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Solubilization of Micellar Cubic Phases and Their Structural Relationships in Anionic-Cationic Surfactant-Dodecane-Water Systems Xingfu Li and Hironobu Kunieda* Graduate School of Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku,Yokohama 240-8501, Japan Received June 15, 2000. In Final Form: September 14, 2000 The morphology and solubilization of micellar cubic phases are investigated as a function of the cationic weight fraction in the mixture of two surfactants, the surfactant-to-water ratio, and the oil weight fraction in the water-dodecane-sodium dodecyl sulfate (SDS)-dodecyltrimethylammonium bromide (DTAB) or didodecyl-dimethylammonium bromide (DDAB) systems at 25 °C. One phase transition H1 f I1 appears at low cationic weight fraction, Y, and the other LR f I1 takes place at high Y upon addition of oil. Solubilization for dodecane of the micellar solution and of the micellar cubic phase increases with an increase in the cationic surfactant weight fraction Y from 0 to 0.30. SAXS measurements index the structure of the cubic phase as the discontinuous Pm3n cubic phase for single surfactant systems and mixed surfactant systems at different levels of oil. The cross-sectional area of the hydrophilic head of the surfactant keeps constant with increase in the oil weight fraction at a fixed cationic surfactant weight fraction as the interlayer spacing of the Pm3n cubic phase greatly increases. However, it decreases with an increase in the cationic surfactant weight fraction at fixed oil weight fraction as the interlayer spacing of the Pm3n cubic phase slowly increases. So the solubilization for oil can be increased by adjusting the mean curvature of the surfactant interface layer with the addition of mixed surfactants and long-chain oil.
Introduction Cubic liquid crystalline phases have been studied widely in water-surfactant or surfactant-like lipid systems.1-5 In recent years, much attention has been devoted to cubic mesophases in some ternary water-oil-surfactant systems containing a low proportion of oil.6-12 It is now well recognized that a large structural diversity arises from variation of the volume fractions, but also from modifications in the interactions between neighboring surfactant molecules. Various cubic structures have been reported with ternary systems containing soap molecules, singlechain surfactants, double-chain surfactants, or a mixture of single- and double-chain surfactants.6-12 The research on binary sodium dodecyl sulfate (SDS)water systems and dodecyltrimethylammonium bromide (DTAB)-water systems shows that no micellar cubic phase (I1) is formed between a micellar solution and a hexagonal phase (H1) upon increasing surfactant concentration.2,13 The addition of long-chain oil in the hexagonal phase, on * To whom correspondence should be addressed. (1) Lindblom, G.; Rilfors, L. Biochim. Biophys. Acta 1989, 988, 221. (2) Balmbra, R. R.; Clunie, J. S.; Goodman, J. F. Nature 1969, 222, 1159. (3) Sakya, P.; Seddon, J. M.; Templer, R. H.; Mirkin, R. J.; Tiddy, J. T. Langmuir 1997, 13, 3706. (4) Kunieda, H.; Shigeda, K.; Ozawa, K. J. Phys. Chem. 1997, 101, 7952. (5) Tabony, J. Nature 1986, 319, 400. (6) Kunieda, H.; Ozawa, K.; Huang, K.-L. J. Phys. Chem. 1998, 102, 831. (7) Kunieda, H.; Umizu, G.; Aramaki, K. J. Phys. Chem. 2000, 104, 2005. (8) De Geyer, A. Progr. Colloid Polym. Sci. 1993, 93, 76. (9) Ciach, Alina; Holyst, Robert J. Chem. Phys. 1999, 110, 3207. (10) Fontell, K.; Jansson, M. Progr. Colloid Polym. Sci. 1988, 76, 169. (11) Strom, P.; Anderson, D. M. Langmuir 1992, 8, 691. (12) Barois, P.; Hyde, S.; Ninhem, B.; Dowling, T. Langmuir 1990, 6, 1136. (13) Marques, E.; Khan, A.; Miguel, M. G.; Lindman, B. J. Phys. Chem. 1993, 97, 4729.
