Microstructure of Alkyl Glucoside Microemulsions: Control of Curvature

It is found that as the interfacial film becomes increasingly rich in C8E0, that is, the phase inversion is passed, the mean area per surfactant molec...
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10692

Langmuir 2003, 19, 10692-10702

Microstructure of Alkyl Glucoside Microemulsions: Control of Curvature by Interfacial Composition Johan Reimer* and Olle So¨derman Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden

Thomas Sottmann, Karsten Kluge, and Reinhard Strey Institut fu¨ r Physikalische Chemie, Universita¨ t zu Ko¨ ln, Luxemburger Strasse 116, D-50939 Ko¨ ln, Germany Received May 16, 2003 The phase behavior of water/n-octane/n-octyl-β-D-glucopyranoside (C8G1)/1-octanol (C8E0) permits formulating temperature-insensitive microemulsions spanning the whole water-oil composition range. The types of microstructures formed along the trajectory of the middle-phase microemulsion are examined by NMR diffusometry, yielding the respective diffusion coefficients of all the components. The diffusion experiments provide clear evidence of the transition from oil-in-water to water-in-oil microemulsions via bicontinuous structures in a remarkably large range around phase inversion. Small-angle neutron scattering (SANS) along the same path confirm the picture. Furthermore, SANS curves on the absolute scale permit extracting the specific internal interface in the microemulsion as it passes through phase inversion. When the composition of the internal interface is known, the mean area per surfactant molecule is determined. It is found that as the interfacial film becomes increasingly rich in C8E0, that is, the phase inversion is passed, the mean area per surfactant molecule C8G1 decreases along the same progression.

I. Introduction In applications, there is a growing need for formulating nonionic, nontoxic, biodegradable microemulsions. Also, the microemulsion should be thermally stable, that is, temperature-insensitive. Alkyl polyglycosides (CmGn) are ideally suited for this purpose and are increasingly being used. These sugar surfactants have m numbers of carbons within the hydrophobic chain and n numbers of glucose units in the hydrophilic headgroup. Although alkyl polyglycosides have been available for more than 40 years,1,2 reports on the formulation of microemulsions with sugar surfactants have only recently begun to appear in the literature. The first experimental studies were performed on commercial blends of CmGn.3-6 Recently, a number of systematic studies dealing with pure CmGn surfactants were reported.7-15 In particular, the binary water/CmGn systems have been investigated.7,8,16,17 The * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Shinoda, K.; Yamanaka, T.; Kinoshita, K. J. Phys. Chem. 1959, 63, 648. (2) Shinoda, K.; Yamaguchi, T.; Hori, R. Bull. Chem. Soc. Jpn. 1961, 34, 237. (3) Balzer, D. Tenside, Surfactants, Deterg. 1991, 28, 419. (4) Balzer, D. Langmuir 1993, 9, 3375. (5) Fukuda, K.; So¨derman, O.; Lindman, B.; Shinoda, K. Langmuir 1993, 9, 2921. (6) von Rybinski, W. Curr. Opin. Colloid Interface Sci. 1996, 1, 587. (7) Sakya, P.; Seddon, J. M.; Templer, R. H. J. Phys. II 1994, 4, 1311. (8) Nilsson, F.; So¨derman, O.; Hansson, P.; Johansson, I. Langmuir 1998, 14, 4050. (9) Kahlweit, M.; Busse, G.; Faulhaber, B. Langmuir 1995, 11, 3382. (10) Stubenrauch, C.; Paeplow, B.; Findenegg, G. H. Langmuir 1997, 13, 3652. (11) Stubenrauch, C.; Findenegg, G. H. Langmuir 1998, 14, 6005. (12) Kahl, H.; Quitzsch, K.; Stenby, E. H. Fluid Phase Equilib. 1997, 139, 295. (13) Ryan, L. D.; Kaler, E. W. Langmuir 1997, 13, 5222. (14) Ryan, L. D.; Kaler, E. W. Langmuir 1999, 15, 92. (15) Ryan, L. D.; Schubert, K. V.; Kaler, E. W. Langmuir 1997, 13, 1510.

weak temperature dependence of the headgroup hydration is an advantageous property of these surfactants but makes it difficult to tune the spontaneous curvature of the surfactant film in ternary water/n-alkane/CmGn systems by changing the temperature. This is contrary to the other main class of nonionic surfactants, that is, the ethylene-oxide based CiEj systems, which are readily tuned by varying the temperature.18-22 To circumvent these difficulties, the surfactant film in alkyl glucosides may be tuned by mixing the rather hydrophilic sugar surfactants with hydrophobic alcohols9-12 or CiEj surfactants.15 In special cases, temperature-sensitive ternary microemulsions with alkyl polyglycosides may still be obtained by employing oils that are more polar than n-alkanes. Alkyl ethylene glycol ethers,13,14 chlorinated hydrocarbons,23 and methyloctanoate24 are examples of such oils. To develop tools for tuning hydrophilic surfactants, Penders and Strey25 have clarified in detail the effect of adding an alcohol (1-octanol) to a ternary microemulsion system, such as the water/n-octane/C8E5 system. They were able to tune the phase behavior by adding 1-octanol (16) Kocherbitov, V.; So¨derman, O.; Wadso¨, L. J. Phys. Chem. B 2002, 106, 2910. (17) Boyd, B. J.; Drummond, C. J.; Krodkiewska, I.; Grieser, F. Langmuir 2000, 16, 7359. (18) Kahlweit, M.; Strey, R. Angew. Chem.-Int. Ed. Engl. 1985, 24, 654. (19) Kahlweit, M.; Strey, R.; Haase, D.; Kunieda, H.; Schmeling, T.; Faulhaber, B.; Borkovec, M.; Eicke, H. F.; Busse, G.; Eggers, F.; Funck, T.; Richmann, H.; Magid, L.; So¨derman, O.; Stilbs, P.; Winkler, J.; Dittrich, A.; Jahn, W. J. Colloid Interface Sci. 1987, 118, 436. (20) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen, J.; Schomacker, R. Langmuir 1988, 4, 499. (21) Kahlweit, M.; Strey, R.; Busse, G. Phys. Rev. E 1993, 47, 4197. (22) Schubert, K. V.; Kaler, E. W. Ber. Bunsen-Ges. Phys. Chem. Chem. Phys. 1996, 100, 190. (23) Egger, H.; Sottmann, T.; Strey, R.; Valero, C.; Berkessel, A. Tenside, Surfactants, Deterg. 2002, 39, 17. (24) Plamper, F.; Reimer, J.; So¨derman, O. To be submitted for publication. (25) Penders, M.; Strey, R. J. Phys. Chem. 1995, 99, 10313.

