pubs.acs.org/Langmuir © 2010 American Chemical Society
Shear-Induced Defect Formation in a Nonionic Lamellar Phase B. Medronho,*,†,‡ M. Rodrigues,† M. G. Miguel,† U. Olsson,‡ and C. Schmidt§ †
Department of Chemistry, University of Coimbra, 3004-535 Coimbra, Portugal, ‡Physical Chemistry 1, Center of Chemistry and Chemical Engineering, Lund University, Box 124, 221 00 Lund, Sweden, and § Department of Chemistry, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany Received February 10, 2010. Revised Manuscript Received March 24, 2010 2 H NMR experiments on a nonionic oriented lamellar phase demonstrate that shear flow induces structural defects in the lamellar structure. These substantial structural changes give rise to a transition from a viscous to a solidlike behavior; the elastic modulus of presheared samples was found to increase, reversibly, with the applied preshear rate. A similar behavior was found when step-cycling the temperature toward the layer-to-multilamellar-vesicle transition and back at constant shear rate. However, while shear rate controls the defect density, the temperature is found to control the defect rigidity. The lamellar phase exhibits a shear-thinning behavior under steady shear conditions, following the power law η ∼ γ_ n, with n ≈ -0.4. Both the shear thinning and the elastic behavior are in agreement with the available theoretical models. The observed shear-induced structural defects are reversible and can be regarded as a pretransition prior to the shear-induced formation of multilamellar vesicles.
Introduction Lamellar surfactant systems are periodic one-dimensional arrangements of stacked two-dimensional amphiphilic bilayers, separated by solvent layers. The topological characteristics are determined by the relative amounts of each component present in the system. The lamellar self-assembly of amphiphilic molecules is the most frequently encountered phase in surfactant/solvent systems and in biological membranes. The stability of the longrange periodicity in lamellar phases is determined by a balance between fundamental interactions such as the van der Waals attraction, the electrostatic repulsion for charged membranes, and the short-range repulsive hydration interactions which, for instance, prevent phospholipid bilayers in water from coming into close contact with each other. Nonionic lamellar phases are stabilized by the long-range entropic repulsion between fluctuating membranes, known as the “Helfrich interaction”. The coupling between shear flow and the internal structure of complex fluids, for instance, a lyotropic lamellar phase, is both of practical and fundamental interest. Under shear flow, lyotropic lamellar phases present stationary states separated by dynamic transitions. Shear flow deformation is known to induce many structural changes in the mesoscopic order. For instance, changes in layer orientation have been extensively reported.1-8 A second interesting feature is the shear-induced formation of
*Corresponding author. E-mail:
[email protected]. (1) Penfold, J.; Staples, E.; Lodhi, A.; Tucker, I.; Tiddy, G. J. Phys. Chem. B 1997, 101, 66. (2) Kannan, R. M.; Kornfield, J. A. Macromolecules 1994, 27, 1177. (3) Zipfel, J.; Berghausen, J.; Lindner, P.; Richtering, W. J. Phys. Chem. B 1999, 103, 2841. (4) Imai, M.; Nakaya, K.; Kato, T.; Takahashi, Y.; Kanaya, T. J. Phys. Chem. Solids 1999, 60, 1313. (5) Zipfel, J.; Berghausen, J.; Schmidt, G.; Lindner, P.; Alexandridis, P.; Tsianou, M.; Richtering, W. Phys. Chem. Chem. Phys. 1999, 1, 3905. (6) Dhez, O.; Nallet, F.; Diat, O. Europhys. Lett. 2001, 55, 821. (7) Panizza, P.; Archambault, P.; Roux, D. J. Phys. II 1995, 5, 303. (8) Burgemeister, D.; Schmidt, C. Prog. Colloid Polym. Sci. 2002, 121, 95. (9) Diat, O.; Roux, D. J. Phys. II 1993, 3, 9. (10) Diat, O.; Roux, D.; Nallet, F. J. Phys. II 1993, 3, 1427. (11) Richtering, W. Curr. Opin. Colloid Interface Sci. 2001, 6, 446.
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multilamellar vesicles, MLVs (also called liposomes, spherulites, or onions).9-16 The classical picture of an ideal lamellar system corresponds to a highly ordered smectic phase of undisrupted bilayers, with a welldefined lamellar spacing. The presence of solvent-filled defects in the membranes and distributions of angular orientations (undulations) of the lamellae are deviations from the ideal case that are frequently observed. Several layered systems exhibit “defective” lamellae, especially in the vicinity of phase transitions.17-23 Nevertheless, the one-dimensionally ordered lamellar phase may sustain larger fluctuations (we may also compare the melting points of the different phases; for a collection of phase diagrams see, e.g., ref 24) and structural defects without losing its one-dimensional order, while the neighboring hexagonal or cubic phases cannot. The large variety of structural defects that exist in liquid crystals has no equivalent in solid crystals, except for dislocations, which are common in both systems. As one-dimensional crystals of parallel layers, the lamellae possess translational symmetry and thus exhibit dislocations (screw and edge dislocations).25-27 These structural defects are an inherent feature of all systems (12) Mortensen, K. Curr. Opin. Colloid Interface Sci. 2001, 6, 140. (13) Butler, P. Curr. Opin. Colloid Interface Sci. 1999, 4, 214. (14) Berni, M. G.; Lawrence, C. J.; Machin, D. Curr. Opin. Colloid Interface Sci. 2002, 98, 217. (15) Medronho, B.; Fujii, S.; Richtering, W.; Miguel, M. G.; Olsson, U. Colloid Polym. Sci. 2005, 284, 317. (16) Leon, A.; Bonn, D.; Meunier, J.; Al-Kahwaji, A.; Greffier, O.; Kellay, H. Phys. Rev. Lett. 2000, 84, 1335. (17) Meyer, C.; Kleman, M. Mol. Cryst. Liq. Cryst. 2005, 437, 1355. (18) Oswald, P.; Allain, M. J. Colloid Interface Sci. 1988, 126, 45. (19) Kekicheff, P.; Cabane, B.; Rawiso, M. J. Phys., Lett. 1984, 45, L813. (20) Holmes, M.; Charvolin, J. J. Phys. Chem. 1984, 88, 810. (21) Allain, M.; Di Meglio, J. M. Mol. Cryst. Liq. Cryst. 1985, 124, 115. (22) Moreau, P.; Navailles, L.; Giermanska-kahn, J.; Mondain-Monval, O.; Nallet, F.; Roux, D. Europhys. Lett. 2006, 73, 49. (23) Dhez, O.; K€onig, S.; Roux, D.; Nallet, F.; Diat, O. Eur. Phys. J. E 2000, 3, 377. (24) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1983, 79, 975. (25) Kleman, M. Points, Lines and Walls in Anisotropic Fluids and Ordered Media; Wiley: Chichester, 1983. (26) Kleman, M. Rep. Prog. Phys. 1989, 52, 555. (27) Kleman, M. Pramana 1999, 53, 107.
