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Micellization and Adsorbed Film Formation of a Binary Mixed System of Anionic/Nonionic Surfactants Tomomichi Okano,† Takamitsu Tamura,† Yutaka Abe,† Takuya Tsuchida,‡ Sannamu Lee,‡ and Gohsuke Sugihara*,‡ Material Science Research Center, Lion Company, 7-13-Hirai, Edogawa-ku, Tokyo 123-0035, Japan, and Department of Chemistry, Faculty of Science, Fukuoka University, Jonan-ku, Fukuoka 814-0180, Japan Received March 19, 1999. In Final Form: September 27, 1999 Micelle formation in water and adsorbed film formation at the air/water interface were investigated by surface tension measurement of a mixed surfactant system: the combination of sodium salt of R-sulfonatomyristic acid methyl ester (R-SMy‚Me) with decanoyl-N-methylglucamide (MEGA-10). R-SMy‚ Me and MEGA-10 can form well-mixed micelles with the aid of a strong interaction between headgroups, and accordingly the critical micelle concentration (cmc) as a function of mole fraction of MEGA-10 in the surfactant mixture (XMEGA10) deviates negatively from ideal mixing. The micellar phase curve (cmcYMEGA10 relation) was simulated by using the interaction parameter ωR ) -2.1; the curve indicated the existence of an azeotrope formed by a 3:2 mixture (at XMEGA10 ) YMEGA10 ) 0.4). Further, we derived equations related to the composition in the adsorbed film (Zi) equilibrated with monomers in bulk solution and to the interaction parameter (WA), and then constructed a phase diagram including two relations of cmc vs XMEGA10 and cmc vs ZMEGA10. From the diagram an azeotrope was found to be formed by the 1:1 mixture (at XMEGA10 ) ZMEGA10 ) 0.5), suggesting that the composition in micelles (Yi) differs from that in the adsorbed film (Zi). The surface tension (γ) vs logarithmic molality (ln m) curve at every 0.1 increment in XMEGA10 showed synergistically enhanced surface activity. From the slope of the γ vs ln m curve just below cmc, the surface excess (Γ) was determined and then the mean molecular area (Am) was calculated as a function of XMEGA10. By analysis of Am data, the partial molecular area (PMA) of each component was determined as a function of XMEGA10; this also showed a large deviation from ideal mixing (the additivity rule).
Introduction For the mixture of two surfactants undergoing micelle formation above a critical micelle concentration (cmc), the solution properties fall either between or outside the solution properties of the two single-surfactant solutions. This is also the case for the cmc of a binary surfactant solution. Clint1 has given us the relation between mole fraction and cmc of the ith component (i ) 1,2) for ideal mixtures, and Rubingh2 has made a comprehensive theoretical attempt to deal with nonideal mixture on the basis of the regular solution theory. Among various combinations of nonideal mixed systems, such mixtures as those composed of fluorocarbon and hydrocarbon surfactants have been found to deviate positively from ideal mixing (predictable from Raoult’s law or Client’s equation).1-6 Recently, a series of novel polymerizable hydrocarbon and fluorocarbon cationic surfactants (N-[(alkoxycarbonyl)methyl]-N-[Z-(N′-alkylacrylamido)ethyl]-N,N-dimethylammonium bromide) were found to form mixed * To whom correspondence should be addressed: Fax 81-92865-6030; E-mail
[email protected]. † Lion Company. ‡ Fukuoka University. (1) Clint, J. H. J. Chem. Soc., Faraday Trans. 1, 1975, 71, 1327. (2) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L, Ed.; Plenum Press: New York, 1979; Vol. 1, p 337. (3) Mukerjee, P.; Yang, S. Y. J. Phys. Chem. 1976, 80, 1388. (4) Fanasaki, N.; Hada, S. J. Phys. Chem. 1986, 84, 736. (5) Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, N. Langmuir 1985, 1, 347. (6) (a) Sugihara, G. In Surfactant in Solution; Mittal, K. L., Ed.; Plenum: New York, 1989; Vol. 7, p 405. (b) Wada, Y.; Ikawa, Y.; Igimi, H.; Makihara, T.; Nagadome, S.; Sugihara, G. Fukuoka Univ. Sci. Rep. 1989, 19, 173.