10.1021/la034847v CCC: $25.00 © 2003 American Chemical Society Published on Web 11/22/2003

Microstructure of Alkyl Glucoside Microemulsions

in the same fashion as if the temperature was increased. Two effects were found to cause the observed changes in the curvature of the amphiphilic film. On one hand, the hydrophobic alcohol acts as a cosolvent, making the oil more polar. On the other hand, it increases the effective hydrophobicity of the surfactant mixture acting as a cosurfactant. Starting from a hydrophilic surfactant, an increase in the solubilization capacity is observed when passing through phase inversion. These results are general and apply both to CiEj and to CmGn surfactants. In conclusion, by adding a suitable alcohol one may tune the microemulsion from an oil-in-water (o/w) to a water-in-oil (w/o) system at constant temperature.3,9,12,26 In a previous paper, the detailed phase behavior of the system D2O/n-octane/C8G1/1-octanol was presented and analyzed. The trajectory of the middle-phase microemulsion could be scaled onto that of the related ones in the CiEj systems27 once the appropriate scaling parameter was determined. The key parameter in describing the phase behavior was shown to be the composition of the internal interface δV,i (see eq 4 for a definition of δV,i).28,29 The aim of this paper is to more closely examine the evolution of the microstructure of the microemulsion phases in the D2O/n-octane/C8G1/1-octanol system by means of NMR diffusometry and small-angle neutron scattering (SANS). NMR diffusometry is a powerful method for obtaining the molecular displacements of matter. In surfactant solutions, such data convey information pertaining to confinement and obstruction effects and, thus, provide direct insight into the solution structure. The principles and applications to study microemulsion structure by NMR are described in detail elsewhere.30-36 While NMR provides valuable information on the nature of the microstructures, that is, droplets either of types or bicontinuous, it conveys little information on the actual values of the length scales pertaining to the interfacial film. Here, the method of choice is SANS. In this study, we focus on the microstructure as a function of the oil to water plus oil volume fraction (φ) along the trajectory of the middle phase. In addition, the evolution of the microstructure upon changing the composition of the internal interface δV,i is analyzed. We start by reviewing the relevant phase behavior as presented earlier.28 We then discuss the results of the NMR diffusometry and SANS experiments. II. Experiment A. Materials. The surfactant n-octyl-β-D-glucopyranoside (C8G1, of purity >98%) and the hydrocarbon n-octane (of purity >99%) were purchased from Sigma Aldrich (Steinheim, Germany). The cosurfactant 1-octanol (C8E0, of purity >99%) was (26) Stubenrauch, C.; Kutschmann, E. M.; Paeplow, B.; Findenegg, G. H. Tenside, Surfactants, Deterg. 1996, 33, 237. (27) Sottmann, T.; Strey, R. J. Phys.: Condes. Matter 1996, 8, A39. (28) Sottmann, T.; Kluge, K.; Strey, R.; Reimer, J.; So¨derman, O. Langmuir 2002, 18, 3058. (29) Kluge, K.; Stubenrauch, C.; Sottmann, T.; Strey, R. Tenside, Surfactants, Deterg. 2001, 38, 30. (30) Jonstro¨mer, M.; Olsson, U.; Parker, W. O. Langmuir 1995, 11, 61. (31) Lindman, B. In Microemulsions: structure and dynamics; Friberg, S., Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1987; p 119. (32) Stilbs, P.; Lindman, B. Prog. Colloid Polym. Sci. 1984, 69, 39. (33) Lindman, B.; Ahlna¨s, T.; So¨derman, O.; Walderhaug, H.; Rapacki, K.; Stilbs, P. Faraday Discuss. 1983, 317. (34) Lindman, B.; Stilbs, P.; Moseley, M. E. J. Colloid Interface Sci. 1981, 83, 569. (35) Lindman, B.; Olsson, U.; So¨derman, O. In Microemulsions: fundamental and applied aspects; Kumar, P., Mittal, K., Eds.; Marcel Dekker: New York, 1999; p 309. (36) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445.

Langmuir, Vol. 19, No. 26, 2003 10693 provided by Merck-Schuchardt (Hohenbrunn, Germany). H2O was double-distilled from a quartz column, while D2O was obtained from Cambridge Isotope Laboratories (Andover, U.S.A.) with a degree of deuteration >99.9%. All components were used as purchased. The D2O/H2O mixture used for pulsed field gradient spin-echo (PGSE) self-diffusion NMR was 90:10 by weight with a density of 1.094 g/cm3. B. Sample Preparation. The samples were prepared by weighing various amounts of D2O (A; or a D2O/H2O mixture, see above), n-octane (B), and C8G1 (C) into sample tubes that were sealed with polyethylene stoppers. Afterward, the samples were placed in a transparent water bath thermostated to 25.00 °C with an accuracy of (0.02 °C. After reaching temperature equilibrium, the stopper was removed and the three-component mixture was titrated with C8E0 (D) using a microliter syringe. The phase behavior was determined visually. The presence of anisotropic phases was determined by means of crossed polarizers. In general, the composition of a quaternary mixture is characterized by three independent composition variables. Here, we used the volume fraction of oil in the oil/water mixture

φ)

VB VA + VB

(1)

the overall volume fraction of the surfactant and cosurfactant

φC+D )

VC + VD VA + VB + VC + VD

(2)

and the cosurfactant to surfactant plus cosurfactant ratio

δV )

VD VC + VD

(3)

An additional but important parameter, which determines the curvature of the interfacial film,28,29 is the composition of the internal interface

δV,i )

VD,i VC,i + VD,i

(4)

Vi is the volume of component i while VC,i and VD,i are the volumes of the components C and D in the internal interface. Volume fractions are used, because this study deals with microstructural changes upon changes in composition. The corresponding mass fractions R, γ, and δ18,25,28,29 were recorded and can be used equivalently. When the monomeric solubility is also taken into account, the interfacial composition δi, the equivalent of δV,i on a weight basis, can be calculated. C. NMR Diffusometry. The PGSE nuclear magnetic resonance technique, sometimes also referred to as DOSY, was used to determine the different self-diffusion coefficients of the components at T ) 25 ( 0.5 °C by monitoring the 1H signal on a Bruker DMX-200 spectrometer, equipped with a field gradient probe unit. In the experiments, the length of the gradient pulse was kept constant and the gradient strength was varied between 0.1 and 4 T/m. Depending on the situation, both Hahn and stimulated echo-type experiments were used.37,38 A problem in these four component microemulsions is the fact that the peaks of the different components overlap. The water peak in all the samples is fully resolved. The same holds for the glucose peaks from the surfactant headgroup. Thus, the NMR signals from these peaks give rise to single exponential decays in the diffusion experiment, and the diffusion coefficients, D, are obtained by fitting

[

(

I ) I0 exp -γ2G2δ2 ∆ -

)]

δ D 3

(37) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (38) Price, W. Concepts Magn. Reson. 1998, 10, 197.

