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J. Phys. Chem. B 1997, 101, 7952-7957
Self-Organizing Structures in Poly(oxyethylene) Oleyl Ether-Water System Hironobu Kunieda,* Kazuki Shigeta, and Kazuyo Ozawa DiVision of Artificial EnVironments Systems, Graduate School of Engineering, Yokohama National UniVersity, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240, Japan
Masao Suzuki Oleochemical Research Laboratory, NOF Corporation, Ohama-cho 1-56, Amagasaki 660, Japan ReceiVed: April 17, 1997; In Final Form: July 31, 1997X
A phase diagram of a water-poly(oxyethylene) oleyl ether (POlE) system was constructed as a function of poly(oxyethylene) chain length at 25 °C. The POlEs contain a highly pure oleyl group, whose purity is above 99.7%. The POlEs are in a liquid state over a wide range of composition. The increase in the poly(oxyethylene) (EO) chain of POlE corresponds to the increase in the curvature of surfactant layer toward water or the increase in HLB (hydrophile-lipophile balance) number of the surfactant. Various self-organizing structures were found: hexagonal and lamellar lquid crystals, four kinds of isotropic liquid crystals, a sponge phase, and reverse hexagonal liquid crystal. The phase transition between normal hexagonal and lamellar liquid crystals were investigated at constant volume fraction of the oleyl group in system by means of smallangle X-ray scattering. Correlation among the phase behavior, the packing of oleyl chain in self-organizing structures, and the HLB of POlE is discussed. The effect of temperature on the phase behavior in the present system is also discussed.
Introduction Various supramolecular assemblies are formed in watersurfactant systems. Types of the self-organizing structures are highly related to the curvature of surfactant molecular layer at the interface and the packing of aggregates in system.1,2 The phase behavior of poly(oxyethylene)-type nonionic surfactants in water has been extensively investigated.2-7 The hydrophilelipophile balance (HLB) of the surfactant or the curvature of the surfactant layer is highly influenced by temperature change because the conformation of the hydrophilic chain is changed with temperature8,9 and the dehydration of the hydrophilic moiety occurs at higher temperature. In most of previous studies,2-7 the binary water-surfactant phase diagrams have been constructed as a function of temperature. However, if the temperature is used as a variable, an additional factor such as thermal motion has to be considered together. Although one can expect the formation of lipophilic liquid crystal such as reverse hexagonal phase at higher temperature, it has been found that it is melted because the thermal motion overcomes the cohesive force of lipophilic chains of surfactants. The cohesive energy increases with the increase in the lipophilic chain of surfactant and the rich phase behavior would be expected in a long-lipophilic-chain surfactant system. In fact, various intermediate phases were found in C22 or C30 surfactant systems.10,11 However, if a long straight hydrocarbon chain surfactant (e.g. C16 or C18) is used, the melting temperature is raised and the Krafft temperature appears, especially in a short poly(oxyethylene) surfactant2,12 because the original long-chain alcohol (e.g. hexadecanol) is in a solid state at room temperature. On the other hand, there is a big advantage in the use of this kind of poly(oxyethylene)-type surfactants because the HLB number13 of the surfactant can be continuously changed by increasing the hydrophilic poly(oxyethylene) chain. Instead of changing temperature, we could construct a phase diagram as * Corresponding author. X Abstract published in AdVance ACS Abstracts, September 15, 1997.
