Mixtures of Hydrogenated and Fluorinated Lactobionamide

Langmuir 2007, 23, 11465-11474

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Mixtures of Hydrogenated and Fluorinated Lactobionamide Surfactants with Cationic Surfactants: Study of Hydrogenated and Fluorinated Chains Miscibility through Potentiometric Techniques Ve´ronique Peyre,*,† Sandeep Patil,† Gre´gory Durand,‡ and Bernard Pucci‡ UniVersite´ Pierre et Marie Curie-Paris 6, UMR7575 (LECA), Paris, F-75005 France, ENSCP, UMR7575, Paris, F-75005 France, CNRS, UMR7575, Paris, F-75005 France, and Laboratoire de Chimie Bioorganique et des Syste` mes Mole´ culaires Vectoriels, UniVersite´ d’AVignon et des Pays du Vaucluse, Faculte´ des Sciences, 33 Rue Louis Pasteur, F-84000 AVignon, France ReceiVed June 1, 2007. In Final Form: July 6, 2007 The work reported herein deals with the aqueous behavior of hydrocarbon and/or fluorocarbon ionic and nonionic surfactants mixtures. These mixtures were studied using potentiometric techniques in NaBr (0.1 mol L-1) aqueous solution as well as in pure water. Mixed micelles were formed from a cationic surfactant (dodecyl or tetradecyltrimethylammonium bromide respectively called DTABr or TTABr) and neutral lactobionamide surfactants bearing a hydrogenated dodecyl chain (H12Lac) or a fluorinated chain (CF3-(CF2)5-(CH2)2- or CF3-(CF2)7(CH2)2-). We showed that concentrations of ionic and nonionic surfactants in the monomeric form as well as the composition of the mixed micelles can be specified thanks to a potentiometric technique. The complete characterization does not request any model of micellization a priori. The activities of the micellar phase constituents, as well as the free enthalpies of mixing, were calculated. The subsequent interpretation only relies on the experimental characterization. Comparison of the behaviors of the various systems with a model derived from the regular solution theory reveals the predominant part of electrostatic interactions in the micellization phenomenon. It also appears that the energy of interaction between hydrogenated and fluorinated chains is unfavorable to mixing and is of much lower magnitude than the electric charges interactions.

Introduction Fluorinated surfactants are of the highest interest, for both their fundamental and practical importance. From a fundamental viewpoint, they are both hydrophobic as well as oleophobic, and the study of their micellization behavior is of great help in the understanding of the “hydrophobicity” or “solvophobicity” effect. On a practical side, they are used in different industrial fields as part of the formulation of fire-fighting foams, emulsifiers, cosmetics, paper, etc. or in biological and medical fields to favor the membrane proteins studies or the emulsification of perfluorocarbon compounds in blood. In many applications, they are used in mixtures with hydrogenated surfactants to improve the efficiency of the desired properties.1 It is well-known that mixed systems composed of one fluorinated and one hydrogenated surfactant can, under some circumstances, form two types of micelles, due to the poor miscibility of the fluorocarbon and hydrocarbon chains.1-4 These systems were investigated by a variety of techniques, but the experimental evidence of such segregation is often difficult5 and, depending on the procedures used, can even lead to contrary conclusions. Nordstierna et al.6 have very recently opened new perspectives about the possibility of segregation of fluorinated and hydrogenated chain as patches in the same micelle. * Corresponding author. E-mail: [email protected]. † UMR7575 (LECA); ENSCP, UMR7575; and CNRS, UMR7575. ‡ Universite ´ d’Avignon et des Pays du Vaucluse. (1) Kissa, E. Fluorinated Surfactants and Repellents; Surfactant Science Series 97; Marcel Dekker: New York, 2001. (2) Funasaki, N. In Mixed Surfactants Systems; Ogino, K., Abe, M., Eds.; Surfactant Science Series 46; Marcel Dekker: New York, 1993; Chapter 5. (3) Fletcher, P. D. I. In Specialist surfactants; Robb, I. D., Ed.; Blackie Academic and Professional: London 1997. (4) Blin, J. L.; Henzel, N.; Ste´be´, M. J. J. Colloid Interface Sci. 2006, 302, 643. (5) Almgren, M.; Garamus, V. M. J. Phys. Chem. B 2005, 109, 11348. (6) Nordstierna, L.; Furo¨, I.; Stilbs, P. J. Am. Chem. Soc. 2006, 128, 6704.

Theoretical predictions could be of help to design and understand segregating systems in a better way, but most of the theories, like for instance the widely used regular solution theory (RST),7 focus on the description of mixed micelles a posteriori. Thermodynamics has also been used for this purpose.8 Molecular thermodynamics was more recently introduced for predictive purposes, in particular for mixed micelles made of ionic and nonionic components.9-13 It calculates each contribution to the Gibbs energy of micellization, among which electrostatic interactions due to polar heads and the hydrophobic contribution due to the formation of the micellar core. In these models only applied to mixtures of hydrogenated surfactants, the interaction parameter of the RST can be predicted but also a wide number of micellar properties if micelles are remaining spherical.10,11 One study considers the possibility of mixing hydrogenated surfactants of different chain lengths13 as a geometrical constraint but the main contribution to synergism is still the reduction of electrostatic repulsions between heads. In the case of fluorinated surfactants, the approach is indeed complicated by the nonspherical shape of the aggregates.14 In this context, the experimental Gibbs energy of mixing of surfactants in the micellar pseudophase was reported for some mixtures of fluorinated and hydrogenated surfactants.12,15,16,17 (7) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1. (8) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948. (9) Bergstro¨m, M.; Eriksson, J. C. Langmuir 2000, 16, 7173. (10) Sarmoria, C.; Puvvada, S.; Blankschstein, D. Langmuir 1992, 8, 2690. (11) Shiloach, A.; Blankschstein, D. Langmuir 1998, 14, 1618. (12) Shiloach, A.; Blankschstein, D. Langmuir 1998, 14, 7166. (13) Reif, I.; Somasundaran, P. Langmuir 1999, 15, 3411. (14) Ravey, J. C.; Ste´be´, M. J. Colloids Surf. A 1994, 84, 11. (15) Hoffmann, H.; Po¨ssnecker, G. Langmuir 1994, 10, 381. (16) De Lisi, R.; Inglese, A.; Milioto, S.; Pellerito, A. Langmuir 1997, 13, 192-202.

