. Phys. Rev. E 2004, 69, 021504.
(1) Yamamoto, J.; Tanaka, H. Phys. Rev. Lett. 1996, 77, 4390. (2) M.Cates, M. E.; Milner, S. T. Phys. Rev. Lett. 1989, 62, 1856. (3) Nettesheim, F.; M€uller, C. B.; Olsson, U.; Richtering, W. Colloid Poym. Sci. 2004, 282, 918. (4) Imai, M.; Nakaya, K.; Kato, T. Eur. Phys. J. E 2001, 5, 391. (5) Diat, O.; Roux, D.; Nallet, F. J. Phys. II 1993, 3, 1427. (6) Weigel, R.; L€auger, J.; Richtering, W.; Lindner, P. J. Phys. II 1996, 6, 529. (7) L€auger, J.; Weigel, R.; Beger, K.; Hiltrop, K.; Richtering, W. J. Colloid Interface Sci. 1996, 181, 521. (8) M€uller, S.; B€orsching, C.; Gronski, W.; Schmidt, C.; Roux, D. Langmuir 1999, 15, 7558. (9) Le, T. D.; Olsson, U.; Mortensen, K.; Zipfel, J.; Richtering, W. Langmuir 2001, 17, 999. (10) Zipfel, J.; Nettesheim, F.; Lindner, P.; Le, T. D.; Olsson, U.; Richtering, W. Europhys. Lett. 2001, 53, 335. (11) Nettesheim, F.; Zipfel, J.; Olsson, U.; Renth, F.; Lindner, P.; Richtering, W. Langmuir 2003, 19, 3603.
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(6 nm). Characterization on the length scale of onion size was not performed. The purpose of this study is to make clear the phase behavior including re-entrant order-disorder transition of the C12E4-water system and investigate the pathway to the 2D hexagonal close-packed onions. First, we establish the dynamic phase diagram in shear rate-temperature space including the ordered onion region by means of the SALS and the SAXS techniques. On the basis of the dynamic phase diagram, we examine the evolution of the disordered and ordered onions from the planar lamellar membranes as a function of the shear strain. Both experiments reveal the difference between the ordered and disordered onions phase, which is relevant to elucidate the formation mechanism of the ordered state.
2. Experiments Material. We investigated a binary mixture of D2O and nonionic surfactant, tetraethylene glycol mono-n-decyl ether, C12E4 (purity >98%), which was purchased from Nikko Chemicals Inc. and used without further purification. The volume fraction of the surfactant is fixed at φC12E4 = 0.44 (40 wt %). The static phase diagram has been reported in other articles.24-26 We have confirmed with SAXS and polarized microscope observation that this system has a micelle phase (T < 20 C: T is the temperature), a lamellar phase in 20 C < T < 60 C, a coexistence of lamellar and sponge phase in 60 C < T < 70 C, and sponge phase in 70 C < T < 72 C. We prepared the sample using the following procedure. The surfactant was mixed with water at room temperature (lamellar phase) and then homogenized using a vortex mixer below 10 C (isotropic micelle phase). The sample again homogenized at room temperature. After the homogenization, bubbles in samples were removed with a centrifuge. Since during the homogenization the planar membranes transform to the onions, we leaved samples for a week to have an equilibrated polycrystalline lamellar structure without onions. We ensured the sample being in the polycrystalline lamellar phase by the polarized light microscope observation. Shear-SALS. The shear-depolarized small-angle light scattering system is a custom-made apparatus with a Couette type shear cell which can apply homogeneous velocity to whole sample without a velocity distribution. The concentric cylinders have radii of 13.5 mm for inner rotor and 14.5 mm for outer stator made of glass. The gap size is 1 mm. The shear rate is defined by γ_ = Fω/D (where ω is the angular velocity, D is the gap size, and F is the radius of the rotor, F = 13.5 mm), and one can control the shear rate from 0 to 1800 s-1. Temperature is controlled by a water jacket system covering the outer cylinder from 20 to 50 C with accuracy of (0.1 C. For SALS measurements, the sample was hermetically sealed by a cap, and we confirmed by the time dependence of the peak position that this cap prevents the water evaporation. The light source is a violet semiconductor laser (SU-61C-405-5, Audio-Technica, Japan) with the wavelength, λ, of 405 nm. We can change the distance from the samples to screen to cover the scattering angle, θ, from 2.5 to 40 corresponding scattering vector, q, from 0.8 to 14.0 μm-1 (q = 4πn sin(θ/2)/λ, where n=1.386 is the refractive index of this sample). We calibrate the magnitude of the q vector using a diffraction grating. The laser beam irradiates the sample from the center of the Couette cell along the radial direction (parallel to the velocity gradient direction). We have adopted a cross-polarizer and an analyzer set, where the polarizer is inclined 45 to the shear direction. The two-dimensional scattering pattern in the shear velocity-neutral plane was visualized on a screen and recorded by a CCD camera (XCD-X700: SONY, Japan). (24) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; Mcdonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (25) Strey, R. Ber. Bunsenges. Phys. Chem. 1996, 100, 182. (26) Bryskhe, K.; Bulut, S.; Olsson, U. J. Phys. Chem. B 2005, 109, 9265.
