Langmuir 1996, 12, 3131-3138
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Phase Transition Induced by Shearing of a Sponge Phase H. F. Mahjoub,* K. M. McGrath,† and M. Kle´man Laboratoire de Mine´ ralogie-Cristallographie, URA CNRS #9, Universite´ Paris VI, Tour 16-4, Place Jussieuscase 115, 75252 Paris, Cedex 05, France Received August 28, 1995. In Final Form: April 3, 1996X For the first time it has been shown that upon shearing of a sponge phase in a Couette cell a phase transition to a new highly birefringent phase with the same viscosity was induced. This transition is dependent upon the concentration of solvent, the length of time of shearing, and the history of the system.
1. Introduction Due to their amphiphilic nature, surfactant molecules are miscible in solutions of oil, water or combinations of the two and form thermodynamically stable assemblies which may be distinguished by their global topologies.1-4 For swollen surfactant systems two well characterized phases exist having a surfactant bilayer as their basic unit. The first, a lamellar phase (LR), is a birefringent one-dimensional array of indefinite bilayers stacked with smectic order.5-7 The second, the sponge phase (L3), by contrast is an optically isotropic three-dimensional random multiply connected bilayer dividing the solvent into two subvolumes.8-23 It has been known since the first observations of this phase that it exhibits a strong flow birefringence9,13 and that in all known occurrences of the phase it is neighbored by a lamellar phase. At present little work has been performed in order to distinguish the different models proposed to explain the behavior of the * To whom correspondence should be addressed. † Present address: Department of Physics, Princeton University, P.O. Box 708, Princeton, NJ 08544. PACS numbers 42.20, 47.15, 61.25, 61.12. X Abstract published in Advance ACS Abstracts, June 1, 1996. (1) Winsor, P. A. Chem. Rev. 1968, 68, 1. (2) Ekwall, P. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1975; Vol. 1, p 1. (3) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley: New York, 1980. (4) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1. (5) Larche, F. C.; Appell, J.; Porte, G.; Bassereau, P.; Marignan, J. Phys. Rev. Lett. 1986, 56, 1700. (6) Nallet, F.; Roux, D.; Prost, J. J. Phys. (Paris) 1989, 50, 3147. (7) Nallet, F.; Roux, D.; Milner, S. T. J. Phys. (Paris) 1990, 51, 2333. (8) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem Soc., Faraday Trans. 1 1983, 79, 975. (9) Gomati, R.; Appell, J.; Bassereau, P.; Marignan, J.; Porte, G. J. Phys. Chem. 1987, 91, 6203. (10) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J. Phys. (Paris) 1988, 49, 511. (11) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243. (12) Gazeau, D.; Bellocq, A.-M.; Roux, D.; Zemb, T. Europhys. Lett. 1989, 9, 447. (13) Porte, G.; Appell, J.; Bassereau, P.; Marignan, J. J. Phys. (Paris) 1989, 50, 1335. (14) Roux, D.; Cates, M. E.; Olsson, U.; Ball, R. C.; Nallet, F.; Bellocq, A.-M. Europhys. Lett. 1990, 11, 229. (15) Snabre, P.; Porte, G. Europhys. Lett. 1990, 13, 642. (16) Strey, R.; Schoma¨cker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253. (17) Strey, R.; Jahn, W.; Porte, G.; Bassereau, P. Langmuir 1990, 6, 1635. (18) Miller, C. A.; Gradzeilski, M.; Hoffmann, H.; Kramer, U.; Thanic, C. Prog. Colloid Polym. Sci. 1991, 84, 243. (19) Skouri, M.; Marignan, J.; Appell, J.; Porte, G. J. Phys. II 1991, 1, 1121. (20) Roux, D.; Coulon, C.; Cates, M. E. J. Phys. Chem. 1992, 96, 4174. (21) Vinches, C.; Coulon, C.; Roux, D. J. Phys. II 1992, 2, 453. (22) Waton, G.; Porte, G. J. Phys. II 1993, 3, 515. (23) Filali, M.; Porte, G.; Appell, J.; Pfeuty, P. J. Phys. II 1994, 4, 349.