S1089-5647(97)01332-1 CCC: $14.00
a function of the HLB number of surfactant or the poly(oxyethylene) chain length. It is considered that the mixing of surfactants with the different poly(oxyethylene) chains does not cause a serious change in the phase behavior in water.14 Monomeric solubility or cmc of the long-chain surfactant is extremely small and the homologues are very soluble in each other in aggregates. As a result, it can be regarded that all the surfactants practically form aggregates except in an extremely dilute region. It should be noted that if a sufficient amount of oil is present in the system, the partition of each surfactant in the mixture has to be taken into account.15-17 To avoid the high melting temperatures of surfactants with the increase in the lipophilic chains, the use of oleyl alcohol derivative surfactant is very effective. However, commercially available oleyl compounds were extremely inpure because they were produced from ordinary oleic acid which contains various kinds of fatty acids and, generally, its purity is only 60%.18,19 Recently, high-purity oleic acid (99.999%) and oleyl alcohol were synthesized.18-20 The poly(oxyethylene) surfactants with the high pure oleyl group were also synthesized.20 In this context, we have investigated the phase behavior of poly(oxyethylene) oleyl ether with a highly pure oleyl group in water at constant temperature. The phase transition between hexagonal and lamellar liquid crystals were also investigated by means of small-angle X-ray scattering. Experimental Section Materials. Pure oleyl alcohol and poly(oxyethylene) oleyl ethers, POlE(5), POlE(10), and POlE(20), were obtained from NOF Co., Japan. The purity of the oleyl group is greater than 99.7%. The end hyroxyl groups of the surfactants were determined by the standard titration method.21 The average EO chain lengths of the above surfactants are 5.1 for POlE(5), 10.7 for POlE(10), and 19.2 for POlE(20). We used these values to calculate the average EO-chain length of the POlE mixture. Other POlE(n) having different poly(oxyethylene) chains are obtained by mixing the above POlEs. For example, POlE with © 1997 American Chemical Society
Poly(oxyethylene) Oleyl Ether-Water System
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7953
EO chain between 0 and 5 is a mixture of oleyl alcohol and POlE(5). Similarly, POlE(5)-POlE(10) or POlE(10)-POlE(20) mixtures was used to construct the phase diagram. Procedures. Preparation of Samples. After mixing POlEs completely to adjust the EO chain, water was added to the mixtures in ampules having a narrow constriction. Homogeneity was attained using a vortex mixer at 50-70 °C and repeated centrifugation through the narrow constriction. This mixing process was continued at least for 1-3 weeks. Small-Angle X-ray Scattering. Interlayer spacing of liquid crystal was measured using small-angle X-ray scattering(SAXS), performed on a small-angle scattering goniometer with an 18 kW Rigaku Denki rotating anode goniometer (RINT-2500) at about 25 °C. The samples of liquid crystals were lapped by plastic films for the measurement (Mylar seal method). The type of liquid crystals was determined by SAXS. For example, the SAXS peak ratios of the lamellar and (reverse) hexagonal phases are 1:1/2:1/3 and 1:1/x3: 1/2, respectively. The liquid crystals were also identified by means of a polarizing microscope. Calculation of the Volume Fraction of Oleyl Group. The densities of surfactants were measured by a digital density meter (Anton Paar 40). We assume that the density of surfactant in the liquid state is unchanged even in aqueous solutions or liquid crystals at constant temperature. The molar volume of surfactant is calculated by the following equation:
Vs )
MS FS
(1)
where MS and VS are the molecular weight and the molar volume of surfactant, respectively. It is also assumed that arithmetic additivity holds concerning the molar volumes of each functional groups in the surfactant.22 3Then, the molar volume of POlE is the sum of molar volumes of each group in the surfactant and the following relation holds:
VS ) VL + nVEO + VOH
(2)
whereVL, VEO, and VOH are the molar volumes of the lipophilic chain (oleyl group), the oxyethylene unit, and the hydroxyl group, respectively, and n is the number of oxyethylene units. VS, VL, VEO, and VOH were determined from the density data for homogeneous poly(oxyethylene) dodecyl ethers (Nikko Chemicals Corp., C12EO1-6) and pure oleyl alcohol because they are in a liquid state at 25 °C. The obtained values of VL, VEO, and VOH are 309, 38.8, and 8.8 cm3 mol-1, respectively. From these data, we can calculate the molar volume of POlE(n) by eq 2. The calculated values are compared with the molar volumes of for POlE(5), POlE(10), and POlE(20) obtained by their density data using eq 1 as shown in Figure 1. Experimental values are in a good agreement with the calculated ones. It is confirmed that the average number of EO chains is 5.1 for POlE(5), 10.7 for POlE(10), and 19.2 for POlE(20). The above values were used to calculate the volume fraction of lipophilic chain (oleyl group), φL, in the system
φL )
VL ML + nMEO + MOH 1 - WS VS + Fw WS
(
Figure 1. Molar volume of POlE(n) as a function of EO chain length. The line is calculated by eqs 1 and 2. Open circles are experimental values obtained from densities of POlE(5), POlE(10), and POlE(20), respectively.
