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Interfacial Films and Wetting Behavior of the Air/ Hexadecane/Aqueous Solution of a Surfactant System Makoto Aratono,*,† Hiroaki Kawagoe,† Takayuki Toyomasu,† Norihiro Ikeda,‡ Takanori Takiue,† and Hiroki Matsubara† Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan; and Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813-8529, Japan Received June 13, 2001. In Final Form: August 13, 2001 The tension of the three interfaces and the dihedral angle of the lens of the air/hexadecane lens/aqueous solution of tetramethylammonium dodecyl sulfate (TMADS) system were measured as a function of the surfactant concentration. The air/water surface tension vs concentration curves both with and without an oil lens exhibited a break point corresponding to the phase transition of the adsorbed films. From the thermodynamic analysis, it was shown that the phase transition drives the spreading of hexadecane molecules into the adsorbed film. The dihedral angle decreased very rapidly from about 50° at zero concentration to about 6° at the phase transition point and then increased slowly to about 20° at the critical micelle concentration (cmc), suggesting the very drastic change in wetting properties at the phase transition point. The plausible gap was observed between the dihedral angles measured and those calculated from the interfacial tension values at the concentration range from just above the phase transition to near the cmc. This suggests a case where the Neumann relation does not hold even when a lens exists stably. One of the possibilities may be that the wetting film is rather thick just above the phase transition point.

Introduction The macroscopic condition for the existence of a threephase contact line is that each of the three interfacial tensions is smaller than the sum of the other two. The triangle formed by the three interfacial tensions is called the Neumann triangle. Under this condition, a small amount of the middle phase contracts to form a lens at the interface. However, when the Neumann condition fails by changing the thermodynamic state such as temperature, pressure, and the surfactant concentration, the lens spreads at the interface. Ever since Cahn has suggested theoretically such a firstorder phase transition at an interface1 and Moldover and Cahn have demonstrated experimentally for the methanol/ cyclohexane/air system,2 this kind of wetting-nonwetting transition for air (or vapor)/liquid/liquid systems has been investigated by many workers.3-9 These are well summarized and reviewed also in some books.10-12 The wetting * To whom correspondence should be addressed. Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki 6-101, Higashiku, Fukuoka 812-8581, Japan. E-mail: m.arascc@ mbox.nc.kyushu-u.ac.jp. † Kyushu University. ‡ Fukuoka Women's University. (1) Cahn, J. W. J. Chem. Phys. 1977, 66. 3667. (2) Moldover, M. R.; Cahn, J. W. Science 1980, 207, 1073. (3) Pohl, D. W.; Goldburg, W. I. Phys. Rev. Lett. 1982, 48, 1111. (4) Telo da Gama, M. M.; Evans, R.; Hadjigapiou, I. Mol. Phys. 1984, 52, 573. (5) Schmidt, J. W.; Moldover, M. R. J. Chem. Phys. 1985, 83, 1829. Schmidt, J. W. J. Chem. Phys. 1986, 85, 3631. (6) Guha, G.; Vani, V. C.; Jayalaxmi, Y.; Kumar, A.; Ravi, R.; Gopal, E. S. R. J. Solution Chem. 1987, 16, 691. (7) Amara, M.; Privat, M.; Bennes, R.; Tronel-Peyroz, E. J. Chem. Phys. 1993, 98, 5028. (8) Neilson, M. M.; Bowers, J.; Manzanares-Papayanopoulos, E.; Howse, J. R.; Vergara-Gutierrez, M. C.; Clements, P. J.; Burgess, A. N.; McLure, I. A. Phys. Chem. Chem. Phys. 1999, 1, 4635. (9) Kahlweit, M.; Busse, G.; Haase, D.; Jen, J. Phys. Rev. 1988, A 38, 1395. (10) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Oxford University Press: New York, 1982; Chapter 8.

