Phase Diagram and Phase Properties of the System

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Phase Diagram and Phase Properties of the System Lecithin-Water-Cyclohexane R. Angelico,*,† A. Ceglie,† U. Olsson,‡ and G. Palazzo§ Consorzio Interuniversitario per lo Sviluppo dei Sistemi a Grande Interfase (CSGI) c/o Department of Food Technology (DISTAAM), Molise University, v. De Sanctis, I-86100, Campobasso, Italy, Department of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O.Box 124, S-221 00, Lund, Sweden, and Department of Chemistry, Bari University, v. Orabona 4, I-70126, Bari, Italy Received July 12, 1999. In Final Form: November 2, 1999 The isothermal quasi-ternary-phase diagram of the lecithin-cyclohexane-water system was determined at 25 °C using a combination of polarizing microscopy, small-angle X-ray diffraction, and NMR techniques. The system contains four lyotropic liquid-crystalline phases and two isotropic liquid phases. Apart from the lamellar (LR) phase, there are only reverse-type aggregates with a water interior, in addition to an essentially pure water phase, whose relative locations in the phase diagram follow the sequence (from the oil corner to the surfactant corner): reverse micellar solution (L2), reverse anisotropic nematic (N2), reverse micellar cubic (I2), reverse hexagonal (H2), and finally, the lamellar phase. The aggregates have a finite swelling with water, and coexistence with excess water is found at higher water contents. The area per lecithin molecule was determined in the H2 and LR phases. This area varies with the mole ratio [H2O]/[Lec] ) W0 at lower W0 values, but saturates at an area of 90 Å2/ molecule for W0 J 15. The phase diagram is discussed in relation to the known formation of giant wormlike reverse micelles in the liquid L2 phase. Of particular interest here is the transition from liquid (L2) to nematic (N2) as the wormlike aggregate concentration is increased.

1. Introduction Luisi1

Since the pioneering study of Scartazzini and about the gel forming properties of organic solutions of soybean lecithin, a large number of studies have focused on the isotropic water-in-oil microemulsion L2 phase of such a mixture. The interesting and unique feature of a transition from a classical droplet-type microemulsion to polymer-like flexible cylindrical reverse micelles can be observed upon an increase in the solubilized water-tosurfactant mole ratio, W0, for lecithin solutions in several nonpolar solvents.1 In this context, for one of the most investigated systems, namely, lecithin-water-cyclohexane, a huge amount of data is now available in the literature,2-4 which demonstrates the polymer-like properties of the micellar aggregates once the parameter W0 has been properly tuned. Recently, for the present system, studies based on lecithin and water NMR self-diffusion have revealed, respectively, a peculiar surfactant curvilinear diffusion5 along giant entangled wormlike micelles and a rod-to-sphere transition6 occurring beyond a certain W0 value. To understand the quite unusual structural properties of the isotropic water-in-oil lecithin micro* To whom correspondence should be addressed. E-mail: [email protected]. † Consorzio Interuniversitario per lo Sviluppo dei Sistemi a Grande Interfase (CSGI. ‡ Lund University. § Bari University. (1) Scartazzini, R.; Luisi, P. L. J. Phys. Chem. 1989, 93, 829. (2) Schurtenberger, P.; Jerke, G.; Cavaco, C.; Pedersen, J. S. Langmuir 1996, 12, 2433, and references therein. (3) Angelico, R.; Balinov, B.; Ceglie, A.; Olsson, U.; Palazzo, G.; So¨derman, O. Langmuir 1999, 15, 1679, and references therein. (4) Angelico, R. Ph.D. Thesis, University of Bari, 1999; Chapter 2 and references therein. (5) Angelico, R.; Olsson, U.; Palazzo, G.; Ceglie, A. Phys. Rev. Lett. 1998, 81, 2823. (6) Angelico, R.; Cirkel, P. A.; Colafemmina, G.; Palazzo, G.; Giustini, M.; Ceglie, A. J. Phys. Chem. B 1998, 102, 2883.

emulsions, quantitative characterizations of the other regions of the phase diagram and, in particular, of the nature of the liquid-crystalline phases are thus clearly needed. Apart from a few and incomplete studies of the phase behavior of diluted7,8 and concentrated 9 lecithin/ water/oil mixtures, a complete phase diagram investigation is still missing. Therefore, it is the aim of the present paper to provide the first detailed study of the quasiternary-phase diagram of the system lecithin-watercyclohexane. We note here that lecithin forms L2 phases with many different oils, but where the phase equilibria of the L2 phase depends on the type of oil. For example, with isooctane as oil there is a liquid-gas-type phase separation where a concentrated and a dilute L2 microemulsion coexists.7 In the present cyclohexane system, on the other hand, an “emulsification failure” (Winsor II equilibria) is obtained at higher water content.8 The underlaying reason for this difference is at present not fully clear but is expected to be related to the degree of oil penetration into the amphiphilic film and its effect on spontaneous curvature. In the following sections we present the isothermal quasi-ternary-phase diagram for the lecithin-watercyclohexane system at 25 °C. The soybean lecithin used in this work is a mixture of phosphatidylcholines with acyl chains of different lengths and degrees of saturation; thus, the phase diagram is not strictly ternary. To determine the phase boundaries and characterize the different phases, we have, besides visual observations, used mainly small-angle X-ray scattering (SAXS) experiments, supported by the polarizing microscopy. 2H NMR (7) Schurtenberger, P.; Scartazzini, R.; Magid, L. J.; Leser, M. E.; Luisi, P. L. J. Phys. Chem. 1990, 94, 3695. (8) Schurtenberger, P.; Peng, Q.; Leser, M. E.; Luisi, P. L. J. Colloid Interface Sci. 1993, 156, 43. (9) Sjo¨lund, M.; Lindblom, G.; Rilfors, L.; Arvidson, G. Biophys. J. 1987, 52, 145. Sjo¨lund, M.; Rilfors, L.; Lindblom, G. Biochemistry 1989, 28, 1323.

