pubs.acs.org/Langmuir © 2009 American Chemical Society
Lamellar-to-Onion Transition with Increasing Temperature under Shear Flow in a Nonionic Surfactant/Water System Yuriko Kosaka, Makiko Ito, Youhei Kawabata, and Tadashi Kato* Department of Chemistry, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan Received August 31, 2009. Revised Manuscript Received October 7, 2009 Simultaneous measurements of small-angle light scattering/shear stress (Rheo-SALS) and small-angle X-ray scattering/shear stress (Rheo-SAXS) have been performed in the lamellar phase of the C16E7/D2O system. As the temperature is increased and exceeds 67 °C at constant shear rates (at 1 and 3 s-1), the shear stress increases abruptly and a four-lobe pattern is observed in the depolarized SALS. These results suggest that the lamellar-to-onion transition occurs with increasing temperature, which has not yet been reported. The diameter of onions obtained from the depolarized SALS pattern at 3 s-1 increases with increasing temperature. The transition is reversible against the change in temperature. The Rheo-SALS measurements have also been made with a stepwise increase in shear rate at constant temperature. The results are consistent with the above temperature-scan experiments at constant shear rate, suggesting that the transition does not depend on the path. The variation of the SAXS pattern at 3 s-1 indicates that the orientation of lamellae becomes isotropic as the temperature is increased from 67 to 69 °C, which also supports the lamellar-to-onion transition. The transition temperature at constant shear rate (at 3 s-1) increases rapidly with a slight increase in surfactant concentration. From this, together with the SAXS results at rest in our previous study, we deduce that an increase in the water-layer thickness is necessary for the lamellar-to-onion transition with increasing temperature.
1. Introduction In the past 15 years, much attention has been paid to the effects of shear flow on the structure of the lyotropic phase, especially the lamellar phase.1-3 Among them, the most striking result may be the transition from the lamellar phase to the “onion state” where all of the space is filled by multilamellar vesicles without excess solvent. This transition has been found for the first time by Roux and co-workers4,5 in a sodium dodecyl sulfate/pentanol/water/ decane system. They have shown that the critical shear rate necessary for the transition to onions is proportional to the cube of the membrane volume fraction and that further increases in the shear rate cause the onion state to transform to oriented lamellae without defects.4 They have also shown that the radius of onions (R) follows the power laws R µ γ_ -1/2 and R µ d-2 µ φ 2 where γ_ is the shear rate, d is the lamellar spacing, and φ is the membrane volume fraction. The transitions for other systems have also been reported by them.6-10 In these studies, it has been revealed that the shape of onions is not spherical but polyhedral7 and that in certain cases the onions organize themselves into long-range-ordered plane structures where onions are hexagonally shaped and close packed on triangular lattices.6 At higher shear rates, there is another transition between the ordered 1 μm onions to another *Corresponding author. Tel: þ81-426-77-2528. Fax: þ81-426-77-2525. E-mail:
[email protected]. (1) Bernia, M. G.; Lawrence, C. J.; Machin, D. Adv. Colloid Interface Sci. 2002, 98, 217. (2) Richtreing, W. Curr. Opin. Colloid Interface Sci. 2001, 6, 446. (3) Roux, D. In Nonequilibrium Dynamics, Metastability and Flow; Cates, M. E., Evans, M. R., Osborne, P., Eds.; Institute of Physics Publishing: Bristol, U.K., 2000; Chapter 7. (4) Diat, O.; Roux, D.; Nallet, F. J. Phys II 1993, 3, 1427. (5) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. (6) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (7) Gulik-Krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. Langmuir 1996, 12, 4668. (8) Sierro, P.; Roux, D. Phys. Rev. Lett. 1997, 78, 1496. (9) Panizza, P.; Colin, A.; Coulon, C.; Roux, D. Eur. Phys. J. B 1998, 4, 65. (10) Leng, J.; Nallet, F.; Roux, D. Eur. Phys. J. E 2001, 4, 77.
