Solution and Liquid Crystalline Microstructures in Sodium

1. Introduction. Owing to their importance in both industry and basic science, surfactant molecules have been the .... immersion thermostats to a prec...
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1990

Langmuir 2003, 19, 1990-1999

Articles Solution and Liquid Crystalline Microstructures in Sodium Taurodeoxycholate/D2O Mixtures Luigi Coppola,* Raffaella Gianferri, Cesare Oliviero, and Isabella Nicotera Department of Chemistry, University of Calabria, 87036 Arcavacata di Rende (CS), Italy Received June 17, 2002. In Final Form: November 14, 2002 Nuclear magnetic resonance (NMR) and rheology were used as two useful and complementary techniques to characterize the solution and liquid crystalline microstructures of the sodium taurodeoxycholate (NaTDC)/ D2O system. NaTDC is very soluble in water. At room temperature NaTDC/D2O mixtures form a lowviscosity isotropic micellar solution up to a concentration of ca. 12 wt % NaTDC. It follows a micellar solution region, 12-25 wt % NaTDC, that behaves as a Newtonian viscous fluid with a well-defined viscosity value. At higher concentration (>25 wt % NaTDC), a region with very high viscosity and viscoelastic behavior exists. At room temperature and at ca. 37 wt % NaTDC, the NaTDC/D2O system exhibits a phase transition into a birefringent phase. In this region, extending to ca. 65 wt %, the samples exhibit a gel-like behavior and behave as a shear thinning fluid. NMR and rheological data indicated that micellar solution is composed of a region with spherical micelles and of another with cylindrical aggregates, starting with 12 wt % NaTDC. The liquid crystalline phase, which disappears to ca. 36 °C, is a direct hexagonal phase as revealed by water self-diffusion NMR and the calculated diffusional obstruction factors. Dynamic viscoelastic measurements showed that micellar solutions (>25 wt % NaTDC) and the liquid crystalline phase behave as a “weak gel”. A possible relationship between the rheological responses and the phase microstructures using a cooperative-flow model was discussed.

1. Introduction Owing to their importance in both industry and basic science, surfactant molecules have been the subject of intense investigation for many years. In the most basic form a surfactant molecule possesses a polar hydrophilic headgroup and a nonpolar paraffinic tail. At sufficiently high concentrations, in an aqueous environment, surfactants can form a variety of structures and phases, including spherical and elongated micelles and cubic, hexagonal, and lamellar phases.1-3 Bile salts are a class of surfactants often used in biology for the extraction of membrane-bound proteins from natural lipid membrane environments and for the transfer of these proteins to smaller, more readily manipulated environments provided by the surfactant. Bile salts are different from each other in number, positions, and site of hydroxyl groups bound to bile salt molecules, and are conjugated to taurine or glycine. The self-assembling behavior of bile salts in water is more complex than that of classical detergents. A whole range of experimental methods has been applied to define their aggregation properties (models), microstructures, shape, and size dependence of molecular aggregates by concentration, temperature, pH, and ionic strength.4-7 A definite con* Corresponding author. Telephone: +39-984-492023. Fax: +39984-492044. E-mail: [email protected]. (1) Lindman, B.; Wennerstrom, H. In Topics in Current Chemistry; Springer-Verlag: Berlin, 1980; Vol. 87. (2) Tiddy, G. J. T. In Surfactant-water liquid crystal phases; NorthHolland: Amsterdam, 1980. (3) Hoffmann, H. From Micellar Solutions to Liquid Crystalline Phases; Verlag Chemie GmbH: Weinheim, 1984. (4) Li, C.-Y.; Wiedmann., T. S. J. Phys. Chem. 1996, 100, 18464. (5) Garidel, P.; Hildebrand, A.; Neubert, R.; Blume, A. Langmuir 2000, 16, 5267. (6) Nagadome, S.; Okazaki, Y.; Lee, S.; Sasaki, Y.; Sugihara, G. Langmuir 2001, 17, 4405.

sensus on the structure of the aqueous aggregates still does not exist.8-11 Owing to the natural occurrence of bile salts in complex mixtures with other compounds, phase behavior investigations have been extended to ternary and quaternary systems.12-14 A study on the phase diagram of the binary sodium taurodeoxycholate (NaTDC)/H2O system has been recently reported by Edlund et al.15 and by Marques et al.16 This system forms a liquid crystalline phase, in addition to the previously known isotropic solution phase at 22 °C. The preliminary assignments reported in refs 15 and 16 lend support to the existence of a mesophase with an arrangement of some hexagonal packing. It was observed that the formation of a liquid crystalline phase requires very long equilibration times and that the equilibrium structure observed was that of a possible reverse hexagonal type. The structure of this phase was characterized by small-angle X-ray scattering, but there is, in our opinion, a need for further characterization. In the last two decades of the twentieth century, a battery of experimental tools was used for character(7) Jover, A.; Meijide, F.; Rodriquez Nunes, E.; Vazquez Tato, J. Langmuir 2002, 18, 987. (8) Small, D. M. Adv. Chem. Ser. 1968, 84, 31. (9) Kawamura, H.; Murata, H.; Yamagushi, T.; Igimi, T.; Tanaka, M.; Sugihara, G.; Kratohvil. J. Phys. Chem. 1989, 93, 3321. (10) Campanelli, A. R.; De Sanctis, S. C.; Giglio, E.; Pavel, N. V.; Quagliata, C. J. Inclusion Phenom. Mol. Recognit. Chem. 1989, 7, 391. (11) D’Alagni, M.; D’Archivio, A. A.; Galanti, L.; Giglio, E. Langmuir 1997, 13, 5811. (12) La Mesa, C.; Khan, A.; Fontell, K.; Lindman, B. J. Colloid Interface Sci. 1985, 103, 373. (13) Svard, M.; Schurtenberger, P.; Fontell, K.; Jonsson, B.; Lindman, B. J. Chem. Phys. 1988, 92, 2261. (14) Marques, E. F.; Regev, O.; Edlund, H.; Khan, A. Langmuir 2000, 16, 8255. (15) Edlund, H.; Khan, A.; La Mesa, C. Langmuir 1998, 14, 3691. (16) Marques, E. F.; Edlund, H.; La Mesa, C.; Khan, A. Langmuir 2000, 16, 5178.