micelles whose interaction parameter (based on regular solution theory2) is 1.25, indicating the formation of one type of mixed micelles7. In contrast, even for a mixed system of fluorocarbon-hydrocarbon surfactants, a negative deviation has been observed: in the mixture of N-methyl-N-octanoyl- and N-methyl-N-nonanoylglucamides (MEGA-8 and MEGA-9, respectively) with sodium perfluorooctanoate (SPFO), the negative deviation is likely to come from a synergistically enhanced interaction between different headgroups.6,8 Lange and Beck9 have shown such negative deviations in mixtures of sodium dodecyl sulfate (SDS) and dodecyl octaoxyethylene. Moroi et al.10 and others11-13 have investigated the mixtures of ionic/nonionic surfactants to evaluate cmc from as early as the 1960s. Showing a decreased cmc of Triton X-100 following the addition of sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB), Moulik et al.14 have concluded that the incorporation of the hydrophobic tails of the ionic surfactants into the interior of Triton X-100 micelles is thermodynamically favored whereas the reverse process is not. Furthermore, they have performed a thermodynamic study on the micelle formation of ternary mixed systems of SDS, Tween(7) Stahler, K.; Selb, J.; Barthelemy, P.; Pucci, B.; Candau, F. Langmuir 1998, 14, 4765. (8) Wada, Y.; Ikawa, Y.; Igimi, H.; Murata, Y.; Nagadome, S.; Sugihara, G. J. Jpn. Oil Chem. Soc. (Yukagaku) 1990, 39, 548. (9) Lange, H.; Beck, K. H. Kolloid Z. Z. Polym. 1973, 251, 424. (10) Moroi, Y.; Nishikido, N.; Sato, M.; Matuura, R. J. Colloid Interface Sci. 1975, 52, 356. (11) Kuriyama, K.; Inoue, H.; Nakagawa, T. Kolloid Z. 1962, 183, 68. (12) Corkill, J. M.; Goodman, J. F.; Tate, J. R. Trans. Faraday Soc. 1964, 60, 986. (13) Shick, M. J.; Manning, D, J. J. Am. Oil Chem. Soc. 1966, 43, 133. (14) Moulik. S. P.; Mandal, A. B.; Ray, S. Ind. J. Chem. 1980, 19A, 620.
10.1021/la990331t CCC: $19.00 © 2000 American Chemical Society Published on Web 12/17/1999
Binary Mixed System of Anionic/Nonionic Surfactants
20, and Brij-35.15 Very recently, Shiloach and Blankschtein16 have investigated synergism in mixed micelle formation and micellar growth in ionic/nonionic surfactant mixturessone is dodecyl hexa(ethylene oxide) (C12E6) mixed with SDS and the other is C12E6 mixed with sodium hexa(ethylene oxide) sulfate (SDE6S)sby applying surface tension and static light scattering measurements. It is noteworthy that the experimental mixture cmc and mixed micelle aggregation numbers compare well with those predicted by a molecular-thermodynamic theory of mixed micellization. From their work plenty of insights can be deduced. By means of small-angle neutron scattering measurements Penford et al.17,18 studied the structure and composition of two surfactant mixtures [SDS with hexaethylene glycol monododecyl ether (C12EO6) and haxadecyltrimethylammonium bromide (C16TAB) with C12EO6] and found that for the SDS/C12EO6 mixture, the micellar aggregation number is essentially constant with composition and concentration, whereas for the C16TAB/C12EO6 mixture, there is marked micellar growth with increasing concentration and mole fraction of C12EO6. Pulsed-field gradient NMR methods have also been shown to be useful for determining the partitioning of surfactants between monomeric and micellar forms in mixed systems, by Eads and Robosky,19 and it was reported that the observed behavior is not consistent with expectations from the regular solution model. But the use of the van Laar expression accounts well for the composition dependence of the activity coefficients. In the mixed system of MEGA10 with a bile salt (sodium deoxycholate), the analysis of cmc data indicated that the properties of mixed micelles are different between the ranges below and above the composition of MEGA-10 (XMEGA10), congruent to 0.2 where an azeotrope exists, and that the composition of mixed micelles is very similar to that of monomeric species in bulk solution.20 As briefly introduced above, primary concerns are furthermore being concentrated on such ionic /nonionic surfactant mixtures by various methodologies and theories. Mixed systems of nonionic surfactants with anionic surfactants seem, in general, to show unique behavior differing from those of ionic/ionic surfactants mixtures. In addition, nonionic surfactants, ones having sugar-type hydrophilic groups, are different from those with poly(oxyethylene) headgroups. A binary mixed system of an anionic surfactant (sodium salt of R-sulfonatomyristic acid methyl ester, R-SMy‚Me) and a nonionic surfactant (Ndecanoyl-N-methylglucamide, MEGA-10) must give us some fresh information, when investigated. The former, a top-heavy-type surfactant assigned to the so-called R-SF series, has been known to be biodegradable, high in detergency, and tolerable against hard water,21-24 while the latter, which has five hydroxy groups with an amide bond, has been used as a membrane protein solubilizer.25 (15) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357. (16) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 7166. (17) Penford, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.: Thomas, B. K.; Warren, N. J. Phys. Chem. B. 1999, 103, 5204. (18) Penford, J.; Staples, E. J.; Thompson, L.; Tucker, I.; Hines, J.: Thomas, B. K. Int. J. Thermophys. 1999, 20, 19. (19) Eads, C. D.; Robosky, L. C. Langmuir 1999, 15, 2661. (20) Yunomiya, Y.; Kunitake, T.; Tanaka, T.; Sugihara, G.; Nakashima, T. J. Colloid Interface Sci. 1998, 201, 1. (21) Yoneyama, Y. J. Jpn. Oil Chem. Soc. 1995, 44, 2. (22) Maurer, E. W.; Cordaon, T. C.; Weil, J. K.; Linfieked, M. M. J. Am. Oil Chem. Soc. 1974, 51, 287. (23) Steber, J.; Wierich, D. Tensid. Surf. Deter. 1989, 26, 406. (24) Masuda, M.; Odake, H.; Miura, K. J. Jpn Oil Chem Soc. 1994, 43, 617. (25) Izawa, S.; Sakai, Y.; Tomita; Kitamura, K.; Kitazawa, S.; Tsude, M.; Tsuchiya, T. J. Biochem. 1993, 113, 573.