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ordered state made of much larger onions (from 10 to 50 μm).8 Following these studies, the shear-induced lamellar-to-onion transition has been reported for many systems; both for ionic4-11,26-33 and nonionic12-25 surfactants and aqueous6-8,10-28,30-32,34 and nonaqueous4,5,9,29,33 solvents. (11) Bergenholtz, J.; Wagner, N. J. Langmuir 1996, 12, 3122. (12) Muller, S.; Borschig, C.; Gronski, W.; Schmidt, C.; Roux, D. Langmuir 1999, 15, 7558. (13) Weigel, L. J.; Richtering, W.; Lindner, P. J. Phys. II 1996, 6, 529. (14) Zipfel, J.; Nettesheim, F.; Lindner, P.; Le, T. D.; Olsson, U.; Richtering, W. Europhys. Lett. 2001, 53, 335. (15) Le, T. D.; Olsson, U.; Mortensen, K.; Zipfel, J.; Richtering, W. Langmuir 2001, 17, 999. (16) Nettesheim, F.; Zipfel, J.; Olsson, U.; Renth, F.; Linder, P.; Richtering, W. Langmuir 2003, 19, 3618. (17) Nettesheim, F.; Olsson, U.; Linder, P.; Richtering, W. J. Phys. Chem. B 2004, 108, 6328. (18) Medronho, B.; Fujii, S.; Richtering, W.; Miguel, M. G.; Olsson, U. Colloid Polym. Sci. 2005, 284, 317. (19) Fujii, S.; Richtering, W. Eur. Phys. J. E 2006, 19, 139. (20) Koshobeck, S.; Fujii, S.; Richtering, W. Prog. Theor. Phys. 2008, 175, 154. (21) Koshobeck, S.; Fujii, S.; Lindner, P.; Richtering, W. Rheol. Acta 2009, 48, 231. (22) Le, T. D.; Olsson, U.; Mortensen, K. Phys. Chem. Chem. Phys. 2001, 3, 1310. (23) Oliviero, C.; Coppola, L.; Gianferri, R.; Nicotera, I.; Olsson, U. Colloids Surf., A 2003, 228, 85. (24) Medronho, B.; Miguel, M. G.; Olsson, U. Langmuir 2007, 23, 5270. (25) Medronho, B.; Shafaei, S.; Szopko, R.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2008, 24, 6480. (26) Hoffmann, H.; Bergmeier, M.; Gradzielski, M.; Thunig, C. Prog. Colloid Polym. Sci. 1998, 109, 13. (27) Escalante, J. I.; Gradzielski, M.; Hoffmann, H.; Mortensen, K. Langmuir 2000, 16, 8653. (28) Soubiran, L.; Staples, E.; Tucker, I.; Penfold, J.; Creeth, A. Langmuir 2001, 17, 7988. (29) Courbin, L.; Delville, J. P.; Rouch, J.; Panizza, P. Phys. Rev. Lett. 2002, 89, 148305. (30) Courbin, L.; Pons, P.; Rouch, J.; Panizza, P. Europhys. Lett. 2003, 61, 275. (31) Partal, P.; Kowalski, A. J.; Machin, D.; Kiratzis, N.; Berni, M. G.; Lawrence, C. J. Langmuir 2001, 17, 1331. (32) Fritz, G.; Wagner, N. J.; Kaler, E. W. Langmuir 2003, 19, 8709. (33) Wilkins, G. M. H.; Olmsted, P. D. Eur. Phys. J. 2006, 21, 133. (34) van der Linden, E.; Hogervorst, W. T.; Lekkerkerker, H. N. W. Langmuir 1996, 12, 3127.
