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Shear Melting in Lyotropic Hexagonal Phases Laurence Ramos,* Franc¸ ois Molino, and Gre´goire Porte Groupe de Dynamique des Phases Condense´ es (CNRS-Universite´ Montpellier 2), CC26, Universite´ Montpellier 2, 34095 Montpellier Cedex 5, France Received February 25, 2000. In Final Form: May 8, 2000 We use small-angle X-ray scattering to investigate the structures under shear of surfactant hexagonal phases swollen with oil. Rheology studies of these materials indicate a shear-induced transition between two states of different viscosity. In the low shear regime, the cylinders are preferentially oriented along the flow and the hexagonal phase exhibits a polycrystalline texture. Unexpectedly, a high shear has the effect of melting the long-range two-dimensional (2D) order of the cylinders, leading to a 2D liquid of cylinders strongly aligned along the flow.
In the past few years, the shear flow properties of lyotropic systems have revealed important common features in materials as varied as surfactant lamellar phases,1 wormlike micelles,2 or cubic phases of copolymer.3 The general framework of structural (or “phase”) transition under flow has emerged from these experiments. In this Letter, we report on similar experiments performed on a new type of lyotropic system: swollen hexagonal phases of surfactant. The general characteristics of the behavior under shear are very similar to those observed with the other categories of systems: the shear induces a transition from one state to another. However, quite unexpectedly, the transition manifests itself, in our experiments, by a melting of the two-dimensional long-range order of the cylinders, the cylinders remaining perfectly aligned along the flow. The samples are composed of a quaternary mixture of sodium dodecyl sulfate, pentanol, cyclohexane, and brine with a NaCl concentration of 0.4 M. We used a composition in weight percent of 24.1% brine, 61.5% cyclohexane, and 4.7% pentanol, which yields, at rest, a structure consisting of oil cylinders of radius 15 nm, immersed in water and arranged on a triangular array with a lattice parameter of 33 nm.4 Rheology experiments were performed in a Couette geometry with a Paar Physica UDS 200 rheometer which imposes either the shear stress σ or the shear rate γ˘ . Figure 1 shows the stress versus shear rate curves (flow curves), obtained imposing either γ˘ or σ. For both low shear rates (γ˘ e 100 s-1) and high shear rates (γ˘ g 1000 s-1), the curves superimpose exactly. At low rates, the system is shear thinning; for γ˘ e 30 s-1, the stress varies as γ˘ 1/3 and thus the effective viscosity η ) σ/γ˘ scales as γ˘ -2/3. At high rates (γ˘ g 1000 s-1), the stress varies linearly with the rate; the system behaves as a Bingham fluid (σ ) σ0 + ηγ˙ with σ0 ) +ηγ˘ , with σ0 ) 8.8 Pa, and η ) 14 mPa‚s). At intermediate rates (between γ˘ c1 ≈ 150 s-1 and γ˘ c2 ≈ 400 s-1), stress- and shear-rate-controlled experiments give different results. In the rate-controlled case, a decreasing * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. Bonn, D.; Meunier, J.; Greffier, O.; Al-Kahwaji, A.; Kellay, H. Phys. Rev. E 1998, 58, 2115. (2) Spenley, N. A.; Cates, M. E.; McLeish, T. C. B. Phys. Rev. Lett. 1993, 71, 939. Berret, J.-F.; Porte, G.; Decruppe, J.-P. Phys. Rev. E 1997, 55, 1668. (3) Eiser, E.; Molino, F. Porte, G.; Diat, O. In press. (4) Ramos, L.; Fabre, P. Langmuir 1997, 13, 682.
Figure 1. Flow curves (shear stress as a function of shear rate) for a swollen hexagonal phase: crosses, steady-state stress as a function of increasing γ˘ ; open circles, steady-state shear rates as a function of increasing and decreasing σ (the line is a guide for the eye; the arrows give the directions of the measurements). The shear-rate-controlled curve (crosses) exhibits two extrema and the stress-controlled (open circles) curve displays a hysteretic loop.