10.1021/la0205607 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/11/2003

Microstructures in NaTDC/D2O Mixtures

ization of surfactant systems, with special advances in NMR self-diffusion methods.17-25 A recent renaissance in rheological studies of surfactant systems has provided important insights into not only the dynamics, but also the structure of these materials.26-28 Oscillatory shear experiments offer an indirect means to determine the inner structure of lyotropic systems over a wide concentration range, and provide evidence of structural changes induced by temperature. In contrast to other structural techniques, dynamic rheometric measurements are extremely advantageous because at small strain amplitudes they are nondestructive, leading to little or no breakup of colloidal quiescent structure. The present study aimed at a more detailed understanding of solution and liquid crystalline microstructures in the NaTDC/D2O system by dynamic NMR and oscillatory rheology. This report differs from the ones cited above15,16 in two major aspects: first, a particularly efficacious approach has been adopted, i.e., rheology coupled with dynamic NMR; second, all experiments reported here refer to bile salt in NaTDC/D2O mixtures. The outline of the paper is as follows. In the next section, pulsed field gradient spin-echo NMR, 1H NMR, and 2H NMR experiments were properly chosen and applied to the micellar (2-30 wt % NaTDC) and liquid crystalline phases (>32 wt %). Surfactant and heavy water selfdiffusion as a function of surfactant composition have been examined in order to monitor changes on microstructures. The shape evolution of micellar aggregates was studied as a function of temperature by a usual self-diffusion model for surfactant/water systems.29 Section 4 reports the rheological behavior of NaTDC/D2O system from oscillatory shear experiments. A micellar solution (28 wt % NaTDC) and a liquid crystalline phase (45 wt % NaTDC) were studied as a function of temperature (25-50 °C). The solution and the lyotropic mixtures have strong viscolestic properties and behave as a weak gel. According to these dynamic viscoelastic data, a cooperative theory of flow (the weak-gel model) was considered in order to define a useful link between microstructures and rheological properties. 2. Experimental Section 2.1. Materials. The experiments were conducted with sodium taurodeoxycholate (NaTDC), Aldrich with 99% nominal purity, after recrystallization from ethanol/ethyl acetate. The recrystallized surfactant was stored in a Teflon-lined screw cap test tube. (17) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1. (18) Callaghan, P. T. Principles of NMR Microscopy; Oxford Science Publ.: New York, 1991. (19) Lindman, B.; Stilbs, P. In Microemulsions “Structure and dynamics”; Friberg, S. E., Bothorel, P., Eds.; CRC: Boca Raton, FL, 1987; Chapter 5. (20) Chidichimo, G.; De Fazio, D.; Ranieri, G. A.; Terenzi, M. Chem. Phys. Lett. 1985, 117, 514. (21) Chidichimo, G.; De Fazio, D.; Ranieri, G. A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1986, 135, 223. (22) Chidichimo, G.; La Mesa, C.; Ranieri, G.A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1987, 150b, 221. (23) Coppola, L.; La Mesa, C.; Ranieri, G. A.; Terenzi, M. J. Chem. Phys. 1993, 98 (6), 5087. (24) Celebre, G.; Chidichimo, G.; Coppola, L.; La Mesa, C.; Muzzalupo, R.; Pogliani, L.; Ranieri, G. A.; Terenzi, M. Gazz. Chim. Ital. 1996, 126, 489. (25) Chidichimo, G.; Coppola, L.; La Mesa, C.; Ranieri, G. A.; Saupe, A. Chem. Phys. Lett. 1988, 145, 85. (26) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869. (27) Valde`s, M.; Manero, O.; Soltero, J.; Felix, A.; Puig, J. E. J. Colloid Interface Sci. 1993, 160, 59. (28) Tepeil, U.; Heymann, L.; Aksel, N. Colloid Surf., A 2001, 193, 35. (29) Celebre, G.; Coppola, L.; Ranieri, G. A. J. Chem. Phys. 1992, 97, 7781.

Langmuir, Vol. 19, No. 6, 2003 1991 Isotropic enriched deuterium oxide, 99.8 atom % 2H, was purchased from Cambridge Isotopes Laboratories. Doubledistilled, filtered, and deionized water was used for liquid crystalline mixtures that were prepared for NMR self-diffusion experiments. 2.2. Phase Diagram. Samples were prepared by adding NaTDC and deuterium oxide directly in glass tubes, which were then flame sealed. Samples with a concentration higher than 38 wt % were homogenized by repeating alternately heating and centrifugation and then left at least 5 days at their original temperature. A phase diagram was studied in “fish tanks” containing 20 L of water. The temperature was regulated with immersion thermostats to a precision of (0.5 K. The liquid crystalline mesophase was determined by ocular inspection, polarizing microscopy, and 2H NMR spectra (Bruker WM-300 superconducting spectrometer). Differential scanning calorimetry (DSC) was employed to characterize the phase behavior and to define the phase transition temperatures. The DSC measurements were performed with a Setaram DCS-92 instrument. Samples (10-20 mg) were introduced into a aluminum pan, and the pan was hermetically sealed. All thermograms were obtained with heating and/or cooling rates of 1 °C/min after the sample was kept at the starting temperature for 5 min. 2.3. NMR Self-Diffusion Measurements. Self-diffusion coefficients were determined using the pulsed field gradient spinecho (PGSE) NMR technique.17 Water and surfactant self-diffusion coefficients were performed in the micellar solutions using Fourier transform PGSE experiments on a WM-300 Bruker spectrometer. The self-diffusion coefficients were obtained from 1H NMR spectra following the intensity of methylene peaks belonging to steroidal Block and of HOD. For all samples a single-exponential decay was observed as deduced from plots of intensity versus δ2; in no instance did we observe dependence on the diffusion time. Consequently, selfdiffusion coefficients were obtained by a nonlinear fitting of the experimental data to17

