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Langmuir 2002, 18, 3058-3067
General Patterns of the Phase Behavior of Mixtures of H2O, Alkanes, Alkyl Glucosides, and Cosurfactants T. Sottmann,* K. Kluge, and R. Strey Institut fu¨ r Physikalische Chemie, Universita¨ t zu Ko¨ ln, Luxemburger Strasse 116, D-50939 Ko¨ ln, Germany
J. Reimer and O. So¨derman Physical Chemistry I, University of Lund, P.O. Box 124, S-221 00 Lund, Sweden Received November 13, 2001. In Final Form: January 7, 2002 We demonstrate how rather hydrophilic surfactants can be used for solubilizing simultaneously water and alkane. The required hydrophilic-lipophilic balance can be achieved by the addition of a mediumchain alcohol, that is, a hydrophobic cosurfactant. Specifically, the phase behavior of the quaternary water-n-octane-n-octyl β-D-glucopyranoside (C8G1)-n-octanol (C8E0) system has been investigated. Sugar surfactants, in general, are hydrophilic and, because of the comparatively large number of hydroxyl groups, much less temperature-sensitive than the well-known alkylpolyglycolether (CiEj) surfactants. Therefore, one has to resort to tuning the phase behavior by mixing with a hydrophobic cosurfactant. Once this is done, the phase behavior mimics that of water-alkane-CiEj microemulsions. To show this, the trajectory of the middle-phase is determined as the phase inversion is passed. A scaling of the trajectory onto the trajectories of conventional temperature-sensitive ternary microemulsions is possible after the composition (i.e. the fraction of n-octanol) of the mixed amphiphilic film is determined from phase behavior and density measurements.
I. Introduction The phase behaviors of microemulsion systemssirrespectiveofthenatureoftheindividualcomponentssexhibit many similarities, if compared in appropriate variables. For instance, the phase behavior of the five-component systems water-n-alkane-ionic surfactant-cosurfactantelectrolyte was first characterized (and therefore associated with his name) by Winsor 50 years ago,1 and he generated the phase sequence Winsor I, Winsor III, and Winsor II by salt addition. After understanding the generic qualities of the phase behavior using very simple wateroil-alcohol systems, Davis and co-workers2 developed the mnemonic nomenclature 2, 3, 2 h , indicating that the nonionic surfactant is at first water-soluble and therefore resides in the lower phase, as indicated by the lower bar. After the surfactant is made sufficiently hydrophobic, it is transferred to the oil-phase indicated by the upper bar. Between, the so-called balanced state3 is passed, where the surfactant is equally soluble in water and oil. At this point, three phases exist, the surfactant forming its own middle-phase swollen to a maximum with water and oil. The same view was developed independently by Kahlweit and co-workers by examining water-n-alkane-shortchain nonionic amphiphile systems.4 Kahlweit and coworkers also showed that the phase behavior of long-chain nonionic surfactants, ionic surfactants, and systems with ionic surfactant mixed with nonionic surfactant displayed the same general patterns.5,6 * Corresponding author. (1) Winsor, P. A. Solvent Properties of Amphiphilic Compounds; Butterworth: London, 1954. (2) Knickerbocker, B. M.; Pesheck, C. V.; Davis, H. T.; Sriven, L. E. J. Phys. Chem. 1982, 86, 393. (3) Shinoda, K. Solvent Properties of Surfactant Solutions; Marcel Dekker: New York, 1967. (4) Kahlweit, M.; Strey, R. Angew. Chem., Int. Ed. Engl. 1985, 24, 654.
The reason for the common features of the phase behavior for a large variety of different surfactant systems became clear through the work of several groups, most notably Olsson and Wennerstro¨m,7,8 Bellocq and Roux,9,10 Langevin and Meunier,11,12 Binks et al.,13 Kahlweit, Strey, and co-workers,14-16 as well as Friberg, Shinoda, and Kunieda.17,18 All these groups envision the surfactant molecules to form an amphiphilic film, so that in “good” microemulsions19 water and oil are separated by an amphiphilic film of variable mean curvature. Starting with the work by de Gennes and Taupin20 and Safran and Turkevic,21 the bending energy of amphiphilic films was (5) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen, J.; Schoma¨cker, R. Langmuir 1988, 4, 499. (6) Kahlweit, M.; Strey, R.; Schoma¨cker, R.; Haase, D. Langmuir 1989, 5, 305. (7) Olsson, U.; Nagai, K.; Wennerstro¨m, H. J. Phys. Chem. 1988, 92, 6675. (8) Lindman, B.; Shinoda, K.; Olsson, U.; Anderson, D.; Karlstro¨m, G.; Wennerstro¨m, H. Colloids Surf. 1989, 38, 205. (9) Bellocq, A. M.; Biais, J.; Bothorel, P.; Clin, B.; Fourche, G.; Lalanne, P.; Lemaire, B.; Lemanceau, B.; Roux, D. Adv. Colloid Interface Sci. 1984, 20, 167. (10) Roux, D.; Safinya, C. R. J. Phys. (Paris) 1988, 49, 307. (11) Guest, D.; Langevin, D. J. Colloid Interface Sci. 1986, 112, 208. (12) Lee, L. T.; Langevin, D.; Meunier, J.; Wong, K.; Cabane, B. Prog. Colloid Polym. Sci. 1990, 81, 209. (13) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I. Langmuir 1989, 5, 1210. (14) Kahlweit, M.; Strey, R.; Haase, D.; Firman, P. Langmuir 1988, 4, 785. (15) Jahn, W.; Strey, R. J. Phys. Chem. 1988, 92, 2294. (16) Kahlweit, M.; Strey, R.; Haase, D.; Kunieda, H.; Schmeling, T.; Faulhaber, B.; Borkovec, M.; Eicke, H.-F.; Busse, G.; Eggers, F.; Funck, Th.; Richmann, H.; Magid, L.; So¨derman, O.; Stilbs, P.; Winkler, J.; Dittrich, A.; Jahn, W. J. Colloid Interface Sci. 1987, 118, 436. (17) Kunieda, H.; Shinoda, K. J. Dispersion Sci. Technol. 1982, 3, 233. (18) Friberg, S.; Kunieda, H. Bull. Chem. Soc. Jpn. 1981, 54, 1010. (19) Safran, S. In Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution; Chen, S. H., et al., Eds.; Kluwer Academic: Dordrecht, 1992. (20) De Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982, 86, 2294.
