Micelle Formation and Phase Equilibria in a Water−Trifluoroethanol

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Langmuir 2000, 16, 7914-7919

Micelle Formation and Phase Equilibria in a Water-Trifluoroethanol-Fluorocarbon Surfactant System Giacomo Gente,† Camillo La Mesa,*,† Rita Muzzalupo,‡ and Giuseppe Antonio Ranieri‡ Dipartimento di Chimica, Universita` di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy, and Dipartimento di Chimica, Universita` della Calabria, Arcavacata di Rende, 87030 Rende (Cs), Italy Received January 19, 2000. In Final Form: July 11, 2000 The solution behavior of the fluorinated surfactant tetraethylammonium perfluorooctane-sulfonate, PFOS, in water-trifluoroethanol, TFE, mixtures has been investigated by surface tension, electrical conductance, and PGSE (pulsed gradient spin-echo) NMR self-diffusion methods. Addition of progressive amounts of TFE in the solvent has little influence on the critical micellar concentration, cmc. Conversely, self-diffusion, counterion binding, and the surface pressure at the cmc are significantly affected by added fluoroalkanol. The above effects have been explained in terms of the solvent viscosity, dielectric permittivity, and surface activity, respectively. The complete phase behavior of the above system has been drawn, and the phase boundaries were determined. According to the above findings, added surfactant promotes the separation of the homogeneous solvent mixture into two coexisting fluid phases. The observed behavior was rationalized on thermodynamic grounds.

Introduction Micelle formation in fluorinated surfactant solutions has been a classical field of investigation in surfactant sciences since Klevens1 and Shinoda.2-5 The reasons for so much interest lie in the fact that fluorinated surfactants are more hydrophobic than hydrocarbon ones.6 In fact, the Gibbs energy of transfer of a fluoromethylene unit from water to the corresponding micelle interior, ∆Gtr, is 1.5 times higher than the CH2 one.7 Such an effect is related to cmc values and indicates the occurrence of strongly unfavorable interactions of CF2 groups with water. Studies reported so far deal with micelle formation,8-11 aggregate size and shape,12 phase diagrams,13 phase transitions,14 and emulsion15 and microemulsion16 formation. Other papers report on the effect of counterions or simple electrolytes17 and of alkanols18 on the solution behavior of fluorocarbon surfactants. * Corresponding author. E-mail: [email protected]. † Dipartimento di Chimica, Universita ` di Roma “La Sapienza”. ‡ Dipartimento di Chimica, Universita ` della Calabria. (1) Klevens, H. B. J. Phys. Colloid Chem. 1950, 54, 1012. (2) Shinoda, K.; Soda, T. J. Phys. Chem. 1963, 67, 2072. (3) Shinoda, K.; Katsura, K. J. Phys. Chem. 1964, 68, 1594. (4) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1976, 80, 2468. (5) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365. (6) Tanford, C. The Hydrophobic Effect. Formation of Micelles, Vesicles and Membranes; Academic Press: New York, 1980. (7) Shinoda, K.; Nakagawa, T.; Tamamushi, B.; Isemura, T. In Colloidal Surfactants; Academic Press: New York, 1963; p 37. (8) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388. (9) Mukerjee, P.; Korematsu, K.; Okawauki, M.; Sugihara, G. J. Phys. Chem. 1985, 89, 5308. (10) Muzzalupo, R.; Ranieri, G. A.; La Mesa, C. Colloids Surf., A 1995, 104, 327. (11) La Mesa, C.; Sesta, B. J. Phys. Chem. 1987, 91, 1450. (12) Fontell, K. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 1, p 69. (13) Chidichimo, G.; Coppola, L.; La Mesa, C.; Ranieri, G. A.; Saupe, A. Chem. Phys. Lett. 1988, 145, 85. (14) Monduzzi, M. Curr. Opin. Colloid Interface Sci. 1998, 3, 467. (15) Gambi, C. M. C.; Senatra, D. Curr. Opin. Colloid Interface Sci. 1999, 4, 88. (16) Bongiovanni, R.; Borgarello, E.; Carlini, F. M.; Fisicaro, E.; Pellizzetti, E. Colloids Surf. 1990, 48, 277. (17) Hoffmann, H.; Schorr, W. J. Phys. Chem. 1981, 85, 3160. (18) Carlfors, J.; Stilbs, P. J. Colloid Interface Sci. 1985, 103, 332.