the other hand, results in a phase transition from H1 to I1 in the ionic surfactant systems,3,6,7,11,14 although the oil solubilization of the above cubic phase is very limited. However, it would be possible to form the cubic phase with large oil solubilization by controlling the surfactant layer curvature in the mixed anionic-cationic surfactant systems.14 The mixture of an anionic and a cationic surfactant has many unique physiochemical properties that arise from the strong electrostatic interactions between the oppositely charged headgroups,15-17 which, for example, makes the surfactant layer curvature less positive and favors the formation of a very stable vesicle at an appropriate mixing ratio of anionic to cationic surfactant. The ultralow surface tension and maximum solubilization of microemulsions for equal amounts of water (or brine) and oil can be also obtained by mixing an anionic and a cationic surfactant as well as alcohol.18-21 Various liquid crystals including the cubic phase appear in the above systems with low surfactant content.8,14 However, it is difficult to determine the space group of cubic phases and the structural variation of micelles within the cubic phases10,14 because of the change in distribution of hexanol between the microoil domain and the surfactant interlayer with increases in the addition of salt and in the mixing of anionic and cationic surfactants. So it is necessary to research the (14) Li, X.; Kunieda, H. J. Colloid Interface Sci., in press. (15) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. J. Phys. Chem. 1992, 96, 6698. (16) Patist, V.; Chhabra, V.; Pagidipati, R.; Shah, D. O. Langmuir 1997, 13, 432. (17) Yu, Z.-J.; Zhang, X.; Xu, G.; Zhao, G.-X. J. Phys. Chem. 1989, 93, 7441; 1989, 93, 7446; 1990, 94, 3675. (18) Li, X.; Zhao, G.; Lin, E.; Xiao, T. J. Dispersion Sci. Techn. 1996, 17, 111. (19) Li, X.; Lin, E.; Zhao, G.; Xiao, T. J. Colloid Interface Sci. 1996, 184, 20. (20) Li, X.; Wang, J.; Wang, J. J. Dispersion Sci. Techn. 1999, 20, 993. (21) Li, X.; Ueda, K.; Kunieda, H. Langmuir 1999, 15, 7973.
10.1021/la000829r CCC: $19.00 © 2000 American Chemical Society Published on Web 11/22/2000
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cubic phase formation and its corresponding structural relations without addition of alcohol and salt in the above systems. In this context, cubic phase formation and phase behavior of the anionic-cationic surfactant-dodecanewater systems were investigated at constant pressure and temperature by visual inspection, polarizing optical microscopy, and small-angle X-ray scattering (SAXS) techniques. Formation of cubic phase and phase transition of liquid crystals with mixed surfactants are explained qualitatively on the basis of curvature of the surfactant layer formed between oil and water. Special attention is also devoted to relations between solubilization for oil and structural variation of cubic phases. Experimental Section Materials. Sodium dodecyl sulfate (SDS) was obtained from SIGMA Chemical Co. with purity greater than 99%. Dodecyltrimethylammonium bromide (DTAB) at G. R., didodecyldimethylammonium bromide (DDAB) at G. R., extra-pure grade n-dodecane (C12) was used as received from Tokyo Kasei Co. Water was distilled and deionized. All chemicals were used without further purification. Sample Preparation and Phase Diagram Determination. Samples were prepared individually by weighing appropriate amounts of the components into glass ampules (10-15 mm in diameter) which were flame-sealed immediately. Approximately 400 samples of 300-500 mg (or more where greater accuracy was needed) were prepared at compositions all over the phase diagram in the course of the present study. However, the samples were concentrated along the phase boundaries with an accuracy of less than 0.3% of surfactant. To attain a homogeneity of samples, a vortex mixer was used for rather dilute samples and concentrated samples were mixed by repeated centrifugation through a narrow constriction around 40 °C. These samples were kept at 25 °C controlled by a thermostat from several hours to several months until equilibration was attained. Phase boundaries were determined by visual observation. Liquid crystals were detected with a crossed polarizer. The type of liquid crystal was also identified with polarizing microscopy and SAXS techniques.4,22 SAXS. The interlayer spacing of different liquid crystals was measured using SAXS, performed on a small-angle scattering goniometer with a 15 kW Rigaku Denki rotating anode generator (RINT-2500) at ∼25 °C. The samples were covered by plastic films for the SAXS experiment (Mylar seal method). The type of liquid crystals was distinguished with the interlayer spacing ratio among the first, second, and third peaks. The peak ratios were 1:1/2:1/3 for the lamellar phase and 1:1/x3:1/2 for the hexagonal phase, respectively.4,6,7 At least three peaks were observed in cubic phases (I1) and their peak ratios are 1:1/x5/4:1/x6/4 for the discontinuous type (I1).3,5,8,10,11
Results 1. Phase Behavior. a. Water-Dodecane-SDS-DTAB (or DDAB) Systems at Fixed Cationic Surfactant Weight Fraction. The ternary phase diagrams for water-dodecane-SDS-DTAB (or DDAB) systems at 25 °C are shown in Figure 1. For the single surfactant SDS-containing system shown in Figure 1a, a micellar solution (Wm) appears at low surfactant concentrations (less than 37 wt %) and a hexagonal liquid crystalline (H1) phase is formed between 39 and 57 wt %. The micellar cubic phase does not appear between Wm and H1 along the SDS-water axis as compared with dodecyltrimethylammonium chloride (DTAC)-water system.2 The oil solubilization of both micellar and hexagonal phases, corresponding to the oil weight fraction (Wo ) C12/(C12 + H2O + SDS + DTAB)) in the system, is limited to 0.03, and the further addition of (22) Edlund, H.; Sadaghiani, A.; Khan, B. Langmuir 1997, 13, 4953.
