Rheology and Dynamics of Micellar Cubic Phases and Related

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Rheology and Dynamics of Micellar Cubic Phases and Related Emulsions Carlos Rodrı´guez-Abreu,† Miguel Garcı´a-Roman,‡ and Hironobu Kunieda*,† Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai 79-7, Hodogaya-ku, Yokohama 240-8501, Japan, and Departamento de Ingenierı´a Quı´mica, Facultad de Ciencias, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada, Spain Received January 13, 2004. In Final Form: April 16, 2004 The rheological behavior of micellar cubic phases in C12EO25 systems and related emulsions has been investigated. In the aqueous C12EO25 binary system, the transition from the cubic phase to the micellar solution is associated with a sudden drop in viscosity and with a small enthalpy of transition. The elastic modulus and viscosity of the cubic phases show a maximum with concentration but remain very high within the range of existence of the cubic phase. Several relaxation processes seem to be present in binary cubic phases, and some of them occur in a time scale that can be followed by both rheology and dynamic light scattering measurements. Upon addition of a small amount of oil (decane), the rheological behavior changes remarkably. As the oil fraction increases, the relaxation times also increase and, finally, highly concentrated, gel-like emulsions are obtained. Contrary to conventional concentrated emulsions, the viscosity of cubic-phase-based emulsions is decreased by increasing the fraction of the dispersed phase. The nonMaxwellian rheological behavior at low oil fractions is described according to the model of slipping crystalline planes, modified by using a distribution of bulk relaxation times, and good fitting to the experimental data is obtained.

Introduction Micellar cubic phases are isotropic and highly viscous liquid crystals composed of discrete aggregates (micelles) ordered in a three-dimensional array.1 In normal micellar cubic phases (referred to simply as micellar cubic phases), the hydrophobic groups of the surfactant molecules form a core inside the aggregates, whereas, in inverse micellar cubic phases, the hydrophobic groups are distributed in the micellar surface, facing the oil-continuous phase. Normal micellar cubic phases have a highly positive surface curvature; therefore, they are usually found in highly hydrophilic surfactants and amphiphilic polymers. Cubic phases have peculiar acoustic properties, such as the ringing phenomenon,2 and have attracted interest due to their relationship with biological systems and potential applications as microreactors and templates. Moreover, in a previous article,3 we found that a large amount of oil can be incorporated in translucent, so-called cubic-phasebased concentrated emulsions. The transparency is attributed to the very small difference in the refractive indices between the cubic and excess-oil phases. These concentrated emulsions have been related to many commercial “gels”.4 Several authors have investigated the rheology of cubic phases, also referred to as “hard gels”.2,5-11 They show viscoelastic behavior, a very high elastic modulus (G′ > * Corresponding author. Phone & Fax: +81-45-339-4190. E-mail: [email protected]. † Yokohama National University. ‡ Universidad de Granada. (1) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (2) Gradzielski, M.; Hoffmann, H.; Oetter, G. Colloid Polym. Sci. 1990, 268, 167. (3) Rodrı´guez, C.; Shigeta, K.; Kunieda, H. J. Colloid Interface Sci. 2000, 223, 197. (4) Kunieda, H.; Rodrı´guez, C.; Tanimoto, M.; Shigeta, K. J. Oleo Sci. 2001, 50, 633. (5) Kossuth, M. B.; Morse, D. C.; Bates, F. S. J. Rheol. 1999, 43, 167. (6) Gradzielski, M.; Hoffmann, H.; Panitz, J.-C.; Wokaun, A. J. Colloid Interface Sci. 1995, 169, 103.