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Figure 1. Surface tension (γ) vs logarithmic concentration plots for R-SMy‚Me (O), MEGA-10 (b), and a mixed system at XMEGA10 ) 0.6 (0). The logarithmic value was calculated from the total concentration of the surfactant mixture (mt) in molality.
In addition to the previous temperature study on the MEGA series,26 micelle and adsorbed film formation of MEGA-10 have been thermodynamically studied by means of surface tension measurements (drop volume method), for comparison with n-nonyl-β-D-thiomaltoside (NTM) also being used as a protein solubilizer.27 In the present paper, following the temperature studies on micelle formation of R-SMy‚alkyl series surfactants28,29 and on MEGA-n (n ) 8, 9, 10) series surfactants,26 we have performed a surface tension study on micelle formation and surface adsorption of mixed systems of R-SMy‚Me with MEGA-10, paying special attention to compositions of micelles and adsorbed films at equilibrium with monomeric surfactant mixture in bulk solution. In this study are shown how much the estimated composition of adsorbed film differs not only from that of singly dispersed species but also from that of micelles and to what extent the intermolecular interaction acts in the phases of adsorbed film and micelles. Experimental Section Materials. The sodium salt of R-sulfonatomyristic acid methyl ester, R-SMy‚Me (from Lion Co., Tokyo) was synthesized and purified in the same manner as in previous papers.28,29 The purity was chromatographically confirmed to be more than 99%, and when checked by surface tension measurement: the plot of surface tension (γ) vs logarithmic concentration gave no minimum (see Figure 1). N-Decanoyl-N-methylglucamide, MEGA-10 (from Doujindo Laboratories, Kumamoto, Japan) was highly purified by repeated recrystallization from ethanol and diethyl ether (1: 9). (26) Okawauchi, M.; Hagio, M.; Ikawa, Y.; Sugihara, G.; Murata, Y.; Tanaka, M. Bull. Chem. Soc. Jpn. 1987, 60, 2718. (27) Oda, H.; Nagadome, S.; Lee, S.; Ohseto, F.; Sasaki, Y.; Sugihara, G. J. Jpn. Oil Chem. Soc. 1997, 46, 559. (28) Fujiwara, M.; Okano, T.; Nakashima, T. H.; Nakamura, A. A.; Sugihara, G. Colloid Polym. Sci. 1997, 275, 474. (29) Nakamura, A. A.; Hisatomi, M.; Sugihara, G.; Fujiwara, M.; Okano, T. J. Surf. Sci. Technol. 1998 14, 23.
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Surface Tension Measurements. The surface tension (γ) measurements were performed on the basis of essentially the same drop volume method as reported previously, but an automated surface tensiometer (Yamashita Giken YDS94) was used in the present study. The measurement temperature was controlled by the use of a system (Yamashita Giken, YSC9211) for the surface tensiometer with an accuracy of (0.03 °C. The first drop was permitted to stand for 1.5 h in order to attain the temperature equilibrium, and then in order to estimate the approximate size of the drop the coarse shift of the micrometer was first determined. To attain the adsorption equilibrium, the drop squeezing process was composed of three steps using a computer system. First, a pendant drop whose size was given by ca. 80% of the micrometer shift for a drop was permitted to stand for 15 min (or 20 min if necessary, depending on the stability of measured values), and then an additional 5% was exposed taking 10 s as the second step. And finally the pendant drop (of ca. 85% of a falling drop) was squeezed out at a speed of 1 µm s-1. One measured point was determined from at least five measured values. Whether the measured values for a sample solution scatter or not, depends in most cases on the chemical species (especially on the molecular structure) or its concentration. The accuracy of this drop volume method has been confirmed to be sufficiently high from comparison with the results determined by the most reliable method of image analysis of pendant drop.30