10.1021/la9909190 CCC: $19.00 © 2000 American Chemical Society Published on Web 01/28/2000

Diagram/Properties of Lecithin-Water-Cyclohexane

quadrupolar splitting and 31P NMR chemical shift anisotropy in the reverse N2 nematic liquid-crystalline phase were also used to investigate the anisotropy of the aggregates. The structure of the cubic phase was examined with NMR self-diffusion and SAXS measurements. The latter technique was also used to investigate the swelling of rods and lamellae respectively in the reverse hexagonal liquid-crystalline H2 phase and in the lamellar liquidcrystalline LR phase. 2. Materials and Methods Materials. Soybean lecithin (Epikuron 200) was a generous gift from Lucas Meyer AG and consists of soybean phosphatidylcholine with a purity of 95% with an average molecular weight of 772 Da. The lecithin used in this work is of the same brand used in most of the published investigations of this system and, as in previous work, it was used without further purification which consequentely means that it is a certain mixture of phosphatidylcholines of different chain lengths and degrees of saturation.10 Cyclohexane of purity >99.0% was obtained from Fluka Chemie AG, Switzerland, while 2H2O (99.80 at. % 2H) was purchased from Dr. Glaser AG, Switzerland. Heavy water was used instead of ordinary H2O to allow for 2H NMR measurements in the investigation of the reverse nematic phase. For the preparation of the rest of the samples, filtered Millipore water was used. Determination of the Phase Boundaries. A large number of samples (≈200), over the whole ternary-phase diagram, which concentrate in the water poor region, were prepared for the determination of the phase boundaries of single phases and of two- and three-phase regions. The samples were prepared by weighing appropriate amounts of surfactant, water, and oil into 8-mm glass tubes with screw caps. The liquid-crystalline samples were mixed by repeated centrifugation at regular intervals for a few days, while the solutions instead were mixed by shaking. Then, they were all allowed to stand for 2-3 weeks at 25 °C, until equilibrium was attained. The equilibrated samples were studied visually to ensure their homogeneity; then, the samples with liquid-crystalline phases were first characterized using a Zeiss Axioplan Universal Microscope, equipped with crossed polarizers, the differential interference contrast (DIC), and a camera (MC 100). Anisotropic phases can be recognized from their optical birifringence. Microemulsion phases and cubic liquid crystals are optically isotropic and therefore they show only a dark background when studied with a polarizing microscope. On the contrary, anisotropic liquid-crystalline phases have their own characteristic textures.11 31P NMR chemical shift anisotropy, performed at 81 MHz on a Varian XL-200 NMR spectrometer, and 2H NMR quadrupolar splitting, performed at 31 MHz on the same spectrometer, in the reverse nematic liquid-crystalline (N2) phase, were also used. Water and lecithin NMR self-diffusion experiments performed in the liquid-crystalline cubic area were carried out by pulsed gradient spin-echo techniques12 (PGSENMR) on a Bruker DMX 200 operating at 200 MHz for 1H. Small Angle X-ray Scattering (SAXS). SAXS measurements were performed on a Kratky compact small-angle system equipped with a position-sensitive detector (OED 50M from MBraun, Austria) containing 1024 channels of width 51.3 µm. CuKR radiation of wavelength 1.542 Å was provided by a Seifert ID-300 X-ray generator, operating at 50 kV and 40 mA. A 10-µm thick nickel filter was used to remove the Kβ radiation. The obtained Bragg peaks were relatively sharp in which case the peak positions were evaluated from the slit-smeared SAXS data. The sample-to-detector distance was 277 mm. The volume between the sample and the detector was kept under vacuum during the measurements to minimize scattering from the air. The samples were filled into a 0.5-mm quartz capillary using a syringe; samples whose consistencies were very stiff were filled into a paste holder with thin mica windows. The temperature (10) Shinoda, K.; Araki, M.; Sadaghiani, A. S.; Khan, A.; Lindman, B. J. Phys. Chem. 1991, 95, 989. (11) Rosevear, F. B. J. Soc. Cosmet. Chem. 1968, 19, 581. (12) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1.

Langmuir, Vol. 16, No. 5, 2000 2125 was controlled by a Peltier element, with an accuracy of (0.1 °C. All SAXS measurements were performed at 25 °C. Definition of Polar and Apolar Domains and Effective Volume Fractions. For the calculations involved in the SAXS analysis of the liquid-crystalline phases identified in the lecithinwater-cyclohexane system, an apolar volume fraction f, containing oil and the lipophilic part of the surfactant molecule, and the remaining polar volume fraction (1 - f), containing water and the polar headgroups, have been defined:

f ) Φo + (vlip/vs)Φs

(1)

1 - f ) Φw + (1 - vlip/vs)Φs

(2)

where Φo, Φw, and Φs are the oil, water, and surfactant volume fractions, respectively, and they were calculated taking do ) 0.77389 and ds ) 1.0198 for the densities of cyclohexane and lecithin at 25 °C, respectively, the latter being evaluated from density measurements;13 vlip is the volume of the lipophilic part and vs is the total volume of the surfactant molecule. For the analysis of the SAXS data, we have used vs ) 1257 Å3 (from the apparent molar volume13 757 cm3 mol-1) and vlip ) vs - vh, taking the volume of the lecithin polar headgroup14 (strictly the phosphorocholine group) vh ) 204 Å3.