Figure 1. Phase diagram for the water-dodecane-SDSDTAB (or DDAB) system at 25 °C. The cationic surfactant weight fraction is fixed at Y ) 0 (a), Y ) 0.20 (b), and Y ) 0.20 (c). Wm, H1, LR, and I1 represent the micellar solution, hexagonal, lamellar, and micellar cubic phases. V, HCP, and “Solid Present” represent vesicle-present, hexagonal phase-present, and solid crystal-present regions, respectively. The compositions are given in weight fraction.
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oil to the H1 phase leads to the formation of a discontinuous cubic phase. The oil content of the cubic phase is between Wo ) 0.035 and 0.08 at fixed surfactant-to-water ratio, Rsw ) 45/55. Solid surfactant is present in the SDS-water system at higher surfactant concentrations, but it is not investigated in detail in this work. Adding a little DTAB to the SDS-containing systems, for example keeping the cationic surfactant weight fraction, Y ) DTAB/(SDS + DTAB), constant at 0.20, the Wm, H1, and I1 phases all appear and move toward the dodecane apex, as can be seen in Figure 1b. The maximum solubilization for oil of micelles reaches 0.10 at Rsw ) 30/ 70. Similar results were also reported in the mixed systems anionic-cationic surfactant-oil-water when the mixing molar ratio of surfactants is fixed at 1.23 This implies that an appropriate mixing of anionic and cationic surfactants can improve the solubilizing capacity for oil in surfactant aqueous systems, which has possible applications to detergent and cosmetic fields. The cubic phase is also formed from the hexagonal phase upon addition of dodecane to the systems, and the solubilization of oil of the cubic phase is between 0.15 and 0.22 at the same surfactant-to-water ratio (45/55). The cubic phase can also be formed from the lamellar phase in SDS-DDAB-dodecane-water systems at Y ) 0.20; and the solubilization for oil in the cubic phase is between 0.30 and 0.33 at the same surfactant-to-water ratio (45/55). The micellar and hexagonal phases are not formed, and the vesicle-present region appears around the water apex with surfactant concentration less than 0.12.13 Compared with the single surfactant SDS, the mixing of anionic and cationic surfactants (SDS and DTAB, or SDS and DDAB) results in the formation of the cubic phase at a high oil level. Furthermore, the SDS-DDAB pair shows the higher solubilizing capacity for oil of cubic phases than the SDS-DTAB pair at the same weight fraction of cationic surfactant due to the low curvature formed with SDS and DDAB containing double chains. b. Phase Transitions of Liquid Crystals as a Function of Y and Wo. As described in the previous section, formation of cubic phase and solubilization for oil of liquid crystals are influenced by many factors, such as temperature, the surfactant-to-water ratio, the cationic surfactant weight fraction, etc. Among those factors, the cationic surfactant weight fraction is a crucial one to form the cubic phase with high oil content.14 Considering the tendency of the cubic phase regions to move toward the dodecane apex, we chose the surfactant-to-water ratio at 40/60 and investigated the phase behavior as a function of the cationic surfactant and oil weight fractions at a constant temperature of 25 °C. The phase diagrams for waterdodecane-SDS-DTAB systems and for water-dodecane-SDS-DDAB systems are shown in Figure 2a and 2b, respectively. The cubic phase is formed from the hexagonal phase after addition of oil and the oil solubilization in the cubic phase increases remarkably with an increase in the cationic surfactant weight fraction Y shown in Figure 2a. The one phase transition H1fI1 appears at low Y and the other one LRfI1 takes place at high Y in SDS-DTABwater-dodecane systems. The maximum oil solubilization of the cubic phase can reach Wo ) 0.25 at Y ) 0.285. The same result is also obtained in the water-dodecaneSDS-DDAB system shown in Figure 2b. The narrow region of the cubic phase is formed with the addition of oil and extends to the high oil level. The maximum oil solubilization arrives at 0.35 around Y ) 0.25. The (23) Zhao, G.-X.; Li, X.-G. J. Colloid Interface Sci. 1991, 144, 185.
Li and Kunieda
Figure 2. Phase diagrams of the cationic surfactant weight fraction, Y, as a function of the oil weight fraction Wo for the SDS-DTAB-water-dodecane system (a) and for the SDSDDAB-water-dodecane system (b) at 25 °C. The surfactantto-water ratio Rsw is fixed at 40/60.