104 Pa), and shear-induced alignment. However, some aspects related to the dynamics of these systems still remain to be clarified, such as the divergences between experimental data and theoretical predictions. Moreover, there is a lack of reports on the rheological behavior of cubic phases in binary surfactant/water systems or macroemulsions stabilized by cubic liquid crystals.3 In this context, we investigated the rheology of the micellar cubic phase and related emulsions in a polyoxyethylene dodecyl ether aqueous system. The discussion is complemented with differential scanning calorimetry (DSC) and dynamic light scattering (DLS) experimental results. Materials and Methods Materials. Polyoxyethylene dodecyl ether containing an average of 25 oxyethylene units per molecule (designated C12EO25) was supplied by Tokyo Kasei Kogyo Co. Ltd. (Japan). N-decane (99%) from Tokyo Kasei Kogyo Co. Ltd. (Japan) was also used. All chemicals were used without further purification. Millipore filtered deionized water was used in the preparation of the samples. Methods. Rheological Measurements. The samples were homogenized and kept in a thermostated bath at 25 °C for at least 24 h before the measurements were performed in an ARES7 rheometer (Rheometric Scientific) using a cone-plate geometry (φ ) 25 mm; cone angle ) 0.1 rad). Dynamic frequency sweep measurements were performed in the linear viscoelastic regime, as determined previously by dynamic strain sweep measurements. Differential Scanning Calorimetry. A differential scanning calorimeter (Seiko Instrument, DSC6200) equipped with an (7) Eiser, E.; Molino, F.; Porte, G.; Pithon, X. Rheol. Acta 2000, 39, 201. (8) Jones, J. L.; McLeish, T. C. B. Langmuir 1995, 11, 785. (9) Jones, J. L.; McLeish, T. C. B. Langmuir 1999, 15, 7495-7503. (10) Radiman, S.; Toprakcioglu, C.; McLeish, T. Langmuir 1994, 10, 61. (11) Daniel, C.; Hamley, I. W.; Wilhelm, M.; Mingvanish, W. Rheol. Acta 2001, 40, 39.

10.1021/la0498962 CCC: $27.50 © 2004 American Chemical Society Published on Web 05/20/2004

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Figure 1. Phase behavior of the C12EO25/water system. I1 indicates a micellar cubic phase, Wm is a micellar solution, S is a solid-present region, and II indicates two liquid phases. This figure is adapted from ref 3. The two-phase region between the Wm and I1 phases, although present, is not shown in the phase diagram, since it is very narrow3. automatic sample changer was used. The samples were introduced in aluminum pans and then tightly sealed by an electric sealer. DSC traces were recorded using a heating rate of 2 °C/ min. An empty aluminum pan was used as a reference. Dynamic Light Scattering. Dynamic light scattering measurements were performed with a Malvern HPPS instrument using backscattering detection (angle ) 173°) and a He-Ne laser (λ ) 633 nm). All measurements were made at a constant temperature of 25 ( 0.01 °C. 10-mm glass cells were used. The distribution of relaxation times was calculated from the intensity correlation function using CONTIN analysis.

Results and Discussion Micellar Cubic Phase in the Binary C12EO25/Water System. A wide micellar cubic phase region (I1) is found in the C12EO25/water system, as shown in the phase diagram3 of Figure 1. The micellar cubic phase is the only liquid crystal formed in the C12EO25 aqueous system. Such a behavior is characteristic of very hydrophilic surfactants and amphiphilic polymers.12,13 It is known that the cubic phase in the C12EO25/water system is formed by discrete aggregates packed in an Im3d body-centered structure, as confirmed by small-angle X-ray scattering (SAXS) measurements.3 Experiments and computer simulations indicate that this structure is favored in systems with long-range interactions among soft spheres.14 The phase boundary between I1 and the micellar solution phase (Wm) was determined visually by a sharp change in viscosity, from a solidlike state to a fluid state, which is similar to a melting phenomenon. To analyze this transition, DSC and rheological measurements were performed at a constant surfactant concentration, and the results are shown in Figure 2. The DSC analysis (Figure 2a) gives a small endothermic peak corresponding to a first-order transition at ∼57 °C, which coincides with the melting temperature determined visually. The melting process takes place in a narrow range of temperatures, an indication of the presence of welldefined structures. The enthalpy associated with the transition is 1.6 kJ/mol of surfactant, which is very low but still within the range of enthalpies of fusion in liquid crystals.15 (12) Shigeta, K.; Olson, U.; Kunieda, H. Langmuir 2001, 17, 4717. (13) Kanei, N.; Watanabe, K.; Kunieda, H. J. Oleo Sci. 2003, 52, 607. (14) Hamley, I. W. Philos. Trans. R. Soc. London, Ser. A 2001, 359, 1017. (15) Lopez-Quintela, M. A.; Akahane, A.; Rodrı´guez, C.; Kunieda, H. J. Colloid Interface Sci. 2002, 247, 186.

Figure 2. (a) DSC curve for a micellar cubic phase sample. Composition: 50 wt % C12EO25; 50 wt % water. (b) Temperature ramp test along line A of Figure 1. |η*| is the complex viscosity and G′ and G′′ are the storage and loss moduli, respectively. Test conditions: ω ) 10 rad s-1; strain ) 1%.