Results and Discussion Figure 1 shows the plot of surface tension against logarithmic concentration (ln m) for pure systems of R-SMy‚Me and MEGA-10 together with a system of a 2:3 mixture as an example. Here it is noted that logarithmic concentration has no dimension, but the figure indicates that logarithmic values are calculated not from millimolality (as is often used) but from molality itself. The concentration giving a break in the curve is assumed to be the cmc for both single systems, while the cmc for the mixed system is taken as the concentration at the minimum. Comparing R-SMy‚Me and MEGA-10, R-SMy‚ Me with a longer hydrocarbon chain as the hydrophobic group has a cmc at 2.8 mM, and MEGA-10 with a shorter hydrophobic chain has its cmc at 4.7 mM, indicating that the former’s ability of micelle formation is higher than the latter. But, in contrast, if the surface activity (surface tension lowering ability) is compared between both single systems, MEGA-10 is superior to R-SMy‚Me. This antagonistic property observed in both surfactants aroused our interest in examining the mixing effect. Upon examination of the γ vs ln m curve of a mixed system given in Figure 1, the γ is lowered more rapidly than both single systems by synergistically enhanced surface activity at very low concentration, and changing the trend at a minimum, the γ is gradually raised and seems to reach a certain constant value within both curves of single systems above their cmcs. All the γ vs ln m plots of the other mixed systems at every 0.1 increment in mole fraction of MEGA-10 in the surfactant mixture (XMEGA10) also demonstrated having a minimum in addition to their synergistically enhanced surface activity (not shown here). This suggests that the surfactant having a higher surface activity has a trend of the more quick (in dynamics) or the more preferential adsorption (in energetics) compared to the other, having a lower surface activity. In addition, the curves of mixed systems show a possibility that measured points may not be those attained at a really thermodynamic equilibrium. That is, in the initial (early) stage after a fresh surface is made, the more active surfactant molecules may have a larger gain in Gibbs free energy upon adsorption and thus the larger gain may cause the faster translation from bulk (30) Matsubara, H.; Aratono, M. Langmuir (submitted for publication.
Figure 2. Phase diagram of R-SMy‚Me/MEGA-10 mixed surfactant system at 30 °C and 1 atm. Circles indicate the measured cmc values as a function of mole fraction of MEGA10 in the surfactant mixture (XMEGA10). The solid line and broken line (-‚‚‚-) were simulated using Rubingh’s equations,2 and the latter may be called the micellar composition curve. The dotted line corresponding to the ideal mixing was calculated from Clint’s equation1 or Raoult’s law.
phase to interface than in the lower active surfactants, even if the molecular sizes are comparable to each other. Therefore, it generally needs a long time to reach a real equilibrium in distribution between bulk and interface. However, as described later, the interaction between the two surfactant molecules may take such a process as preferential formation of surfactant complex (like dimer) formation in bulk and then migration to interface. The determination of cmc for mixed systems was made at the concentration giving a minimum as mentioned above, because it is the least considered for surfactant molecules to start micelle formation. Next, cmcs thus determined are plotted against mole fraction of MEGA10 (XMEGA10) as is shown in Figure 2. The open circles are points measured by the present surface tension method. In the figure is shown a theoretical curve (dotted line) calculated for ideal mixing from Raoult’s law or Clint’s equation.1 The cmc-composition curve for the present mixed system is known to deviate negatively a great deal from that of ideal mixing. (a) Mixed Micelle Formation. To interpret the negative deviation shown in Figure 2, we employed widely applicable equations by Rubingh.2 At the cmc the composition of surfactant i (i ) 1, 2) in the micelle, Yi is related to the monomeric concentration of surfactant i, Cim and to the cmc of pure i, Ci° as Yi ) Cim/Ci°. In the system of surfactants 1 and 2, the Rubingh’s equations are expressed as
Y12 ln(CmX1/C1°Y1) (1 - Y1)2 ln{Cm(1 - X1)/C2°(1 - Y1)}
)1
(1)
where Cm is the cmc of the mixed system. Rubingh has
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introduced an interaction parameter, ωR in the mixed micelle on the basis of the regular solution approximation:
ωR ) ln(CmX1/C1°)/(1 - Y1)2
(2)