)(
)
(3)
where Fw is the density of water and WS is the weight fraction of POlE(n). In the present study, n and WS are variables at constant temperature.
Notation. We use the following notations to distinguish each phases. The subscript 1 denotes “hydrophilic” or “normal”type self-organizing structure or phase, whereas the subscript 2 indicates “lipophilic” or “reverse”- type assemblies. H1, hexagonal liquid crystal; H2, reverse hexagonal liquid crystal; I1, discontinuous-type cubic phase (water-continuous); V1, bicontinuous cubic phase (normal type); V2a and V2b, bicontinuous cubic phase (reverse type); LR, lamellar liquid crystal; D2, isotropic bicontinuous surfactant phase (reverse type); this phase is denoted by D′ or L3 phase in the previous papers;7,23 Wm, aqueous phase containing surfactant aggregates; Om, oily phase like reverse micellar solution phase or surfactant liquid; W, excess water phase. Results and Discussion Phase Diagram of POlE(n)-Water System at 25 °C. The phase diagram of the water-POlE(n) system as a function of surfactant concentration was determined at 25 °C and is shown in Figure 2. The weight fraction of POlE in the system, Ws, is plotted horizontally. The volume fraction of the hydrophilic part (EO chain) in the total surfactant molecule, φEO/φS, is plotted vertically where φS is the volume fraction of each surfactant in the system and φEO is the volume fraction of the hydrophilic chain of the surfactant in the system. The φEO/φS is directly related to the Griffin’s HLB number13 as follows:
( )( )
HLB number ) 20
FEO(v)
FPOlE(n)
φEO φS
(4)
where FPOlE(n) and FEO(n) are the densities of POlE(n) and the poly(oxyethylene) chain, respectively. The average number of EO chain, n, is also plotted on the right-hand axis in Figure 2. In long-hydrophilic-chain POlE systems (n is more than 7), aqueous micellar phase (Wm) is formed in a dilute region, and the cubic phase (I1), hexagonal liquid crystal (H1), bicontinuous cubic phase (V1), lamellar liquid crystal phase (LR), and isotropic
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Figure 2. Phase diagram of POlE-water system as a function of the volume fraction of EO chain in the surfactant molecule and weight fraction of POlE at 25 °C.
Om phase are successively formed with increasing the surfactant concentration. In the concentrated region of very hydrophilic surfactant systems (n is higher than 15), the hexagonal liquid crystal is directly changed to the Om phase. The I1 phase is considered to be a discontinuous type. Lamellar phase and hexagonal phase are confirmed by the SAXS data and by optical microscopic texture as shown in Figure 3a,b. The very viscous isotropic phase (V1) appears between the hexagonal and lamellar phases when the EO chain length is between 8 and 15. The phase change from the H1 phase to the LR phase in the POlE(10) - water system will be discussed in the following section. The V1 phase is considered to be a bicontinuous cubic phase.24 The SAXS peak ratio was 1:x3/ x4:x3/x8:x3/x10:x3/x11:x3/x12:x3/x13. Although the third peak (x3/x7) is missing, the V1 phase has a bodycentered cubic structure (space group Ia3d).25 The phase transition from the hexagonal phase to lamellar liquid crystal occurs with decreasing the number of oxyethylene unit in the POlE at constant surfactant concentration. When the EO chain length of the surfactant is 3-4, other viscous isotropic phases appear. Judging from the position of these phases in the phase diagram, these phases are considered to be reverse bicontinuous type cubic phases (V2a and V2b). The V2a and V2b phases are connected with each other at higher temperature. The isotropic isolated fluid phase, D2, appears in the dilute region. This phase is often called L3 or D′ or a sponge phase.7,23 This phase is related to a middle-phase microemulsion (surfactant phase) which coexists with excess water and oil phases.23,24 Relatively lipophilic surfactant forms this phase and the surfactant curvature is somewhat negative.7 For these reasons, D2 phase is used in this paper. Normal-type sponge phase, D1, or reverse L3 phase is produced in an oil-rich region of hydrophilic surfactant systems.23, 26 The transition from lamellar liquid crystal (LR) to reverse hexagonal (H2) liquid crystal takes place via the bicontinuous cubic phase (V2a and V2b) as shown in Figure 2. The H2 phase is confirmed by means of SAXS and optical microscopy. The texture of the H2 phase is shown in Figure 3c. This phase has been reported in a lipophilic biological lipid-water system,27-29 and it has not been reported in ordinary poly(oxyethylene) alkyl ether-water systems, although the H2 phase appears in a ternary water/triethylene glycol dedecyl ether/cyclohexane system.30 The
Figure 3. Typical birefringent textures of the liquid crystals in the POlE-water system: (a, top) lamellar phase; (b, middle) hexagonal phase; (c, bottom) reverse hexagonal phase.
