Nonideal Mixed Micelles of Fluorinated and Hydrogenous Surfactants

Dec 16, 2009 - Colloids and Surfaces A: Physicochemical and Engineering Aspects 2018, 536, 242-250. ... Kabir-ud-Din, Gaurav Sharma, P. Ajmal Koya...
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Nonideal Mixed Micelles of Fluorinated and Hydrogenous Surfactants in Aqueous Solution. NMR and SANS Studies of Anionic and Nonionic Systems Mats Almgren,*,† Vasil M. Garamus,‡ Lars Nordstierna,§ Jean Luc-Blin, and Marie-Jose Stebe

Department of Physical and Analytical Chemistry, Uppsala University, Box 579 SE-751 23 Uppsala, Sweden, ‡ GKSS Research Centre, Max-Planck-Strasse, 21502 Geesthacht, Germany, §Division of Applied Surface Chemistry, Department of Chemical and Biological Engineering, Chalmers University, SE-41296 G€ oteborg, Sweden, and Equipe Physico-chimie des Colloı¨des, UMR SRSMC No. 7565 CNRS/Nancy Universit e, F-54506 Vandoeuvre-les-Nancy, cedex, France )

†

Received October 5, 2009. Revised Manuscript Received November 26, 2009 Contrast variation SANS and 19F chemical shifts were measured for three mixed equimolar micelle systems: sodium perfluorooctanoate (SPFO) and sodiumdecylsulfate (SDeS) in 200 mM NaCl, lithium perfluorononanate (LiPFN) and lithium dodecylsulfate (LiDS) in 200 mM LiCl, and a nonionic system C8F17C2H4(OC2H4)9 and C12H25(OC2H4)8 in water, all at 25 C. The chemical shift measurements allow the calculation of the average fraction of nearest neighbors of each kind around the reporter group (the trifluoromethyl group). A preference for like neighbors were found in all systems, smallest in the SDeS/SPFO system and largest in the nonionic system, but in all cases substantially smaller than expected at critical conditions. From the SANS measurements the width of the micelle composition distribution was obtained. For the ionic systems similar values were obtained, showing a broadening compared to ideal mixtures, but not broad enough for demixing or clearly bimodal distributions. In the nonionic system the width was estimated as σ = 0.18 and 0.22 using two different evaluation methods. These values suggest that the system is close to critical conditions. The lower value refers to a direct modeling of the system, assuming an ellipsoidal shape and a Gaussian composition distribution. The modeling showed the nonionic mixed micelles to be prolate ellipsoids with axial ratio 2.2 and an aggregation number larger than 100, whereas the two ionic systems fitted best to oblate shapes (axial ratios 0.8 and 0.65 for SDeS/SPFO and LiDS/LiPFN, respectively) and aggregation numbers of 60 for both.

Introduction Alkanes and perfluoroalkanes form nonideal mixtures and separate into two liquid phases below a critical solution temperature. For mixtures of n-hexane and perfluoro-n-hexane, the critical temperature is just above room temperature, 23 C,1 and it increases with increasing length of both molecules. In micellar solutions containing mixtures of hydrogenous and perfluorinated surfactants, some sort of microscopic demixing would be expected. It was suggested early on that fluorocarbon rich and hydrocarbon rich micelles might form and coexist in one and the same solution.2,3 Later, some authors have inferred that instead (or in addition) a demixing within the micelle might occur, resulting in micelles with hydrocarbon rich and fluorocarbon rich domains.4-8 It has shown difficult to obtain direct proof of the coexistence in solution of hydrocarbon-rich and fluorocarbon-rich populations of mixed micelles.9 Asakawa et al.10 demonstrated the coexistence of two kinds of micelles in mixtures of lithium *Corresponding author. (1) Hicks, C. P.; Hurle, R. L.; Toczylkin, L. S.; Young, C. L. Aust. J. Chem. 1978, 31, 19. (2) Tiddy, G. J. T.; Wheeler, B. A. J. Colloid Interface Sci. 1974, 47, 59. (3) Murjerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, 9, 239. (4) Kamogawa, K.; Tajima, K. J. Phys. Chem. 1993, 97, 9506–9512. (5) Asakawa, T.; Shiraishi, T.; Shinichi, S.; Miyagishi, S. Bull. Chem. Soc. Jpn. 1995, 68, 2503–2509. (6) Kadi, M.; Hansson, P.; Almgren, M.; Furo, I. Langmuir 2002, 18, 9243. (7) Amato, M. E.; Caponetti, E.; Chillura Martino, D.; Pedone, L. J. Phys. Chem. B. 2003, 107, 10048. (8) Nordstierna, L.; Furo, I.; Stilbs, P. J. Am. Chem. Soc. 2006, 128, 6704. (9) Peyre, V. Curr. Opin. Colloid Interface Sci. 2009, 14, 305. (10) Asakawa, T.; Miyagishi, S.; Nishida, M. Langmuir 1987, 3, 821.

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perfluorooctanoate and lithium tetradecylsulfate with gel filtration. Haegel and Hoffmann11 used ultracentrifugation to show convincingly that fluorocarbon rich and hydrocarbon rich surfactant micelles coexist in mixtures of SPFO (sodium perfluorooctanoate) and dimethyltetradecylaminoxide. The separation of the micelles in the ultracentrifuge was made visible by staining with two dyes, one having a perfluorinated anchor group that preferred fluorocarbon-rich micelles, the other an alkyl anchor preferring micelles rich in hydrogenous surfactant. A weak point of this investigation is that extraneous probes have to be added. The same weakness is inherent in fluorescence and fluorescence quenching methods.12,13 Indirect evidence of demixing has been obtained from measurements of the cmc (or free surfactant concentrations14) in surfactant mixtures at various compositions. Interpretation of cmc results was the basis of the first report on demixing and gave immediately rise to a controversy (still going on8) concerning mixtures of C7H15COONa and C7F15COONa and similar surfactants. Murkerjee and Yang15 claimed that demixing occurred in this system, whereas Shinoda and Nomura maintained that the two surfactants were mixed in the micelles, and went on to show by application of the regular solution theory that also some similar surfactant pairs, among them SPFO and sodium decylsulfate (SDeS) should form mixed micelles in all proportions.16 (11) Haegel, F.-H.; Hoffmann, H. Prog. Colloid Interface Sci. 1988, 76, 132. (12) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1996, 12, 4672. Langmuir 1996, 12, 1204. (13) Almgren, M.; Wang, K.; Asakawa, T. Langmuir 1997, 13, 4535. (14) Peyre, V.; Patil, S.; Durand, G.; Pucci, B. Langmuir 2007, 23, 11465. (15) Murkerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388. (16) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365.