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Shear-SAXS. For the shear-SAXS measurement, a Couette cell made of polycarbonate for SAXS measurement was installed to AR 550 rheometer (TA Instruments). The concentric cylinders have radii of 13.5 mm for inner rotor and 14.5 mm for outer stator, and the height of the inner cylinder is 23 mm. The thicknesses of the inner cylinder at the X-ray beam position and the outer cylinder are both 0.5 mm. The temperature 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. We confirmed prevention of the water evaporation by the fact that the scattering peak kept the constant position before and after the measurements. Details of the apparatus for shear-SALS experiments have been described in the previous paper.12 SAXS measurements were performed using a synchrotron radiation SAXS apparatus installed in BL-15A instrument at the photon factory (PF) in the high-energy accelerator research organization (KEK), Tsukuba. In experiments we used 1.5 A˚ wavelength X-ray beam having 0.8 0.8 mm2 square cross section.27 The sample-to detector distance was 115 m. The scattered beam was recorded with CCD area detector (1024 pixel 1024 pixel) covering scattering q range from 0.015 to 0.33 A˚-1. The obtained scattering images were corrected for the dark current noise and the nonuniformity caused by the detector distortion and efficiency and then subtracted the background scattering. In the experiments, we used two instrument configurations: a radial configuration where the beam is directed through the center of the cell and a tangential configuration where the beam is directed through the edge of the cell. Thus, the scattering profiles in the shear velocity-neutral plane are obtained in the radial configuration, while those in the velocity gradient-neutral plane are obtained in the tangential configuration. In our apparatus, the configuration can be changed within 10 s by using an automatic stage. The exposure time was 30 s for the radial configuration and 60 s for the tangential configuration. To get one image, the Couette cell rotate more than 360 in our experimental range.
3. Results and Discussion Dynamic Phase Diagram under Shear. First we examined the morphological behavior of lamellar phase under the shear field using the SALS and the SAXS techniques, where the former addresses the averaged shape and the configuration of onions in micrometer scale and the latter reveals the orientation of lamellar membranes in nanometer scale. The experimental results are summarized in a dynamic phase diagram in Figure 1a where the steady-state structure is shown in temperature-shear rate space. Characteristic SALS patterns are shown in Figure 1b. The marks in Figure 1a are the positions where we measured the SALS patterns shown in Figure 1b. It is known that the morphology transition of lamellar membranes gradually proceeds depending on the shear strain, γ.11,23 In a nonionic system of C10E3 and D2O mixture, the viscosity becomes constant after γ ≈ 2.0 104 and the formation of disordered onions becomes steady-state structure at γ ≈ 3.0 104.11 In the C12E4 and D2O system, we applied the shear strain up to 3.0 105 for γ_ g 10 s-1 and 1.0 105 for γ_ < 10 s-1 to obtain the steady states in the SALS experiment. As shown later, the formation of ordered onions requires many strain units to reach the steady state. In Figure 1b, we find three types of scattering images: the hexagonal six-spot pattern observed in dotted region in the dynamic phase diagram (Figure 1b, images IIIb to IIIe), a fourarc pattern in white region (Figure1b, images IIa to IIe, IIIa, and IVa to IVe), and a vertical streak pattern observed in hatched (27) Amemiya, Y.; Wakabayashi, K.; Hamanaka, T.; Wakabayashi, T.; Matsusita, T.; Hashizume, H. Nucl. Instrum. Methods 1983, 208, 471.
