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Shear-Induced States of Orientation of the Lamellar Phase of C12E4/Water Stefan Mu¨ller, Claus Bo¨rschig, Wolfram Gronski, and Claudia Schmidt* Institut fu¨ r Makromolekulare Chemie, Universita¨ t Freiburg, Stefan-Meier-Strasse 31, D-79104 Freiburg, Germany
Didier Roux Centre de Recherche Paul Pascal, CNRS, Avenue A. Schweitzer, F-33600 Pessac, France Received April 9, 1999 The shear-induced states of orientation of the lamellar lyotropic mesophase of tetraethylene glycol monododecyl ether (C12E4) in water are investigated by polarizing microscopy, viscometry, small-angle light scattering, and deuteron NMR spectroscopy. The solution containing 40 w/w % surfactant shows a continuous transition from a state of aligned layers, whose normal is parallel to the velocity gradient, to a close packing of multilamellar vesicles (onion state). The size of the vesicles (diameter d) is controlled by the shear rate γ˘ , following the relationship d ∝ γ˘ a with a ≈ -0.5.
1. Introduction Shear-induced changes of structure and orientation in lyotropic liquid crystalline phases of surfactant solutions have met increasing interest over the past few years.1 The rheological properties of lyotropic liquid crystals are often affected by their mechanical history, which may result in a modification of the microscopic structure of the material. Knowledge about such effects is important for applications, which often depend on the viscosity of a lyotropic phase. To investigate structural changes in shear flow, the in situ application of techniques that monitor microscopic structures on different length scales has proven very powerful. Especially materials with a lamellar structure show a rich variety of shear-induced orientation states. Different states of orientation under shear have been observed not only for lyotropic lamellar phases2-18 but also for ther* Author for ruf.uni-freiburg.de.
correspondence:
E-mail:
schmidtc@
(1) Herb, C. A., Prud’homme, R. K., Eds.; Structure and Flow in Surfactant Solutions; ACS Symposium Series 578; American Chemical Society: Washington, DC, 1994. (2) Diat, O.; Roux, D. J. Phys. II Fr. 1993, 3, 9. (3) Diat, O.; Roux, D.; Nallet, F. J. Phys. II Fr. 1993, 3, 1427. (4) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. (5) Roux, D.; Nallet, F.; Diat, O. In Structure and Flow in Surfactant Solutions; ACS Symposium Series 578; Herb, C. A., Prud’homme, R. K., Eds.; American Chemical Society: Washington, DC, 1994; Chapter 21. (6) Soubiran, L.; Coulon, C.; Sierro, P.; Roux, D. Europhys. Lett. 1995, 31, 243. (7) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (8) Sierro, P.; Roux, D. Phys. Rev. Lett. 1997, 78, 1496. (9) Lukaschek, M.; Mu¨ller, S.; Hasenhindl, A.; Grabowski, D. A.; Schmidt, C. Colloid Polym. Sci. 1996, 274, 1. (10) La¨uger, J.; Linemann, R.; Richtering, W. Rheol. Acta 1995, 34, 132. (11) Weigel, R.; La¨uger, J.; Richtering, W.; Lindner, P. J. Phys. II Fr. 1996, 6, 529. (12) Richtering, W. Prog. Colloid Polym. Sci. 1997, 104, 90. (13) Zipfel, J.; Lindner, P.; Richtering, W. Prog. Colloid Polym. Sci. 1998, 110, 139. (14) Berghausen, J.; Zipfel, J.; Lindner, P.; Richtering, W. Europhys. Lett. 1998, 43, 683. (15) Zipfel, J.; Berghausen, J.; Lindner, P.; Richtering, W. J. Phys. Chem. B 1999, 103, 2841. (16) Penfold, J.; Staples, E.; Khan Lodhi, A.; Tucker, I.; Tiddy, G. J. T. J. Phys. Chem. B 1997, 101, 66.