properties of three liquid-phase systems such as watersurfactant-oil mixtures have been also inspected and examined mainly from the viewpoint of the structure of the middle phase microemulsions.13-17 Furthermore, the wetting and other interfacial properties of alkane molecules in the surfactant adsorbed films at the air/aqueous solution interface have been investigated extensively by the thermodynamic analysis of the surface tension data,18-21 the structure and composition analysis of the neutron reflection,21 the ellipsometry,22,23 and the vis(11) Israelachivili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1991; Chapter 11. (12) Davis, H. D. Statistical Mechanics of Phases, Interfaces, and Thin Films; VCH Publishers: New York, 1996; Chapters 7 and 13. (13) Shinoda, K. Prog. Colloid Polymer Sci. 1983, 68, 1. (14) Kahlweit, M.; et al. J. Colloid Inteface Sci. 1987, 118, 436. Kahlweit, M.; Busse, G. J. Chem. Phys. 1989, 91, 1339. Kahlweit, M.; Strey, R.; Aratono, M.; Busse, G.; Schubert, K.-V. J. Chem. Phys. 1991, 95, 2842. Aratono, M.; Kahlweit, M. J. Chem. Phys. 1991, 95, 8578; 1992, 97, 5932. Kahlweit, M.; Strey, R.; Busse, G. Phys. Rev. 1993, E47, 4197. (15) Robert, M.; Jeng, J. F. J. Phys. Fr. 1988, 49, 1821. Chen, L.-J.; Jeng, J.-F.; Robert, M.; Shukla, K. P. Phys. Rev. 1990, A42, 4716. Chen, L.-J.; Yan, W.-J.; Hsu, M.-C.; Tyan, D.-L. J. Phys. Chem. 1994, 98, 1910. (16) Schubert, K.-V.; Strey, R. J. Chem Phys. 1991, 95, 8532. Schubert, K.-V.; Strey, R.; Kline, S. R.; Kaler, E. W. J. Chem. Phys. 1994, 101, 5343. (17) Gomper, G.; Schick, M. Lattice Theories of Microemulsion. In Micelles, Membranes, Microemulsions, and Monolayer; Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; Springer-Verlag: New York, 1994; Chapter 8. (18) Aveyard, R.; Cooper, P.; Flecher, P. D. I. J. Chem. Soc., Faraday Trans. 1990, 86, 3623. (19) Aveyard, R.; Binks, B. P.; Flecher, P. D. I.; MacNab, J. R. Langmuir 1995, 11, 2515. (20) Jayalalshmi, Y.; Langevin, D. J. Colloid Interface Sci. 1997, 194, 22. (21) Lu, J. R.; Thomas, R. K.; Aveyard, R.; Binks, B. P.; Cooper, P.; Flecher, P. D. I.; Sokolowski, A.; Penfold, J. J. Phys. Chem. 1992, 96, 10971. Lu, J. R.; Li, Z. X.; Thomas, R. K.; Binks, B. P.; Crichton, D.; Flecher, P. D. I.; McNab, J. R.; Penfold, J. J. Phys. Chem. B 1998, 102, 5785. Lu, J. R.; Thomas, R. K.; Binks, B. P.; Flecher, P. D. I.; Penfold, J. J. Phys. Chem. 1995, 99, 4113. (22) Kellay, H.; Meunier, J.; Binks, B. P. Phys. Rev. Lett. 1992, 69, 1220.