3. Results Overview of the Ternary-Phase Behavior. The complete quasi-ternary-phase diagram for the system lecithin-water-cyclohexane at 25 °C is presented in weight fractions in Figure 1. The accuracy in the location of the phase boundaries is within 5 wt %. There are three anisotropic liquid-crystalline phases, namely, a reverse nematic N2 phase, a reverse hexagonal H2 phase, and a lamellar LR phase and one isotropic liquid-crystalline reverse cubic phase I2. There are also a reverse micellar L2 phase and an aqueous solution phase, although the latter can dissolve very small quantities of oil and surfactant. Tentatively two- and three-phase regions are indicated in accordance with Gibbs’ phase rule. They were not investigated in detail and deviations from a pure ternary behavior may occur due to the multicomponent character of the lecithin. The L2, H2, and LR phases dominate the triangular diagram, whereas the cubic and nematic phases have more limited stability ranges. A short description of the single regions are given below. Reverse Micellar Solution Phase, L2. About 45 wt % of lecithin can be dissolved in cyclohexane. The binary lecithin-cyclohexane solutions have been investigated by density and PGSE-NMR self-diffusion measurements in a wide range of phospholipid concentrations and the data are discussed elsewhere.13 These binary solutions can dissolve small amounts of water up to a maximum of about 12 wt %, producing an isotropic L2 phase. A major part of this phase contains long reverse wormlike micelles that entangle to form a network similar to conventional polymer solutions in a semidilute regime. The contour length of these wormlike micelles increases with increasing the value of W0 up to W0 ) 10-12, as has been shown from scattering experiments in dilute and semidilute regimes,2 and supported by lecithin NMR self-diffusion experiments in the semidilute regime.5 Moreover, it has been shown that further water addition induces a rod-to-sphere transition,6 and at higher water contents (W0 ≈ 20) the structure approaches spherical reverse micelles,15 coexist(13) Angelico, R.; Palazzo, G.; Olsson, U.; Ambrosone, L.; Ceglie, A. Prog. Colloid Polym. Sci. 1999, 112, 1. (14) Small, D. J. Lipid Res. 1967, 8, 551. (15) Eastoe, J.; Heterington, K. J.; Sharpe, D.; Steytler, D. C.; Egelhaaf, S.; Heenan, R. K. Langmuir 1997, 13, 2490.

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Figure 1. Complete isothermal phase diagram of the ternary system lecithin-water-cyclohexane at 25 °C with single- and multiphase areas. Phase abbreviations are as follows: L2, reverse micellar solution phase; N2, reverse nematic phase; I2, reverse cubic phase; H2, reverse hexagonal; LR, lamellar phase. The N2 and I2 areas are shown approximately with dashed lines.

ing with excess water (Winsor II equilibrium). The L2 phase boundary is not characterized by a constant ratio between water and lecithin but, instead, reveals that the maximum W0 value compatible with a single-phase increases with the lecithin fraction. The viscosity of the samples shows a peculiar trend when measured as a function of the water content: At low W0 it increases dramatically in agreement with the water-induced micellar growth, and above W0 ≈ 10 it falls again. The overall W0 dependence can be described as bell-shaped.16 Up to about 25 wt % of lecithin, the micellar solutions are in equilibrium with water at the phase boundary. When the lecithin concentration is increased, the L2 phase boundary is in equilibrium with a reverse cubic I2 phase and water. We note that the region of coexistence, L2-I2, appears unusually large. At still higher lecithin concentrations the micellar threads orient at a large scale as a result of excluded volume interactions, resulting in an ordered phase of hexagonal symmetry (vide infra). But, more interestingly, a nematic17 N2 phase of reverse type is observed at intermediate concentrations between the isotropic L2 and the reverse hexagonal phase H2. Nematic Liquid-Crystalline Phase, N2. The reverse nematic N2 phase is found in a restricted region, 35% < φ < 45% (φ, being the lecithin plus water volume fraction), where the samples are birefringent (in Figure 2A the (16) Schurtenberger, P.; Magid, L. J.; Lindner, P.; Luisi, P. L. Prog. Colloid Polym. Sci. 1992, 89, 274. (17) Hendrikx, Y.; Charvolin, J.; Rawiso, M.; Lie´bert, L.; Holmes, M. C. J. Phys. Chem. 1983, 87, 3991. Berret, J.-F.; Roux, D. C.; Porte, G.; Lindner, P. Europhys. Lett. 1994, 25, 521.