10.1021/la011665x CCC: $22.00 © 2002 American Chemical Society Published on Web 03/09/2002
Phase Behavior of Mixtures
analyzed and found to be a suitable concept for explaining the individual observations. From the experimental point of view, it is common to use several parameters, that is, temperature, T, salt fraction in the water, ,5 or cosurfactant fraction in the mixture of the two amphiphiles, δ,5,22 to tune the mean curvature of the amphiphilic film in order to achieve characteristic and desired features, such as phase behavior and ultralow interfacial tension, of microemulsions. Up to now, only the temperature variation of the mean curvature was determined quantitatively from extensive investigations of the microstructure by SANS for ternary water-n-alkane-n-alkyl-polyglycol ether (CiEj) systems.23 Having realized that the temperature affects the mean curvature in all these systems in a similar fashion, two of us postulated the existence of corresponding states in microemulsions.24 This idea was supported by a quantitative analysis of the oil/water interfacial tensions for a large number of different systems.25 Finally, the general description in terms of a bending energy led to a scaling of all interfacial tension curves.26 The physical reason behind the observed scaling behavior can be understood from the fact that the bending energy originates from relatively short-ranged molecular interactions. Scaling of properties on length scales larger than the local interaction scale is then possible. A prominent example is the scaling in the vicinity of critical points. To demonstrate that the description in terms of bending energy indeed holds for all systems irrespective of the actual nature of the components, we chose the watern-octane-n-octyl β-D-glucopyranoside (C8G1)-n-octanol (C8E0) system with the aim of examining the phase behavior, the interfacial tension, and the microstructure quantitatively. The study of glucopyranoside-surfactant systems is interesting for several other reasons. They are nontoxic and biodegradable.27,28 In addition, they are hydrophilic and show only a weak temperature dependence of the phase behavior, and consequently also of the mean curvature,29-31 which makes the addition of a hydrophobic cosurfactant necessary if one wants to tune the system through the phase inversion. Recently, a number of investigations dealing with systems using medium-chain alcohols,30,32-34 CiEj,35 or alkyl sulfates36 as cosurfactants and n-alkanes or more hydrophilic oils such as alkylethyleneglycol ethers37,38 were reported. A quantitative determination of the dependence of the mean curvature on the composition of the amphiphilic film, and, thus, an analysis of the results in terms of bending energy, is missing. (21) Safran, S.; Turkevich, L. Phys. Rev. Lett. 1983, 50, 1930. (22) Penders, M. H. G.; Strey, R. J. Phys. Chem. 1995, 99, 10313. (23) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (24) Sottmann, T.; Strey, R. J. Phys.: Condens. Matter 1996, 8, A39. (25) Sottmann, T.; Strey, R. J. Chem. Phys. 1997, 106, 8606. (26) Leitao, H.; Somoza, A. M.; Telo da Gama, M. M.; Sottmann, T.; Strey, R. J. Chem. Phys. 1996, 105, 2875. (27) Balzer, D. Tenside, Surfactants, Deterg. 1991, 28, 419. (28) Eskuchen, R.; Nitsche, M. In Alkyl Polyglycosides; Hill, K., Rybinski, W. v., Stoll. G., Eds.; VCH: Weinheim, 1997. (29) Kunieda, H.; Ushio, N.; Nakano, A.; Miura, M. J. Colloid Interface Sci. 1993, 159, 37. (30) Fukuda, K.; So¨derman, O.; Lindman, B.; Shinoda, K. Langmuir 1993, 9, 2921. (31) Kahlweit, M.; Busse, G.; Faulhaber, B. Langmuir 1995, 11, 3382. (32) Kunieda, H.; Nakano, A.; Pes, M. A. Langmuir 1995, 11, 3302. (33) Stubenrauch, C.; Paeplow, B.; Findenegg, G. H. Langmuir 1997, 13, 3652. (34) Stubenrauch, C.; Findenegg, G. H. Langmuir 1998, 14, 6005. (35) Ryan, L. D.; Schubert, K. V.; Kaler, E. W. Langmuir 1997, 13, 1510. (36) Ryan, L. D.; Kaler, E. W. J. Phys. Chem. B 1998, 102, 7549. (37) Ryan, L. D.; Kaler, E. W. Langmuir 1997, 13, 5222. (38) Ryan, L. D.; Kaler, E. W. Langmuir 1999, 15, 92.
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Before performing extensive studies of microstructure by NMR diffusometry and SANS measurements, the dependence of the phase behavior on the nature and amount of cosurfactant has to be known in detail. While the latter topic will be described in detail below, the former will be the subject of forthcoming papers. II. Experiment A. Materials. The surfactants n-octyl β-D-glucopyranoside (C8G1) and n-hexyltrioxyethylene (C6E3) were purchased from Sigma Aldrich (Steinheim, Germany) and Bachem (Bubendorf, Switzerland), respectively (both with a purity >98%). The cosurfactants n-octanol (C8E0) and n-hexanol (C6E0) were provided by Merck-Schuchardt (Hohenbrunn, Germany) with the purity >99%. As oil, n-octane from Sigma Aldrich with the purity >99% was used. Water was double-distilled from a quartz column. D2O was provided by Cambridge Isotope Laboratories (Andover, MA) with a degree of deuteration of >99.9%. All components were used without further purification. B. Phase Diagrams. To determine the phase diagrams, desired amounts of water (A), oil (B), and surfactant (C) were weighed into test tubes, which were then sealed with polyethylene stoppers. The samples were placed in a transparent water bath thermostated at 25.00 ( 0.02 °C. When temperature equilibrium was reached, the stopper was lifted and the three-component mixture was titrated with a cosurfactant using a calibrated microliter syringe. The added amount was controlled by weight with an accuracy of (0.001 g. After stirring, the system was allowed to equilibrate and the number and appearance of the phases were visually determined by inspection in scattered and transmitted light. The occurrence of the anisotropic lamellar phase was seen in transmitted light between crossed polarizers. The composition of a quaternary mixture of water (A)-oil (B)surfactant (C)-cosurfactant (D) is characterized by three independent composition variables, and weight or mole fractions are the proper variables. Since we will discuss structures and length scales of the microemulsions in a forthcoming paper, we will use volume fractions, that is, the volume fraction of oil to water plus oil
φ)
VB VA + VB
(1)
and the volume fraction of the surfactant and cosurfactant in the total mixture
φC+D )
VC + VD VA + VB + VC + VD
(2)
and, finally, the volume fraction of cosurfactant in the surfactant plus cosurfactant mixture
δV )
VD VC + VD
(3a)
as composition variables. Furthermore, the volume fraction of each component i is defined by
φi )
Vi
∑V
(3b)
i
i
We note that the calculation of volume fractions involves assumptions concerning the ideality of mixing; however, the error is presumably small and is neglected. At all times the corresponding mass fractions R, γ, and δ4,22 and the mass fractions of surfactant γC and cosurfactant γD in the overall mixture were also recorded. C. Density Measurements. The density of the coexisting oil excess phases in the three phase region was determined by using a digital vibrating tube densiometer (AP Paar DMA 602 P, Graz,
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Figure 1. Experimentally determined phase behavior of the quaternary system H2O-n-octane-C6E3-C6E0 at T ) 25 °C represented in an unfolded phase tetrahedron: (O) experimental data; (b) critical points. The negative slope of the schematically drawn tie lines in the system H2O-n-octane-C6E3 indicates the preferred solubility of the surfactant in the water-rich phase. Note that there is no miscibility gap in the n-octane-C6E3C6E0 system. Austria). After phase separation the oil excess phase was poured into the densiometer. The temperature was controlled to 25.00 ( 0.02 °C.