motropic smectic liquid crystals,19,20 and for lamellar block copolymers.21 To characterize different orientation states, the three principal orientations of the layer normal (director) are labeled a, b, and c, if the director points parallel to the vorticity, parallel to the velocity, and parallel to the velocity gradient, respectively.19,22 Often the orientations a, b, and c are referred to as perpendicular, transverse, and parallel. A theoretical stability analysis of the smectic A phase under shear has shown that different stable orientations should be possible, depending on the viscosity parameters.23 In experiments on lamellar surfactant mesophases both the c (parallel)2-4,13-16,19 and the a orientation (perpendicular)12-16 as well as mixtures of c and a15,16 have been observed. In addition, a unique defect structure, consisting of close-packed, almost monodisperse, multilamellar vesicles, also called onions, was found.2-4 This shear-induced state was first investigated in detail by Roux and collaborators in the systems sodium bis(2ethylhexyl)sulfosuccinate (AOT)/brine2,6,24,25 and sodium dodecyl sulfate (SDS)/pentanol/dodecane/water,3-6,25 and has later been also reported for other surfactant systems, such as C12E4/water,9,11-13 SDS/octanol/brine,7,8 and a cationic/nonionic surfactant lamellar phase.17 Studies of the shear-induced formation of onions as a function of surfactant concentration have shown that the shearinduced transition from aligned lamellae to onions is shifted to higher shear rates when the volume fraction of the surfactant layers is increased.3-5,9 In some binary systems with a relatively high surfactant concentration, (17) Penfold, J.; Staples, E.; Tucker, I.; Tiddy, G. J. T.; Khan Lodi, A. J. Appl. Crystallogr. 1997, 30, 744. (18) Bergenholtz, J.; Wagner, N. J. Langmuir 1996, 12, 3122. (19) Safinya, C. R.; Sirota, E. B.; Bruinsma, R. F.; Jeppesen, C.; Plano, R. J.; Wenzel, L. J. Science 1993, 261, 588. (20) Panizza, P.; Archambault, P.; Roux, D. J. Phys. II 1995, 5, 303. (21) Wiesner, U. Macromol. Chem. Phys. 1997, 198, 3319. (22) Miesowicz, M. Nature 1946, 158, 27. (23) Carlsson, T.; Leslie, F. M. Liq. Cryst. 1996, 20, 697. (24) Gulik-Krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. Langmuir 1996, 12, 4668. (25) Panizza, P.; Roux, D.; Vuillaume, V.; Lu, C.-Y. D.; Cates, M. E. Langmuir 1996, 12, 248.
10.1021/la9904105 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/19/1999
Orientation of the Lamellar Phase of C12E4/Water
no vesicles have been observed,9,10 probably because of an insufficient bending flexibility of the membranes.26 Even when solid particles are dispersed in the lamellar phase, the onion state can be induced by shear.27 This was demonstrated both for sterically stabilized poly(methyl methacrylate) particles in the SDS/dodecane/pentanol/ water system and for charge-stabilized poly(styrene) particles in AOT/brine mixtures. In both cases, the particles were encapsulated in the onion cores, forming “stuffed” onions.27 In analogy to equilibrium phase diagrams, the different shear-induced states can be presented in a dynamic orientation diagram that shows the state of orientation as a function of sample composition and shear rate.3,4 The orientation diagrams of AOT/brine2,6 and SDS/pentanol/ dodecane/water3-6,19,25 show three regimes. Region I at lowest shear rates is a state of flow-aligned lamellae with the layer normal parallel to the velocity gradient (c orientation), region II at intermediate shear rates is the onion state, and region III at high shear rates shows again lamellae aligned in the c orientation. The dynamic transitions between the different states may be continuous or discontinuous.3-5,8 The different states of orientations and the transitions in these two surfactant systems have been studied by a variety of different techniques, for instance, light,2,3 neutron3 and X-ray scattering,19 microscopy,2,3 birefringence,3 rheology,4,5,25 conductivity measurements,6 and freeze-fracture electron microscopy.24 The shear-rate dependent states do not always follow the same sequence, parallel/onions/parallel; there is a considerable variation in the orientation diagrams for different systems. C12E4/water, for example, shows only the c state at low shear rates and the onion state,9 while SDS/octanol/brine7,8 shows a hexagonal packing of onions and a transition from small onions to large onions.8 A hexagonal structure was also observed for AOT/brine, but only in a biphasic regime together with ordered lamellae, which survive at high shear stress.18 For other systems, no vesicles but a transition from the c to the a orientation has been observed, with a superposition of both orientations in between. Such a behavior was found for C16E6/ water.16,17 A superposition of parallel and perpendicular orientations is also a possible explanation for the NMR spectra observed at higher shear rates in the C12E6/water system.9 A similar sequence, c orientation (or c + a) at low shear rate and a orientation at high shear rate, has been reported for the thermotropic smectic A phase of 4-n-octyl4′-cyanobiphenyl (8CB).19,20 The perpendicular orientation, which has been observed not only in surfactant systems but also in lamellar block copolymers,21 is only possible if the layers are liquid because a relative motion between the molecules in one layer must be possible to sustain the flow.19 A more complex orientation diagram was found for the system SDS/decanol/water which was studied in the regime of the defective and defect-free lamellar phase, depending on the decanol concentration.12-15 The defectfree LR phase shows only a transition c to a, whereas in the defective LR phase a region of vesicles in the orientation diagram has been reported. At very low decanol content in the defective LR phase, the sequence c/a/c was observed in the experimentally accessible range of shear rates. Multilamellar vesicles have been found in the LR region of several surfactant phase diagrams, even when no explicit shear was applied to the system. The vesicles were (26) Roux, D.; Safinya, C. R.; Nallet, F. In Micelles, Membranes, Microemulsions, and Monolayers; Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; Springer-Verlag: New York, 1994; Chapter 6. (27) Arrault, J.; Grand, C.; Poon, W. C. K.; Cates, M. E. Europhys. Lett. 1997, 38, 625.