(5)

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Figure 1. Top: schematic phase tetrahedron of a quaternary water/oil/surfactant/cosurfactant system. The section at constant oil in water plus oil volume fraction φ ) 0.50 shows the phase boundaries resembling the shape of a fish. Bottom, left: corresponding section through the phase tetrahedron for the system D2O/n-octane/C8G1/C8E0 at T ) 25 °C. The X point specifies the composition of the middle-phase microemulsion, the Y point specifies that of the NMR and SANS samples. Point Z depicts the fish head. Bottom, right: projection of the trajectory of the middle-phase microemulsion onto the D2O/C8G1/C8E0 face of the tetrahedron. Starting from φ ) 0.1, the mass fractions of both the surfactant and the cosurfactant increase continuously up to φ ) 0.6. Subsequently, the mass fraction of C8G1 decreases while the C8E0 mass fraction stays nearly constant. to the data.37,39 In eq 5, I denotes the observed echo intensity, I0 is the echo intensity in the absence of field gradient pulses, γ is the magnetogyric ratio, G is the field gradient strength, δ is the duration of the gradient pulse, and ∆, finally, is the time between the leading edges of the field gradient pulses. The main peaks from the cosurfactant 1-octanol and the hydrocarbon n-octane overlap with the peak from the surfactant (C8G1) tail. As a consequence, the diffusion coefficients from the two former components were obtained from bi- and tri-exponential fits to the echo intensities. In the process, the value of the surfactant diffusion coefficient is kept constant (at the value obtained from the glucose peak). The random errors in the obtained values amount to at most a few percent, with the data for the components having nonoverlapping peaks having somewhat lower errors than the components having overlapping peaks. D. SANS. The scattering experiments were carried out at the Institute Laue Langevin (ILL) in Grenoble, France, instrument D22. Neutrons of wavelength λ ) 6 Å with a spread of ∆λ/λ ) 10% were collimated and focused on samples in 1-mm quartz cells (Hellma). The home-built cell holder was preset to and kept at the desired temperature T ) 25.0 °C to within 0.02 °C. Filling the cells only to half height allowed for the mixing and homogenizing of the sample by tilting the whole cell holder after mounting. More details have been given previously.40 The wave vector q ) (4π/λ) sin(Θ/2) ranged from 0.005 to 0.466 Å-1, Θ being the scattering angle. The collimation was fixed at the largest distance to the sample (14.4 m) to maximize the resolution. Measurements at two sample-to-detector distances (2.0 and 14.0 m) were performed with the detector 38-cm off axis to provide a large q range. For reducing the raw data, ILL software was used. Each data set was put on the absolute scale by measuring the incoherent scattering of H2O. The data sets from the two distances overlapped without scale adjustment. A few data points at the highest and lowest q values were removed from each set. (39) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Clarendon Press: Oxford, 1991. (40) Schubert, K. V.; Strey, R. J. Chem. Phys. 1991, 95, 8532.

III. Results and Discussion A. Phase Behavior. The presently studied system contains four components, water (A), oil (B), a hydrophilic nonionic surfactant (C), and a hydrophobic cosurfactant (D). Thus, at constant pressure the isothermal phase behavior has to be represented in a phase tetrahedron, as shown in Figure 1 (top). The phase behavior inside the phase tetrahedron is conveniently studied by performing two-dimensional sections through the tetrahedron. One useful section is that at a constant oil to water plus oil volume fraction of φ ) 0.5, as drawn in Figure 1 (top). The schematic phase boundaries in this plane resemble the shape of a fish. By adding the hydrophobic cosurfactant (D) to a hydrophilic ternary system (A, B, and C), at first an o/w microemulsion can be observed that coexists with an oil excess phase (denoted as 2). A further increase of the cosurfactant content drives the system through phase inversion, so that at a high cosurfactant content a w/o microemulsion coexists with a water excess phase (2 h ). Between, a coexistence of a microemulsion with an excess water and oil phase (3) or, at sufficiently high surfactant concentrations, a one-phase microemulsion (1) are observed. In Figure 1 (bottom, left), such a section for the system under study, that is, D2O/n-octane/C8G1/1-octanol (C8E0) is shown at φ ) 0.5 and T ) 25 °C.28 As expected, the phase progression 2-3-2 h is found for low mass fractions of surfactant plus cosurfactant γ while at higher γ the progression 2-1-2 h is observed. If γ is increased even further, a lamellar phase appears. An important parameter of the microemulsion phase behavior is the location of the fish-tail point X, which denotes the minimum amount of surfactant plus cosurfactant needed to solubilize a certain amount of oil and water. This point

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Table 1. Variation of the Diffusion Coefficients along the Trajectory of the Middle Phase of the System D2O/H2O (A)/ n-Octane (B)/C8G1 (C)/C8E0 (D)a φ

R

γ

δ

φC,i+D,i

DA (10-10 m2/s)

DB (10-10 m2/s)

DC (10-10 m2/s)

DD (10-10 m2/s)

δV,i

0.0997 0.1999 0.3006 0.3504 0.3997 0.4499 0.5005 0.5503 0.6000 0.6504 0.7000 0.8002 0.8500 0.8999 0.9130

0.0663 0.1382 0.2162 0.2572 0.2994 0.3443 0.3914 0.4399 0.4905 0.5442 0.5996 0.7199 0.7843 0.8523 0.8707

0.0721 0.1067 0.1401 0.1571 0.1693 0.1757 0.1715 0.1767 0.1763 0.1699 0.1641 0.1362 0.1196 0.0946 0.0931

0.1881 0.2099 0.2106 0.2287 0.2311 0.2418 0.2650 0.2800 0.2935 0.3222 0.3377 0.3999 0.4439 0.5266 0.5407

0.0667 0.0967 0.1228 0.1360 0.1437 0.1456 0.1379 0.1384 0.1340 0.1237 0.1145 0.0828 0.0657 0.0428 0.0407

16.10 14.00 12.40 11.40 10.50 9.85 8.83 7.63 6.53 5.31 4.41 1.95 1.63 0.80 0.76

0.62 1.40 3.33 4.70 5.39 8.83 9.35 11.70 12.80 14.90 15.50 17.70 19.00 20.30 20.40

0.36 0.34 0.32 0.33 0.34 0.35 0.39 0.38 0.36 0.32 0.29 0.19 0.18 0.14 0.15

0.36 0.34 0.84 1.05 1.10 1.32 1.85 2.40 2.72 3.16 3.60 4.44 6.34 8.04 8.09

0.2256 0.2280 0.2324 0.2401 0.2476 0.2575 0.2680 0.2768 0.2819 0.2961 0.2981 0.3056 0.3071 0.3068 0.3084

a The mass fractions R, γ, and δ as well as the volume fractions φ and φ C,i+D,i are given along with the compositions of the amphiphilic films δV,i and the diffusion coefficients Di.