S0743-7463(95)00723-2 CCC: $12.00
phase,24-33 or on the controlled shearing of the sponge phase to investigate the important phenomenon of flow birefringence.34-37 Previously the transition between the sponge, L3, and lamellar, LR, phases has been induced by varying the temperature,8,38,39 the salt concentration,40,41 or in the case where a cosurfactant is present the cosurfactant/surfactant ratio.9,10,13 While these transitions take place at equilibrium between thermodynamically stable phases, it is possible that the act of shearing of the sponge phase may be a new method capable of yielding insight into this type of phase transition. The two major theoretical works on the shearing of the sponge phase present conflicting results: Cates and Milner34 stipulated that the lamellar phase should be stabilized over the sponge phase upon shearing whereas the contrary was concluded in the work of Bruinsma and Rabin.35 Experimentally, Diat and Roux37 found a regime of flow birefringence above some shear rate threshold for the L3 phase in a quaternary system housed in a Couette cell with observations made in a perpendicular orientation to that adopted here. The value of the shear rate threshold increased on decreasing dilution. It was stated in this reference that it would be necessary to go to much higher shear rates than those experimentally available to obtain dynamic lamellar domains under shear. Bruinsma et al.35,36 have also studied the behavior of the L3 and Helfrich lamellar phases under the influences of an applied shear and claimed that the L3 phase is not unstable under such conditions. Hoffmann et al.42-44 have stated but not rigorously shown that a transition to a birefringent state may be induced (24) Cates, M. E.; Roux, D.; Andelman, D.; Milner, S. T.; Safran, S. A. Europhys. Lett. 1988, 5, 733. (25) Huse, D.; Leibler, S. J. Phys. (Paris) 1988, 49, 605. (26) Milner, S. T.; Cates, M. E.; Roux, D. J. Phys. (Paris) 1990, 51, 2629. (27) Huse, D. A.; Leibler, S. Phys. Rev. Lett. 1991, 66, 437. (28) Porte, G.; Delsanti, M.; Billard, I.; Skouri, M.; Appell, J.; Marignan, J.; Debeauvais, F. J. Phys. II 1991, 1, 1101. (29) Wennerstro¨m, H.; Olsson, U. Langmuir 1993, 9, 365. (30) Gompper, G.; Hennes, M. J. Phys. II 1994, 4, 1375. (31) Gompper, G.; Goos, J. Phys. Rev. E 1994, 50, 1325. (32) Gompper, G.; Schick, M. Phys. Rev. E 1994, 49, 1478. (33) Daicic, J.; Olsson, U.; Wennerstro¨m, H.; Jerke, G.; Schurtenberger, P. J. Phys. II 1995, 5, 199. (34) Cates, M. E.; Milner, S. T. Phys. Rev. Lett. 1989, 62, 1356. (35) Bruinsma, R.; Rabin, Y. Phys. Rev. A 1992, 45, 994. (36) Plano, R. J.; Safinya, C. R.; Sirota, E. B.; Wenzel, L. J. Rev. Sci. Instrum. 1993, 64, 1309. (37) Diat, O.; Roux, D. Langmuir 1995, 11, 1392. (38) Quilliet, C.; Kle´man, M.; Benillouche, M.; Kalb, F. C. R. Acad. Sci., Ser. II 1994, 319, 1469. (39) Nastichin, Y.; Lambert, E.; Boltenhagen, P. C. R. Acad. Sci., Ser. II 1995, 321, 205. (40) Fontell, K. Colloid Dispersions and Micellar Behaviour; American Chemical Society: Washington, DC, 1975; p 270. (41) Miller, C. A.; Ghosh, O. Langmuir 1986, 2, 321. (42) Hoffmann, H.; Hofmann, S.; Rauscher, A.; Kalus, J. Prog. Colloid Polym. Sci. 1991, 84, 24.
© 1996 American Chemical Society
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Figure 1. Partial phase diagram at 24 °C of the quasiternary system CPCl/hexanol/1 wt % NaCl brine. Vertical axis represents the ratio (h/c) of cosurfactant (hexanol) to surfactant (CPCl): LR, lamellar phase; L3, sponge phase; diagonally shaded area, region of coexistence between the L3 and LR phases. At high values of h/c a multiphase region exists which has not been characterized.
upon shearing of the L3 phase. Recently this transformation has also been observed in a surface forces apparatus.45 In this case the sponge phase was confined between two macroscopic walls. On decreasing the distance between the walls a first-order transition to a lamellar phase was induced, but this lamellar phase was metastable, relaxing back to the original sponge phase over a short period of time. Presented here is a rheo-optical study performed on the sponge phase of a quasiternary system. The phase exhibits completely reversible flow birefringence only for low rates of shear followed by a phase transition when the rate of shear exceeds a critical value dependent on several experimental conditions, yielding a new highly birefringent phase, LR*, which displays defects typical of a lamellar phase. A study is in progress at present on the rheological properties of this new birefringent phase. The newly formed lamellar phase was found to relax completely to the original L3 phase once shearing had ceased with the time of relaxation being dependent on the concentration and rate of shearing. 2. Experimental Section The system studied (consisting of a quaternary ammonium surfactant, cetylpyridinium chloride (CPCl, H2O content 1 mol/ mol), a cosurfactant, hexanol (98% pure), and brine (1 wt % NaCl (99.999% purity) solution) where all reagents were used as received) has been described in detail previously.9,10,13,28,38,39,46,47 The partial phase diagram is given in Figure 1. A first-order phase transition is induced between the lamellar and sponge phases for values of h/c (the ratio of cosurfactant (hexanol) to surfactant (CPCl)) in excess of 1.05 at 70% solvent by weight. As the system is diluted, the lamellar phase has the greater stability of the two phases for a given h/c. This has been found to be true on increasing temperature also.38,39 Both phases are able to be swollen extensively by the addition of solvent.10,13,26,47 All rheo-optical work was performed using a Rheometer Optical Analyzer (ROA, γ˘ max ) 500 s-1) equipped with a Couette cell (gap between cylinders ) 1 mm, radius of interior cylinder ) 16 mm, volume of fluid ) 5 mL). This rheometer allows optical measurements only (birefringence in the plane of flow (shear plane, V ∇ V), angle of extinction and transmitted light intensity) while shearing the sample. The light beam (helium-neon laser, (43) Platz, G.; Thunig, C.; Hoffmann, H. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 667. (44) Hoffmann, H.; Thunig, C.; Munkert, U.; Meyer, H. W.; Richter, W. Langmuir 1992, 8, 2629. (45) Antelmi, D. A.; Ke´kicheff, P.; Richetti, P. J. Phys. II 1995, 5, 103. (46) Boltenhagen, P.; Lavrentovich, O.; Kle´man, M. J. Phys. II 1991, 1, 1233. (47) Boltenhagen, P.; Kle´man, M.; Lavrentovich, O. D. J. Phys. II 1994, 4, 1439.