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identified, for example, by direct observation with freezefracture transmission electron microscoy.28-33 In some cases, the vesicles seemed to form spontaneously,28,32,34,35 and the corresponding regions of the phase diagrams have 36-38 and L or L .28,39 It has been shown, been labeled L+ Rv R1 R however, that weak shear forces may be sufficient to transform stacked layers into vesicles,29 and the vesicle “phases” are probably metastable states of the LR phase. While the vesicles generated during simple mixing of the sample are usually polydisperse, the vesicles produced by constant-rate shear have a very narrow size distribution. It has been shown that the diameter d of the vesicles decreases upon increasing shear rate, following the scaling law d ∝ γ˘ a with an exponent a ≈ -0.5.2,3 The decrease of the size under increasing shear rate was also confirmed by deuteron NMR spectroscopy9 and has been observed by Bergmeier et al.30 For the AOT/brine system the applied shear stress was considered as the control parameter for the generation of a well-defined steady state and it was reported that controlled shear rate rheometry does not lead to a pure vesicle state.18 Panizza et al., on the other hand, have demonstrated in the case of SDS/pentanol/ dodecane/water that a sudden change of the shear rate leads to a transient size change and a well-defined final state.40 For the present study we have chosen the system C12E4/ water. The phase diagram41 shows a broad lamellar phase with a L+ R region, which has been assumed to consist of vesicles.36 A more detailed, but still incomplete phase diagram can be found in refs 37 and 38. First indications for the shear-induced formation of multilamellar vesicles that become smaller with increasing shear rate came from deuteron NMR spectra obtained in situ under shear.9 The onion state occurs only in the dilute regime; for higher concentrations no vesicles have been found.9,10 Besides the state of onions, which may show elongations and/or disorder at high shear rates,13 no other state of orientation was found. The relationship d ∝ γ˘ -0.3 has been reported for this system.13 In this paper, the transition from the c orientation to the onion state in C12E4/water is studied for the first time by different techniques, namely, NMR, microscopy, and light scattering, and the results obtained by the different methods are correlated. The focus of this work is on the transition from aligned lamellae to multilamellar vesicles. In addition, the scaling law relating vesicle size and shear rate is investigated. (28) Hoffmann, H.; Thunig, C.; Schmiedel, P.; Munkert, U. Langmuir 1994, 10, 3972. (29) Bergmeier, M.; Hoffmann, H.; Thunig, C. J. Phys. Chem. B 1997, 101, 5767. (30) Bergmeier, M.; Gradzielski, M.; Hoffmann, H.; Mortensen, K. J. Phys. Chem. B 1998, 102, 2837. (31) Bergmeier, M.; Hoffmann, H.; Witte, F.; Zourab, S. J. Colloid Interface Sci. 1998, 203, 1. (32) Versluis, P.; van de Pas, J. C.; Mellema, J. Langmuir 1997, 13, 5732. (33) Auguste, F.; Douliez, J.-P.; Bellocq, A.-M.; Dufourc, E. J. Langmuir 1997, 13, 666. (34) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J. Chem. Phys. 1992, 96, 6698. (35) Oberdisse, J.; Couve, C.; Appell, J.; Berret, J. F.; Ligoure, C.; Porte, G. Langmuir 1996, 12, 1212. (36) Jonstro¨mer, M.; Strey, R. J. Phys. Chem. 1992, 96, 5993. (37) Olsson, U.; Nakamura, K.; Kunieda, H.; Strey, R. Langmuir 1996, 12, 3045. (38) Strey, R. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 182. (39) Schoma¨cker, R.; Strey, R. J. Phys. Chem. 1994, 98, 3908. (40) Panizza, P.; Colin, A.; Coulon, C.; Roux, D. Eur. Phys. J. B 1998, 4, 65. (41) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.