III. Results A. Quaternary CiEj Microemulsions. In general, insight into the phase behavior of an unknown system is facilitated by considering the phase diagrams of the systems representing the faces of the body corresponding to the appropriate phase space.4 Accordingly, in the case of a quaternary system, one has to consider the diagrams of the four ternary systems forming the faces of the phase tetrahedron. In the following, we will exemplify this general approach on the basis of a simple quaternary CiEj system in order to apply it subsequently to the actual scope of this paper, the study of rather complex quaternary alkyl glucoside systems. Therefore, the phase behavior of the quaternary H2O-n-octane-n-hexyltrioxyethylene (C6E3)-1-hexanol (C6E0) system at T ) 25 °C is represented in an unfolded phase tetrahedron in Figure 1. Three of the four ternary systems show large miscibility gaps. The base of the prism is formed by H2O-n-octaneC6E3. The miscibility gap displays a negative slope of the tie lines, indicating the coexistence of an oil-in-water (o/w) microemulsion with an oil excess phase. Noteworthy is the almost straight phase boundary starting in the water corner indicating a constant ratio of C6E3/n-octane in the o/w microemulsion. This behavior is typical for the emulsification failure boundary. In the H2O-n-octane-C6E0 system, a large miscibility gap appears. Its presence is caused by the insolubility of H2O in n-octane as well as the poor solubility of H2O in C6E0. On account of the complete miscibility of n-octane and C6E0, the tie lines converge in the water corner. The third ternary system H2O-C6E3-C6E0 begins with the miscibility gap between H2O and C6E0, which closes upon adding C6E3. The high mutual solubility of C6E3 and C6E0 leads to tie lines pointing toward the water corner. The position of the plait point is indicated by the filled symbol and faces the H2O-C6E3 side. If the temperature were raised to the cloud point of the binary H2O-C6E3 system at Tc ) 46.0 °C,39 the plait point would touch the binary H2O-C6E3 side.
Sottmann et al.
Figure 2. Section through the phase tetrahedron of the H2On-octane-C6E3-C6E0 system at an oil to water plus oil volume ratio of φ ) 0.5 and T ) 25 °C. Note that the phase boundaries resemble the shape of a fish with a three-phase region at small mass fractions and a one-phase region at large surfactant mass fractions.
Since n-octane and C6E0, n-octane and C6E3, and C6E3 and C6E0 are completely miscible at T ) 25.0 °C, no miscibility gap can be found in the fourth ternary n-octane-C6E3-C6E0 system. The interplay of the miscibility gaps in the four Gibbs triangles at the faces of the tetrahedron determines the phase behavior inside the tetrahedron. To examine the details of the phase behavior inside the phase tetrahedron, it is useful to perform vertical sections through the tetrahedron at constant oil to water plus oil ratio φ. In Figure 2, such a section is shown for the H2O- n-octaneC6E3-C6E0 system for φ ) 0.50 and at T ) 25.0 °C. At low n-hexanol content, an o/w microemulsion coexists with an oil excess phase (denoted as 2), as expected from Figure 1 for the base system. As discussed above in connection with Figure 1, for high n-hexanol content, a w/o microemulsion coexisting with a water excess phase (2 h ) is expected. Therefore, within the section considered, a phase inversion with increasing n-hexanol content has to occur. As in other systems,4-6 a three-phase region is found with the typical phase boundaries and adjacent onephase region resembling the shape of a fish. Depending on the C6E3 mass fraction, a coexistence of a microemulsion with an excess water and oil phase (3) or a one-phase microemulsion (1) is observed. Knowing the phase behavior of the four ternary systems, the behavior of the quaternary system can be understood as follows: The 2 region has its origin in the miscibility gap of the H2On-octane-C6E3 base system, whereas the 2h region stems from the miscibility gap of the H2O-n-octane-C6E0 system. In addition, the demixing tendency of the H2OC6E0-C6E3 system overlaps inside the phase tetrahedron and induces the formation of the three-phase region. Thus, by adding a medium- or long-chain alcohol (C6E0) to a ternary microemulsion, the same progression in phase behavior is found as that found when increasing the temperature4 in conventional ternary H2O-n-alkaneCiEj systems. Two effects quantitatively determine the observed evolution when an alcohol is added. On one hand, the alcohol acts as a cosolvent making the oil more hydrophilic. (39) Schubert, K.-V.; Strey, R.; Kahlweit, M. J. Colloid Interface Sci. 1991, 141, 21.
Phase Behavior of Mixtures
Figure 3. Schematic representation of the phase behavior in an unfolded phase tetrahedron. In comparison to Figure 1, the phase behavior of a system with a more hydrophilic CiEj surfactant (e.g. C8E6) and a more hydrophobic n-alkane (e.g. n-hexadecane) is shown. The main difference from Figure 1 is the additional miscibility gap in the binary oil (B)-surfactant (C) system, which implies a miscibility gap in the ternary B-C-D system. Also, the central miscibility gap of the A-B-C system connects to the B-C side.