( )

I(δ) ) I0f(J) exp -

2∆ exp(-kD) T2

(1)

In eq 1, I0 is the peak intensity at ∆ ) 0 while f(J) takes into account J modulation for the proton in question. The time function k ) (γδg)2(∆ - δ/3) depends on experimental variables: γ is the proton gyromagnetic ratio; g and δ are the magnitude and the width of the magnetic gradients, respectively. ∆ is the delay between the first and the second gradient pulses and represents the “diffusion time”. δ was varied between 5 and 25 ms to measure the surfactant self-diffusion, Ds, and between 2 and 12 for the water self-diffusion, Dw. g was kept constant to 40 G/cm, and ∆ was set to 40 ms. The accuracy of measurements was estimated to be (3%. Water self-diffusion measurements in the liquid crystalline phase (NaTDC/H2O mixtures) were performed on a home-built (low-resolution) NMR spectrometer operating at a proton resonance frequency of 16 MHz. From PGSE experiments we measured the echo intensity as a function of k. When the water diffusion coefficient is determined for a powder sample, the resulting echo has contributions from liquid crystalline domains of all orientations with respect to field gradient direction. With the conditions of this experiment, the spin-echo intensities of water, E(δ), followed a single-exponential decay, and an apparent self-diffusion coefficient, Dapp, was obtained by fitting the experimental data with the equation20

E(δ) ) E0 exp(-kDapp)

(2)

E0 represents the echo intensity in the absence of gradient pulses, and it is only related to relaxation time T2. Experimentally, the time of the pulsed field gradient was varied between 0.5 and 10 ms with a constant diffusion time, ∆, of ca. 60 ms. The T2 relaxation times of the surfactant protons in the liquid crystalline phases were found to be ca. 8 ms in samples prepared with heavy water only and at room temperature. Thus, the undesired signals of the aggregate proton did not interfere with the solvent water signal that was desired. The magnitude of the gradient pulse (g)

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was 70 G/cm, as calibrated by the use of known D of water in H2O/2H2O mixtures at 25 °C. The accuracy of measurements was estimated to be (3%. Details of the pulsed current supply and related thermostatic unit have been reported elsewhere.21 2.4. Rheological Techniques. During oscillatory shear flow experiments, the material is subjected to periodic stress, σ(t) ) σo sin (ωt), with a stress amplitude σo at an angular frequency ω. At sufficiently small stress amplitude, i.e., in the linear viscoelastic region, the oscillatory shear stress gives rise to a sinusoidal shear strain response γ(t), with a shear strain amplitude γo. For viscoelastic material there is a phase shift, δ, between shear strain response γ(t) and the stress input σ(t). The shear strain response can be described as a function of the frequency-dependent complex shear modulus:30

G*(ω) )

σ ) G′(ω) + iG′′(ω) γ

(3)

The storage modulus G′(ω) is a measure of the reversible, elastic energy while the loss modulus G′′(ω) is a measure of viscous dissipation. The ratio of the viscous component to elastic component is called the dissipation or loss factor, tan δ:

tan δ )

G′′(ω) G′(ω)

(4)

Linear viscoelastic behavior is evidenced by the proportionality between the applied strain amplitude γo and the resulting shear stress amplitude σo. Under these conditions, the viscous resistance of the material can be described by the magnitude of the complex viscosity |η*|, which is related to complex moduli according to31

|η*(ω)| )

1 (G′(ω) + G′′(ω))1/2 ω

(5)

In this study, oscillatory shear flow experiments were carried out on a dynamic rheometer DSR 200 (Rheometrics, USA) equipped with parallel plates (φ ) 40 mm) and with a Peltier temperature control system. All samples had similar thermal conditions and rheological histories. To prevent changes in composition during measurements, an environmental chamber with water-saturated air was used around the plates. Dynamic viscoelastic experiments consisted of several sequential tests. First, stress amplitude sweeps were conducted to determine the linear viscoelastic region. Such experiments have been performed at different temperatures and at the frequency of 1 rad/s. Second, frequency sweeps were realized by applying to the mixtures the deformations characterized in the preceding experiments, in an interval of frequency between 0.01 and 100 rad/s. Temperature sweep experiments were, finally, realized in which the behavior of the material was studied as function of temperature at a fixed frequency (1 rad/s). The thermal ramp adopted was 0.5 °C/min, a suitable compromise between the experimental times and an acceptable accuracy of collected data.

3. Phase Diagram In a detailed study of the phase behavior of NaTDC/ water system, Marques et al.16 demonstrated the existence of a liquid crystalline phase. Small-angle X-ray scattering and polarizing microscopy clearly evidenced the formation of polar cylinders with a two-dimensional hexagonal order in the plane perpendicular to the cylinder axes. In this study, nevertheless, the authors concluded the presence of “...a hexagonal liquid crystalline phase, possibly of the reverse type...”. The phase equilibria of NaTDC/D2O system were reinvestigated and compared with the studies done on aqueous mixtures. The phase diagram was constructed by heating and cooling macroscopic samples in a water (30) Ferry, J. D. In Viscoelastic properties of polymers; 3rd ed.; Wiley: New York, 1980. (31) Hoffman, H. In Surfactant solutions: new methods of investigation; Zana, R., Ed.; Marcel Dekker: New York, 1980.