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with long-range order. They play a crucial role in determining many properties of these materials and may be involved in shearinduced structural transformations.1,6,18,22,28 Since the earliest studies of lamellar surfactant mesophases, their rheological complexity has been known.9,10,18,29-38 The study of the rheological behavior of different smectic systems has focused on steady-state viscous flow,18,27,33,39 plastic flow behavior,40-42 and transient flow phenomena.38 In all cases, the importance of the appearance of shear-induced structural defects has been recognized. Historically, less attention has been paid to the linear viscoelastic behavior of lamellar liquid-crystalline phases.43-45 A perfectly ordered and oriented lamellar state should not be able to store elastic energy, when sheared parallel to the bilayers. Rather, a liquid response would be expected since the layers should be free to slide past one another. However, defects can change this scenario. Paasch et al.29 reported a systematic rheological study of several nonionic surfactantwater lamellar liquid crystalline phases and found that all exhibit shear-thinning behavior and yield stresses, the values of which depended on the mechanical pretreatment of the samples. Herke et al.42,46 have presented the first study in dynamics of oscillatory plastic flow in a smectic A liquid crystal. A macroscopic sample, in response to the application of a constant rate of layer strain, can exhibit oscillatory layer normal stress. They justified this effect as a consequence of the helical instability of screw dislocations. Bandyopadhyay et al.47 found in thermotropic smectic 8CB an almost linear increase of the elastic modulus, G0 , with temperature decrease which was explained by a dense population of defects in the smectic at lower temperatures. In some cases, annealed disorder in the form of colloids suspended in lamellar systems can anchor line defects leading to a cross-linked network that enhances the elastic modulus, G0 .48-50 Of special interest for the present report, Basappa et al.48 showed, using a rheo-optical technique, that a homeotropically oriented lamellar state can be obtained in the limit of large strain. However, when increasing the shear rate, G0 was found to increase, too. (28) Blanc, C.; Meyer, C.; Asnacios, S.; Kleman, M.; Lelidis, I.; Marin, J. Philos. Mag. Lett. 2005, 85, 641. (29) Paasch, S.; Schambil, F.; Schwuger, J. Langmuir 1989, 5, 1344. (30) Groves, M. J.; Abroad, A. B. Rheol. Acta 1976, 15, 501. (31) Tamamushi, B.; Kodaira, Y.; Matsumura, M. Colloid Polym. Sci. 1976, 254, 571. (32) Mufioz, J.; Gallegos, C.; Flores, V. Tenside, Surfactants, Deterg. 1991, 28, 204. (33) Robles-Vasquez, O.; Corona-Galvan, S.; Soltero, J. F. A.; Puig, J. E. J. Colloid Interface Sci. 1993, 160, 65. (34) Hoffmann, H.; Rauscher, A. Colloid Polym. Sci. 1993, 271, 390. (35) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. (36) Soltero, J. F. A.; Robles-Vasquez, O.; Puig, J. E. J. Rheol. 1995, 39, 235. (37) L€auger, J.; Linemann, R.; Richtering, W. Rheol. Acta 1995, 34, 132. (38) Franco, J. M.; Mufioz, J.; Gallegos, C. Langmuir 1995, 11, 669. (39) Nemeth, Z.; Halasz, L.; Palinkas, J.; Bota, A.; Horanyi, T. Colloids Surf., A 1998, 145, 107. (40) Bourgoin, D.; Shankland, W. Rheol. Acta 1980, 19, 226. (41) Blanc, C.; Zuodar, N.; Martin, J. L.; Lelidis, I.; Kleman, M. Mol. Cryst. Liq. Cryst. 2004, 412, 85. (42) Herke, R. A.; Clark, N. A.; Handschy, M. A. Science 1995, 267, 651. (43) Cordobes, F.; Franco, J. M.; Gallegos, C. Grasas Aceites (Sevilla, Spain) 2005, 56, 96. (44) Riise, B. L.; Fredrickson, G. H.; Larson, R. G.; Pearson, D. S. Macromolecules 1995, 28, 7653. (45) Medronho, B.; Miguel, M. G.; Olsson, U. Langmuir 2007, 23, 5270. (46) Herke, R. A.; Clark, N. A.; Handschy, M. A. Phys. Rev. E 1997, 56, 3028. (47) Bandyopadhyay, R.; Liang, D.; Colby, R. H.; Harden, J. L.; Leheny, R. L. Phys. Rev. Lett. 2005, 94, 107801. (48) Basappa, G.; Kumaran, V.; Nott, P.; Ramaswamy, S.; Naik, V.; Rout, D. Eur. Phys. J. B 1999, 12, 269. (49) Ramos, L.; Zapotocky, M.; Lubensky, T. C.; Weitz, D. A. Phys. Rev. E 2002, 66, 031711. (50) Zapotocky, M.; Ramos, L.; Poulin, P.; Lubensky, T.; Weitz, D. Science 1999, 283, 209.