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Theoretical approaches have also been reported by several authors. In the pioneering work of Diat et al.,4 it has been shown that the observed relation R µ γ_ -1/2 can be explained using a simple equation derived by balancing the viscous stress with the elastic stress. However, another observed relation R µ d-2 µ φ 2 cannot be explained by this theory. However, van der Linden34 has derived a theoretical expression R µ φ2γ_ -1/2 balancing the surface stress with the shear stress. (See the last paragraph of the Discussion section.) It should be noted that these theories deal with the steady state after onions are formed. Zilman and Granek35 have proposed a model for the lamellar-to-onion transition. Accounting for the coupling with the shear flow of the short-wavelength undulation modes, they predict that onions are formed via the coherent buckling of lamellae above a critical shear rate γ_ C µ d-5/2D-1/2 µ φ5/2D-1/2 where D is the gap spacing. This power law has been confirmed experimentally by Courbin et al.29,30 However, the absolute value of the critical shear rate predicted by Zilman and Granek is about 3 103 s-1 for typical values of the parameters (D = 1 mm, d = 10 nm, η = 3 mPa s, and κ = kBT where η is the viscosity of solvent, κ is the bending modulus of the membranes, kB is the Boltzmann constant, and T is the absolute temperature), which is about 103 times larger than the observed values. Mallow and Olmsted36 have studied the suppression of the undulations in shear flow by modeling the flow as an effective anisotropic tension, which decreases the compression modulus. They consider two cases; if new layers can be generated by permeation or defects, then a decrease in lamellar spacing occurs. If the system cannot change the number of layers or the process is very slow, then an instability is induced for tension larger than σC µ (dD)-1 and this instability produces either cylinders or onions. Using the relation σC = ηγ_ Cd, they predicted the critical shear rate to be γ_ C µ d-2D-1 µ φ2D-1, which is a slightly different power law from that obtained by Zilman and Granek. However, the absolute values are about 2 104 s-1 for the same parameter values as described earlier, which is again 104 times larger than the experimental values. Thus, despite these intensive efforts, the necessary conditions and mechanism of the transition are still unclear. Binary systems of water and polyoxyethylene surfactants CnH2nþ1(OC2H4)mOH, abbreviated as CnEm, may be useful in investigating the transition mechanism because it has been known that a variety of phase behaviors can be observed at rest just by changing the temperature without any additives such as cosurfactants and salt. Richtering and co-workers13-21 have extensively studied the lamellar-to-onion transition in C10E3/water and C12E4/water systems. They have found that an intermediate structure oriented in the flow direction exists during the lamellar-to-onion transition in the C10E3 system, corresponding to long, multilamellar cylinders before the formation of spherical onions.14-16 It has also been shown that onion size varies reversibly with shear rate.17,18 In recent shear quench experiments, they have also found discontinuous size growth in addition to continuous size growth.20,21 In discontinuous growth, lamellar domains are formed and then transform into larger onions. Olsson and co-workers14-18,22-25 have reported that lamellae are transformed into onions with decreasing temperature at constant shear rate for the C10E3 and C12E4 systems. They explain their results in terms of the change in the saddle-splay modulus of bilayers with decreasing temperature (see later). Recently, they have also studied the shear-induced transitions by using deuterium Rheo-NMR spectroscopy as a function of time at several (35) Zilman, A. G.; Granek, R. Eur. Phys. J. B 1999, 11, 593. (36) Mallow, S.; Olmsted, P. D. Eur. Phys. J. E 2002, 8, 485.
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Figure 1. Phase diagram of the C16E7/D2O system at rest, adapted from ref 37. L1, micellar phase; W, dilute micellar phase; H1, hexagonal phase; V1, bicontinuous cubic phase; LR, lamellar phase. (a) Summary of the Rheo-SALS experiments at a shear rate of 3 s-1. The circles and crosses indicate the onion and lamellar states, respectively. The dotted line is used to guide the eyes. The diamonds indicate the points where the sample is presheared. (b) Constant contours of (d - δ)/d obtained from the results in Figure 10 (see the text) where d and δ are the repeat distance and the total thickness of bilayers in the lamellar phase at rest, respectively. The numbers indicate the values of (d - δ)/d.