texture for N2 sample is shown), but the SAXS spectra do not show the typical pattern for the hexagonal symmetry. A SAXS diffraction spectrum obtained for a sample in the N2 phase is shown in Figure 2B. The scattering function is dominated by a single broad correlation peak at q ) 0.09 Å-1, whose position decreases slightly, increasing the water content at a constant lecithin concentration. Thus, starting from the L2-phase region, an isotropicnematic phase transition occurs when the lecithin concentration is increased. Concerning the structure, the nematic phase consists of very long cylindrical micelles closely packed parallel to each other, thus producing long-range orientational order, lacking the positional order. At higher length scales, the nematic phase results in a polydomain structure, each domain being characterized by a homogeneous average molecular orientation, which defines the director axis, and by a local angle (θ) between the tangent to the micellar contour and the director of a nematic domain.17 We found that the transition to a nematic phase can be induced also under the effect of moderate shear on samples at high lecithin concentrations in the isotropic L2 phase.18 The anisotropy of a nematic phase is evidenced not only from the optical birefringence but also through the chemical shift anisotropy effect in a 31P NMR spectrum and the quadrupolar splitting in a 2H NMR spectrum, for samples made with heavy water. (18) Angelico, A.; Olsson, U.; Mortensen, K. Annual Progress Report of Condensed Matter Physics and Chemistry Department; Risø National Laboratory: Roskilde, Denmark, 1998.


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Figure 3. (A) 31P NMR spectrum, at 25 °C, for a nematic sample of composition 31/10/59 in wt % of lecithin/water/cyclohexane. (B) 2H NMR spectrum, at 23 °C, for the same nematic sample.

Figure 2. (A) Microscopic texture for a nematic sample of composition 47/6/47 in wt % of lecithin/water/cyclohexane. Magnification: ×20. (B) Representative SAXS diffraction pattern obtained for a sample in the nematic region. The position of the maximum is indicated.

In Figure 3A the chemical shift anisotropy of the 31P NMR resonance of the lecithin phosphocholine moiety for a nematic sample is shown. Because the electron shell of the 31P nucleus is not spherically symmetric, the chemical shift, σ, is not a scalar but a tensor and depends on the orientation of the phosphorus group relative to the external magnetic field. Therefore, the chemical shift expected when the field is parallel to this axis is labeled σ| while that expected for the field perpendicular to the axis is labeled σ⊥.19 The parameter ∆σ ) σ|-σ⊥ determines the width of the spectrum; the left border of the signal corresponds to σ| and the right to σ⊥ in Hz or ppm. The width and asymmetry of 31P spectra can usually be used as a diagnostic tool for determing lipid phases.19 The orientation behavior of the nematic phase determines both the observed ∆σ and the water quadrupolar splitting in the 2H NMR spectrum shown in Figure 3B, performed at 23 °C on the same sample with heavy water. In the spectrum the inner splitting comes from water molecules in aggregates aligned at 90° with respect to the direction of the magnetic field, while the outer splitting originates from aggregates with the director axis parallel to the applied field.20 (19) Gorenstein, D. G. Phosphorus-31 NMR, Principles and Applications; Academic Press: New York, 1984; Chapter 15. (20) Wennerstro¨m, H.; Persson, N.-O.; Lindman, B. ACS Symp. Ser. 1975, 9, 253.

Figure 4. (A) The angular texture in the reverse hexagonal phase. Sample composition 37/17/46 in wt % of lecithin/water/ cyclohexane. Magnification: ×20. (B) Representative SAXS diffraction pattern obtained for a sample in the reverse hexagonal region. Also shown are the position of the maxima and their order (in brackets).

Reverse Hexagonal Phase, H2. The samples in this region are all anisotropic. Their consistency is rather stiff and the texture in the polarizing microscope can be seen in Figure 4A, showing the characteristic angular and nongeometric texture.11 The reverse H2 phase appears between about 34 and 77 wt % of lecithin with a maximum water content of about 40 wt %. The two-dimensional

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Table 1. Geometrical Parameters of the H2 Phase as a Function of the Composition (wt %) lecithin

water

C6H12

φ

d w, Å

d, Å

R, Å2

34 40 38 37 45 43 51 41 48 42 62 46 54 61 48 42 56 63 73 49 67 41 49 40 45

16 10 15 17 11 14 6 19 13 19 0 16 10 6 20 28 15 10 0 25 10 36 30 43 39

50 50 47 46 44 43 43 40 39 39 38 38 36 33 32 30 29 27 27 26 23 23 21 17 16

0.43 0.44 0.47 0.48 0.49 0.51 0.51 0.53 0.54 0.55 0.55 0.57 0.58 0.61 0.62 0.64 0.65 0.67 0.67 0.69 0.71 0.72 0.74 0.79 0.80

37 28 32 34 27 30 20 38 29 36 13 34 27 20 37 48 30 24 14 40 23 60 50 70 51

44 40 37 39 37 35 31 36 34 35 28 35 32 29 33 32 30 27 26 28 27 30 28 26 43

89 78 91 89 77 84 74 85 80 87 64 79 73 68 78 88 74 70 59 87 68 88 79 89 81

hexagonal structure was established by SAXS experiments, while the reverse morphology was ascertained from the location of the hexagonal region in the ternary-phase diagram and from the dependence of the determined R on the water content (see below). Figure 4B shows the SAXS diffraction pattern obtained for a H2 sample, with four Bragg peaks, the first-order peak (10) being larger than the higher order peaks. The relative positions of the four peaks resolved in the diffraction pattern with q values in the relationship 1:x3:2:x7 confirm the hexagonal structure. Moreover, from SAXS data, the diameter of the water cylinders, dw ) 2Rcyl, the distance between the nearest-neighbor polar/apolar interface, d ) ah - dw, and the polar headgroup area at the interface, R, have been determined using the following equations, for several samples within the stability range of the H2 phase (see Table 1):

qhk ) Rcyl )

