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Langmuir 1996, 12, 5048-5051
Hydrocarbon/Fluorocarbon Mixed Micelle Diagram from Surface Tensiometry M. Ben Ghoulam,† N. Moatadid,† A. Graciaa,‡ G. Marion,‡ and J. Lachaise*,‡ Faculty of Sciences, University Moulay Ismail, Mekne` s, Morocco, and L.T.E.M.P.M., Universite´ de Pau et des Pays de l'Adour, Pau, France Received January 9, 1996. In Final Form: July 15, 1996X The demixing diagram of the 6ΦC12/NF system has been determined by surface tensiometry. It is possible to fit approximately both the first cmc from the regular solution theory with a pair interaction coefficient equal to 2.2 and the second cmc from a mass balance of the surfactants between the solution and the mixed micelles. But the regular solution theory accounts neither for the coordinates of the “eutectic” point on the first cmc curve nor for the compositions in the demixing zone.
Introduction The possibility of demixing in micelles was first suggested by Mukerjee.1 Since, evidence of demixing or the formation of more than one stable population of micelles in mixed systems has been observed or investigated by many different workers.2 The possibility of demixing seems to require a significant physical basis such as immiscibility of surfactant hydrophobic groups in the core of the micelle or steric effects which restrict mixing on the basis of the molecular geometries of the surfactants. The strongest evidence for the phenomena of demixing in micelles has been found in mixed fluorocarbon/ hydrocarbon surfactant systems of like charge3 where the poor miscibility of fluorocarbons and hydrocarbons in the micellar core can provide a basis for phase separation. This is supported by observations of positive deviations from ideal mixing in the behavior of the critical mixed micelle concentration,4-10 derived from a variety of techniques: electrical conductimetry,4 surface tensiometry,6,11-13 ultra-filtration,14,15 UV spectroscopy,16 fluorescence,17 NMR,13,17,18 or pulse radiolysis,19 etc. It has been shown that surface tension can fully correlate the phase behavior of fluorocarbon/hydrocarbon surfactant * To whom correspondence should be addressed: L.T.E.M.P.M., Centre Universitaire de Recherche Scientifique, Avenue de l’Universite´, 64000 PAU, France. † University Moulay Ismail. ‡ Universite ´ de Pau et des Pays de l’Adour. X Abstract published in Advance ACS Abstracts, October 1, 1996. (1) Mukerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, 239. (2) Holland, P. M.; Rubingh, D. N. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; American Chemical Society: Washington, DC, 1992; Chapter 1, p 8. (3) Funasaki, N. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New-York, 1992; Chapter 5. (4) Mukerjee, P.; Yang, A. Y. J. Phys. Chem. 1976, 80, 1388. (5) Smith, I. H.; Ottewill, R. H. Surface Active Agents; Society of Chemical Industry: London, 1979; pp 77-87. (6) Funasaki, N.; Hada, S. Chem. Lett. 1979, 717. (7) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365. (8) Funasaki, N.; Hada, S. J. Phys. Chem. 1983, 87, 342. (9) Yoda, K.; Tamori, K.; Esumi, K.; Meguro, K. J. Colloid Interface Sci. 1985, 104, 279. (10) Zhao, G. X.; Zhu, B. Y. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986; Chapter 14. (11) Funasaki, N.; Hada, S. J. Phys. Chem. 1980, 84, 736 (12) Funasaki, N.; Hada, S. J. Colloid Interface Sci. 1980, 78, 376. (13) Carlfors, J.; Stibs, P. J. Phys. Chem. 1984, 88, 4410. (14) Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, M. Langmuir 1988, 4, 136. (15) Asakawa, T.; Miyagishi, S.; Nishida, M. Langmuir 1987, 3, 821. (16) Meguro, K.; Ueno, M.; Suzuki, T. J. Jpn. Oil Chem. Soc. 1982, 31, 909. (17) Asakawa, T.; Mouri, M.; Miyagishi, S.; Nishida, M. Langmuir 1989, 5, 343.