Almost nothing is known of the effect played by a fluorinated alcohol on the solution properties of fluorocarbon surfactants. Apart from the possible technological applications of the above mixtures in refrigerators19 and biotechnological applications (for instance, in the preparation of blood substitutes20 and in protein stabilization),21 there are fundamental aspects of the above systems, which deserve investigation. In particular, interactions between fluoroalkanols and fluorinated surfactants are very poorly investigated. For this purpose we report on micelle formation, phase equilibria, and other physicochemical properties in ternary systems containing water, a fully fluorinated surfactant, tetraethylammonium perfluorooctane-sulfonate, hereafter termed as PFOS, and 2,2,2-trifluoroethanol, TFE, as cosolvent. Experimental data by surface tension, electrical conductance, self-diffusion, and, in part, viscosity are reported and discussed. The above data are supported by a detailed investigation of the phase diagram for the water-TFE-PFOS system at 25 °C. Knowledge of the phase diagram is useful to quantify the observed surfactant partitioning between solution phases and to discuss relevant physicochemical aspects of this system. Experimental Section A. Materials. Tetraethylammonium perfluorooctane-sulfonate, PFOS, (from Riedel) was used as received. No surfaceactive impurities were detected in surface tension versus log [molal] plots. 2,2,2-Trifluoroethanol (from Riedel) was distilled and stored as indicated elsewhere.22 Water was doubly distilled, deionized, and degassed before use: its electrical conductance, κ, is about 10-6 s cm-1 at room (19) Sanyo Electric Corp. Ltd., Japanese Patent 58,21982,1,877. (20) Lo Nostro, P.; Monici, M.; Baglioni, P.; Fossombroni, V.; Bernabei, P. A. Colloid & Interface Group Ital. Chem. Soc. Meeting; Rome, Italy, October, 1999. (21) Sonnichsen, F. D.; Van Eik, J. E.; Hodges, R. S.; Sykes, B. D. Biochemistry 1992, 31, 8790. (22) Gente, G.; La Mesa, C. J. Solution Chem. 2000, 29, 859.

10.1021/la000074o CCC: $19.00 © 2000 American Chemical Society Published on Web 09/13/2000

Surfactant Micelle Formation and Phase Equilibria

Langmuir, Vol. 16, No. 21, 2000 7915 Table 1. PFOS Molality, m (mol kg-1), and Relative Viscosity, ηrel, of the Systems H2O-PFOS, H2O-3% TFE-PFOS, and H2O-5% TFE-PFOS at 25 °C H2O-PFOS

Figure 1. Surface pressure data, π (τ° - τ), in mN m-1, as a function of surfactant molality, m, in semilogarithmic scale for the system H2O-PFOS (top) and the system H2O-10 wt % TFE-PFOS (bottom) at 25 °C. As can be seen, cmc’s do not change much. temperature. Heavy water (from Carlo Erba, 99.5% isotopic enrichment) was used when required. Mixtures of TFE and water were made on a weight percent basis and corrected for buoyancy effects. They were kept in tightly closed glass bottles, equipped with rubber stoppers, until use. The solutions were prepared by weighing out the appropriate amount of each component. They were used immediately after preparation. Mixtures used to determine the phase diagram were prepared by weight and corrected for buoyancy. Proper amounts of each component were mixed into 2-mL glass vials, which were centrifuged and flame sealed. They were placed in an air oven, at 40 °C, for 1 day. Later on the vials were equilibrated at room temperature for 1 day. Finally, they were located in a thermostatic bath, whose temperature was constant to (0.1 °C. The accuracy of the phase boundaries is about 1%, depending on composition. Temperature has a moderate effect on the phase boundaries, as can be inferred from the macroscopic appearance of selected ternary mixtures on increasing T. B. Methods. B.1. Surface Tension. A Kruss K10T unit equipped with a measuring vessel, thermostated to within 0.1 °C by circulating water, measured τ values (in mN m-1). Details on calibration and measuring procedures are reported elsewhere.23 Surface tension data are average values obtained from five or more independent determinations on freshly prepared mixtures. The accuracy of the τ values is (0.2 mN m-1. Some surface pressure data, π ()τ° - τ), are reported in Figure 1. Surface tension data were rationalized by the Gibbs adsorption isotherm according to

dτ ) -Γ2[RT d ln a2] ≈ -Γ2[RT d ln m2]