[

[

]

2π(h2 + k2 + hk) (1 - f)x3

]

(1 - f)x3 2π

1/2

ah )

ΦsR vs

1/2

2(1 - f)vs ΦsR

(3)

(4)

where h and k are the Miller indices and ah is the lattice parameter for the hexagonal array (nearest neighbor distance). From Table 1 it is evident that as a result of increasing the water content, there is a corresponding swelling of the cylinders whose diameters range from 13 to 70 Å, depending on the sample composition.The highest value is obtained in the water-rich part of the phase diagram and the lowest value in the water-lean portion of it. Please note that the diameter of the polar core of “dry” reverse micelles (13 Å at W0 ) 0) corresponds to the phosphorocholine moiety alone (without the glycerol backbone) according to our definition of the polar/apolar interface (see Materials and Methods). Moreover, the half thickness d/2, taking the lowest value for d, gives the minimum length of the hydrocarbon chain of phospholipids, that is, 13 Å, to compare with the extended length of 18 Å. The polar headgroup area of lecithin in the H2

Figure 5. Polar head area (R) data of Table 1 plotted vs W0 in the reverse hexagonal region for different water dilution lines. The amount of lecithin in the original binary mixture lecithin/oil is reported as wt %.

phase is found to be essentially lecithin-concentrationindependent, as is shown in Figure 5 where one can see that the R values increase with increasing the water content up to reach a plateau at R ≈ 90 Å2. Such a feature can be thought of as an a posteriori confirmation of the reverse nature of the hexagonal arrangement.21 Lamellar Phase, Lr. The one-dimensional lamellar structure was established by SAXS measurements. In Figure 6A a representative diffraction pattern is shown, with four peaks. Their relative positions correspond to the 1:2:3:4 relationship, which is a confirmation of the lamellar structure. The samples in this region are soft and have a cloudy appearance. All samples show the typical textures for lamellar phases, with a mosaic pattern in the polarizing microscope11 as can be seen from Figure 6B. The LR phase can swell and take up about 45 wt % of water, in the presence of 5 wt % of oil. The average interbilayer spacing (repeat distance), d, the bilayer thickness h ) fd of the apolar domain of the lamellae, and the area per polar headgroup, R, have been calculated from SAXS data using the following equation:

q1 )

2π πΦsR ) d vs

(5)

(where q1 is the first-order Bragg peak), for samples in the LR region, (see Table 2). Like in the case of the liquidcrystalline hexagonal phase, the polar headgroup area obtained in the LR phase remains almost unchanged with varying lecithin concentrations, but is dependent on W0, (Figure 7). Cubic Liquid-Crystalline Phase, I2. A small cubic “island” is found close to the hexagonal phase, almost in the center of the phase diagram. The samples in this region, whose boundaries are not accurately determined, are very stiff, with a clear glassy appearance and they are isotropic when examined between crossed polarizers. Judging from the location of this phase, below the reverse (21) Seddon, J. M.; Templer, R. H. In Structure and Dynamics of Membrane from Cells to Vesicles; Lipowsky, R., Sackmann, E., Eds.; Elsevier: Amsterdam, 1995; Vol. 1, p 97.


Figure 6. (A) SAXS diffraction pattern of a sample in the lamellar area. Also shown are the position of the maxima and their order (in brackets). (B) Mosaic texture of the lamellar phase. Sample composition 63/25/12 in wt % of lecithin/water/ cyclohexane. Magnification: ×10.

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Figure 7. Polar head area (R) data of Table 2 plotted vs W0 in the lamellar phase for different water dilution lines. The amount of lecithin in the original binary mixture lecithin/oil is reported as wt %.

Table 2. Geometrical Parameters of the Lr Phase as a Function of the Composition (wt %) lecithin

water

C6H12

φ

d, Å

h, Å

R, Å2

76 72 63 81 51 72 63 50 88 78 68 60 100

10 15 25 10 40 20 30 45 7 18 28 37 0

14 13 12 9 9 8 7 5 5 4 4 3 0

0.83 0.84 0.85 0.89 0.90 0.90 0.91 0.94 0.94 0.95 0.95 0.96 1.00

48 51 56 46 65 51 56 61 44 49 55 61 54

37 38 37 35 34 35 34 29 35 34 33 33 45

71 72 74 69 78 70 73 84 65 66 69 70 47

isotropic L2 phase and close to the reverse anisotropic H2 phase, its structure is expected to be made of discrete reverse micellar aggregates,22 which was also confirmed by a NMR self-diffusion experiment (see below). A few reflections have been obtained from X-ray measurements, as shown in Figure 8A, for a sample with micellar volume fraction (lecithin plus water) φ ) 0.52. The first strong correlation peak and other weaker reflections have been indexed according to a body-centered structure (bcc, space group Im3m) that allows the Bragg reflections hkl ) 110, 200, 211, 220, 310, 222, 321, 400, 441, and so forth, which give peaks in the relative (scattering vector q) positions x2, x4, x6, x8, x10, x12, x14, x16, x18, and so forth. Here, the first five reflections have been identified and the indexing of the diffraction data has been assessed as shown in Figure 8B by a plot of 1/dhkl versus (h2+k2+l2)1/2. (22) Cubic liquid-crystalline phases are reviewed in detail in the following articles: Fontell., K. Colloid Polym. Sci. 1990, 268, 264. Lindblom, G.; Rilfors, L. Biochim. Biophys. Acta 1989, 988, 221. Seddon, J. M.; Templer, R. H. Philos. Trans. R. Soc. London A 1993, 344, 377. Eriksson, P. O.; Lindblom, G.; Arvidson, G. J. Phys. Chem. 1985, 89, 1050. Eriksson, P. O.; Lindblom, G.; Arvidson, G. J. Phys. Chem. 1987, 91, 846.