On the other hand, the alcohol increases the effective hydrophobicity of the surfactant mixture. Interestingly, this combined action leads to an increase in solubilization capacity of the amphiphile mixture, if compared to that of pure C6E3. While in the ternary system H2O-n-octaneC6E3 a surfactant mass fraction of γ˜ ) 0.39 is needed at T ) 42.2 °C to solubilize equal volumes of water and oil (φ ) 0.5),40 γ˜ amounts to 0.34 in the quaternary system at T ) 25.0 °C. Here γ˜ is taken as the sum of the mass fractions of C6E3 (γC ) 0.295) and C6E0 (γD ) 0.045), not subtracting the monomerically (mainly in the oil domains) dissolved C6E0, which would reduce the total amount of active surfactant even further. The main topic of this contribution deals with a considerably more hydrophilic class of surfactants, namely, alkyl glucosides (CnGm). Therefore, it is of interest to discuss first the replacement of C6E3 by a more hydrophilic surfactant, for example, C8E6, and to use a more hydrophobic oil, for example, n-hexadecane. In Figure 3 the schematic phase behavior expected for such a system is presented. An important difference to the H2O (A)-n-octane (B)C6E3 (C)-C6E0 (D) system is the miscibility gap in the binary oil (B)-surfactant (C) system, which at the chosen temperature extends into the ternary oil (B)-surfactant (C)-cosurfactant (D) system. Therefore, the miscibility gap of the ternary water (A)-oil (B)-surfactant (C) system is connected to the oil (B)-surfactant (C) side of the tetrahedron. Because of the higher hydrophilicity of the surfactant, the miscibility gap of the water (A)-surfactant (C)-cosurfactant (D) system shrinks and, together with it, the (critical) plait point shifts closer to the water (A)cosurfactant (D) side. Only small changes, like a somewhat expanded miscibility gap, should be expected for the water (A)-oil (B)-cosurfactant (C) system. After these introductory considerations, we now turn our attention to the seemingly more difficult alkyl glucoside systems. B. Quaternary CnGm Microemulsions. Before treating the phase behavior of alkyl glucosides in detail, we will present some general remarks pertaining to their phase behavior in water and oil. In some respects, the phase behavior of the alkyl glucosides (CnGm) is different (40) Kluge, K. Der Schlu¨ ssel zum Versta¨ ndis von Mikroemulsionen aus Zuckertensiden: Die interne Grenzfla¨ che; Logos Verlag: Berlin, 2000.
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from that of the well-known n-alkylpolyglycol ether (CiEj).4,41,42 The observation is that already in the binary water-alkyl glucoside system often extensive miscibility gaps exist,43-46 which do not change with temperature. Some studies of water, technical grade CnGm’s, and shortchained alcohols (C4-C6) show extremely narrow onephase regions.47,48 With increasing surfactant concentrations, often cubic, hexagonal, and lamellar lyotropic mesophases are observed. Depending on the nature of the alkyl glucoside and the temperature used, a lower solubility limit, the so-called Krafft-boundary, is found, where a fluid phase coexists with a crystalline phase.37,46 Also, the phase behavior of binary n-alkane-CnGm systems differs from that of the n-alkane-CiEj systems. While in the experimentally accessible temperature range (0 < T < 100 °C) the CiEj surfactants are usually completely miscible with n-alkanes, CnGm’s are nearly insoluble in n-octane31 and precipitate as solids. However, the basic phase behavior of the isotropic fluid phases does not differ from the schematic picture in Figure 3. Many of the features encountered when examining the phase behavior of n-alkyl glycoside systems are connected with temperature-insensitivity. With these points in mind, the phase behavior of the quaternary system water-noctane-n-octyl β-D-glucopyranoside (C8G1)-n-octanol (C8E0) can be analyzed. C. Four Ternary Diagrams of the Quaternary System Water-n-Octane-n-Octyl β-D-Glucopyranoside (C8G1)-n-Octanol (C8E0). In the previous section, the usefulness of studying the phase behavior of the four ternary systems found in the faces of the phase tetrahedron was demonstrated. In Figure 4, the phase behavior of the faces for the water-n-octane-n-octyl β-Dglucopyranoside (C8G1)-n-octanol (C8E0) system at T ) 25.0 °C is represented in an unfolded tetrahedron. All ternary systems show extensive miscibility gaps. In h particular, the D2O-n-octane-C8E0 system displays a 2 region, while the D2O-n-octane-C8G1 system displays a 2 region. Therefore, a phase inversion, as in Figure 2, can be expected to exist in the interior of the tetrahedron. The system D2O-n-octane-C8E0 shows the typical 2h behavior. Considering the binary mixtures, D2O and n-octane as well as D2O and C8E0 are nearly nonmiscible pairs. Experimentally, 7.1 wt % D2O is found to be soluble in C8E0, whereas all other mutual solubilities are below 0.06 wt % (cf. 0.0014 wt % n-octane in H2O at 16 °C49 and 0.059 wt % C8E0 in H2O at 25 °C50). In contrast, n-octane and C8E0 are completely miscible at T ) 25 °C. Therefore, the tie lines converge in the water corner of the ternary D2O-n-octane-C8E0 system; that is, the amphiphile resides in the oil (2 h behavior). In contrast, the base of the tetrahedron, that is, the system D2O-n-octane-C8G1, shows the tie lines inclined toward the oil corner, that is, 2, with only small amounts of oil solubilized in the C8G1 microemulsion droplets and an almost straight emulsification failure boundary. In (41) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen J.; Schoma¨cker, R. Langmuir 1988, 4, 499. (42) Kahlweit, M.; Strey, R.; Busse, G. J. Phys. Chem. 1990, 94, 3881. (43) Sakya, P.; Seddon, J. M.; Templer, R. H. J. Phys. II 1994, 4, 1311. (44) Balzer, D. Langmuir 1993, 9, 3375. (45) Nilsson, F.; So¨derman, O.; Hansson, P.; Johansson, I. Langmuir 1998, 14, 4050. (46) Boyd, B. J.; Drummond, C. J.; Krodkiewska, I.; Grieser, F. Langmuir 2000, 16, 7359. (47) Kahl, H. Dissertation, Universita¨t Leipzig, 1996. (48) Stradner, A.; Mayer, B.; Sottmann, T.; Hermetter, A.; Glatter, O. J. Phys. Chem. B 1999, 103, 6680. (49) Fu¨hner, B. Ber. 1924, 57, 514. (50) Butler, J. A.; Thomson, D. W.; Maclennon, W. H. J. Chem. Soc. 1933, 674.