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coelastic properties.20 Among them, Bain et al.23 have proved, and Aveyard et al.18 and Jayalakshmi et al.20 have referred to, the first-order phase transition of the mixed monolayers of the alkane and surfactant. Recently two kinds of the wetting transition have been reported for the alkane/water/air and alkanol/alkane/air systems by using the ellipsometry; the first order (discontinuous) transition takes place between the microscopic and mesoscopic films under the presence of a lens at a temperature far from the bulk critical temperature and the critical (continuous) wetting transition from the mesoscopic to a macroscopic film very near to the bulk critical temperature.24 These experimental findings have confirmed the theoretical predictions25,26 and demonstrated the importance of long-range forces between the interfaces below and above the thin film.11 We have reported the wetting behavior of an alcohol lens of the water/long chain alcohol/air systems by measuring the dihedral angles and the three interfacial tensions as a function of temperature under atmospheric pressure.27 Taking account of the phase transitions of the water/alkanol interfacial films28 and the soluble monolayers of alkanols at the air/water interfaces,29,30 it was shown for the water/undecanol/air system that the phase transition of the water/alkanol interfacial film drives the intruding small lens of the water phase into the air/alkanol interface and on the other hand, the phase transition of the alkanol/air interfacial film inhibits the nonwettingwetting transition. These findings suggest that the phase transition of interfacial films has a strong effect on the wetting behavior. The purpose of this paper is to examine the relationship between the wetting behavior of alkane lens floating at the air/aqueous solution of a surfactant and the phase transition of the adsorbed film at the air/its aqueous solution interface31 by measuring the three interfacial tensions as a function of the surfactant concentration and the dihedral angle of the alkane lens and then by analyzing the data according to the thermodynamic equations developed previously.32 Experimental Section Materials. n-Hexadecane of the high purity of more than 98% was purchased from Tokyo Kasei Kogyo Co. Ltd. (Japan) and distilled fractionally under reduced pressure. Its boiling point was 430-431 K at 3.8 mmHg. The purity was estimated to be more than 99.7% by a gas-liquid chromatography (column, silicon OV-101; column temperature, 323-523 K by temperature(23) McKenna, C. E.; Knock, M. M.; Bain, C. D. Langmuir 2000, 16, 5853. (24) Ragil, K.; Meunier, J.; Broseta, D.; Indekeu, J. O.; Bonn, D. Phys. Rev. Lett. 1966, 77, 1532. Shahidzadeh, N.; Bonn, D.; Ragil, K.; Broseta, D.; Meunier, J. Phys, Rev. Lett. 1998, 80, 3992. Indekeu, J. O.; Ragil, K.; Bonn, D.; Broseta, D.; Meunier, J. J. Stat. Phys. 1999, 95, 1009. Ross, D.; Bonn, D.; Meunier, J. Nature 1999, 400, 737. Bertrand, E.; Dobbs, H.; Broseta, D.; Indekeu, J. O.; Bonn, D.; Meunier, J. Phys. Rev. Lett. 2000, 85, 1282. Ross, D.; Bonn, D.; Meunier, J. J. Chem. Phys. 2001, 114, 2784. (25) Nakanishi, H.; Fisher, M. E. Phys. Rev. Lett. 1982, 49, 1565. (26) Lipowski, R.; Kroll, D. M. Phys. Rev. Lett. 1984, 52, 2303. (27) Aratono, M.; Toyomasu, T.; Shinoda, T.; Ikeda, N.; Takiue, T. Langmuir 1997, 13, 2158. Toyomasu, T.; Takiue, T.; Ikeda, N.; Aratono, M. Langmuir 1998, 14, 7313. (28) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1992, 96, 9422. Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1993, 97, 5141. (29) Casson, B. D.; Braun, R.; Bain, C. D. Faraday Discuss. 1996, 104, 209. (30) Casson, B. D.; Bain, C. D. J. Phys. Chem. B. 1998, 102, 7424. Casson, B. D.; Bain, C. D. J. Phys. Chem B. 1999, 103, 4678. Casson, B. D.; Bain, C. D. J. Am Chem. Soc. 1999, 121, 2615. (31) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 93, 33. (32) Aratono, M.; Toyomasu, T.; Ikeda, N.; Takiue, T. J. Colloid Interface Sci. 1999, 218, 412.

Langmuir, Vol. 17, No. 23, 2001 7345 programmed analysis) and confirmed by the absence of time dependency of the interfacial tension against water. Ionexchanged water was distilled, refluxed, and then finally distilled under the presence of alkaline permanganate. Tetramethylammonium dodecyl sulfate (TMADS), an anionic surfactant, was synthesized as follows:33,34 1-dodecanol distilled under reduced pressure (370 K at 1 mmHg) was sulfonated at around 276 K with chlorosulfonic acid in ether and then neutralized by the aqueous solution of tetramethylammonium hydroxide. The product was freeze-dried by a dehydration equipment. The obtained crystals were purified by recrystallization from 2-propanol solution for three times and from ethanol solution for two times. The purity was confirmed by observing no time dependence of interfacial tension and no minimum on the interfacial tension vs concentration curves around the critical micelle concentration. Interfacial Tension. There are three kinds of interfaces for the system of a floating oil lens (phase O) at the air (phase A)/ aqueous solution (phase W) interface. Let γAW, γOW, and γAO refer to the air/water, oil/water, and air/oil interfacial tensions, refer to the air/water interrespectively. Furthermore, let γAW 0 facial tension in the absence of an oil lens. They were measured as a function of the molality mW 4 of TMADS in the aqueous solution at 298.15 ( 0.01 K by a shape analysis of a pendant drop hanging on a glass capillary tip.27,35,36 The interfacial tension was calculated by using the equation

