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Langmuir 1997, 13, 2184-2190
Articles DDAB MicroemulsionssDependence on the Oil Chain Length M. Monduzzi,*,† F. Caboi,† F. Larche´,‡ and U. Olsson§ Dipartimento Scienze Chimiche, Universita′ Cagliari, Via Ospedale 72, I-09124 Cagliari, Italy, Groupe de Dynamique des Phases Condense´ es, Case 026, Universite´ Montpellier II, F-34095 Montpellier Cedex 05, France, and Physical Chemistry 1, Centre for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received September 30, 1996. In Final Form: December 27, 1996X In this work we discuss the oil chain length dependence of ternary DDAB microemulsions, comparing decane, dodecane, and tetradecane. With dodecane and shorter alkanes the L2 microemulsion phase extends to the oil corner, while with tetradecane the microemulsion phase forms an island in the center of the ternary phase diagram. We present new NMR self-diffusion and 14N NMR relaxation data, where the three systems are compared at similar compositions. It is argued that the disconnection of the microemulsion phase from the oil corner with longer oils is associated with the Winsor II to Winsor III transition known from nonionic microemulsions. It follows that the tetradecane microemulsion has, in a major part, a monolayer rather than a bilayer structure.
Introduction For a given surfactant, the location and extention of a microemulsion region is generally dependent on the oil chain length. This is due to differences in oil penetration into the surfactant film. For alkanes (CnH2n+2) the oil penetration increases with decreasing n. The oil penetration contributes to the spontaneous curvature, H0, of the surfactant film. Increasing the degree of oil penetration by decreasing n leads to a decrease in spontaneous curvature, where we have defined curvature toward oil as positive. This is also the case for ternary systems of the doublechained cationic surfactant didodecyldimethylammonium bromide (DDAB),1-3 as it is for nonionic surfactant systems.4,5 For DDAB microemulsions, H0 is generally negative and reverse structures are formed in the microemulsion phase. H0 is however dependent on the oil chain length. With a short alkane like hexane (n e 12) the microemulsion phase extends from the oil corner near the oil-surfactant binary axis. Increasing the oil chain length up to n ) 12 (dodecane) gradually shifts the microemulsion region to higher water-to-surfactant ratios, φw/φs, where φw and φs denote water and surfactant volume fraction, respectively.6 With tetradecane, however, the microemulsion phase is no longer connected to the oil * To whom correspondence should be addressed. Phone: (39) 70 669098. Direct: 6758604. Fax: (39) 70 669272. E-mail: monduzzi@ vaxca1.unica.it. † Universita′ Cagliari. ‡ Universite ´ Montpellier II. § Lund University. X Abstract published in Advance ACS Abstracts, March 1, 1997. (1) Chen, S. J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S. J. Phys. Chem. 1986, 90, 842. (2) Hyde, S. T.; Ninham, B. W.; Zemb, T. J. Phys. Chem. 1989, 93, 1464-1471. (3) Ninham, B. W.; Chen, S. J.; Evans, D. F. J. Phys. Chem. 1984, 88, 5855. (4) Kahlweit, M.; Lessner, E.; Strey, R. J. Phys. Chem. 1983, 87, 5032. (5) Kahlweit, M.; Strey, R.; Firmin, P. J. Phys. Chem. 1986, 90, 671. (6) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. W. Acta Chem. Scand. 1986, A40, 247.