extension of the hexagonal phase, compared with that in SDS-DTAB-dodecane-water systems, is small and is transformed into the other phases with the addition of dodecane or with increasing cationic surfactant weight fraction. The phase transitions H1f Wm and H1fI1 both appear as the oil weight fraction increases. This implies that the mechanism to form Wm and to form I1 may be the same to some extent. The further addition of oil to the cubic phase can change the single phase into the two-phase regions containing the cubic phase and oil. Generally the very stable cubic emulsions are formed in the two-phase regions with mixed anionic and cationic surfactants. The mixtures containing the lamellar phase are formed in the regions at higher Y, around Y ) 0.50 for example, and this was not investigated in detail. 2. Structures of Micellar Cubic Phases. a. Interlayer Spacing of Liquid Crystals. To investigate the structural change of H1 and I1 phases with increasing oil content and with mixing of anionic and cationic surfactants, the interlayer spacing, d, was measured along lines LA, LB, and LC at Rsw ) 45/55 and Y ) 0 or 0.20 along the dilution pathways with oil dodecane for different systems by means of SAXS. In the two-phase region the separated liquid crystal was used for the SAXS measurement. Figure 3
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Figure 3. The interlayer spacing and its corresponding crosssectional area of cubic phase samples as a function of the oil weight fraction. The ratio of surfactant-to-water is fixed at 45/ 55 along line LA for SDS-C12-H2O systems at Y ) 0, line LB for SDS-DTAB-C12-H2O systems at Y ) 0.20, and line LC for SDS-DDAB-C12-H2O systems at Y ) 0.20.
Figure 4. The interlayer spacing and its corresponding crosssectional area of cubic phase samples as a function of the cationic surfactant weight fraction at surfactant-to-water ) 40/60 and Wo ) 0.10 along line LU for SDS-DTAB-C12-H2O systems (a) and along line LV for SDS-DDAB-C12-H2O systems.
shows that the interlayer spacing increases from d ) 5.9 to 6.5 nm at Wo ) 0.035-0.08 and then becomes constant at d ) 6.5 nm at Wo g 0.08 along line LA for SDS-C12H2O systems at Y ) 0. Similar results can also be obtained along lines LB and LC for the systems SDS-DTAB-C12H2O and SDS-DTAB-C12-H2O at Y ) 0.20, respectively. In other words, the interlayer spacing increases upon dilution with oil in the cubic phase and keeps constant upon further addition with dodecane in the two-phase region containing the cubic phase and oil. It implies that the micellar cubic phase is an isotropic single liquid crystal, and the micellar size increases as the value of d increases with increasing oil weight fraction because the oil is located at the center of the micelles. Figure 4 shows that the interlayer spacing of the cubic phase samples, at Rsw ) 40/60 and Wo ) 0.10, increases slowly from 7.9 to 9.0 between Y ) 0.064 and 0.17 for the SDS-DTAB-C12-H2O system and from 8.2 to 8.5 nm between Y ) 0.06 and 0.09 nm for the SDS-DDAB-C12H2O system. Since the contents of oil and water are almost fixed and all the surfactants have the same hydrophobicchain-length, C12H25-, the d value changes little although
Figure 5. (a) SAXS diffraction patterns (a, top) for the representative sample in the systems SDS-C12-H2O (43.12/ 3.88/52.99 in weight fraction) at 25 °C. The arrows mark the positions of the reflections afforded by the Pm3n crystallographic space group. Filled arrows indicate observed reflections while shadow arrows indicate reflections that are anticipated but not clearly observed in the SAXS spectrum. (b) Plot (bottom) of the reciprocal d spacing (1/dhkl) of the reflections marked in the SAXS diffraction pattern of Figure 5a plotted versus m ) (h2 + k2 + l2)1/2, which indexed to the space group Pm3n with a lattice parameter a ) 118.2 Å. Also shown are the anticipated positions (empty marks) for the three extra reflections allowed by the Pm3n space group but not observed in our SAXS spectrum.
the cross sectional area is obviously changed, which is due to electrostatic interactions between the hydrophilic heads of the anionic and cationic surfactants. b. Space Group for Single Surfactant Systems. The resultant phase diagram is given in Figure 1a. The X-ray diffraction data for the representative sample in the cubic region is shown in Figure 5 (a, top). More than 8 peaks were observed in cubic phases (I1) dominated by three strong correlation peaks at d ) 59.0, 51.9, and 49.4 A. The space group can be indexed to the Pm3n (Q223) with a lattice parameter a ) 118.2 A from the 1/dhkl vs m ) (h2 + k2 + l2)1/2 plot (Figure 5b, bottom). This space group3,5,8-10,24 allows the Bragg reflections hkl ) 110, 200, 210, 211, 220, 310, 222, 320, 321, 400, ..., which give the d ratios at the peaks follow the order x2, x4, x5, x6, x8, x10, x12, ..., of which the first reflection, corresponding to hkl ) 110, is usually weak and sometimes cannot be observed, and the second and third reflections, corresponding to hkl ) 200 and 210 respectively, are the most intense. Though indexing of SAXS diffraction patterns has enabled us to identify the space groups of the cubic phases, (24) Mariani, P.; Amaral, L. Q.; Saturni, L.; Delacroix, H. J. Phys. II 1994, 4, 1393.