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2. Experimental Section 2.1. Materials. The surfactant tetraethylene glycol monododecyl ether (C12E4, 98% purity by gas chromatography) was purchased from Fluka and used without further purification. The phase diagram of C12E4 with H2O shows a lamellar phase over a large range of concentrations at room temperature.37,38,41 The region of the lamellar phase at low surfactant concentration and low temperature where multilamellar vesicles are easily formed and 37,38 At stable for a long time has been denoted L+ R. concentrations below approximately 50 w/w % surfactant, the lamellar phase has a transition to an isotropic micellar phase (L1) at about 20 °C or lower, depending on the surfactant concentration. The investigations presented here were performed in the L+ R region, mostly on a mixture of 40 w/w % surfactant in heavy water. Homogeneous samples were obtained by cooling the mixtures to 10 °C into the isotropic phase and homogenizing them in a vibrating mill. On heating, the 40 w/w % mixture has an isotropic to lamellar transition at 18 °C. To avoid any uncontrolled preshearing of the lamellar phase, the samples were filled into the shear tools while in the isotropic phase and then heated into the lamellar phase. All shear experiments were performed on the lamellar phase at room temperature. 2.2. Viscometry and Rheo-SALS. Shear experiments with simultaneous measurements of viscosity and smallangle light scattering (SALS) were carried out with the rheo-SALS apparatus shown schematically in Figure 1a.42 The instrument consists of a stress-controlled Bohlin CS 50 melt rheometer that is equipped with a setup for smallangle light scattering. The experiments were performed in a 3° cone-and-plate cell with a diameter of 40 mm, made of quartz glass. The tight construction of the cell and the large filling volume of about 900 µL keep evaporation of water negligible for about 12 h. The primary light source is a He-Ne laser operating at a wavelength (λ) of 632.8 nm. The total intensity is adjusted by neutral density filters (A). After passing through a rotating glass plate to avoid speckle patterns (B) and a focusing lens (C), the beam is repolarized by a linear polarizer (D). A λ/2 plate (E) allows the plane of polarization to be turned. Behind two pinholes to avoid stray light, the primary beam is diverted by a mirror into the shear cell. The scattered light passes through a polarization analyzer (G) and is detected by a twodimensional CCD chip with 512 × 512 pixels and a dynamic range of 18 bits, allowing a direct intensity detection over 4 orders of magnitude. A special focusing system consisting of four lenses is used to focus the scattered light onto the small active chip area with minimum smearing effects. The intensity of the unscattered primary beam is reduced by a small piece of a neutral density filter located directly in front of the detector. Thus, both the detection of very low scattering intensities and the control of the position of the primary beam during the experiment are possible. For the experiments presented here, the primary beam was located close to one of the corners of the chip in order to enhance the range of the scattering vector q ) (4π/λ) sin(θ/2), where θ is the scattering angle. The q values detected range from 0.3 to about 5 µm-1. A sample containing 40 w/w % surfactant with an average refractive index of n ) 1.38 was used. 2.3. Optical Microscopy. First microscopic observations were performed in situ using a home-built shear cell. Since the shear-induced states are very stable, later (42) La¨uger, J.; Gronski, W. Rheol. Acta 1995, 34, 70.
Figure 1. Experimental setup for rheo-SALS (a) and rheoNMR experiments (b).
experiments were performed on samples that had been sheared either in the SALS or in the NMR shear cell until a characteristic shear state, as verified by SALS or NMR, was reached and had then been transferred onto a microscope slide. The samples were observed between crossed polarizers using a Leitz Ortholux Pol BK II microscope. The optical axis of the samples was determined by inserting a λ plate between the crossed polarizers. 2.4. 2H NMR Spectroscopy. For the NMR experiments under shear a cone-and-plate cell, as shown schematically in Figure 1b, was used.43 This cell is integrated into an NMR probe for a superconducting magnet. Its axis is aligned parallel to the external magnetic field. Thus the observed quadrupole splittings yield the angle β between the director (the bilayer normal) and the velocity gradient axis, which is parallel to the magnetic field. The diameter of the shear tools is 15 mm, and the gap angle is 5°. Shear is applied by driving the plate with an external motor located below the NMR magnet. The shear cell is surrounded by a cylinder filled with perfluorotri-n-butylamine (boiling point 437 K) serving as a solvent trap to avoid water evaporation. Measurements can be run for 30 h without detectable loss of D2O from the shear cell. The spectra were recorded with a Bruker MSL 300 (43) Grabowski, D. A.; Schmidt, C. Macromolecules 1994, 27, 2632.