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Figure 1. (a) Dynamic phase diagram in the temperature-shear rate space. Schematics of structures are shown on the right-hand side. Dots represent measured points using either SALS or SAXS. The marks represent the measured positions of SALS images shown in (b) and (c). (b) Map of the depolarized SALS patterns at a variety of shear rate (10, 30, 60, 80, and 100 s-1) and temperatures (20.0, 25.0, 38.0, and 47.0 C). Images are detected after γ = 3.0 105 for γ_ g 10 s-1 and 1.0 105 for γ_ < 10 s-1 to obtain steady states. (c) SALS images in the ordered onion phase without analyzer to show the hexagonal packing. The incident beam was polarized to the horizontal direction.
region (Figure 1b, images Ia to Ie). In order to deduce the morphology in each region, we show the temperature dependence of the SAXS patterns in the radial configuration (Figure 2, images Ia to Va) with the azimuthal traces averaged in a 0.07 < q < 0.11 A˚-1 band and those in the tangential configurations (Figure 2, images Ib to Vb) at γ_ = 60 s-1. Each SAXS image was taken at γ ≈ 2.0 105. It should be noted that the scattering profiles in the tangential configuration are not symmetric; i.e., the 7990 DOI: 10.1021/la904862e
intensity in the left-hand side is greater than that in the righthand side. This is due to path differences of the scattered X-ray beam.28 A part of the scattered X-ray is attenuated by the rotor, and this decreases the scattering intensity on the right-hand side. (28) Nettesheim, F.; Olsson, U.; Lindner, P.; Richtering., W. J. Appl. Crystallogr. 2004, 37, 438.
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Figure 2. Typical SAXS spectra under shear rate of 60 s-1 measured with radial configuration (Ia to Va: left column) and tangential configuration (Ib to Vb; right column) at 20.0 C (Ia, Ib), 25.0 C (IIa, IIb), 38.0 C (IIIa, IIIb), 47.0 C (IVa, IVb), and 60 C (Va, Vb). The middle column shows azimuthal traces averaged around a q-band 0.07-0.11 A˚-1 for the radial configuration.
At the lowest temperature in the lamellar phase (T ≈ 20 C), planar lamellae are stable under shear (Figure 1a). Here, the SAXS pattern in the radial configuration (Figure 2, image Ia) shows two peaks in the neutral direction, indicating oriented lamellar membranes in the gradient-velocity plane, whereas that in the tangential configuration (Figure 2, image Ib) shows two strong peaks in the gradient direction, indicating oriented lamellar membranes in the velocity-neutral plane. Taking into account that both lamellar orientations in the gradient-velocity plane and the velocity-neutral plane can be simultaneously observed in the tangential configuration, the most lamellar membranes are aligned in the velocity-neutral plane. The orientation in the gradient-velocity plane is a trapped metastable state on which there is no torque.9 The orientation in the velocity-neutral plane is the most common orientation of lamellar phases in shear flow and is often referred to as the c-orientation.29 The observed SAXS and SALS patterns were independent of the shear rate in a (29) Dhez, O.; Nallet, F.; Diat, O. Europhys. Lett. 2001, 55, 821.