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Figure 6. Schematic representation of the structure of the cubic phase. The space group is Pm3n [no 223 (International Tables, 1952)]. The structure consists of two types of micelles.
there is no direct evidence to tell us whether these phases are bicontinuous or micellar. However, their positions in the phase diagrams, at higher hydration than the H1 phase, strongly suggest that this Pm3n cubic phase is an I1 phase.3,5-7 In addition, the variation in intensity of the diffraction peaks for the cubic phase is similar to the variation in intensity exhibited by the same micellar cubic phase identified in the C12EO12-water system.3 Whereas the bicontinuous cubics possess negative Gaussian interfacial curvature, the micellar cubics have positive Gaussian interfacial curvature and are discontinuous, consisting of discrete micellar aggregates. The structure of the Pm3n micellar cubic phase, with detailed X-ray scattering25 and fracture electron microscopy studies,26 consists of two spherical and six disk-shaped (oblate) micelles per unit cell. For the Pm3n cubic phase,3,24-26 the positions of the micelles in the unit cell are given in Figure 6. Black circles represent the spherical micelles, and pale gray circles represent the disk-shaped micelles. Thick lines outline the unit cell cube, while fine black and gray lines mark out the positions of the micelles. They show that the spherical micelles pack on a body-centered cubic lattice, while the oblate micelles are arranged in a parallel row on opposite faces of the unit cell cube. c. Space Group for Mixed Surfactant Systems. Figure 7 shows that SAXS diffraction patterns for the samples chosen along the central lines of the cubic phase regions in Figure 2a and b with increasing the cationic surfactant and oil weight fractions. The results are also summarized in Tables 1 and 2. For the SDS-DTAB-C12-H2O systems, the SAXS diffraction patterns show a similar type indexed to the same cubic phase of Pm3n although the peak position moves toward the left. The first peak, corresponding to hkl ) 200, is weaker than the second peak, corresponding to hkl ) 211, for the Y0 sample at Y ) 0. After the mixing of SDS and DTAB the first peak became the most intense as compared the intensities of first peaks shown in Figure 7a and b. Although the peak number decreases for samples Y5, Y6, and Y7 at Y > 0.20 and Wo > 0.15, the cubic phase is indexed to Pm3n. It is attributed (25) Vargas, R.; Mariani, P., Gulik, A.; Luzzati, V. J. Mol. Biol. 1992, 225, 137. (26) Delacroix, H.; Gulik-Krzywichi, T.; Mariani, P., Luzzati, V. J. Mol. Biol. 1993, 229, 526.
Li and Kunieda
to the step-by-step and similar variations in SAXS diffraction spectrums and the same ratios between the interlayer spacing values of different peaks including the characteristic value of 1: d200/d210 fixed at 0.8944 () x4/x5) for all the samples. Furthermore, there is no twophase domain within the cubic phase body. So we think the indexing of the cubic phase to the Pm3n structure is rational within the whole region, although the evidence presented in Figures 7 and 8 does not seem to conclusively rule the other structures of the cubic phases out at high Y and Wo. The same result can also be obtained in the SDS-DDAB-C12-H2O systems. The lattice parameter of the Pm3n cubic phases, as shown in Tables 1 and 2, increases greatly with increasing Y and Wo along the central lines in cubic phase regions in Figure 2a and b. d. Radius of Micelles and Area per Surfactant Molecule of the Pm3n Cubic Phase. From the measured lattice parameters of the micellar cubic phases, the space group symmetry, and the volume fraction of the surfactant, we can calculate the radius rP of the micelle and the crosssectional area of hydrophilic head per surfactant molecule, aS, at the interface surfactant layer, assuming the two kinds of micelles to be spherical with the same radius. Certainly such an approximate calculation can bring a small error; however, the result with this treatment is useful to qualitatively explain the relationships between solubilization of oil and the structural variation of the Pm3n cubic phase. Similarly, we can also calculate these quantities, rH and aS, for the hexagonal H1 phase. The volume fraction of surfactant is given by
( [
])
][
WO WH WS WD + / + FO FH FS FD
φsurf ) 1 +
-1
(1)
Similarly, the volume fraction of oil core is
( [
] )
WS WD WH WO + + / FS FD FH FO
φo ) 1 +
-1
(2)
where MS, MD, MO, and MH are the molar masses of SDS, DTAB (or DDAB), oil, and water molecules, respectively. FS, FD, FO, and FH are the densities of SDS, DTAB (or DDAB), oil, and water, respectively. In this paper, the values of FS, FD, FO, and FH are 1.1475, 1.0442 (for DTAB) or 0.9622 (for DDAB), 0.747 25, and 0.9970 g cm-3 respectively.14 Substituting the masses and measured densities into eqs 1 and 2 allows us to calculate φsurf and φo, and hence the radius of the micelle, rP and rH, given by the generalized equation3,6,7
rP )
) (
(
3 [φ + φo] 4νπ surf
rH )
1/3
a(spheres);
)
2 [φS + φo] x3π
1/2
d(cylinders) (3)
where d is the measured interlayer spacing, a is the lattice parameter, and ν is the number of micelles per unit cell. For the Pm3n cubic phase, a ) (h2 + k2 + l2)1/2d ) 2d200, and ν ) 8 was used to calculate the rP.3,9 The effective cross-sectional area, aS, is3,6,7
aS )
(
)
3Vs φsurf + φo (spheres); rNA φsurf 2Vs φS + φo aS ) (cylinders) (4) rNA φS
(
)
where Vs is the volume of surfactant molecule, and NA is
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Figure 7. SAXS diffraction patterns of the samples with increases in the cationic surfactant and oil weight fractions along the central line in the cubic phase regions shown in Figure 2a for the SDS-DTAB-C12-H2O system at 25 °C.