Figure 1. Composition phase maps of the NaTDC/D2O system at four temperatures. L, LC, and Sh denote a micellar solution, a liquid crystalline phase, and a hydrated surfactant crystal region. The dark areas show a two-phase region (L + LC). NaTDC content is in percent by weight (wt %).

bath and by observing them through crossed Polaroid plates. To a lesser extend, DSC and deuterium NMR spectroscopy was used, particularly to verify the temperature at which the lyotropic mesophase melts to form an isotropic solution. Figure 1 shows a collection of phase sequences for the NaTDC/D2O system at four temperatures. When the surfactant content is increased at room temperature, the transformation sequence is isotropic micellar solution, L; anisotropic liquid crystalline mesophase, LC; hydrated solids, Sh. At 25 °C, the liquid crystalline phase is seen to extend from 36 to 65 wt % NaTDC. The borders of the liquid crystalline phase do not change markedly with temperature, but the liquid crystalline phase melts at about 36 °C and at higher temperature an optically isotropic phase forms. The liquid crystal-solution phase transitions were also investigated using DSC ramps (22 f 50 °C) along isoplethal lines (dot points in the figure). All DSC showed, during the first heating cycle, a single endothermic peak and a change in enthalpy (∆H ≈ 18 kJ/mol) similar to that observed in melting processes of several surfactant/water mixtures.32 By decreasing the temperature (50 f 22 °C), a plateau in the heat flow was registered, showing that a viscous solution phase survives for an extended time (not less than 2 h at 25 °C) without crystallization. When the mixture content attained 70 wt % NaTDC, the endothermic peak in the thermogram is a singlet again, with a transition temperature of about 42 °C and ∆H ≈ 38 kJ/mol (Sh to L transition). Notice that this partial phase diagram is in agreement with the findings reported by Marques et al.16 (32) Fukuda, K.; Kawasaki, M.; Kato, T.; Maeda, H. Langmuir 2000, 16, 2495.

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4. Results and Discussion 4.1. Solution Microstructure. Gradient NMR has proven to be a very convenient method to measure selfdiffusion of each component separately in multicomponent surfactant systems. Because the translational mobilities are greatly affected by association phenomena, selfdiffusion coefficients can be of considerable help in the determination of solution structures. To investigate the solution structure of NaTDC/D2O system, a comprehensive self-diffusion study by PGSE NMR has been performed on samples along the micellar region. Surfactant and water diffusion coefficients have been determined with great accuracy. The self-diffusion study already realized by Edlund et al.15 has been, here, expanded to higher temperatures and over a much larger concentration range of bile salt. Surfactant Self-Diffusion. Surfactant NMR self-diffusion in aqueous solutions represents a convenient procedure for (1) verifying the existence of micelles, (2) knowing the form of the micellar aggregates, and (3) acquiring information on the interparticle and hydrodynamic interactions following the reduction of diffusion coefficients with the surfactant composition. To monitor the micelle diffusion, a hydrodynamic probe, hexamethyldisiloxane (HMDS), was added to samples. Because of its hydrophobicity, HMDS is solubilized inside micelles.33 The self-diffusion coefficients of all components at 25 °C are reported in Figure 2a. As can be seen, the diffusion of heavy water is high and is comparable to neat water, while the diffusion of bile salt, Ds, is about 2 orders of magnitude less. Diffusion coefficients of HMDS are equal to surfactant self-diffusion coefficients, within the composition range investigated. These findings indicate the existence of micelles in this system and the equivalence between surfactant and micellar self-diffusion, i.e., Ds ≈ Dmic. Figure 2b stresses our attention to the composition dependence of micellar self-diffusion at 25 °C. Dmic, which is high at low NaTDC content, gives direct evidence of the presence of small (spherical) micelles.34 A rapid initial decrease of Dmic with increasing concentration of NaTDC can be observed while, at still higher surfactant concentrations (>10 wt %), the change in the micellar selfdiffusion is less marked. A quantitative analysis of these results was conducted following the procedure developed by Soderman et al.35,36 In accordance with that study, we considered that the micellar self-diffusion could be written as an expansion in the volume fraction of aggregates. Initially, we analyzed the simple case of a spherical model with the assumption that NaTDC micelle size does not change with the concentration. A hydrodynamic radius of 18.7 ( 0.4 Å was obtained by using the Einstein relation for spheres diffusing at infinite dilution; this result was used inside the master diffusion equations (i.e., eqs 2-4 in ref 35) to obtain the opportune fittings to experimental PGSE data. In the calculation of the volume fraction of aggregates, the amount of surfactant present in monomeric form has not been included and, moreover, we decided to use a value for the micellar interaction constant of 1.7.35 Reported in Figure 2b is the prediction for spheres (dashed line). From this fitting it is clear that the (33) Karlsson, S.; Friman, R.; Bjorkquist, M.; Lindstrom, B.; Backlund, S. Langmuir 2001, 17, 3573. (34) Coppola, L.; Gordano, A.; Procopio, A.; Sindona, G. Colloids Surf., A 2002, 196, 175. (35) Nilsson, F.; Soderman, O.; Johansson, I. Langmuir 1996, 12, 902. (36) Nilsson, F.; Soderman, O.; Johansson, I. Langmuir 1997, 13, 3349.