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Figure 4. Unfolded phase tetrahedron of the quaternary system D2O-n-octane-C8G1-C8E0 at T ) 25 °C. Note that the extensive miscibility gaps between the liquid phases (tie lines are shown schematically) are qualitatively similar to the schematic diagram in Figure 3. These determine the microemulsion phase behavior. In addition, regions where the lamellar phase (LR), the cubic phase (V1), and the bicontinuous bilayer phase (L3) exist can be identified. The dashed lines illustrate phase boundaries which were not exactly determined. Note that within the ternary system D2O-C8G1-C8E0, a threephase triangle appears (shaded in the figure), where a dilute water-rich phase (L1) coexists with a L3 phase and a LR phase.
addition, the ternary system D2O-C8G1-C8E0 shows a miscibility gap with tie lines inclined toward the water corner; the plait point therefore faces the water-C8G1 axis. When the concentration of the cosurfactant is increased, the plait point touches the emulsification failure boundary extending from the base system D2O-n-octaneC8G1 into the tetrahedron. As in conventional ternary systems, the middle-phase forms and moves with increasing cosurfactant content from the aqueous side to the oil side of the tetrahedron, where it joins with the oil phase; that is, the 2 h state is reached. We will demonstrate the trajectory of the middle-phase microemulsion below. The solid C8G1 and the mesophases shown in Figure 4 lead to complications in the phase behavior which need to be addressed. The ternary n-octane-C8G1-C8E0 system is dictated by the binary mixtures at T ) 25 °C. C8G1 is nearly insoluble in n-octane, and only 3.5 wt % C8G1 can be dissolved in C8E0. Thus, in the ternary system, a large miscibility gap between the crystalline C8G1 and the liquid mixture of n-octane and C8E0, in which some C8G1 is dissolved, can be observed. Of interest is a small synergistic effect, which leads to an increasing amount of C8G1 (9 wt %) soluble in symmetric n-octane-C8E0 mixtures. The phase behavior of the ternary system D2O-C8G1C8E0 shows a lamellar phase (LR), a cubic phase (V1), and a bicontinuous bilayer phase (L3). All three phases have in common a mean curvature of the bilayer of 〈H〉 ) 0. The lamellar phase and the cubic phase are both liquid crystalline mesophases. The microstructure of V1 is bicontinuous with a space group of Ia3d,45 and that of LR consists of stacked bilayers. The L3 phase is optically isotropic, is birefringent under shear, and scatters light strongly. It consists of bilayers, which are multiply connected without edges and seams. The phase boundaries of the liquid crystalline phases in the D2O-C8G1-C8E0 system are derived on the basis of deuterium NMR spectroscopy51 and shown as dashed lines in Figure 4. (51) Reimer, J. To be published.
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Within the three-phase triangle, a micellar L1 region coexists with L3 and LR phases, which appear in the test tube in this sequence from bottom to top because of their decreasing density. The lamellar and cubic phases of the binary D2O-C8G1 system45 also intersect the central miscibility gap of the base system D2O-n-octane-C8G1. The intersection with the central miscibility gap is shown as the dashed line, which declines from the funnel shaped L1 region into the n-octane corner. Samples prepared at this line show a complex multiphase coexistence but appear optically clear at first sight because of optical matching, that is, the similarity of the refractive indices of the coexisting phases. This behavior and the high viscosity, which hinders phase separation, make the exact determination of the phases at surfactant concentrations above the dashed line extremely difficult. Even though a study of the complex phase behavior of the liquid crystal phases is interesting and will be the subject of a forthcoming paper, we focus here on the development of the three-phase region, that is, the trajectory of the middlephase microemulsion. Therefore, it is important to discuss the variation of the central miscibility gap with increasing n-octanol content. D. Phase Behavior inside the Tetrahedron. The knowledge of the ternary systems forming the face of the tetrahedron facilitates the understanding of the rather complex phase behavior of the quaternary sugar-surfactant system. To examine especially the variation of the composition of the middle-phase microemulsion with the oil to water plus oil ratio φ, 15 sections through the tetrahedron at constant φ have been investigated. In Figure 5 (top) we show an example of the section at symmetric water and oil fractions, that is, φ ) 0.5, through the phase tetrahedron at T ) 25.0 °C for the systems D2O-n-octane-C8G1-n-octanol (O) and H2O-n-octaneC8G1-n-octanol (b). The reason for using D2O is that we intend to investigate the microstructure of the various phases by means of NMR diffusometry and small angle neutron scattering. At low surfactant mass fractions for both systems, the phase sequence 2-3-2 h is found as the alcohol content is increased. At higher surfactant mass fractions, the expected phase sequence 2-1-2 h is observed. For even higher surfactant mass fractions, a lamellar phase appears, denoted LR, although at first the lamellar phase only coexists with the bicontinuous microemulsion. The composition of the middle-phase microemulsion is given by the point X (cf. Figure 5), where the three-phase region touches the one-phase region. In the H2O system the X-point is located at γC ) 0.112 and γD ) 0.047. When H2O is replaced by D2O, the shapes of the phase boundaries do not change, but both the boundaries and the X-point are slightly shifted to a lower mass fraction of C8E0. Furthermore, the coexistence region (denoted as LR) of the lamellar phase and the bicontinuous phase is shifted toward smaller C8G1 fractions. In Figure 5 (bottom) the variation of the X-point with φ, that is, the trajectory of the middle phase, is shown as a projection onto the D2O-C8G1-C8E0 side of the tetrahedron. Starting from the water-rich side at φ ) 0.10, the mass fraction of surfactant and cosurfactant increases continuously up to φ ) 0.60. Subsequently, the mass fraction of C8G1 decreases at a nearly constant C8E0 fraction. The determination of the critical end points of the trajectory, which is relatively easy in a threecomponent system,52 is much more complex in the quaternary system. (52) Burauer, S.; Sachert, T.; Sottmann, T.; Strey, R. Phys. Chem. Chem. Phys. 1999, 1, 4299.
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Figure 5. (top) Section through the phase tetrahedron at an oil to water plus oil volume fraction of φ ) 0.5 for the systems H2O-n-octane-C8G1-C8E0 and D2O-n-octane-C8G1-C8E0 at T ) 25 °C. Note that the systems show similar phase behaviors. The phase boundaries of the D2O system are shifted to slightly smaller n-octanol fractions. (bottom) Projection of the composition of the middle-phase microemulsion onto the D2O-C8G1C8E0 face of the tetrahedron. Starting from the water-rich side at φ ) 0.10, the mass fraction of surfactant and cosurfactant increases continuously up to φ ) 0.60. Subsequently, the mass fraction of C8G1 decreases while the C8E0 fraction stays nearly constant.
E. Composition of the Mixed Amphiphilic Film. Comparing the shapes of the trajectories of quaternary and ternary systems at the oil-rich side, the γD(γC) trajectory of the X-points in the quaternary system is nearly flat (i.e. the X-points have roughly the same content of C8E0), whereas in the temperature-dependent threecomponent system the T(γ) trajectory of the X-points tends toward higher temperatures (see, e.g., Figure 2 in ref 16). This difference can be explained, if one keeps in mind that many properties of microemulsion systems are determined by the properties of the interfacial film.19,26,53 At constant temperature in quaternary systems these properties are mainly determined by the composition of the interfacial film δi, which dictates in particular the spontaneous curvature and the efficiency of the amphiphilic mixture.22 To determine δi, the monomeric solubilities of n-octanol (γD,mon,b) in n-octane and C8G1 in D2O (γC,mon,a) have to be known, while the solubilities of n-octanol in D2O and C8G1 in n-octane can be neglected. To be able to apply the analysis by Kunieda and coworkers54,55 to the present system, the volume fractions of the middle-phase Vc/Vtotal were measured as a function of the overall surfactant mass fraction γ in the three(53) Morse, D. C. Phys. Rev. E 1994, 50, R2423. (54) Yamaguchi, S.; Kunieda, H. Langmuir 1997, 13, 6995. (55) Kunieda, H.; Yamagata, M. Langmuir 1993, 9, 3345.