Published on Web 12/16/2009

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Variations of cmc with composition of mixed micelles have been employed in two different ways. The most straightforward way is to map the behavior and also measure changes associated with a transition from a region with two types of coexisting micelles to a region with only one type, seen as a “second cmc” in various methods, often employing added probes. Asakawa and co-workers have made extensive investigations of this type,5,10,17,18 with results that often convincingly matches the predictions from their group contribution model.19,20 Usually the compositions of the two types of coexisting micelles are strongly asymmetric. In some systems one micelle seems to be almost entirely composed of one of the surfactants whereas the other micelle holds a substantial amount of the minority component.21 The other way to use cmc data involves a more demanding thermodynamic analysis based on a Gibbs-Duhem equation and thus requiring reliable values for the derivative of the cmc with respect to composition, over the full composition range. As pointed out by Maeda22 precise values of this derivative are difficult to determine. This difficulty, and the fact that a theory for uncharged micelles23 was employed, is the probable explanation of some peculiar results obtained for charged surfactant mixtures in salt free solutions.24 Even though a separation into two liquid phases would normally not be expected in micellar systems, phase studies of ternary systems of fluorinated and hydrogenous surfactants in water can give important information on where to look for demixing. Only nonionic surfactant mixtures, comprising hydrogenous and fluorinated ethoxylated surfactants, have been systematically investigated.25-28 In the system C8F17C2H4(OC2H4)9-C12H25(OC2H4)8, separation of two micellar phases, one rich in the fluorinated surfactant, the other in the hydrogenous surfactant, is indeed suggested by the phase diagram at high surfactant concentrations. With still more surfactant two hexagonal phases were found, the one containing mainly fluorinated, the other mainly hydrogenous surfactants.26 Other systems gave no indication of demixing, however, with continuous L1 areas, and hexagonal phases spanning the whole composition range from pure hydrogenous to pure perfluorinated surfactant. The phase behavior depends on the size of both the hydrophobic and the hydrophilic groups of the surfactants. The question we address in this contribution is whether the nonideality of a given system is strong enough to produce two distinct sets of micelles, or if it only broadens the composition distribution. This question is not only of academic interest. Solutions containing different types of micelles have for instance been used to produce mesoporous silica materials with bimodal pore size,27 and other applications in the buildup of nanostructured materials are conceivable. In order to assess the nonideality and its effects on the distribution of the surfactants over the (17) (a) Asakawa, T.; Mouri, M.; Miyagishi, S.; Nishida, M. Langmuir 1989, 5, 343. (b) Asakawa, T.; Fukita, T.; Miyagishi, S. Langmuir 1991, 7, 2112. (18) Asakawa, T.; Amada, K.; Miyagishi, S. Langmuir 1997, 13, 4569. Asakawa, T.; Ishikawa, K.; Miyagishi, S. J. Colloid Interface Sci. 2001, 240, 365. (19) Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, M. Langmuir 1985, 1, 347. (20) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1995, 11, 478. (21) Asakawa, T.; Ishino, S.; Hansson, P.; Almgren, M.; Ohta, A.; Miyagishi, S. Langmuir 2004, 20, 6998. (22) Maeda, H. J. Phys. Chem. B 2005, 109, 15933. (23) Motomura, K.; Yamanka, Y.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948. (24) Villeneuve, M.; Nomura, T.; Matsuki, H.; Kaneshina, S.; Aranato, M. J. Colloid Interface Sci. 2001, 234, 127. (25) Ravey, J. C.; Gherbi, A.; Stebe, M. J. Prog. Colloid Polym. Sci. 1989, 79, 272. (26) Blin, J. L.; Henzel, N.; Stebe, M. J. J. Colloid Interface Sci. 2006, 302, 643. (27) Michaux, F.; Blin, J. L.; Stebe, M. J. Langmuir 2007, 23, 831. (28) Michaux, F.; Blin, J. L.; Stebe, M. J. J. Phys. Chem. B. 2008, 112, 11950.

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micelles we employ noninvasive methods based on NMR, and on contrast variation small angle neutron scattering, CV-SANS. The NMR methods are those used earlier in a study of SPFO and SDeS: self-diffusion measurements on both surfactants, and 1 H and 19F chemical shifts.8 The self-diffusion measurements give direct information on the presence of two types of micelles only if the size of the micelles differs substantially,6 otherwise they give the concentrations of free surfactants. Since the exchange of the surfactants between micelles normally is fast on the NMR time scale, NMR methods utilizing the environmental sensitivity of the chemical shifts of 1H or 19F measure the time average of the density and composition close to the reporter atoms, independent of how the surfactants distribute over micelles. In mixtures of SPFO and SDeS it was thus found that the fluorinated surfactant preferred fluorinated nearest neighbors by a factor of about 1.15 over the random mixing situation.8 In this case the large volume excess in mixtures of alkanes and perfluoroalkanes29 had to be taken into account as its effect on the chemical shifts is of similar magnitude as that from nonrandom mixing. In small angle neutron scattering perfluorinated and hydrogenous surfactants have very different scattering length densities. By using mixtures of H2O and D2O, the scattering length density of the aqueous solvent can be varied to provide different contrasts for the micelles. One solvent mixture would match the scattering length density of fully mixed micelles. The scattering length density at this “nominal match point” can be calculated from the micelle composition and the molecular volumes of the surfactants in the micelles. The neutron scattering would be zero at this point for fully mixed micelles, but if the surfactants demix into two populations of micelles the scattering will not disappear. Both types of micelle will have a contrast to the solvent, with different signs, and contribute to the scattered intensity. Thus, contrast variation SANS measurement appears as a powerful noninvasive method to investigate this sort of micellar demixing. Results from some early measurements suggested that only mixed micelles were present in the systems investigated, ammonium perfluorooctanoate mixed with ammonium decanoate in NH4OH/NH4Cl buffer30 and SPFO/sodium dodecanoate without added salt.31 In later studies of HFDePC with C16TAC, C16PC, and C12PC, however, evidence was obtained for broad composition distributions, indicating a partial demixing of the micelles.32-34 The interpretation of the new measurements was based on a simple theory for the neutron scattering at zero angle of noninteracting spherical micelles with a distribution of compositions but of constant size.33,35 dΣ ð0Þ ¼ nm Vm 2 ½σ2 ðFFS - FHS Þ2 þ ðF - FS Þ2  dΩ