S0743-7463(96)00026-1 CCC: $12.00
mixtures.20 So in this paper we use surface tensiometry to explore the demixing diagram of one of these surfactant mixtures. We pay special attention to the measurement of the second micellization and to the determination of an hypothetical critical demicellization concentration predicted by Mysels.21 Experimental Section Materials and Methods. The two surfactants used are anionic surfactants. The fluorocarbon surfactant is sodium p-[(perfluoro-3-(1methylethyl)-4-methylpent-2-en-2-yl)oxy]benzenesulfonate, named Neos Ftergent (NF or surfactant f) because it was provided by the Neos Company. It was recrystallized several times from acetone until disparition of the minimum of surface tension that it presented at its critical micelle concentration, cmcf, which was measured equal to 1.53 × 10-4 M at 0.05 M sodium chloride. Its chemical structure is
The hydrocarbon surfactant is a branched alkylbenzenesulfonate (6ΦC12 or surfactant h) synthesized at the University of Texas in Professor Wade’s laboratory. It was purified until disappearance of any minimum of surface tension at its critical micelle concentration, cmch, which was found equal to 2.85 × 10-4 M at 0.05 M sodium chloride. Its chemical structure is
The use of this surfactant is one of the originalities of this work because until now NF has been mixed only with linear hydrocarbons.3 All surfactant solutions contained 0.05 M sodium chloride to decrease the electrical interactions and to keep constant the surface tensions of the pure surfactants above their critical micelle concentrations.11 (18) Fung, B. M.; Guo, W.; Christian, S. D.; Guzman, E. K. In Mixed Surfactant Systems; Holland, P. M., Rubingh D. N., Eds.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992; Chapter 15. (19) Aoudia, M.; Hubig, S. M.; Wade, W. H.; Schechter, R. S. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992; Chapter 16. (20) Ravey, J. C.; Gherbi, A.; Ste´be´, M. J. Prog. Colloid Polym. Sci. 1989, 79, 272. (21) Mysels, K. J. J. Colloid Interface Sci. 1978, 66, 331.
© 1996 American Chemical Society
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the initial mixture. Such variations are given in Figure 2 for overall concentrations of 0.0003 and 0.0004 M. The surface tensions of the fluorocarbon surfactant solutions are much lower than the surface tensions of the hydrocarbon surfactant solutions because their surface activity is higher. In the composition range where two kinds of micelles coexist, the surface tensions of the solutions are constant and all equal to 19.25 mN/m, the same value which was obtained after the second micellization in the first series of experiments. This remarkable behavior confirms that the composition of the solution in which are immersed the two kinds of micelles remains constant in the demixing zone. The two (second) critical micelle concentrations are located at the extremities of this demixing zone, as indicated in Figure 2. This second mode of determination is more precise than the first one, because the discontinuities of the slope of the curves are much more marked in this case, as is shown in the windows of Figure 2. We estimate that the relative incertitude of this new measurement of the second critical micelle concentration is of the order 3%. The complete mixed micelle diagram of the studied fluorocarbon and hydrocarbon surfactants is represented in Figure 3. It illustrates the difficulty of the determination of the second critical micelle concentration by surface tensiometry. The determination at constant 6ΦC12 mole fraction is appreciably different from the determination at constant overall concentration. The zone where the two kinds of mixed micelles are present meets the first cmc curve at the “eutectic” point E, the coordinates of which are Figure 1. Variations of the surface tension of 6ΦC12/NF solutions as function of the overall concentration of the surfactants, at constant 6ΦC12 molar fraction of the surfactant mixture. The NaCl concentration is 0.05 M, and xh is the 6ΦC12 mole fraction of the surfactant mixtures. Surface tension measurements were performed at (25.0 ( 0.1) °C with a digital tensiometer Kru¨ss.