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Figure 2. Viscosity of a lamellar sample (40 w/w % C12E4) under steady-state shear conditions as a function of the shear rate γ˘ . Three different regimes are observed: a shear-thinning region (I), a shear-thickening region (I-II), and a second shearthinning region at high shear rates (II). The data points are connected to guide the eye.
spectrometer using a quadrupole echo sequence with full phase cycling. With the saddle-shaped NMR coil surrounding the shear cell, pulse durations of 18 µs for a 90° pulse at the resonance frequency of 46.07 MHz for deuterons are obtained. Typically, 128 scans were accumulated for each spectrum, and a recycle delay of 0.5 s was used.
Figure 3. Optical micrographs of the different shear regimes. (a) Mosaic texture of the unsheared sample; (b) region I-II with isolated multilamellar vesicles dispersed in a lamellar matrix (γ˘ ) 1 s-1); (c) beginning of region II showing a close packing of multilamellar vesicles (γ˘ ) 3 s-1); (d) region II at higher shear rate with smaller close-packed vesicles (γ˘ ) 10 s-1).
3. Results 3.1. Viscometry. The sample was sheared in the rheoSALS apparatus at different shear rates (γ˘ ), starting from the lowest shear rate of 0.1 s-1. Each shear rate was applied until the viscosity (η) remained constant. At shear rates below 10 s-1 it takes about 2 h to reach the steady state of constant viscosity. The steady-state viscosity in dependence on the shear rate is shown in Figure 2. Three regions with different rheological behavior, labelel I, I-II, and II, can be discerned. In region I, at shear rates below 0.4 s-1, shear thinning is observed. The viscosity reaches its minimum of about 5 Pa s at approximately 0.4 s-1. This first region is followed by a regime of increasing viscosity, the transition region I-II. This region of shearthickening extends approximately from 0.4 to 5 s-1. As the shear rate is further increased, a second shear-thinning regime (region II) is observed. Here, the viscosity decreases to values well below the initial viscosity. The lowest value measured was η ≈1.5 Pa s at γ˘ ) 80 s-1. 3.2. Optical Microscopy. The different regions described above can also be identified by their textures observed by polarizing microscopy, as shown in Figure 3. Figure 3a shows the characteristic mosaic texture of the nonoriented lamellar phase of the 40 w/w % C12E4 solution, while Figure 3b-d shows textures of samples that were presheared at different shear rates. After the sample had been sheared at a rate of γ˘ ) 1 s-1 (Figure 3b), isolated spherulites with diameters from 10 to 20 µm are observed within a flow-oriented lamellar matrix that shows no characteristic texture. The optical axis of the matrix is perpendicular to the flow caused by shear forces imposed on the sample during its transfer onto the microscope slide. When the optical axis of the matrix is parallel to one of the crossed polarizers, the spherulites appear as very weak, but regular Malthesian crosses, while the matrix itself is dark (not shown). Figure 3b shows the sample with the optical axis of the matrix diagonal to the crossed polarizers. For both diagonal orientations, the two quadrants parallel to the optical axis of the matrix are bright, whereas the remaining two quadrants are dark. At higher shear rates, the texture becomes more regular, indicating close-packed monodisperse spherulites, as shown in Figure 3c for a sample
Figure 4. Depolarized SALS pattern recorded for a sample with 40 w/w % surfactant under shear flow at the shear rates indicated. Only one quadrant is detected in the velocityvorticity plane. In region I-II a four-lobe pattern is observed, whereas region II gives rise to a Bragg peak.
presheared at γ˘ ) 3 s-1. With increasing shear rate, the characteristic size of the structure becomes smaller, as can be seen in Figure 3d for a sample presheared at γ˘ ) 10 s-1. The observed textures are stable; even after several days, no change was recognized. 3.3. Rheo-SALS. The rheo-SALS experiments confirm the shear-induced shear-rate-dependent formation of the structure detected by polarizing microscopy. No significant scattering pattern is observed at low shear rates (region I). The SALS patterns obtained in regions I-II and II are shown in the first pictures of Figures 4 and 5 for the depolarized and polarized case, respectively. Only one quadrant of the pattern was detected, with the origin near the upper left corner. The beginning of region I-II is characterized by the appearance of a four-lobe pattern, as shown in Figures 4 and 5. This type of pattern can be explained by the isolated anisotropic spherulites or vesicles,44,45 which are also observed in real space by microscopy. With increasing shear rate, the size of the four-lobe pattern becomes larger, indicating that the spherulites become smaller. At the beginning of region II (44) Stein, R. S.; Rhodes, M. B. J. Appl. Phys. 1960, 31, 1873. (45) Stein, R. S.; Wilkes, G. L. In Structure and Properties of Oriented Polymers; Ward, I. M., Ed.; Applied Science Publishers Ltd.: London, 1975; Chapter 13.