temperatures and shear rates.25 It has been shown that the transition is continuous when onions are formed, starting from the oriented lamellar phase. However, a discontinuous nucleation-and-growth process with a coexistence region is observed when transforming onions into an oriented lamellar phase. It should be emphasized that the forgoing studies using polyoxyethylene surfactants under shear flow are performed only on the C10E3 and C12E4 systems that exhibit the lamellar-to-onion transition with decreasing temperature. In this article, we report for the first time the lamellar-to-onion transition with increasing temperature at constant shear rate by using simultaneous measurements of small-angle light scattering/shear stress (RheoSALS) and small-angle X-ray scattering/shear stress (RheoSAXS). This transition has been found in a C16E7/water system where phase behaviors and structures of the lamellar phase at rest have been studied in detail in our previous study.37 Because our findings are apparently controversial with respect to the results of the C10E3 and C12E4 systems, we discuss the necessary conditions for the lamellar-to-onion transition based on phase behavior and the change in lamellar spacing with temperature at rest.
2. Experimental Section Materials and Sample Preparation. C16E7 was purchased from Nikko Chemicals, Inc. in crystalline form (>98%) and used without further purification. Deuterium oxide purchased from ISOTEC, Inc. (99.9%) was used after being degassed by bubbling nitrogen to avoid oxidizing the ethylene oxide group of the surfactants. (We used D2O as the solvent instead of H2O following our previous study where 2H NMR is used to determine the phase diagram.37) Samples containing the desired amounts of surfactant and water (∼10 g) were sealed in an Erlenmeyer flask. For homogenization, we annealed samples for 3 h at about 55 °C with occasional shaking and then held them at room temperature for 21 h. This treatment was repeated for about 1 week. Figure 1a shows a previously reported phase diagram of the C16E7 system at rest.37 In the Rheo-SALS and Rheo-SAXS experiments, we first sheared the sample at a shear rate of 1 s-1 for 10 min at 48 °C corresponding to the bicontinuous cubic (V1) phase. Then the shear was stopped, and the sample was heated to the initial temperature in the lamellar phase without shear.
(37) Minewaki, K.; Kato, T.; Yoshida, H.; Imai, M.; Ito, K. Langmuir 2001, 17, 1864.
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Figure 2. Apparatus for simultaneous measurements of small-angle X-ray scattering/shear stress (Rheo-SAXS).
Rheo-SALS. The apparatus for Rheo-SALS experiments is almost the same as reported previously38 except for the insertion of the polarizer and analyzer. A schematic diagram for the apparatus is shown in detail in Figure 1 of Supporting Information. Rheo-SAXS. The apparatus for Rheo-SAXS experiments is schematically shown in Figure 2. A Couette cell made of polycarbonate consists of two concentric cylinders whose diameters are 27 and 29 mm. The thicknesses of the inner cylinder at the X-ray beam position and the outer cylinder are both 0.5 mm, and the height of the inner cylinder is 23 mm. The outer cylinder is fixed and the inner cylinder is attached to an AR550 rheometer (TA Instruments). The temperature of the cell is controlled to (0.1 °C by Peltier elements attached to the rheometer through the copper block surrounding the outer cylinder. To prevent sample evaporation, a vapor seal is incorporated into the cell. The experiments were carried out on beamline 15A at the photon factory (PF) of the High Energy Accelerator Research Organization (KEK), Tsukuba, Japan. The scattered X-rays were detected using the CCD area detector. The exposure time was 30 s. The approximate q range is from 0.3 to 3 nm-1. Two scattering configurations were used; one is the so-called radial configuration where the X-ray beam is directed through the center of the cell (along the velocity gradient direction), and the other is the tangential configuration where the beam is directed through the end of the cell (along the flow direction). The 2-D SAXS pattern in the flow-neutral (vorticity) plane is obtained in the radial configuration, whereas that in the velocity gradientneutral plane is obtained in the tangential configuration. For the lamellar structure, there are three principal orientations;perpendicular (or A), transverse (or B), and parallel (or C);with the layer normal along the neutral, flow, and velocity gradient directions, respectively. These three orientations can be detected by using both radial and tangential configurations. In our apparatus, the configuration can be changed within 10 s by using an automatic stage.