10.1021/la701579e CCC: $37.00 © 2007 American Chemical Society Published on Web 10/13/2007

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Scheme 1. Structure of the Lactobionamide Surfactants

This Gibbs energy is an interesting quantity because it reflects the interactions between the constituents of the micellar phase and enables the detection of possible segregation phenomenon. However, such various contributions are seldom considered and isolated. This was attempted by Shiloach et al.,12 who investigated mixed micelles of sodium dodecyl hexa(ethylene oxide) sulfate (SDE6S)/dodecylhexa(ethylene oxide) (C12E6) to separate the electrostatic contribution from the steric one. This system was compared to a mixture of sodium dodecylsulfate (SDS)/C12E6 to isolate the effect of the ethylene oxide group. The overall behavior of the mixture is understood by theoretical considerations where each contribution to mixed micellization is accounted for, but these contributions are not individually determined experimentally for comparison with the theory. More recently, Villeneuve et al.17 studied a mixture of neutral surfactants having the same polar head to emphasize the effect of the mixing of fluorinated and hydrogenated chains. The excess free energy was calculated and the results compared to RST, indicating that this last model is not suitable. The main difficulty in this kind of study is to characterize the partition equilibrium of the surfactant between the micellar pseudophase and the solution without having recourse to a model for the description of the interactions between the various constituents of the micelle. It means that, for the known total concentrations of each surfactant, their concentrations in solution as monomer form and the composition of the mixed micelles must be determined experimentally and independently. In our earlier studies, we have shown that this was feasible by a potentiometric technique.18,19 Our approach and subsequent interpretation rely only on the experimental results without taking into account any a priori model of micellization. The first part of this study aims to explore various experimental procedures for the determination of free monomeric surfactant concentrations in solution and the composition of the micelle. We studied the behavior, in water and in NaBr solution (0.1 mol L-1), of mixed systems involving one ionic surfactant (dodecyltrimethylammonium bromide (DTABr) or tetradecyltrimethylammonium bromide (TTABr)) and one nonionic fluorinated or hydrogenated surfactant derived from lactobionolactone (Scheme 1). For these systems, the segregation of two kinds of micelles is not likely to occur due to the highly favorable electrostatic contribution toward synergism.2 The second part of this work deals with some models for the mixing of surfactants in micelles and the information that can be deduced on the interactions between hydrogenated and fluorinated chains, starting from the RST. Materials and Methods Materials. Dodecyltrimethylammonium bromide (DTABr) was purchased from Acros Organics and recrystallized twice from acetone/ ether mixture before being used. Tetradecyltrimethylammonium bromide (TTABr) was purchased from Aldrich and was recrystallized twice from acetone-ethanol. (17) Villeneuve, M.; Nomura, T.; Matsuki, H.; Kaneshina, S. Aratono, M. J. Colloid Interface Sci. 2001, 234, 127. (18) Peyre, V. Langmuir 2002, 18, 1014-1023. (19) Palous, J. L.; Turmine, M.; Letellier, P. J. Phys. Chem. B 1998, 102, 5886.

Figure 1. Examples of calibration. ([) emf vs log[DTABr] in NaBr 0.1 mol L-1. The break in the curves corresponds to cmc. (/): emf vs log[F6Lac] in a solution of DTABr 3.63 10-4 mol L-1 (i.e., log [DTABr] ) -3.44) and NaBr 0.1 mol L-1. The initial plateau indicates the insensitivity of the electrode to F6Lac, and the break in the curve indicates the beginning of the formation of mixed micelles. N-Docedyl lactobionamide (H12Lac), N-1H,1H,2H,2H perfluorooctyl lactobionamide (F6Lac), and N-1H,1H,2H,2H perfluorodecyl lactobionamide (F8Lac) were synthesized according to a prodecure already published.20 All solutions were made up with 18 MΩ cm high-quality water. Swamping electrolyte was 0.1 mol L-1 NaBr solution. The concentrations of stock solutions of surfactants were 0.1 mol L-1 for DTABr, 0.01 mol L-1 for H12Lac, 0.05 mol L-1 for F6Lac, and 1.6 × 10-3 mol L-1 for F8Lac. The F6Lac solution was slightly turbid, but still homogeneous, ensuring accurate volumetric measurements and transfers in good conditions. The F8Lac solution is slightly viscous and forms gels at higher concentrations. When H12Lac was used, experiments were carried out at 313.0 ( 0.1 K to avoid precipitation.21 Otherwise, the experimental temperature was 298.0 ( 0.1 K. Surface Tension. Surface tension of F8Lac was measured with a Wilhelmy platinum plate controlled by a Kruss K10T instrument, in 20 mL initial volume, thermostated at 298.0 ( 0.1 K. Potentiometry. The chemical potential of DTA+ and TTA+ was followed by an in-house specific electrode already described elsewhere.22-24 It is composed of a liquid PVC membrane, plasticized by dinonylphtalate, and the ion exchanger is tetraphenylborate. The reference solution is DTABr 10-3 mol L-1 in water or in NaBr 0.1 mol L-1. The electromotive force (emf) of the electrode is linear with the logarithm of the concentration of free ammonium (slope 59 mV/decade at 298 K) in the conditions we used. Micellar aggregation is indicated by a break in the slope. We checked that none of the neutral surfactants studied interfered with the response of the electrode (Figure 1).Reference electrodes are classical calomel electrodes, protected from the diffusion of amphiphile by an agaragar salt bridge in KCl 2 mol L-1. It is necessary to recall some essential thermodynamic relations on which our work is based, before reporting the experimental procedures used to characterize the equilibrium in solution. Thermodynamical Behavior of Mixtures: Activities in the Micellar Phase. We consider a mixture of an ionic (M+, X-) and a nonionic (P) surfactant in aqueous solutions. We have used the following abbreviations: nw the number of moles of water, nMX the number of moles of ionic surfactant, and np that of nonionic surfactant. The Gibbs energy of the system is (20) Lebaupain, F., Salvay, A. G.; Olivier, B.; Durand, G.; Fabiano, A. S.; Michel, N.; Popot, J. L.; Ebel, C.; Breyton, C.; Pucci, B. Langmuir 2006, 22, 8881. (21) Kjellin, U. R. M.; Claesson, P. M.; Vulfson, E. N. Langmuir 2001, 17, 1941. (22) Jezequel, D.; Mayaffre, A.; Letellier, P. Can. J. Chem. 1991, 69, 1865. (23) Jezequel, D.; Mayaffre, A.; Letellier, P. J. Chim. Phys. 1991, 88, 391. (24) Martin, J. V.; Turmine, M.; Letellier, P.; Hemery, P. Electrochim. Acta 1995, 40, 2749.