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measured range 5 e γ_ e 100 s-1, indicating the oriented lamellar membranes are stable against the shear flow. It should be noted that in the vicinity of the phase boundary between lamellar phase and sponge phase (T ≈ 60 C) we observed similar SAXS patterns to those in the region of T ≈ 20 C as shown in Figure 2, images Va and Vb. Judging from the SAXS patterns, we concluded that the lamellar membranes in the vicinity of the lamellae-sponge phase boundary (upper hatched region) has the same orientation as those in the lamellaemicelle phase boundary (lower hatched regions). Unfortunately, our SALS equipment was unable to reach on high T as 60 C. Thus, in the vicinity of the both phase boundaries in the lamellar phase, the membranes prefer the planar lamellar structure, which is consistent with the previously reported observation.9,12,30,31 (30) Oliviero, C.; Coppola, L.; Gianferri, R.; Nicotera, I.; Olsson, U. Colloids Surf., A 2003, 228, 85. (31) Medronho, B.; Miguel, M. G.; Olsson, U. Langmuir 2007, 23, 5270.
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Figure 3. Schematic representation of 2-D hexagonal closepacked onions in the velocity-neutral plane.
With increasing temperature from 20 C, the SAXS patterns in both configurations change from the anisotropic to the isotropic ring, keeping the peak position constant as shown in Figure 2, images IIa and IIb. These changes of scattering patterns clearly demonstrate the formation of the isotropic onions. The corresponding SALS pattern in the white region in Figure 1a is the four-arc pattern. A characteristic depolarized SALS pattern to the spherulite having radially oriented internal structure is the fourlobe cloverleaf pattern.32 In this region, we observe densely packed onions by the polarized microscope observation. Thus, the four-arc pattern in the SALS is due to the structure factor of the onions in a random configuration (disordered onions). The SALS pattern at 25 C depends on the shear rate. At the low shear rate region (γ_ ≈ 10 s-1), we observe a small four-arc pattern. With increasing shear rate, the arcs position shifts to higher angles. A similar shear rate dependence of the SALS patterns is observed at 47 C, which indicates that the size of the disordered onion decreases with an increase of the shear rate. At 38 C, we observe a similar four-arc patterns in the low shear rate region (3 e γ_ e 10 s-1), however, the SALS pattern is transformed to a hexagonal six spots pattern at γ_ ≈ 15 s-1. Since the SALS patterns under the cross polarizer and analyzer configuration obscure the hexagonal spots, SALS images in this ordered region without analyzer are shown in Figure 1c, images IIIb to IIIe. The hexagonal spots are well-defined under shear at γ_ = 60 (IIIc), 80 (IIId), and 100 s-1 (IIIe). In the narrow dotted region in Figure 1a (35 < T < 42 C and γ_ > 15 s-1) we observe the characteristic hexagonal SALS pattern. Simultaneously, the SAXS pattern in the radial configuration transforms from the isotropic ring to hexagonal spots pattern (Figure 2, image IIIa), demonstrating a disorder-order transition of the onion packing. The SAXS patterns show the hexagonal orientation of lamellar membranes in the velocity-neutral plane (Figure 2, image IIIa) and the isotropic distribution in the gradient-neutral plane (Figure 2, image IIIb). Thus, onions have 2D hexagonal closepacking structure. Here it should be noted that the azimuthal trace in the ordered phase (Figure 2, image IIIa) has the nonequivalent intensity distribution with the peak positions at (25, ( 90, and (155, indicating an elastic deformation of ordered onions due to the applied shear. On the other hand, the SALS pattern (Figure 1c, image IIIc) has an equiangular hexagonal pattern. Thus, the onions in the ordered phase have slightly deformed shapes but are packed in an exact hexagonal manner. On the basis of these observations, we schematically show the (32) Samuels, R. J. J. Polym. Sci., Part A-2 1971, 9, 2165.