3. Results Temperature Dependence of the Shear Stress and Depolarized SALS at Constant Shear Rate. Figure 3 shows the temperature dependences of the shear stress and typical 2-D depolarized SALS patterns at constant shear rate. At a shear rate of 1 s-1, the shear stress slightly decreases as the temperature is increased up to 66 °C. When the temperature exceeds 67 °C, the shear stress increases abruptly and, at the same time, the SALS intensity at a particular azimuthal angle begins to increase. The shear stress is maximized at around 71 °C, above which a four-lobe pattern is observed in the SALS. At a shear rate of 3 s-1, the temperature dependence of the shear stress is similar to that at 1 s-1 (38) Kato, T.; Minewaki, K.; Miyazaki, K.; Kawabata, Y.; Komura, S.; Fujii, M. Prog. Colloid Polym. Sci. 2004, 129, 9.
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Figure 3. Temperature dependences of the shear stress and 2-D depolarized SALS patterns at shear rates of 1 s-1 (b) and 3 s-1 (O) for the sample containing 48 wt % C16E7 in D2O. The symbols on the upper abscissa indicate that the shear stress exceeds the limit of our apparatus (16.5 Pa). The directions of the flow and the polarizer are both horizontal.
up to 67 °C. At 68 °C, the shear stress increases more rapidly than at 1 s-1. Unfortunately, the upper limit of our apparatus is 16.5 Pa, so we could not measure the shear stress above 68 °C at this shear rate. The SALS exhibits a typical four-lobe pattern above 68 °C, which is much larger (extends to larger angles) than at 1 s-1. These results strongly suggest that the lamellae are transformed to onions when the temperature exceeds 67 °C. In these experiments, the temperature was increased stepwise and kept constant at each temperature until the SALS pattern did not change any more. At a shear rate of 1 s-1, however, the shear stress does not become constant near the transition temperature (Figure 2a of Supporting Information), suggesting that the system does not reach steady state. Therefore, the shear stress may increase more rapidly if the temperature is increased more slowly. The same does not always hold true for the results at 3 s-1, but we could not confirm it because of the saturation of the shear stress (Figure 2b of Supporting Information). A change in the SALS pattern for the cooling process at 3 s-1 is also included in Figure 3. As the temperature is decreased from 68 to 66 °C, the four-lobe pattern disappears, indicating that the transition is reversible against the change in temperature. As stated in the Introduction, the deuterium Rheo-NMR study of the C10E3 system25 shows that the transition is continuous when onions are formed from the oriented lamellar phase whereas a discontinuous nucleation-and-growth process with a coexistence region is observed when onions are transformed into an oriented lamellar phase. At present, we do not have enough data demonstrating such a difference between the heating and cooling processes. This point should be clarified in future studies. The 2-D SALS patterns were reduced to 1-D patterns in the direction of μ = 45° by integrating the scattering intensity over a segment of width of Δμ = (10° where μ is the azimuthal angle (the flow direction is set to 0°). Typical results are shown in Figure 4. It has been established that optically anisotropic spheres with a radius of R give a four-lobe pattern that has an intensity maximum at the scattering vector qmax given by39 4:1 qmax ¼ ð1Þ R (39) Samuels, R. J. J. Polym. Sci., Part A-2 1971, 9, 2165.
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Figure 4. One-dimensional depolarized SALS patterns in the direction μ = 45° where μ is the azimuthal angle (the flow direction is set to 0°) at 70 °C (0), 74 °C (4), and 78 °C (O) at a shear rate of 3 s-1 for the sample containing 48 wt % C16E7 in D2O.