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G ) nwµw + nMXµMX + npµp

(1)

µw, µMX, and µp are the chemical potentials of the components of the mixture. If mixed micellization occurs in solution, we consider formally two phases in equilibrium: one bulk phase containing nw mol of water, nbMX and nbp mol of surfactant and a micellar pseudophase containing nσMX and nσp mol of surfactant. The free enthalpies of the two phases can be written as Gb ) nwµw + nbMXµMX + nbpµp

(2a)

Gσ ) nσMXµMX + nσp µp

(2b)

The corresponding Gibbs-Duhem equations, at constant temperature and pressure, are 0 ) nwdµw + nbMXdµMX + nbpdµp 0)

nσMX

dµMX +

nσp

dµp

(3a) (3b)

The expressions of the chemical potentials of the two surfactants MX and P can be developed with reference to the model behaviors conventionally chosen for each phase. The concentration of the charged surfactant MX, in the bulk phase, is such that CbMX ) CbM ) CbX for electroneutrality reasons. The chemical potential of MX will be written with reference to the infinitely dilute behavior in the concentration scale, introducing the activity of MX, abMX. By definition, abMX is the product of the individual activities of the ions M+ and X- (abM; abX). µMX ) µ∞MX + RT ln abMX ) µ∞MX + RT ln abM abX

(4)

µ∞MX

is the standard chemical potential at infinite dilution of MX in the bulk phase. In our present study, solutions are dilute enough to allow assimilation of the value of the activity of the ions with their concentration. abM ) {CbM}; abX ) {CbX}

(5)

Notation {X} means “value of X”. It is a dimensionless quantity. If M+ and X- are the only ions present in the aqueous bulk phase, we write abMX ) {CbM}{CbX} ) {CbMX}2

(6)

In the micellar pseudo-phase, we will note aσMX the activity of MX, with reference to the behavior of the pure micelle of MX. The equilibrium between the bulk phase and the micellar phase is expressed as µMX )

µ/MX

+ RT ln

aσMX

)

µ∞MX

+ RT

ln{CbMX}2

(7)

When the micelle of MX is pure, the value of its activity is conventionally set to 1. The concentration of MX in solution is then equal to the critical micellar concentration, cmcMX. µ/MX ) µ∞MX + RT ln{cmcMX}2

(8)

Using these conventions, the activity of MX is calculated through relation (9) aσMX )

{CbMX}2 {cmcMX}2

(9)

Surprisingly, in most of the studies dealing with the behavior of mixtures of ionic surfactants, this relation is not taken into account. In the expression of the activity of the ionic surfactant, the ratio of the concentrations is not raised to the square power. In such a case,

one cannot be sure about the validity of the reasoning and of the resulting data treatment, particularly in the frame of the RST. However, it is correct to not consider the power term when the surrounding medium is a concentrated salt solution, Na+,X- for example. In this case, since the activity of X- is set constant by the swamping electrolyte, the activity of MX is equal to the ratio of the concentration of M+ over the cmc of MX in the chosen electrolyte medium. Following the same thermodynamic consideration, the activity of the neutral surfactant, aσP, is written as aσP )

CbP cmcP

(10)

CbP is the concentration of P in the bulk phase, and cmcP is the critical micellar concentration of P considered alone in the medium. Once the values of CbMX and CbP are accessible, the activities of both components of the pseudo-phase can be determined. The quantities of mixing of the surfactants in the micellar phase can then be calculated. The molar Gibbs energy of mixing is conventionally written as ∆mixGmol ) RT(xMX ln aσMX + xP ln aσP)

(11)

In order to compare our results to a reference behavior, we define an ideal mixed micelle as a mixture in which the activity of each surfactant is equal to its molar fraction in the mixed micelle. In this case, surfactant MX is considered as nondissociated in the micellar phase. xMX )

nσMX nσMX + nσP

(12)

This leads to the following expression for the ideal molar Gibbs energy of mixing: ∆mixGmol,id ) RT(xMX ln xMX + xP ln xP)

(13)

Other descriptions do exist, in particular some models consider the ionic surfactant and its counterion as two different components in the composition of the micelle25 or use a volume fraction in the micelle.26 However, because the objective of our study is to compare the behavior of fluorinated/hydrogenated with hydrogenated systems, the choice of the reference system is not essential. From these considerations, the excess molar Gibbs energy can be deduced ∆exGmol ) gE ) RT(xMX ln γMX + xP ln γP)

(14)

γMX and γP are the activity coefficients of MX and P, respectively, in the micellar phase. They are classically defined as the ratio of the activity over the molar fraction γMX ) aMX/xMX and γP ) aP/xP. The notation gE is introduced for simplification. Experimental Methods for Determination of the Solution Composition. (1) Direct Determination of the Concentration of M+ Free in Solution, CbMX, by Potentiometry. The activity of M+ in solution can be readily determined using an electrode sensitive to M+. When the two surfactants, MX and P, are free in solution, the response of the electrode is not influenced by the neutral component, as can be seen in Figure 1. The plot displays the calibration curve of the electrode (emf ) f(log C)) for DTABr in NaBr 0.1 mol L-1, as well as the response of the electrode when the neutral surfactant F6Lac is added to a solution of DTABr of concentration 3.63 × 10-4 mol L-1. The break point in the calibration curve corresponds to the micellization of DTABr. The slight decrease of emf upon addition of the neutral surfactant is due to dilution, and the observed break (25) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H.; J. Colloid Interface Sci. 1998, 200, 161. (26) Eads, C. D.; Robosky, L. C. Langmuir 1999, 15, 2661.

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Figure 2. Alternated additions of F6-Lac and DTABr in NaBr 0.1 mol L-1, at 298 K, for initial values of log[DTABr] as indicated in the legend. on this curve corresponds to the formation of mixed micelles as is explained later. (2) Determination of the Micelle Composition xMX. (2a) By Alternated Additions. The method we used was first presented by Palous et al.19 and is briefly summarized here. It requires an electrode sensitive to one cationic surfactant M+ and insensitive to the other surfactant, P. In a solution of given concentration CbMX of M+ (i.e., of fixed emf), below its cmcMX, one adds an aliquot δnP of P (in mole unit). If the concentration of P is too low to form a mixed micelle, the emf does not change: the concentration of “free” M+ remains unaltered (except for dilution). If mixed micelles form, the emf decreases because part of the M+ is consumed due to the formation of micellar aggregates. A quantity δnMX of MX is then added to restore the initial emf. At the end of this procedure, the system returns to its initial equilibrium state. This is repeated several times. The added quantity δnMX exactly corresponds to the amount of free M+ that has disappeared from the solution owing to the formation of the mixed micelles. One has thus access, for a chosen concentration CbMX, to the composition of the micelle, xMX. During these successive operations, the quantity of the micellar phase increases in the medium, at identical equilibrium position. This can be easily verified by plotting ΣδnP vs ΣδnMX. A straight line is obtained, whose slope, p(CbMX), depends on the chosen concentration of MX and whose y intercept corresponds to the concentration of free P, CbP. The molar fraction of MX in the micelle is calculated through xMX )

nσMX nσMX + nσP

)