Figure 6. Determination of the amount of C8G1 and C8E0 dissolved monomerically in water and n-octane, respectively, at φ ) 0.5 and T ) 25.0 °C using the concept of Yamaguchi and Kunieda.54 (top) Volume fraction of the middle-phase microemulsion Vc/Vtotal as a function of the overall surfactant mass fraction γ. Note that at every value of γ the cosurfactant to surfactant plus cosurfactant ratio δ was adjusted to equal volumes of water and the n-octane excess phase to keep the composition of the interfacial film constant. (bottom) δ versus 1/γ - 1 plot to determine the composition of the interfacial film δi according to eq 4. (O) represents the X-point (γ˜ , δ˜ ) and the composition where the three-phase body appears (γ0, δ0).
phase region at φ ) 0.5 (which corresponds to R ) 0.39). In these measurements δ was adjusted until equal volumes of the water and n-octane excess phase signaled that the system is balanced, and thus the curvature of the interfacial film was kept constant. As is illustrated in Figure 6 (top) by the test tubes, the middle-phase first appears at γ0 ) 0.016 ( 0.003. With increasing γ, the volume fraction of the middle-phase Vc/ Vtotal increases linearly. At γ˜ ) 0.161 ( 0.005 the X-point is reached and Vc/Vtotal ) 1; that is, the whole test tube only contains the microemulsion. Here, γ0 denotes the sum of C8G1 and C8E0 solubilized monomerically in D2O and n-octane, respectively. To determine both solubilities individually, we apply the approach of Kunieda and coworkers.54,55 Following their work and neglecting the
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solubilities of n-octanol in D2O and of C8G1 in n-octane, the relevant relation is
[
(1 - δi)γD,mon,b
δ) R
(1 - γD,mon,b) γC,mon,aδi 1 1 - 1 + δi ) A - 1 + δi (4) (1 - R) γ (1 - γC,mon,a) γ
]( )
( )
In Figure 6 (bottom) the cosurfactant to surfactant plus cosurfactant ratio δ in the middle of the three-phase region is plotted versus (1/γ - 1). As one can see, all data points fall onto a straight line ranging from the X-point (δ˜ , γ˜ ) to the point where the three-phase region disappears (δ0, γ0). At this point, δ0 ) 0.86 ( 0.06. Furthermore, the intercept with the δ-axis yields the composition of the interfacial film δi ) 0.21 ( 0.06 at the considered value of R ) 0.39. When δ0 and γ0 are known, the monomeric solubilities of C8G1 in water
γC,mon,a )
(1 - δ0)γ0 γ0 - δ0γ0 + (1 - R)(1 - γ0)
(5)
and of C8E0 in n-octane
γD,mon,b )
δ0γ0 γ0 - (1 - δ0)γ0 + R(1 - γ0)
(6)
can be calculated.54,55 One finds that γD,mon,b ) 0.0347 ( 0.0007 is almost 1 order of magnitude larger than γC,mon,a ) 0.0037 ( 0.0004. It is interesting to compare the latter value with the cmc of C8G1 in H2O, which is 0.0073,56 that is, roughly twice the value found in D2O. To further investigate to what extent the value of δi influences the phase behavior and other important features of quaternary microemulsions, the knowledge of δi together with the monomeric solubilities along the trajectory of the middle-phase is essential information. From ternary CiEj microemulsions it is known that the monomeric solubilities vary with temperature.42 In the quaternary temperature-insensitive C8G1 system, the corresponding variable to temperature is apparently the composition of the interfacial film (see also below). Therefore, we measured the monomeric solubility of n-octanol in the oil-rich excess phase γD,mon,b as a function of δi. Since the corresponding monomeric solubility of C8G1 in water is small (γD,mon,b . γC,mon,a), it was assumed to be constant, that is, not a function of δi. To determine the variation of γD,mon,b with δi, samples were prepared along a titration line within the threephase region starting from a C8G1 weight fraction of γc ) 0.04 at different values of φ (0.4, 0.5, 0.6). After phase separation, the density of the oil excess phase is measured using a digital densiometer. Under the assumption that only cosurfactant is dissolved in the oil excess phase, the amount of n-octanol in n-octane can easily be determined via comparison with a calibration line (for details, see ref 40). In Figure 7 (top), this procedure is illustrated for φ ) 0.5 and T ) 25.0 °C. The procedure was limited to the three-phase region for the following reasons: in the 2 region the phase separation process is very slow, whereas in the 2 h region the oil-rich phase is no longer the excess phase. Knowing the amount of n-octanol in n-octane γD,mon,b and taking into account the monomeric solubility of C8G1 in D2O, the fraction of C8E0 and C8G1 residing at the (56) Pastor, O.; Junquera, E.; Aicart, E. Langmuir 1998, 14, 2950.
Figure 7. (top) Density of n-octane-C8E0 mixtures as a function of the mass fraction of C8E0 at T ) 25.0 °C. (b) represents the densities of the oil excess phase, separated from the sample in the three-phase region. γD,mon,b can be determined by comparing these densities with the calibration curve (]). (bottom) Amount of C8E0 dissolved monomerically in n-octane γD,mon,b versus the composition of the interfacial film δi determined by taking into account both γD,mon,b and the amount of C8G1 dissolved monomerically in D2O. Note that the linear correlation of γD,mon,b and δi implies a constant partition coefficient of C8E0 between n-octane and the interfacial film.