ð1Þ

where dΣ/dΩ(0) is the scattering cross section at modulus of scattering vector |qB| = 0, nm the number density of micelles, Vm the micelle volume, F the scattering length density, with subscript FS for fluorinated surfactant, HS for hydrogenous surfactant, S (29) Lepori, L.; Matteoli, E.; Spanedda, A.; Duce, C.; Tine, M. R. Fluid Phase Equilib. 2002, 201, 119. (30) Burkitt, S. J.; Ottewil, R. H.; Hayter, J. B.; Ingram, B. T. Colloid Polym. Sci. 1987, 265, 628. (31) Caponetti, E.; Chilura Martino, D.; Floriano, M. A.; Triolo, R. Langmuir 1993, 9, 1193. (32) Kadi, M.; Hansson, P.; Almgren, M.; Bergstr€om, M.; Garamus, V. M. Langmuir 2004, 20, 3933. (33) Almgren, M.; Garamus, V. M. J. Phys. Chem. B 2005, 109, 11348. (34) Almgren, M.; Garamus, V. M.; Asakawa, T.; Jiang, N. J. Phys. Chem. B 2007, 111, 7133. (35) Avdeev, M. V. J. Appl. Crystallogr. 2007, 40, 56.

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for solvent, and F representing the scattering length density of the (hypothetical) fully mixed micelle. σ is the width of the micelle composition distribution, f(xFS), and given by Z σ ¼ 2

1

ðxFS - xFS Þ2 f ðxFS Þ dxFS

ð2Þ

0

where xFS is the mole fraction fluorinated surfactant in a micelle. For micelles of a single composition eq 1 reduces to the usual expression with zero scattering at the contrast match point between solvent and micelle.30 Only the width of the micelle composition distribution is thus obtained directly in this analysis. The value of σ has some implications. The binominal distribution of an ideally mixed system can be calculated as σ = 0.05 at an average equimolar composition and an aggregation number of 100 (the value is larger for smaller micelles).34 Nonideally mixed systems with attractive interactions between the surfactants would have more narrow distributions, and repulsive interactions such as between fluorinated and hydrogenous surfactants would lead to a broadening. In the hypothetical case of complete demixing into pure surfactant micelles of the two types, eq 2 shows that the width should reach a maximum value of σ = 0.5, whereas a square composition distribution representing the broadest possible monomodal distribution will have σ = 0.289. Thus, the value of σ provides a nonideality scale, from σ ≈ 0.05 for ideally mixed to σ = 0.5 for strong repulsive interactions leading to complete demixing. As discussed earlier34 a solution theory must be adopted in order to relate σ to thermodynamic measures of nonideality. Using the strictly regular solution theory36 for the nonideal mixed micelles, a one-to-one relationship is found between σ and the interaction parameter, for a given aggregation number of the micelles. The composition distribution can then be calculated, and give an indication of what can be expected for real systems. In this contribution we first report the results from NMR measurements and contrast variation SANS studies of three systems: SPFO and SDeS in 200 mM NaCl, lithium perfluorononanoate, LiPFN, and LiDS in 200 mM LiCl, and a nonionic system, C8F17C2H4(OC2H4)9 and C12H25(OC2H4)8.The first system was recently studied by NMR methods (in aqueous solution without added salt).8 Salt was added to reduce the electrostatic interactions (but not so much as to risk a sphere-to-rod transition). Strong demixing was neither expected nor found for this system. To increase the nonideality the chain lengths of both surfactants were increased in the second system, and Li substituted for Na in order to reduce the Krafft point of the surfactant mixture. The nonionic system was chosen since previous studies; including a determination of the outlines of the ternary phase diagram;suggested that the nonideality is strong enough to promote demixing under certain conditions.27 The SANS results were evaluated using both the simple theory referred to above and also by direct modeling assuming the micelles to be ellipsoids of revolution with a Gaussian composition distribution, and interacting by effective hard-sphere interactions.34 The results from all mixed systems studied by contrast variation SANS will then be considered, and the degree of nonideality of the systems compared with the extensive literature data on demixing in alkaneperfluoroalkane mixtures.

Experimental Section Materials. Sodium perfluorooctanoate (SPFO), and lithium perfluorononanoate (LiPFN) were prepared by neutralizing the (36) Guggenheim, E. A. Mixtures; Oxford University Press: Oxford, U.K., 1952.

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corresponding acids (Aldrich, 96%) with aqueous solutions of NaOH (Riedel-de Ha€en, g99%) or LiOH (LiOH 3 H2O Riedel-de Ha€en, g98.5%). The solutions were recrystallized twice from water at about 0 C. The crystals were redissolved in water and the solution filtered twice to remove dust or microparticles. Finally, the solution was freeze-dried. Sodium decylsulfate (SDeS, Fluka, g99%), sodium dodecyl sulfate (SDS, BDH specially pure), lithium dodecylsulfate (LiDS, Sigma >98.5%), lithium chloride (Merck, pro analysi) and deuterium oxide (Isotec, 99.9 atom % D) were used as received. Both nonionic surfactants had hydrophilic chains with a Gaussian chain length distribution. The fluorinated surfactant, CF3(CF2)7.2C2H4(OC2H4)9, labeled RF8 (EO)9 (DuPont, Belgium), was polydisperse also in the hydrophobic part. The hydrogenous surfactant C12H25(OC2H4)8, labeled RH 12 (EO)8, was provided by Hunstman, France. NMR Self-Diffusion Measurements. The NMR measurements were performed at the Division of Physical Chemistry at the Royal Institute of Technology, Sweden. Mixed surfactant solutions were contained in 5 mm NMR tubes. The NMR diffusion measurements were performed as described earlier.8 The measurements were carried out on a Bruker DMX500 spectrometer equipped with a standard 5 mm 1H/19F tunable bbi-probe with maximum gradient strength of 55.5 G/cm. All diffusion experiments were performed at 25.0 ( 0.1 C with Δ = 200 ms diffusion time, δ = 1-3 ms gradient pulse length, and the gradient strength linearly ramped in 15 steps from 3.6 to 54.3 G/cm in the conventional stimulated-echo sequence.37 The obtained self-diffusion coefficients were calibrated to a standard of HDO trace in D2O.38 Small Angle Neutron Scattering. The SANS measurements were performed at the GKSS Research Centre, Geesthacht, Germany.39 Three different instrumental settings were used (sample-to-detector distance was varied from 0.7 to 4.5 m). Experimental data were collected in the interval from 0.01 to 0.25 A˚-1of the modulus of the scattering vector q (q = 4π/λ sin θ/2, where θ is the angle between the direct and scattered beam and λ = 8.5 A˚ is the neutron wavelength). The data were corrected for background scattering and put on an absolute scale by dividing with the known scattering spectrum of pure H2O.