Figure 6. Shear rate dependences of the shear stress and the 2-D depolarized SALS pattern at 65 °C (0), 67 °C (2), and 75 °C (O) for the sample containing 48 wt % C16E7 in D2O.
Figure 5. Temperature dependence of the diameter of onions obtained from the 1-D depolarized SALS pattern in Figure 4 at a shear rate of 3 s-1 for the sample containing 48 wt % C16E7 in D2O.
This relation is derived for isolated spheres. In the onion state, multilamellar vesicles of various sizes are closely packed so the observed SALS pattern is affected by interparticle diffraction. Then the observed 1-D SALS intensity is proportional to the product of the form factor for an anisotropic sphere and the structure factor depending on interparticle interactions. However, eq 1 can still be used to estimate the approximate onion size for the following reason. If the onion state is modeled as fcc closely packed spheres, the strongest peak is the (111) reflection expressed as 3π 3:9 q111 ¼ pffiffiffi ¼ R 6R
ð2Þ
Equations 1 and 2 indicate that a 1-D depolarized SALS pattern for fcc close packing has the strongest peak at almost the same position (the difference is about 10%) as that for isolated spheres, although the peak width should become narrow. In this study, therefore, we have estimated the onion size by using eq 1. Figure 5 shows the temperature dependence of the diameter of onions (2R) at a shear rate of 3 s-1. The error due to the uncertainty in the determination of the peak position is within the size of the symbol. It can be seen from the Figure that the onion size increases with increasing temperature. Such a temperature dependence has not yet been reported. As seen from Figure 4, the growth in onion size accompanies the narrowing of the size distribution. Shear-Rate Dependence of the Shear Stress and Depolarized SALS at Constant Temperature. We have also performed Rheo-SALS measurements as a function of the shear rate at different temperatures. The results are shown in Figure 6. At 65 °C, the SALS pattern does not change, at least not below 10 s-1. This suggests that the transition to the onion does not occur at this temperature, which is consistent with the results of the temperature-scan experiments shown in Figure 3. The doublelogarithmic plot of the shear stress (σ) versus the shear rate _ becomes a straight line with a slope of 0.52 ( 0.02, corre(γ) _ γ_ -0.48(0.02. sponding to the power law σ µ γ_ 0.52(0.02 or η = σ /γµ 23 Oliviero et al. have measured the viscosity for the lamellar phase 3838 DOI: 10.1021/la903251v
Figure 7. Temperature-shear rate diagram for the sample containing 48 wt % C16E7 in D2O. The circles and crosses indicate the onion and lamellar states, respectively, and the triangles indicate the transition region where the scattering intensity in the low-q region ( flow direction. When the temperature increases from 67 to 69 °C, both radial and tangential patterns become isotropic. At the same time, the shear stress increases more than 1 order of magnitude. (The upper limit (42) Miyazaki, K.; Kosaka, Y.; Kawabata, Y.; Komura, S.; Kato, T. J. Appl. Crystallogr. 2007, 40, s332.
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Figure 9. Temperature dependences of the shear stress and 2-D SAXS patterns for the radial (upper patterns) and tangential (lower patterns) configurations at a shear rate of 3 s-1 for the sample containing 48 wt % C16E7 in D2O. The numbers at the bottom of the SAXS pattern indicate q values in nm-1. Letters a-g are added to refer to the azimuthal intensity distributions in Figure 5 of the Supporting Information.
of the Rheo-SAXS apparatus is much larger than that that of the Rheo-SALS apparatus.) These results are consistent with the SALS results (i.e., the lamellar-to-onion transition with increasing temperature). It should be noted, however, that the temperature is raised every 30 min in these experiments and that near the transition temperature the shear stress does not reach the steady-state value (Figure 4 of Supporting Information). We have also obtained azimuthal intensity distributions recorded at the Bragg peak position for the radial configuration. The results are shown in Figure 5 of the Supporting Information, where the flow direction is set to 0°. At 67 °C (a in Figure 5 of Supporting Information), there are two sharp peaks at 90 and 270° (neutral direction). These two peaks become broad as the temperature increases, and at 71.4 °C (d in Figure 5 of Supporting Information), the intensity distribution becomes almost flat, as expected from the structure of the onions. As the temperature increases further, however, additional peaks appear at 0, ∼70, ∼110, and 180°, which may be a precursor of the transition into the long-range-ordered structures reported for other systems.6,22 This expectation is confirmed by the variation in the 1-D SALS patterns in Figure 4 that suggests that the size distribution of onions becomes narrow with increasing temperature.