Avogadro number. All the data along lines LA, LB, and LC at Y ) 0 and 0.20 for the SDS-DTAB (or DDAB)C12-H2O systems, as a function of Wo, is shown in Figure 3. The effective cross-sectional area is also shown along lines LU and LV, and along the central lines of the cubic phase regions in Figure 4 and in Tables 1 and 2. The cross-sectional area, aS, as can be seen in Figure 3, keeps almost constant as Wo increases along lines LA, LB, and LC within the single-phase region of the Pm3n cubic phase. However, it decreases with an increase in the cationic surfactant fraction, Y, along lines LU and LV at the same composition of water and oil (see Figure 4), and increases along the central lines within the cubic phase regions
shown in Figure 2a and b with increases in C12 and DTAB (or DDAB) weight fractions. Discussion 1. The H1-Pm3n Transition and Its Mechanism. The hexagonal phase formed at the SDS weight fraction between 0.39 and 0.57 can be transformed into the other phases as the cationic surfactant and oil weight fractions increase. The phase transition directly from the H1 phase to the Pm3n phase takes place for a large range of cationic surfactant weight fractions (Y < 0.22) in SDS-DTABC12-H2O systems and for a narrow range of the weight fractions in SDS-DDAB-C12-H2O systems (see Figure
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Table 1. X-ray Diffraction Finding in Cubic Samples in Systems SDS-DTAB-water-C12 Obtained from Figure 7a composition DTAB water
C12
symmetry
lattice parameter, Å
as nm2
0.5779
0.0399
Pm3n
124.6
0.508
0.0097
0.5670
0.0550
Pm3n
135.1
0.493
0.3532
0.0185
0.5588
0.0695
Pm3n
146.9
0.472
Y3
0.3253
0.0361
0.5427
0.0959
Pm3n
167.1
0.447
Y4
0.2967
0.0523
0.5276
0.1234
Pm3n
193.8
0.420
Y5
0.2706
0.0679
0.5040
0.1576
Pm3n
221.5
0.414
Y6
0.2383
0.0799
0.4760
0.2058
Pm3n
253.9
0.392
Y7
0.2227
0.0837
0.4610
0.2326
Pm3n
292.5
0.378
no
SDS
Y0
0.3822
0
Y1
0.3683
Y2
interlayer spacing, A
hkl
(h2 + k2 + l2)m
intensities
62.6 55.9 45.5 36.0 29.5 67.4 60.9 55.5 47.0 39.4 30.1 73.6 65.9 60.0 42.4 36.6 84.1 75.4 67.9 59.2 41.6 97.0 88.3 79.5 56.9 47.4 107.6 96.0 91.9 71.8 55.2 129.8 116.1 66.9 63.5 144.7 126.1 74.2
200 211 220 222 400 200 210 211 220 222 420 200 210 220 222 400 200 210 211 400 400 200 210 211 222 400 200 210 211 310 400 200 210 321 400 200 210 400
4 5 8 12 16 4 5 6 8 12 20 4 5 8 12 16 4 5 6 8 16 4 5 6 12 16 4 5 6 10 16 4 5 14 16 4 5 16
vs vvs vw w w vvs vs m vw w vw vvs vs m w vw vvs vs m w vw vvs s m vw w vvs m m vw w vvs m w vw vvs m w
a The composition of each sample is given in weight percent. Peak intensities are given as vvs ) extremely strong, vs ) very strong, s ) strong, m ) medium, w ) weak, and vw ) very weak.
Table 2. X-ray Diffraction Finding in Cubic Samples in Systems SDS-DDAB-water-C12 Obtained from Figure 8a composition DDAB water
C12
symmetry
lattice parameter, Å
a s m2
0.5779
0.0399
Pm3n
124.6
0.508
0.0093
0.5639
0.0612
Pm3n
140.1
0.483
0.3506
0.0186
0.5510
0.0798
Pm3n
153.8
0.464
Z3
0.3155
0.0349
0.5258
0.1239
Pm3n
182.9
0.434
Z4
0.2819
0.0497
0.4947
0.1737
Pm3n
226.0
0.406
Z5
0.2414
0.0603
0.4475
0.2509
Pm3n
285.2
0.399
no
SDS
Z0
0.3822
0
Z1
0.3655
Z2
a
interlayer spacing, A
hkl
(h2 + k2 + l2)m
intensities
62.6 55.9 45.5 36.0 29.5 70.0 62.2 50.4 40.1 76.8 67.9 54.5 44.6 92.9 83.3 65.4 45.0 113.2 102.6 81.0 55.9 140.1 101.4 82.5
200 211 220 222 400 200 210 220 222 200 210 220 222 200 210 220 400 200 210 220 400 200 220 222
4 5 8 12 16 4 5 8 12 4 5 8 12 4 5 8 16 4 5 8 16 4 8 12
vs vvs vw w w vvs vs w w vvs vs w w vvs vs w w vvs vs w w vvs w w
Peak intensities are given as vvs ) extremely strong, vs ) very strong, s ) strong, m ) medium, w ) weak, and vw ) very weak.