is identical to the composition of the middle-phase microemulsion. As mentioned in the Introduction, the aim of this paper is to study the variation of the microstructure along the trajectory of the X point. This trajectory, which is schematically shown as a dashed line in Figure 1 (top), extends from the critical endpoint on the water-rich side to the critical endpoint on the oil-rich side of the phase tetrahedron. A projection of the trajectory onto the A-C-D side of the tetrahedron is presented in Figure 1 (bottom right) for the C8G1 system. Starting at φ ) 0.10, the mass fractions of surfactant plus cosurfactant γ increase continuously up to φ ) 0.60. Subsequently, the mass fraction of C8G1 decreases at a nearly constant C8E0 fraction and finally terminates at the critical endpoint. The exact compositions of the critical endpoints have not been determined in this work. Two further important points are indicated in Figure 1, bottom left. The point Y specifies the composition of the samples investigated by NMR diffusometry and SANS, while Z indicates the location of the so-called fish-head point. The latter point allows, as shown by Kunieda and Shinoda41 and later applied by Penders and Strey,25 the determination of the amounts of surfactant and cosurfactant, which are dissolved monomerically in the oil and water subphases. In this analysis, it is assumed that water is not dissolved in oil and vice versa and that the monomer solubilities of C8G1 in n-octane (γC,mon,b) and 1-octanol in D2O (γD,mon,a) are negligible. When the procedure suggested in refs 41 and 42 is used and in combination with density measurements, the composition of the surfactant film δV,i was determined along the trajectory of the middle-phase microemulsion.28 B. NMR Measurements. The microstructure of a microemulsion is conveniently studied using the NMR diffusometry technique, where the self-diffusion coefficients, Di, of all the components can be measured without the need to label the compounds or to add probe molecules.43,44 Diffusion of Water and Oil along the Trajectory. To study how the microstructure varies along the trajectory of the middle phase, the self-diffusion coefficient of the four components have been determined for 15 different values (41) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1985, 107, 107. (42) Yamaguchi, S.; Kunieda, H. Langmuir 1997, 13, 6995. (43) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445. (44) Lindman, B.; Shinoda, K.; Olsson, U.; Anderson, D.; Karlstro¨m, G.; Wennerstro¨m, H. Colloids Surf. 1989, 38, 205.

of φ. It should be remarked that the compositions of the samples, indicated as point Y in Figure 1 (bottom left), are prepared close to the fish-tail points in the one-phase region (γ˜ < γ < γ˜ + 0.01, with γ˜ denoting the mass fraction of C8G1 and C8E0 at the fish-tail point, X). The compositions of the samples and the interfacial film are compiled together with the diffusion coefficients Di in Table 1. Figure 2a shows the variation of the water and n-octane diffusion coefficients as a function of φ. We have, as is customary, chosen to present the reduced diffusion coefficients D/D0, where D0 is the value for the neat liquids at T ) 25 °C [D0(A) ) 19.3 × 10-10 m2/s, D0(B) ) 24.8 × 10-10 m2/s). At low values of φ, the water diffusion is rapid while the n-octane diffusion is slow. The opposite situation holds for high values of φ, while at intermediate values of φ the diffusion of both components is relatively rapid and the reduced diffusion coefficients are equal in magnitude. Before the variation of the reduced diffusion coefficients is discussed in terms of changes in the microstructure, one has to keep in mind that within temperatureinsensitive n-alkylglucoside systems the composition of the amphiphilic film δV,i is the relevant tuning parameter. As noted in the Introduction, we have found that the parameter δV,i corresponds to the parameter temperature in the ternary water/oil/CiEj systems.28,29 In Figure 2b, δV,i is plotted versus φ along the trajectory of the middle phase. The appearance of the δV,i(φ) trajectory resembles the corresponding quantity in the temperature-dependent ternary CiEj systems, where the projection onto the A-B-T face of the phase prism is sigmoidal.27 Thus, in Figure 2c the reduced diffusion coefficient of water and n-octane are plotted versus the relevant tuning parameter δV,i. Compared to the representation in Figure 2a, the appearance of the diffusion coefficient curves has changed systematically. Approaching the limits of the three-phase region δV,i,l and δV,i,u the reduced diffusion coefficient of the minority component asymptotically approaches 0, whereas the reduced diffusion coefficient of the majority component approaches 1, respectively. Therefore, the data given in Figure 2 imply a change in the structure from o/w droplets over a bicontinuous structure to w/o droplets with increasing δV,i. This observation can be rationalized in terms of changing the spontaneous curvature H0 with the fraction of 1-octanol in the amphiphilic film with δV,i as the tuning parameter. Remarkably, a large range of bicontinuity is observable around the phase inversion. The crossover point (when the reduced diffusion coefficients of water and oil are equal)

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Figure 3. Surfactant diffusion coefficient as a function of φ. The overall decrease of the diffusion coefficient of the C8G1 molecules is a consequence of the decreasing amount of C8G1 molecules monomerically dissolved in water. Superimposed is a maximum around φ ≈ 0.55, which can be attributed to the lateral diffusion of the C8G1 molecules along the samplespanning, connected amphiphilic film of the bicontinuous structure. The solid lines are the contribution from various diffusion mechanisms (see text for details).

Figure 2. (a) Reduced diffusion coefficients D/D0 of water and n-octane measured at the Y point (cf. Figure 1, bottom left) as a function of φ. (b) Variation of the composition of the interfacial film δV,i as a function of φ, that is, trajectory of the middle phase. (c) Reduced diffusion coefficients shown in part a now as function of δV,i. Note that in the middle of the three-phase region δV,i,m ) 0.27,28 where water and n-octane diffuse with reduced coefficients of the same magnitudesproof of bicontinuity.

appears at a value of δV,i,m ) 0.27.28 This corresponds to the balanced state of the microemulsion, and here the microemulsion is truly bicontinuous, having a dividing film between water and the oil component, which is sample-spanning. Diffusion of Surfactant and Cosurfactant along the Trajectory. Complementary information can be obtained from the surfactant diffusion data, DC, which is presented in Figure 3 (see also Table 1). Starting at low φ, DC decreases mildly with increasing φ, then goes through a broad minimum, and subsequently goes through a maximum at φ ) 0.5. The initial decrease of the C8G1 diffusion coefficient is a consequence of the combined effect of aggregate growth and a decreasing contribution from the fraction of C8G1 molecules dissolved monomerically in water. The maximum in the surfactant diffusion is given by lateral diffusion over the surfactant film that constitutes the bicontinuous structure and which divides space into two domains of equal volume. Taking into account that the surfactant film exerts a geometrical obstruction factor for the surfactant diffusion,45 the observed value of DC is roughly half of the lateral surfactant diffusion in the film. Thus, the lateral diffusion coefficient of the surfactant along the film in the balanced state is 8 × 10-11 m2/s. When the lateral surfactant diffusion in a bicontinuous microemulsion is compared with that in the bicontinuous cubic phase found in the binary C8G1/water system (DC ≈ 7 × 10-12 m2/s), a 1 order of magnitude faster diffusion is found. Although the data in the cubic phase is obtained at a considerably higher surfactant concentration, it is clear that the presence of the cosurfactant increases the lateral diffusion of the surfactant in the surfactant film. As φ is further increased, the value of DC decreases as the bicontinuous structure evolves into a closed w/o structure. Let us now consider the diffusion coefficients at φ ) 0.1, 0.5, and 0.91 more quantitatively (see Table 1). It should (45) Anderson, D. M.; Wennerstro¨m, H. J. Phys. Chem. 1990, 94, 8683.