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In all these examples it is clear that the presence and stability of structural defects influence dramatically the rheological properties of a lamellar system. Unfortunately, macroscopic rheological measurements alone do not reveal structural details of sheared samples, and explanations for the observed phenomena remain mostly speculative when based merely on rheological data. Deuterium NMR of D2O-enriched surfactant/water mixtures is a well-established method for the study of surfactant phase diagrams and the microstructure of the different phases51-53 and here will prove to be a powerful tool for our purposes. The paper is organized as follows: The experimental part will be followed by a description of the results, starting with a presentation of the influence of the shear rate at constant temperature on the lamellar phase, evident from both deuterium line shapes and rheometry. Subsequently, the temperature influence will be presented. Later on in the paper, we will discuss our results and connect them to the available theoretical models and finally conclude.
Experimental Section Materials. Triethylene glycol mono-n-decyl ether (C10E3) with a purity higher than 99.8% was purchased from Nikko Chemical Co. (Tokyo, Japan). Deuterium oxide (D2O) was obtained from Sigma Chemicals (Steinheim, Germany). Samples containing 40 wt % surfactant were prepared by weighing the desired amounts of surfactant and water into vials, mixing them in a vortex mixer, and centrifuging them in order to remove air bubbles. All samples were prepared with D2O as a probe for deuterium NMR spectroscopy. Deuterium NMR Spectroscopy. The 2H rheo-NMR experiments were carried out using a cylindrical Couette cell with 14 and 15 mm inner and outer diameters, respectively. This cell is integrated into an NMR probe for a wide-bore superconducting magnet. The axis of the shear cell is aligned parallel to the external magnetic field. Shear is applied by rotating the outer cylinder with an external motor located below the NMR magnet. The spectra were recorded with a Tecmag Apollo 300 MHz NMR spectrometer operating at the deuterium resonance frequency of 46.073 MHz. Spectra were obtained by Fourier transformation of the signal following a single pulse. Typically, 4-16 scans were accumulated for each spectrum, and a recycle delay of 1 s was used. The temperature of the sample was maintained constant with an accuracy of (0.2 C using an air-flow system. For each series of experiments, reproducible initial conditions were achieved by filling the shear cell with the sample and increasing the temperature until the isotropic signal of the sponge phase was reached. The sample homogenization and adjustment of the magnetic field homogeneity (“shimming”) took place at around 49 C under shear at a constant rate of 10 s-1. Under these conditions, the sponge phase, L3, is stable, and the typical 2 H NMR fingerprint is a narrow singlet. Afterward, still under shear, the temperature was decreased slowly (0.5 C/min) to 42 C to obtain a shear-aligned lamellar phase, and further experimental protocols described below were applied. The 2H NMR technique probes the motionally averaged electric quadrupole couplings between the deuterium nuclei (spin I = 1) and the electric field gradients at the sites of the observed nuclei.54 The residual couplings arise from the anisotropy of the rotational motions of the water molecules and thus (51) M€uller, S.; B€orschig, C.; Gronski, W.; Schmidt, C.; Roux, D. Langmuir 1999, 15, 7558. (52) Lukaschek, M.; M€uller, S.; Hasenhindl, A.; Grabowski, D. A.; Schmidt, C. Colloid Polym. Sci. 1996, 274, 1. (53) Halle, B.; Wennerstrom, H. J. Chem. Phys. 1981, 75, 1928. (54) Abragam, A. Principles of Nuclear Magnetism; Clarendon: Oxford, 1961. (55) Douliez, J. P.; Bellocp, A. M.; Dufourc, E. J. J. Chim. Phys. 1994, 91, 874. (56) Auguste, F.; Douliez, J. P.; Bellocp, A. M.; Dufourc, E. J. Langmuir 1997, 13, 666.
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depend on the curvature of the hydrophobic/hydrophilic interface.52,55-58 When D2O molecules experience a macroscopically anisotropic environment, like in a lamellar phase, the quadrupolar interaction has a nonzero average, leading to a splitting (ΔυQ) of the resonance. In a uniaxial phase, ΔυQ can be related to the angle θ between director (phase axis) and magnetic field by53,54 ΔυQ ¼
3 δð3 cos2 θ - 1Þ 4
ð1Þ
where δ denotes the quadrupole coupling constant, averaged over the fast motions of D2O. Rheometry. The rheology experiments were performed on a Physica UDS 200 rheometer using the cylindrical geometry Z3 DIN (gap between the inner and outer cylinder of 1 mm) and on a Stress Tech rheometer, using the cylindrical geometry CC 25. The instruments are equipped with a temperature control unit that was calibrated to give a temperature in the sample chamber within 0.1 C of the set value. A solvent trap was used to prevent water evaporation. The viscoelastic properties of the system were studied by small frequency oscillatory tests in the linear regime, which was verified by prior stress sweep tests at the different temperatures. The small-amplitude dynamic tests provided information on the linear viscoelastic behavior of materials through the determination of the complex shear modulus: GðωÞ ¼ G ðωÞ þ iG ðωÞ 0
00
ð2Þ
where the storage modulus G0 (ω) is a measure of the reversible elastic energy, while the loss modulus G00 (ω) represents the irreversible viscous dissipation of the mechanical energy.