Cubic phases are usually formed at surfactant concentrations below the minimum required for a close packing of spheres; therefore, there is a contribution to the effective micellar volume fraction coming from the hydration of the surfactant headgroups. The enthalpy change associated with the total dehydration of polyoxyethylene (EO) chains16,17 is much higher than that obtained for the cubic phase; hence, the melting of the cubic phases might occur by a decrease in intermicellar interactions (and, consequently, in the effective volume fraction) due to the partial dehydration of the terminal ends of the EO chains. Figure 2b corresponds to a rheological temperature ramp test. The sample shows viscoelastic behavior, and the storage (elastic) modulus (G′) prevails over the loss (viscous) modulus (G′′) up to 50 °C, indicating the solid character of the sample. The values of G′ are well above 104 Pa, which is typical for cubic phases.11 As temperature increases, G′ approaches G′′ and the crossover takes place at ∼50 °C. This indicates a decrease in the relaxation times as temperature increases. The viscosity slightly decreases with temperature but remains very high up to 57 °C, and then, a sudden decrease is found, corresponding to the melting point observed visually and in the DSC curve. After melting, the sample does not show viscoelastic properties but behaves as a Newtonian fluid, as confirmed by steady shear rate viscosity measurements (not shown), which is a common behavior for solutions of spherical or quasi-spherical micelles. The order-disorder phase transition has been previously determined via the temperature dependence of the dynamic shear moduli.9,18,19 (16) Seimiya, T. J. Colloid Interface Sci. 2003, 266, 422. (17) Inoue, T.; Ohmura, H.; Murata, D. J. Colloid Interface Sci. 2003, 258, 374. (18) Brown, W.; Schillen, K.; Almgren, M.; Hvidt, S.; Bahadur, P. J. Phys. Chem. 1991, 95, 1850. (19) Hvidt, S.; Jorgensen, B.; Brown, W.; Schillen, K. J. Phys. Chem. 1994, 98, 12320.

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Figure 4. Complex viscosity (|η*|) at ω ) 0.01 rad s-1 (9) and the storage modulus (G′) at ω ) 10 rad s-1 (O) as a function of the C12EO25 concentration in the C12EO25/water system at 25 °C (strain ) 1%). The lines are only guides to the eyes.

Figure 3. (a) Dynamic frequency sweep test (strain ) 1%) for a micellar cubic phase sample at 25 °C. Composition: 50 wt % C12EO25, 50 wt % water. The lines are power law fittings to the experimental data. (b) Change of the exponent (∆) for the G′(ω) and G′′(ω) power laws as a function of temperature. Filled circles, ∆G′; open circles, ∆G′′.

Figure 3a shows the results of a dynamic frequency sweep test for a micellar cubic phase at 25 °C. The change of G′ with frequency is much more pronounced than that observed in the cubic phases formed by block copolymers.14 This might be attributed to a hard-sphere-like behavior20 of C12EO25 micelles, contrary to block copolymers with a long corona block relative to the core, which behave as soft spheres.21,22 According to the Maxwell model for viscoelasticity, G′ ∼ ω2 and G′′ ∼ ω in the low frequency range. However, the fitting of the experimental data to a power law gives exponents that are much lower than the above-mentioned ones, indicating highly non-Maxwellian behavior, probably associated with multiple relaxation times. The observed viscoelastic behavior is qualitatively similar to that predicted by the model of soft glassy rheology.23,24 In this model, the interactions are represented by a “mean-field noise temperature” related to the exponent (∆) of the power law G ∼ ω∆. A similar tendency is predicted by the percolation theory of complex fluids,25 but the expected exponent is much higher than those (20) Rueb, C. J.; Zukoski, C. F. J. Rheol. 1998, 42, 1451. (21) Hamley, I. W.; Daniel, C.; Mingvanish, W.; Mai, S.-H.; Booth, C.; Messe, L.; Ryan, A. J. Langmuir 2000, 16, 2508. (22) Gast, A. P. Langmuir 1996, 12, 4060. (23) Sollich, P.; Lequeux, F.; Hebraud, P.; Cates, M. E. Phys. Rev. Lett. 1997, 78, 2020. (24) Sollich, P. Phys. Rev. E. 1998, 58, 738. (25) De Gennes, P. G. J. Phys., Lett. 1976, 37, L1-L2.