Mahjoub et al. emitting plane polarized light of λ ) 632.8 nm) is parallel to the long axis of the Couette cell (light path ) 1.2 cm) in the region between the two cylinders. The form of the Couette is such that evaporation of water or hexanol was found not to be a problem (the vapor pressures of water and hexanol at 24.4 °C are 22.9 and 1.0 mmHg, respectively; i.e., the evaporation of water is potentially a greater problem than that of hexanol, see paragraph 3.5), the Couette being fitted with a cover (quartz window) transparent to the laser beam (i.e. the sample is not in contact with air and during the course of an experiment the composition of the sample remained constant). Repeated runs on samples which did not undergo transitions (i.e. those where either the concentration of water was too low and/or the rate of shearing was too weak) were identical, and no transition could be induced under the experimental conditions employed; note that this would not have been the case if slight evaporation of hexanol had occurred. Reproducibility of phase transitions was found to be easily obtained for all concentrations and rates of shearing. The birefringence (∆n) was determined from the measured intensity of the transmitted laser beam using a linear polarizer (transmission axis perpendicular to the optical rail) placed before the sheared sample and a left-handed circular polarizing detector after, as follows
I ) I0(1 + sin δ cos 2θ sin 4ωt + sin δ sin 2θ cos 4ωt) (1) where
δ)
2π∆nd λ
(2)
is the optical path difference, d is the total distance traveled by the light beam through the sample, λ is the wavelength of the light beam, θ is the angle between the polarizer and the optic axis of the sample, ω is the angular frequency, and Io is the incident intensity. Using the ROA, the evolution of the birefringence may be monitored as a function of the duration of shearing for a set value of the rate of shear (γ˘ ). Experiments were in general performed by imposing set times for the time of shear (∆tshear) and time of no shear (∆trel) as γ˘ was increased in a stepwise fashion for a single sample. The angle of extinction (χ), also measured by the ROA, is the smaller of the two angles between the cross of the isocline48,49 and the polarization planes; i.e., the direction of the optical axis is oriented at an angle χ or χ + π/2 with respect to the flow lines which is also some average direction of the molecules. All viscosity measurements were performed using a Contraves Low Shear-30 Couette viscometer (LS30, γ˘ max ) 100 s-1, gap 1 mm, internal radius 6.5 mm, and liquid volume 1 mL). The Couette cell used in this apparatus allowed contact of the sample with air. In order to control evaporation, all work was performed in a water-saturated atmosphere (see paragraph 3.3). Viscosity measurements were performed on samples in the sponge phase and in the lamellar phase close to the LR/L3 border. Small angle X-ray scattering/rheological studies were also performed at LURE, Orsay, where an X-ray transparent Couette cell of internal radius 10 mm and gap 0.5 mm (γ˘ max ) 2000 s-1) was oriented such that the X-ray beam was transmitted perpendicular to the axis of the cylinder, traversing 1 mm in total through the sample (i.e. two times 0.5 mm). A side conclusion of these measurements (see paragraph 3.5) is that there is no evaporation of hexanol or water during experiments. All measurements were performed at ambient temperature using samples between 75 and 95 wt % solvent and h/c ) 1.15 (note that, for 95 wt % brine, h/c ) 1.225; see Figure 1).
3. Results and Discussion The rheo-optical behavior (measurement of ∆n and χ) of the sponge phase under shearing shows the existence of two regions which are dependent upon the value of the rate of shear (γ˘ , see Figure 2). The initial region of linear flow (where the samples exhibit reversible linear flow birefringence) as a function of shear rate is distinguished (48) Maxwell, J. C. Proc. R. Soc. London 1873, 22, 46. (49) Maralt, A. C.; Edsall, J. T. J. Biol. Chem. 1930, 89, 319.
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Figure 2. Evolution of birefringence (∆n, a and b) and angle of extinction (χ, c and d) upon shearing for various solvent concentrations (95 (9, h/c ) 1.225), 90 (], h/c ) 1.15), 85 (2, h/c ) 1.15), and 75 wt % solvent (O, h/c ) 1.15)). Measured on a ROA at 24 °C with ∆tshear ) 300 s and ∆trel ) 200 s. a and b (note difference in both ∆n and γ˘ scales) show an initial linear variation of ∆n on increasing the rate of shear (γ˘ ), for γ˘ < γ˘ c. For γ˘ ) γ˘ c there is an abrupt increase in this value for 95, 90, and 85 wt % solvent samples, indicating the occurrence of a phase transition. This break was not observed for the 75 wt % solvent sample, which remained isotropic for all values of γ˘ applied. ∆n continued to increase in a nonlinear fashion for those samples which underwent the phase transition. This behavior was mirrored by the variation of χ with γ˘ (c and d). For γ˘ < γ˘ c, χ tends to -45° and changes dramatically at γ˘ ) γ˘ c to ca. -5°, where it remained for all subsequent values of γ˘ , again indicating the presence of a phase transition. Note that the negative realm for χ is represented in these figures, since this was found to be favored experimentally over the positive orientation (see Figure 3).