4. Discussion Elastic Properties of Isolated Bilayers and the Lamellarto-Onion Transition. Le et al. have shown that the lamellae are transformed to onions with decreasing temperature at constant shear rate for the C10E3/water15 and C12E4/water22 systems. They explain their results in terms of the saddle-splay modulus of isolated bilayers at rest as shown below. The free energy of a vesicle relative to a flat bilayer can be written as43 F ¼ 4πð2K þ KÞ
ð3Þ
where κ and κh are the bending modulus and saddle-splay modulus of a bilayer, respectively. Saddle-splay modulus κh is negative (43) Helfrich, W. J. Phys.: Condens. Matter 1994, 6, A79.
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unless the L3 phase is stable. By using κ and the saddle-splay modulus of a monolayer κhm, κh can be expressed as44,45 K ¼ 2K m -δH0m K
ð4Þ
where δ is the thickness of a bilayer and H0m is the spontaneous curvature of a monolayer. In the polyoxyethylene surfactant systems, H0m strongly depends on temperature. Anderson et al.46 have approximated the temperature dependence of H0m by a firstorder Taylor expansion around T = T0 where H0m = 0 H0m = βðT0 -TÞ
ð5Þ Figure 10. (a) Temperature dependences of the repeat distance
to explain the phase boundary of the L3 phase for various surfactant systems including binary systems of CnEm/water (β is an empirical constant). Strey47 have shown experimentally that eq 5 holds over the temperature range of T0 ( 30 K (T0 = 32.6 °C and β = 1.22 10-3 A˚-1) for the water/n-octane/C12E5 system by using small-angle neutron scattering. For binary systems of CnEm/ water, T0 corresponds to the temperature where the dilute lamellar phase extends to the lowest surfactant concentration.46,48 By inserting eq 5 into eq 4, we obtain K ¼ 2K m þ δKβðT -T0 Þ
ð6Þ
According to eq 6, κh decreases (becomes more negative) as the temperature is decreased, which leads to a decrease in the free energy of a vesicle relative to a flat bilayer assuming that the temperature dependence of κ can be neglected compared to that of κh. Although the effects of shear flow are not taken into account in these equations, the results are consistent with the lamellar-toonion transition with decreasing temperature reported for the C10E3 and C12E4 systems. However, the same does not hold true for the C16E7 system, which exhibits the lamellar-to-onion transition with increasing temperature. In the next paragraph, therefore, we consider factors other than the elastic properties of isolated bilayers. Necessary Conditions for Lamellar-to-Onion Transition with Increasing Temperature. Figure 1a demonstrates that the transition temperature increases rapidly with a slight increase in surfactant concentration. In other words, the onion cannot be formed above a certain critical concentration at constant temperature and shear rate. As described in the Introduction, Diat et al.4 have made an orientation diagram under shear for the lamellar phase of the SDS/pentanol/water/decane system. They have shown that the critical shear rate (γ_ C) necessary for the transition to onions increases with increasing surfactant volume fraction (φ). This means that the onion cannot be formed above the critical volume fraction at constant shear rate. The most significant difference is that the critical volume fraction decreases with increasing temperature in our system. For theoretical approaches in the lamellar phase, effects of surfactant concentration are taken into account through the repeat distance d assuming the relation φ = δ/d, which holds true for the lamellar phase without any defects. Therefore, the existence of the critical volume fraction may come from the existence of the critical repeat distance (dC), below which the onion state becomes unstable. (44) Porte, G..; Appel, J.; Bassereau, P.; Marignan, J. J. Phys. (Paris) 1989, 50, 1335. (45) Sziefer, I.; Kramer, D.; Ben-Shaul, A.; Gelbart, W. M.; Safran, S. A. J. Chem. Phys. 1990, 92, 6800–6817. (46) Anderson, D.; Wennerstrom, H.; Olsson, U. J. Phys. Chem. B 1989, 93, 4243. (47) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (48) Zilman, A.; Safran, S. A.; Sottmann, T.; Strey, R. Langmuir 2004, 20, 2199.