shown in Figure 3a, which has been attributed to the presence of an excess of effective cross-links.26 As can be seen in Figure 3b, ∆ tends to increase with temperature for both G′ and G′′. The values of ∆ for G′ and G′′ approach each other in the vicinity of the order-disorder transition, but at a value of ∆ higher than that expected from percolation theories25 and previous data on block copolymer systems.27 Dynamic frequency sweep measurements were also performed at different C12EO25 concentrations within the micellar cubic phase region. All the samples exhibited shear thinning and similar trends for |η*|, G′, and G′′ as a function of frequency. Moreover, the crossing point between G′ and G′′ did not change much with concentration, indicating little variation in the relaxation processes. The crossing point was found at around ωc ) 1 rad/s, which corresponds to relatively fast relaxation processes when compared to other colloidal gels.14 However, the crossing point alone is not enough to detect some changes in the relaxation process. On the other hand, no viscosity plateau was found in the low frequency range. Similarly, some of the samples did not show a defined plateau modulus (a “rubbery plateau”), as should be obtained in Maxwellian systems at high frequencies. For comparison, the complex viscosity (|η*|) and elastic modulus (G′) at fixed frequencies (a low frequency value for |η*| and a high frequency value for G′) were plotted as a function of the C12EO25 weight fraction in Figure 4. As can be observed, |η*| and G′ show a maximum with surfactant concentration. In our previous study,3 we found that in the C12EO25 system the size of the unit cell decreases with surfactant concentration; namely, the number density of structural units (N) increases. From a simple network theory of elasticity,28 the elasticity modulus at high frequencies (G0) should be proportional to N and T:

G0 ∼ NkT

(1)

The experimental results of Figure 4 do not follow this proportionality. In the present case, the magnitudes of |η*| and G′ might depend on how far the system is from the order-disorder transition (the melting point). The (26) Lobry, L.; Micali, N.; Mallamace, F., Liao, C.; Chen, S.-H. Phys. Rev. E 1999, 60, 7076. (27) Mallamace, F.; Chen, S.-H.; Liu, Y.; Lobry, L.; Micali, N. Physica A 1999, 266, 123. (28) Thurn, H.; Lobl, M.; Hoffmann, H. J. Phys. Chem. 1985, 89, 517.

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Figure 5. (a) DLS correlation function for a micellar cubic phase sample at 25 °C. Composition: 50 wt % C12EO25; 50 wt % water. The lines are the exponential fittings to the experimental data. (b) Distribution of relaxation times from CONTIN analysis of the data in part a.

maximum melting temperature of the cubic phase corresponds to the 50 wt % sample, so that |η*| and G′ are also maximum for this sample. However, a more detailed analysis should be done in the context of first-order transitions. To determine the distribution of relaxation times, DLS and stress relaxation experiments were carried out. As can be seen in Figure 5a, the DLS normalized correlation function shows several decays associated with various relaxation processes. The exponential fit to the first decay together with the Stokes-Einstein equation gives a correlation length of ∼2 nm, very close to the radius of the core of micelles forming the cubic phase, as determined by SAXS.3 Therefore, the first DLS peak seems to correspond to micellar fluctuations. The distribution of relaxation times (Figure 5b) obtained using CONTIN analysis gives four peaks, the main one (fast mode) associated with the micellar dynamics, as mentioned previously, similar to that reported for the cubic phases in other systems.29 The two small peaks in the middle time range might correspond to the dynamics of clusters, whereas the broad peak at longer times is likely to be associated with rearrangement of large crystalline domains. Cubic phases are usually polycrystalline, with large domains of crystalline material imbedded in an amorphous medium.30 As a matter of fact, the results of DLS measurements performed at different temperatures (29) Papadakis, C. M.; Almdal, K.; Mortensen, K.; Rittig, F.; Fleischer, G.; Stepanek, P. Eur. Phys. J. E 2000, 1, 275.