Data Analysis by Generalized Indirect Fourier Transformation. Data analysis by Indirect Fourier Transformation (IFT)

was performed at q > 0.02 A˚-1 where the effects of intermicellar interactions are small.40 In order to allow for larger interactions a generalized method (GIFT) was employed,41 treating the interactions as effective hard sphere repulsions. The effective radius of the charged micelles was chosen to be compatible with the micelle radius increased by a Debye length. The analysis yields the scattering at zero angle, I(0) = (dΣ(0)/dΩ), and the radius of gyration without any presumptions regarding particle size and shape. The radius of gyration is given by R Dmax pðrÞr2 dr Rg 2 ¼ 0R Dmax 2 0 pðrÞ dr

ð3Þ

where p(r), the pair distribution function, is approximated by a linear combination of a number of basis functions. The value of Dmax, the limit for the maximum dimension of the particle, was chosen so as to give a stable and smooth solution for the p(r) function that after Fourier transformation was fitted to the experimental scattering data. Too much stabilization of the p(r) solution gives rise to oscillations at high q values, but could not be (37) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523. (38) Holz, M.; Weing€artner, H. J. Magn. Reson. 1991, 92, 115. (39) Stuhrmann, H. B.; Burkhard, N.; Dietrich, G.; Junemann, R.; Meerwin, W.; Shmitt, M.; Wadzack, J.; Willumeit, R.; Zhao, J.; Nierhaus, K. H. Nucl. Instrum. A 1995, 356, 124. (40) Glatter, O. in Small Angle X-ray Scattering; Glatter, O.; Kratky, O., Eds.; Academic Press: London, 1982. (41) Bergmann, A.; Fritz, G.; Glatter, O. J. Appl. Crystallogr. 2000, 33, 1212.

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avoided for the noisy data from measurements close to the match point. The method and program used were those of Glatter42 as modified by Pedersen, also including correction for instrumental smearing.43 Direct Modeling of SANS Results. The micelles were modeled as uniform ellipsoids of revolution, without a separate headgroup shell. We applied an effective excluded volume interaction, within the decoupling approximation.44 The scattering intensities are given by Z dΣ ðqÞ ¼ nm Vm 2 ½ÆFðr, qÞ2 æo ðF -Fs Þ2 f ðFÞ dF dΩ Z þ ðÆFðr, qÞæo ðF -Fs Þf ðFÞ dFÞ2 ðSðqÞ -1Þ þ Binc

ð4Þ

where F(r,q) is the form factor of the micelles and Æ æo denotes orientation average. The expression for the orientation averaged form factor is found in the literature.45,46 S(q) is the structure factor which reflects interactions among the micelles, and Binc is the residual incoherent scattering. The composition distribution of the micelles gives a scattering length density distribution f(F). The integration is performed over all scattering length densities in the full composition range, from pure surfactant 1 to pure surfactant 2. For the mixed micelles a Gaussian composition distribution was chosen. The dispersion around the average value of F was fitted to match the experimental data. For S(q) we used an effective hard-sphere expression as calculated with the Percus-Yevick approximation for the closure relation.46,47 SðqÞ ¼

1 1 þ 24ηHS GðqRHS Þ=qRHS

ð5Þ

where ηHS is the hard sphere volume fraction, and RHS is the effective hard-sphere radius. The detailed expression of the function G(qRHS) can be found in the literature.46 RHS is allowed to take on a value larger than Req, the radius of a sphere with the same volume as the micelle. The residual electrostatic interactions that are not completely screened by addition of salt, and the increased range of the hard sphere interactions due to the departure from spherical shape, are intended to be accounted for by this scaling of RHS and ηHS. Typically, eight scattering curves were fitted simultaneously using five global parameters and a residual incoherent scattering Binc for each curve.

Results Monomer Concentrations from Self-Diffusion Measurements. The measurements and data treatment were carried out in essentially the same way as in the study of Nordstierna et al.8 The main difference is in the treatment of the electrostatic interactions for the ionic systems. A detailed account is given in the Supporting Information. The results with respect to the free surfactant concentrations in solutions with total surfactant concentrations as used in the SANS study were as follows: For SDeS/SPFO in 200 mM NaCl, we obtained cmon SDeS = 6.2 ( 0.2 mM and cmon SPFO = 7.5 ( 0.1 mM at equimolar ratio and a total surfactant concentration of 127 mM. For the LiPFN/LiDS system the monomer concentrations were negligible at a total surfactant concentration of 80 mM. The monomer concentrations of the nonionic system are also very low compared to the (42) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415. (43) (a) Hansen, S.; Pedersen, J. S. J. Appl. Crystallogr. 1991, 24, 541. (b) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321. (44) Koltarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (45) Bergstr€om, M.; Pedersen, J. S. Phys. Chem. Chem. Phys. 1999, 1, 4437. (46) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171. (47) Kinning, D. J.; Thomas, E. L. Macromolecules 1984, 17, 1712.