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configuration of the ordered onions in the velocity-neutral plane in Figure 3. Similar deformed SAXS pattern and equiangular hexagonal SALS pattern were observed at other shear rate, γ_ = 30 and 100 s-1. With an increase of shear rate from 20 s-1, the peak position in SALS images shifts toward higher angles, demonstrating the decrease of onion size. After a cease of the shear flow, the nonequivalent intensity distribution in the hexagonal spots transforms to an equivalent one as reported in ref 21, although the peaks keep their position. Onion Sizes. The disordered onions transform to the ordered onions in the particular shear rate-temperature region. The ordered onion region is surrounded by the disordered onion region, indicating reentrant nature of the disorder-order transition. It is well-known that a disorder-order transition of the hard spheres is governed by the volume fraction and the polydispersity, and the crystallization of the spheres is suppressed when the polydispersity, s = Æσ2æ/Æσæ2 - 1 (σ: diameter of the sphere), exceeds a value of ca. 6%.33 In the onion phase, the volume fraction of onions is ∼1.16 Thus, the size polydispersity of the disordered onions might be larger than 6%, although the SALS patterns show a definite structure factor peak (Figure 1b). Analytical expressions for the static structure factor for a polydisperse Percus-Yevick fluid with Schultz distributed particle diameter was obtained by Griffith et al.34 They showed that the disordered hard spheres with the size polydispersity of 7% still have a definite peak in the structure factor at the volume fraction of 0.5. Thus, the definite structure factor peak observed in the SALS pattern is not contradictory to the disordered onions with polydisperse onion size and the disorder-order transition of the onions might take place with a small change of the polydispersity. Then we hypothesize that the disorder-order transition is caused by the polydisperese-monodisperse transition, although we could not estimate the polydispersities of onions in disordered and ordered state experimentally. In this context we investigate the temperature dependence of the onion size. By assuming a densely packing of the onions, we estimate the mean onion radius, R, from the scattering peak position of the SALS pattern, q0. For the disordered onion phase, the peak position of the four-arc pattern indicates the averaged center-to-center distance of onions, expressed by q0 = 2π/2R.9,11 For the ordered onion phase, we estimate the onion size from the first-order peak position of the hexagonal pattern using the relation q0 = 2π/31/2R. The obtained temperature dependence of the onion radius at γ_ = 60 s-1 is plotted in Figure 4a. With an increase of temperature from 24 C, R decreases slightly in the disordered onion phase. At the entry of the ordered phase, R abruptly increases from 0.3 to 1.7 μm. The onion size keeps constant in the ordered phase but returns to 0.3 μm at the upper order-disorder transition temperature. Then with increasing temperature, R increases slightly in the upper disordered onion phase. Thus, the temperature dependence of the onion size is completely symmetric against the ordered phase, i.e. 38 C. Here we address the nature of the onion size in each phase. It has been reported that the mean onion size depends on the shear rate with a power law of R ∼ γ_ 1/2.5,8,11,15,23 Unfortunately, the origin of the shear rate dependence is still not fully clear, although the balance between the shear stress and the bending elasticity and/or the surface tension seems to determine the onion size. We measured the shear rate dependence of the onion size at three temperatures: 25 C in the disordered phase below the ordered phase, 38 C at the center of the ordered phase, and 47 C in the (33) Bolhuis, P. G.; Kofke, D. A. Phys. Rev. E 1996, 54, 634. (34) Griffith, W. L.; Triolo, R.; Compere, A. L. Phys. Rev. A 1986, 33, 2197.
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Figure 4. (a) Onion size as a function of temperature under shear flow of 60 s-1. (b) Onion size as a function of shear rate at 25 (0), 38 (b), and 47 C (þ). Solid lines show a power low R ∼ γ_ 1/2.