1 1 + p(CbMX)

(15)

nσMX and nσP are the numbers of mole of MX and P in the micellar pseudo-phase. We report in Figure 2 an example of such plots obtained for the system DTABr/F6Lac in NaBr 0.1 M. Thus, for each value of CbMX, the micelle composition and the concentration CbP of free nonionic surfactant in solution is determined. However, when the later quantity is very small, its determination through the y intercept close to zero becomes highly imprecise. In such a situation, an alternative method has to be used to specify CbP independently. (2b) By Successive Additions. When the cmc of the nonionic surfactant is very low, as is often the case, the determination of the micelle composition can be very easily carried out. It was used for a mixture of DTABr/H12Lac. The initial sample is a solution of H12Lac at a concentration much higher than its cmc: one can thus consider that the concentration of free H12Lac is very low (comparatively to the surfactant incorporated within the micelles), constant, and equal to the cmc value. Aliquots of DTABr are added to this solution, and the emf is recorded. Since DTABr and H12Lac can form mixed micelles, only part of the DTA+ introduced remains in the solution and is responsible for the observed emf. The

Figure 3. ([) Calibration curve with DTABr at 313 K. Initial solution: NaBr 0.1 M. (0) Calibration curve with DTABr at 313 K. Initial solution: H12Lac 0.01 mol L-1 in NaBr 0.1 mol L-1.

Figure 4. Variation of the emf upon addition of F6Lac in a solution containing initially 3.63 × 10-4 mol L-1 of DTABr in NaBr 0.1 mol L-1 at 298 K. The break in the curve corresponds to CbP. complementary part is engaged into the micelles. Thus, one can obtain the free DTABr concentration (through emf measurement) and the micellized DTABr by subtraction (mass balance). Under the approximation that all H12Lac is included within micelles, the composition of these micelles is known. A few points by alternated additions are then necessary to check the validity of this hypothesis. An example of such behavior is reported in Figure 3. (3) Determination of Free Surfactant Concentration CbP. The concentration of the neutral surfactant in the bulk CbP can be determined through the y intercept of the alternated additions as explained above. However, two others techniques enable the confirmation of this determination: (3a) Break Point of emf. CbP can be determined by direct recording of the emf E. Aliquots of compound P are added to a sample volume of MX having an initial molarity CMX below the cmc of MX. The initial emf value, Einit, is representative to the concentration CMX. As long as the concentration of P is lower than CbP, the emf does not change (except for the small change of CMX due to dilution effect), because both surfactants are in monomer forms and do not interact (between themselves). As soon as the P concentration reaches CbP, mixed micelles are formed. Some molecules of the surfactant MX initially present in solution are used up in micelles formation and the emf decreases strongly. The break in the plot (E-Einit) vs (concentration of P) is the concentration, CbP, of P, in equilibrium with micelles and MX at the initial concentration CMX ) CbMX (dilution effects being compensated). Figure 1 is an example of raw emf data and the corresponding E-Einit plot is displayed in Figure 4. As can be seen on this representation, the determination of CbP is only about 10% precise, because it is always very difficult to determine from which exact concentration the emf varies. However, this approach leads to reasonable and, above all, independent values for CbP, as compared to those obtained using other determination procedures.

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Table 1. Characteristics of the Surfactants Used cmc (mol L -1)

technique for cmc (temp)

(2.7 ( 0.2) × 10-4 in watera 1.8 × 10-4 in waterb 3.5 × 10-4 in waterc 2.5 × 10-4 in waterd (2.5 ( 0.3) × 10-4 in watere (1.5 ( 0.2) × 10-3 in watere (2.5 ( 0.3) × 10-5 in watera

surf. tens.(313 K) surf. tens.(313 K) surf. tens.(323 K) surf. tens. (298 K) fluorimetry (298 K) surf. tens. (298 K) surf. tens. (298 K)

surfactant H12Lac

H12Lac F6Lac F8Lac a

γplateau (mN m-1)

A (Å2/molecule)

33.0 ( 0.3 36.1 35 35

51 ( 2 44 47 39

21 ( 1 20 ( 0.5

40 ( 4 47 ( 2

This work. b Reference 29. c Reference 21. d Reference 30. e Reference 20.

Among these procedures the use of thermodynamic properties of pseudophases is the most general and the most precise approach. (3b) Integration of the Gibbs-Duhem Relation. The activity of the neutral surfactant in the bulk is obtained by integration of the Gibbs-Duhem relation in the micellar phase (relation 3b), according to d ln aσP ) d ln(CbP) ) -

nσMX nσP

1 d ln(CbMX)q ) - b d ln(CbMX)q p(CMX) (16)

where q ) 1 in NaBr 0.1 mol L-1 and q ) 2 in water. The values of p(CbMX) for different concentrations of CbMX are determined by the alternated additions technique. After plotting the curve 1/p(CbMX) vs ln CbMX, relation 16 is integrated (graphically by the trapeze method or analytically after fitting) between a given state (CbMX; CbP) of the solution and the pure micelle of P (CbMX ) 0; CbP ) cmcp). ln(CbP) ) ln(cmcP) - q

∫

C bMX

C bMX)0

1 d ln(CbMX) p(CbMX)

(17)

This relation had already been demonstrated via another thermodynamic route.27 The advantage of this method of alternated additions is that the results obtained are valid in a large range of concentrations. xMX and CbMX are readily obtained from experiments. cmcP is determined by surface tension measurements, whereas the calculation of CbP does not require any model for the micelle. Of course, all these methods should lead to the same values for CbP, which we systematically checked when the experimental conditions permitted it.