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total concentration (44 mM) but nevertheless available from the self-diffusion coefficients. The nonionic result at equimolar ratio mon is cmon R12H(EO)8 = 0.28 ( 0.03 mM and cR8F(EO)9 = 0.45 ( 0.14 mM, showing that the free concentrations can be ignored at a total concentration of 44 mM as used in the SANS studies. Chemical Shifts. The exchange of the surfactants between micelles is fast on the NMR time scale. The effects on the chemical shift of a nucleus from the surroundings is therefore a population average of the instantaneous chemical shifts from all different environments. Following the reasoning originally used by Muller48 in NMR studies of hydrocarbon-fluorocarbon mixtures, it was shown that the 19F chemical shifts in mixed micelles of SDeS and SPFO deviated from those expected for ideally mixed micelles.8 A part of this deviation can be explained by the excess volumes of the mixture. The excess volumes were estimated from data for hydrocarbon/fluorocarbon mixtures,29 and the effect on the chemical shift estimated as described earlier.48 The remaining part of the deviation was attributed to nonrandom mixing, and indicated a preference for like neighbors. In the SDeS/SPFO system it was shown that within the first approximation of the regular solution model (the quasi chemical model) the deviations from random mixing were in accord with a value w/z = 0.28 ( 0.08 of the ratio between the exchange energy w (in units of 1 kT) and the number of nearest neighbors, z. Using also the self-diffusion results z = 4.5 ( 1.0 was obtained.8 For the nonionic system and LiDS/LiPFN the free surfactant concentrations were negligibly small and the experimental values are taken to represent the chemical shifts in the micelles. The experimental data are displayed in Figure 1, together with the calculated effect of excess volume, and the fit to the quasi chemical model. The results are collected in Table 1. Since the critical value of w = 2.77 for z = 4 in the quasi chemical model,49 these results seem to indicate that all systems are safely non-critical. SANS Results. For each system eight solvent mixtures were prepared, containing D2O and H2O in appropriate proportions and for the ionic systems also containing salt. Samples were prepared by carefully weighting in the surfactants, adding the appropriate solvent mixture, saving a portion of the solvent mixture as reference. The SDeS-SPFO samples all contained 62 mM SDeS, 65 mM SPFO and 200 mM NaCl. The concentrations of the two surfactants were deliberately chosen different in order to compensate for an expected difference in the concentration of the free surfactants. It turned out to be somewhat overcompensated: in the experiments the concentrations of micellized surfactants were 55.8 and 57.5 mM of SDeS and SPFO, respectively. The LiDS/LiPFN system was measured in 200 mM LiCl. The total surfactant concentration was 79.2 ( 1.5 mM and the fraction of fluorinated surfactant xFS = 0.50 ( 0.01. The nonionic system contained 44.0 ( 0.3 mM total surfactant with xFS = 0.500 ( 0.002. Results from the measurements at 25 C are displayed in Figures 2 and 3, together with fittings to be discussed in the following. Scattering results for SPFO/SDeS are shown in Figure 2, together with the fits from GIFT (Figure 2a) and direct modeling (Figure 2b, discussed below). The values of I(0) and the radius of gyration, Rg, resulting from the GIFT analysis are collected in Table S1, accessible as Supporting Information. The curves in Figure 2 show that interactions are important. The effective hard sphere interactions used in the GIFT method seem to handle the effects rather well. The large deviations in the range below q= 0.02 are due to difficulties in the background subtraction. The (48) Muller, N. J. Phys. Chem. 1979, 83, 1393.

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Figure 1. Micellar 19F chemical shift of the trifluoromethyl group as a function of the mole fraction. The chemical shift variation calculated under the assumption of nonideal volume excess for a spatially homogeneous mixture within a micelle is shown as a dashed line. The solid line was obtained by fitting the first approximation of the regular solution theory and nonideal excess volume to the chemical shift data. (a) LiDS/ LiPFN, xHS = 0.5, ctot = 80 mM, [LiCl] = 200 mM. (b) The nonionic system C12H25(OC2H4)8OH/C8F17C2H4(OC2H4)9OH, xHS = 0.5, ctot = 44 mM. Table 1. w/z and w at z = 4 Obtained by Fitting the Chemical Shifts to the Quasichemical Model system w/z (1kT) w at z = 4, (1kT)

SDeS/SPFO 0.28 ( 0.08 1.11

LiDS/LiPFN 0.293 ( 0.003 1.17

nonionic 0.320 ( 0.008 1.28

samples scatter weakly with a transmission that was 97-99% of that of the solvent. In the lowest q-region, parasitic scattering from the beam stop or the cells, never perfectly removed by background subtraction, will have large influence. Because of the low scattering intensities the data collected for solvent composition close to the match point are obtained with low accuracy and have been taken with lower weighting in the fitting. The corresponding scattering data and GIFT results for LiDS/ LiPFN and the nonionic system are shown in Figure 3 and Tables S2 and S3. The scattering curves are of much higher quality in these systems than in SDeS/SPFO, without the excessive spread of the scattering at the low q values. Plots of I(0) vs XD2O is shown in Figure 4 for the three systems The scattering length density of the solvent is linearly related to XD2O: FS ¼ AXD2 O -B;

A ¼ 6:94  1010 cm -2 ,

B ¼ 0:556  1010 cm -2

ð6Þ

Taking this into account fits of eq 1 to the results for the three systems were made and the resulting parabolas are shown in Figure 4. The parameters determined were σ 2, (A2 nm Vm2), and solvent composition XD2O at the scattering minimum. Using the known concentrations of micellized surfactants and the volumes of the surfactants in the micelles (the estimated molecular volumes are given as Supporting Information), the aggregation number of the micelle is obtained from the second parameter. The results obtained are collected in Table 2. The scattering length density at the intensity minimum is smaller than expected for the match point of the mixed micelle. The deviation is particularly large for the LiDS/LiPFN system. A deviation of similar magnitude, but in the opposite direction, was observed for the system HFDePC/C12PC.34 It was then argued that a deviation of this type could be expected if the micelle size varied with the micelle composition, such that micelles rich in the fluorinated surfactant were substantially larger than those rich in the hydrogenous surfactant. In the present case, however, the dependence had to be in the opposite direction with the micelles rich in the fluorinated component being the smaller ones. The aggregation number for LiPFN (at 100 mM concentration, Langmuir 2010, 26(8), 5355–5363

no added salt) has been determined as 37 from fluorescence quenching measurements as compared to 88 for LiDS (surfactant concentration 10 mM in 100 mM LiCl),13 so a dependence of this type is possible. The widths of the composition distributions, reflecting the nonideality of the mixtures, are small enough to indicate that demixing into pronounced bimodal distributions hardly occurs, not even in the nonionic system. The small residual contribution to the scattered intensity due to the finite width of the composition distribution is difficult to determine precisely. Close to the match point there is almost nothing to measure, and at larger contrasts, this contribution is only a tiny part of the measured scattering. We cannot claim that the composition distribution really is broader for the SDeS/SPFO system than for LiDS/LiPFN, as the results indicate, but only that both systems have fairly narrow distributions. We shall return to a discussion of these results below. That the micelles in the Li-system are smaller than with Na as counterion is reasonable in view of the fact that both LiPFN and LiDS form smaller micelles than their Na-counterparts, as discussed above. For 97 mM SDeS in 73 mM NaCl an aggregation number of 58 was reported.50 Aggregation numbers of SPFO alone have only been reported for solutions without added salt. A value close to 39 was obtained at a surfactant concentration of 0.33 M,31 and values growing from 26.5 at 0.10 M to 40.9 at 0.51 M were reported in another SANS study.51 The concentration dependence in the latter study suggests that the aggregation numbers would grow with addition of salt as well, and a value above 50 under conditions as in the present measurements seems probable. Information about the size of the micelles can also be obtained from the radius of gyration. A plot of Rg2 versus (xD2O - xmp)-1, a Stuhrmann plot,52 allows the determination of the radius of gyration at infinite contrast. Here xmp is the mole fraction D2O of the match point solvent mixture. Table 3 shows the values obtained from the Stuhrmann treatments of all systems. The corresponding plots are available as Supporting Information. Assuming that the radius of gyration at infinite contrast comes from a solid sphere, the aggregation number can be calculated from the volume of the sphere and the volumes of the surfactants. The direct modeling results (in Table 4 below) indicate that the micelles are nonspherical, however. Assuming instead that the (49) Hill, T. L. Introduction to Statistical Thermodynamics; Addison Wesley: Reading, MA, 1960. (50) Raganathan, R.; Tran, L.; Bales, B. L. J. Phys. Chem. B 2000, 104, 2260. (51) Berr, S. S.; Jones, R. R. M. J. Phys. Chem. 1989, 93, 2555. (52) Stuhrmann, H. B.; Kirste, R. G. Z. Phys. Chem. 1967, 56, 334.