from the second by a critical value of the rate of shear γ˘ c. For values of γ˘ in excess of γ˘ c the sponge phase acquires a large birefringence due to the occurrence of a phase transition to a metastable (with its lifetime being dependent on the initial concentration of the solution) birefringent phase. During these experiments an effect on changing the solvent concentration was also observed. Concentrated solutions (e80 wt % solvent) showed no transition for all γ˘ < 500 s-1 whereas the more highly diluted sponge phases readily underwent a transition (i.e. as the concentration of solvent increases, γ˘ c decreases; see paragraph 3.4.1). The value of ∆n for reversible flow birefringence only in the plane of the flow (i.e. in the initial linear flow regime) was of the order of 10-8 to 5 × 10-7 for all brine concentrations (including samples of low brine concentration, where no phase transition to the new highly birefringent phase could be induced; see Figure 2a and b). The angle of extinction, χ, for this type of flow, initially equal to ca. (20°, altered sparingly for γ˘ < γ˘ c but changed dramatically for γ˘ e γ˘ c, attaining a value of (45°. It is therefore possible to distinguish in the γ˘ < γ˘ c region a pretransitional range of values from the behavior of χ. This behavior of χ (tending to (45° upon shearing) has not been documented for solutions of macromolecules whose χ initial value is system dependent;50 most usually, such systems show a monotonous decrease of χ with ∆n, indicating an elongation of the macromolecules along the flow. The present results are therefore interpreted as a laying out of lamellar domains at an angle R ≈ (45° with the direction of the flow (see Figure 3a). (50) Cerf, R.; Scheraga, H. A. Chem. Rev. 1952, 51, 185.
When γ˘ > γ˘ c, χ dramatically falls to ca. -5° (see Figures 2c and d). Simultaneously the value of ∆n is observed to increase at γ˘ c to 10-6 and continues to increase to saturation (ca. 10-5, see Figure 2a and b). This behavior indicates a modification in the response of the system to shearing and the presence of a new highly birefringent and ordered phase. Note that for 75 wt % solvent this behavior was not observed and the sample remained L3 for the values of γ˘ available (i.e. ∆n remained linear with respect to increasing γ˘ , Figure 2b). Upon ceasing shearing, the newly formed birefringent LR* relaxes toward the sponge phase with ∆n decreasing toward 5 × 10-8 and χ tending to 25-30°. It should be noted that the time for complete relaxation is dependent on the initial solution concentration and the time of shearing. 3.1. Variation of χ and ∆n under Shearing. 3.1.1. γ˘ , γ˘ c. In this regime the geometry of the membranes which undergo anisotropic deformations relaxes completely (i.e. the original sponge phase can be rapidly recovered; see paragraph 3.5) for very weak rates of shearing (i.e. γ˘ far from γ˘ c), i.e., their time of relaxation (τr) < γ˘ -1, before a new shear rate is applied to the samples. As the value of γ˘ tends to γ˘ c, this relaxation (during time ∆trel) becomes only partial. The deformation under shear yields an intrinsically perturbed state, where the membrane on average no longer has the characteristics observed for the original sponge phase (i.e., its curvature may be altered locally and/or globally). The phase remains however, on complete relaxation, isotropic; the response to the flow is linear, indicating that the L3 phase is a quasi-Newtonian fluid for γ˘ < γ˘ c. The birefringence in this linear regime may
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Figure 4. Variation of the dynamic viscosity (η (cp)) with γ˘ for an L3 phase (2, h/c ) 1.15 and 85 wt % solvent) which undergoes a phase transition to the LR* phase at γ˘ c ) 64 s-1 and a bulk lamellar phase (LR, O, h/c ) 1.075 and 85 wt % solvent) measured at 24 °C using the LS30.
Figure 3. Model for local layering under shear. (a) Coordinate system, where V is the velocity vector and R the angle of the bilayers with respect to this system. (b) Compressive case: normal of the bilayers makes an angle of -45° with the direction of flow, and the mobile edge dislocations created at the inner boundary move toward the outer, relieving the deformation caused by the curvature of the Couette cell. (c) Tensile case: contrary to the compressive case, here the normal to the layers is at an angle of +45° and the edge dislocations move in the opposite sense.