S0743-7463(96)00953-5 CCC: $14.00
corner but forms an island near the center of the ternary phase diagram.7 In recent years, the microstructure of these microemulsions has been investigated using a variety of experimental techniques.1,6-15 Except at very high oil content, the general trend in the case of n e 12 is that the structure is bicontinuous at lower φw/φs and approaching a closed droplet structure at higher φw/φs, characteristic for a system with a preferred curvature of the surfactant film. For the tetradecane microemulsion only a limited amount of conductivity or self-diffusion data exists however, indicating a wider area of bicontinuity. It was recognized at an early stage1,16 that the DDAB microemulsions were formed with a constrained curvature of the polar-apolar interface and that the constraint was modulated by the chain length of the oil. Ninham and co-workers developed a geometrical structural model, the DOC cylinder model,17,18 with which they were able to predict small angle scattering,17,18 conductivity,19 NMR self-diffusion coefficients,20 and phase diagram data2 with reasonable success. (7) Blum, F. D.; Pickup, S.; Ninham, B. W.; Chen, S. J.; Evans, D. F. J. Phys. Chem. 1985, 89, 711. (8) Barnes, I. S.; Hyde, S. T.; Ninham, B. W.; Derian, P.-J.; Drifford, M.; Zemb, T. N. J. Phys. Chem. 1988, 92, 2286. (9) Barnes, I. S.; Derian, P. J.; Hyde, S. T.; Ninham, B. W.; Zemb, T. N. J. Phys. 1990, 51, 2605. (10) Eastoe, J. Langmuir 1992, 8, 1503. (11) Eastoe, J.; Heenan, R. K. J. Chem. Soc., Faraday Trans. 1994, 90, 487. (12) Samseth, J.; Chen, S.-H.; Litster, J. D.; Huang, J. S. J. Appl. Crystallogr. 1988, 21, 835-839. (13) Observations of Sphere to Rod Transition in a Three-Component Microemulsion; Samseth, J., Chen, S.-H., Litster, J. D., Huang, J. S., Eds.; Plenum Press: New York, 1989. (14) Skurtveit, R.; Olsson, U. J. Phys. Chem. 1991, 95, 5353. (15) Skurtveit, R.; Olsson, U. J. Phys. Chem. 1992, 96, 8640. (16) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J. Phys. Chem. 1986, 90, 2817-2825. (17) Ninham, B. W.; Barnes, I. S.; Hyde, S. T.; Derian, P.-J.; Zemb, T. N. Europhys. Lett. 1987, 4, 561. (18) Zemb, T. N.; Hyde, S. T.; Derian, P.-J.; Barnes, I. S.; Ninham, B. W. J. Phys. Chem. 1987, 91, 3814. (19) Knackstedt, M. A.; Ninham, B. W. Phys. Rev. E 1994, 50, 2839. (20) Monduzzi, M.; Knackstedt, M. A.; Ninham, B. W. J. Phys. Chem. 1995, 99, 17772.
© 1997 American Chemical Society
DDAB Microemulsions
The fact that the microemulsion phase with tetradecane is disconnected from the oil corner may at first seem puzzling, and it has been proposed9 that the microemulsion area in the tetradecane system is an L3 phase with a multiply connected bilayer structure. At closer inspection, however, this does not seem to be consistent with the extention of the phase in the phase diagram. In all other known occurrences of the L3 phase, it is found to be very narrow in one direction, extending essentially as a line in two-dimensional phase diagrams (for a collection of phase diagrams, see for example ref 21). In the DDAB/water/ tetradecane system on the other hand, the phase occupies an area rather than a line, as is normally the case for the monolayer microemulsions. The striking narrowness of the L3 phase is a characteristic feature which is associated with a constraint that the mean curvature of the two monolayers is close to the spontaneous curvature value.21 In this paper we have readdressed the effect of varying the oil chain length on DDAB microemulsions with particular emphasis on the disconnection of the microemulsion phase from the oil corner. 14N NMR relaxation and NMR self-diffusion experiments on water and oil have been performed along three different oil dilution lines, and the results from three different oils, decane, dodecane, and tetradecane, are compared. The dilution lines were chosen so that they crossed the microemulsion phase of all three oils. Experimental Section Materials. Didodecyldimethylammonium bromide (DDAB) was from Fluka and used as received. The few samples prepared with recrystallized DDAB (from ethyl acetate) did not show appreciable differences of the phase behavior. D2O, 99% enriched, was from Carlo Erba-Pharmacia, and n-decane, n-dodecane, and n-tetradecane (99% purity) were from Sigma and used as received. For the DDAB/water/tetradecane phase diagram, DDAB obtained from SOGO Pharmaceutical Company (Japan) and n-tetradecane (purity > 99%) from Sigma were used as received. The samples were prepared with distilled water by weight in screw-cap tubes and vigorously shaken. When necessary they were heated up to 100 °C. A desk centrifuge (maximum speed 3200 rpm) was used to separate the phases. In the case of particularly thick mixtures, several cycles of heating, vigorous shaking, and centrifugation were necessary. Experiments were performed at room temperature (20-22 °C). But when phase boundaries were particularly sensitive to temperature, the samples were equilibrated in a water bath at 20 ( 0.1 °C. Birefringence was investigated macroscopically between crossed polarizers. The samples were also examined in a polarizing microscope. Water analyses were made by the Karl-Fischer method with reagents provided by BDH. Microemulsion samples for NMR measurements were prepared by weighing the components and were homogenized by gentle mixing. Before any measurements were performed, the samples were stored at 25 °C for at least 6 days. Methods. 1H NMR experiments were performed at 1.88 T on a Varian FT 80A spectrometer. The temperature was always kept constant with an accuracy better than (1 °C. At any temperature, the samples were equilibrated in the probe for at least 5 min before any measurements were performed. Diffusion measurements were performed using the Fourier transform pulsed-magnetic-field gradient spin-echo (FT-PFGSE) technique, as previously described.22-24 The experiments were carried out by varying the gradient pulse length (δ) while keeping the gradient strength (G) and the pulse intervals (∆) constant. For such a case, the echo intensity decay as the value of δ is increased is given by (21) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243-4253. (22) Callaghan, P. T. Aust. J. Phys. 1984, 27, 359. (23) Stilbs, P.; Moseley, M. E.; Lindman, B. J. Magn. Reson. 1980, 40, 401-4. (24) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1.