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Table 2. Compositions of Samples Used in SANS Experimentsa φ

R

γ

δ

φC,mon

φD,mon

φC,i

φD,i

φC,i+D,i

δV,i

0.0997 0.1999 0.3006 0.3997 0.5005 0.6000 0.7000 0.8002 0.8500 0.8999 0.9130

0.0657 0.1371 0.2146 0.2974 0.3892 0.4881 0.5973 0.7180 0.7827 0.8512 0.8696

0.0715 0.1059 0.1392 0.1684 0.1707 0.1756 0.1635 0.1359 0.1194 0.0945 0.0930

0.1881 0.2099 0.2106 0.2311 0.2650 0.2935 0.3377 0.3999 0.4439 0.5266 0.5407

0.0030 0.0026 0.0022 0.0018 0.0015 0.0012 0.0009 0.0006 0.0005 0.0003 0.0003

0.0022 0.0047 0.0067 0.0095 0.0135 0.0175 0.0226 0.0276 0.0300 0.0325 0.0332

0.0516 0.0735 0.0943 0.1081 0.1009 0.0962 0.0804 0.0575 0.0455 0.0297 0.0282

0.0151 0.0229 0.0285 0.0356 0.0369 0.0378 0.0341 0.0253 0.0201 0.0131 0.0125

0.0667 0.0964 0.1228 0.1437 0.1379 0.1340 0.1145 0.0828 0.0657 0.0428 0.0407

0.2256 0.2373 0.2324 0.2476 0.2680 0.2819 0.2981 0.3056 0.3071 0.3068 0.3084

a The mass fractions R, γ, and δ, the volume fraction φ, and the fractions of monomerically dissolved C G and C E , φ 8 1 8 0 C,mon and φD,mon are given along with the volume fractions of C8G1 and C8E0 in the amphiphilic film, φC,i and φD,i and the composition of the film δV,i. Note that these samples are made with D2O.

be noted that the observed diffusion coefficient for the surfactant must be corrected for the contribution from the fraction of surfactant molecularly dispersed in water. This is done by assuming a two-site exchange model in which the observed surfactant diffusion coefficient is a population-weighted average according to

DC ) PMDC,mic + (1 - PM)DC,free

(6)

where PM is the fraction of micellized surfactant and DC,mic and DC,free are the diffusion coefficients of micellized and “free” surfactants, respectively. From the phase diagram, the volume fraction of surfactant in the D2O/H2O mixture at φ ) 0.1 is φC,mon ) 0.003 (see Table 2),28 from which the value of PM can be obtained. Using the value of DC,free ) 3.6 × 10-10 m2/s obtained from measurements below the critical micelle concentration in the binary surfactant/ water system, we arrive at DC,mic ) 2 × 10-11 m2/s for φ ) 0.1. However, the magnitude of the contribution from the surfactant molecularly dispersed in water becomes less significant as φ increases. Comparing the diffusion coefficients for aggregated surfactant, cosurfactant, and oil, we find that DC,mic < DD < DB. If the o/w microemulsion consists of closed aggregates and the diffusion of the aggregated components is given solely by the aggregate diffusion, then one would expect DC,mic ≈ DD ≈ DB. Thus, the results imply that an additional diffusional pathway is operating for the aggregated components, already at φ ) 0.1. Moreover, the mechanism is selective because the diffusion of oil is more rapid than that of cosurfactant and surfactant. This mechanism, thoroughly discussed by Olsson et al.,46 is a molecular diffusive transfer across a contact zone of two directly interacting surfactant aggregates. This process signals the onset of the structural evolution from discrete aggregates to a bicontinuous structure in which the surfactant aggregates have essentially an infinite aggregation number. On the assumption that this exchange process is negligible for the surfactant, we can estimate from the Stokes-Einstein relation a hydrodynamic radius RH of the aggregate

role of the water and the oil exchanged. When the assumption that the surfactant reports on the diffusion of the reversed aggregate is used, its hydrodynamic radius is RH ) 250 Å. We next turn our attention to lateral surfactant diffusion around φ ) 0.5. It is of interest to compare the data for surfactant lateral diffusion with what would be expected from predictions based on continuum fluid mechanics. Modeling the surfactant molecule by a cylinder of length l and radius R, embedded in a planar fluid layer of thickness l and viscosity η, the lateral diffusion is given by47

DLAT )

[

2 kT 8 - ln  + O(-2) ln  - γ + 4πηl π 2

]

(8)

where γ ) 0.5722 is Euler’s constant and the parameter  is given by

 ) lη/(Rη j)

(9)

where η is the viscosity of the medium, k is the Boltzmann constant, and T is the absolute temperature. The value obtained at φ ) 0.1 is RH ) 100 Å. In the opposite situation, where φ ) 0.91, the water diffusion is more rapid than the surfactant diffusion, indicating that the same situation holds here with the

Here, η j is the average viscosity of the two media on either side of the surfactant monolayer. Using the reasonable values l ) 13 Å, R ) 3.6 Å, η j ) 0.75 × 10-3 Pa s, and η ) 1 × 10-3 Pa s,47 we obtain DLAT ) 3.5 × 10-10 m2/s, which is 1 order of magnitude larger than the observed value. This result indicates that the lateral diffusion of the surfactant in the monolayer is not determined by the viscosity of the film, but rather is dependent on the interactions in the headgroup region. The glucose region of the surfactant is presumably rather tightly packed, and this fact determines the lateral diffusion coefficients. Addition of the cosurfactant alters the glucose-glucose interaction in the headgroup region leading to changes in the surfactant lateral diffusion coefficient (compare values in the cubic and bicontinouos microemulsion phases). The cosurfactant diffusion DD, on the other hand, is continuously increasing with increasing φ (cf. Figure 4). This is due to the fact that the cosurfactant is soluble in the oil, where its diffusion is comparatively rapid. Upon increasing φ, the fraction of cosurfactant monomerically dissolved in the oil domains increases, leading to an increased cosurfactant diffusion. Summary of the Surfactant and Cosurfactant Diffusion Mechanism. To summarize the different diffusion mechanisms operating for the surfactant and cosurfactant, we present in Figures 3 and 4 the contributions from the plausible mechanisms. Starting with the surfactant diffusion, three calculated diffusion curves are included

(46) Olsson, U.; Nagai, K.; Wennerstro¨m, H. J. Phys. Chem. 1988, 92, 6675.

(47) Hughes, B. D.; Pailthorpe, B. A.; White, L. R. J. Fluid Mech. 1981, 110, 349.

RH ) kT/(6πηD)

(7)

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Table 3. Scattering Length Densities of the Water, Ga, and Oil Domain, Gb, as well as the Interfacial Film Gi Calculated Taking into Account H-D Exchange and the Monomeric Solubilities of C8G1 in D2O and C8E0 in n-Octanea φ

Fa (1010 cm-2)

Fb (1010 cm-2)

Fi (1010 cm-2)

fQ

Iincoh (cm-1)

S/V (Å-1)

t (Å)

aC (Å2)

0.0997 0.1999 0.3006 0.3997 0.5005 0.6000 0.7000 0.8002 0.8999 0.9130

6.27 6.23 6.17 6.11 6.08 6.02 5.98 5.94 5.87 5.82

-0.51 -0.51 -0.51 -0.51 -0.51 -0.51 -0.51 -0.50 -0.50 -0.50

1.18 1.15 1.15 1.13 1.09 1.07 1.04 1.02 1.01 1.01

1.11 1.08 1.04 1.01 0.91 0.97 0.95 0.92 0.90 0.90

0.24 0.34 0.43 0.50 0.58 0.63 0.68 0.45 0.79 0.80

0.0098 0.0125 0.0167 0.0183 0.0170 0.0153 0.0129 0.0085 0.0046 0.0041

2.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

66 57 60 56 54 49 48 42 46 42

a

Fit parameters fQ, Iincoh, S/V, t, and aC obtained from the description of the large-q part of the scattering curves.