(1)

where R is the gas constant, T is the temperature in Kelvin, and the solute activity, a2, has been replaced by the corresponding molality m2. Γ2 is the surface excess concentration of the surfactant solute. Critical micelle concentration values were determined by the abrupt changes in slope of the surface tension versus log [molal] plots. Because of the high surface activity of the above surfactant, cmc’s can also be obtained according to Phillips,24 who defines the cmc as the locus where ∂3τ/∂m23 ) 0. Areas per polar headgroup, A ˆ , in angstroms squared, were calculated from Γ2 data below the cmc, according to the relation

A ˆ ) 1020/NΓ2

(2)

where N is Avogradro’s number. B.2. Determination of the Phase Diagram. The isothermal phase diagram of the water-TFE-PFOS ternary system at 25 °C was determined by optical methods and visual inspection of individual samples. A homemade polarized light detector performed preliminary investigation of the sample appearance. In the surfactant-rich part of the phase diagram, as well as in the (23) La Mesa, C.; Ranieri, G. A. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 530. (24) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561.

H2O-3% TFE-PFOS H2O-5% TFE-PFOS

m

ηrel

m

ηrel

m

ηrel

0.00 1.73× 10-4 3.56 × 10-4 5.87 × 10-4 7.92 × 10-4 9.03 × 10-4 1.13 × 10-3 1.75 × 10-3 2.86 × 10-3 4.15 × 10-3 6.31 × 10-3 8.47 × 10-3 9.96 × 10-3 1.25 × 10-2 1.45 × 10-2

1.000 0.999 1.002 1.004 1.005 1.007 1.009 1.017 1.032 1.065 1.113 1.189 1.275 1.389 1.450

0.00 1.68 × 10-4 3.65 × 10-4 6.01 × 10-4 8.02× 10-4 9.36 × 10-4 1.09 × 10-3 1.71 × 10-3 2.74 × 10-3 4.25 × 10-3 6.67 × 10-3 8.59 × 10-3 1.01 × 10-2 1.31 × 10-2

1.000 1.003 1.004 1.005 1.006 1.006 1.016 1.027 1.049 1.080 1.145 1.226 1.291 1.418

0.00 1.52 × 10-4 3.50 × 10-4 5.77 × 10-4 8.22 × 10-4 9.08 × 10-4 1.07 × 10-3 1.68 × 10-3 2.68 × 10-3 4.10 × 10-3 6.35 × 10-3 8.95 × 10-3 1.00 × 10-2 1.27 × 10-2 1.40 × 10-2

1.000 1.004 1.006 1.007 1.009 1.009 1.018 1.029 1.054 1.088 1.160 1.250 1.322 1.464 1.593

emulsion region, a CETI Laborlux microscope performed optical microscopy investigation (in white and/or polarized light). B.3. Viscosity. The mixture viscosity η, in cP, was measured by Ubbelhode-type viscometers (Schott) having flow times for the solvent close to 200 s, to ensure negligible kinetic effects. Because of the low surface tension of the investigated mixtures, care was taken to avoid bubble formation in the capillary tube. The relative viscosity was calculated by the equation

ηrel ) η/η° ) (t/t°)(F/F°)

(3)

where t and t° are the flow times of the solution and the solvent, respectively. F and F° are the corresponding densities. Relative viscosity data of some ternary mixtures are reported in Table 1. The viscosities of mixtures at concentrations above 0.015 m PFOS are subject to a large uncertainty (dη ≈ 3%), because of the stability of small air bubbles entrapped in such solutions. They are not reported here. B.4. Density. The solution density F, in g cm-3, was measured by an Anton Paar DMA 60 unit thermostated to within (0.003 °C by a Heto water circulating bath. The uncertainty on F values is ∼3 × 10-6 g cm-3. Partial molal volumes of PFOS were obtained according to standard procedures.11,12 Because of the low cmc values and the significant data scattering in the critical micellar concentration region, the volume change associated with micelle formation, ∆Vmic, is subject to a large uncertainty. It is assumed to be 14 ( 2 cm3 mol-1. B.5. Dielectric Permittivity. A Bontoon electronic direct capacitance bridge model 75D measured the dielectric permittivity of the solvent media at 1.00 MHz. The vessel containing the permittivity cell (consisting of two stainless steel coaxial cylinders) was thermostated to within (0.01 °C by circulating oil. Details on the apparatus setup and measuring procedures are reported elsewhere.22,25 B.6. Electrical Conductance. An Amel bridge model 730 equipped with a conductivity cell made of Pyrex glass measured electrical conductance. The cell constant is 1.001 cm-1. The vessel containing the measuring cell was thermostated to within (0.01 °C by a circulating liquid. An F25 precision thermometer from Automatic System Laboratories was used, and temperature readings are to (2 × 10-3 °C. Electrical conductance data were used to determine cmc values as well as the counterion binding degree β (i.e., the ratio of electrical conductance, κ, versus concentration slopes above and below the cmc, respectively).26 The accuracies of cmc and β values inherent to such a technique are (3% and (2%, respectively. Electrical conductance, κ, versus molality plots are reported in Figure 2. B.7. NMR Self-Diffusion. Self-diffusion was measured by pulsed field gradient spin-echo methods, PGSE NMR, on a (25) Mauro, V. Ph.D. Thesis, “La Sapienza” University, Rome, Italy, 1998.