Results Critical micelle concentrations have been first researched by measuring surface tensions of 6ΦC12/NF solutions as a function of the overall concentration of the surfactants, their relative proportions being maintained constant. The variations of the surface tensions as a function of the logarithm of the overall concentration are reported in Figure 1 for various surfactant mixtures. For the NF solution or concentrated 6ΦC12 solutions, these variations present a single change in the slope at the (first) critical micelle concentration. Above this cmc, the surface tension is constant for the pure NF solution or weakly decreasing for the concentrated 6ΦC12 solutions. For the mixtures whose concentrations are intermediate, a careful examination of the surface tension variations reveals two changes in the slope. The first change corresponds to the first cmc; it is associated with the formation of one kind of mixed micelles. The second change corresponds to the second cmc; it is associated with the formation of a second kind of mixed micelle. After this second change, whatever the surfactant proportions in the mixture are, the surface tension stays constant and equal to 19.25 mN/m. In the following in this paper, in the demixing zone we shall distinguish the hF mixed micelles which are poor in hydrocarbon surfactant from the Hf mixed micelles which are rich in hydrocarbon surfactant. The second critical micelle concentrations can also be estimated by studying, at constant overall surfactant concentration, the variations of the surface tension as a function of the relative proportions of the surfactants in
xhE ) 0.1 and cE ) csolE ) 1.69 × 10-4 M The coordinates of point E joined to the mass balance of the surfactants between the solution of monomers and the two kinds of mixed micelles gives the composition of the micelles. In effect, on the curve sol/hF, on which c < csolE, the mass balance of the two surfactants between the hF mixed micelles and the solution of monomers can be written as
c ) chF + csol
(1)
where c, chF, and csol, respectively are the total concentration of the two surfactants in the system, in the hF mixed micelles, and in the solution of monomers. As in the whole demixing zone the composition of the solution of monomers is constant, csol ) csolE, and relation 1 becomes
c ) chF + csolE
(2)
The mass balance of the surfactant h between the hF mixed micelles and the solution of monomers can be written as hF sol + xsol xhc ) xhF h c h Ec E
(3)
By eliminating chF from relations 2 and 3, it is possible to write xhF h as
xhF h )
sol xsol h Ec E - xhc
csolE - c
(4)
sol xsol h E and ch E being known, it is possible to calculate hF xh for the different couples xh, c of the curve sol/hF. The mean value of xhF h is found equal to 0.03. It is also possible to write the equation of the sol/hF curve under the form
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Ben Ghoulam et al.
Figure 2. Variations of the surface tension of 6ΦC12/NF solutions as a function of the 6ΦC12 mole fraction of the surfactant mixture, at constant overall surfactant concentration.
c ) cHf + csolE
(2′)
Hf sol xhc ) xHf + xsol h c h Ec E
(3′)
xHf h )
c)
(
sol xhc - xsol h Ec E
c - csolE
)
sol xHf h - x E
xHf h - xh
csolE
(4′)
(5′)
The sol/Hf curve drawn from relation 5′ is represented in Figure 3. It has the vertical asymptote xh ) xHf h ) 0.85. It is in relatively good agreement with the experimental values determined at constant overall concentration. Discussion
Figure 3. Mixed micelle diagram of the 6ΦC12/NF system at 25 °C: (O) first cmc; (b) second cmc determined at constant 6ΦC12 mole fraction; (0) second cmc determined at constant overall concentration.
(
)
x E - xhF h hF xh - xh sol
csolE
The development of the pseudophase separation model for the formation of nonideal multicomponent mixed micelles22,23 shows that there exist relatively simple relations between the critical micelle concentration cmchf of the mixture, the critical micelle concentrations cmch and cmcf of the components, and the mole fractions of the surfactants in the mixture and in the mixed micelles: HF 2 ch ) xh cmchf ) xHF h cmch exp[βhf(1 - xh ) ]
(6)
(5)
HF 2 cf ) (1 - xh) cmchf ) (1 - xHF h ) cmcf exp[βhf(xh ) ] (7)
The sol/hF curve drawn from relation 5 is represented in Figure 3. It has the vertical asymptote xh ) xhF h ) 0.03. It is in relatively good agreement with the experimental values determined at constant overall concentration. All that has just been said for the hF mixed micelles and the sol/hF curve can be easily transposed to the Hf mixed micelles and to the sol/Hf curve on which c > csolE. Relations 2-5 are respectively replaced by
In these relations ch and cf are the concentrations of the monomers of the two surfactants in the system; xh is the mole fraction of the hydrocarbon surfactant in the mixture, and xHF h is its mole fraction in the mixed micelle; βhf is the interaction parameter of the two surfactants.
c)
(22) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984. (23) Ben Ghoulam, M. Thesis, University of Pau, 1984.