variation of σ with γ˘ is measured. By contrast, when σ is imposed, shear rate jumps are observed. The jumps occur exactly at γ˘ c1 when increasing the stress and at γ˘ c2 when decreasing the stress. A perfectly reproducible hysteretic loop is therefore obtained. Both the existence of jumps of the shear rate and the nonmonotonic behavior of the ratecontrolled flow curve indicate that, in the range γ˘ c1 < γ˘ < γ˘ c2, the flow is nonhomogeneous.5 Several complex fluids have been found to display similar behavior, as resulting from the coexistence of two states of different effective viscosity.1-3 The goal of the remainder of this Letter is to present the structures induced by low and high shear rates6 and to emphasize the unexpected features observed at high rates. The structures were studied by small-angle X-ray scattering (SAXS) under shear. The experiments were performed at the High Brilliance beamline ID2 at the European Synchrotron Radiation Facility, Grenoble, France, using a Couette cell. The scattering profiles were (5) Schmitt, V.; Marques, C. M.; Lequeux, F. Phys. Rev. E 1995, 52, 4009. Olmsted, P. D. Europhys. Lett. 1999, 48, 339. (6) In principle, slip could also produce such type of rheological data. However, the X-ray measurements prove unambiguously that the system presents indeed two types of structure under shear.
10.1021/la000276k CCC: $19.00 © 2000 American Chemical Society Published on Web 06/17/2000
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Figure 2. SAXS patterns of the sample submitted to a shear rate γ˘ ) 51 s-1 in (A) tangential and (B) radial geometry. (Inset C) Azimuthal dependence of the intensity contained within an annulus centered on q0 for pattern B. (C) Variation of the angular width of the azimuthal scans of radial pattern as a function of the shear rate.
recorded in two planes, one containing the vorticity ω and velocity v (radial geometry) and the other containing ω and the velocity gradient ∇v (tangential geometry). Figure 2 shows the SAXS pattern obtained for both geometries in the low shear rates regime. Isotropic rings are obtained in the tangential geometry, which correspond to diffraction peaks in the ratio q0:31/2q0:2q0, in agreement with the triangular symmetry of the hexagonal phase. This pattern corresponds to a powder sample with randomly oriented grains. By contrast, the spectrum obtained in radial geometry is strongly anisotropic, with maxima of intensity appearing normal to the flow, indicative of the cylinders aligning along the direction of the flow. At low rates, the system can thus be regarded as a polycrystal, the cylinders
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being preferentially oriented along the flow. A similar alignment has been observed for several lyotropic hexagonal phases7 and cylindrical phases of copolymers.8 The anisotropy under shear can be easily quantified through an azimuthal scan of the pattern, where the intensity averaged over a narrow band of scattering wavevectors centered around q ) q0 is plotted as a function of the azimuthal angle θ (inset Figure 2C). The scan exhibits two marked maxima along ω (θ ) 90° and 270°), with the intensity along ω being 2 orders of magnitude higher than the intensity along v. The decreasing angular width at half-maximum, ∆θ, of these maxima gives a measure of the increasing orientation of the grains with the shear rate. When γ˘ increases, ∆θ decreases from 25° for γ˘ ) 1.2 s-1 to 15° for γ˘ ) 10 s-1 (Figure 2C). We now focus on the novel structure obtained at high shear rates. In parts A and B of Figure 3 are reported the tangential and radial patterns obtained in this regime. The tangential profile displays a very broad isotropic ring. The intensity versus q plot obtained from an azimuthal integration of this pattern reveals a liquidlike structure, whose essential features are a strong low-angle scattering, a broad peak at the position of the first order of diffraction of the hexagonal phase q0, and the absence of higher orders of diffraction. On the other hand, the radial profile displays nearly round spots together with a strong scattering at low q. The azimuthal narrowness of the spots (the angular width ∆θ is around 10°) is the signature of a very good orientation of the cylinders along the flow. A structure consisting of a liquid of very well aligned surfactant cylinders accounts for all the essential features of the scattering data reported above. Therefore, the experiments prove that a high shear induces a melting of the longrange two-dimensional order of the cylinders. Surprisingly, after abrupt cessation of the high shear, a 6-fold symmetry is obtained in the tangential pattern within a few seconds (Figure 3E). The wave vectors of the diffraction peaks are the same as those for the initial hexagonal phase, and up to the fourth order of diffraction can be detected. As shown in Figure 3F, the azimuthal scan of the profile reveals the excessive sharpness of the spots. This pattern is the signature of an extremely well-oriented sample. The orientation is such that the dense planes (100) are parallel to the plane (ω,v), that is, to the cell walls. Consistently, the (100) diffractions cannot be seen in the radial profile since the (100) planes do not satisfy the Bragg conditions (Figure 3D). The single crystal morphology pertains for hours if the sample is left at rest but is immediately destroyed by applying a shear. SAXS patterns obtained at intermediate shear rates are full of information. In Figure 4 we show a series of blowups of the radial profiles centered on the first diffraction spot (θ ) 90°). As already mentioned, in the low shear regime, the spot is azimuthally elongated (though becoming narrower with increasing γ˘ , Figure 4A,B), while in the high shear regime it becomes almost round (Figure 4E). Interestingly, at intermediate shear rates the patterns (Figure 4C,D) strongly suggest the superposition of the two types of spots, indicative of the coexistence, under shear, of two types of structures, namely, the polycrystalline hexagonal phase and the (7) Lukaschek, M.; Grabowki, D. A.; Schmidt, C. Langmuir 1995, 11, 3590. Koltover, I.; Idziak, S. H. J.; Davidson, P.; Li, Y.; Safinya, C. R.; Ruths, M.; Steinberg, S.; Israelachvili, J. N. J. Phys. II 1996, 6, 893. Mu¨ller, S.; Fischer, P.; Schmidt, C. J. Phys. II 1997, 7, 421. (8) Almdal, K.; Bates, F. S.; Mortensen, K. J. Chem. Phys. 1992, 96, 9122. Morrison, F. A.; Mays, J. W.; Muthukumar, M.; Nakatani, A. I.; Han, C. C. Macromolecules 1993, 26, 5271. Balsara, N. P.; Dai, H. J.; Kesami, P. K.; Ganetz, B. A.; Hammouda, B. Macromolecules 1994, 27, 7406.