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Figure 2. SANS data and (a) GIFT fits (solid lines) or (b) direct modeling (solid lines) for SPFO-SDeS, in 200 mM NaCl. Different contrasts were obtained by variation of the mole fraction D2O in the solvent: 0 (empty squares), 0.15 (empty triangles up), 0.3 (empty circles), 0.42 (empty triangles down), 0.55 (filled triangle down), 0.7 (filled circles), 0.85 (filled triangles up), and 1.00 (filled squares). Table 2. Solvent Composition at Minimum Intensity, Width of the Composition Distribution, and Micelle Aggregation Number As Obtained from Fits of Eq 1 to the I(0) Values from the GIFT Treatment

Figure 3. (a) SANS data and GIFT fits for a. LiDS/LiPFN in 0.200 M LiCl, total surfactant concentration 79.2 ( 1.5 mM, xFS = 0.50 ( 0.01. Different contrasts in fraction of D2O: 1.00 (filled squares), 0.843 (filled triangles up), 0.701 (filled circles), 0.55 (filled triangles down), 0.399 (empty triangle down), 0.254 (empty circles), 0.11 (empty triangles up), 0 (empty squares). (b) C8F17C2H4(OC2H4)9OH and C12H25(OC2H4)9OH in water (D2O/H2O). Total surfactant concentration 44.0 ( 0.3 mM; xFS = 0.500 ( 0.002. Surfactant concentration corresponds to 2.5 vol %. Different contrasts in fraction of D2O: 1.00 (empty squares), 0.771 (empty triangles up), 0.578 (empty triangles down), 0.395 (empty circles), 0.292 (filled circles), 0.208 (filled triangles down), 0.101 (filled triangles up), and 0 (filled squares).

Figure 4. I(0) from GIFT analysis for the three systems, with eight solvent mixtures of each. The solid lines are fits of eq 1: SDeS/ SPFO (circles), LiDS/LiPFN diamonds, and nonionic system (triangles). The samples with most D2O are not displayed for the nonionic system.

radius of gyration refers to a spheroid, a smaller volume and lower aggregation number result, as shown in Table 3. 5360 DOI: 10.1021/la903764u

system XD2O at minimum scattering XD2O calcd at match point σ Naggr

SDeS/SPFO 0.41 ( 0.01

LiDS/LiPFN 0.38 ( 0.01

nonionic 0.23 ( 0.01

0.42

0.41

0.24

0.126 ( 0.009 50.3 ( 0.3

0.115 ( 0.006 58.8 ( 0.3

0.217 ( 0.009 85.4 ( 0.8

Table 3. Results from Stuhrmann Plots system slope Rg inf contr, A˚ Nagg, sphere a, A˚ (γ) Nagg spheroid (γ from Table 4)

SDeS/SPFO -8.4 13.7 64.9 18.8 (0.8) 62

LiDS/LiPFN -10.8 15.2 78.7 21.8 (0.66) 71

nonionic 21.2 25.9 162 22.1 (2.2) 103

These aggregation numbers are substantially larger than those in Table 2, in particular for the non-ionic system, where the aggregation number obtained under assumption of a spherical shape is about twice as large as the value from Table 2, indicating that the shape is strongly elongated. The slope of the Stuhrmann plot informs on the distribution of the scattering length densities in the micelle. A negative value, as obtained for the ionic systems, indicates that the scattering length density is larger in the outer parts than in the core region, as expected both from the large scattering density of the headgroups, and from a concentration of the short fluorinated surfactants in the outer parts of the micelle. The large positive value of the nonionic system is at least partly due to the low scattering density of the headgroup layer in these nonionic micelles, but may also be an indication of a more central placement of the fluorinated tails. Such a situation would be realized in elongated micelles where the hydrogenous surfactants would be expected to be preferentially situated at the highly curved ends, and the fluorinated surfactants in cylindrical part. SANS Modeling. Direct fitting of results from all contrasts simultaneously was performed using eq 4. In the model, we allowed for a nonspherical micelle shape (which has similar effects as a size polydispersity of spherical micelles) and assumed a Gaussian composition distribution. A two-shell model appears more realistic and should improve the fitting. We checked it and found that in our case the improvement was small and that the values of the parameters (axis ratio and composition distribution) in which we are interested stayed approximately the same. In order to avoid complications we used the simple model of ellipsoids of revolution. The fits to this model are shown in Langmuir 2010, 26(8), 5355–5363

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Table 4. Values of Parameters γ, a, σ, RHS/Req, Binc, Obtained from Model Fits to Data of Mixtures, together with χ 2 for the Fit, and Nagg Calculated from Micelle and Surfactant Volumes

γ a, A˚ σ RHS/Req Binc, cm-1 χ2 Nagg

SPFO/SDeS in 200 mM NaCl Gaussian, oblate

LiPFN/LiDS in 200 mM LiCl Gaussian, oblate

F RH 12 (EO)8/R8 (EO)9 Gaussian, prolate

0.8 ( 0.1 18.5 ( 0.5 0.145 ( 0.01 1.5 ( 0.1 0.005-0.03 3.3 59 ( 8

0.65 ( 0.05 20.6 ( 0.5 0.13 ( 0.01 1.6 ( 0.1 0.005-0.02 6.5 59 ( 7

2.2 ( 0.1 27 ( 1 0.18 ( 0.02 1 0.015-0.03 11 188 ( 15

Figure 3 for the SDeS/SPFO system, and for the two other systems in the supplement. The values of the parameters are presented in Table 4. For the ionic systems best fits were obtained for oblate spheroids. For SPFO/SDeS both the dispersion of the composition distribution and the aggregation number are larger than what was obtained from the GIFT treatment, Table 2. The results for LiPFN/LiDS are in fair agreement with those from the GIFT analysis. The most severe disagreement between the evaluation methods was found for the nonionic system where already the Sthurmann analysis indicated elongated micelles. The assumption of spherical micelles makes the GIFT results less credible in this case. Even so the estimated widths of the composition distribution are not too different. SANS methods have indicate that small micelles may have an average oblate shape, whereas prolate structures fit best under conditions where a growth into elongated structures starts.45 The difference in shape of the systems in this study may be explained in this way.