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Gente et al. Table 2. TFE and PFOS Weight Percent and Water (Dwat), Trifluoroethanol (DTFE), and Counterion (DTEA) Self-Diffusion Values (in m2 s-1) for Samples in the Low Concentration Regime, at 25 ˚Ca

Figure 2. Electrical conductance, κ - κ° (in mS), versus molality plots, m, for PFOS in H2O: full symbols, in 3 wt % TFE-H2O mixtures; empty symbols, at 25 °C. For clarity, the curve in pure water has been shifted 10-5 units upward. The inset at the bottom of the figure shows equivalent conductance data corrected for the solvent viscosity, λη°, as a function of xm. Data in H2O (lower curve) and in 3 wt % TFE-H2O (upper curve) are reported therein. Bruker WM 300 and a Bruker W 80 spectrometer (upgraded by STELAR with pulse field gradient probes), respectively. Typical experimental conditions for the former unit are as follows: δ ) 2-7 ms, ∆ ) 250 ms, G, the field gradient strength, is 6.3 G/cm, with the number of transients ) 32. As to the W 80 unit, the experimental conditions are as follows: δ ) 1-10 ms, ∆ ) 90 ms, G ) 5.2 G/cm, with the number of transients ) 16. Further details on the apparatus setup and information on datafitting procedures, as well as on experimental accuracy, are reported elsewhere.27,28 The PGSE NMR units were equipped with thermostatic units to ensure the constancy of temperature to within (0.2 °C. The errors on experimental self-diffusion are (2% of the measured values. The line width in all NMR spectra is narrow, and no signal integration is required to get accurate self-diffusion values.29 Selected self-diffusion data for some components at different concentrations are reported in Table 2. Measurements were performed on the resonance peaks of the HDO proton of water, of the methylene group of trifluoroethanol, and of the ethyl groups of tetraethylammonium ions. This ensures the simultaneous determination of water, cosolvent, and counterion self-diffusion values. Accordingly, the simultaneous decay of the different proton signals as a function of δ can be used to control the data consistency. The decay of echo signals was analyzed in terms of the following relation:

ln(A°/AG) ) (γδG)2(∆ - δ/3)D

(4)

where A° and AG are the echo pulse signal amplitudes without and with applied gradient pulses, respectively, γ is the gyromagnetic ratio of the proton, δ is the field gradient width, and ∆ is the separation between two field gradient pulses. D is the measured self-diffusion coefficient.

Results and Discussion A. Solvent Properties. The basic physicochemical properties of selected water-TFE mixtures (i.e., their density, F, viscosity, η, surface tension, τ, and dielectric permittivity, ) are reported in Table 3. Such data were used to account for counterion binding (and its variation with the solvent permittivity), to observe the surface pressure at the cmc, to normalize equivalent conductance, and so forth. (26) Stilbs, P.; Lindman, B. J. Phys. Chem. 1981, 85, 2587. (27) Muzzalupo, R.; Ranieri, G. A.; La Mesa, C. Langmuir 1996, 12, 3157. (28) Celebre, G.; Chidichimo, G.; Coppola, L.; La Mesa, C.; Muzzalupo, R., Pogliani, L.; Ranieri, G. A.; Terenzi, M. Gazz. Chim. Ital. 1996, 126, 489. (29) Regev, O.; Kang, K.; Khan, A. J. Phys. Chem. 1994, 98, 6619.