2). The hexagonal phase has one radius (r) of curvature of about 1.5 nm (between 1.3-1.7 nm), while the second one is infinite. The cubic phase has two almost identical
radii, but the radius (R ≈ 1.5r) is larger than that for the hexagonal phase at the same composition. Hence, the curvature increases at the H1-Pm3n transition when a
Micellar Cubic Phases in Surf-SDS-H2O
Langmuir, Vol. 16, No. 26, 2000 10099
Figure 8. SAXS diffraction patterns of the samples with increases in the cationic surfactant and oil weight fractions along the central line in the cubic phase regions shown in Figure 2b for the system SDS-DDAB-C12-H2O at 25 °C.
long saturated hydrocarbon is solubilized in the liquid crystal; it tends to make an oil pool inside the rod micelles while the effective cross-sectional area per surfactant is almost unchanged.7 Therefore, the total surface area of micelles is kept constant whereas the volume of the micelles increases upon addition of oil. For this reason, the H1-Pm3n transition takes place in order to keep the total surface area of the aggregate constant. The result for this transition was similar to those for the Im3m-Pm3n and H1-Pm3n transitions researched in the C12EO12-water3 nonionic surfactant system when the temperature is changed. The mechanism for the H1Wm transition could be applied to that for the H1-Pm3n transition. In the former case, one would expect an increase in curvature to drive the pinching of the hexagonal phase and the formation of micelles. But instead of arranging themselves in a stable Pm3n cubic lattice, as is the case for the H1-Pm3n transition at low Y shown in Figure 2b, these micelles would be randomly dispersed in solution,3,23 and then rearranged into the Pm3n cubic lattice upon further addition of oil. This suggests that the phase transition takes place by a rearrangement and deformation of the micelles, with no fusion events occurring, providing a low-energy transition pathway.3 This latter result is at variance with the finding of a study of the H1 f Pm3n transition in the DTAC-water type I system,24 that suggested that the n direction (the
cylinder direction) of the hexagonal phase becomes the [111] direction of the micellar cubic phase and that the (10) planes of the hexagonal phase transform into the (211) planes of the Pm3n phase. However, it must be emphasized3 that these results were only theoretical predictions based on powder diffraction patterns and not actual epitaxial relationships determined experimentally. Whatever the details of the molecular mechanism involved in mesophase-mesophase transitions, the sequence of cubic phases observed has important implications for the underlying factors that determine surfactant mesophase formation for water-continuous systems. Previously,3,27 it has been proposed that the major considerations are as follows: (i) the structure (size, shape) of micelles in dilute solution (spheres, rods, or disks) (when the interactions between the micelles become large enough, an ordered phase (mesophase) occurs); (ii) the maximum volume fraction that each different mesophase can tolerate, which increases in the sequence simple cubic f body centered cubic (Im3m) f face-centered cubic (Fm3m) f Pm3n f hexagonal (H1) f lamellar (LR); (iii) the ordered phase formed is the one with the largest possible micellar curvature that can accommodate the volume of the aggregates. (27) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.