The substitution of Y1 value calculated from eq 1 into eq 2 produces an ωR value at each X1. In Figure 2, the solid line along open circles was calculated by applying eqs 1 and 2, where the interaction parameter ωR value was taken as -2.1. The simulated curve completely satisfies the experimental result. In the figure the broken line corresponds to the correlation between micellar composition Y1 (in this case YMEGA10) and cmc. In other words, the micellar phase curve is equivalent to the cmc-YMEGA10 curve and the singly dispersed (monomeric) phase curve is equivalent to the cmc-XMEGA10 curve. The figure indicates that the present mixed system has an azeotropic point at XMEGA10 ) ca. 0.4, and also at this mole fraction the most stabilization in free energy is afforded for the mixture. The negative interaction parameter as well as its absolute value (-2.1) suggests an interaction acting especially between N-methylglucamine and R-methylsulfonic groups, which is greatly superior to the hydrophobic interaction between hydrocarbon chains. A similar negative deviation has been observed for a mixed system of nonyl N-methylglucamine (MEGA-9) with sodium perfluoroctanoate (SPFO).6,8 Since fluorocarbon surfactants have not only hydrophobicity but also oleophobicity, the interaction between fluorocarbon and hydrocarbon chains in micelle is mutually phobic (repulsive), causing a positive deviation from ideal mixing; this phenomenon has been observed for various ionic-ionic surfactant mixtures,3,31-36 and from the aspects of chemical structure the mixed micelle formation has been examined.37 Nevertheless, the combination of MEGA-9 with SPFO shows lower cmc and higher surface activity than those of the individual components. The negative deviation was interpreted as follows; SPFO and MEGA-9 are miscible in micelles with aided reduction in the repulsive forces between headgroups probably resulting from the penetration of the nonionic surfactant into the space between the ionic headgroups.6,8,36 This is the case for the present mixed system. (b) Composition of Mixed Adsorbed Film. Next, turning our attention to the composition of the adsorbed film phase, we suppose an equilibrium between the mixed adsorbed film and the bulk, the concentration of which is cmc (denoted as m1 + m2 ) mt). And it is assumed that the amount of adsorbed species (in the adsorbed phase) is negligible compared with that in the bulk phase. When the adsorption amounts of the mixed systems and the respective single systems at a given surface area are denoted as Γmix and Γi° (i ) 1, 2), and the composition (in mole fraction) of surfactant i in the adsorbed film phase, (31) Mukerjee, P.; Mysels, K. J. In Colloidal Dispersion and Micellar Behavior; Mittal, K. L., Ed.; ACS Symposium Series 9; American Chemical Society: Washington, DC, 1975; p 239. (32) Lange, H.; Beck, K. H. Kolloid Z. Z. Polym. 1973, 251, 424. (33) Funasaki, N.; Hada, S. J. Phys. Chem. 1980, 84, 736. (34) Funasaki, N.; Hada, S. J. Phys. Chem. 1982, 86, 2504. (35) Yoda, K.; Tamori, K.; Esumi, K.; Meguro, K. J. Colloid Interface Sci. 1989, 131, 282. (36) Kissa, E. Fluorinated Surfactants; Surfactant Science Series, Vol. 50, Chapter 7; Marcel Dekker: New York, 1994. (37) Nagrarjan. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501, Chapter 4; American Chemical Society: Washington, DC, 1992.
Figure 3. Schematic illustration of the equilibrium relations among singly dispersed (monomeric) species, micelles, and adsorbed film phases, the compositions of which are denoted as Xi, Yi, and Zi, (i ) 1, 2),when X2 ) 0.3 as an example.
which has a substantially negligible but definite thickness, is denoted as Zi (Z1 + Z2 ) 1), the equilibrium scheme might be expressed as
Zifi′Γi° mi a ziΓmix ) (adsorbed film) (bulk)
(3)
where, f′ corresponds to the activity coefficient and also has the relation f i′ ) Γmix/Γi°. Of the equilibrium shown in eq 3, we consider the following equality of the factor fi, which involves an equilibrium constant:
mi ) ZifiΓi°
(3a)
Describing in terms of chemical potentials, the standard chemical potentials for both sides are included in eq 3a as the following: For the bulk phase (b)
µi(b) ) µi(b)° + RT ln mi ) RT ln mi
(4)
where µi(b)° + RT ln 1 ) 0. For the adsorbed film phase (a)
µi(a) ) µi(a)° + RT ln fiZi ) RT ln fiZiΓi°
(5)
where µi(a)° ) RT ln Γi°. Needless to say, when Zi approaches unity, fi also reaches unity. Here it is noted that we are interested in how Xi, Yi, and Zi, compositions of bulk, micelle, and adsorbed film phases, respectively, are related to each other; a schematic diagram of the equilibria among them is shown in Figure 3. With respect to determination of surface excess based on the Gibbs adsorption isotherm, Γi° for a single system and Γmix for a mixed system we will describe later. The mass balance in bulk solution gives the following relations for the mixed system of surfactants 1 and 2 when the mole fractions in the mixture and concentrations are denoted as X1 and X2 (X1 + X2 ) 1) and m1 and m2, respectively.