γRβ ) ∆FRβgde2/H

(1)

where ∆FRβ, g, de, and H are the density difference between the R and β phases, the acceleration of gravity, the maximum diameter of the equatorial plane of the drop, and the correction factor. The equation proposed by Misak37 was employed for estimating H values in this study. It was confirmed that the solubility of the surfactant in the oil phase is negligibly small, so that the quantity ratio, oil/water/ surfactant, does not change any kind of interfacial tension. A great care was taken on the measuring procedure to ensure the thermal and adsorption equilibrium and this was confirmed by observing that all the interfacial tensions were reproducible within 0.05 mN m-1 and exhibited no time dependence. Dihedral Angle. The angle between the A/O interface and the plane of the three-phase contact line, θU, and the angle between the O/W interface and the plane, θL, was measured as a function of the molality of TMADS at 298.15 K by using a drop shape analysis based upon the Young-Laplace equation of capillarity. Then the dihedral angle of a lens interposing the oil phase, θO, was calculated as the sum of θU and θL. The equipments and procedure for the angle measurements have been described in detail in our previous paper.27 To avoid the effect of line tension, the sizes of lenses were about 3 mm to 6 mm in their diameters.

Results and Discussion Figure 1 shows the interfacial tension vs molality curves of three kinds of interfaces for the air/hexadecane lens/ aqueous solution of TMADS system at 298.15 K under atmospheric pressure. The A/W interfacial tension γAW decreases only slightly and almost linearly at very low concentrations, passes through a break point, and then decreases steeply up to the critical micelle concentration (cmc) of TMADS in the aqueous solution. Let us desig. The O/W nate the molality at the break point by mW,eq 4 interfacial tension γOW decreases with the concentration in a manner similar to the γAW value, but the break point at a very low concentration is not observed. The A/O (33) Szajdzinska-Pietek, E.; Maldonado, R.; Kevan, L.; Berr. S.; Jones, R. R. M. J. Phys. Chem. 1985, 89, 1547. (34) McIntire, G. L. J. Electrochem. Soc. 1981, 128, 427c. (35) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 523. (36) Rusanov, A. I.; Prokhorov, V.A. Interfacial Tensiometry; Elsevier, Amsterdam, 1996; p 101. (37) Misak, M. D. J. Colloid Interface Sci. 1968, 27, 141.

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Figure 3. Angles vs concentration curves: (1) dihedral angles; (2) the lower angles; (3) the upper angles.

Figure 1. Interfacial tension vs concentration curves with an oil lens: (1)γAW; (2) γAO; (3) γOW.

Figure 4. Schematic representation of a lens and the definition of the angles.

Figure 2. A/W interfacial tension with and without a lens vs concentration curves: (1) without a lens; (2) with a lens.

interfacial tension γAO was not varied appreciably with the concentration. To demonstrate how the oil lens affects the A/W interfacial tension, the interfacial tension values in the were also measured and comabsence of the lens γAW 0 pared to the γAW values in Figure 2, where the magnified figure of the low concentration region is also inserted. It is found that there is no difference between them at low concentrations. This may suggest that hexadecane molecules do not spread at all or so much on the A/W interface that the interfacial tension is not influenced. However, the difference in the interfacial tension appears suddenly and evidently by a further increase of the concentration; in the the break point exists at the lower molality mW,eq 4 presence of an oil lens compared to the molality at the in the absence of the lens and, the break point mW,eq 4,0 shape of the curves above the break points are different