Figure 8. (A) Representative SAXS diffraction pattern obtained for a sample in the reverse micellar cubic phase. Also shown are the position of the maxima and their order (in bravkets). (B) Plot of the reciprocal d spacing (1/dhkl) of the reflections marked in the SAXS diffraction pattern of Figure 8A plotted vs (h2 + k2 + l2)1/2.

For the correct choice of space group, this plot gives a straight line passing through the origin, having a slope of 1/ac, where ac is the unit cell lattice parameter which,

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in the present case, is found to be 153 Å. The results of this analysis follow the trend expected for structures of cubic aspect 8 and, more specifically, for the centrosymmetric bcc or Im3m (Q229) space group.23 A lattice parameter of 140 Å was also obtained using simple geometrical arguments, according to the following equation:

vs ac ) [36πN(1 - f)2]1/3 ΦsR

(6)

for the volume occupied by the (N) 2) spherical reverse micelles which make up the unit cell of the bcc structure, and taking into account the water plus polar headgroups volume fraction (1 - f) for the 34/25/41 lecithin/water/oil wt % sample composition and the interfacial area per lecithin molecule, assumed to be 80 Å2 as in the neighboring H2 sample of 42/28/30 wt % lecithin/water/oil. Further (and stronger) proof of the presence of a discrete micellar cubic phase in the system lecithin-water-cyclohexane comes from NMR self-diffusion data. Indeed, the water self-diffusion coefficient, Dcub w , measured for the same sample of Figure 8 is 3.3 × 10-12 m2 s-1, that is, 3 orders of magnitude smaller than the self-diffusion coefficient in neat water (2.3 × 10-9 m2 s-1). In a recent PGSE-1H NMR study24 of water diffusion in the LR phase of egg PCwater the measured Dw at 25 °C is found to be between 1.2 × 10-10 and 4.0 × 10-10 m2 s-1, depending on the water/ lipid mole ratio. Because Dcub w is 2 orders of magnitude slower than the water diffusion in water-continuous domains (parallel to the bilayers in the lamellar phase), we can safely conclude that the present cubic phase is built up of discrete reverse micelles. Experiments performed at different time scales give the same Dcub w , characteristic of an unrestricted diffusion within the micellar matrix. A reasonable diffusion mechanism is then one in which the water molecules perform a random walk in the cubic lattice from micelle to micelle. Therefore, it is possible to derive information regarding the dynamics of water in micellar aggregates from the measured diffusion coefficient using the relation25

Dcub w )

〈l2〉 6τR

(7)

where l is the (average) distance between neighboring micelles and τR is the mean residence time of water molecules in the micelles. Here, one assumes that jumps occur between neighboring micelles and that there is no correlation between the points of entry and exit into the micelles of the migrating species. For the Im3m lattice the value of l is equal to the half of the space diagonal to the cubic cell with volume ac3. Using the value 153 Å for ac (see above), we estimate from eq 7 the mean residence time in the micelles to be τR ≈ 9 µs and fully consistent with the estimated τR calculated by us from water selfdiffusion data in the L2 phase.3 Such an intermicellar exchange process is also valid for lecithin molecules, although it works on a different time scale. Indeed, from the lecithin self-diffusion coefficient measured for the same sample, found to be Dcub lec ) 3 × (23) Mariani, P.; Luzzati, V.; Delacroix, H. J. Mol. Biol. 1988, 204, 165. (24) Wassal, S. R. Biophys. J. 1996, 71, 2732. (25) Johansson, L. B.-A˙ .; So¨derman, O. J. Phys. Chem. 1987, 91, 7575. Walther, K. L.; Gradzielsi, M.; Hoffmann, H.; Wokaun, A.; Fleischer, G. J. Colloid Interface Sci. 1992, 153, 272. So¨derman, O.; Johansson, L. B.-A˙ . J. Colloid Interface Sci. 1996, 179, 570.

10-16 m2 s-1, it is possible to estimate the mean residence time of the lecithin molecules in the micelles using the previous equation. The obtained τR value for lecithin is of the order of 0.1 s, namely, a factor of 104 longer than the corresponding residence time for water. This means that the dynamics of the mechanism underlying the exchange process is very different for water and lecithin, as has been demonstrated by the self-diffusion investigations of water,3 and lecithin5 in the L2 phase. Considering that Dcub lec has been measured for ∆ ) 3 s (∆ being the experimental time scale in the PGSE technique), and taking into account the previous estimated τR for lecithin, the number of micelles involved in this exchange process for 3 s is found to be about 30 (supposing the micelles are “frozen” in that time scale because of the dense packing in the cubic lattice). Multiphase Regions. All heterogeneous regions (twoand three-phase areas) are identified, but their boundaries are not accurately determined. On the binary surfactantoil axis, the isotropic micellar solution phase is in equilibrium with the nematic liquid-crystalline phase (L2 + N2). This two-phase area is quite narrow, indicating similarity in shape between the polymer-like micelles in the concentrated part of the solution phase and the nematic rods. The L2 phase is also in equilibrium with water in the water-rich part of the isotropic region (L2 + W) where now the reverse micelles have spherical shapes.6 A couple of two-phase areas are also found, one between the reverse hexagonal H2 and the reverse cubic I2 phases and one between the reverse hexagonal H2 and the lamellar LR, as confirmed by SAXS data.26 4. Discussion The Flexible Surface Model and the L2 + W, I2 + H2 Equilibria. In the flexible surface model of microemulsions27,28 one focuses on the curvature elasticity of the polar-apolar interface. Within the harmonic approximation the curvature free energy density can be written as29