Results Pure Surfactants: cmc and Surface Active Properties. The critical micellar concentrations of ionic surfactants was specified by potentiometry either in water or in the presence of electrolyte. The cmc values of DTABr in water are 1.5 × 10-2 mol L-1 at 298 K and 1.4 × 10-2 mol L-1 at 313 K; in NaBr 0.1 mol L-1 solution, the cmc reaches 4.5 × 10-3 mol L-1 at 298 K. The cmc of TTABr is 5.5 × 10-4 mol L-1 in NaBr 0.1 mol L-1 at 298 K. The cmc’s of nonionic surfactants alone were determined by surface tension measurements for F8-Lac at 298 K and H12-Lac at 313 K in water (curves displayed in Figure 5), and the values along with those obtained from different sources are reported in Table 1. No minimum is observed in the γ vs log c curves for H12Lac and F8Lac. The cmc was taken at the beginning of the plateau, and the area per molecule, A, was estimated from the Gibbs adsorption isotherm

A ) 1/NAΓ and (27) Peyre, V.; Letellier, P. J. Colloid Interface Sci. 1999, 213, 371-378.

Γ)-

1 dγ RT d ln{Cp}

(18)

where γ is the surface tension (Nm-1), {Cp} is the value of the neutral surfactant concentration, RT is the usual, and NA is the Avogadro number. Comparing the cmc values of fluorinated surfactants, F6Lac and F8Lac, to the hydrogenated series represented by H12Lac and H10Lac (cmcH10Lac ) 1.6 × 10-3 mol L-1 (ref 20)), one can calculate that one CF2 group is equivalent to 1.4 to 1.5 CH2. This value is slightly lower than what is usually reported (1.5-1.7)1,3 and is coherent with the fact that the ethyl spacer between the polar head and the fluorinated chain contributes very little to the micellization process.28 The substitution of hydrogen atoms by fluorine atoms on the carbon chain does not result in important modification of the area per molecule. However, the decrease of surface tension is much larger with fluorinated compounds than with their hydrogenated homologues; this property was also observed by different groups.31 Determination of the Free Surfactant Concentration CbP in Mixed Systems. The experimental techniques presented above allow the determination of the CbP of the neutral component in three ways. The coherence of the three values gives an indication of their validity. In particular, when the direct determination is coherent with the integration method, this validates the mixed micelle composition, too. In Figure 6, with an example mixture DTABr/F6Lac in NaBr 0.1M, we show the different values of P concentration obtained either by direct determination or through the integration according to the alternated addition technique. The value of the slope is 1, showing complete agreement between the two determination procedures. This validates the thermodynamic framework necessary to the integration technique and the description of the micelles as a pseudophase. For the calculation of the activity coefficients, we chose to work on the values obtained through integration. Composition of Mixed Micelles. Values of each surfactant concentration in monomer form, as well as mixed micelle compositions, are reported in Tables 2 and 3 in water and in NaBr (0.1 mol L-1), respectively. These values enable the discussion on the behavior of the different systems studied here.

Discussion Though the cmc values for hydrogenated and fluorinated surfactants were not obtained at the same temperature (313 K (28) Sadtler, V. M.; Giulieri, F.; Krafft, M. P.; Riess, J. G. Chem. Eur. J. 1998, 4 (10), 1952. (29) Arai, T.; Takasugi, K.; Esumi, K. Colloid Surf. A 1996, 119, 81. (30) Syper, L.; Wilk, K. A.; Sokolowski, A.; Burczyk, B. Prog. Colloid Polym. Sci 1998, 110, 199. (31) (a) Shinoda, K.; Hato, M.; Hayashi, T. J. Phys. Chem. 1972, 76, 909. (b) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1976, 80, 2468. (c) Ravey, J. C.; Gherbi, A.; Stebe, M. J. Prog. Colloid Polym. Sci.1988, 76, 234.

11470 Langmuir, Vol. 23, No. 23, 2007

Peyre et al. Table 2. Experimental Data for Surfactant Mixtures in Watera DTABr/H12Lac

DTABr/F6Lac

b CDTABr , mol L-1

b CH12Lac , mol L-1

xDTA

0 7.04 × 10-6 1.37 × 10-5 4.45 × 10-5 9.07 × 10-5 1.00 × 10-4 2.12 × 10-4 5.72 × 10-4 8.03 × 10-4 1.00 × 10-3 2.19 × 10-3 3.23 × 10-3 4.91 × 10-3 5.41 × 10-3 6.92 × 10-3 7.87 × 10-3 8.73 × 10-3 1.50 × 10-2

3.00 × 10-4 2.94 × 10-4 2.88 × 10-4 2.69 × 10-4 2.51 × 10-4 2.48 × 10-4 2.21 × 10-4 1.71 × 10-4 1.53 × 10-4 1.41 × 10-4 9.35 × 10-5 6.86 × 10-5 4.26 × 10-5 3.70 × 10-5 2.31 × 10-5 1.63 × 10-5 1.05 × 10-5 0

0.00 0.01 0.02 0.04 0.06 0.05 0.09 0.13 0.14 0.17 0.25 0.32 0.40 0.44 0.54 0.61 0.72 1.00

b CDTABr , mol L-1

b CF6Lac , mol L-1

xDTA

0 1.00 × 10-5 2.45 × 10-5 4.79 × 10-5 1.00 × 10-4 3.72 × 10-4 5.75 × 10-4 1.00 × 10-3 1.82 × 10-3 1.82 × 10-3 4.17 × 10-3 6.92 × 10-3 1.00 × 10-2 1.55 × 10-2

2.04 × 10-3 1.96 × 10-3 1.88 × 10-3 1.78 × 10-3 1.65 × 10-3 1.29 × 10-3 1.16 × 10-3 9.88 × 10-4 7.85 × 10-4 7.85 × 10-4 4.80 × 10-4 2.80 × 10-4 1.29 × 10-4 0

0.00 0.02 0.04 0.04 0.06 0.10 0.11 0.14 0.18 0.17 0.28 0.41 0.60 1.00

For each value of CbMX, xMX is obtained from the slope of alternated additions curves (eq 15) and CbP from the integration of eq 17. T ) 313 K for DTABr/H12Lac. T ) 298 K for DTABr/F6Lac. a

Figure 5. Surface tension in water: (a) H12Lac at 313 K and (b) F8Lac at 298 K.

Figure 6. Comparison of the CbP of the neutral surfactant obtained by direct determination (i.e., break in the emf) and by integration (eq 17) after alternated additions, for DTABr/F6Lac in NaBr 0.1 mol L-1. Each point corresponds to a different value for the cmcM of the cationic surfactant. T ) 298 K. The straight line is y ) x.

for H and 298 K for F), we may consider that cmc’s are not strongly affected by this temperature difference21 and that we may compare in these conditions the behaviors of the two surfactant families. The first remark concerns the description of the systems allowed by our approach. Its particularity is to enable the experimental determination of the two surfactants concentrations in solution, CbMX and CbP as well as the micelle composition without requiring any sophisticated model. Indeed, the description of the systems only requests the pseudo-phase concept, which is verified as long as identical values for CbP are obtained either using the extrapolation to the y intercept (alternated addition method), the direct method (emf break), or through the integration of the Gibbs-Duhem relation in the micellar phase.