be written as28
∆n ) Bflowγ˘ ∝ βφ
(3)
where β is a structural anisometry constant induced by shearing and φ is the volume fraction of the membrane. The induced anisometry β is related to the finite time required for relaxation of the deformation of the membrane: β ∝ τ1γ˘ with a prefactor of the order of unity, where
τ1 ∝
ηd h3 kBT
)
ηδ3 -3 φ kBT
(4)
d h , which is proportional to δ/φ, is the correlation distance as measured in scattering experiments, and δ is the bilayer thickness.28 This leads therefore to Bflow being proportional to φ-2, since τ1 scales as φ-3. In the linear (flow birefringence) regime where complete relaxation occurs, the origin of birefringence is the formation of lamellar microscopic regions whose normals tend to orient about the direction of the extinction angle, with some unknown probability distribution. One can speculate, as in ref 37, that these domains form at the expense of strangling and fusion of passages in the sponge phase. The first process is induced by stress and consists of a narrowing of a passage by hydrodynamic diffusion,
h 2/D may in the rather short time τ1. The expression τ1 ) d be adopted, where D is a diffusion constant which has h ) 335 been measured directly for this system;22 taking d Å for φ ≈ 0.11 (see paragraph 3.1.3), τ1 ≈ 0.0035 ms, i.e. ω1 ≈ 2.9 × 105 s-1. This value of τ1 agrees reasonably well with our experimental data for β (from eq 3). The second process, according to the same reference, is the longest characteristic relaxation process of the L3 phase and involves topological changes (relaxation of passages): τ3 ≈ 400 ms, ω3 ≈ 2.5 s-1. Since here γ˘ is always greater than ω3, it may be concluded that, for the experimental conditions applied, the system is above the threshold for relaxation of the passages, which are therefore partly quenched. Hence the structure is anisotropic, either due to the production and/or annihilation of oriented passages upon shearing, or the orientation of the passages by the shear. It is this anisotropy which is responsible for the linear birefringence observed below γ˘ c, where the phase is able to relax fully and readily to the original sponge phase. This quasi-Newtonian nature of the L3 phase was confirmed by measurements of its viscosity under shear using the LS30 (see paragraph 3.3): the viscosity remained practically constant for all values of γ˘ applied (i.e. in fact not only in the L3 phase below γ˘ c but also in the LR* phase above γ˘ c, see Figure 4). 3.1.2. γ˘ e γ˘ c. This region, where χ tends towards (45°, deserves some special comments. The stress tensor,
|0110 |
σ ) ηγ˘
is introduced having axes Ox along the direction of the velocity and Oy along the velocity gradient. It is easy to show that these stresses yield pure shear forces in planes parallel to the coordinate planes and pure normal forces in planes bisecting the latter. Therefore, for planes at an angle of (45° with the coordinate axes, the situation is comparable to that described by Antelmi et al.45 The forces acting on a slice of the sponge phase, whose normal makes an angle R ) -45° with the Ox, axis suffer compressive normal surface forces (σc ) x2-1ηγ˘ , Figure 3b), transforming the sponge phase into a lamellar phase given that they are sufficiently large; contrarily the forces acting on a slice of the sponge phase whose normal makes an angle R ) +45° with the Ox axis suffer tensile normal surface forces (σt ) x2-1ηγ˘ , Figure 3c) and stabilize the sponge phase. The experimental tendency of the extinction angle (χ) to take a value of -45° indicates that the compressive normal forces are dominant. Note that an important difference between the surface forces apparatus
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and the Couette cell exists: neighboring layers in the Couette cell lie at a small angle to one another due to the curvature of the cell. This deformation is however relaxed by a density (F ) 1/rd h )51 of mobile edge dislocations parallel to the Oz axis, which continuously move toward the outer boundary of the Couette cell, having been created at the inner boundary (compressive case, Figure 3b, and vice versa for the tensile case shown in Figure 3c). This is therefore the motor of the transition. Another proof of this lies in the fact that the critical shear rate measured in the LS30 (under the same experimental conditions) is approximately two times smaller than that measured in the ROA, probably being due to the fact that the radius of the LS30 is also approximately two times smaller, and therefore the density of the defects is twice as large. This variation of γ˘ c with internal radius of the Couette cell for otherwise identical conditions has been confirmed by using other Couette cells of differing internal radius. 3.1.3. γ˘ > γ˘ c. In this regime the sponge phase underwent a phase transition yielding a new highly birefringent metastable phase. The angle of extinction changed dramatically to ca. -5° following this transition, indicating that in the plane of flow the membranes are oriented on average parallel to the axes of the cylinders of the Couette. One of the axes of this new birefringence is therefore quasiparallel to the flow lines. It should be noted that this does not indicate a perfect orientation of the molecules with the walls of the cylinders. This orientation has been shown to be adopted initially for lyotropic lamellar phases under shear,35,37,52-55 at this stage further rheological experiments on this new birefringent phase have not been conducted. The value of ∆n is of the order of 5 × 10-6 to 10-5, similar to that measured for a normal Helfrich lamellar phase. This change in structure under shearing was confirmed by observation of the phase directly after shearing between crossed polarizers and also by crossed polarizing microscopy. The optical observation of these birefringent samples showed the existence of defects characteristic of a normal lamellar phase.46,56,57 Initial small angle X-ray scattering studies on the sponge phase before (d h (L3) ≈ 335 Å, 90 wt % solvent, h/c ) 1.15) and after (d h (LR*) ≈ 270 Å) shearing confirmed that the newly formed birefringent phase was of the lamellar type by the presence of a fine Bragg peak not observed for the original sponge phase (this will be discussed in detail in a forthcoming article). 3.2. Dynamic Features of the Phase Transition Induced in a ROA Couette Cell. Presented in Figure 5 are schematics following the evolution of ∆n and χ for L3 samples under increasing shear. Scheme 1 (γ˘ < γ˘ c) shows ∆n and χ initially: Under shear ∆n increases to ca. 7 × 10-7 and χ tends to -45°. On ceasing shearing, the phase relaxes completely, with ∆n and χ returning to their original values. In Scheme 2 (γ˘ is still less than γ˘ c) a local lamellar stacking is created during the second half of the shearing time (∆tshear). This is detected by the increase in ∆n and by χ no longer oscillating between (45°. Once the shear is stopped, the newly formed birefringent phase relaxes rapidly back to an isotropic state (∆n ≈ 4 × 10-8). In Scheme 3, under the application of a higher value of γ˘ the liquid under shear shows a flow birefringence initially