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(not shown) indicated that the three slow modes in Figure 5b shift to lower relaxation times as temperature increases and eventually disappear above the melting temperature of the cubic phase, so that only one fast mode remains. This confirms that the slow modes are related to crystalline domains or clusters that break down when melting takes place. A stress relaxation test was also performed on the sample of Figure 5, and the results are shown in Figure 6a. The analysis of the normalized stress relaxation curve using CONTIN gives a broad distribution of relaxation times (Figure 6b) corresponding to a time scale closer to that of the broad peak (slow mode) observed in the DLS measurements; namely, the observation window can be expanded by coupling both experimental methods. Micellar Cubic Phases in the Ternary C12EO25/ Decane/Water System and Related Emulsions. Figure 7 shows the phase diagram of the C12EO25/decane/ water system.3 Only a little amount of decane is solubilized inside the micellar cubic phase, so a wide two-phase region is observed in the phase diagram. It is known that, inside this region, highly viscous and stable cubic-phase-based emulsions can be formed. Rheological measurements were performed along line B of Figure 7, and the results are shown in Figure 8. All the samples exhibited shear thinning. As in the binary cubic system, |η*| and G′ showed no plateau in the measured frequency range. For comparison, the complex viscosity (|η*|) and elastic modulus (G′) at fixed frequencies (a low frequency region for |η*| and a high frequency region for G′) were plotted as a function of the volume fraction of decane in Figure 9. Both |η*| and G′ first slightly increase and then decrease with an increasing oil fraction. The maximum is close to the phase separation boundary. The rheological behavior of cubic-phase-based emulsions (in the two-phase region) is opposite to that usually found in two-liquid concentrated emulsions, in which viscosity increases with oil content.31 It is considered that the viscosity of the cubic-phase-based emulsions is mainly determined by the cubic phase; therefore, it can be expected that the viscosity will decrease with the cubic phase fraction in the system. The slight increase in viscosity with oil content at low oil fractions is probably associated with an increase in the strength of interactions as the micelles swell with oil.3 Representative data of the dynamic frequency sweep experiments at different oil contents are presented in Figure 10. The addition of very small amounts of oil changes remarkably the dynamic rheological behavior. The systems show highly non-Maxwellian behavior, as can be deduced by the slope of the curves in the low frequency range and by the presence of a minimum in G′′(ω). The variation of G′ and G′′ with frequency is qualitatively similar to that found in solutions of starlike polymers that exhibit a micellar-like structure.32 The crossover between G′ and G′′ shifts to lower frequencies with increasing oil content, indicating an increase in the relaxation time, similar to what is found in concentrated two-liquid emulsions.33 As a matter of fact, the system passes from being liquidlike or glasslike in the absence of oil (G′′ prevailing over G′) to gellike (G′ prevailing over (30) Wanka, G.; Hoffmann, H.; Ulbricht, W. Colloid Polym. Sci. 1990, 268, 101. (31) Princen, H. M. J. Colloid Interface Sci. 1983, 91, 160. (32) Vega, D.; Sebastian, J. M.; Loo, Y. H.; Register, R. A. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 2183. (33) Nemer, M.; Blawzdziewics, J.; Loewenberg, M. In Mechanics for a new millennium; Aref, H., Philips, J. W., Eds.; Kluwer: Dordrecht, The Netherlands, 2001; p 75.

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Figure 6. (a) Stress relaxation test for a micellar cubic phase sample at 25 °C (strain ) 0.05%). Composition: 50 wt % C12EO25; 50 wt % water. Gn(t) is the normalized stress modulus. (b) Distribution of relaxation times from CONTIN analysis of the data in part a.

Figure 7. Phase behavior of the C12EO25/water/decane system at 25 °C. O indicates an excess-oil phase. The other notations are the same as those in Figure 1. This figure is adapted from ref 3.

Figure 8. Complex viscosity (|η*|) as a function of frequency for different volume fractions of decane (along line B of Figure 7) in the C12EO25/water/decane system at 25 °C (strain ) 1%). The C12EO25/water weight ratio is fixed at 50/50. The lines are only guides to the eyes.

G′′) as the oil fraction is increased. The polydispersity of the systems as well as the presence of aging phenomena34 might play a role in this behavior. Flow in cubic liquid crystals has been reported to occur with the close packed direction along the shear direction.35 (34) Fielding, S. M.; Sollich, P.; Cates, M. E. J. Rheol. 2000, 44, 323.

Figure 9. Complex viscosity (|η*|) at ω ) 0.01 rad s-1 and the storage modulus (G′) at ω ) 10 rad s-1 as a function of the volume fraction of decane in the C12EO25/water/decane system at 25 °C (strain ) 1%). The lines are only guides to the eyes.

Figure 10. Dynamic frequency sweep tests for the C12EO25/ water/decane system at 25 °C for different volume fractions of decane (strain ) 1%). The filled symbols correspond to G′, whereas the open symbols correspond to G′′. The C12EO25/water weight ratio is fixed at 50/50.