m1 + m2 ) X1mt + X2mt ) (1 - X2)mt + X2mt ) mt (6) where mt is the total concentration of the surfactants, and simultaneously, mt corresponds to cmc. Thus, when an equilibrium is attained between the bulk and the adsorbed film phases, the relations are expressed as
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follows:
m1 ) f1Z1Γ1° ) f1(1 - Z2)Γ1° ) (1 - X2)mt (7)
m2 ) f2Z2Γ2° ) X2mt
The mole fraction of 2 in bulk solution is expressed by using eq 7
X2 )
m2 f2Z2Γ1° ) m1 + m2 f1(1 - Z2)Γ1° + f2Z2Γ1°
(8)
The concentrations in bulk are the same as those prepared, since the amount forming the film is negligible compared with those in bulk. Equation 8 tells us that if Γ1°, Γ2°, f1, and f2 are known, the composition in the film can be estimated. Based on the regular solution theory, the activity coefficients f1 and f2 are given as
f1 ) exp[WAZ22] f2 ) exp[WA(1 - Z2)2]
(9)
where WA corresponds to the interaction parameter. From analogy with the derivation of Rubingh’s equations,2 we obtain the following equations: 2
(1 - Z2) ln[(1 - X2)mt/(1 - Z2)Γ1°] Z22 ln [X2m2/Z2Γ2°]
)1
WA ) [ln (X2mt/Z2Γ2°)]/(1 - Z2)2
(10) (11)
Equations 10 and 11 simultaneously tell us that if the surface excesses of the respective single systems (Γi°) and the cmc of a binary mixture (mt) are determined against the net mole fraction X2, then the adsorbed film composition Zi is given by eq 10, and WA can be evaluated from eq 11 by using the Z2 value. As was done for ωR in eqs 1 and 2, and as was pointed out by Moroi,38 the single parameter was determined by averaging the WA values against each Z2 value over the entire composition range. Substituting the data of cmc and Γi° into eqs 10 and 11, the composition of surfactant 2 (corresponding to MEGA10) in the adsorbed film phase, Z2, was calculated as a function of the net mole fraction, X2, and the result is demonstrated in Figure 4. Figure 4 is a phase diagram indicating the composition of the adsorbed film formed at cmc, in other words, the curves of the phase equilibrium between the adsorbed film and monomeric species. To obtain the cmc vs Z2 curve along with simultaneous satisfaction of the relation of cmc vs X2, the WA value was given as -44; this absolute value is much larger than that of the cmc vs Y2 (see Figure 2) and might come from Γi° values determined per unit area . Interestingly, the composition of the adsorbed film of the present mixed system has a marked trend to become 0.5 and as a result the film of 1:1 mixture forms an azeotrope. This suggests that, in the adsorbed film formation, molecules having a dimeric form of MEGA-10 with R-SMy‚Me are preferentially adsorbed at the air/water interface. Anyway, it is known that the most free energetically stabilized film is formed by a 1:1 mixture (X2 ) Z2 ) 0.5), while micelles are formed by a 2:3 mixture (X2 ) Y2 ) 0.4). Here, it may (38) Moroi, Y. Micelles; Plenum Press: New York, 1992.
Figure 4. Phase diagram of monomers in bulk solution and adsorbed film at air/water interface for R-SMy‚Me/MEGA-10 mixed surfactant system at 30 °C and l atm, simulated from our theory.
be noted, for comparison with the present work, that Poulin and Bibett recently investigated the adsorption of mixed surfactant systems onto isolated oil/water interface according to the Gibbs equation (although the details are not introduced here).39 (c) Surface Excess and Partial Molecular Area. The amount of adsorbate per unit area (e.g., moles per square meter) is called surface excess or surface concentration or surface-adsorbed amount depending on the defined model of surface, i.e., either the surface phase or the Gibbs dividing surface. If the Gibbs approach is to be used, the usual convention is to place the dividing surface such that Γ(solvent) ) 0, and then the excess of adsorbate is written Γ(adsorbate), to denote this choice. This term Γ(adsorbate) may be called the relative adsorption.40 Up to the above section the adsorbed film is sometimes called the surface phase if it had a certain thickness; however, from our concept the solvent was excluded for conciseness. So, the relative adsorption or the surface excess is hereafter employed. Here, let us consider how the surface excess of such a system consisting of an ionic and nonionic mixture is represented. When the combination of surfactants 1 and 2 is composed of a 1-1 type of ionic and nonionic ones, respectively, the surface phase formulation, neglecting the amount of water at air/water interface, is given as40
-
dγ ) 2Γ1 d ln m1 + Γ2 d ln m2 RT
(12)
Since the total molality is denoted as mt ) m1 + m2 and the mole fraction of nonionic surfactant 2 is given as X2 ) m2/mt, for ionic surfactant 1 is given the following (39) Poulin, P.; Bibett, J. Langmuir 1999, 15, 4731. (40) Aveyard, R.; Haydon, D. A. An Introduction to the Principle of Surface Chemistry; Cambridge Chemistry Texts; Cambridge University Press: London, 1973.