Langmuir, Vol. 13, No. 8, 1997 2185 I(δ) ) I(0) exp[-(γGδ)2D(∆ - δ/3)] where D is the self-diffusion coefficient, I(0) is the echo intensity in the absence of any gradient, and γ is the magnetogyric ratio. Self-diffusion coefficients were calculated by means of a twoparameter nonlinear fit of the echo intensity decay measured at 14-20 different δ values. The error in the measurements, as judged by repeated measurements, is estimated to be smaller than (8%. 14N NMR measurements were performed by a Varian VXR300 (7.05 T) spectrometer at the operating frequency of 21.67 MHz. A standard variable-temperature control unity, with an accuracy of (0.5 °C, was used in the NMR experiments. The 14N NMR spin-lattice relaxation experiments were performed by means of the usual inversion recovery pulse sequence (PD-180°-t-90°-AC). The spin-lattice relaxation rates, R1, were obtained by a three-parameter nonlinear fit of the partially relaxed NMR signal intensities obtained at 10-14 different τ values.
I(τ) ) A - Be(-τR1) The error in the obtained value of R1 from the fitting procedure is lower than (2%. The spin-spin relaxation rates, R2, were deduced from 14N NMR spectra recorded with a 90° pulse angle. R2 values were calculated from the bandwidths taken at half height, ∆ν1/2.
Phase Diagrams The phase diagram of the DDAB/water/tetradecane system at 20 °C is presented in Figure 1a. For comparison, the ternary phase diagrams with dodecane at the same temperature (redrawn from ref 15) and decane at 25 °C (redrawn mainly from ref 7) are shown in Figure 1b and c, respectively. Turning our attention to the tetradecane system, we see that it is dominated by a large central microemulsion phase which we here denote L2, located as an island in the center of the phase diagram. Its extent is in agreement with the results of Blum et al.7 except for the surfactant-rich side. This phase boundary was found to be extremely temperature sensitive. This can easily explain the discrepancy (the temperature was 25 °C in ref 2). The main difference compared to the shorter oil systems is that it does not reach the oil corner. Instead a whole range of microemulsions is in equilibrium with almost pure oil. Two very small isotropic phases have been localized in the water and oil corners, respectively. In the water corner, the DDAB/water solutions containing more than 1 wt % of DDAB were turbid. Under the microscope, they showed birefringent drops floating in an isotropic liquid. No sedimentation was observed with either time or extended centrifugation (1 h at maximum speed). The addition of tetradecane in quantities as low as 0.5% to these solutions produces a layer of stable emulsion on top of the test tube. Thus the tetradecane solubility in the water phase is lower than 0.5%. At the oil corner, the water content was determined along the phase boundary, in particular at the three-phase equilibrium points. The value is always between 150 and 250 ppm. On comparing this value with the water solubility in tetradecane, 58 ppm at 25 °C,25 it may be suggested that a small amount of surfactant is also dissolved in this liquid phase. The third corner of the composition triangle is occupied by the solid surfactant. It is not known if water is present in the DDAB crystallographic structure. Analysis of our starting product revealed a water content of 0.11 ( 0.01% by weight. No correction was applied for such a small amount. The microscopic appearance of the solid does not permit a good separation from the nearby liquid crystal (25) Schwartzberg, P. J. Phys. Chem. 1963, 67, 776.