TFE wt %

PFOS wt %

109Dwat

1010DTFE

03.21 (0.33) 05.01 (0.53) 89.98 03.21 (0.33) 03.21 (0.33) 03.21 (0.33) 03.21 (0.33) 05.01 (0.53) 05.01 (0.53) 05.01 (0.53) 05.01 (0.53) 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0

0 0 0 01.29 (0.021) 02.20 (0.036) 03.27 (0.054) 04.21 (0.070) 01.35 (0.022) 02.63 (0.043) 04.05 (0.067) 05.37 (0.090) 00.75 (0.012) 01.05 (0.018) 02.50 (0.041) 03.63 (0.060) 04.77 (0.080) 06.35 (0.11) 07.59 (0.13) 08.95 (0.16)

2.12 2.00 0.82 1.97 1.79 1.77 1.71 1.90 1.78 1.65 1.58 2.20 2.09 1.98 1.95 1.80 1.75 1.60 1.47

10.3 9.80 6.92 9.67 7.64 5.72 3.24 8.25 6.71 3.75 1.71

1010DTEA

1.96 1.63 1.16 1.03 1.82 1.52 1.07 0.85b 2.30 2.04 1.62 1.29 0.86b 0.68b 0.66b 0.60b

a The estimated uncertainty on self-diffusion values is (2 %. The corresponding molalities are given in parentheses. b The uncertainty is about 10%.

Table 3. Density, G (g cm-3), Viscosity, η (cP), Relative Dielectric Permittivity, E, and Surface Tension, τ (mN m-1), of Some Water-Trifluoroethanol Binary Mixtures at 25 ˚Ca TFE wt %

F

η



τ

0.00 (0.00) 1.51 (0.15) 3.03 (0.31) 5.25 (0.55) 7.54 (0.82) 8.50 (0.93) 9.96 (1.11) 10.22 (1.14) 12.51 (1.43) 15.36 (1.89)

0.99707 1.00221 1.00762 1.01373 1.01552 1.02358 1.03227 1.03321 1.04138 1.05169

0.8904 0.9173 0.9476 0.9897 1.0317 1.0490 1.0751 1.0798 1.1206 1.1717

78.34 78.00 77.63 77.05 76.41 76.12 75.67 75.58 74.83 73.81

69.7 64.5 59.8 54.0 49.2 47.4 45.1 44.7 41.9 39.2

a

The alcohol molality is reported in parentheses.

Table 4. Critical Micellar Concentration, cmc (mmol kg-1), and Counterion Binding Degree, β, in Some Water-TFE Mixtures, at 25 ˚Ca TFE wt %

cmc

β

0.00 1.50 3.03 4.75 5.25 7.54 8.50 9.96 12.51 15.36

1.13 (1.05) 1.11 (1.06) 1.03 0.93 0.91 (0.99) (0.92) 0.91 (0.89) 1.07 (0.87) (0.89) 1.31 (1.07)

0.62 (0.60 ( 0.05) 0.65 0.69 0.73 (0.70 ( 0.05) 0.75 0.81 0.84 0.88 (0.90 ( 0.07) 0.93 0.94

a Critical micelle concentration and β data from electrical conductance were obtained as described in the text. Critical micelle concentrations from surface tension and β values from self-diffusion are reported in parentheses.

B. Micelle Formation. Critical micelle concentration values, obtained from surface tension and electrical conductance, are reported in Table 4. Some discrepancy can be found between the two sets of data, as expected. Critical micelle concentrations from electrical conductance are close to those reported by Hoffmann.30 Added TFE has a small effect on cmc values, Figure 3, compared to the effect of added alcohol on micelle formation.31

Surfactant Micelle Formation and Phase Equilibria

Langmuir, Vol. 16, No. 21, 2000 7917

-∆ ln Kb ) ∆[1/]

(6′)

where the temperature, T, and the distance of closest approach between ions, a, are constant. Comparison of data for two different systems having solvent permittivities 1 and 2, counterion binding constants β1 and β2, and concentrations m1 and m2, respectively, can be made.35 Accordingly, combination of eqs 5, 6, and 6′ leads to

-∆ ln Kb ) 2 ln[β1/β2] + ln[m1/m2] - ln[1 - β1/1 β2] ) [1 - 2]/12 (7) Figure 3. Critical micelle concentration of tetraethylammonium perfluorooctane-sulfonate, in mol kg-1, as a function of TFE wt % in the mixture, according to surface tension measurements at 25 °C. The line is a guide to the eye. In the inset is reported the dependence of surface pressure at the cmc, πcmc (in mN m-1), on the amount of TFE in the solvent medium.