as expected followed by a strong and steady increase in ∆n, which attains a value of ca. 7 × 10-6, this value being greater than that observed in the later stages of shearing in Scheme 2. Once the shearing is stopped, ∆n does not drop back to its initial value (i.e. no immediate relaxation of the newly formed birefringent phase occurs, contrary to the case for flow birefringence alone). Intriguingly in fact ∆n continues to increase after shearing, finally reaching a plateau at ca. 8 × 10-6. (In fact, if the sample is removed at this point, two phases are observed (L3 plus LR*).) This implies that on average the fluid between the cylinders has a structure pertaining to that of the newly formed birefringent phase. This is also confirmed by χ maintaining a value of -5°. The difference in the situations in Schemes 2 and 3 is therefore due to the birefringent phase relaxing during ∆trel for Scheme 2 but not for Scheme 3. Scheme 4 shows the continued growth and refinement of the birefringent phase as shown by the increase of ∆n to 10-5. At this stage a lamellar phase oriented on average with its bilayers quasiparallel to the shearing plane is formed. As γ˘ is increased, the lamellar phase becomes increasingly ordered and stable due to a mechanism which at present is unknown. If at this point the newly formed single LR* phase is allowed to relax, the original sponge phase is recovered in all instances with the time of relaxation depending on the concentration of the original solution and the time of shearing. For example the LR* phase formed initially from a 90 wt % sample with h/c ) 1.15 relaxed in approximately 1 h, but if the time of shearing was increased (i.e., shearing was continued passed that required for a transition to occur) the relaxation time was increased markedly. 3.3. Viscosity Measurements. The newly formed birefringent phase (LR*) was found to have the same viscosity as the sponge phase from which it originated (i.e. this transition could not be detected by viscosity changes). The constancy of the viscosity over the entire range of applied shears gave confirmation that no evaporation of either water or hexanol occurred upon shearing the sponge phase in the Couette cell (see also paragraph 3.5), since the viscosity in this region of the phase diagram was dependent on both h/c and solvent concentration for both the thermodynamically equilibrated sponge and lamellar phases (see paragraph 3.4.1). This was not the case for bulk lamellar phase (LR) samples close to the LR/L3 phase transition. Here η varied strongly with γ˘ and was considerably higher than that found for the sponge phase at the same solvent concentration (Figure 4). How can these observations for the behavior of the viscosity of these three phases be correlated? At low rates of shear, the measured viscosity of the bulk lamellar phase is considerably higher than that for the sponge phase at the same solvent concentration but different h/c ratio. The lamellar phase, in comparison to the L3 phase and to the LR*, is initially full of defects (e.g. dislocations, disclinations and focal conics46,47,58 ) on which the viscosity of the phase is critically dependent, leading to a high initial value of η. As the rate of shearing is increased, the lamellar phase experiences the phenomenon of shear thinning due to the gradual loss of defects, or equivalently the increasing perfection of its smectic order. The viscosity decreases continuously with increasing γ˘ due to these phenomena. It should be noted though that it is highly unlikely that a “perfect” state would ever be reached. The sponge phase
(51) Nye, J. F. Acta Metall. 1953, 1, 153. (52) Diat, O.; Roux, D.; Nallet, F. J. Phys. II 1993, 3, 1427. (53) Roux, D.; Nallet, F.; Diat, O. Europhys. Lett. 1993, 24, 53. (54) Safinya, C. R.; Sirota, E. B.; Bruinsma, R. F.; Jeppesen, C.; Plano, R. J.; Wenzel, L. J. Science 1993, 261, 588. (55) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (56) Rosevear, F. B. J. Am. Oil Chem. Soc. 1954, 31, 628. (57) Rosevear, F. B. J. Soc. Cosmet. Chem. 1968, 19, 581.
(58) Boltenhagen, P.; Kle´man, M.; Lavrentovich, O. D. In Soft Order in Physical Systems; Rabin, Y., Bruinsma, R., Eds.; Plenum Press: New York, 1994; p 5.
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Figure 5. Schematics for ∆n and χ evolution with shearing of the L3 phase. Scheme 1: γ˘ < γ˘ c, the sponge phase exhibits flow birefringence only (∆n is of the order of 1 × 10-7 and χ ≈ -45°, during shearing) in this linear region of shear. Upon ceasing shearing, the sample relaxes back to an isotropic state with a random orientation with respect to the walls of the cylinders (∆n ≈ 4 × 10-8 and χ ≈ 20°). Scheme 2: γ˘ e γ˘ c, the sample shows the first formation of an unstable birefringent state (∆n tends to 10-6) which relaxes immediately to an isotropic state after shearing has stopped. Scheme 3: γ˘ g γ˘ c, the flow birefringence observed in the initial linear regime gives way to a steadily increasing ∆n with increasing shear time due to the existence of the now stable/metastable birefringent phase (LR*). Simultaneously χ tends to -5°. Here, in contrast to the situation in Scheme 2 relaxation does not occur on ceasing shearing; instead χ is stable at -5° and ∆n continues to increase. Scheme 4: γ˘ > γ˘ c, the formation of LR* continues at the cost of L3, ∆n increases to a final steady value of ≈ 10-5, and χ remains at ≈ -5°.
in contrast does not experience shear thinning, since inherently it is an isotropic phase; it is possible however to envisage possible structural changes under shear
(reserving isotropicity), which could yield a change in the viscosity, but this was not the case here. Why then does the viscosity remain constant throughout
Phase Transition Induced by Shearing of a Sponge Phase
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Figure 6. Dependence of the critical shear rate (γ˘ c) on the volume fraction of the membrane (φ) for two different shear times, ∆tshear ) 60 (9) and 300 s (b), as measured by the ROA at 24 °C, with ∆trel ) 200 s.