The behavior of micellar systems can be represented like for classical balanced binary systems (solid-liquid, liquid-gas, ...) by plotting a thermodynamic quantity characteristic of the system vs the composition of the micellar phase xMX and the composition of the bulk phase RMX ) CbMX/(CbMX + CbP). As an example, we report in Figure 7a the variations of the bulk composition RMX as a function of the micellar composition xMX for the mixture DTABr/F6Lac in water and in Figure 7b the variations of the activity of MX in the micelle as a function of xMX and RMX. It can be observed in Figure 7a that for very low xDTABr, the micelles are richer in DTABr than the bulk, though the cmc of DTABr (1.5 × 10-2 mol L-1) is higher than the cmc of F6Lac (1.5 × 10-3 mol L-1). In mixed systems, two phenomenon are in balance to determine the micellar composition: on the one hand, if the surfactants are ideally miscible, the micelles are richer than the bulk in the component that micellizes more easily, i.e., the component with the lower cmc (F6Lac). On the other hand, in the case of highly favorable synergy in the micelle, the other surfactant (DTABr) is comicellized with the first one, causing the micelle composition in F6Lac to decrease or xDTABr to increase. If the synergy is strong enough, the micellar composition xDTABr can even become higher than the bulk composition RDTABr as it is observed here. The second remark concerns the values obtained for all the systems. If two micellar phases should coexist, resulting from the segregation of hydrogenated and fluorinated surfactants, the variance of the system would be equal to 0, thus the composition of the bulk phase as well as the activity aMX would be fixed. In the systems we present herein, the variations of the activities are monotonous with their compositions, which suggests that no demixing or segregation of surfactants is evidenced in the micellar phase. The negative values of the molar free enthalpies of mixing reported in Figure 8 confirm this observation. We reported in Figure 8 the ideal Gibbs energy of mixing as define by eq 13. A very large effect of the swamping electrolyte on the Gibbs energy of mixing of surfactants in the micellar phase is evidenced. The addition of a salt decreases a lot the deviation from ideality. This evolution is the result of the screening of the electrostatic repulsions between charged headgroups in the micelle when a swamping electrolyte is present. The electrostatic effects have a preponderant role on the stability of

Hydrogenated/Fluorinated Chains Miscibility

Langmuir, Vol. 23, No. 23, 2007 11471

Table 3. Experimental Data for Surfactant Mixtures in NaBr 0.1 mol L-1a DTABr/H12Lac

DTABr/F6Lac

b CDTABr , mol L-1

b CH12Lac , mol L-1

xDTABr

0 1.26 × 10-5 3.25 × 10-5 5.75 × 10-5 1.00 × 10-4 2.87 × 10-4 3.72 × 10-4 3.80 × 10-4 8.99 × 10-4 1.00 × 10-3 1.56 × 10-3 2.16 × 10-3 2.36 × 10-3 2.89 × 10-3 3.02 × 10-3 3.23 × 10-3 3.61 × 10-3 4.50 × 10-3

2.82 × 10-4 2.77 × 10-4 2.69 × 10-4 2.62 × 10-4 2.51 × 10-4 2.19 × 10-4 2.08 × 10-4 2.08 × 10-4 1.58 × 10-4 1.51 × 10-4 1.18 × 10-4 8.93 × 10-5 8.05 × 10-5 6.03 × 10-5 5.53 × 10-5 4.76 × 10-5 3.47 × 10-5 0

0.00 0.02 0.04 0.06 0.07 0.16 0.17 0.18 0.29 0.31 0.41 0.51 0.54 0.63 0.68 0.69 0.77 1.00

b CDTABr , mol L-1

b CF6Lac

0 2.45 × 10-5 4.79 × 10-5 1.00 × 10-4 3.63 × 10-4 5.50 × 10-4 1.00 × 10-3 1.74 × 10-3 2.19 × 10-3 3.39 × 10-3 4.47 × 10-3

mol

L-1

1.45 × 10-3 1.39 × 10-3 1.34 × 10-3 1.27 × 10-3 1.06 × 10-3 9.80 × 10-4 8.28 × 10-4 6.52 × 10-4 5.61 × 10-4 2.40 × 10-4 0

TTABr/F8Lac xDTABr

b CTTABr , mol L-1

b CF8Lac , mol L-1

xTTABr

0.00 0.04 0.05 0.08 0.15 0.18 0.25 0.35 0.44 0.78 1.00

0 1.00 × 10-5 2.45 × 10-5 4.79 × 10-5 1.00 × 10-4 2.00 × 10-4 2.51 × 10-4 3.16 × 10-4 3.24 × 10-4 3.98 × 10-4 5.50 × 10-4

2.40 × 10-5 2.19 × 10-5 1.98 × 10-5 1.79 × 10-5 1.50 × 10-5 1.16 × 10-5 1.03 × 10-5 9.04 × 10-6 8.90 × 10-6 7.31 × 10-6 0

0.00 0.08 0.11 0.16 0.21 0.33 0.33 0.40 0.42 0.55 1.00

For each value of CbMX, xMX is obtained from the slope of alternated additions curves (eq 15) and CbP from the integration of eq 17. T ) 313 K for DTABr/H12Lac. T ) 298 K for DTABr/F6Lac and TTABr/F8Lac. a

substitution of hydrogenated chains by fluorinated chains, or the increase of the number of carbon atoms in the chains, do not dramatically change the phenomena. The energy of interaction between chains of different nature, though always unfavorable as can be seen in Figure 8, are of much lower magnitude than those implied by the charges. To account for this more precisely, the second part of this work will deal with modelization of the Gibbs energy of mixing. Models for Mixed Micelles. The behavior of mixtures of surfactants in micellar form can be analyzed using the thermodynamic quantities of mixing and in particular the molar excess Gibbs energy, gE, defined by eq 14. In our study, gE is an experimental quantity that can be calculated without any model for nonideality. Though many models exist (for a review, see refs 32 and 33), we chose to start from the widely used regular solutions theory (RST) to analyze the variations of gE according to the composition of the mixtures. Regular Solution Theory (RST) or Symmetrical Mixture. Due to its simplicity and also because of the fruitful descriptions that can be deduced about the interactions between the components of the micellar system, this model developed by Rubingh7 is widely used, gE is expressed as a series expansion limited to the first term

gE ) βxMXxP

Figure 7. Mixture DTABr/F6Lac in water at 298 K (a) bulk composition RDTABr vs micelle composition xDTA (b) activity of DTABr in the micelle, aDTA vs bulk composition RDTABr (*) and micelle composition xDTABr ([).