interface and, therefore, the composition of the interface δi can be calculated for any composition along the titration line. In doing so, one implicitly assumes that the concentration of C8E0 and C8G1 in the excess oil and excess water phase equals the monomeric C8E0 and C8G1 concentration in the oil and water domains in the microemulsion. In Figure 7 (bottom), γD,mon,b is plotted versus δi. All data points can be described by the relation
γD,mon,b ) 0.2345δi - 0.0134
(7)
It should be noted that a distribution coefficient of C8E0 between n-octane and the interfacial film independent of the water to oil ratio is found. We note that this finding is not an assumption but is an experimental observation. Since structural aspects, for example, the variation of the curvature of the amphiphilic film, play a decisive role in the theoretical description of microemulsions, volume
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Figure 8. Composition of the interfacial film δV,i as a function of the monomerically dissolved C8E0 in n-octane φD,mon,b at the X-points (left φ ) 0.10, right φ ) 0.913) calculated from eqs 10 and 11. Note that φD,mon,b increases with increasing δV,i, as do the monomeric solubilities of CiEj surfactants in n-alkanes with increasing temperature.42
fractions are used as compositional variables in what follows. The analogues to γC,mon,a, γD,mon,b, and δi are
φC,mon,a )
φC,mon φA + φC,mon
(8)
φD,mon,b )
φD,mon φB + φD,mon
(9)
and
δV,i )
φD - φD,mon ) φD - φD,mon + φC - φC,mon φD,mon,bφB φD (1 - φD,mon,b) (10) φD,mon,bφB φC,mon,aφA φD + φC (1 - φD,mon,b) (1 - φC,mon,a)
In eqs 8-10, φi are the volume fractions of the components, and φC,mon and φD,mon are the volume fractions of C8G1 and C8E0 monomerically solubilized in the overall mixture. Combining eq 7 with eqs 8-10 yields
φD,mon,b ) 0.1701δV,i - 0.0147
(11)
Thus, the composition of the internal interface δV,i and the monomeric solubility φD,mon,b along the trajectory of the middle-phase can be calculated by solving eqs 10 and 11 for the compositions of the X-points. The results are shown in Figure 8, where δV,i is plotted as a function of φD,mon,b. As can be seen in Figure 8, δV,i increases with increasing monomeric solubility φD,mon,b. The data point at the smallest δV,i corresponds to the X-point at φ ) 0.10, and the point at the highest δV,i, to the X-point at φ ) 0.913. This behavior is analogous to the temperature dependence of the monomeric solubility of the CiEj surfactants in n-alkanes.42 In ternary and quaternary systems, the monomeric
Figure 9. Trajectories of the middle-phase with (O) and without (b) taking into account the monomerically dissolved C8E0 in n-octane and C8G1 in D2O. (top) Volume fraction of C8G1 and C8E0 in the overall mixture φC+D and in the interfacial film φC,i+D,i as a function of φ. (bottom) C8E0/(C8G1 + C8E0) volume fraction in the overall mixture δV and in the interfacial film δV,i as a function of φ. While δV increases more with increasing φ, the δV,i(φ) trajectory of the middle-phase has a sigmoidal shape as is known for the T(φ) trajectory in ternary CiEj systems.4,24
solubility of CiEj surfactants and alcohols in n-alkanes increases with temperature and δV,i, respectively. F. Trajectory of the Middle-Phase. Having determined the relation between δV,i and φD,mon,b, the trajectory of the middle phase can be calculated taking into account the monomerically dissolved C8E0 in n-octane and C8G1 in D2O. The compositions of the X-points along the trajectory of the middle-phase together with the fraction of C8G1 and C8E0 in the internal interface are compiled in Table 1. In Figure 9 (top), the volume fraction of C8G1 and C8E0 in the overall mixture φC+D (b) is shown together with that in the interfacial film φC,i+D,i (O) as a function of φ. Qualitatively both trajectories have a similar shape of an almost symmetric parabola. While on the water-rich side the trajectories nearly match, with increasing φ, that is, amount of n-octane, the φC,i+D,i(φ) parabola is increasingly lowered with respect to the φC+D(φ) line. This behavior can be attributed to the large monomeric solubility of C8E0 in n-octane, which is 1 order of magnitude larger than
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that of C8G1 in D2O. The influence of the monomeric solubilities on the trajectory of the middle phase becomes particularly clear if the C8E0/(C8G1 + C8E0) volume fraction in the overall mixture δV and that in the interfacial film δV,i are plotted as a function of φ. As is evident in Figure 9 (bottom), δV (b) is increasingly increasing with φ. Taking into account the monomeric solubilities, the main part of C8E0 is dissolved in n-octane and is therefore not available for the internal interface. As a result, the δV,i(φ) (O) trajectory increases continuously, displaying a sigmoidal shape. The appearance of the δV,i(φ) trajectory resembles the corresponding quantity in temperature-dependent ternary CiEj systems, where the projection onto the A-B-T face of the phase prism is sigmoidal.5 For these systems, two of us have shown that the trajectories collapse onto a single curve, if the surfactant scale is reduced by the maximum of the parabolic trajectory and if the temperature is reduced by the difference of the upper and lower critical end point temperatures, Tu - Tl.24 A scaling description could be developed,26 which we will extend here to quaternary systems. IV. Discussion As already indicated in the Introduction, the understanding of the complex phase behavior of the quaternary systems is possible if the bending energy of the systems is considered. The key assumption is that the spontaneous curvature and the elastic moduli of the amphiphilic film determine the equilibrium structures and thereby the phase behavior. In order for the bending approach to be applicable, the length scale of the local structure has to be large compared to the range of molecular interactions. This fact suggests an analogy to critical phenomena. Upon approaching the critical point, the correlation length scale exceeds the range of molecular interactions, and all systems behave similarly, if one treats them in suitable reduced variables. A law of corresponding states can be formulated. With this in mind, it seems likely that one can rationalize the observed phase behavior of the model system watern-alkane-n-alkyl glycoside-n-alcohol. It had been observed previously that under normal conditions (1 bar, 25 °C) n-alkyl glycoside systems formed o/w microemulsions which did not change noticeably when temperature was increased up to the boiling point, nor did the addition of salt change the situation. However, when adding a medium-chain alcohol, that is, a relatively hydrophobic cosurfactant, the full Winsor phase progression can be observed. The picture is as follows: The ternary system water-n-octane-C8G1 forms at 50:50 water/oil and, say, 10% surfactant an o/w microemulsion. Only small amounts of the oil are solubilized. As one adds alcohol, the sparingly water-soluble alcohol mixes into the surfactant layer, thereby lowering its curvature. Note that a sugar headgroup is much larger than the OH-group of the alcohol. As the alcohol, which partitions between the bulk water phase, the bulk oil phase, and the amphiphilic film, increases in concentration, the film is enriched in alcohol and changes its curvature until it inverts to form a w/o microemulsion. This change in curvature with increasing fraction of alcohol in the interfacial film δi (i.e. δV,i) is qualitatively discussed by Kluge et al. (see Figure 857). They concluded that δi is the tuning parameter in quaternary temperature-insensitive n-alkyl glycoside systems corresponding to the role of the temperature in (57) Kluge, K.; Stubenrauch, C.; Sottmann, T.; Strey, R. Tenside, Surfactants, Deterg. 2001, 38, 30.