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LR2 phase. The data from Fontell et al.6 were used for the limits of the lamellar phases LR1 and LR2 on the binary DDAB-water axis. Tetradecane solubility was determined in both phases. The LR2 phase can dissolve an increasing amount of oil as its water content increases. The maximum tetradecane uptake is ∼l7%. The LR1 shows only a very narrow region of equilibrium with the oil phase. The existence of such a region is consistent with the observation of a much larger three-phase area, were LR1, the oil phase, and the microemulsion are in equilibrium. Separation of these phases, within the triangle, is easily obtained by a short centrifugation. The maximum solubility of tetradecane in the LR1 phase is ∼3%. It is worth mentioning that a very stable emulsion was systematically found in the triangle oil + water + LR1. At low oil content, between the microemulsion phase and the binary water-surfactant axis, a region of a bicontinuous cubic phase (V2) is formed.26 Samples here are transparent, optically isotropic, and stiff. As with other oils, the region seems to consist of several cubic phases.26 The three-phase triangle(s) involving L2 + LR2 + V2 is very small, and its limits were not carefully determined. For the NMR experiments, which are presented in the following section below, samples were prepared with D2O instead of H2O, for which the phase diagrams apply. Besides the trivial effect on weight fraction based diagrams coming from the change in water density, there are some additional shifts of phase boundaries, which are likely to arise from the higher energy associated with D2O hydrogen bond structure, as observed in the case of the DDAB/D2O system.27 In the DDAB/D2O/oil systems under investigation, at 25 °C, the observations concerning the phase behavior were limited to the microemulsion region and in particular to the chosen oil dilution lines. For example the phase boundary on the water-rich side of the DDAB/ D2O/decane system shifts to lower water content significantly, with the s/w ) 0.43 dilution line appearing almost overlapped to the limit of the isotropic L2 phase. In addition, the cubic phase and the stability limit of the microemulsion phase in the tetradecane system are shifted to lower oil content. These effects, which, however, were not investigated in detail, are of less importance to this paper, which mainly concerns the disconnection of the microemulsion phase from the oil corner when increasing the oil chain length from dodecane to tetradecane. Microemulsion StructuresDependence on Oil Chain Length For recent reviews on the application of NMR relaxation and self-diffusion experiments to study microemulsion structure, see e.g. refs 28-30. Water (Dw) and oil (Do) self-diffusion coefficients and 14N longitudinal (R1) and transverse (R2) relaxation rates were measured along three oil dilution lines for the three oils decane, dodecane, and tetradecane. In these NMR experiments heavy water (D2O) was used instead of ordinary H2O. The surfactantto-D2O weight ratios of the three dilution lines were s/w ) 0.43, 0.55, and 1.22, respectively. The results are presented in Figures 2-4 as a function of the oil volume fraction, φo. Figure 2 shows the data from the s/w ) 0.43 (26) Maddaford, P. J.; Toprakcioglu, C. Langmuir 1993, 9, 2868. (27) Caboi, F.; Monduzzi, M. Langmuir 1996, 12, 3548. (28) So¨derman, O.; Olsson, U. In Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M., Harris, R. K., Eds.; Wiley: Chichester, 1995. (29) Lindman, B.; Olsson, U.; So¨derman, O. In Dynamics of Solutions and Fluid Mixtures by NMR; Delpuech, J.-J., Ed.; John Wiley: Chichester, 1995. (30) Lindman, B.; Olsson, U. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 344-363.
Figure 1. (a) Phase diagram of the ternary DDAB/water (W)/ tetradecane (TETRA) system at 20 °C. (b) Phase diagram of the ternary DDAB/water (W)/dodecane (DODEC) system at 20 °C, redrawn from ref 15. (c) Phase diagram of the ternary DDAB/ water (W)/decane (DECA) system at 25 °C, redrawn mainly from ref 7.