Figure 4. Variation of the C8E0 diffusion coefficient as a function of φ. The increase of the diffusion coefficient of the C8E0 molecules can be attributed to the increasing volume fraction of n-octane along with the increasing concentration of C8E0 molecules. The solid line is the predicted diffusion of C8E0 (see text for details).

in Figure 3. At low φ, the surfactant diffusion coefficient is calculated from aggregated and free surfactant diffusion coefficients using eq 6. The aggregated diffusion coefficient, DC,mic, is calculated from the hydrodynamic radius, RH, using the Stokes-Einstein relation (eq 7), assuming spherical geometry. RH is calculated from the volumes and areas per headgroup (taken from Table 3), assuming a contribution of 10 Å from the water of hydration. DC,mic is compensated for the aggregate-obstruction effect by means of the factor 1 - 2φagg. At high φ, the surfactant diffusion is calculated from the radius of an inverse spherical micelle using the Stokes-Einstein relation (eq 7) and compensated with the aggregate-obstruction effect. Please note that the prediction for discrete aggregate diffusion is an upper limit because any deviation from the spherical shape would give rise to a slower diffusion. The surfactant diffusion coefficient in a bicontinuous network (φ ≈ 0.5) is calculated from the lateral and free diffusion coefficients using eq 6. The free diffusion coefficient is reduced by 1/3. The lateral diffusion coefficient is calculated from eq 10:48

DLAT ) [2/3 - 1.807(1 - φ - 0.5)2]5 × 10-11 m2/s (10) (48) Jonstro¨mer, M.; Nagai, K.; Olsson, U.; So¨derman, O. J. Dispersion Sci. Technol. 1999, 20, 375.

where 5 × 10-11 m2/s is a reasonable value for the lateral diffusion of the surfactant. It is clear from Figure 3 that the droplet diffusion does not capture the diffusion mechanism in the microemulsions, not even at the lowest and highest value of φ, where they overestimate the diffusion. This is due to the fact that we assume a spherical shape; other geometries, such as oblate-shaped micelles (see next section), would predict a lower diffusion. We note that there are no adjustable parameters in the calculations of the diffusion for the droplet model. In addition, the dependence of the diffusion on φ for the droplet model is not in agreement with the observed trends. This implies that additional diffusion mechanisms (as discussed above) start to become important already at low and high values of φ, the surfactant diffusion is in fact dominated by these, and over a rather large range of φ values the surfactant diffusion is not mediated by aggregate diffusion. At values of φ in the vicinity of φ ) 0.5, the diffusion is well-described by diffusion along a surface separating oil domains from water domains. Turning to the diffusion coefficient for 1-octanol, we require the diffusion coefficient of 1-octanol in n-octane to predict the evolution of the 1-octanol diffusion with φ. The value obtained from the NMR diffusion measurement on a sample equivalent to the monomeric solubility of 1-octanol in n-octane (φDmon,b ) 0.0378)28 is DD,free ) 11.3 × 10-10 m2/s. The solid line in Figure 4 is calculated using eq 6. The aggregated diffusion coefficient, DD,mic, is calculated from the hydrodynamic radius, RH, with the Stokes-Einstein relation (eq 7), assuming spherical geometry. RH is calculated from the volumes and area per headgroup. DD,mic is compensated with the aggregate-obstruction effect (1 - 2φagg). The free 1-octanol diffusion DD,free is taken as the measured value of free 1-octanol in n-octane and compensated for obstruction effects. As can be seen, the agreement between the experimental and calculated diffusion coefficients is excellent. Obstruction Effects. A particular feature of the data in Figure 2 is the large effect on the reduced self-diffusion coefficients of water and oil as the tuning parameter δV,i is changed close to either of the two critical lines. This implies large changes in the microstructure by only small variations in the composition of the internal interface. As indicated above on the basis of the surfactant diffusion, the aggregates initially grow in size when φ is increased from the water-rich end. In fact, the reduction in the water diffusion coefficient can be rationalized in terms of the obstruction of the surfactant aggregates on the water diffusion. This situation has been analyzed by Jo¨nsson et al.49 In short, these workers present results for the (49) Jo¨nsson, B.; Wennerstro¨m, H.; Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77.

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Figure 5. Reduced diffusion coefficient of water as a function of the dispersed volume fraction of n-octane, surfactant, and cosurfactant φB+C+D, that is, 1 - φA. For comparison, the obstruction effect for aggregates of various geometries and sizes, which are calculated from the cell model,49 are shown as dotted lines.

Figure 7. Top: section through the phase tetrahedron at φ ) 0.5 to illustrate exemplarily the path across the fish-tail region along which the diffusion coefficients of water and n-octane were determined. Bottom: variation of the reduced diffusion coefficients for water and n-octane as a function of the composition of the mixed amphiphilic film δV,i measured along the titration line within the one-phase region (open symbols) at φ ) 0.1, 0.2, 0.35, and 0.5. The closed symbols denote samples prepared in the 2h two-phase region. The dotted lines correspond to the respective phase boundaries 2 f 1 and 1 f 2 h . Note that close to the lower limit δV,i,l ) 0.23 ( 0.0228 of the three-phase body the diffusion of water starts to decrease, while that of n-octane increases.

Figure 6. Variation of the reduced diffusion coefficient of n-octane as a function of the dispersed volume fraction 1 - φB. As in Figure 5, the calculated obstruction effects for aggregates of various geometries and sizes49 are shown as dotted lines.

obstruction effects of spheres, prolates, and oblates. The results are presented in Figure 5, together with the water diffusion data from Table 1. We do not wish to imply by default that the description in terms of discrete aggregates is valid when φ reaches 0.5 but rather use the comparison with discrete structures here to highlight where such description begins to fail. The water diffusion data are compatible with either prolates of substantial axial ratios or oblates of moderate axial ratios. The existence of very long prolates seems unlikely; the viscosity is rather low and the NMR line widths are comparatively narrow. Thus, the data in Figure 5 favor aggregates of an oblate shape at low φ. Interestingly, the same analysis can be carried out at high values of φ (cf. Figure 6). In conclusion, the rather rapid changes in the reduced values of the diffusion coefficients of water and oil at either end of the middlephase trajectory suggests the presence of oblate aggregates with moderate axial ratios.