Results A dynamic “phase” map of 40 wt % C10E3 in water, showing the stability regimes of different states of the lamellar phase as a function of temperature and shear rate, is presented in Figure 1.59 This diagram is a rather simple representation hiding important features like, for instance, the dependence of the MLV size on the applied shear rate and the characteristics of the transition region. Actually, the nature of the transition region seems to depend on the direction we take when approaching it: there is an incomplete transition when going from planar layers to MLVs but a coexistence of both structures when going from MLVs to planar layers.60 The questions we address in the present work concerns only the region of planar lamellae and its response to shear flow. Three experimental routes were undertaken in this study, and they are indicated by arrows in Figure 1. In (1) we investigate the effect of shear at different rates at a constant temperature of 42 C, where no vesicles have been found. In (2) the influence of temperature is investigated at a constant shear rate of 1 s-1. Finally, in (3) the shear rate effect is studied at a lower temperature, 34 C, where MLVs are formed above a critical shear rate. However, we stress again that all experiments reported here are within the region of planar lamellae, where no vesicles are formed. Shear-Induced Structural Changes at Constant Temperature. 2H NMR Spectroscopy. 2H NMR spectroscopy was used to investigate how shear influences the lamellae. After generating the initial state of shear-aligned lamellae in the NMR (57) Baciu, M.; Olsson, U.; Leaver, M.; Holmes, M. J. Phys. Chem. B 2006, 110, 16. (58) Gotter, M.; Strey, R.; Olsson, U.; Wennerstrom, H. Faraday Discuss. 2005, 129, 327. (59) Oliviero, C.; Coppola, L.; Gianferri, R.; Nicotera, I.; Olsson, U. Colloids Surf., A 2003, 228, 85. (60) Medronho, B.; Shafaei, S.; Szopko, R.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2008, 24, 6480.
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Figure 1. Shear diagram of the C10E3/water system. The stability regions of MLVs and planar layers as a function of temperature and shear rate are shown. The arrows indicate the different experimental routes.
instrument as described in the Experimental Section, the shear rate was varied at 42 C (arrow 1 in Figure 1) using the following values: 10, 25, 50, 75, 100, 75, 50, 25, 10, 5, 1, and 0.1 s-1. Each shear rate was applied until reaching the steady state, which was checked by following the time evolution of the 2H NMR spectra. In the cylindrical Couette cell a lamellar phase with layers aligned parallel to the walls of the cylinders is generated. Hence, the normal vectors of the layers are aligned perpendicular to the magnetic field, and the observed quadrupole splitting, ΔυQ, corresponds to the splitting of the 90 singularities (θ=90) of a powder spectrum. In other words, the measured value is half of the splitting corresponding to parallel alignment of layer normal and magnetic field (θ=0). The width and symmetry of the deuterium line shape depend on the natural line width (due to relaxation) and on the orientational distribution function of the local director. Both slow motion (short transverse relaxation time) and a broad distribution of orientations lead to broadened lines. Figure 2 shows three selected spectra, obtained upon increasing the shear rate. From each spectrum ΔυQ can be obtained. The spectrum at the lowest shear rate, 0.1 s-1, has a quadrupolar splitting of 740 Hz and narrow lines. At this shear rate, the lamellae are highly oriented and closest to the “classical” picture of the defect-free lamellar phase. When the shear rate is increased, ΔυQ decreases and the lines get broader. The splitting and the average full width of the lines at half-height, fwhh, as a function of the applied shear rate are represented, in parts a and b of Figure 3, respectively, for two temperatures, 35 C (cf. Figure 1, arrow 3) and 42 C (cf. Figure 1, arrow 1). The influence of shear flow is found to be reversible and reproducible. In different experiments we always observe the same qualitative trend, although the values of ΔυQ may change slightly. It is important to mention that we do not observe a change in layer configuration from the so-called “C” orientation61 (also called parallel orientation, layer normal parallel to the velocity gradient, here perpendicular to the magnetic field) to the “A” orientation (perpendicular orientation, (61) Zipfel, J.; Nettesheim, F.; Lindner, P.; Le, T. D.; Olsson, U.; Richtering, W. Europhys. Lett. 2001, 53, 335.
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Figure 2. 2H NMR spectra for three selected shear rates: 0.1, 25,
and 50 s-1 at 42 C.
layer normal parallel to the vorticity axis, here parallel to the magnetic field) found in some other lamellar systems,1,3,62-64 but instead, we identify a continuous transition from a well ordered to a less ordered lamellar phase, keeping, on average, the “C” orientation. The decrease of the motionally averaged quadrupole coupling ΔυQ together with the broadening of the lines upon the increase of shear rate indicates that, on the time scale of the NMR measurement, the water molecules probe a more strongly curved interface by their lateral diffusion in the hydrophilic layer. The decrease in ΔυQ as the sample is sheared at increasing rate can be explained by an increase of layer undulations, which may be coupled or not to a decrease of the lateral extension of defect-free flat layers. The introduction of more strongly curved structures results in an additional (besides the local tumbling of the molecules) averaging of the quadrupolar interaction. This additional motional narrowing leads to the observed decrease of the splitting. The line broadening, on the other hand, indicates that the correlation time of the reorientations is at least of the order of the inverse splitting, for example, because the curvature is still low. The data in Figure 3 suggest, qualitatively, a similar behavior at both temperatures; i.e., the closer we are to the transition to the onion state (which might occur at very high shear rates even at 42 C), the less ordered is the lamellar phase. At 35 C the planar lamellar phase is stable only at shear rates lower than 2 s-1, and our experiments had to be carried out at shear rates lower than this value. At such low shear rates the time needed to reach the steady state at a certain deformation is long, and sample losses, due to evaporation, have to be taken into consideration. Therefore, the number of experiments at this lower temperature was considerably reduced. Shear Thinning. Let us now focus on the rheological properties. First, the shear viscosity in steady-state flow was investigated at a constant temperature of 42 C (route 1 in Figure 1). The shear rate was varied in the following way: 0.1, 0.5, 1, 5, 10, 25, 50, 25, 10, 5, 1, 0.5, and 0.1 s-1. Each shear rate was applied until reaching the steady state (plateau in viscosity), as can be seen in (62) Mang, J. T.; Kumar, S.; Hammouda, B. Mol. Cryst. Liq. Cryst. 1997, 303, 255. (63) Schmidt, G.; M€uller, S.; Schmidt, C.; Richtering, W. Rheol. Acta 1999, 38, 486. (64) Burgemeister, D.; Schmidt, C. Prog. Colloid Polym. Sci. 2002, 121, 95.