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Figure 3. SAXS patterns of the sample submitted to a shear rate γ˘ ) 1490 s-1 in (A) radial and (B) tangential, geometry. (D) Radial and (E) tangential SAXS patterns of the same sample taken immediately after cessation of the shear. (C) Intensity I versus q, obtained from an azimuthal integration of patterns B (dotted line) and E (full line). (F) Azimuthal scan of pattern E; I is averaged over an annulus of radius q0.
Figure 4. Blowups of the SAXS patterns in radial geometry: (A) γ˘ ) 12 s-1; (B) γ˘ ) 39 s-1; (C) γ˘ ) 295 s-1; (D) γ˘ ) 393 s-1; (E) γ˘ ) 1257 s-1. The zone corresponding to the first-order peak around the vorticity direction is shown.
melted phase.9 Such coexistence would be consistent with the concept of a first-order structural transition under shear. Experimentally, the coexistence appears to occur for shear rates between γ˘ c1 and γ˘ c2, the critical shear rates determined in rheology. This underlines the excellent quantitative agreement between the rheological measurements and the SAXS. The major and novel result of this paper is that a high shear can induce the melting of the long-range order of a hexagonal phase. Furthermore, after cessation of the shear, the melted phase leads to a single crystal of hexagonal phase. Such single-crystal morphology is of crucial importance in particular to study the anisotropic spectrum of thermal diffuse scattering, giving access to elastic moduli of the materials.10 Moreover, the investigation of the mechanisms and kinetics of crystallization of
this type of soft materials, by using a fast detector to record the time evolution of the pattern after the cessation of shear, is conceivable. Melting transitions under shear have been observed for cubic crystals.11,12 In this case, the existence of a periodic potential in the direction of the velocity seems to be the key point for the understanding of the transition.13 Such a periodic potential does not exit in our case: a system with all the cylinders strictly parallel to the velocity should flow at low viscosity. What is intriguing is thus the loss of the crystal order perpendicular to the flow. The specific mechanisms of the shear melting at work in our systems remain to be clarified.
(9) As pointed out by one of the reviewers, the rheological data would correspond to phase separation at common shear rate (bands perpendicular to ω).5 Therefore, scattering in the tangential geometry would not be expected to show such coexistence, unless the band structure were very fine; the experimental data seem to support this hypothesis. (10) Davidson, P.; Clerc, M.; Gosh, S. S.; Maliszewskyj, N. C.; Heiney, P. A.; Hynes, J., Jr.; Smith, A. B. J. Phys. II 1995, 5, 249. Impe´ror-Clerc, M.; Davidson, P. Eur. Phys. J. B 1999, 9, 93.
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Acknowledgment. We thank V. Urban for technical assistance during the SAXS experiments and L. Cipelletti for the use of his program. Discussions with A. Colin, O. Diat, and U. Peter are acknowledged.
(11) Ackerson, B. J.; Clark, N. A. Phys. Rev. Lett. 1981, 46, 123. Chen, L. B.; Hayter, J. B.; Clark, N. A.; Cotter, L. J. Chem. Phys. 1986, 84, 2344. (12) Olsson, U.; Mortensen, K. J. Phys. II 1995, 5, 789. (13) Stevens, M. J.; Robbins, M. O. Phys. Rev. E 1993, 48, 3778.