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xh, cmch and cmcf, cmchf are parameters accessible to measurements. So relations 6 and 7 form a system which allows us to calculate βhf and xHF h . The measured variations of the (first) critical micelle concentration of the mixture as a function of the mole fraction of the hydrocarbon surfactant are correctly represented for βhf ) 2.2 (Figure 3). This value, higher than 2, indicates that there exists a demixing zone where two types of mixed micelles coexist within a solution of monomers. The demixing zone begins at point E of the curve of the (first) critical micelle concentration and thus is getting broader as the total surfactant concentration increases. At this point there is simultaneous formation of the first micelles of the two types, and the surfactant mass balance is
for the surfactant h:
sol csol h E ) xhEc E
(8)
for the surfactant f:
sol csol f E ) (1 - xhE)c E
(9)
The equality of the chemical potentials in the solution of monomers and in the two types of mixed micelles leads to the relation hF 2 xhEcsolE ) xhF h cmch exp[βhf(1 - xh ) ] ) Hf 2 xHf h cmch exp[βhf(1 - xh ) ] (10)
for the surfactant h and to the relation hF 2 (1 - xhE)csolE ) (1 - xhF h ) cmcf exp[βhf(xh ) ] ) Hf 2 (1 - xHf h ) cmcf exp[βhf(xh ) ] (11)
for the surfactant f. Hf sol In these relations xhF h , xh , xhE, and c E are unknown. hF Hf xh and xh can be calculated by eliminating cmch from relation 10 and cmcf from relation 11 to obtain hF 2 Hf Hf 2 xhF h exp[βhf(1 - xh ) ] ) xh exp[βhf(1 - xh ) ]
(12)
hF 2 Hf Hf 2 (1 - xhF h ) exp[βhf(xh ) ] ) (1 - xh ) exp[βhf(1 - xh ) ] (13)
These two equations are equivalent to the system: Hf xhF h ) xh ) 1
( )
ln
1 - xhF h xhF h
) (1 - 2xhF h )βhf
the solutions of which for βhf ) 2.2 are
(14a) (14b)
Hf xhF h ) 0.248 and xh ) 0.752
Working on relations 10 and 11, it is easy to express the coordinates of point E as follows
xsol h E )
cmch ) 0.65 cmch + cmcf
(15)
hF 2 csolE ) xhF h exp[βhf(1 - xh ) ](cmch + cmcf) )
3.37 x 10-4 M (16) The comparison between theory and experiment shows a discrepancy principally on the coordinates of the “eutectic” point E. Its abscissa calculated from the regular solution theory is independent of the interaction coefficient βhf; it only depends on the critical micelle concentrations of the two surfactants, and consequently no adjustment Hf is possible. There is also a discrepancy in xhF h and xh , the experimental values of which do not follow the theoretical Hf law for the demixing of regular solutions xhF h + xh ) 1. But theses discrepancies are not surprising, because the high repulsions of the two surfactants make probably their behavior in solution very different from that of regular solutions. We have not tried to use the group contribution method because it requires a lot of information on the involved surfactants that we have not collected; furthermore, to our knowledge, there has been no attempt in that way as far as the second cmc is concerned. A better approach of the experimental results could be obtained by using a more complex polynomial excess function for the surfactant mixture, because obviously increasing the number of parameters should improve the fitting with the first cmc curve. But we have worked in that direction without noticeable result up to now. Conclusion The demixing diagram of the 6ΦC12/NF system can be fully determined by surface tensiometry. The measurement of second critical micelle concentrations allows us to delimit the frontiers of a large demixing zone. These frontiers are well fitted through a mass balance of the surfactants between the solution of monomers and the two kinds of mixed micelles. No critical demicellization concentration has been observed. The regular solution theory does not account quantitatively for the observed behavior. There are marked discrepancies in the coordinates of the “eutectic” point of the first cmc curve and in the compositions of the two kinds of mixed micelles. These failures could be attributed to the high hydrocarbon/fluorocarbon repulsions. LA960026X