the aggregates so formed, and the synergy in the formation of mixed micelles is mainly due to this effect. This peculiar behavior can be seen directly on the plot of the activities of the two surfactants vs the composition of the micelle; the curves are displayed in Figure 9a in water and panel b in NaBr 0.1 M, for all of the systems of this study. In each medium, the representative points of the different systems define very similar behaviors; the curve approaches the ideal one upon addition of salt. One can conclude that the

(19)

β is the interaction parameter, related to the interaction enthalpies between surfactants. It is a constant over the entire range of composition and the mixture is symmetric with respect to each surfactant. A positive β corresponds to an unfavorable mixing, and on the other hand, a negative value corresponds to favorable synergism. One essential assumption of this symmetrical model is the random mixing of the surfactants of similar sizes in the micelle. This assumption is certainly not true when one of the surfactants is charged and the other is nonionic, because the charges tend to be as widely spaced as possible onto the surface of the micelle to limit unfavorable electrostatic interactions. Though β was initially an empirical parameter, molecular thermodynamic models attempted to predict it. These models (32) Hines, J. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 6350. (33) Mixed Surfactant Systems; Abe, M., Scamehorn, J. F., Eds.; Surfactant Science Series 124; Marcel Dekker: New York, 2005.

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Peyre et al.

consider the various contributions of the different parts of the molecules to the excess Gibbs energy: transfer and packing of the chains, formation of the interface between the micellar core and the aqueous medium, and steric and electrostatic interactions between the heads.11 It can predict various properties of the mixed system (cmc, interaction parameter, composition of the system, and structural parameters of the micelle). Following this model, the main contributions are the electrostatic interaction between heads, gEelst, and the interaction between the hydrophobic moieties of the two surfactants, gEcore.10

gE ≈ gEcore + gEelst

(20)

In the case where the two hydrophobic moieties are of the same nature (hydrocarbon-based or fluorocarbon based), gEcore is equal to zero. This working model enables the easy calculation of the electrostatic part and the prediction of β when one of the surfactant is ionic in the presence of swamping electrolyte. Asymmetrical Mixture of Hydrocarbon Surfactants.When β is not a constant over the entire range of composition, the excess Gibbs energy gE can be written as the mathematical form β(xMX)xMX(1 - xMX), where β is now allowed to vary with the micelle composition.34,13 This form has no physical basis, but it is convenient for its similarity with the regular solution model. gE is not symmetrical any more with the micelle composition. Using this description, the electrostatic interaction parameter, βelst, is calculated for spherical micelles, introducing structural parameters for the surfactants (chain length, charge, and distance from micellar core to charge) and solution conditions (ionic strength and temperature). The ionic strength I has to be high enough so that κR > 0.5 (κ is the screening constant and R the radius of the micelle). For a classical radius of spherical micelle R ) 2 nm, it corresponds to I > 0.006 mol L-1. Once βelst(xMX) has been calculated using the electrostatic model, we have shown in a preceding article18 that it can be described by a more simple linear function in the range 0.1 < xMX < 0.9

βelst(xMX) ) dxMX + e

(21)

The parameters d and e are fitting parameters of the complete expression of βelst. In the case of the mixture of DTA+ and any neutral surfactant bearing a hydrocarbon chain of 12 carbons, in 0.1 mol L-1 supporting electrolyte at 298 K, it was found that d ) 0.92RT and e ) -2.67RT. Asymmetrical Mixtures of Hydrocarbon and Fluorocarbon Surfactants and Contribution of the Chains to the Gibbs Energy of Micellization. When the chains of the two surfactants are of different nature, their contribution gEcore to the Gibbs energy of micellization is not equal to zero. We chose to express gEcore with the same mathematical form as before, with the same physical limitations.

gEcore ) βcore(xMX)xMX(1 - xMX)

(22)

βcore(xMX) is characteristic of the interactions between chains and is allowed to vary with the composition of the micelle.

gE ≈ [βcore(xMX) + βelst(xMX)]xMX(1 - xMX)

(23)

If βelst is known by a distinct mean, the study of gE will enable the determination of βcore. A reference system (DTABr/H12Lac in this study) is used to estimate the electrostatic contribution to gE in eq 20. This system (34) Maeda, H. J. Phys. Chem B 2004, 108, 6043.

Figure 8. Molar Gibbs energy of mixing ∆mixGmol in the mixed micelles. The line is the ideal mixing. (4) DTABr/H12Lac in NaBr 0.1 mol L-1; (0) TTABr/F8Lac in NaBr 0.1 mol L-1; (×) DTABr/ F6Lac in NaBr 0.1 mol L-1; (2) DTABr/H12Lac in water; and (*) DTABr/F6Lac in water.

is made of two surfactants with identical hydrocarbon tails, so that the contribution of the packing of the chain, gEcore, to the excess Gibbs energy is zero. In the other mixed systems (DTABr/ F6Lac and TTABr/F8Lac), the polar heads being the same as in the reference system, βelst is known and βcore can be deduced by subtraction

βcore ) β - βelst

(24)

Application to our Systems. In a classical characterization of mixed micelles, the values of free concentrations of species MX and P are experimentally determined at the cmc, for example by surface tension. The values of β and the composition of the mixed micelle are then calculated by iteratively solving two equations.7 In our case, we determined experimentally the free concentrations and the composition of the micelles. We have only the quantity β to calculate and thus proceeded differently. For each system, the excess free energy gE is calculated thanks to eq 14. β is then readily obtained as gE/(xMxP). In the NaBr 0.1 mol/L System. The β plots for the reference system DTABr/H12Lac, for DTABr/F6Lac, and for TTABr/F8Lac in NaBr 0.1 mol L-1 are displayed in Figure 10 and all fitting parameters are summarized in Table 4. For all of the systems, in the range of concentration explored, β is found to be negative, a sign of a favorable synergism. However, β increases with xM, which indicates that the mixing becomes less favorable when the ionic proportion increases. For DTABr/H12Lac, β is modeled by a straight line of equation, y ) 1.71x - 1.89. These values are in good agreement with the theoretical ones (d ) 0.92RT and e ) -2.67RT). For DTA+/ F6Lac, a second-order polynomial is necessary to fit the function β(xDTABr), whereas for TTABr/F8Lac, a straight line was used. The fitted experimental β are used in eq 25 to calculate the contribution of the chain βcore

βcore,MX/P ) βMX/P - βelst(DTABr/H12Lac)

(25)

where MX stands for the cationic surfactant and P for the nonionic one.