disordered phase above the ordered phase. The obtained shear rate dependences are plotted in Figure 4b with the R ∼ γ_ 1/2 laws (solid lines). In the disordered phase, the shear rate dependence of the onion size at 25 and 47 C lies on the same line R = aγ_ 1/2 where a = 2.9 μm s-1/2, indicating that the onion size is mainly governed by the shear rate. This shear rate dependence in the disordered onion phase agrees with that measured by M€uller et al.8 At 38 C the onion size follows the same R = 2.9γ_ 1/2 law in the low shear rate region (3 < γ_ < 10 s-1), whereas in the ordered phase, the onion size obeys another power law of R = 11γ_ 1/2. The same exponent suggests that the onion size in the ordered phase is governed by the same mechanism that in disordered phase. A similar size jump of onions has been previously reported in a quaternary system composed of water, brine, SDS, and octanol. 17,18 In that system, the disorder-order transition takes place without size jump and the size jump occurs in the ordered onions region; i.e., the small ordered onions jump to large ordered onions with an increase of shear rate. This behavior is different from our observation that the onion size jump accompanies with the Langmuir 2010, 26(11), 7988–7995
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disorder-order transition. However, in the quaternary system, a slope of the shear rate dependence of the onion size changes at the disorder-order transition of onions. Thus, the disorderorder transition of onions might be coupled with the size of onions, although the relation between the transition and the size change is not clear. Pathway of Onion Formation. In order to understand the formation mechanism of the ordered onions, we followed the shear-induced morphology transition pathways from the planar lamellar membrane phase to the disordered onion phase and the ordered onion phase using both the SALS and SAXS techniques. The pathway for disordered onions from planar lamellae has been investigated and discussed previously.35-38 There have been extensive experimental investigations showing that the planar membranes transform to onions through an intermediate structure characterized by a pronounced Bragg peak in a neutral direction in SAXS image and an intense streak in the neutral direction in the SALS pattern. The intermediate structure has been interpreted as the multilayer cylinders or the coherent stripe buckling of the lamellae with the axis in the velocity direction.10,11,35 This intermediate structure breaks into onions and finally develops to the dense polydisperse onion state. A theoretical model suggests a buckling layers structure as an intermediate structure. The buckling originates from an increase of effective membrane area, which is induced by a restriction of the thermal fluctuation by shear flow.22,23,36,37 In this model, the buckled membranes break up into onions. It has also been proposed that edge dislocations triggered by the instability of membranes under shear flow grow to onions.38 In this study, we compare the pathway of the ordered onion formation with that of the disordered onion formation. Pathway of Onion Formation in the Disordered State. We show the shear strain evolution of the SALS patterns in Figure 5a and the SAXS patterns in the radial configuration in Figure 5b at 38 C under a shear flow of 10 s-1 (disordered onion state). The evolutions of the SAXS intensity at the lamellar Bragg peak in the neutral direction, In, and the velocity direction, Iv, are plotted in Figure 5c. Without shear field, the sample shows light scattering at very small angle and intensities in the neutral direction in the SAXS pattern. This initial state is not well-defined as it results after mounting the sample. When the inner rotor is lowered into the cup, the sample is being sheared in the vertical direction, leading to a partial c-orientation. By applying the shear field, streak scattering in the neutral direction appears in SALS image and In increases keeping constant Iv (γ = 600). The streaks in the SALS pattern and the strong In are characteristic to the intermediate structure. Iv begin to increase in the SAXS profile after γ ≈3000, and the four-lobe cloverleaf pattern gradually appears in the streak spectrum in SALS at γ ≈ 3600, indicating that the intermediate structure starts changing to onions. The four-lobe pattern originates from the form factor of the onions. SAXS pattern is becoming circularly symmetric as the onion formation becomes completed.10,11 At higher values of γ, onions finally fill the space, i.e., above γ = 30 000, the four-lobes pattern in SALS images is developed to the four-arc pattern which originates from the structure factor peak of dense onions. The peak becomes sharper with increasing γ. (35) Medronho, B.; Shafaei, S.; Szopko, R.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2008, 24, 6480. (36) Zilman, A. G.; Granek, R. Eur. Phys. J. B 2001, 11, 593. (37) Courbin, L.; Delville, J. P.; Rouch, J.; Panizza, P. Phys. Rev. 2002, 89, 148305. (38) Meyer, C.; Asnacios, S.; Bourgaux, C.; Kleman, M. Rheol. Acta 2000, 39, 223.
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Figure 5. Strain evolution of SALS images (a) and SAXS images in radial configuration (b) from planar lamellar membranes to disordered onions structure at 38 C under shear rate of 10 s-1. Values of the strain, γ are shown on the top of images. (c) The evolutions of the SAXS intensity at the lamellar Bragg peak in the neutral direction, In, and the velocity direction, Iv, in the transition pathway shown in (b).