Figure 2. (a) NMR self-diffusion coefficients versus NaTDC content (wt %) for different components in the system NaTDC/ HMDS/D2O at 25 °C. (b) Micellar self-diffusion in the solution phase at 25 °C. The dashed line is the prediction for spherical micelles obtained by fitting the experimental data with eqs 2-4 in ref 35.

assumption of spherical micelles refutes the experimental data within the whole micellar composition regime. The use of further models (i.e., rodlike or disklike models) to interpret the experimental data (Dmic) was not taken in consideration. Nonspherical shapes lead to more complicated excluded-volume dependences. For concentrated nonspherical micelles, further considerations on the flexibility and interpenetrability are needed; otherwise, unreasonable values of the shape may be obtained. For all these reasons, we decided on the analysis of the micellar structure for a study of water self-diffusion results. Water Self-Diffusion. We continued the present structural analysis by considering a cylindrical aggregate as the more conceivable micellar candidate. This condition is not entirely unsound if we consider that the solution phase is in equilibrium, at a higher composition of bile salt, with a hexagonal lyomesophase.16 Water self-diffusion coefficients were determined as a function of surfactant concentration along the micellar solution at three different temperatures (25, 40, and 50 °C). In micellar solutions, large and almost stationary aggregates obstruct the path of water molecules and the solvent near an aggregate has to diffuse a longer path in order to reach the other side of the aggregate. This phenomenon, called the “obstruction effect”, may be obtained, in very simple cases, by the ratio Dw/D0, where

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Figure 3. Relative NMR self-diffusion coefficients of D2O (relative to neat D2O) versus NaTDC content (wt %) for samples investigated in the system NaTDC/D2O. Profiles (continuous lines) for different spheroidal shaped particles are taken from ref 37: (a) sphere; (b) long prolate; (c) oblate (axial ratio 1:10); (d) oblate (1:100). Dashed lines represent a guide for experimental data at different temperatures.

Dw is the measured self-diffusion coefficient of D2O in the presence of obstructing particles and D0 refers to the heavy water “free” state. The key point is that the ratio Dw/D0 is sensitive to the shape of the aggregates. It is rather easy to discriminate between large rodlike and disklike aggregates, since their shape gives rise to different obstruction effects. A theoretical preview of the obstruction effects in colloidal systems was given by Jonsson et al.37 in the well-known “cell diffusion model”. When Dw/D0 is plotted as a function of obstruction volume, a decision can be made on the aggregate shape. In Figure 3 the relative self-diffusion coefficient of water, Dw/D0, is reported as a function of bile salt concentration and temperature. The experimental behavior is compared with some theoretical functions giving the obstruction effect of spherical, prolate, and oblate aggregates at a different axial ratio. A strong decrease of the Dw/D0 ratio was observed at all temperatures. In the present case we note that the reduced diffusion coefficient at 25 wt % NaTDC is around 0.55, which is lower than the obstruction limit due to infinite disklike aggregates measured in randomly oriented LR mesophases.25 The inconvenience of these results made us reconsider the experimental diffusion data in light of a combination of obstruction effects and of direct hydration. In fact, a problem encountered when analyzing the reduction of the water diffusion in terms of particle obstruction effects in micellar solution is that the fraction of water molecules hydrates the surfactants and thus has different traslational properties than the “free” water molecules. In accordance with the above considerations, the measured self-diffusion coefficient of D2O was interpreted using the following equation:23

Dw ) f[(1 - P)D0 + PDb]

(6)

which can be applied to water in micellar and liquidcrystalline phases. In eq 6, P is the fraction of bound water and Db the corresponding self-diffusion coefficient. Physically, the obstruction factor (f) accounts for the constraints to water self-diffusion due to surfactant aggregates. (37) Jonsson, B.; Wennestrom, H.; Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77.

Figure 4. Obstruction factor (calculated from eqs 6 and 7) plotted versus NaTDC content (wt %) for mixtures within the solution micellar phase. The dashed line is a guide for experimental data at different temperatures, while the solid curve is the lamellar obstruction factor (f ≈ 2/3) reported along the composition range investigated.

Singular considerations supported by experimental results permitted obtaining obstruction factors in different lyotropic structures. As demonstrated in ref 20, the obstruction factor from eq 6 can be calculated by measuring the D2O diffusion coefficients as a function of surfactant concentration, provided that the structure and f do not change. Under these conditions

f)

Dwi - KijDwj 1 - KijD0

(7)

where Dwi and Dwj are the diffusion coefficients measured at water weight fractions wi and wj and Kij is given by

Kij )

wj(1 - wi) wi(1 - wj)

(8)