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Figure 5. Polarized SALS pattern recorded for a sample with 40 w/w % surfactant under shear flow at the shear rates indicated. Only one quadrant is detected in the velocityvorticity plane. As in Figure 4, the crossover to region II at about 4 s-1 can be seen.
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Figure 7. Value of the q vector at the maximum of the Bragg peak, qmax, as a function of the square root of the shear rate, γ˘ 1/2.
Figure 6. Scattered intensity I of the Bragg peaks in region I as a function of the scattering vector q for depolarized scattering at shear rates of 8 (a), 15 (b), and 35 s-1 (c).
(γ˘ ≈ 5 s-1), the four-lobe pattern transforms into a Bragg peak with a sharp intensity maximum. Upon increasing shear rate the Bragg peak is shifted to larger q values, showing that the characteristic size of the pattern in real space decreases. When circularly polarized light is used, a ring of scattered light is observed. This ring can be regarded as a superposition of the polarized and the depolarized pattern. Both the depolarized and the polarized scattering patterns yield the same value of qmax, the q value where the maximum intensity is observed. Figure 6 depicts the scattering intensity vs q for the depolarized case, showing the Bragg peaks for several shear rates. The range of shear rates where the Bragg peaks are observed coincides well with both the observation of a close-packed structure by microscopy and with the detection of NMR spectra characteristic of region II, as described below. The plot of the Bragg peak position, qmax, vs the square root of the shear rate, depicted in Figure 7, shows an almost linear relationship. A linear regression of ln(qmax) vs ln(γ˘ ) yields an exponent of 0.61, if the whole range of shear rates is taken into account, and qmax ∝ γ˘ 0.53 if only the range 10 s-1 < γ˘ < 70 s-1 is considered. The latter value of the exponent appears more reliable as it is not clear whether the state of monodisperse, perfectly packed vesicles was really reached at the lower shear rates. Using the relationship d ) 2π/qmax, derived from the Bragg equation with N ) 1 for the order of the observed peak, the diameter d of the close-packed vesicles has been calculated. In region II, the diameter of the vesicles ranges from 6 µm at γ˘ ) 4.5 s-1 to 1.5 µm at γ˘ ) 45 s-1. The sizes determined in this way agree well with the microscopic observations. The shear-induced vesicle structure remains stable for at least several days after cessation of shear. The SALS
Figure 8. Deuteron NMR spectra obtained at different shear rates, given to the right of each spectrum in s-1 for samples with 35 w/w % surfactant (left) and 40 w/w % surfactant (right).
patterns do not change, indicating the stability of the structure. This provides the possibility to perform further experiments under shearless conditions to investigate the shear-induced structure in more detail, for example, by microscopy as described above. In region II, the state of close-packed vesicles, the experimental observations are fully reproducible and reversible. Lowering the shear rate leads to an increase of the vesicle size. The light scattering pattern is controlled only by the shear rate; it is independent of the mechanical history of the sample, showing that a true steady state is reached. 3.4. Deuteron NMR. NMR spectra of D2O in the lamellar phase during shear are shown in Figure 8 for samples with surfactant concentrations of 35 and 40 w/w %. The spectra were recorded under steady-state shear conditions. The deuteron NMR spectra are governed by the electric quadrupole interaction between the quadrupole moment of the spin I ) 1 nucleus and the electric field gradient at the site of the nucleus. This interaction is averaged by the rapid anisotropic motion of the water molecules, resulting in a reduced quadrupole splitting
∆ν ) (3/4)δ(3 cos2 β - 1)
(1)
is the motionally averaged quadrupole where δ ) e coupling constant and β the angle between the director and the external magnetic field. Only molecular motions involving rotations affect the average value δ. The overall line shape depends on the orientational distribution of 2qQ/h