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relation:
2(1 - X2)mt + X2mt ) m ˆ t ) mt(2 - X2)
(13)
ˆ t ) 2m1 + m2, according to where m ˆ t was taken as m Motomura et al.41 Using m ˆ t, we obtain by intuition the following equation from the analogy of the Gibbs adsorption isotherm:
-
dγ ) Γmix d ln m ˆt RT
(14)
Considering the adequacy of eq 14, it is known that when X2 is fixed at a constant, the differentiation of the logarithmic expression of eq 13, ln mt + ln(2 - X2) ) ln m ˆ t, leads to
ˆt d ln mt ) d ln m
(15)
Therefore, eqs 12 and 14 are understood to result in the same relation:
-
dγ ) (2Γ1 + Γ2) d ln mt ) (2Γ1 + Γ2) d ln m ˆ t (16) RT
Thus, the Gibbs adsorption isotherm is given for the 1-1 ionic/nonionic surfactant mixture at constant temperature, pressure, and mole fraction, as follows:
Γmix ) -
1 dγ dγ 1 )) 2Γ1 + Γ2 (17) RT d ln m ˆt RT d ln mt
This tells us that from the slopes below cmc of the γ vs ln mt curves, we can determine the surface excess at the respective mole fractions. The derivative (dγ/d ln mt) was plotted as a function of net mole fraction of MEGA-10 (not shown here). The maximum surface excess was attained at X2 ) 0.5, i.e., at 1:1 mixing ratio. As the composition of MEGA-10 is increased up to X2 ) 0.5, the surface excess is rapidly increased by more than 15% and then the surface excess goes down with increased XMEGA10. This change with XMEGA10 is likely to be in parallel with the existing ratio of dimeric unit, and the curve seemed to reflect the cmcZMEGA10 curve in Figure 4, at least suggesting that intermolecular interaction between MEGA-10 and R-SMy‚Me acts more strongly than those between themselves. This interaction can be seen from the behavior of the partial molecular surface area in the adsorbed film. Mean surface (occupation) area per molecule, Am, can be calculated from the relation Am ) 1/Γ × L , where L denotes Avogadro’s number. By the use of surface excess data, Figure 5 was constructed; needless to say, the obtained curve shows a minimum at X2 ) 0.5. Here from analogy of the partial molar volume of a solute in solution, the partial molecular area (PMA) is evaluated from the next equation for each component:
( )
h 1 + X2 Am ) A
∂Am ∂X2
(18)
Here A h 1 is the PMA of component 1, defined as
A h1 )
( ) ∂At ∂n1
(19)
T,V,γ,n2
h 1 + n2A h2 when n1 plus n2 moles form a surface area At (n1A (41) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948.
Figure 5. Change in mean molecular area (Am) with mole fraction in the surfactant mixture (XMEGA10) and an example of determination of partial molecular area (PMA) at point P. Table 1. Values of cmc, Y2, XM, ωR, f1, and f2 for Mixed Micelles of Anionic-Nonionic Binary Combinations at 30 °C for r-SMy‚Me - MEGA-10 Systems XMEGA-10
cmc (mmol‚kg-1)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2.8 2.4 2.2 2.0 2.0 2.0 2.1 2.4 2.6 3.2 4.7
avg
Y2
XM
ωR
f1
f2
0.18 0.28 0.35 0.39 0.44 0.49 0.54 0.61 0.71
0.31 0.34 0.39 0.40 0.40 0.43 0.47 0.55 0.69
-2.0 -2.1 -2.3 -2.3 -2.3 -2.3 -2.1 -2.0 -1.9
0.93 0.85 0.78 0.72 0.66 0.60 0.54 0.45 0.34
0.24 0.33 0.40 0.46 0.51 0.57 0.64 0.72 0.84‘
-2.1
) At). It is noted here that when the mixing is ideal, the PMA should be linear with X2 (the additivity rule). Equation 18 means that A h 1 and A h 2 are determinable from the respective intercepts on the Am axis at X2 ) 0 and X2 ) 1 under the condition of constant temperature and volume or pressure and of a fixed surface tension. The Am curve obtained from Γmix data satisfies the given condition and allows us to evaluate PMA as a function of X2. A tangential line drawn at any given point on the Am-X2 curve gives two intercepts on the Am axes; the respective intercepts themselves are A h 1 and A h 2 (see Figure 5). The estimated PMA values are listed together with the mean molecular surface area, Am, and Γmix at every 0.1 in XMEGA10 in Table 2. And also the PMA is plotted against XMEGA10 for R-SMy‚Me and MEGA-10, respectively (see Figure 6). Both curves intersect at XMEGA10 ) 0.5, showing a decreasing tendency; beyond the middle point the decrease is especially rapid. Accompanied by mixing, both surfactant’s PMAs decrease due to a strong interaction; in particular, the molecule of the minor component shrinks more than the major one. Here, it should be noted that strictly speaking we have to employ Z2 (the film composition) instead of X2 (the bulk composition) in eqs 18 and 19 when we evaluate PMA. However, to overview indi-
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Okano et al.
Table 2. Values of Z, Γ, Am, A h 1, A h 2, πcm, and ξ for Mixed Micelles of Anionic - Nonionic Binary Combinations at 30 °C for r-SMy‚Me-MEGA-10 Systems XMEGA-10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Z 0.45 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.55
Am Γ; (×10-6 mol‚m-2) (Å2) 3.82 4.22 4.46 4.59 4.66 4.68 4.63 4.54 4.39 4.15 3.90
43.5 39.3 37.2 36.2 35.6 35.5 35.9 36.6 37.9 40.0 42.6
A h1 (Å2)
A h2 πcm (Å2) (mN‚m-1)
43.5 41.8 40.1 38.3 36.4 35.3 32.4 29.7 24.4 19.7 0
0 16.8 25.0 30.5 34.1 35.8 38.3 39.8 41.2 41.9 42.6
avg
30.6 34.3 36.6 38.1 38.6 38.9 39.3 39.8 40.1 40.4 40.5
ξ -0.2 -1.1 -1.7 -1.9 -1.9 -2.0 -2.2 -2.2 -2.2 -1.7
Figure 6. Changes in partial molecular areas of R-SMy‚Me and MEGA-10 as a function of mole fraction in the surfactant mixture.