Equations 6-8 were applied to experimental water selfdiffusion behaviors. The composition dependence of the obstruction factor, f, for the NaTDC/D2O system is reported in Figure 4, showing an analogous trend in the temperature range 25-50 °C. A close inspection of results in Figure 4 shows that f remains close to unity for mixtures with a composition 25 wt %) becomes a viscoelastic micellar fluid built up of long cylindrical micelles with a weak-gel rheological behavior. Dynamic viscoelastic data in this concentration range will be described in detail later. 4.2. Kinetics of the Formation of Liquid Crystalline Phase. A topic of considerable importance to modern colloid science concerns the kinetics and mechanism of phase transitions. The separation of a liquid crystal phase from a liquid (e.g., by cooling along isoplethal paths) requires a finite time, but it is too short to be perceived by direct observation. This is true of all the major classes of liquid crystal phases.39 A study of kinetics for the NaTDC/D2O system was conducted on a 45 wt % NaTDC mixture, which was cooled from 50 °C, a solution temperature, to 25 °C in a rapid and programmable refrigerated bath. This liquid-liquid crystal transition was followed by isothermal 2H NMR experiments. A singlet (zero splitting) characterizes the spectra, just after that mixture equilibrates at 25 °C. This result indicates the presence of a liquid solution where water molecules reorient isotropically. After ca. 2 h, the quadrupolar spectrum becomes a superposition of a singlet (isotropic phase) and a powder pattern (liquid crystal). The quadrupolar splitting, which is a direct result of anisotropic molecules of D2O at the aggregate-water interface, increases in magnitude with further increase in time. Finally, after the mixture has cooled for 6 h, the spectra are well-defined powder patterns. As already observed by Edlund et al.,15 the quadrupolar splitting values in this final equilibrium state range between 300 and 400 Hz. The mechanism for a complete transformation of the solution in a stable liquid crystalline phase was studied by the variation of longitudinal relaxation times of the surfactant (T1,s) and the variation of self-diffusion coefficients of D2O (Dw) at 25 °C. From Figure 5 it is evident that an induction period follows the temperature jump (50 f 25 °C) in which no observable changes in the NMR parameters appear. In this case the induction period is the time taken for the volume of the new phase to be large enough to have a detectable effect on the NMR parameters. In Figure 5, a rapid increase of both T1,s and Dw with (38) Small, D. M. In Molecular association in biological and related systems; Gould, R. F., Ed.; American Chemical Society: Washington, DC, 1968. (39) Laughlin, R. G. In The aqueous phase behavior of surfactants; Academic Press: New York, 1994.

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Figure 5. Time dependence of surfactant longitudinal relaxation times and of self-diffusion coefficients (D2O), along the solution-liquid crystal phase transition, reported for 45 wt % NaTDC mixture at 25 °C. Longitudinal relaxation times were measured by the “progressive-saturation method”. The errors bars represent conventional estimates of (σ error ranges and are calculated from the deviation of experimental points from the fitted theoretical functions.

increasing time reflects the formation of liquid crystalline phase. These NMR experiments clearly confirmed that the structural changes occur in ca. 6 h. One plausible explanation for this behavior is a mechanism that involves nucleation and growth. These data are consistent with a nucleation/growth mechanism observed by Knight et al.40 on the transition from micellar solution to lamellar bilayers in poly(oxyethylene) surfactant/water systems. The kinetics of the formation of liquid crystalline phase of the NaTDC/D2O system is dependent on the rate with which the mixtures were cooled. The nuclei of the new phase form within macroscopic defects, whose concentration depends on sample treatment. The dependence on the “cooling rate” appears clear in Figure 6, where the surfactant longitudinal relaxation times (T1,s) for the mixture at 45 wt % NaTDC were reported as a function of time. We studied the behavior at several “cooling rates”. For “fast” cooling rates (less than 1 h), the complete transformation of solution in liquid crystalline phase takes about 6 h. A dramatic increase of the kinetics of formation (ca. 20 h) was observed after a cooling rate of 3 h. It is interesting to note that changes in longitudinal relaxation times obtained in this study correspond to changes recorded at the micellar-direct hexagonal phase transition for the hexadecyltrimethylammonium bromide/water system at 50 °C.41 (40) Knight, P.; Wyn-Jones, E.; Tiddy, G. J. T. J. Phys. Chem. 1985, 89, 3447. (41) Coppola, L.; Muzzalupo, R.; Ranieri, G. A.; Terenzi, M. J. Phys. II (Fr.) 1994, 4, 2127.

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Figure 7. Apparent self-diffusion coefficients as a function of temperature for the 57 wt % H2O mixture. The arrows indicate the measurements performed by increasing (liquid crystalline phase) or decreasing the temperature (melted liquid crystalline phase). The underlying arrow shows the liquid crystal-solution transition during the heating ramp.

Figure 6. Time dependence of surfactant longitudinal relaxation times, along the solution-liquid crystal phase transition, reported for 45 wt % NaTDC mixture at 25 °C. Different cooling rates were realized. The error bars represent conventional estimates of (σ error ranges.

From these findings it may be concluded that the overall time scale for the solution f liquid crystal transition of the bile salt/water system is very long and is dependent on the cooling rates. The phase transition is characterized by an induction period (i.e., nucleation) followed by a period of growth. Nucleation of the new phases is induced by macroscopic defects. Long cooling rates reduce the amount of the structural defects, increasing, as a consequence, the time for a complete formation of liquid crystalline structure. Because of long time scales, micelle fusion rather than monomer-micelle exchange is a likely mechanism for the formation of liquid crystalline phase. 4.3. Liquid Crystalline Microstructures. We now concentrate our attention on the composition and temperature dependence of water self-diffusion in liquid crystalline mixtures. Phases with a hexagonal periodicity may occur in several binary surfactant/water systems. In macroscopic samples one usually observes a piled polydomain structure. Beyond the structures in which the cylindrical aggregates are considered filled with amphiphiles and surrounded by water, with the polar group located in the interface between the two regions, there is the reverse structure of polar cylinders in a nonpolar lipophilic environment. Recently PGSE NMR experiments were performed by Coppola et al.42 in order to characterize the liquid crystalline structure of a ternary nonionic surfactant system. From the apparent self-diffusion coefficients of water they calculated an average obstruction factor of 0.33 ( 0.04 and so confirmed the presence of a reverse hexagonal microstructure (f ≈ 1/3 for a onedimensional diffusion18). The temperature dependence of the apparent selfdiffusion of water for the 43 wt % NaTDC mixture is (42) Coppola, L.; Oliviero, C.; Olsson, U.; Ranieri, G. A. Langmuir 2000, 16, 4180.