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The sequence of cubic phases observed in nonionic surfactant-water systems clearly tallies with this simple picture; several kinds of cubic phases such as Im3m, Fm3m, and Pm3n, appear in the cubic phase regions. However, for the CTAC-water system, the space group of cubic phase was indexed to Pm3n.3,24 The addition of oil indeed transforms the hexagonal phase formed in the SDS-water system, as shown in Figure 1, into the Pm3n cubic phase, even with a small amount of DTAB (or DDAB). The Pm3n phase consists of micelles of different sizes and the polydisperse aggregates of the same shape can pack to higher volume fractions than monodisperse aggregates.3,10,24 It could be expected that the micelles of the Pm3n phase dominate the whole part of the cubic phase region with increases in the cationic surfactant and oil weight fractions in SDS-DTAB (or DDAB) -C12-H2O systems here. 2. Solubilization of Micellar Cubic Phases and Their Structural Relationships. To explain the relations between solubilization of the Pm3n phase and structural variation in the mixed surfactant systems, the interlayer spacing of the cubic phase was measured as a function of Wo at fixed surfactant composition and of Y at constant surfactant-to-water ratio. The cross-sectional area of the hydrophilic head of the surfactant molecule was calculated and is shown in Figures 3 and 4 and Tables 1 and 2. There is no mystery to the observation that the lowest water content cubic phases are also those that contain the highest levels of long-chain oil and the highest oilto-surfactant ratios, for it is at low water volume fractions that the highest (reversed) curvatures are required.3 The cubic phase bodies shown in Figure 1 deviate from the surfactant-water axis and point at the surfactant-oil axis, especially with mixed surfactants. So the crosssectional area of hydrophilic head changes, and then the curvature of the surfactant interface layer changes very much as the surfactant-to-water ratio changes. As can be seen in Figure 3, the interlayer spacing d increases in the cubic phase region and the corresponding area of surfactant head keeps almost constant upon addition of oil accordingly. At a fixed surfactant weight fraction, without affecting the preferred mean curvature, it can affect the actual monolayer curvature by forming a separate layer of pure hydrophobe between the ends of the surfactant chains of the bilayer, thus increasing in the formula 〈H〉 ≈ φB2/γ L.3,6-8,11 The addition of oil to the micelles causes a decrease of the curvature required by volume fractions through increasing L.9,11 So the packing parameter Vs/asL decreases accordingly due to the almost constant as, this make the micelles not stable, and then results in the phase transition I1f I1 + O. The cross-sectional area, as, as shown in Figure 4, decreases as the cationic surfactant weight fraction, Y, increases at fixed weight fractions of water and oil. The volume of surfactant molecule, Vs, also increases slowly resulting from the introduction of DTAB and DDAB to the surfactant interface layer due to the low densities for DTAB and DDAB. These data are also influenced by the concentration of electrolyte present from the NaBr, which changes with increase in the mixing ratio of surfactants. However, this ratio is related to the cationic surfactant weight fraction Y, and the structure is influenced dominantly by the surfactant mixing ratio and the oil weight fraction. So in this work we do not consider the effect of salt on the structural variation in detail in the systems without addition of salt. In terms of the Vs/asL packing parameter of the Ninhem and Israelachvili school, Vs/ asL increases and the preferred mean curvature at the
Li and Kunieda
polar-apolar interface moves toward negative, which is concave toward water. Further increase in the cationic surfactant weight fraction would lead to the phase transition I1 f H1. For the systems H2O-C12-SDS-DTAB (or DDAB), the mixing of anionic and cationic surfactants and the addition of oil are working in the same direction at stabilizing the present cubic phases at a fixed surfactant-to-water ratio; namely, the presence of the cationics and oil is acting to reduce the disparity between the high preferred mean curvature (which is generally high in the binary SDSwater system) and the low mean curvature required by the constraints of volume fractions, both by decreasing the preferred mean curvature through mixing of surfactants and increasing the curvature required by volume fractions from I1 to I1 + O region. Thus a precise determination of the bilayer width bears directly on a delicate balance that contains information about the underlying physics of this and related systems. In addition this question may also bear on the general question of whether cubic phases made with ionic surfactants can be swollen with oil, where by swollen we mean the actual increase of structural dimensions due to separate regions of pure oil; the answer in this case of lamellar phases made with single-tailed ionic surfactants appears to be no.3 So to get the maximum solubilization of cubic phases, the mean curvature must be adjusted carefully to keep at roughly constant values. The mixing of anionic and cationic surfactant and the addition of oil have opposite effects on the curvature of the interface surfactant layer. So the solubilization of the Pm3n phase increases accordingly as the cationic surfactant weight fraction increases. However, when Y increases to above 0.30, near 0.50, the curvature becomes zero and forms the lamellar containing mixture. Conclusion In the systems containing an anionic and a cationic surfactant with SDS and DTAB or DDAB, the addition of oil results in the phase transitions H1 f I1 at low Y, and LR f I1 at high Y. Solubilization of dodecane in the micellar solution and in the micellar cubic phase increases with increase in the cationic surfactant weight fraction Y from 0 to 0.30. SAXS measurements index the structure of the cubic phase as the Pm3n cubic phase as Y changes for the single surfactant systems and mixed surfactant systems at different levels of oil. The cross-sectional area of the hydrophilic head of the surfactant, at fixed cationic surfactant weight fraction, keeps constant with increase in the oil weight fraction as the interlayer spacing of the Pm3n cubic phase greatly increases. This implies that the curvature of the surfactant interface layer does not change very much along the oil dilution curve at a constant surfactant-to-water ratio. However, the cross-sectional area of the hydrophilic head of the surfactant, at fixed oil weight fraction, decreases with an increase in the cationic surfactant weight fraction as the interlayer spacing of the Pm3n cubic phase increases slowly. In other words, the curvature of the surfactant interface layer becomes negative as the cationic surfactant weight fraction increases at constant oil weight fraction. So the solubilization of oil can be increased by adjusting the mean curvature of the surfactant interface layer with addition of mixed surfactants and long-chain oil. LA000829R