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(d) and the thickness of bilayers (δ) at different concentrations obtained from the analyses of SAXS patterns at rest reported previously.37 (b) Temperature dependence of the water-layer fraction (d - δ)/d obtained from the data shown in panel a.
In our previous study,37 we have investigated phase behaviors and structures of the lamellar phase at rest for the C16E7/water system by using small-angle X-ray scattering. We have shown that the concentration dependence of the repeat distance follows the power law d µ φhc-s where φhc is the volume fraction of the hydrophobic part. The exponent s at 70 and 75 °C is unity as expected for the usual lamellar phase. As the temperature decreases below about 70 °C (∼T0), however, s decreases to about 2 /3. This may result from the fact that there exist water-filled defects (holes) in bilayer sheets49 below 70 °C and that their fraction increases with decreasing temperature. Figure 10a shows the temperature dependence of the repeat distance at rest for different concentrations. This Figure demonstrates that the repeat distance increases with increasing temperature (which corresponds to the decrease in the fraction of waterfilled defects). Suppose that there exists the critical repeat distance dC for a given shear rate and that the repeat distance at the given temperature is slightly smaller than dC. Onions cannot be formed at this temperature. As the temperature increases, the repeat distance exceeds dC, which enables the transition to the onion . If we set dC equal to 6.5 nm at a shear rate of 3 s-1, then the lamellarto-onion transition temperatures at 48 and 51 wt % are obtained to be about 60 and 65 °C, respectively, from Figure 10a. In addition, the transition does not occur at 55 wt % in the temperature range studied. These predictions are qualitatively consistent with the results in Figure 1a in the sense that the transition temperature increases rapidly with increasing concentration. However, quantitative agreement could not be obtained even when other dC values were chosen. This may result from the fact that the repeat distance and the thickness of the bilayers are of the same order of magnitude in the concentration range studied. In our previous study,37 we also obtained the half-thickness of the hydrophobic layer (dhc) and the thickness of the hydrophilic layer (deo) from the analysis of the SAXS pattern. Figure 10a includes the total thickness of bilayers δ calculated from dhc and deo (δ = 2dhc þ 2deo). It can be seen from the Figure that δ slightly decreases with increasing temperature. Therefore, the water-layer thickness (d - δ) increases with increasing temperature more rapidly than d itself does. Figure 10b illustrates the temperature dependence of the water-layer fraction (d - δ)/d. From these data, we have obtained constant contours of (d - δ)/d and have plotted them in the phase diagram at rest. The results are shown in Figure 1b. Comparing panels a and b of Figure 1, one may deduce that the onion can be formed only when (d - δ)/d exceeds a critical value (∼0.24). In other words, an increase in the water-layer (49) Fairhurst, C. E.; Holmes, M. C.; Leaver, M. S. Langmuir 1997, 13, 4964.
Langmuir 2010, 26(6), 3835–3842
Kosaka et al.
Article
Table 1. Lamellar/Onion Transition Temperatures at Constant Shear Rate, Upper Limit of the Lamellar Phase at Rest, and T0 (Temperature Where the Spontaneous Curvature Becomes Zero) systems
types of transitions with increasing temperature
transition temperature (°C)
shear rate (s-1)
concentration
upper limit of the lamellar phase at rest (°C)a
T0 (°C)
onion to lamellar 36-39 10 44 vol % ∼40