Figure 7. ln(ηγ˘ c) as a function of ln φ at 24 °C for two values of ∆tshear (60 (9) and 300 s (b)), with ∆trel ) 200 s for all samples. Note that ηγ˘ c shows a similar dependence on φ for both ∆tshear as expected; i.e., ηγ˘ c scales as φ-2.6 and φ-2.4 for ∆tshear ) 60 and 300 s, respectively.
the phase transition between L3 and LR*? LR* is formed from an already highly sheared sample and hence has a low defect concentration. It is also feasible that it maintains many of the characteristics of the L3 phase, for example a high density of passages, as already proposed for swollen lamellar phases close to the L3 border.17,47 These two factors combined yield a lamellar phase with the same viscosity as the L3 phase. Also as γ˘ increases further, η(LR) tends toward η(LR*) and therefore the two phases may be identical under shear, although the ratio h/c remains that of the L3 phase for LR*. Unfortunately the LS30 is limited in the available γ˘ range and it was not possible to investigate this hypothesis further at this stage. Experiments are planned on a rheometer with transparent tools, allowing direct observation of the sample while under shear. It should be noted that this explanation is very simplistic, since the viscosity of all three phases is dependent on parameters other than just the defect nature and concentration, such as the density of connectivity and the pore size for the L3 phase and perhaps also LR*. 3.4. Experimental Conditions for Inducing the Phase Transition from L3 to Lr*. The value of γ˘ c depends on several experimental factors. 3.4.1. Concentration of the Solvent. Using the ROA and keeping all experimental conditions identical (e.g. a fixed time of shearing (∆tshear) and relaxation (∆trel)), the value of γ˘ c (taken to be that value of γ˘ , for which ∆n changes dramatically from 10-7 to 10-6 and χ from -45 to -5°) was observed to increase with decreasing dilution. Figure 6 shows the evolution of γ˘ c with φ for two different values of ∆tshear. In the simple models discussed by previous authors,34,35 the origin of the dependence of γ˘ c on φ is understood as follows. The critical value of L (the characteristic length for energy dissipation) may be defined as the limit at which the system is perturbed and the structure modified by the act of shearing for γ˘ ) γ˘ c and is approximately equal to d h . Substituting this value of Lc into the general equation for L
kBT ηγ˘
(5)
kBT 3 φ δ3
(6)
L3 ∝ yields
ηγ˘ c ∝
i.e. ηγ˘ c is proportional to φ3. It was noted previously (paragraph 3.3) that the viscosity of the L3 phase is dependent upon φ and cannot therefore be regarded as a constant. Figure 7 shows the experimentally determined
Table 1. Variation of γ3 1 and γ3 2 with ∆Tsheara sample
∆Tshear (s)
γ˘ 1 (s-1)
90 wt % solvent h/c ) 1.15 95 wt % solvent h/c ) 1.225
60 300 60 80 120 180 300
≈27.7 0.23 < γ˘ 1 < 0.277 ≈5.9
γ˘ 2 (s-1)
≈100 1 < γ˘ 2 < 1.285 51 < γ˘ 2 < 69 ≈13 ≈3.25 0.204 < γ˘ 1 < 0.277 0.695 < γ˘ 2 < 0.95 0.8 < γ˘ 1 < 0.149 0.15 < γ˘ 2 < 0.204
a Note that the values of γ ˘ 1 and γ˘ 2 determined here were obtained under much shorter ∆Tshear and ∆Trel times than those applied in the ROA experiments, leading to much lower values of γ˘ 1. When identical experimental conditions were applied, γ˘ 1 ≈ γ˘ c/2 (see text paragraph 3.1.2).