H2 phase coexists with excess water phase in the dilute region. Finally, the reverse hexagonal liquid crystal is changed to an isotropic fluid phase, Om phase, with decreasing the hydrophilic chain of the oleyl surfactant. Phase Diagram of POlE(n)-Water System as a Function of OL. The hydrophilic chain of surfactant is highly miscible with water whereas the lipophilic oleyl group forms the hydrocarbon core in self-organizing structures. In order to understand the influence of the packing of the oleyl group on the phase behavior, the horizontal axis of Figure 2 is replaced with the volume fraction of oleyl group in system, φL. The
Poly(oxyethylene) Oleyl Ether-Water System
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7955 The formation of these self-organizing structures are highly dependent on the EO chain length of POlE. Interlayer Spacing in Hexagonal and Lamellar Liquid Crystals. Interlayer spacings for hexagonal and lamellar liquid crystals were determined in the POlE(10)-water system by SAXS measurement. The results are shown in Figure 5. We assumed that hexagonal liquid crystal consists of infinitely long cylinders. In this case, the radius of the cylinder dL and the cross-sectional area of hydrocarbon core (as) per surfactant molecule can be calculated by the following equations: 1
dL ) (2φL/x3π) /2 d aS )
Figure 4. Phase diagram of the POlE-water system as a function of the volume fraction of EO chain in the surfactant molecule and the volume fraction of oleyl group in POlE at 25 °C.
Figure 5. Interlayer spacing in the POlE(10)-water system at 25 °C: (O) d, (0) as, (4) dL.
revised phase diagram is shown in Figure 4. The vertical axis is the same as that in Figure 2. In the hydrophilic POlE system, the maximum φL at 100% surfactant is very low because the POlE contains a very long EO chain. Normal-type self-organizing structures such as micelles (Wm), I1, H1, and V1 do not coexist with excess water phase. Hence, in the hydrophilic POlE system having a long EO chain more than 7, the phase change takes place with increasing surfactant concentration. The limiting volume fractions are 0.68 for bodycentered cubic and 0.91 for hexagonal phases. It is known that phase transition takes place in the range 70-80% of the closedpacked volume fractions.2,27 However, the limiting values of φL for I1 and H1 phases are much lower than the above values as shown in Figure 4. The horizontal axis in Figure 2, the weight fraction of surfactant, is roughly equal to the volume fraction of total surfactant molecule, φS, because the densities of water and POlE(n) are not very different. The limiting volume fractions of total surfactant for I1 and H1 phases are still smaller than the above limiting values. This fact suggests that the steric hindrance of water-swollen hydrophilic chain causes the phase transition from cubic to hexagonal phases or hexagonal to LR phases. On the other hand, LR, D2, V2a, H2, and Om phases coexist with excess water phase, respectively, as is shown in Figure 4.