Discussion The main conclusion from the SANS measurements of the ionic systems is that the composition distributions are broad but not demixed into two separate micelle populations. The fact that no substantial demixing is observed in the SANS studies is in line with the conclusions from the 19F chemical shift measurements summarized in Table 1. The NMR results indicate, however, that LiDS/LiPFN is somewhat more nonideal than SDeS/SPFO, as would be expected for the mixture with longer chains. From the experimental results shown in Figures 2 and 3a, it is obvious that the estimate of the width would be most uncertain for the SDeS/ SPFO system. It is more probable that the width of the composition distribution was overestimated in this system than that it was underestimated in LiDS/LiPFN. Both the NMR and the SANS results disagree with the results by Asakawa and co-workers mentioned in the Introduction.12,17 The NMR and SANS methods are noninvasive and rather direct. It is hard to believe that substantially broader composition distributions would be concealed in these results. Further detailed studies would be required to find the reasons for the disagreement with the conclusions drawn from careful analysis of cmc and “second” cmc data, and from fluorescence studies. Some aspects of results presented by Asakawa and Miyagishi53 and by Nakano et al.54 suggest that the disagreement might be merely apparent. The conclusions drawn from cmc studies pertain to conditions just at this concentration; in some systems a transition to a region with only mixed micelles occurs at higher total concentration.53 Added salt may also be (53) Asakawa, T.; Miyagishi, S. Langmuir 1999, 15, 3464. (54) Nakano, T.-Y.; Sugihara, G.; Nakashima, T.; Yu, S.-C. Langmuir 2002, 18, 8777.

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Figure 5. Composition distributions for micelles with Nagg = 100 composed of two surfactants. The most narrow curve represents ideal mixing, the next curve with a central maximum is a Gaussian with σ = 0.18, as obtained from direct modeling of the SANS results. The two curves with a central minimum represents distributions according to the regular solution lattice theory.55 A weak minimum is obtained already at an interaction parameter of 2.05, giving σ = 0.183, whereas the minimum is more pronounced for an interaction parameter of 2.16 corresponding to σ = 0.219.

of importance. Other systems may be strongly asymmetric. In a study of STDS (sodium tetradecylsulfate)/SPFN Nakano et al. analyzed cmc data using a modified regular solution theory where also the difference in ion binding of the two surfactants were taken into account. The results indicated that two types of micelles were formed only at mole fractions STDS below 0.2, where micelles of an azeotropic composition (xSTDS = 0.05) coexisted with almost pure STDS micelles. Above xSTDS = 0.2 almost ideal mixed micelles were present.54 Clearly, so complex a behavior would not be captured by measurements at only one concentration and composition. F Both SANS and NMR show RH 12 (EO)8/R8 (EO)9 to be more nonideal than the other two systems of this study. The σ-values obtained, 0.18-0.22, are in a range that would be close to the critical, at least according to the regular solution lattice model.55 In a regular solution of two components, the interaction parameter, w, is the work in units of 1kT, of exchanging a molecule of A in pure A by a molecule of B in pure B.36 In the zeroth order approximation an interaction parameter g2 results in separation into two liquid phases, with symmetric compositions so that xA (phase 1) = xB (phase 2). In micellar systems the phase separation would correspond to a demixing into coexisting micelles of different types. Even before a demixing into separate micelle populations, the effect of repulsive interactions;positive interaction parameter;will give rise to a broadening of the micelle composition distribution. In Figure 5, composition distributions, calculated within the regular solution model from eq 22 in ref 55 are displayed for both an ideally mixed system and for two systems with aggregation numbers and widths of the composition distributions chosen to match the results for the nonionic system, as shown in Table 5. Note that the Gaussian has to be truncated at the end points and does not well represent a composition distribution of this width. The distributions with σ-values of 0.183 and 0.219 according to the regular solution lattice model are in the critical regime with interaction parameters of 2.05 and 2.19, respectively, and the latter is clearly bimodal.

(55) Barzykin, A. N.; Almgren, M. Langmuir 1996, 12, 4672.

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Table 5. Aggregation Number, Variance of the Micelle Composition Distribution, and Scattering Length Density at the Intensity Minimum for Micelles Formed in Mixtures of Hydrogenous and Fluorinated Surfactants, Using I(0) Values from IFT Analysis systema

[NaCl], mM

T, C

Nagg

σ

σ direct modeling

Fb

F bcalc

C16TAC/HFDePCc 65 25 84 0.31 ( 0.003 0.35 0.34 65 60 61 0.19 ( 0.01 0.34 C16TAC/HFDePCc 63 25 79 0.37 ( 0.003 0.38 0.375 C16PC/HFDePCc 63 60 71 0.19 ( 0.01 0.38 0.375 C16PC/HFDePCc 200 25 64 0.22 ( 0.003 0.17 ( 0.02 0.46 0.42 C12PC/HFDePCc 200 25 79 0.006 ( 0.03 0.006 ( 0.03 0.57 0.59 SDS/SDS-d25c SDeS/SPFO 200 25 50 0.13 ( 0.009 0.145 ( 0.01 0.41 0.42 25 59 0.12 ( 0.006 0.13 ( 0.01 0.38 0.41 LiDS/LiPFN 200d F RH (EO) /R (EO) 25 85 0.22 ( 0.009 0.18 ( 0.02 0.23 0.24 12 8 8 9 a C16TAC = hexaddecyltrimethylammanium chloride, HFDePC = N-1(1,1,2,2-tetrahydroperfluorodecanoyl)pyridinium chloride, C16PC = N-1hexadecylpyridinium chloride, C12PC = N-1-dodecylpyridinium chloride, SDS = sodium dodecyl sulfate, SDeS = sodium decylsulfate, SPFO = b F sodium perfluorooctanoate, LiPFN = lithium perfluorononanate, RH 12(EO)8 = C12H25(OC2H4)8, and R8 (EO)9= C8F17C2H4(OC2H4)9. Scattering c d length densities are expressed as mole fraction D2O in the matching D2O/H2O solvent mixture. Results from refs 32-34. LiCl used as added electrolyte.