To quantify the solvent effect on cmc values, equivalent conductance data have been corrected for the solvent viscosity and are reported as λη° versus xm plots (see the inset in Figure 2). The shape of the different curves drastically changes in close proximity to the cmc, since counterion binding (see below) changes in proportion to the amount of TFE in the solvent medium. C. Counterion Binding. β values, reported in Table 4, are quite sensitive to the medium permittivity. To ascertain the relation between counterion binding (i.e., the dissociation from the micellar surface of charges) and solvent properties, counterion binding was rationalized in terms of the solvent permittivity. As can be seen from the data in Tables 3 and 4, there are, in fact, some links between the two quantities. To quantify the above effect, we assume that β values are only controlled by . Accordingly, the solvent is considered to be a structureless dielectric continuum (i.e., no solvation and TFE partitioning occur). The role of  on counterion binding can be inferred from the detailed statistical thermodynamic model of Bjerrum for ion association.32 If we assume, in addition, that the distance of closest approach between ion and counterion, a, is not sensitive to the medium,33 the binding constant, Kb, shall be explicitly dependent on the medium permittivity. Kb, defined as [(βf()2m/(1 - β)], where β is the counterion binding degree, f( is the average activity coefficient (f( ≈ 1 in the dilute concentration regime), and m is the surfactant concentration, can be rewritten as

ln Kb ) 2 ln β + ln(m/(1 - β))

(5)

Equation 5 can be related to the equilibrium constant, calculated according to Born’s approximation.34 In fact,

-ln Kb ) [e°2/(akT)]

(6)

where e° is the ion charge and k is Boltzmann’s constant. Accordingly, the dependence of Kb on the medium permittivity can be written as (30) Reizlein, K.; Hoffmann, H. Prog. Colloid Polym. Sci. 1984, 69, 83. (31) Treiner, C.; Chattopadhyay, A. K. J. Colloid Interface Sci. 1984, 98, 447. (32) Bjerrum, N. In Selected Papers; Munksgaard: Copenhagen, 1949; p 108. (33) Denison, J. T.; Ramsay, J. B. J. Am. Chem. Soc. 1955, 77, 2615. Fuoss, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1959, 79, 3304. (34) Monk, C. B. Electrolytic Dissociation; Academic Press: New York & London, 1961.

Equation 7 indicates that variations in the medium permittivity imply changes in counterion binding, as can be inferred from the plot in Figure 4. Some remarks need to be made. The selective solvent capacity of the fluorinated alcohol with respect to anions36 and its partitioning in the micellar pseudophase are not considered in eq 7. The model underlying the above equation is purely electrostatic and does not account for ion solvation. Within the above mentioned limits, the model qualitatively accounts for the observed behavior. This is partly due to the fact that interactions between tetraethylammonium ion and TFE are weak and repulsive. The small discrepancies between experimental and calculated values can be ascribed to a partial TFE partitioning between the micellar pseudophase and the bulk, inferred from self-diffusion findings. Alcohol partitioning into micelles is not peculiar to the present system and has been observed, for instance, in water-alcoholhydrocarbon surfactant systems.37 Self-diffusion data, reported in Table 2, support the occurrence of some links between binding and solvent properties and suggest a significant role of the solvent medium in counterion self-diffusion. The combined effect of solvent viscosity, controlling ion motion, and permittivity (which influences the aggregates’ net charge, that is, the number of free ions) has a large influence on the self-diffusion of the components. In particular, some uptake of TFE from fluorinated micelles can be inferred from self-diffusion experiments. D. Surface Properties. The surface pressure at the cmc, Figure 3, is regularly dependent on the amount of TFE in the mixtures when cmc data are not very sensitive to it, as indicated in Figures 1-3. No minima in the surface tension versus log [molal] plot are observed, even in the presence of noticeable amounts of the fluorinated alcohol. Such behavior can be ascribed to the following effects: (i) the strong surface activity of fluorocarbon surfactants and (ii) the ideality of mixing of TFE with fluorocarbon surfactants at the airsolution interface. Effect ii can be related to the significant solvent capacity of trifluoroethanol with respect to anions, described in detail by Evans.36 Areas per polar headgroup, A ˆ , are sensitive to the addition of TFE. There is a nearly regular increase of such values upon addition of the fluorinated alcohol, from about 35 to 50 Å2. E. Diffusion and Viscosity. According to data in Tables 1 and 3, there is a regular dependence of transport properties on the amount of TFE in the mixture. This is because of the increasing medium viscosity, with obvious (35) In the solvent systems 1 and 2, respectively, the terms m1 and m2 refer to the concentration of surfactant in micellar form (i.e., m1 ) m1,tot - cmc). (36) Evans, D. F.; Nadas, J. A.; Matesich, S. M. A. J. Phys. Chem. 1971, 75, 1708. (37) Langenfeld, A.; Lequeux, F.; Ste`be, M.-J.; Schmitt, V. Langmuir 1998, 14, 6030.