2VL dL L
(5) (6)
where d is an interlayer spacing measured, φL is the volume fraction of oleyl group in system and L is the Avogadro constant. It is reported that the cylinder in the H1 phase is not infinitely long in the sodium dodecyl sulfate-water system.31 In the present case, however, there is no evidence that the cylinder length is finite. Concerning the lamellar liquid crystal, dL is the half thickness of hydrocarbon part of the bilayer. The as and dL can be calculated by the following equations:
dL ) φLd/2
(7)
aS ) VL/dLL
(8)
as and dL were not calculated for a cubic phase between the H1 and LR phases because the detailed structure was not completely identified. The values of as and dL for H1 and LR phases are also shown in Figure 5. The effective cross-sectional area gradually decreases with increasing surfactant concentration. However, there is no big difference between the H1 and LR phases. The cross-sectional area of close-packed hydrocarbon chains is 0.22 nm2 per chain in a liquid state.32 Hence, dL ) VL/0.22L ) 2.33 nm is considered to be the oleyl-chain length in the most extended form. Compared with this value, the radius of hexagonal cylinder is short and especially the lipophilic thickness in lamellar liquid crystal is extremely short. As is shown in Figure 5, when the H1 phase is changed to LR phase, the reduction in the length of lipophilic part takes place whereas the cross-sectional area is only slightly decreased in the water-POlE(10) system. The distance between the surfaces of cylinders of lipophilic core in the H1 phase is 3.0 nm at φL ) 0.28 whereas that between the lipophilic plates in the LR phase is 3.5 nm at φL ) 0.32. The length of the extended decaoxyethylene chain is approximately 3.6 nm in the solid state.33 Since the volume of decaoxyethlene chain is calculated to be 0.64 nm3 per chain, using the molar volume described in the Experimental Section, the cross-sectional area of poly(oxyethylene) chain is roughly estimated as 0.18 nm2 in the solid state. The effective cross-sectional area of the hydrocarbon part in H1 or LR phase is around 0.55 nm2 and more than twice the above-calculated values. Although it is not clear that the poly(oxyethylene) chains are in the extended form in the liquid crystals, it is considered that the hydrophilic chain of surfactant almost reaches another cylinder in the H1 phase at the phase boundary. Therefore, to reduce the steric repulsion of hydrophilic chains, the phase transition between H1 and LR phases occurs in the POlE(10) system. In a dilute region, the type of self-organizing structures is determined by the curvature of
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Figure 6. Change in interlayer spacing as a funtion of φEO/φS at constant φL ) 0.20: (O) d, (0) as, (4) dL.
surfactant layer, but the packing of the self-assemblies is an additional factor to decide the type in a concentrated region. Phase Transition between H1 and Lr Phase with the Change in EO Chain Length. Phase transition between H1 and LR phases also takes place with decreasing EO chain as shown in Figures 2 and 4. We measured the change in interlayer spacing as a function of φEO/φS at constant φL ) 0.20 and the result is shown together with as and dL in Figure 6. In the present study, an intermediate phase was not observed between the two phases. However, since the composition was changed in the present study, it is possible to miss the intermediate phase because of the narrowness. In the H1 phase, the interlayer spacing increases with decreasing the EO chain length. On the other hand, the effective cross-sectional area is continuously decreased due to the decrease in the hydrophilicity of POlE. To compensate the decrease in as, the radius of the cylinder, dL, increases and eventually the phase transition to LR phase occurs. As is shown in Figure 6, the radius of the cylinder of the hydrocarbon core approaches the chain length of the oleyl group in the extended form, 2.33 nm, at the phase boundary between H1 and LR phases. Hence, the shape of the cylinder cannot maintain for a further reduction of the effective cross-sectional area. Effect of Temperature on the Phase Behavior. The cloud temperature of POlE(n) was determined at 2 wt % surfactant and is plotted as a function of φEO/φS as is shown in Figure 7. The cloud temperatures for poly(oxyethylene) dodecyl ethers34 are also plotted in Figure 7. The horizontal axis is related to the HLB number of each surfactant and both experimental data are almost coincident. A linear relationship holds between the cloud temperature and HLB number in a poly(oxyethylene)type nonionic surfactant in this temperature range. However, it is known that the cloud temperature tends to be constant in a very long hydrophilic-chain surfactant system. The phase diagram of the POlE(n)-water system as a function of temperature is also shown in Figure 8, in which the surfactant concentration is fixed to 50 wt % in the system. All the liquid crystals are shifted to higher value of φEO/φS with the increase in temperature. A linear relationship also holds between the HLB number and the center temperature for the LR phase.35 The maximum temperature for reverse hexagonal liquid crystal is much lower than those for lamellar and hexagonal liquid crystals. Furthermore, the range of EO chain of POlE is very narrow for the formation of the H2 phase. As described before, for these reasons, it is difficult to observe H2 phase in a poly-
Figure 7. Change of clouding temperature in POlE-water (O) and poly(oxyethylene) dodecyl ether-water (3) systems as a function of the volume fraction of EO chain in the surfactant molecule. The concentration of POlE is fixed to 2 wt %.