Orientation of the Lamellar Phase of C12E4/Water
the director in the sample. A uniform director orientation parallel to the external magnetic field generates a doublet with the maximum splitting of (3/2)δ (the outer doublets in Figure 8), whereas a uniform director orientation perpendicular to the magnetic field gives rise to a doublet with half the maximum splitting (the inner doublets in Figure 8). For a polydomain sample with a nonuniform director orientation, the superposition of doublets results in a spectrum characteristic of the orientational distribution. If the distribution is isotropic, for instance, the wellknown Pake pattern (powder pattern) results. However, not only the orientation of the domains but also their size has an effect on the line shape. If the domain size is small such that diffusion of water between domains of different orientation takes place during the measurement, the value of δ is affected and an additional decrease or even a vanishing of the splitting is observed. A similar effect on the NMR line shape33,46-48 is found when the membranes forming the lamellar phase have a strong curvature, as in vesicles, so that the diffusive motion of the water molecules along the membranes has a rotatory component. In Figure 8 shear-induced changes in both orientation and domain size can be observed. If the sample is annealed at rest at the isotropic-lamellar phase transition, the lamellar domains align with their normal perpendicular to the magnetic field, as can be seen in the first spectrum of Figure 8. Upon increasing shear rate, the layers tend to align with their normal axes parallel to the velocity gradient, which is parallel to the magnetic field. This type of alignment gives rise to a doublet with almost twice the initial splitting. The flow-oriented state of region I is best developed at shear rates of 0.09 s-1 for the 35 w/w % sample and 0.2 s-1 for the 40 w/w % sample. However, the flowinduced orientation is far from perfect as can be seen from the considerable intensity of the inner doublet. At these low shear rates already a small decrease of δ is observed, indicating that the size of the domains decreases, in other words, that the contribution from defects with stronger curvatures increases. Upon further increase of the shear rate, a gradual transformation to a new line shape is observed: The spectrum becomes narrower while, at the same time, its features become less distinct. The inner doublet coalesces and a broad single peak appears. The transition is continuous; a separation of the spectra into different components is not possible. Initially the broad peak has still an even broader base (cf. the spectra at 2.4 and 4 s-1 in Figure 8, right) that vanishes eventually, approximately at the same shear rate at which the fully developed structure of close-packed vesicles is first observed by either microscopy or light scattering. Hence, the broad peak can be assigned to the state of close-packed vesicles. Figure 9 depicts the full width at half-height, ∆νfwhh, of the NMR spectra of the 40 w/w % sample as a function of the shear rate. In this plot, the transition region I-II is characterized by a rapid decrease of ∆νfwhh and the beginning of region II can be identified as a change in the slope of the curve. Within region II, ∆νfwhh initially decreases, reflecting the shrinking of the vesicles. At γ˘ ≈ 14 s-1 a constant plateau is reached, indicating that the vesicles have become so small that the water diffusion corresponds to a completely isotropic motion on the NMR (46) Douliez, J. P.; Bellocq, A. M.; Dufourc, E. J. J. Chim. Phys. 1994, 91, 874. (47) Heaton, N. J.; Althoff, G.; Kothe, G. J. Phys. Chem. 1996, 100, 4944. (48) Blum, F. D.; Franses, E. I.; Rose, K. D.; Bryant, R. G.; Miller, W. G. Langmuir 1987, 3, 448.
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Figure 9. Full width at half-height, ∆νfwhh, of the NMR spectra of the 40 w/w % sample as a function of the shear rate γ˘ .