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Figure 4. Dependence of counterion binding constant, expressed as ∆ ln Kb, on the solvent permittivity (1 - 2)/12. The curve fitting was calculated according to eq 7.

consequences on hydrodynamic volumes, friction, and state of charge. The observed self-diffusion of tetraethylammonium, TEA, counterions is the weight-averaged result of two different contributions, due to free and micelle-bound ions, according to38

DTEA ) PTEA,fDTEA,f + (1 - PTEA,f)DTEA,b ) PTEA,fDf + (1 - PTEA,f)Dm (8) where PTEA,f is the relative amount of free counterions and Df and Dm are the diffusivities of free and micellebound ions, respectively. The latter ones behave as a whole kinetic entity with micelles. The above relation comes from the empirical equality

PTEA,f ) (C/cmc) + (1 - β)((C/cmc) - 1)

(9)

where the counterion binding degree is assumed to be independent of the amount of surfactant in micellar form.39 At moderately high surfactant content, the average counterion self-diffusion is close to 10-10 m2 s-1. Attempts were made to determine the obstruction played by perfluorinated surfactant micelles on the selfdiffusion of water and of TFE. Drastic assumptions were made for this purpose. In fact, the obstruction factor to the solvent self-diffusion, fobstr, refers to an unspecified micellar aggregate and is mainly controlled by the volume fraction of the aggregates, φ, according to the empirical law fobstr ) 1/(1 + φ/2).40 The above relation works quite well for water. As for TFE self-diffusion, the observed behavior cannot be solely explained in terms of obstruction effects. Evidence of its partitioning between micelles and the bulk is inferred from experiments. In fact, the self-diffusion of TFE decreases much more steeply than that of water. The effect is evident when the amount of surfactant in the mixture increases. For instance, the self-diffusion of trifluoroethanol in mixtures containing about 200 mmol of surfactant is very close to 10-10 m2 s-1 (i.e., nearly the same value for micelles). Viscosity findings in Table 1 indicate significant variations of the micelle hydrodynamic volume, which increases in proportion to the amount of TFE in the solvent. Thus, previous hypotheses on the partitioning of TFE between micelles and the bulk are enforced. (38) Fabre, H.; Kamenka, N.; Khan, A.; Lindblom, G.; Lindman, B.; Tiddy, G. J. T. J. Phys. Chem. 1980, 84, 3428. (39) The β values increase (slightly) in proportion to the amount of micellar surfactant. This effect is ascribed to the medium ionic strength. See, for instance, ref 11. (40) Nilsson, P. G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377.

Figure 5. Isothermal phase diagram of the ternary systems H2O-TFE-PFOS at 25 °C. The light gray area on the lower left-hand side of the two-phase region indicates the occurrence of an emulsion region. The emulsion stability is roughly proportional to the water amount in the mixture. Table 5. Electrical Conductance K (mS) of a 9.99 wt % PFOS Solution in TFE upon Addition of Progressive Amounts of Water, at 25 ˚C κ