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Figure 3. (a) Quadrupolar splitting, ΔυQ, as a function of the
applied shear rate at 35 C (filled symbols) and 42 C (open symbols). (b) Average line width (“full width at half-height”, fwhh) as a function of the applied shear rate at 35 C (filled symbols) and 42 C (open symbols). The errors were estimated to be ∼10 Hz.
Figure 4. For easier visual analysis, only the data above 1 s-1 upon increasing shear rate are shown in this figure. Generally, less than 2000 strain units (strain, γ = γ_ t) are needed to reach the steady state. Figure 5 shows the steady-state viscosities (cf. Figure 4) as a function of shear rate, including the data for both increasing and decreasing shear rates. A reversible shear thinning is observed, which follows the power law η ∼ γ_ n, with n ≈ -0.4. Viscoelastic Properties of Presheared Samples. The 2H NMR data suggest a substantial change of structure in the sheared samples which is accompanied by a shear-thinning behavior. We now turn to the question if and how the structural changes are reflected in the dynamic viscoelastic response of the lamellar sample. The linear viscoelasticity was investigated by small-amplitude oscillations imposed on the presheared sample. After shearing the lamellar phase at the desired shear rate for 1 h, DOI: 10.1021/la100627z
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Figure 4. Time evolution of shear viscosity for different shear rates at 42 C.
Figure 6. (a) Storage and loss moduli, G0 and G00 , in the linear Figure 5. Log-log plot of the steady-state viscosity (cf. Figure 4)
regime vs frequency at three selected preshear rates: 0.1, 5, and 25 s-1 at a constant temperature of 42 C. (b) G0 (filled symbols) and G00 (open symbols), recorded at 4 Hz, vs preshear rate. The dotted line represents the best fit to the elastic modulus.
shear was stopped and a frequency sweep experiment was performed immediately. This procedure was applied in the directions of both increasing and decreasing shear rate (cf. route 1 in Figure 1). In Figure 6a, we present the frequency dependence of the storage (G0 ) and loss (G00 ) moduli, at three selected preshear rates (0.1, 5, and 25 s-1) at 42 C. The mechanical spectrum at 0.1 s-1 shows a typical viscoelastic response with a clear frequency dependence of both moduli and a dominantly liquid-like behavior45 (G00 > G0 ) at frequencies lower than 2 Hz. This liquid-like behavior is in agreement with the picture of uniformly aligned lamellae with a low defect density suggested by the 2H NMR results. However, when the shear rate is increased, both G0 and G00 become almost frequency independent, and G0 remains approximately an order of magnitude larger than G00 in the whole frequency range studied. This behavior is characteristic of a gel-like sample. The variation of the viscoelastic spectra with shear rate is reversible as demonstrated in Figure 6b, where the dependence of G0 and G00 on shear rate for a constant oscillation frequency of 4 Hz is presented. The data in Figure 6b represent the results of a step cycle experiment in which, after each preshear rate, an oscillatory test was performed. G0 strongly increases with shear rate, whereas G00 remains about constant. In Figure 6b the dotted
line represents the best linear fitting, showing that G0 scales with shear rate as G0 ∼ γ_ 1/3. Temperature Dependence. 2H NMR. The observations at constant temperature suggest a proliferation of structural changes in the sample as shear rate is increased. These changes may be related to the formation of onions that occurs at higher shear rates, at least at lower temperatures. Alternatively, the “phase” boundary to the onion regime can be approached by keeping the shear rate constant and decreasing the temperature as schematically shown in Figure 1, route 2. In order to follow any structural changes along this path, 2H NMR spectra were collected as a function of temperature under constant shear. In this case, the changes in ΔυQ, which are depicted in Figure 7a, are much smaller than the ones observed when increasing the shear rate. Initially, ΔυQ slightly increases until reaching a maximum (at about 39 C) and then slightly decreases. Figure 7b shows that the peaks of the doublet spectra get broader as the temperature is decreased until 35 C. As in the shear rate scan, the temperature scan at constant shear rate is fairly reversible. Two factors contribute to the change of ΔυQ with temperature. One is the “normal” thermal behavior usually found in surfactant liquid crystalline phases due to a temperature-dependent local
as a function of shear rate at 42 C. The observed shear thinning follows the power law η ∼ γ_ n, with η ≈ -0.4.
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Figure 7. (a) Quadrupolar splitting, ΔυQ, as a function of temperature at a constant shear rate of 1 s-1. (b) Average line width, fwhh, as a function of temperature at a constant shear rate of 1 s-1. The errors were estimated to be ∼10 Hz.
motional anisotropy of the water molecules. For C10E3/water this temperature dependence was reported by us in a previous study,45 where ΔυQ was measured in a wider temperature range in a polycrystalline sample without any applied force except the external magnetic field. The quiescent sample showed a significant increase in ΔυQ upon lowering the temperature from 42 to 7 C. Hence, the decrease in ΔυQ below 39 C seen in Figure 7a must be related to the second factor, namely, the structural change of the lamellar phase due to shear. This structural change is also the cause of the increase of the line width (cf. Figure 7b) when the temperature is lowered. The observed line broadening cannot be attributed to the slowing down of the diffusion of the water molecules. In the temperature range considered the diffusion coefficient of D2O Langmuir 2010, 26(13), 11304–11313
changes only by about 10%,65 and no notable effect on the line width is expected. This is confirmed experimentally by the spectra shown in Figure 8. A lamellar sample sheared at 42 C at a constant shear rate of 10 s-1 (dotted line) shows a spectrum that remains essentially unchanged (solid line) when the temperature is decreased to room temperature (no shear applied at this temperature). This demonstrates that temperature alone does not change significantly the 2H NMR line shape. Only a slight increase in ΔυQ, as discussed above, is observed, whereas the line width of the peaks remains the same. This clearly shows that shear is needed to induce the structural changes that lead to the changes of the line width presented in Figure 7b. (65) Mills, R. J. Phys. Chem. 1973, 77, 685.