Figure 8. Arrhenius plots of apparent self-diffusion coefficients on selected lyotropic mixtures of the NaTDC/H2O system. The dashed line indicates the behavior of pure water. Composition of mixtures: a ) 57 wt %, b ) 52 wt %, c ) 49 wt % water. Obstruction factors: f(a-b) ) 0.78 ( 0.04; f(b-c) ) 0.77 ( 0.04; f(c-a) ) 0.78 ( 0.04.

reported in Figure 7. Here we compared (i) the pure water self-diffusion, (ii) the water self-diffusion in the powder lyomesophase and the transition to liquid phase, and (iii) the water self-diffusion during a cooling ramp (from 50 to 25 °C). The total time taken for the cycle was ca. 1 h. The apparent self-diffusion coefficients of water for samples at different compositions, within the liquid crystalline phase only, are reported in Figure 8. The plot of (log Dapp) versus 1/T gives satisfactory straight lines which are parallel with the pure water self-diffusion trend. This behavior agrees with the temperature dependence of water self-diffusion observed in lamellar, direct hexagonal, and nematic phases of several surfactant systems.24 Following the procedure reported above, eqs 6-8 have been used to calculate the obstruction factor f by pairing, in three possible combinations, the set of data shown in Figure 8. These values are reported as an insert in the figure. It is interesting to observe that (i) the average

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high, on the order of 105 Pa, and demonstrates the elastic nature of this lyomesophase. The complex viscosity is strongly frequency dependent: the higher the frequency is, the lower the complex viscosity is. These dynamic viscoelastic data are typical for surfactant/water mixtures within the liquid crystalline region.44,45 A study of RoblesVa´squez et al.44 reported that the Aerosol OT/water lamellar phase behaves as a “weak gel”, with the dynamic moduli nearly dependent on frequency and G′, at least, 1 order of magnitude greater than G′′. A study of the temperature dependence of solution and liquid crystal structure was done by frequency sweep experiments performed in the temperature range 25-50 °C. Rheograms with the characteristics of Figure 9 were obtained. The experimental data were analyzed according to the theory of Bohlin46 and Winter,47 reported in the literature as the “weak-gel model”.48,49 This model considers a weak-gel material as a flowing system characterized by a three-dimensional network where weak interactions cooperatively ensure the stability of the structure. The real structure of this material is made by a cooperative arrangement of flow units to form a stand. The weak-gel model provides a direct link between the microstructure of the material and its rheological properties. The most important parameter introduced is the “coordination number”, z, which is the number of flow units interacting with each other to give the observed flow response. This cooperative region is characterized by a flow equation: 48,49

Figure 9. Angular frequency dependencies of storage and loss shear moduli and of dynamic viscosity at 25 °C. (a) Solution at 28 wt % NaTDC, investigated with a shear stress of 0.1 Pa. (b) Liquid crystalline phase at 45 wt % NaTDC, investigated with a shear stress of 100 Pa.

obstruction factor is ca. 0.78, and is greater than those obtained in the case of reverse hexagonal phases, and (ii) this average value fits very well the diffusion obstruction factor measured on the direct hexagonal phase of the potassium palmitate/water system.21 These findings suggest the liquid crystalline microstructure of NaTDC/water system is compatible with a direct hexagonal phase with large and nondefected lyotropic domains. 4.4. Rheological Properties. Micellar and liquid crystalline structures were also analyzed by smallamplitude oscillatory shear rheology. Frequency and temperature sweep experiments were carried out on two NaTDC/D2O mixtures: (i) a micellar solution at 28 wt % and (ii) a liquid crystalline phase at 45 wt % NaTDC. Figure 9 reports the frequency dependence (as a log-log plot) of dynamic parameters for these mixtures at 25 °C. A close inspection of the data reveals that G′ and G′′ show an approximate linear and parallel dependence within the explored angular frequency range. This power-law behavior (i.e., G′ ≈ G′′ ≈ ωn) indicates for both samples a weak gel-like structure with a multiple relaxation process.43 The rheological response of micellar solution (Figure 9a) is characterized by the fact that G′′(ω) > G′(ω) and, as expected for a concentrated liquid mixture, the complex viscosity is slightly frequency dependent. At concentrations below 25 wt % NaTDC, the dynamic elastic modulus was hardly measured. Frequency sweep experiments performed on the liquid crystalline sample (Figure 9b) show that G′(ω) . G′′(ω), within all frequency ranges investigated. It is to be noted that the value of G′ is very (43) Nakamura, K.; Kiriyama, M.; Takada, A.; Maeda, H.; Nemoto, N. Rheol. Acta 1997, 36, 252.

|G*(ω)| ) xG′(ω)2 + G′′(ω)2 ) Aω1/z

(9)

where A is a proper constant which can be interpreted as the “strength” between the rheological units, a sort of amplitude of cooperative interactions. Clearly, |G*| log plots versus ω should yield a straight line with slope 1/z and intercept A. Figure 10 shows the temperature dependence of z and A obtained by fitting the experimental data to eq 9. The solution phase shows a flow coordination number close to unity and constant with increasing temperature. The values of z and A, measured in the liquid crystalline phase, change strongly with increasing temperature. In the temperature interval 25-32 °C, the flow coordination number changes from 10 to 2 while the gel strength is reduced by a factor of 104. Above 36 °C, the solution and the liquid crystalline mixtures report analogous values for z and A. Flow measurements on the direct hexagonal phase of the hexadecyltrimethylammonium bromide/H2O system were realized by Bohlin.46 At 25 °C, a 70 wt % water mixture showed a cooperative flow with a 6-fold coordination (z ≈ 6) which is consistent with the results of this study. The effect of the temperature to produce structural changes or to induce thermally activated transitions was monitored by temperature sweep experiments. Figure 11 shows the temperature dependence of dynamic moduli recorded on the liquid crystalline mixture. In this case we can determine three different rheological regimes. First, (44) Robles-Va´squez, O.; Corona-Galva´n, S.; Soltero, F. A.; Puig, J. E.; Tripodi, S. B.; Valle´s, E.; Manero, O. J. Colloid Polym. Interface 1993, 160, 65. (45) Oliviero, C.; et al. Results not published. (46) (a) Bohlin, L. J. Colloid Interface Sci. 1980, 74, 423. (b) Bohlin, L. J. Colloid Interface Sci. 1979, 69, 195. (47) Winter, H. H. Polym. Eng. Sci. 1987, 27, 1698. (48) Gabriele, D.; de Cindio, B.; D’Antona, P. Rheol. Acta 2001, 40, 120. (49) Oliviero, C.; Coppola, L.; La Mesa, C.; Ranieri, G. A.; Terenzi, M. Colloids Surf., A 2002, 201, 247.