dilution line, Figure 3 those from the s/w ) 0.55 line, and Figure 4 those from the s/w ) 1.22 line. The diffusion data are presented as relative diffusion coefficients, Dw/Dw° and Do/Do°, where Dw° (D°w ) 1.902
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× 10-9 m2/s, valid for the HOD species31) and Do° (see Table 1) are the diffusion coefficients of pure water and oil, respectively. They report on the connectivity of water and oil domains.32 The relaxation data are presented as the relaxation rate difference ∆R ) R2 - R1. The relaxation rates depend on the rate of reorientation of the surfactant molecule.33 Since the surfactant is adsorbed with a preferred orientation at the polar/apolar interface, the rate of reorientation depends on the shape and geometry of the interface. Taking the difference, one subtracts a constant offset associated with local fast motions which are independent of the interface geometry,33,34 leaving a dependence on slow geometry-dependent motions only. These slow motions involve surfactant lateral diffusion along the curved interface and reorientation of the interface itself. R1 was found to be essentially constant, small (≈25 ( 5 s-1), and almost independent of the composition and oil chain length. R2 was generally much higher and concentration dependent. When R2 . R1, we can use the approximation15,35,36
∆R )
9π2 (χS)2js(0) 40
(1)
where χ is the quadrupolar coupling constant, S is the order parameter, and js(0) is the zero-frequency spectral density of the slow motion. Since js(0) corresponds to the integral over the time correlation function, it can be interpreted in terms of an effective correlation time, js(0) ) 2τeff. The absolute product |χS| can be obtained from quadrupolar splittings in the anisotropic phases. In the reverse hexagonal phase, the quadrupolar splitting, ∆νhex, is given by ∆νhex ) 3|χS|/8, whereas in the lamellar phase ∆νlam ) 3|χS|/4. In the decane system, we have measured ∆νhex ) 4.8 kHz (DDAB/D2O/decane ) 25.6/59.9/14.5 in wt %). A similar but slightly lower value has been measured previously in the dodecane system, ∆νhex ) 3.9 kHz (DDAB/H2O/dodecane ) 17.2/66.0/16.8 in wt %).15 For the tetradecane system we have measured ∆νlam ) 9 kHz (DDAB/D2O/tetradecane ) 29.4/68.6/2.0). These values allow us to estimate τeff from the ∆R values in the microemulsion using τeff ) 5∆R/(4π∆νhex)2 ≈ 5∆R/ (2π∆νlam)2 ≈ A∆R, with A ) 1.56 × 10-9 s2. ∆R values are generally in the range 100-600 s-1, corresponding to τeff values in the range 0.2-1 µs. By comparing the results in Figures 2-4 from different oils, we can directly draw an important conclusion. Neither the self-diffusion coefficients nor the relaxation rates differ significantly when varying the oil chain length at a given composition. Rather, they show the same qualitative behavior upon oil dilution, with only a minor quantitative difference at the lowest surfactant to water ratio (Figure 2). Thus, the conclusion is that the microemulsion microstructure is only weakly dependent on the oil chain length. A much more important parameter for structure is the overall composition. This conclusion holds in particular at lower oil content, where all three systems are stable. Hence, the disconnection of the microemulsion phase from the oil corner when increasing the oil chain length cannot be the result of a very different microstructure being stabilized. (31) Mills, R. J. Phys. Chem. 1973, 77, 685. (32) Lindman, B.; Shinoda, K.; Olsson, U.; Anderson, D.; Karlstro¨m, G.; Wennerstro¨m, H. Colloids Surf. 1989, 38, 205. (33) Wennerstro¨m, H.; Lindman, B.; So¨derman, O.; Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. Soc. 1979, 101, 6860. (34) Halle, B.; Wennerstrom, H. J. Chem. Phys. 1981, 75, 1928. (35) Monduzzi, M.; Olsson, U.; Soderman, O. Langmuir 1993, 9, 2914. (36) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R. J. Phys. II 1994, 4, 515-531.
Figure 2. Variation of (a) the relative water self-diffusion coefficient, (b) the relative oil self-diffusion coefficient, and (c) the 14N NMR relaxation rate difference with the oil volume fraction for a constant surfactant-to-water weight ratio s/w ) 0.43. L2 region: (filled circle) DDAB/water/decane; (square with slant) DDAB/water/dodecane; (triangle) DDAB/water/tetradecane. V2 cubic phase: (open circle) DDAB/water/decane; (square) DDAB/water/dodecane.