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Figure 8. 2H NMR spectra for a lamellar sample sheared at 42 C at 10 s-1 (dashed line). The spectrum at 25 C was obtained quenching the temperature without shear flow (solid line).
Viscoelastic Properties. The linear viscoelasticity was studied when step-cycling the temperature from 41 to 35 C and back to 41 C at a shear rate of 1 s-1. In Figure 9a we present the frequency dependence of G0 and G00 for three selected temperatures. Each dynamic experiment was performed after preshear at the given temperature. At the low preshear rate of 1 s-1 and at 41 C, both moduli show a strong frequency dependence and, for frequencies lower than 2 Hz, a dominantly liquid-like behavior. The decrease of temperature results in a change of the viscoelastic properties. At 37 C the liquid-like behavior is still observed, but the crossing point of G0 and G00 is shifted to lower frequencies (less than 0.5 Hz), compared to 41 C, and at 35 C G0 remains larger than G00 in the range of frequencies studied. Additionally, the elasticity (storage modulus) is found to increase, reversibly, with decreasing temperature. Figure 9b shows the values for G0 and G00 at 4 Hz from the step-cycle experiment where after each temperature change an oscillatory test was performed. G0 increases with decreasing temperature, and the behavior is essentially reversible upon temperature cycling, as in the case of the shear cycling. However, a drift may be observed, when returning to 41 C, due to a loss of sample, as each individual temperature was kept constant for 2 h before the oscillatory test was carried out. Fitting a straight line to G0 (T) using the values measured at decreasing temperature (cf. Figure 9b), which are more reliable, yields a slope of -16 Pa/K. Qualitatively, increase of shear rate and decrease of temperature have similar effects on the viscoelastic behavior. The properties of the sample change from predominantly liquid-like to gellike when the preshear rate is increased or the temperature is decreased. The gel-like behavior can be attributed to defects of the lamellar structure (cf. discussion below.) However, at this stage, we do not know whether the observed enhancement of the elastic modulus (Figure 9) is a pure consequence of an increase in the density of shear-induced defects as temperature is decreased. In principle, it is possible that we are not observing a change in the 11310 DOI: 10.1021/la100627z
Figure 9. (a) Linear storage and loss moduli, G0 and G00 , vs
frequency at three selected temperatures: 41, 37, and 35 C. A constant preshear rate of 1 s-1 was applied for each temperature before the dynamic test. (b) Linear moduli, G0 (filled symbols) and G00 (open symbols), recorded at 4 Hz, vs temperature.
density of defects but rather a temperature-related change in their rigidity while the number of defects remains constant. In a previous study we found, starting from a well-defined planar lamellar state generated by preshearing the sample at a rate of 10 s-1 only once at a 42 C, a dominantly elastic response across the whole temperature range from 42 to 0 C and an increase of G0 at 4 Hz with decreasing temperature.45 These observations were suggested to be a consequence of an increase of defect density when lowering the temperature. In order to separate both possible effects of temperature (increase of defect density vs increase of defect rigidity), additional experiments of the type reported in ref 44 were performed. In Figure 10, one can see the results from these step-cycle experiments, in which after preshearing the sample only once at 42 C a first oscillatory test was performed, the temperature then changed, and the next oscillatory test carried out and so forth; in other words, after one initial preshear all subsequent measurements at different temperatures were performed without further preshear. Thus, these experiments are different from the one presented in Figure 9 where shear was applied at each new temperature. In Figure 10, only the values of G0 at 4 Hz are reported. Again, G0 increases with Langmuir 2010, 26(13), 11304–11313
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Figure 11. Storage modulus, G0 , recorded at 4 Hz vs temperature
Figure 10. Storage modulus, G0 , recorded at 4 Hz vs temperature for three different preshear rates. In this case the sample was presheared only once at a temperature of 42 C before the temperature-dependent measurements were performed.
decreasing temperature, and the behavior is reversible upon temperature cycling. First of all, Figure 10 clearly confirms the dependence of the elastic modulus on the preshear rate, found also in the experiment at constant temperature described above. If temperature were the only parameter controlling the defect density, similar elastic moduli independent of the initial shear rate would be observed for each temperature, and the three curves would be superimposed on each other. On the other hand, if only a change in the defect rigidity occurred and the defect density remained constant, the curves would be expected to be parallel to each other. This is the case in a first approximation. Thus, from Figure 10 we can conclude that the initial density of defects defined by the applied preshear at 42 C is maintained approximately constant during the temperature decrease, and most probably, the changes observed can be explained by changes in the rigidity of an almost constant number of defects. The slopes of the best fitted straight lines shown in Figure 10 are -4.1, -6.6, and -8 Pa/K for preshear rates of 0.1, 1, and 10 s-1, respectively. In comparison, the previously reported experiment of this type at 10 s-1 yields a similar slope of ca. -7 Pa/K, in rather good agreement with the new measurement for this preshear rate. Most importantly, however, these slope values differ significantly from the slope of the other type of experiment shown in Figure 9b. This is illustrated more clearly in Figure 11, which shows a direct comparison of the temperature dependence of G0 from the two different experiments: one with shear at each temperature and the other one without. Figure 11 shows that, for a given temperature within the lamellar region, shear increases the elastic modulus when compared to the nonsheared sample. The initial state (shear at 42 C, 10 s-1) is the same. The difference in G0 simply arises from the fact that in one of the cases, at each new temperature, shear was performed while in the other case no shear was applied. Thus, as shown by the NMR experiments above (cf. Figures 7 and 8), not only the shear rate but also the temperature at which shear is applied is relevant for the extent to which the lamellar structure changes. Langmuir 2010, 26(13), 11304–11313
for a sample sheared (1 s-1) at each new temperature (open circles) and a sample only sheared at 42 C (open squares).