time scale. The further decrease of the vesicle size as seen by light scattering no longer affects the NMR spectrum at higher shear rates. A comparison of Figures left and right shows that equivalent states of orientation are observed at higher shear rates if the surfactant concentration is higher, in keeping with earlier observations on the same system9 and with the dependence of the transition shear rates on the lamellar period described by Roux and collaborators.3,4 4. Discussion All results taken together yield the following picture: region I consists of flow-aligned lamellae, in the transition region I-II a continuous change from one state of orientation to another takes place, during which the density of defects increases, and region II corresponds to a fully developed fairly regular defect structure, the onion state. The first shear thinning in region I is caused by an orientation of the lamellae which align parallel to the velocity-vorticity plane. The flow is maintained by the sliding of the bilayers upon each other. In this aligned state, there is less structural resistance to the flow than in a nonoriented polydomain; hence the decrease of viscosity. This orientation is best observed by NMR measurements, yielding the typical spectra of a lamellar liquid crystalline phase with a director orientation mainly in the direction of the velocity gradient. Rheo-SALS experiments in this regime show only a weak unspecific scattering. The shear thickening in region I-II is caused by the development of a new structure. The defects, that is, the initially polydisperse spherulites, disturb the flow, and their increasing number causes an increase of the viscosity. All observations indicate that the development of the new structure is a continuous process. Microscopy shows that the number of vesicles increases continuously, and both SALS and NMR show a gradual transformation of patterns, not a superposition of two distinct ones. Thus, there is no evidence for a discontinuity at the transition or for a coexistence of two states of orientations. The exact nature of the structures in the transition regime is not yet known, but there is some evidence that multilamellar tubuli aligned parallel to the flow axis may be involved. The NMR spectra showing four distinct peaks (cf. the ones at 0.12 and 0.14 s-1 in Figure 8) are in agreement with the planar director distribution with orientations in the velocity gradient/vorticity plane expected in this case. This model of tubuli could also explain the fact that an overall orientation of the matrix with its optical axis (the layer normal) perpendicular to the flow is observed by microscopyslamellae in homeotropic orientation do not contribute to the birefringence. In the
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depolarized SALS experiment, the flow-aligned tubular matrix is not observed and only the sperulites having different indices of refraction in their radial and tangential directions give rise to the characteristic four-lobe patterns depicted in Figure 4. Moreover, this model is consistent with observations on other surfactant and smectic systems, for which a superposition of the parallel (c) and perpendicular (a) orientation has been reported.16,17 In fact, tubuli were first suggested by Panizza et al.20 for the thermotropic smectic phase of 8CB. The number of vesicles increases and they become more uniform in size during the transition until a close packing is reached in region II. In this region, the vesicle size is controlled by the shear rate, and the shear thinning in this regime is due to the decrease of their size. Flow in this regime may occur by the sliding of vesicle layers upon each other. The SALS pattern in region II is clearly different from the four-lobe pattern of isolated vesicles that is observed in the transition region. The regular structure gives rise to a sharp diffraction peak. Therefore, we use the Bragg equation to determine the size of the vesicles, since the relationship R ) (4.1λ/4π)(1/(sin θmax/ 2)) derived for the radius R of isolated spherulites44,45 is not appropriate here. The exponent a of the scaling law, d ∝ γ˘ a, is not affected by this choice. Our result of a ) -0.53 confirms previous results obtained for the systems SDS/pentanol/dodecane/water3-5,40 and SDS/octanol/brine,7 but it is different from the exponent of -0.3 for C12E4/ water reported previously.13 The authors of the study on C12E4/water, however, do not specify the range of shear rates for which the exponent -0.3 was observed. By combining the results from SALS and NMR, the self-diffusion coefficient (D) of water can be estimated. The NMR line shapes are governed only by the molecular diffusion and not by an additional rotation of the vesicles, since the spectra during shear and after cessation of shear are identical. Assuming that the exchange of water between layers is negligible and that the line width is determined by the outer shell of the vesicle, we can
Mu¨ ller et al.
estimate D for the 40 w/w % solution in the following way: The plateau of a constant line width of ≈150 Hz is reached at γ˘ ) 14 s-1. At this shear rate the rotational motion appears isotropic; i.e., diffusion covers the area of a halfsphere, A ) 2πR2, where R is the vesicle radius. Relating A to the mean-square displacement of the diffusing molecules during the time T ) 1/∆νfwhh, A ) 2DT, results in D ) 7 × 10-10 m2 s-1, which seems a reasonable value for the lamellar phase. Molecular diffusion limits the range of vesicle sizes in which the deuteron NMR spectra are sensitive to a change. Typically, the lower limit should be 1 µm or more; in our case it is ≈2.5 µm. On the other hand, our light scattering setup works best for somewhat smaller structures so that by the combination of both techniques the range down to d ≈ 1.5 µm can be well observed. 5. Conclusions We have illustrated how the shear-induced state of multilamellar vesicles manifests itself in observations made with different experimental techniques. Viscosity, optical textures, SALS patterns, and deuteron NMR spectra have been correlated. The results confirm that the onion state is a shear-rate-controlled steady state. The power law dependence of the vesicle size on the shear rate with an exponent of approximately -0.5, reported previously for other lyotropic lamellar systems, can be confirmed for shear rates below 80 s-1. The transition from the state of flow-aligned lamellae to the state of closepacked vesicles is a continuous transformation between different structures. Acknowledgment. We thank Alfred Hasenhindl for help with the NMR experiments. Financial support by the Deutsche Forschungsgemeinschaft and by the TMR program of the European Union under Contract No. ERBFMRX-CT960003 is gratefully acknowledged. LA9904105