A quantitative interpretation of the microstructure from the self-diffusion and relaxation data is more difficult, partly due to the relatively high surfactant concentration in these microemulsions. However, a few remarks can be made. At low oil content, all three systems have a bicontinuous cubic phase with a multiply connected bilayer structure. The two-phase region between the cubic and microemulsion phases is generally narrow, indicating that the microemulsion structure near the microemulsioncubic phase transition is similar to that in the cubic phase. This is also consistent with the self-diffusion and relaxation data from the lowest surfactant-to-oil ratio (Figure 2), where a smooth variation across the cubic-to-microemulsion phase transition is observed, indicating a gradual
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Figure 3. Variation of (a) the relative water self-diffusion coefficient, (b) the relative oil self-diffusion coefficient, and (c) the 14N NMR relaxation rate difference with the oil volume fraction for a constant surfactant-to-water weight ratio s/w ) 0.55. L2 region: (filled circle) DDAB/water/decane; (square with slant) DDAB/water/dodecane; (triangle) DDAB/water/tetradecane.
evolution of the microstructure when entering the microemulsion from the cubic phase. In the case of water diffusion, where hydration effects are small due to the relatively high water content, we also show in Figure 2a the predicted diffusion in a multiply connected bilayer (cubic phase) structure.37
Dw/D° ) 0.66 - βφb
(2)
where β is a coefficient which is weakly depending on the bilayer topology and φb is the bilayer volume fraction, which here is taken as φb ) φo + 0.85φs. 0.85 corresponds (37) Anderson, D. M.; Wennerstro¨m, H. J. Phys. Chem. 1990, 94, 8683-8694.
Figure 4. Variation of (a) the relative water self-diffusion coefficient, (b) the relative oil self-diffusion coefficient, and (c) the 14N NMR relaxation rate difference with the oil volume fraction for a constant surfactant-to-water weight ratio s/w ) 1.22. L2 region: (filled circle) DDAB/water/decane; (square with slant) DDAB/water/dodecane; (triangle) DDAB/water/tetradecane. Table 1. Data and Calculated Parameters for DDAB Microemulsions along the Three Oil Dilution Lines, at 25 °Ca Dsph°/Dw° oil
Doil°, 1010 m2/s
line A RH ≈ 94 Å
line B RH ≈ 78 Å
line C RH ≈ 46 Å
decane dodecane tetradecane
13.80 8.62 5.77
0.0157 0.0089 0.0058
0.0175 0.0106 0.0069
0.0299 0.0181 0.0118
a In the calculation of D -9 sph°/Dw° the value Dw° ) 1.902 × 10 m2/s, valid for the HOD species,31 was used. The values of Doil° are calculated from ref 51.
to the volume fraction of alkyl chains in the surfactant molecule. For β we have used the value 0.27 obtained for the case of the D minimal surface structure,37 which also
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appears to be the relevant cubic phase structure near the boundary to the microemulsion phase.26 For comparison, we also show the corresponding relation for a bicontinuous monolayer constant mean curvature structure, which is given by37
Dw/D° ) 0.66 - β(1 - 2φint)
(3)
where φint ) φw + 0.15φs (0.15 represents the contribution of the counterion and the polar head to the volume fraction of the internal domain). As can be seen in Figure 2a, there is good agreement between the cubic phase data and the prediction from eq 2. The fact that the experimental Dw/Dw° values are slightly lower than the calculated ones can be ascribed to hydration effects. When entering the microemulsion phase, Dw/Dw° decreases much more rapidly with φo than is expected for the bilayer structure. The disagreement is even worse if we compare with the constant mean curvature monolayer structure. The decrease in Dw/Dw° rather shows that the water labyrinths become gradually disconnected as we increase the oil content. Also in the case of the 14N relaxation, only a minor variation in ∆R with φo is expected in the case of a multiply connected bilayer structure.38 Instead, we observe a significant increase in ∆R, which is qualitatively consistent with a disconnection of the microstructure. A similar maximum in ∆R was for example observed at a micellarto-bicontinuous transition in a nonionic microemulsion.36 In a bicontinous structure the relaxation is brought about by the lateral diffusion of the surfactant molecule along the monolayer film. The corresponding correlation time depends on the magnitude of the principal curvatures,38 which may still be relatively large even though the mean curvature is small, thus resulting in a low ∆R value. For a particle structure, unless it is spherical, the isotropic reorientation has to involve the tumbling of the aggregate,39 which can be very slow if the deviation from spherical shape is large.40 The high ∆R values measured here indicate that the disconnection of the microstructure involves initially nonspherical water