rectly the interaction in the film, we used not the calculated Z2 values but the experimental X2 values. Finally, let us look at the mixed monolayer, which has been treated as the adsorbed film up to here. The γ value at cmc, γcm, may be regarded as a kind of collapse pressure at which a liquidlike film (formed below cmc) is subject to collapse and change into a solidlike film (above cmc), the collapse pressure πcm is defined as πcm ) γo - γcm, where γo and γcm correspond to the surface tension of pure solvent and that at cmc, respectively. Since the composition in the monolayer is given by ZMEGA10, the curve of πcm against ZMEGA10 constructs a two-dimensional phase diagram. And if the Joos equation42 is applied, the interaction parameter (ξ) may be estimated. No figure of the phase diagram is shown here, but a curve that deviated negatively from ideal mixing was obtained and the interaction parameter was calculated from the Joos equation at each Z value and πcm value; the averaged value of ξ was -1.7 (see Table 2). This negative value also indicates that R-SMy‚Me molecules interact strongly with MEGA-10 molecules in the formed monolayer, as is seen in the mixed micelles. (42) Joos, P. Bull. Soc. Chem. Belg. 1969, 78, 207.
Conclusion A surface tension study was performed on a mixed surfactant system composed of an anionic surfactant, one of the R-sulfonato myristic acid alkyl ester sodium salts series (RSMy‚Me), and a nonionic surfactant, one of the alkanoyl N-methylglucamides(MEGA-10) in water. On the basis of the data obtained from the plots of the surface tension (γ) vs logarithmic total molality (ln mt) of the surfactant mixtures at every 0.1 mole fraction of MEGA10 in the mixture (XMEGA10, or X2), cmcs and the surface excesses for mixed systems (Cm and Γmix, respectively) together with those for the respective single systems (C1°, C2° Γ1°, and Γ2°) were determined at 30 °C. The purpose of the present study was to examine the interaction between the two surfactants not only in micelles but also in the adsorbed film phase. The relation between monomeric species and micelles was observed from the plot of cmc vs XMEGA10, which gave a curve that negatively deviated from ideal mixing. By application of Rubingh’s equations (derived from regular solution theory) to simulation of the cmc vs XMEGA10 curve, the interaction parameter value of ωR ) - 2.1 resulted simultaneously in a micellar composition curve, or curves of cmc vs mole fraction of MEGA-10 in micelles (YMEGA10). The curves indicated the existence of an azeotrope formed by a 3:2 mixture (at XMEGA10 ) YMEGA10 ) 0.4). To estimate the composition of the adsorbed film phase formed at cmc (ZMEGA10), we derived equations using the surface excess and cmc data as a function of XMEGA10, which was also based on regular solution theory. That is, the equations are related to the composition in the adsorbed film, ZMEGA10, equilibrated with monomers in bulk as well as with micelles and also to the interaction parameter (WA). Then, a phase diagram including the relations of cmc vs XMEGA10 (singly dispersed phase curve) and cmc vs ZMEGA10 (adsorbed film phase curve) was constructed. From the diagram an azeotrope was found to be formed by the 1:1 mixture (at XMEGA10 ) ZMEGA10 ) 0.5), indicating that the composition in micelles (Yi) differs from that in the adsorbed film (Zi). In addition, the γ vs ln mt curve was found to show synergistically enhanced surface activity, probably coming from effectively enhanced hydrophobicity by dimerization caused by a strong interaction between the headgroups of both surfactants. This speculation may be supported by the following PMA behavior, as well as by the azeotrope found at ZMEGA10 ) 0.5. Calculating the mean molecular area (Am) from Γmix data, the partial molecular area (PMA) of each component was determined as a function of XMEGA10. The plot of PMA against XMEGA10 for each surfactant demonstrated that both the curves intersect at XMEGA10 ) 0.5 (the Γmix vs XMEGA10 curve, accordingly, has a maximum of XMEGA10 ) 0.5), suggesting that a paired form of RSMy‚Me with MEGA10 acts like a unit surfactant. Anyway, all the data obtained demonstrated that the two surfactants strongly interact with each other, showing a synergism in surface activity and micellization. Acknowledgment. The present work was in part supported by grants from Ministry of Education, Culture and Science of Japan (Grant-in-Aid for Scientific Research C-07680729 and that on Priority Areas 09261240), the Central Institute of Fukuoka University, and Tokyo Tanabe Co. Ltd., Tokyo. We are grateful to Miss K. Iwaki for her fundamental work from which we could start the present study. LA990331T