gc ) 2κ(H - H0)2 + κjK

(8)

Here, H and K are the local mean and Gaussian curvatures of the interface and H0 is the spontaneous curvature. κ and κj are the bending rigidity and saddle splay constant, respectively. The κ should always be positive because only in this case the spontaneous curvature is favored. On the contrary κj might be either negative, in which case structure with c1 ) c2 (spherical droplets and lamellae) will be favored or positive which will favor saddle-shaped structures as are found in bicontinuous microemulsions and L3 phases. In the case of spherical droplets of radius Rwc the curvature energy density gc will be

gc ) 2κ

(

)

1 - H0 Rwc

2

+

κj Rwc2

(9)

For infinitely long cylinders one can write (26) Angelico, R. Ph.D. Thesis, University of Bari, 1999; Chapter 4. (27) Safran, S. A. J. Chem. Phys. 1983, 78, 2073. Safran, S. A.; Turkevich, L. A.; Pincus, P. A. J. Phys. Lett. 1984, 45, L69. Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces and Membrane; Addison-Weseley Publishing Company: New York, 1994; Chapter 8. (28) Olsson, U.; Wennersto¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113. (29) Helfrich, W. Z. Naturforsch. 1973, 28C, 693.


gc ) 2κ

(

)

1 - H0 2Rwc

2

Langmuir, Vol. 16, No. 5, 2000 2131

(10)

Starting from these relations Safran and co-workers have calculated the relative stability of spherical and cylindrical films.27 It should be noted that in the case of spherical droplets the curvature which minimizes this form of bending energy is not H0, if κj * 0 but rather c* which is related to H0 by c* ) H0/(1+ κj/2κ). For spherical droplets, the sphere radius Rwc is determined by the conservation of surfactant (total interfacial area of the drop) and of the interior phase. For the lecithin L2 phase,30

Rwc )

ls 3(W0vw + vh) ) 3(1 - f) R φs

(11)

where ls is the surfactant length, defined as ls ≡ vs/R, Rwc is the radius of the water core containing also the lipid headgroup, and vW is the molecular water’s volume. Neglecting the entropy contribution, the maximum droplet’s size is Rwc ) 1/c*; adding more water to the system results in a two-phase Winsor II equilibrium between excess water and droplets of the optimal size, a situation usually called “emulsification failure”.27 For small values of Φw/Φs (Rwc, 1/c*) cylindrical micelles are more stable and wormlike reverse micelles are expected.27 When the water content is increased, the aggregates’ structure evolves toward spherical reverse micelles which are always present at the emulsification failure for κj e 0. Depending on the κ and κj values, the spheres and the cylinders can coexist in a certain range of composition. In general, more negative values of κj move the transition toward lower Φw/Φs ratios and shrink the range of composition where cylinders and spheres are degenerate.27 The L2 phase closely follows the prediction of the flexible interface model. Indeed, at low W0 we find giant wormlike reverse micelles while at high W0 the system presents a Winsor II equilibrium between globular reverse micelles and excess water. Furthermore, at intermediate W0 values (15-19) there is evidence of a coexistence of cylindrical and spherical aggregates (see Discussion in ref 6). More importantly, the same behavior can be recognized in the sequence of mesophases (H2 f I2) found increasing the water content at high φ. In the above description entropic contribution has been neglected. For the case of spherical reverse micelles, however, the entropy of mixing contribution to the free energy can be taken into account as described for example in ref 31. A (globular) microemulsion that is in equilibrium with the excess of solubilized material may now adjust its radius in such a way as to minimize its free energy. From the relation between the maximum radius of the aqueous core and the system composition, the following relation holds:

(

W0,ef ) W0* + W0* +

)

kBT vh F(φ) vw 4π(2κ + κj)

(12)

where F(φ) is a term which takes into account the entropic contribution and depends on certain assumptions regarding the system which is summarized elsewhere.31 W0,ef is the W0 at the emulsification failure and is a function of (30) Strictly, eq 11 holds for monodisperse droplets only. However, because of their low polydispersity such a relation describes microemulsion systems with good approximation. (31) Gradzielski, M.; Langevin, D.; Farago, B. Phys. Rev. E 1996, 53, 3900. See in particular Appendix B.