H2O wt %

κ

H2O wt %

2.71 3.61 22.7 35.6 51.1 62.2 77.7 88.4 106

0.00 0.14 3.01 5.02 7.51 9.32 11.89 14.36 16.32

2.87 19.6 27.9 46.3 55.3 69.4 81.9 97.6

0.03 2.52 3.81 6.72 8.18 10.51 12.56 15.21

F. Phase Diagram. The complete phase diagram of the above system, at 25 °C, is reported in detail in Figure 5. No liquid crystalline phases have been detected in the present experimental conditions. The width of the twophase region, located in the center of the phase diagram, is noticeable. Its width is practically independent of temperature up to 50 °C. Significant, too, is the occurrence of an emulsion region close to the water-rich corner of the phase diagram. The emulsion stability is more or less significant, depending on its location in the phase diagram. For instance, samples located close to the water-rich corner are stable for weeks. The whole solution region has been investigated to determine whether reversed micelles are formed. Electrical conductance data, reported in Table 5, indicate a regular increase of the solute mobility upon increasing the amount of added water. No occurrence of reversed micelles can be inferred from ionic conductivity experiments. The phase behavior depicted in Figure 5 is quite unusual compared to that of most water-alcohol-surfactant mixtures. Systems investigated so far, in fact, do not show significant surfactant-induced phase separation.41,42 As a rule, short and medium chain hydrocarbon alcohols are partitioned between the micellar pseudophase and the bulk, in proportion to their lipophilic character.37 Long alkyl chain alcohols, conversely, are almost completely solubilized into micelles and are responsible for the formation of reversed micelles and/or lyotropic mesophases. (41) Ekwall, P. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1975; Vol. 1, p 1.

Surfactant Micelle Formation and Phase Equilibria

Langmuir, Vol. 16, No. 21, 2000 7919

(µ°PFOS,TFE - µ°PFOS,wat)/RT ) ln(aPFOS,TFE/aPFOS,wat) ) ln Krip (10) The partition coefficients calculated by eq 10 reflect the hydrophilic-lipophilic balance of the above mixtures. Within the limits set up by the experimental accuracy, which is estimated to be (3%, evidence of a preferred PFOS partitioning toward the TFE-rich phase (Krip is ∼34) was found. The observed trends are in line with the observed phase behavior, as well as with the experimental information given above. Conclusions Figure 6. Plot of the TFE concentration, in wt %, associated with the onset of upper (full squares) and lower (empty circles) limits of the two-phase region. Data therein are reported as a function of the overall weight percent of fluorinated matter in the mixture, expressed as (PFOS + TFE) wt %.

According to the phase diagram reported in Figure 5, the mutual solubility of water and TFE is complete, and the surfactant is soluble in both solvents. The observed phase separation, thus, implies a much stronger affinity between the surfactant and one of the two solvents. In other words, the Gibbs energy of interaction between PFOS and TFE is significantly different from that between PFOS and water (or even between water and TFE). To quantify the above effect, the amount of each component in the two coexisting phases has been evaluated from the phase diagram. For any given water-TFE mixture, the concentration of PFOS required to have phase separation and/or complete redissolution was determined from the experimental phase diagram. The resulting phase borders are plotted as a function of the overall amount of fluorinated components in Figure 6. Similar plots can be drawn for the partitioning of water and TFE in the two coexisting phases. The ratio between the upper and the lower limit of the curves, for a given amount of fluorinated matter in the mixture, is related to the partitioning of each species in the two phases. On thermodynamic grounds, the Gibbs energy of transfer from one solvent to another can be expressed as43 (42) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1.

The system composed of water, TFE, and PFOS has been investigated, and some physicochemical properties were determined. Particularly interesting are the results inferred from the phase diagram, with the occurrence of a surfactant-induced phase separation. Similar effects have been reported in aqueous mixtures containing two polymers.44 Another interesting aspect inferred from the experimental results is the dependence of counterion binding on the solvent permittivity. This is a very special case of a more general behavior. It can be easily rationalized because the interactions between tetraethylammonium counterions and cosolvent (i.e., between hydrocarbon and fluorocarbon chains) are weakly repulsive. Presumably, the relatively low charge density of tetraethylammonium ion and its hydrophobic nature maximize the observed behavior compared to, for example, that of alkali metal ions. These are the reasons why the dependence of binding can be qualitatively evaluated from the simple Born model. Efforts should be spent, in our opinion, to rationalize the above behavior in a more general formulation. Acknowledgment. MURST, the Italian Ministry for University, Technical, and Scientific research is acknowledged for financial support by the grant 97 C.F.S.I.B. LA000074O (43) Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. Soc. 1982, 17, 11. (44) Bergfeldt, K.; Piculell, L.; Linse, P. J. Phys. Chem. 1996, 100, 3680.