from each other. Therefore, it is expected that a certain amount of hexadecane molecules are spread at the A/W interface above mW,eq . However, judging from that the 4 γAW values are still much higher than the γOW values, the quantity of oil molecules spread is expected to be not so large. Figure 3 shows the experimental values of θU and θL and the dihedral angle θO ) θU + θL vs molality curves. It is seen that the θO value decreases very rapidly from and about 50° at zero concentration to about 6° at mW,eq 4 then increases slowly to about 20° at the cmc. Comparing AW vs mW, we notice that the the θO vs mW 4 curve with the γ 4 change in the shape of the lens is mainly responsible for that in the O/W interfacial state as will be mentioned later. Now, let us analyze the results of the interfacial tension and the dihedral angles by using the thermodynamic relations to shed light on the states of the interfacial films and wetting behavior of the air/water interface. In our previous paper,32 we have developed the general form of the thermodynamic equations of interface formation and adsorption of surfactants at the interface with a floating lens and then derived the equations applicable to a simple case such as schematically shown in Figure 4. Here the A/W interface is assumed to be planar (the experimental value of θM was in the range of zero to about 3 at almost all concentrations), while the A/O and O/W interfaces are curved and then the hydrostatic pressure of the inside of a lens pO is different from that of the outside, p. Hereafter, subscripts 1-4 refer to water, air, hexadecane, and TMADS, respectively. It is indispensable that quantities inherent in the interfacial region are defined in terms of surface excess quantities with respect to the bulk phases being relevant to the formation of the interface.38,39 For (38) Defay, R.; Prigogine, I.; Bellemans, A. Surface tension and adsorption (translation, Everett, D. H); Longmans: Harlow, England, 1966; Chapters 2 and 7. (39) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348.

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this purpose, two advantageous ways have been proposed in our previous paper.32 The first is called the H convention, where the air and water phases are chosen as the reference phases and the A/W interfacial tension is a function of temperature T, pressure p, the chemical potential of hexadecane µ3, and that of TMADS µ4. Employing this convention, γAW is expressed as a function of T, p, and the molalities mW 3 and mW as 4 H AW H dγAW ) -∆AW W s dT + ∆W v dp W H,AW W (RT/mW (2RT/mW ΓH,AW 3 3 ) dm3 - Γ4 4 )dm4 (2)

The second is called the P convention, where all the three phases are chosen as the reference phases and all the interfacial tensions are considered to be a function of T, p, pO, and µ4. Within the P convention, γAW is expressed as a function of T, p, pO, and mW 4 as AW P P P,O ) dp + vP,O dpO dγAW ) -∆AW W s dT + (∆W v - v W ΓP,AW (2RT/mW 4 4 ) dm4 (3) AW R R,AW R are the In eqs 2 and 3, ∆AW W s and ∆W v , and Γ4 entropy and volume changes associated with adsorption and interfacial density of TMADS at the A/W interface in the convention R (R ) H,P) and vP,O is the thickness of the reference oil phase at the A/W interface, respectively. Although both conventions are correct and respectively have some advantages, the P convention is chosen in this study because of the following reasons. First, a thickness of the reference oil phase is introduced in the P convention. This may suggest the possibility that this thermodynamic treatment will be developed for a study of a thin film being in equilibrium with the lens at the A/W interface. Second, the partial derivative (∂pO/∂mW 4 )T,p can be assumed to be constant for a large lens employed in the ordinary experimental conditions. However, it is doubtful whether W the derivative (∂mW 3 /∂m4 )T,p is assumed to be constant or not even for a large lens, e.g., air/oil/aqueous solution of a nonionic surfactant system where the surfactant is soluble in the oil phase as well as in the water phase. Finally, the P convention shows the symmetry for the three interfaces. For example, the interfacial density of the Rβ interface can be estimated by

W Rβ ) - (mW ΓP,Rβ 4 4 /2RT)(∂γ /∂m4 )T,p,pO

(4)

with respect to three interfaces in the P convention. However, in the H convention, the interfacial density is estimated by using different equations for the A/W and O/W interfaces and the A/O interface.32 This final point comes from the fact that the three phases participate equally in defining the surface excess quantities in the P convention but unequally in the H convention. The interfacial densities were evaluated by applying eq 4 to the interfacial tension vs mW 4 curves given in Figure 1 and shown in Figures 5 and 6. Figure 5 reveals that the air/water interfacial density in the absence of the oil lenses, ΓAW 4,0 , increases linearly at very low concentrations, changes abruptly at mW,eq 4,0 , and then increases monotonically up to the cmc. Judging from the areas occupied by one TMADS molecule just below and above the discontinuous change, the abrupt change is resulted from the phase transition of adsorbed film from the gaseous to the expanded state.27,30,31 The A/W interfacial density in , traces correctly ΓAW the presence of the oil lens, ΓP,AW 4 4,0 vs

Figure 5. A/W interfacial density with and without a lens vs concentration curves: (1) without a lens; (2) with a lens.