Figure 8. Phase diagram of the POlE-water system as a function of temperature and the volume fraction of EO chain in the surfactant molecule. The concentration of POlE is fixed to 50 wt %.
(oxyethylene)-type nonionic surfactant system. An intermediate phase like a bicontinuous cubic phase was not found between the LR and H1 phase at this surfactant concentration as is shown in Figure 8. The V2 phase is melted and changes to isotropic surfactant solution, Om, at higher temperature as shown in Figure 8. However, the effect of temperature on the phase behavior is not very significant compared with the effect of EO-chain length of POlE. Acknowledgment. The authors thank for Mr. Y. Maki in Rigaku Corp. for the SAXS measurement. The authors also thank for Dr. C. Solans (CID/CSIC, Spain) for her critical reading of the manuscript.
Poly(oxyethylene) Oleyl Ether-Water System References and Notes (1) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976 , 72, 1525. (2) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (3) Clunie, J. S.; Goodman, J. F.; Symons, P. C. Trans. Faraday Soc. 1969, 65, 287. (4) Shinoda, K. J. Colloid Interface Sci. 1970, 34, 278. (5) Saito, H. Nihon Kagaku Zasshi 1971, 92, 223. (6) Lang, J. C.; Morgan, R. D. J. Chem. Phys. 1980, 73 , 5849. (7) Strey, R.; Schomacker, R.; Roux, D.; Nallet, F.; Olsson U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253. (8) Karlstroem, G. J. Phys. Chem. 1984, 88, 4769. (9) Matsuura, H.; Fukuhara, K. J. Mol. Struct. 1985, 126, 251. (10) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1992, 96, 11029. (11) Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054. (12) Adam, C. D.; Durrant, J. A.; Lowry, M. R.; Tiddy, G. J. T. J. Chem. Soc., Faraday Trans., 1 1984, 80, 789. (13) Griffin, W. C. J. Soc. Cosmet. Chem. 1954, 5, 249. (14) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic Press: Inc.: San Diego, CA, 1994 p 304. (15) Kunieda, H.; Yamagata, M. Langmuir 1993, 9, 3345. (16) Muto, M.; Naito, N.; Kunieda, H. J. Jpn. Oil Chemists’ Soc. (Yukagaku) 1994, 43, 502. (17) Kunieda, H.; Nakano, A.; Akimaru, M. J. Colloid Interface Sci. 1995, 170, 78.
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7957 (18) Suzuki, M. Fine Chemicals 1987, 16, No. 13, 12 (in Japanese). (19) Suzuki, M. Fragrance J. 1995, April, 105 (in Japanese). (20) Shigeta, K.; Suzuki, M.; Kunieda, H. Prog. Colloid Polym. Sci., in press. (21) Standard Methods for the Analysis of Fats, Oils and Related Materials. J. Oil Chem. Soc. 1996, No. 2.3.6.2. (22) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (23) Kunieda, H., Shinoda, K. J. Dispersion Sci. Technol. 1982, 3, 233. (24) Conroy, J. P.; Hall, C.; Leng, C. A.; Rendall, K.; Tiddy, G. J. T.; Walsh, J.; Lindblom, G. Prog. Colloid Polym. Sci. 1990, 82, 253. (25) Rancon, Y.; Charvolin, J. J. Phys. 1987, 48, 1067. (26) Olsson, U.; Nagai, K.; Wennerstroem, H. J. Phys. Chem. 1988, 92, 6675. (27) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (28) Hato, M.; Minamikawa, H. Langmuir 1996, 12, 1658. (29) Kirk, G. L.; Gruner, S. M.; Stein, D. L. Biochemistry 1984, 23, 1093. (30) Kunieda, H.; Rajagopalan, U. Kimura, E.; Solans, C. Langmuir 1994, 10, 2570. (31) Amaral, L. Q.; Gulik, A.; Itri, R.; Mariani, P. Phys. ReV. A 1992, 46, 3548. (32) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; WileyInterscience: New York, 1990; p 133. (33) Rosch, M. In Nonionic Surfactants; Schick, M., ed.; Marcel Dekker: New York, 1967; Chapter 22. (34) Rosen, M. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley: New York, 1989; Chapter 4. (35) Kunieda, H. J. Colloid Interface Sci. 1986, 114, 378