dependence of ηγ˘ c on the membrane volume fraction. An exponential of ca. 2.5 was derived from these graphs for both values of ∆tshear. The origin for the difference between this value and that predicted is as yet unknown. More data are required to discuss this point further, and experiments are in progress. 3.4.2. Time and Rate of Shearing. For a sample of given concentration the rate of shearing for which ∆n tends to the value observed for a normal lamellar phase in this system increases as the duration ∆tshear decreases (see Figure 5). That is the value γ˘ c is dependent on both the rate of shear (γ˘ ) and the shearing time (∆tshear). Note that this dependence may be reduced to one parameter only. By exploiting the relative ease with which experiments may be performed on the LS30, it was possible to follow the evolution of γ˘ c in a qualitative manner while measuring the sample viscosity. Using this apparatus, two rates of shearing were distinguished by following the evolution of the volume of the lamellar phase after shearing; γ˘ 1 ) the rate of shearing corresponding to the first stable formation of the new birefringent phase (i.e. that regime where flow birefringence is no longer observed), and γ˘ 2 ) the rate of shearing corresponding to the complete transition of the L3 phase into the new birefringent phase LR*. Table 1 gives the values of γ˘ 1 and γ˘ 2 for samples containing 90 and 95 wt % solvent for various values of ∆tshear. It must be emphasized that the evolution of γ˘ 1 and γ˘ 2 follows the same evolution as that observed for γ˘ c measured quantitatively from the ROA experiments. 3.4.3. History of the Sample. A fourth parameter is also important when explaining the transition from the L3 to LR* phasesthe history of the sheared sample. The value of γ˘ c may differ for two identical samples for the same value of ∆tshear due to a difference in the exact experimental conditions: samples are sheared at a given γ˘ for a time ∆tshear; they then remain at rest for a time ∆trel before being resheared at a new higher value of γ˘ for the
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which are ongoing were performed on a 90 wt % sponge phase with h/c ) 1.15. The system was observed for a constant shear rate with increasing time. In the flow birefringent regime it was observed that the original sponge phase was rapidly and fully recovered in all cases on ceasing shearing for times ranging from 9 min to 10 h. No evaporation of either hexanol or water leading to a transition of a stable birefringent phase was observed at any time in this linear regime. Using a shear rate capable of inducing formation of the LR* phase (30 s-1), it was observed, as a function of time that a two-phase region formed initially eventually transformed completely to the LR* phase. This transition was followed by the initial observation of a new narrower peak at larger q values which continued to grow unmoved at the expense of the L3 peak. As was observed in the ROA experiments on ceasing shearing, after a complete phase transition to the LR* phase had been induced, slow relaxation to the original sponge phase occurred (i.e. the original L3 phase peak was seen to grow at the expense of the LR* peak), with the rate of relaxation being dependent on the time of shearing. As the rate of shearing was increased, the time required for a complete phase transition to occur diminished, as observed for all other experimental setups. In fact at γ˘ ) 400 s-1 a complete transition could be induced in less than 30 s. Figure 8. Dependence of ∆n (a) and χ (b) on γ˘ for three identical sponge phase samples at 95 wt % solvent, h/c ) 1.225 with initial γ˘ ) 0.08 (4), 5 (b), and 8 (O) s-1 yielding γ˘ c ) 6, 9, and 16 s-1, respectively. Measured at 24 °C by the ROA for ∆tshear ) 300 s and ∆trel ) 200 s. Note that the form of these dependencies is the same as that shown in Figure 2.
same shear time ∆tshear. Hence if ∆trel or the initial value of γ˘ is different for the two samples, a different value of γ˘ c is obtained. That is for samples having a different ∆trel the value of γ˘ c will be greater for that sample having the greater ∆trel value. In addition if two samples have identical ∆trel but different initial γ˘ values (afterwards following the same sequence of γ˘ ), that with the lower initial γ˘ will have the lower value of γ˘ c. This follows since during the period when no shearing occurs (∆trel), it is not necessary that complete relaxation to the original L3 phase occurs. Thus the sample when resheared at a new higher value of γ˘ is already deformed. This condition leads one to the conclusion that the phase L3, which undergoes shearing following this sequence has a “memory” and that the accumulation of the effects of the deformations with and without a period of relaxation acts differently, leading to a variation in γ˘ c. Parts a and b of Figure 8 show ∆n and χ for a series of three identical samples (95 wt % solvent, ∆tshear ) 300 s, ∆trel ) 200 s) with initial values of γ˘ ) 0.08, 5, and 8 s-1 yielding γ˘ c ) 6, 9, and 16 s-1, respectively. 3.5. In-Situ X-ray Scattering. Preliminary results have been obtained at LURE, Orsay, where small angle X-ray scattering is being performed during shearing of the sample in order to follow the apparition, evolution, and relaxation of the LR* phase and also to ensure that no evaporation of water or hexanol occurred throughout the experimental sequence. These initial experiments
4. Conclusions It has been shown that a phase transition from an isotropic sponge phase to a new highly birefringent metastable lamellar phase (LR*) may be induced upon shearing in a Couette cell. The value of the rate of shear for which this transition occurs is dependent on several experimentally observable parameters: (a) On increasing the concentration of solvent, the transition becomes more feasible; i.e., γ˘ c decreases as the volume fraction of solvent increases. (b) The transition occurs more readily on increasing the time over which a certain shear rate is applied to the sample; i.e., as ∆tshear increases γ˘ c decreases. (c) For a given value of ∆tshear and sequence of applied shear rates, γ˘ c increases as the time of relaxation increases (∆trel). (d) For a given ∆tshear and ∆trel, γ˘ c decreases as γ˘ ini decreases. The dependence on these four experimentally controllable parameters is nontrivial. The experimental findings detailed indicate that during shearing the lamellar phase is stabilized over the sponge phase but that on ceasing shearing the sponge phase is returned as the true equilibrium state. Finally note that this ongoing study indicates the importance of factors such as stress and defect densities on the behavior of these phases, which has not been alluded to previously. Acknowledgment. We would like to thank JeanFranc¸ ois Tassin for allowing us to use his ROA at the University of Le Mans, France and for many useful discussions, Franc¸ oise Lafuma at ESPCI, Paris, France for allowing us the use of the LS30, and Claudie Bourgaux at the LURE facility Orsay and Bernard Coleman and Abdehafidh Gharbi for their useful comments. LA950723+