Figure 6. Interfacial density vs concentration curves: (1) A/W interfacial density with a lens; (2) O/W interfacial density.

mW 4 in the gaseous state. Furthermore, we note that the presence of oil molecules in the adsorbed film enhances the adsorption of surfactant molecules at a relatively low interfacial density but retards it at a relatively high interfacial density. The one of the important differences between the two is definitely smaller than mW,eq cases is that mW,eq 4 4,0 ; the phase transition is induced at a lower value of the interfacial density by the presence of an oil lens. Hexadecane molecules exist in the air phase or oil lens, or maybe even in the A/W interface as mentioned above, and they can be in contact with TMADS molecule adsorbed at the A/W interface through the air phase or the three-phase contact line, or directly. Then the penetration of hexadecane molecules into the adsorbed film takes place due to the interaction between the hydrophobic chains of oil and surfactant molecules. This helps the phase transition of the adsorbed film.

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In Figure 6 are compared the O/W interfacial density ΓP,OW with the A/W interfacial density ΓP,AW in the 4 4 presence of an oil lens. It is noted that the former goes up monotonically without a discontinuous change and is . Also larger than the latter at concentrations below mW,eq 4 it is substantial that both the interfacial tension and density at the O/W interface are definitely different from the corresponding ones at the A/W interface. Therefore, the thickness of oil layer spread at the A/W interface is suggested to be so thin, probably several molecular layers, that surfactant molecules at the A/W interface can feel the presence of the air phase even in the presence of this thin oil films. The studies on the structure by neutron reflection and/or on the thickness by ellipsometry of this mixed adsorbed film may draw a conclusion.21-23 Summarizing the results of Figures 5 and 6, we can say that the hexadecane lens is in equilibrium with the A/W adsorbed film containing (almost) no hexadecane molecules before the phase transition point, but it is in equilibrium with the A/W adsorbed film containing thin, molecular level hexandecane films above the phase transition point. This means that the transition between nonspread and spread states of hexadecane molecules is induced by the phase transition of the adsorbed film and vice versa. In this respect, the phase transition of adsorbed film and the nonspread-spread transition is said to be cooperative. With respect to the solubilization of hydrocarbons in surfactant monolayers,18 Aveyard et al. have referred to the possibility of some kind of phase changes within the monolayers judging from the discontinuities of the ratio Γa/Γs and the film thickness δ vs Γs plots, where Γa and Γs are the surface concentration of alkane and surfactant and δ the average film thickness. Furthermore, they have reported that the surface concentration of tetradecyltrimethylammonium bromide with dodecane and that without dodecane are inversed at a lower surfactant concentration.21 Although the authors have not drawn any conclusion on the existence of a phase transition and the inversion, the present results and thermodynamic analysis demonstrate them. Now let us move on to the examination of the relation between the dihedral angle, interfacial tensions, and interfacial densities. The Neumann relation for the dihedral angle θO is given by

cos θO ) [(γAW)2 - (γAO)2 - (γOW)2]/2γAOγOW

(5)

where the line tension effect is assumed to be negligible.10,27 This shows that the dihedral angle is determined by the values of the interfacial tension themselves. On the other hand, the change of the dihedral angle with the concentration of the surfactant is correlated to the interfacial densities as W -(mW 4 /2RT)(∂(cos θO)/∂m4 )T,p,pO )

(γAW/γAOγOW)(ΓP,AW + ΓP,AO cos θA + ΓP,OW cos θW) (6) 4 4 4 Taking into account that the A/W interface is assumed to be planar and the A/O interfacial density of the surfactant ΓP,AO is almost zero, eq 6 is further simplified to 4 W (mW 4 /2RT)(∂θO/∂m4 )T,p,pO ≈ W P,AW (sin θO/sin θU sin θL)(mW - ΓP,OW cos θL) 4 /m3 )(Γ4 4 (7)