Figure 10. Reduced representations of the trajectories of the middle-phase for the temperature-dependent system H2O-noctane-CiEj24 and the quaternary D2O-n-octane-C8G1-C8E0 system. (top) Volume fraction of surfactant or surfactantcosurfactant mixture in the interfacial film reduced by the maximum of each trajectory versus φ. (bottom) Reduced red temperature τ and composition of the interfacial film δV,i versus φ. Note that for both representations all trajectories collapse onto a single curve.
the ternary water-oil-CiEj systems.23-26 Since all ternary CiEj systems behave quantitatively similarly if appropriate reduced parameters are considered,24-26 this scaling procedure has to be adapted to the present quaternary system. In the following, we introduce the relevant reduced parameters, which have to be defined in order to normalize the trajectory of the middle-phase and thus the phase behavior of the quaternary water-n-octane-C8G1-C8E0 system onto that of the ternary CiEj systems. Starting with the φC,i+D,i(φ) trajectory, every data point has to be divided by the maximum of the trajectory φ h C,i+D,i. In Figure 10 (top), the reduced trajectory of the C8G1 system is shown together with the reduced trajectories of five ternary water-n-octane-CiEj systems.24 As can be seen, all trajectories collapse onto a single curve, independently of whether they describe the phase behavior of three- or four-component systems. To reduce the δV,i(φ) trajectory of the middle-phase, one has to adapt the scaling procedure, which was used to
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Table 1. Compositions of the X-Points along the Trajectory of the Middle Phase in Mass Fraction (r, γ, and δ) and red Volume Fraction (O, OC, OD, OC,i, OD,i) Together with the Reduced Parameters δV,i and OhC,i+D,i R
γ
δ
φ
φC
φD
φC,i
φD,i
φC,i+D,i/φ h C,i+D,i
δV,i
red δV,i
0.0660 0.1371 0.2141 0.2550 0.2977 0.3422 0.3887 0.4373 0.4881 0.5414 0.5973 0.7178 0.7827 0.8512 0.8697
0.0633 0.0936 0.1221 0.1487 0.1627 0.1644 0.1609 0.1646 0.1668 0.1603 0.1530 0.1286 0.1130 0.0887 0.0888
0.1975 0.2190 0.2342 0.2286 0.2336 0.2482 0.2759 0.2837 0.3058 0.3275 0.3431 0.4121 0.4569 0.5558 0.5597
0.100 0.200 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.800 0.850 0.900 0.913
0.0478 0.0664 0.0820 0.0990 0.1058 0.1029 0.0950 0.0943 0.0908 0.0826 0.0753 0.0538 0.0420 0.0264 0.0260
0.0161 0.0254 0.0343 0.0401 0.0440 0.0464 0.0495 0.0510 0.0546 0.0550 0.0537 0.0515 0.0493 0.0451 0.0452
0.0448 0.0638 0.0797 0.0970 0.1039 0.1012 0.0935 0.0929 0.0895 0.0815 0.0743 0.0531 0.0416 0.0261 0.0257
0.0137 0.0205 0.0266 0.0317 0.0344 0.0350 0.0353 0.0354 0.0363 0.0342 0.0312 0.0236 0.0187 0.0118 0.0115
0.4459 0.6425 0.8110 0.9802 1.0541 1.0381 0.9817 0.9779 0.9596 0.8826 0.8049 0.5846 0.4596 0.2881 0.2843
0.2341 0.2427 0.2506 0.2462 0.2499 0.2567 0.2744 0.2756 0.2885 0.2959 0.2954 0.3070 0.3103 0.3114 0.3103
-0.9115 -0.7002 -0.5061 -0.6150 -0.5233 -0.3563 0.0786 0.1081 0.4251 0.6069 0.5946 0.8796 0.9607 1.0000 0.9607
reduce the temperature in ternary CiEj systems to the tuning parameter composition of the interfacial film δV,i. The essential parameters are the lower limit δV,i,l, the upper limit δV,i,u, and the mean δV,i,m (δV,i,m ) (δV,i,l + δV,i,u)/ 2) of the three-phase region. δV,i,l and δV,i,u can be determined from limiting values of the δV,i(φ) trajectory for small and large φ. One finds that δV,i,l ) 0.23 ( 0.02, δV,i,u ) 0.31 ( 0.01, and consequently δV,i,m ) 0.27 ( 0.02. In analogy with the procedure used for the reduced temperature,
τ)
2(T - Tm) Tu - T1
(12)
a reduced composition of the internal interface red ) δV,i
2(δV,i - δV,i,m) (δV,i,u - δV,i,1)
(13)
can be defined. When the reduced τ(φ) trajectory of the ternary water-n-octane-CiEj systems24 is plotted together red (φ) trajectory of the nearly temperaturewith the δV,i independent quaternary C8G1 system, all data points fall onto one single curve. As can be seen in Figure 10 (bottom), the sigmoidal shape of the trajectory remains unchanged. red and The numerical values of the reduced parameters δV,i h C,i+D,i are also compiled in Table 1. φC,i+D,i/φ The significance of the observed scaling of the quaternary system along with the previous scaling of the ternary systems is that the assumptions concerning the role of temperature T and fraction δV,i of n-octanol in the film are
indeed correct: In both cases the spontaneous curvature is tuned. As Kahlweit emphasized,42 the equivalence is a consequence of the Gibbs-Duhem equation
0 ) SdT +
∑i nidµi
(14)
which states that instead of changing temperature one may add a fourth component (at constant pressure). V. Conclusions The phase behavior of the four-component system water-n-octane-C8G1-n-octanol at 25.0 °C has been determined. The trajectory of the middle-phase has been determined as the amphiphilic mixture was varied so that the phase inversion was passed. It is found that the fraction of n-octanol in the mixture of the two amphiphiles that constitute the amphiphilic film plays the same role as the temperature T in the conventional water-n-alkane-CiEj systems. Therefore, the trajectory of the middle-phase microemulsion of the quaternary C8G1 system falls onto the trajectories of conventional temperature-sensitive ternary microemulsions if the tuning variable temperature is exchanged for the variable composition of the mixed amphiphilic film. The logic consequence of the observed phase behavior is that the underlying microstructure should vary from o/w microemulsion droplets at low n-octanol fractions to bicontinuous to w/o microemulsion droplets as the fraction of n-octanol in the film increases. That this sequence is indeed observed will be shown in a forthcoming paper. LA011665X