It is interesting to note that Iv has a maximum at γ ≈ 42 000, and the Bragg ring of SAXS spectra changes to the anisotropic pattern with the intensity difference between In and Iv up to γ ≈ 150 000. Above γ ≈ 42 000, the four-arc pattern becomes slightly elongated to the neutral direction, and the peak position in the SALS shifts to higher angles. We considered that the isotropic onions break into small onions slightly elongated to the velocity direction due to the shear stress. This pathway to the disordered onion phase is consistent with the previously observation10,11,35 Pathway of Onion Formation in the Ordered State. In Figure 6 we present selected SALS and SAXS (radial configuration) patterns and the variation of the intensities, In and Iv, for a lamellar sample sheared at 38 C with the shear rate of 30 s-1. At this temperature and shear rate the steady state is the ordered state. The structural evolution with strain is similar that observed at lower shear rate (disordered onion region), but with a few 7994 DOI: 10.1021/la904862e
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Figure 6. Strain evolution of SALS images (a) and SAXS images in radial configuration (b) from planar lamellar membranes to disordered onions structure at 38 C under shear rate of 30 s-1. Values of the strain, γ, are shown on the top of images. (c) The evolutions of the SAXS intensity at the lamellar Bragg peak in the neutral direction, In, and the velocity direction, Iv, in the transition pathway shown in (b).
significant differences. First, onion formation requires a larger number of strain units (γ ≈ 252 000) to be ordered. Second, In is always larger than Iv, even for γ > 5 104, where onions have been formed in the disordered phase. Here, a close inspection of the SALS pattern at γ = 14 400 also shows that the pattern is slightly stretched in the neutral (vertical) direction, indicating in turn that the onions are slightly elongated in the velocity direction. Despite the elongation in early stage, the six spots pattern is the perfectly hexagonal one in the steady state. Third, prior to the 2D hexagonal packing of the onions, the SALS pattern shows a characteristic streak in the neutral direction (γ = 126 000), indicating alignment of onions in the velocity direction. Finally, we compare the onion formation at different temperatures under shear rate of 30 s-1 in Figure 7 where we present selected SALS patterns in the evolution toward the steady state. An important feature here is that the shear strain evolution pathways of the onion formation are completely symmetric against the temperature as shown in Figure 7. The reentrant nature of the dynamic phase diagram is in contrast to the static Langmuir 2010, 26(11), 7988–7995
Suganuma et al.
Article
Figure 7. Strain evolution of SALS images from a lamellar structure to disordered onions at 25 and 47 C and to ordered onions at 38 C under shear rate of 30 s-1.
phase diagram of the nonionic surfactant/water system where the system shows the phase sequence from the micelle, micelle/ lamellar coexistence, lamellae, lamellae/sponge coexistence, and sponge. One may consider that the reentrant behavior can be related to the change of the spontaneous curvature of monolayer; thus, the spontaneous curvature becomes zero at the center of the symmetric phase behavior (38 C). However, Bryskhe et al. have reported that the temperature, T0, where the spontaneous curvature becomes zero is ∼50 C.26 On the other hand, Kosaka et al. have suggested that T0 ≈ 25 C.12 So T0 is still an unresolved parameter. At present, we cannot reveal a “hidden” parameter which controls the symmetric phase behavior of onions under the shear field and does not work without shear.
4. Conclusions We have investigated onion formation, varying temperature and shear rate, of a lamellar sample in the water-C12E4 system.
Langmuir 2010, 26(11), 7988–7995
An ordered onion state with layers of 2D hexagonally oriented is formed in a narrow temperature region at higher shear rates. For temperatures above and below, such an ordered state is not obtained. The onions in the ordered state are ∼6 times larger compared to the disordered state at the same shear rate. While more experimental work is necessary, this finding may shed some light to what dictates the onion size in these kinds of systems. The reentrant nature of the ordering transition is striking. By coupling with the shear field, a hidden order parameter might be effective, which governs the shear-induced morphology transition. Acknowledgment. This work was supported by KAKENHI (Grant-in-Aid for Scientific Research) on Priority Area “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Y.S. acknowledges a Fellowship for Young Researchers provided by the Japan Society for the Promotion of Science (JSPS).
DOI: 10.1021/la904862e
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