droplets, which is also consistent with the presence of a reverse hexagonal phase in the decane and dodecane systems. At the highest surfactant content, s/w ) 1.22 (Figure 4), the structure is bicontinuous and varies only weakly with φo, as is seen by the minor variations in Dw/Dw°, Do/Do°, and ∆R. The disconnection process becomes stronger the lower s/w is. At very high oil content (infinite dilution), in the decane and dodecane systems, we also know that the structure eventually should approach spherical water swollen reverse micelles for entropic reasons. This has been confirmed for example in the dodecane system.15 Thus, the water self-diffusion coefficients, which then correspond to the micellar diffusion coefficients, should approach the Stokes-Einstein value. The radius of a spherical polarapolar interface enclosing water, counterions, and the dimethylammonium head groups is
r)
3φintls φs
(4)
where ls ≈ 12 Å is the volume-to-area ratio of the surfactant.15 Assuming a hydrodynamic radius of RH ) r + 15 Å, we have calculated the expected Stokes-Einstein diffusion coefficient Dsph° and report in Table 1 the (38) Halle, B.; Ljunggren, S.; Lidin, S. J. Chem. Phys. 1992, 97, 1401. (39) Halle, B. J. Chem. Phys. 1991, 94, 3150. (40) Olsson, U.; So¨derman, O.; Gue´ring, P. J. Phys. Chem. 1986, 90, 5223.
corresponding values of Dsph°/Dw°. A value of Dw/Dw° near the Stokes-Einstein value is obtained for the s/w ) 0.43 dilution line at the highest oil content. In the tetradecane system, on the other hand, the microemulsion phase cannot be diluted infinitely with oil. Here the maximum oil limit is reached before a full disconnection of the water labyrinths is obtained, as is seen by the Dw/Dw° value of ≈0.1. At lower s/w and higher oil content (Figures 2 and 3) ∆R decreases with increasing φo. Extrapolating the ∆R values in the dodecane system to infinite dilution, we obtain approximately ∆R ≈ 200 s-1. This value is in good agreement with the value obtained previously by Skurtveit and Olsson15 and corresponds to a spherical reverse micelle. The ∆R values from decane and dodecane differ approximately by a factor of 2. This reflects mainly the difference in viscosity of the two solvents, which affects the rotational diffusion tumbling of the reverse micellar aggregates. Thus the structures in the decane and dodecane systems are very similar also at high oil content, as is also seen by the similar Dw/Dw° values. Microemulsion Phase EquilibriasWinsor II-to-Winsor III Transition For n e 12 the maximum water solubility in the microemulsion phase is related to the emulsification failure problem discussed by Safran et al.41-43 Here, the flexible surface model predicts spherical reverse micelles at the phase boundary at high water content with a radius R ≈ -H0-1. Since the radius is essentially proportional to the water-to-surfactant ratio, φw/φs, the phase boundary moves to higher φw/φs as H0 becomes less negative. However, microemulsion droplets cannot grow infinitely large. When H0 becomes near zero, a bicontinuous structure is favored over the droplet structure of the same mean curvature.44 Since the mean curvature in a bicontinuous structure depends on the water-to-oil ratio, the bicontinuous microemulsion phase cannot be diluted with water or oil but forms an island in the ternary phase diagram.45 In ternary systems with nonionic surfactant, one sees the disconnection of the microemulsion phase from the oil corner from the phase equilibria at low surfactant concentration.46-49 When H0 , 0, a two-phase equilibrium between the microemulsion phase and excess water is observed. This situation is often also referred to as a Winsor II equilibrium.50 As H0 approaches zero, the microemulsion disconnects from the oil corner, and there is a transition to a three-phase equilibrium where the microemulsion phase is in simultaneous equilibrium with excess water and oil (Winsor III). Here, the transition from Winsor II to Winsor III is generated by tuning a continuous variable, such as temperature; it occurs at a critical end point. For H0 , 0 there is a critical point (41) Safran, S. A.; Turkevich, L. A.; Pincus, P. A. J. Phys. Lett. 1984, 45, L69. (42) Safran, S. A. Phys. Rev. A 1991, 43, 2903-2904. (43) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: 1994. (44) Olsson, U.; Wennerstro¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113-146. (45) Daicic, J.; Olsson, U.; Wennerstro¨m, H. Langmuir 1995, 11, 2451-2458. (46) Saito, H.; Shinoda, K. J. Colloid Interface Sci. 1970, 32, 647. (47) Kunieda, H.; Friberg, S. Bull. Chem. Soc. Jpn. 1981, 54, 10101014. (48) Kunieda, H.; Shinoda, K. J. Dispersion Sci. Technol. 1982, 3, 233-244. (49) Kahlweit, M.; Strey, R.; Haase, D.; Firman, P. Langmuir 1988, 4, 785-790. (50) Winsor, P. A. Solvent Properties of Amphiphilic Compounds; Butterworth: London, 1954. (51) Ertl, H.; Dullien, F. A. L. AIChE J. 1973, 19, 1215.