In summary, the following picture of the evolution of the microstructure emerges. At low and high values of φ, oblate structures are present. There is some attractive interaction between these aggregates that allows for the formation of contact zones through which the oil (at low φ) and water (at high φ) may diffuse. As φ approaches 0.5 from below and above, the surfactant forms a dividing surface between the water and hydrocarbon components. Self-Diffusion Coefficients versus the Evolution of Microstructure with δV,i. To shed some light on the evolution of the microstructure as the ratio of surfactant to cosurfactant is changed at constant values of φ, the diffusion coefficients of water and oil were determined across the fish-tail region. In Figure 7, top, the investigated path is shown exemplary by means of the phase diagram at φ ) 0.5. The experiments were performed by mixing appropriate amounts of samples taken close to the upper and lower boundaries of the one-phase microemulsion region. Additional diffusion data were also obtained from the microemulsion samples in the 2 h regions. The experiments were carried out at four different values of φ, namely, φ ) 0.1, 0.2, 0.35, and 0.5, and the results are given in Figure 7, bottom. Starting with the data for φ ) 0.1, it is evident that, at low φ, discrete aggregates with curvature toward the oil

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are present in the entire one-phase region. The sample in the 2 h region possesses a relatively large reduced water diffusion (D/D0 ≈ 0.7), while the reduced oil diffusion is low (D/D0 ≈ 0.1), indicating the presence of oil-swollen micelles here also. Thus, it would appear that we have discrete oil-swollen micelles over the entire investigated path across the fish-tail area. For φ ) 0.2, the situation is similar. The reduced water diffusion for all samples is faster than that of the oil component. As the sample composition approaches that of the “upper” phase limit, the values of the water and oil diffusion components approach each other. The trend observed for φ ) 0.2 continues for φ ) 0.35. Finally, at φ ) 0.5 the reduced diffusion coefficients of oil and water are equal and roughly D/D0 ≈ 0.5, also in the microemulsion sample from the 2 h region. This would then indicate that in this case the structure is bicontinuous in all the samples investigated. C. SANS. As shown above, the NMR diffusiometry technique is a suitable method for studying the evolution of microstructures. It does, however, provide less detailed information about the length scale of microemulsions. Here, SANS is the method of choice. Therefore, the variation of the microstructure along the trajectory of the middle phase was studied by SANS. Previous related studies deal with the transition of microemulsions to weakly structured mixtures approaching the critical endpoints of inefficient ternary H2O/n-alkane/CiEj systems.50,51 Thus, the variation of the scattering behavior along the trajectory of the rather efficient quaternary D2O/ n-octane/C8G1/1-octanol system is of special interest. In analogy with the NMR diffusometry experiments, the samples are prepared in each case at the Y point within the one-phase region. The compositions of the SANS samples are given in Table 2. From the compositions, the scattering length densities of the water and oil domain as well as the interfacial film are calculated taking into account the H-D exchange and the monomeric solubilities of C8G1 in D2O and C8E0 in n-octane. As can be seen from Table 3, the scattering length density of the interfacial film does not exactly match the scattering length density of the oil. This means that a small fraction of the film contrast exists in addition to the bulk contrast. However, because the scattering intensity of the bulk contrast is in general more than 1 magnitude larger than the film contrast, we neglected the fraction of the film contrast in the analysis of the scattering curves. Scattering Curves. Figure 8 shows the scattering curves obtained plotted in a double logarithmic graph. The scattering curve at φ ) 0.1 is given on the absolute scale and, for clarity, the other spectra are displaced by factors of 5. As can be seen, the scattering curve of the nearsymmetrical microemulsion at φ ) 0.6 shows a characteristic interaction peak typical for a bicontinuous microstructure.52 At large values of the scattering vector q, the scattering intensity I decreases as q-4 exp{-q2t2}53,54 until the incoherent background Iincoh is reached. Both with decreasing and increasing values of φ, one finds a weakening of the characteristic peak, while at the same time the scattered intensity at small q increases. For φ between 0.3 and 0.7, the position of the peak remains (50) Schubert, K. V.; Strey, R.; Kline, S. R.; Kaler, E. W. J. Chem. Phys. 1994, 101, 5343. (51) Gradzielski, M.; Langevin, D.; Sottmann, T.; Strey, R. J. Chem. Phys. 1996, 104, 3782. (52) Teubner, M.; Strey, R. J. Chem. Phys. 1987, 87, 3195. (53) Porod, G. In Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: London, 1982. (54) Strey, R.; Winkler, J.; Magid, L. J. Phys. Chem. 1991, 95, 7502.

Reimer et al.

Figure 8. SANS curves of D2O/n-octane/C8G1/C8E0 mixtures as a function of φ. All the samples are measured at T ) 25 °C near the respective X point (point Y, cf. Figure 1, bottom left). The scattering curve at φ ) 0.1 corresponds to absolute intensities while the others are separated by factors of 5. As an example for the curve at φ ) 0.1, the fit of eq 14 to the large-q part is shown. Each scattering curve can similarly be welldescribed by the Porod decay for diffuse profiles.54 Note that only for the sample at φ ) 0.6 a scattering curve is obtained, which resembles that of a symmetrical bicontinuous microemulsion. The peak is well-fitted by the Teubner-Strey formula.52

almost constant, indicating that the periodicity of the structure is nearly invariant. Decreasing φ further, that is, toward the lower critical endpoint, the position of the remaining shoulder shifts to larger q. Contrary, if φ is increased, that is, toward the upper critical endpoint, the position of the shoulder shifts to lower q. These opposite trends in scattering behavior could be the result of two effects: On one hand, approaching a critical endpoint, a wetting transition occurs; hence, the position of the peak should move toward lower q.55 On the other hand, as deducted from the NMR measurements, the structure changes from bicontinuous to smaller and discrete oblatelike structures, which could be responsible for the shift of the peak to larger q. Length Scale. To determine the length scale of the microstructure, we described the scattering curves, which show a distinct peak, by the Teubner-Strey formula52

I(q) )

8πc2φaφb(∆F)2/ξTS a2 + c1q2 + c2q4

+ Iincoh

(11)

where ∆F is the scattering length density difference of the two subphases a and b and the parameters a2, c1, and c2 stem from the coefficients of an order parameter expansion. The correlation length

ξTS ) and the periodicity

[ ( ) ( )] 1 a2 2 c2

1/2

+

c1 4c2

-1/2

(12)

Microstructure of Alkyl Glucoside Microemulsions

[ ( ) ( )]

dTS 1 a2 ) 2π 2 c2

1/2

-

c1 4c2

Langmuir, Vol. 19, No. 26, 2003 10701

-1/2

(13)

may also be expressed in terms of the order parameter coefficients. More details are discussed in refs 40, 50, 55, and 56. The solid line in Figure 8 emphasizes that the peak of the scattering curve at φ ) 0.6 can be described quantitatively by the Teubner-Strey formula. A periodicity of the domains of dTS ) 240 Å and a correlation length of ξTS ) 90 Å are obtained. When the scattering curves at the neighboring φ ) 0.5 and 0.7 are analyzed, systematic deviations are found, especially at low q values. As mentioned above, the position of the peak and the periodicity dTS stays almost constant. For all other scattering curves, the Teubner-Strey relation does not provide a sufficient description, as increasing attractive interactions become important as the respective critical endpoints are approached. Specific Internal Interface S/V. In general, the overall length scale ξ in microemulsions is set by the specific area of the internal interface S/V, that is, ξ ∝ (S/V)-1. As elaborated by Porod,53 S/V can be determined from the large-q part of the scattering spectrum, where the scattering intensity should decrease as q-4. Taking into account the diffuseness of the locally flat interfacial film, Strey and Magid showed by convolution of the usual step profile in the scattering length density with a more realistic Gaussian profile of standard deviation t that the scattering intensity at large q can be described by54