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>36 °C, the viscous modulus shows again a small temperature dependence while the storage modulus disappears. It may be concluded that relevant structural modifications on LC structures of this system are induced by the temperature increase. In the interval 24-28 °C, the liquid crystalline structure seems not to suffer any structural changes and in terms of rheological responses it shows an elastic nature. At ca. 28 °C, the inversion of the dynamic moduli underlines a structural modification toward a weak-gel network with a more viscous nature. There is no recorded evidence of similar behavior in the experimental literature. Therefore, the simplest explanation of this finding is that intermicellar hydrogen bonds (the most important molecular forces involved in this system11) are sensitively weakened by the temperature increase, reducing the strength of the lyotropic network. This progressive structural change continues up to 36 °C, when the lyotropic phase melts in an isotropic phase. This phase behaves like a viscous micellar solution in accordance with the temperature trends of z and A discussed above. 5. Conclusions

Figure 10. Weak-gel model as applied to 28 and 45 wt % NaTDC mixtures. (a)“Gel strength”, A, versus temperature. (b) “Flow coordination number”, z, versus temperature.

Figure 11. Temperature dependence of storage and loss shear moduli and their ratio (tan δ) in a temperature sweep experiment (heating rate 0.5 °C/min, equilibration time 2 min). Liquid crystalline phase at 45 wt % NaTDC, investigated with a shear stress of 100 Pa and ω ) 1 rad/s.

in the lower temperature range (25-28 °C) the storage and loss moduli show only a small temperature dependence and G′ > G′′. Second, in the temperature range 2836 °C the dynamic moduli decrease strongly with the temperature increase. A G′-G′′ crossover is observed at 28 °C; above this temperature tan δ starts to increase and assume values bigger than unity. Third, for temperatures

A combination of NMR and rheology has been used to study the microstructures of NaTDC in D2O. The main findings of the present work are summarized as follows. (1) At room temperature, NaTDC/D2O mixtures form an isotropic solution (L) up to a concentration of ca. 35 wt %. After a small two-phase region, at ca. 37 wt % this binary system exhibits a phase transition into a birefringent phase (LC) of hexagonal texture, which extends to ca. 65 wt %. When the concentration is increased to more than 65 wt % NaTDC, a hydrated crystal region is formed (Sh). At temperatures slightly above 36 °C, the liquid crystalline phase melts reversibly in a viscous isotropic solution. The phase diagram of the NaTDC/D2O system is in accordance with the phase equilibria of NaTDC in water, already reported in the literature. (2) Surfactant self-diffusion coefficients reported within the micellar region showed that a spherical model is inconsistent with NMR data for NaTDC micelles. Water self-diffusion, within the temperature interval 25-50 °C, was used to obtain the obstruction factors. A progressive decreasing of these parameters from ca. 0.97 to 0.78 was observed in the composition interval from 12 to 28 wt % NaTDC. We concluded that, first, a spherical-to-cylindrical phase transition in the shape of micelles takes place at the composition of ca. 12 wt %. Second, by increasing the surfactant composition the micelles progressively grow in size and, close to the liquid crystalline boundary, large cylindrical aggregates exist as inferred by obstruction factor values which became similar to that of the ordered phase. (3) Obstruction factors of liquid crystalline samples were obtained by water NMR self-diffusion on the NaTDC/H2O system. We followed a procedure similar to that in our previous studies. The values of f were about 0.78, greater than those expected of a one-dimensional diffusion and not compatible with a reverse hexagonal structure as suggested in ref 16. We concluded that the liquid crystalline phase of NaTDC/D2O system is a direct hexagonal phase. (4) The kinetics of formation of the liquid crystalline phase was followed on 45 wt % NaTDC mixture by water self-diffusion and surfactant longitudinal relaxation times.

Microstructures in NaTDC/D2O Mixtures

The formation of liquid crystalline phase is peculiarly slow (about 6 h), and it is dependent on the cooling rate. The NMR data are consistent with a nucleation/growth mechanism. (5) Dynamic viscoelastic experiments revealed that the solution (>25 wt % NaTDC) and liquid crystalline phase of NaTDC/D2O system behave as a “weak-gel” material. After the studies realized by Bohlin, we applied here, for the first time, the theory of cooperative flow (weak-gel model) to a new surfactant/water system. The coordination numbers, z, were calculated from dynamic shear flow

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measurements as a function of temperature. We compared the results obtained both in an isotropic solution (28 wt %) and in a liquid crystalline mixture (45 wt %). Acknowledgment. This work was partly supported by a scientific research grant from the Department of Chemistry, University of Calabria. We are grateful to Dr. Domenico Gabriele for making the dynamic viscoelastic measurements. LA0205607