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systems are slightly more complex, and DDAB cannot be treated exclusively as a nonionic surfactant. While in the Winsor II situation we expect the microemulsion phase to be in equilibrium with essentially pure water, a detailed study of the dodecane system has shown that this is not the case. For example, the phase boundary on the high φw/φs side also contains a critical point possibly separating spheres from cylinders, since a reverse hexagonal phase is present at low oil content. Also there is equilibrium with a dilute lamellar phase rather than with the water or L1 phase. This additional complexity in the DDAB systems is not yet fully understood. A more complete analysis would need to include electrostatic effects. Due to the electrostatic contribution to the spontaneous curvature, its value is expected to vary with the composition and so also the values of the elastic modulii, the saddle splay modulus being particular important, since it influences the micellar-to-bicontinuous transition. Concerning phase equilibria, there is also the osmotic pressure contribution from the dissociated counterions. To summarize this section, we conclude that while the DDAB systems show additional complexity, a comparison with the more simpler nonionic microemulsions is still useful, since the systems share some basic features, one of which is the disconnection of the microemulsion phase from the oil corner when the spontaneous curvature approaches zero.
Figure 5. Schematic illustration of the evolution from a Winsor II to a Winsor III type of phase equilibrium via a critical end point. In part a, the microemulsion can still be diluted infinitely with oil (Winsor II). In part b, the two phase boundaries merge at the critical end point. In part c, the microemulsion phase is disconnected from the oil corner. The sequence a-c occurs as the spontaneous curvature of the polar-apolar interface approaches zero.
located on the low φw/φs side of the microemulsion phase which also moves to higher φw/φs with increasing H0. Eventually the critical point touches the phase boundary on the high φw/φs side of the microemulsion phase and the phase disconnects from the oil corner. This critical point is also seen in DDAB microemulsions, for example, with dodecane (Figure 1b). The transition from Winsor II to Winsor III via a critical end point is schematically illustrated in Figure 5. We conclude that the disconnection of the microemulsion phase with the oil corner, when switching from dodecane to tetradecane in DDAB microemulsions, is closely related to the Winsor II-to-Winsor III transition of nonionic systems. However, the resemblance with nonionic surfactant is not total. The phase equilibria in the DDAB
Conclusions In this paper we have addressed the question: why is the DDAB/water/tetradecane microemulsion disconnected from the oil corner while it is connected with shorter alkanes? We conclude that the disconnection, when moving from dodecane to tetradecane, is closely related to the Winsor II-to-Winsor III transition observed for example with nonionic surfactant. It follows that the tetradecane microemulsion also has a monolayer structure. We find no evidence in self-diffusion and 14N NMR relaxation data for the tetradecane system to behave significantly differently from the dodecane and decane systems. In fact, a similar structural evolution in the microemulsion phase upon diluting with oil is found in the three systems. At very low oil content, near the bicontinuous cubic phase, the structure is presumably a connected bilayer similar to that in the cubic phase. Upon diluting with oil the microstructure evolves into a monolayer which on the water-rich side gradually disconnects into reverse micelles. While a fully disconnected structure is obtained at high oil content in the decane and dodecane systems, the tetradecane system phase separates before becoming fully disconnected. Acknowledgment. The Italian MURST, CNR, and CSGI are thanked for support. U.O. acknowledges the Swedish Natural Science Research Council (NFR) for financial support. F.L. wishes to thank for support the Department of Applied Mathematics (A.N.U. Canberra), where part of this work was performed. LA9609534