Therefore, the decrease or increase in θO with increasing

Figure 7. Dihedral angle vs concentration curves: (O) measured values; (-) calculated values. P,AW mW and ΓP,OW is 4 is closely related to which one of Γ4 4 larger than another. The experimental results demonstrated in Figure 3 show that the decrease in θO values changes suddenly to the increase with increasing the surfactant concentration at . Judging from the values the phase transition point mW,eq 4 of θU and θL (cos θL ) 0.94-0.99) given in Figure 3 and eq 7, the following approximate inequalities are expected W,eq < ΓP,OW at mW and ΓP,AW > ΓP,OW to be hold; ΓP,AW 4 4 4 < m4 4 4 W W,eq at m4 > m4 , respectively. Actually Figure 6 proves this expectation. Therefore, considering this observation together with the finding that hexadecane molecules do not W,eq , the steep spread at all at the concentrations mW 4 < m4 decrease in θO is not caused by the wetting of the A/W interface by the oil molecules but by the larger adsorption at the O/W interface compared to that at the A/W interface. Furthermore, taking note the relation

γAWcos θM ) γAOcos θU + γOWcos θL

(8)

and the experimental observation that cos θM ≈ 1 and W,eq , we have the cos θU ≈ cos θL ≈ 0.99 at mW 4 ) m4 approximate relation

γAW ≈ γAO + γOW

(9)

Then it can be said that the oil molecules spread and almost completely wet the interface just above the phase transition point. That means that the very drastic change in wetting properties happens at the phase transition point in the adsorbed film. Figure 3 shows that an oil lens is stable at all the concentrations. However, it was found that the condition of the stability of a lens for the interfacial tensions given by10

γAW < γAO + γOW

(10)

fails at a certain concentration range above mW,eq . This 4 is clearly shown by comparing the dihedral angle calculated from the interfacial tension values from eq 5, θO,c, with that measured from the experiments, θO. In Figure 7 are depicted the θO,c values by a solid line and the θO values by circles. The error bar corresponds to the scattering in θO,c values resulting from the reproducibility of the interfacial tensions. It is said that, even taking into account the experimental reproducibility of the interfacial

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tensions and dihedral angles, there exists a region where the dihedral angle should be zero judging from the Neumann relation. However, the experiments showed that oil lenses existed even at this region. The line tension effect is reasonably neglected in our present experiments because line tension has been estimated to be on the order of 10-10-10-11 N40 and the sizes of the oil lenses are on the order of millimeters. In our previous studies,27 we have claimed that θO and θO,c values are coincide with each other within the experimental error and, even when the small gap exists, this gap is observed at very high dihedral angles around 150° and is attributable to the meniscus near the three-phase contact line. In the present case, the discrepancy is observed at rather low dihedral angles, and the shape of the A/W interface near the three-phase contact line was confirmed to be almost planar. Although the purity of materials, the experimental procedure, and the reproducibility of angles and interfacial tensions were examined with great care, we found no essential problem. Furthermore, the very similar behavior to that demon-

strated in Figure 7 was observed also for the air/ hexadecane/aqueous solution of the dodecyltrimethylammonium bromide system.41 Taking all these things together into account, the gap between the values of θO and θO,c is plausible and suggests a case where the Neumann relation does not hold even when a lens exists stably. One of the possibilities may be that the thickness of the wetting film just above the phase transition point is so thick, although this may be inconsistent with our suggestion on the results in Figure 6, that the long-range forces such as the forces between the two surfaces above and below the wetting films is taken into account. It will be explained on the basis of further experimental results and theoretical consideration in our forthcoming paper.41

(40) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. Colloids Surf. A 1999, 146, 95.

(41) Matsubara, H.; Takiue, T.; Ikeda, N.; Aratono, M. Langmuir, to be submitted.

Acknowledgment. This work was supported in part by Grant-in-Aid for Exploratory Research No. 13874092 from Japan Society for the Promotion of Science. LA0108961