S lim[I(q)] ) 2π(∆F)2 q-4 exp(-q2t2) + Iincoh (14) qf∞ V In Figure 8, the description of the data at large q by eq 14 is shown as a solid line for the scattering curve at φ ) 0.1. As can be seen, the curve is well-described by the Porod decay for diffuse profiles. Furthermore, inaccuracies in the absolute calibration of I(q) cancel out, if the “invariant”

Q)

∫0∞q2I(q) dq ) 2π2φaφb(∆F)2

(15)

is used in eq 14. The specific area of the internal interface S/V is then given by 4 2 2 S πφaφbq exp(q t ) ) (lim[I(q)] - Iincoh) qf∞ V Q

(16)

The determination of the “invariant” Q can be performed either numerically (Q) from the given spectra by integration57 or analytically (Qan), if the scattering length density difference ∆F is known and the spectrometer is wellcalibrated. Thus, the ratio fQ ) Q/Qan quantifies the accuracy of the calibration. When eq 16 was used, the specific area of the internal interface S/V was determined directly from the scattering curves. Figure 9 shows the variation of S/V along the trajectory of the middle phase of the quaternary D2O/n-octane/C8G1/ 1-octanol system. Starting from the water-rich side at φ ) 0.1, S/V increases continuously up to a maximum at φ (55) Gompper, G.; Shick, M. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J., Eds.; Academic Press: New York, 1994; Vol. 16. (56) Leitao, H.; da Gama, M. M. T.; Strey, R. J. Chem. Phys. 1998, 108, 4189. (57) Kluge, K. Der Schlu¨ ssel zum Versta¨ ndis von Mikroemulsionen aus Zuckertensiden: Die interne Grenzfla¨ che; Logos Verlag: Berlin, 2000.

Figure 9. Total specific internal interface S/V extracted from the large-q part of the scattering curves as a function of φ along the trajectory of the middle phase. Note that the data points resemble almost the shape of a parabola with a maximum at φ ) 0.4, which is in agreement with the trajectory of the volume fraction of C8G1 and C8E0 in the internal interface φC,i+D,i presented in Figure 9, top, of ref 28.

) 0.4. Subsequently, the specific area of the internal interface decreases back to small values on the oil-rich side. The error in S/V is caused mainly by the increasing incoherent part of the intensity at large q and the inaccuracy in determining the “invariant” Q. The error in the latter amounts to at maximum 10%, as can be seen from the variation of fQ (0.90 e fQ e 1.11, cf. Table 3), which is within the error limits of absolute calibrations of SANS experiments. Furthermore, the parabolic shape of the S/V versus φ curve is very similar to the trajectory of the middle phase, in which the volume fraction of C8G1 and C8E0 in the interfacial film φC,i+D,i is plotted as a function of φ (see Figure 9 in ref 28). This similarity is not unexpected because the total specific area of the internal interface S/V, which consists of the area created by both the C8G1 and the C8E0 molecules should be given to first order by

aD S aC ) φC,i + φD,i V vC vD

(17)

where aC and aD are the areas and vC ) 429 Å3 and vD ) 261 Å3 are the molecular volumes of the C8G1 and C8E0 molecules, respectively. Assuming that the partial area of a C8E0 molecule aD ) 29.3 Å2 58 remains constant and knowing the composition of the interfacial film as well as the specific area of the internal interface S/V, the area of a C8G1 molecule can be calculated according to

aC ) vC

(

)

S aD - φ /φ V vD D,i C,i

(18)

In Table 3, the area of a C8G1 molecule aC determined this way is given together with the scattering length densities, the specific area of the internal interface S/V, the diffuseness of the interfacial film t, and the ratio fQ. Figure 10 shows the variation of the area of a C8G1 molecule aC as a function of the composition of the (58) Sottmann, T.; Strey, R.; Chen, S. H. J. Chem. Phys. 1997, 106, 6483.

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IV. Conclusions

Figure 10. Area per C8G1 molecule aC calculated from eq 18 as a function of the composition of the interfacial film δV,i determined from phase behavior and density measurements.28 Note that aC decreases with increasing δV,i, that is, decreasing curvature of the amphiphilic film.

interfacial film δV,i together with the errors calculated by error progression. As can be seen, aC decreases with increasing δV,i, that is, increasing fraction of C8E0 in the mixed amphiphilic film. As it is shown by NMR measurements (see above), the increase of δV,i inverts the interfacial curvature from discrete o/w to w/o structures (see also Figure 8 in ref 29). We note that the same trend is observed if C8E0 is added to the lamellar phase in the binary C8G1/ water system. Thus, on the basis of small-angle X-ray scattering experiments it was found that the quantity aC decreased when C8E0 was added to the lamellar phase.59 It is interesting to note that, in temperature-dependent ternary systems of the water/n-alkane/CiEj-type, it was found that the area per surfactant molecule stays constant, even if a wide temperature range was spanned and, therefore, different microstructures were considered.60 (59) Nilsson, M.; Reimer, J.; So¨derman, O. To be submitted for publication.

We have shown that the temperature-insensitive, rather hydrophilic sugar surfactant C8G1 can be tuned through phase inversion by addition of the hydrophobic cosurfactant C8E0 (1-octanol). The diffusion behavior as determined NMR diffusometry mimics that of well-known ternary microemulsions of the water/n-alkane/CiEj-type. However, there are two important aspects to mention. First, the whole evolution of the microstructure from o/w droplets to w/o droplets has been studied at a constant temperature. Second, moving along the trajectory of the middle phase, the vicinity of the critical endpoints is explored for the first time in greater detail. Here, surprisingly, the obstruction of diffusion of the abundant medium, that is, water on the water-rich side and vice versa, indicates structures of a more flat nature than the cylindrical network usually expected. SANS results in this region indicate strong interaggregate attractive interactions but are not able to elucidate whether the aggregate structure is flat or cylindrical. Furthermore, the SANS experiments provide the specific internal interface in the microemulsion as the system moves along the trajectory of the middle phase. In this course, the interfacial film becomes enriched by C8E0 and the area per C8G1 molecule decreases. Both trends are plausible: The increasing penetration of C8E0 is a consequence of the increasing activity of C8E0 as the system is titrated with C8E0, which leads to an increased surface pressure of C8E0. The increasing fraction of C8E0 in the interfaces lets the structure invert from oil droplet (convex), through bicontinuous (flat), to water droplets (concave). In this progression, there is less space for the headgroups of G8G1 surfactant molecules. Acknowledgment. J.R. and O.S. acknowledge support from the Competence Centre for Surfactant Based on Natural Products, SNAP. T.S., K.K., and R.S. would like to thank our local contact S. Egelhaaf at the ILL. LA034847V (60) Strey, R.; Glatter, O.; Schubert, K. V.; Kaler, E. W. J. Chem. Phys. 1996, 105, 1175.