Hydrogenated/Fluorinated Chains Miscibility

Langmuir, Vol. 23, No. 23, 2007 11473 Table 4. Fitting Parameters of the Interaction Parameter β(x) ) cx2 + dx + ea system

conditions

c

d

e

DTABr/P DTABr/H12Lac DTABr/F6Lac TTABr/F8Lac DTABr/H12Lac DTABr/F6Lac

I ) 0.1 M NaBr 0.1M NaBr 0.1M NaBr 0.1M water water

0 0 -3.96 0 -21.8 -28.7

0.92 1.74 5.47 3.68 23.3 30.6

-2.67 -1.88 -2.33 -2.07 -11.4 -12.0

a The first line corresponds to the electrostatic contribution calculated according to the model of ref 13, for the mixing of DTABr with a neutral surfactant with a dodecyl chain in 0.1 mol L-1 swamping electrolyte. All coefficients are in RT units.

Figure 11. Electrostatic (- - -: DTABr/H12Lac) and packing of the chains contributions to the interaction parameter β (s, TTABr/ F8Lac; - - -, DTABr/F6Lac) in NaBr 0.1 mol L-1.

Figure 9. Ionic surfactant MX activity (left scale) or neutral surfactant P activity (right scale) vs composition of the micelle xMX (a) in water. System DTABr/H12Lac: 2, DTABr; 4, H12Lac. System DTABr/F6Lac: ×, DTABr; *, F6Lac (b) in NaBr 0.1 mol L-1. System DTABr/H12Lac: 2, DTABr; ∆, H12Lac. System DTABr/F6Lac: ×, DTABr; *, F6Lac. System TTABr/F8Lac: b, TTABr; O, F8Lac. The lines y ) x and y ) 1 - x stand for the ideal behavior.

Figure 12. Interaction parameter (β) in water (2) for DTABr/H12Lac 313 K (*) for DTABr/F6Lac in water at 298 K. The parameters of the fit are in Table 4.

Figure 10. Interaction parameter β for the system in NaBr 0.1 mol L-1 (4) DTABr/H12Lac at 313 K. (×) DTABr/F6Lac at 298 K. (0) TTABr/F8Lac at 298 K. The parameters of the fit are in Table 4.

The results are displayed in Figure 11. The electrostatic parameter is always found to be negative, which indicates a favorable mixing of cationic and nonionic heads, whereas the chains contribution is always positive, coherent with an unfavorable mixture of hydrocarbon and fluorocarbon moieties. The results for the two mixed systems are very close, the system

TTABr/F8Lac with longer chains being only slightly above the DTABr/F6Lac curve in the range of composition explored. In the Water System. Figure 12 shows the β plots for DTABr/ H12Lac and DTABr/F6Lac in water. The fitting parameters are given in Table 4. Here again, for all of the systems in the range of concentration explored, β is negative and growing, but the magnitude is about 5 times higher than in NaBr. The β coefficient is much more difficult to predict in pure water, because the ionic strength, which is due only to the cmc of the cationic surfactant, changes with the composition of the micelle and the condition κR > 0.5 is no longer verified. Moreover, with the ionic screening being very low due to the absence of added salt, the electrostatic contribution to micellization is indeed the main part of micellization. We plot in Figure 13 the packing interaction parameter of the chains extracted from the former results, βcore, for the system DTABr/F6Lac. This quantity being the subtraction of two quantities of close values, it is submitted

11474 Langmuir, Vol. 23, No. 23, 2007

Figure 13. Electrostatic [DTABr/H12Lac in NaBr 0.1 mol L-1 (- - -) and in water (s)] and packing of the chains contributions to the interaction parameter β [DTABr/F6Lac in NaBr 0.1 mol L-1 (‚‚‚) and in water (-‚-)].

to large error bars. The order of magnitude is in complete agreement with the results of Villeneuve et al.17 for a mixture of alkyltetraethyleneglycol. We observe that it is positive, indicating an unfavorable contribution to mixed micellization and lower than 2, which is the critical value predicted by RST for the apparition of two populations of micelles. The values of βcore are reasonably close in NaBr 0.1 mol L-1 and in water, which is coherent with the idea that the packing of the chain is not influenced by the electrolyte.

Conclusion The aqueous behavior of mixtures of a ionic surfactant with hydrogenated or fluorinated nonionic surfactant at different concentrations was studied. We showed that the concentrations of the two surfactants in the bulk phase as well as the mixed micelles composition can be accessed experimentally and independently, thanks to potentiometric techniques. Even though

Peyre et al.

specific electrodes for ionic surfactant or zwitterionic surfactants35 are not always commercially available, their preparation and realization in a laboratory are easy and well described in the literature.36,37 The procedure we propose to study the aqueous behavior of surfactants mixture is very different from the one adopted by many authors. They usually determine the values of the surfactant concentrations in balanced systems using an a priori model behavior, usually the regular solution theory. Consequently, the discussion is constrained by the initial hypothesis. If the model is not adapted, the discussion lacks sense. The approach we propose closely relies on the following experience: the activities of the constituents are first determined and an interpretation of their behaviors is afterward discussed in the frame of a model for the interactions. Concerning the analysis of the interactions, we chose to remain in the RST frame. The model can be criticized as soon as the interaction parameter β depends on the composition of the mixture. However, in our study, we used this approach to be able to compare the mixtures of an ionic surfactant (DTABr or TTABr) with nonionic hydrogenated or fluorinated neutral surfactants. The advantages of this model are to permit the separation of the electrostatic contributions from the other contributions (the packing of the core in our case) in the excess Gibbs energy. The interactions between hydrogenated and fluorinated chain can thus be quantified. We have shown that whatever the situation, they are unfavorable to mixing, though not sufficient to segregate into two distinct populations of micelles because of the highly favorable electrostatic contribution that prevails over them. Acknowledgment. We thank Pierre Letellier for his support and for many helpful discussions and suggestions. LA701579E (35) Peyre, V.; Baillet, S.; Letellier, P. Anal. Chem. 2000, 72, 2377. (36) Blanco, E.; Messina, P.; Ruso, J. M.; Prieto, G. Sarmiento, F. J. Phys. Chem. B 2006, 110, 11369. (37) Sirieix-Ple´net J., Turmine M., Letellier P. Talanta 2003, 60, 1071.