Discussion Let us start by commenting on the observed shear-thinning behavior which might be little intuitive and difficult to understand regarding the 2H NMR and dynamic rheometry data. The observed shear thinning with an exponent n ≈ -0.4 is in good agreement with previous measurements on the lamellar phase. A few theories have been published recently, which explain the shear thinning of smectic systems, for example, of the lyotropic lamellar phase, on the basis of the density and mobility of structural defects. Meyer et al. have investigated the steady rheological behavior of lamellae of different lyotropic and thermotropic systems.28,66-68 Power laws characterized the relationship between the imposed stress, σ, and the measured shear rate, and both types of systems were similar, following the relationship γ ∼ σm, with m=1.7. The power laws of the form γ_ ∼ σm are equivalent to η ∼ γ_ n since m=1/(n þ 1). These authors found the same behavior in a controlled strain experiment. This shear thinning behavior, because of the variety of systems used, was suggested to be a universal property of lamellar systems under weak shear. It was considered to be due to screw dislocations whose gliding under an applied shear counterbalances, plastically, the applied vorticity, thus stabilizing the layers and making their slip past each other more feasible. More recently, Lu et al.69 measured the nonlinear relationship between shear stress and shear rate in a nonionic lyotropic lamellar system and proposed a theory where γ_ ∼ σm, with m=1.5. They showed that the defect-mediated layer tilting and dilation under shear flow could cause a continuous production of dislocations even starting from a “perfect” homeotropically aligned sample. They also suggest that the main energy dissipation is caused by the shear flow passing through the defective structure. Thus, as the defect line density varies with shear rate, a shear thinning behavior would arise. Although both theories have similar assumptions and important differences, mainly related to the mechanism for the observed (66) Meyer, C.; Asnacios, S.; Bourgaux, C.; Kleman, M. Mol. Cryst. Liq. Cryst. 1999, 332, 531. (67) Meyer, C.; Asnacios, S.; Bourgaux, C.; Kleman, M. Rheol. Acta 2000, 39, 223. (68) Meyer, C.; Asnacios, S.; Kleman, M. Eur. Phys. J. E 2001, 6, 245. (69) Lu, C. Y. D.; Chen, P.; Ishii, Y.; Komura, S.; Kato, T. Eur. Phys. J. E 2008, 25, 91.
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rheological responses, as pointed out by Lu et al.,69 we will not focus our discussion on the comparison of theories or the slight difference between the predicted exponents. Our exponent, n ≈ -0.4 (m ≈ 1.6), is within the range of the predicted values and does not allow us to discriminate between the two different theoretical models. Both the viscoelastic spectra and the 2H NMR spectra are consistent with the idea of shear-induced defects that occur when shear rate and/or temperature are changed toward the onion region of the shear diagram. These structural defects are most probably the dislocation loops believed to be also responsible for the shear thinning behavior. Screw dislocations in smectics can be seen as spiral staircases, the dislocation line being the axis of the staircase. The strength and handedness of the defect are defined by the Burgers vector. For topological reasons, finite-size thermally excited edge and screw dislocations in smectics must form loops associating two screw dislocations of equal strength but opposite handedness to two edge dislocations. Dislocation loops, due to their topological nature, are thus expected to connect layers through screw dislocations, avoiding the free sliding of layers past each other. Fluctuations in the screw dislocation shape are difficult due to the large conformational line tension of the screw line. Presumably, this is the origin of elastic energy storage since the shear deformation is expected to tilt the screw axis from its equilibrium position. With an increase of rigidity of the defect this tilting of the axis would cost more energy resulting in an increase of G0 . Thus, we expect a lamellar phase that contains a large number of screw dislocations to behave as an elastic material (G0 higher than G00 ) instead of a Newtonian liquid as expected for a “classical” defect free lamellar system. In fact, as for other gels or networks, the elastic modulus can be expected to be proportional to the number density of “cross-links” or defects. An increase in G0 can then be related to a proliferation of screw dislocations and an increase of their number density, Fs. As shown in Figure 6b, the elastic modulus, G0 , increases, indeed, with the shear rate, following the scaling relationship G0 ∼ γ_ 1/3. The theoretical model of Lu et al.69 predicts the screw dislocation density, Fs, to be proportional to γ_ 2/3 (cf. eq 26 in ref 65). We should be careful in our analysis, however, since we are not reporting the plateau modulus, G0 ¥, which is proportional to Fs, but, instead, G0 at 4 Hz. We note from Figure 6a a variation in the viscoelastic properties mainly at low frequencies due to a dramatic change in relaxation time (crossover frequency) with the applied preshear and can only estimate a less pronounced increase in G0 ¥ with increasing shear rate. Interestingly, Basappa et al.48 studying an anionic surfactant lamellar system found a shear rate dependence of the elastic modulus similar to the one we present here (cf. Figure 3 in their work). They observed that “... shear on the one hand reduces an initially high modulus, but is equally capable of increasing an initially low modulus.” The first shear effect is related to the transition from a polycrystalline (“polydomain” or “powder”) lamellar phase to a well-oriented system.45 This is known to occur in several systems, resulting also in a decrease of the yield stress. It does not need to be considered here since our experiments always start from prealigned samples. The second observation is most probably related to the G0 dependence on structural defects as previously discussed; i.e., the increase in preshear rate results in an increase in the density of structural defects, which leads to a higher elastic modulus, as predicted by Lu’s model. The possible influence of temperature on the density of defects was also analyzed by Lu et al.69 They suggested that the defect density is determined by a dynamic balance between the 11312 DOI: 10.1021/la100627z