φ, while W0* is the ratio beween water and lecithin corresponding to Rwc* ) 1/c* ) H0/(1+ κj/2κ). The interesting feature of eq 12 is that F(φ) is always less than zero and becomes more and more negative with the dilution. This is in qualitative agreement with the observed increase in W0,ef with lecithin content (see Figure 1). Excluded Volume Effects and the L2 f N2 f H2 f LR and the L2 f I2 f H2 f Lr Transitions. The flexible surface model describes in a consistent way the transition with increasing the water content from cylindrical to spherical geometries found in the L2 and liquid-crystalline phases. Departures from the prediction manifest themselves only at high volume fractions where interaggregates interactions essentially due to excluded volume effects become very important. Increasing the number density of threadlike micelles at (fixed) low W0 leads to oriented aggregates at large scale, with a degree of ordering which grows with φ, resulting in the sequence of phases L2 f N2 f H2. It is only at very high φ that the cylindrical aggregates are forced toward lamellar sheets. On the other hand, at high W0 the spherical reverse micelles prefer to pack themselves in a cubic lattice when φ is increased. Let us discuss in some detail the boundaries of such transitions. The close packing or maximum volume fraction are 91 and 74 vol % for cylinders and spheres, respectively. Oil must fill the voids between the surfactant chains within the packing units. This oil is contained in the spheres and/or cylinders volume fractions. For spherical micellar systems behaving as hard spheres the packing units volume fraction, φpu, and the dispersed-phase volume fraction are usually related simply by a multiplicative constant.32 In the formulas, φpu/φ ) constant, where the constant is close to 1 in the absence of a strong electrostatic effect. It seems that a similar relationship should hold for a cylinder as well. In Figure 9A we report the ratio between the theoretical limits, φmax, and the experimental volume fraction of the dispersed phase evaluated along the phase boundaries. In other words, for spheres φmax ) 0.74 and the φ’s are collected along the I2 boundary, while for cylinders φmax) 0.91 and the φ’s refer to the H2/H2 + LR equilibrium. It is evident that φmax/φ is almost constant and independent from φ and W0 and we can express the sphere and/or the cylinder volume fraction as 1.23φ. With this in mind the phase behavior can be rationalized in a fully consistent way in terms of bending energy and excluded volume (EV) effects as schematically shown in Figure 9B. At low values of volume fraction of the packing units, φpu, and of W0, the L2 phase is composed of cylindrical wormlike aggregates. When the W0 is increased, the curvature energy leads to the formation of spheres. For the cylindrical micelles the increase in φpu induces the classical L2 f N2 f H2 transition because of EV effects. It is only when φpu ) 0.91, because the low amount of oil is not enough to fill the voids between cylinders, that the aggregates are forced to change themselves into lamellae and the H2 f LR transition is expected and experimentally found. At high W0 the EV effects drive the spherical micelles toward the L2 f I2 transition. It should be noted that for φpu < 0.74, the I2 “island” can be reached from the H2 phase by increasing the W0 with a phase transition governed by the curvature energy. However, at the upper limit the spherical units can occupy on close packing, the aggregates are forced to change their shape first in the cylinder and, over the cylinders’ close packing limit, in lamellae. Therefore, we find a spherical micelles f discrete (32) See for example Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389.

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Angelico et al.

similar to what is often found in water continuous systems. As a consequence, the H2 phase strongly protrudes toward the water corner in the phase diagram, separating the cubic from the lamellar phases (see Figure 1). A final remark should be done. For cylindrical polymer-like micelles at the L2/N2 boundary, the micellar persistence length λp should be related to φpu by33

d λp ) 7.77 φpu

(13)

Using a value of the micellar diameter d ) 60 Å, we found for all the samples a persistence length larger than 700 Å. A so large value of the λp was previously inferred by self-diffusion studies5 in the semidilute regime of the L2 phase and by investigation in microemulsions formed in isooctane.34 However, careful SANS studies in the dilute regime suggests a persistence length of 120 Å.2 At the present time we cannot rationalize this discrepancy and further studies are needed to justify it. Conclusions The complete phase diagram for the system lecithin/ water/cyclohexane has been determined at 25 °C. The L2 phase (present at low φ) shows a complex microscopic behavior, being composed of wormlike reverse aggregates at low water contents and almost spherical reverse micelles at high water contents (these last in equilibrium with water at the emulsification failure). The remaining part of the phase diagram can be understood on this basis. taking into account the excluded volume effects upon decrease of the oil content. The larger presence of phases of reverse structure indicates a negative spontaneous curvature, H0, of the lipidic film. The absence of bicontinuous intermediate phases suggests a negative value of the Gaussian bending modulus, κj, in agreement with the lack of branched micelles in the L2 phase, previously demonstrated by us.5 Figure 9. (A) Ratio between the thoretical close packing limits (φmax) and the experimental dispersed-phase volume fractions (φ) taken from the boundaries at a high lecithin weight fraction of Figure 1. O, H2 boundary. b, I2 boundary. (B) Schematic representation of the curvature energy-driven (simple arrows labeled fb) and of the excluded-volume- (double arrows labeled EV) driven transitions in a stability diagram W0 vs packing units volume fraction, φpu. See text for details.

cubic f hexagonal f lamellar sequence of phases which is quite unusual for systems of reverse curvature, but

Acknowledgment. This paper is dedicated to the memory of our dear friend and colleague Professor Americo Inglese (1946-1998).This work was supported by MURST of Italy (Prog. Naz. Cofinanz. 1998) and by the Swedish Natural Science Research Council (NFR). LA9909190 (33) Van der Schoot, P.; Cates, M. E. Europhys. Lett. 1994, 25, 515. (34) Cirkel, P. A.; Koper, G. J. Langmuir 1998, 14, 7095.

Phase Diagram and Phase Properties of the System

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