Jones and McLeish8 proposed the following model of slipping planes for the stress in colloidal crystals: (35) Castelletto, V.; Hamley, I. W.; Yang, Z. Colloid Polym. Sci. 2001, 279, 1029.

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Figure 11. Dynamic frequency sweep test for a micellar cubic phase in the C12EO25/water/decane system at 25 °C (strain ) 1%). The volume fraction of decane is 0.013, and the C12EO25/ water weight ratio is fixed at 50/50. The dashed lines are calculated by eqs 5 and 6 using a unique bulk relaxation time (τ), whereas the solid lines are fittings to the same equations but were calculated using a log-normal distribution function for τ. Filled circles, G′; open circles, G′′.

σ ) GP + η dP/dt

(2)

where G is a bulk stress modulus and P is the gradient of displacement in the bulk sample. When a periodical strain, γ ) γ0 sin ωt, is applied to the system, σ will be given by

σ ) γ0(G′(ω) sin ωt + G′′(ω) cos ωt)

(3)

For the case where the lattice potential is 0,8

ω2τ2 ωτ sin ωt + γ0A cos ωt (4) P ) γ0A (1 + ω2τ2) (1 + ω2τ2) In eq 4, A ) η2Np/(η + η2Np), where η is the bulk viscosity, η2 is the slip plane viscosity, and Np is the number of slipping planes in the crystal. By combining eqs 2-4, we found that the stress moduli can be expressed as

(ω2τ2 - ω2ττL)

G′(ω) ) GA

(1 + ω2τ2) ωτ(1 + ω2ττL)

G′′(ω) ) GA

(1 + ω2τ2)

(5)

(6)

where ω is the frequency and τ and τL are the bulk and local relaxation times, respectively. τ is determined from the inverse of the frequency at the peak of G′′; τL ) τmin2/τ,

where τmin is the inverse of the frequency at the minimum of G′′. Using these definitions and taking a ) GA as a fitting parameter, we estimated G′ and G′′, but the calculated values deviate considerably from the experimental data, as shown in Figure 11. It should be pointed out that eqs 5 and 6 lead to a Maxwellian behavior at very low frequencies, namely, G′ ∼ ω2 and G′′ ∼ ω. Such a tendency was not found in the measured frequency range. It can be argued that in micellar cubic phases there is not a single τ value but a distribution of relaxation times, as actually indicated by the experimental results on the aqueous C12EO25 binary system. Following the so-called parsimonium model,36 a log-normal distribution of bulk relaxation times (τ's) with a maximum at τc ) 1/ωc, where ωc is the frequency at the intersection of G′ and G′′, was used in eqs 4, 5, and 6 (keeping a unique value for τL) to estimate the stress moduli. Figure 11 shows that a relatively good fitting to the experimental data is obtained for low fractions of oil. The experimental data differ from the predicted values at low frequencies, probably due to the presence of slip-stick mechanisms.8 Conclusions In the aqueous C12EO25 binary system, micellar cubic phases show a maximum in the viscosity and the elastic modulus with surfactant concentration, although both parameters remain very high within the cubic phase region. The transition from the cubic phase to the micellar solution takes place with a sudden drop in the viscosity and the stress modulus, and the associated enthalpy change is small. Several relaxation processes seem to be present in the cubic phases, and some of them fall in a time scale that can be followed both by rheology and by dynamic light scattering. Upon addition of decane, the rheological behavior of C12EO25 is highly changed, the relaxation times increase, and highly concentrated gel emulsions are formed. The viscosity of these emulsions decreases with oil content. The non-Maxwellian behavior of the cubic phases in the presence of oil can be described by the model of slipping planes in a colloidal crystal if a log-normal distribution of bulk relaxation times is used to fit the data. Acknowledgment. We are grateful to Prof. Jose Gutierrez (Universidad de Barcelona, Spain) and Prof. Arturo Lopez-Quintela (Universidad de Santiago de Compostela, Spain) for their guidance in rheometry and DLS measurements. C.R.A. is thankful to the Japanese Society for the Promotion of Science (JSPS) for a research grant. M.G.R. acknowledges a grant from the Ministerio de Educacio´n, Cultura y Deporte (Spain). LA0498962 (36) Baumgaertel, M.; Winter, H. H. Rheol. Acta 1989, 28, 511.