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production and annihilation processes where the characteristic relaxation time could, in principle, be related to the time scale of the collision process between defects. We observe that the decrease of temperature results in a mechanical spectrum where both moduli have a weak frequency dependence, and no cross over between them is observed in the window of frequencies studied. In a complementary way, Meyer’s theory suggests that the steady velocity of mobile dislocations is proportional to a mobility coefficient which contains a Boltzmann factor, exp(-w/ kbT), expressing explicitly the activated mechanism responsible for the motion of defects.67,68 Thus, temperature influences the mobility and rigidity of defects by affecting the mechanism of their production and annihilation which, eventually, controls the viscoelastic properties of the lamellae. Instead of analyzing the mobility of defects, a different approach to the temperature dependence can be taken by looking at the bilayer curvature since the nonionic surfactant used is quite temperature sensitive. We should remember that a nonionic monolayer, in general, is very flexible, and its spontaneous curvature, H0, exhibits a strong temperature dependence. For ethylene oxide-based surfactants, H0 decreases linearly with increasing temperature over a large temperature range as expressed by the following equation:70,71 H0 ¼ βðT0 - TÞ
ð3Þ
Here β is a temperature coefficient and T0 the balanced temperature where H0 = 0. This dependence has been explained as a consequence of the dehydration of the surfactant polar heads at high temperatures.72 Thus, at lower temperatures, the surfactant film prefers to curve away from water (H0 > 0). Moreover, it is important to mention that the line energy associated with the unfavorable packing of molecules along the edge dislocation is a linear function of their length and depends on the spontaneous curvature. Bryskhe et al.,73 modeling the line energy of an edge as a monolayer bent cylindrically (with a cylindrical radius of δ/2, δ being the bilayer thickness), derive the line tension, λ, as λ ¼
πkm ð1 - δH0 Þ2 δ
ð4Þ
where km is the bending energy. The main free energy penalty for the formation of dislocation loops in a lamellar phase comes from the line energy of the edge dislocations. As expressed by eq 4, λ is expected to decrease with increasing H0 and, hence, as temperature decreases. Consequently, at lower temperatures, dislocation loops are expected to form more easily and to be more stable. Moreover, since H0 can be tuned by varying temperature, eventually this parameter controls the rigidity of the structural defect. Summarizing the rheological and NMR observations, we can say that, essentially, similar pretransitional effects are observed when approaching the transition region to the onion regime by cooling the temperature or increasing the shear rate. Shear seems to control the density of defects while temperature controls the bilayer spontaneous curvature and probably determines their mobility and rigidity. The dependence of both the shear thinning and the dynamic properties on temperature and shear rate is in reasonable agreement with the recently proposed theoretical models. A final remark has to be made concerning the possible (70) (71) (72) (73)
Olsson, U.; Wennerstrom, H. Adv. Colloid Interface Sci. 1994, 49, 113. Strey, R. Colloid Polym. Sci. 1994, 272, 1005. Lindman, B.; Karlstrom, G. C. R. Chim. 2009, 12, 121. Bryskhe, K.; Bulut, S.; Olsson, U. J. Phys. Chem. B 2005, 109, 9265.
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relation between defects in a lamellar phase and the shear-induced formation of MLVs. The observation of an elastic response to small-amplitude shear deformations and the strong temperature and preshear rate dependence of the elastic modulus are remarkable. Both rheology and 2H NMR data are essentially reproducible and reversible when cycling shear rate at constant temperature or cycling temperature at constant shear rate. The data suggest (in accordance with the available theories) layers in the stack to be connected by dislocation loops (screw dislocations across lamellae). The density, mobility, and rigidity of defects definitely play an important role in the flow instability of the lamellar “C” orientation and, hypothetically, in the shear-induced formation of MLVs. The transition from planar lamellae to MLVs has been proposed to be a consequence of a mechanical flow instability in the lamellar phase at higher shear rates. Therefore, it seems reasonable to fit the picture of defects and how they depend on temperature and/or shear rate into the one of flow instabilities of the lamellae and, ultimately, consider the pretransitional defects as a crucial part of the mechanism of shearinduced MLV formation.
Conclusions The influence of shear flow on a nonionic lamellar system has been studied. 2H NMR spectroscopy clearly shows considerable structural changes which become more pronounced when the applied shear rate is increased. Similar to other smectic systems, the lamellar system used in this study shows a shear thinning behavior in continuous steady shear conditions obeying a power law of the form η ∼ γ_ n, with n ≈ -0.4. On the other hand, in the dynamic oscillatory tests, the elastic modulus was found to
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increase with the preshear rate. Both the 2H NMR and the rheological data suggest an increased density of structural defects with increasing shear rate. Temperature, on the other hand, which is known to cause changes in the spontaneous curvature of the bilayer, seems to influence the mobility and rigidity of defects. The defect density apparently does not change considerably with temperature, if the sample is not sheared again after setting the new temperature. With respect to the shear-induced onion transition, the following picture arises from our observations: When approaching the transition to the onion regime by increasing shear rate and/or decreasing temperature, the state of planar lamellae suffers a kind of continuous pretransition where structural defects play a crucial role. This pretransitional behavior is a dynamic phenomenon and not related to the pretransitional behavior often observed for equilibrium phase transitions. One may speculate that the transition to onions sets in once the density of structural defects becomes too high and their mobility is no longer sufficient to support the flow of the lamellae. This may be the key point in the mechanism of shear-induced onion formation and may explain why, in the C10E3/water system studied here, onions do not form at higher temperatures and low shear rates, where the density and rigidity of defects are low and, most likely, their dynamics high. Acknowledgment. This work was supported by grants from the Swedish Research Council, the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), and the German Academic Exchange Service (DAAD). Bruno Medronho thanks Fundac-~ao para a Ci^encia e tecnologia (FCT) (project ref SFRH/BD/21467/2005).
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