It should be noted that the distributions illustrated in Figure 5 do not represent the true distributions. They are all obtained within the framework of a two-dimensional lattice model with a single interaction parameter, and are then symmetrical. There are good reasons to believe that this is not correct. Furthermore, within this framework the interaction parameter chosen to reproduce the observed σ-values refers to the zeroth order approximation of the regular solution theory. The regular solution model, in the zeroth order approximation, neglects the nearest neighbor preference completely. The first order or quasichemical approximation is somewhat better in this respect, but far from satisfactory, as shown by the value of the critical interaction parameter: in exact calculations available for a square lattice with 4 nearest neighbors, the critical value is 3.53, as compared to 2.77 in the quasi-chemical approximation and 2 in the zeroth order regular solution theory.49 In order to reproduce a given σ value, a larger value of the interaction parameter would be required in an exact model.55 The results from the 19F chemical shift measurements as reported in Table 1 seem to suggest less nonideality than the SANS results. The 19F chemical shift informs on the nearest neighbor distribution, and how it deviates from the random distribution that pertains in ideal mixing (and is assumed in the zeroth order regular solution theory). The shifts are not sensitive to the distribution of the surfactants over the micelles. The chemical shift information is thus complementary to that from the contrast variation SANS experiments, where a measure of the surfactant distribution among the micelles is determined. Although both effects are caused by the nonideality of mixing, they are not easily linked together. In the evaluation of the 19F chemical shift results within the quasi-chemical model, the excess volumes in the mixture are important. This effect is large and was calculated using excess volumes for hydrocarbon/fluorocarbon mixtures. It is possible that the excess volumes of the surfactants in the mixed micelles are much smaller. In fact the nonideality as expressed by the critical temperature for demixing is much smaller for molecules with polar groups than for normal hydrocarbon/fluorocarbon mixtures.16 The observed deviations from ideal mixing would then correspond to a larger excess of like neighbors, and a stronger nonideality than suggested in Table 1. Comparison with Earlier Results. In Table 5 results are compiled for all systems studied at the GKSS Research Centre in Geeshacht for the determination of the width of the composition distribution. The results for the cationic surfactant mixtures have been discussed earlier.32-34 Taken together the most important factors for the degree of nonideality, which determines the width of the composition distribution, are the length of the alkyl and 5362 DOI: 10.1021/la903764u

perfluoroalkyl tails of the surfactants and the temperature, whereas the nature of the polar headgroup is less important. It should also be noted that the system of SDS and SDS-d25 gave a σ value much smaller than what corresponds to the binominal distribution of an ideal mixture. It is difficult to find any reason for this system not to be randomly mixed. This result, therefore, may be taken as a warning that small values of σ are uncertain. Turning to the other anionic systems, the value for SDeS/SPFO is substantially larger than that measured for the ideal system. It corroborates the conclusion that nonideal mixed micelles without demixing are present in this system.8 In the other anionic system, LiDS/LiPFN, the fluorocarbon chain length is increased by one unit, and the alkyl chain by two units, still the σ value is comparable with that for SDeS/SPFO. As remarked above a good part of this inconsistency is probably due to uncertainties in the results for the latter system, but the effect from the change of counterion to Liþ should also be considered. Clearly this change has profound effects on other properties of the micelles, giving smaller aggregation numbers and lower Krafft point. The surfactants in the nonionic system have the same hydrophobic groups as C12TAC/HFDePC (and almost the same as LiDS/LiPFN). In the first two systems the broad distribution signals a strong nonideality. The conclusion is again that the nonideality is mainly determined by the size of the hydrophobic groups. In Figure 6a, literature values1,56 of the upper critical solution temperatures for n-hydrocarbon and n-perfluorocarbons are presented. For x-axis the sum of the number of hydrogenous carbons and one-fourth of the number fluorinated carbons was chosen, since with this choice the liquid-liquid critical temperatures fall approximately on the same master curve. We have found no simple explanation for this correlation in the literature;it seems not to have been noticed. The interesting and surprising observation is the fact that the length of the alkyl chain is much more important than that of the fluorocarbon chain. The graph indicates that phase separation occurs at 25 C already at a value of (nCH þ 0.25nCF) ≈ 7.5. There is no direct way to compare these results with those for the surfactant mixtures. The plot in Figure 6b shows the measured σ-values using the same x-axis as in Figure 6a. Note that the variation in this case is not expected to be linear; a sigmoid change from a value of about 0.05 for the ideal mixture to a maximum of 0.5 for completely immiscible surfactants could be anticipated. According to the composition distributions obtained from regular solution models of micelles, the width of the distribution changes (56) Gilmour, J. B.; Zwicker, J. O.; Katz, J.; Scott, R. L. J. Phys. Chem. 1967, 71, 3259.

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Figure 6. (a) Critical solution temperatures for mixtures of n-hydrocarbons and n-fluorocarbons, data from the literature.1,56 (b) Width of distributions from SANS results for mixtures of fluorinated and hydrogenous surfactants, from Table 5. The abscissa is the sum of the number of hydrogenous carbons and one-fourth of the number of fluorinated carbons in the chains.

most rapidly for interaction parameter values close to the critical, where the value of σ is about 0.19.34 In Figure 6b this value requires (nCH þ 0.25nCF) to be about 15, corresponding to surfactant pairs with 13 hydrogenous and 8 fluorinated carbons. Much larger components are thus required to reach critical conditions in the mixed micelles than in ordinary fluid mixtures. In addition to the fact that polar components give lower critical temperatures already in fluid mixtures,16 the decreased nonideality could be further enhanced by the localization of the polar headgroups at the micelle surface.

Conclusions Contrast variation SANS investigations of mixed micelle systems formed in binary mixtures of fluorinated and hydrogenous surfactants allow a determination of the broadness of the micelle composition distribution, providing a measure of nonideality of mixing. For surfactants with the same type of headgroups; cationic, anionic, or nonionic;the width of the distribution increases with the size of the hydrophobic tails of the surfactants, and may reach values for which a bimodal composition distribution is necessary. The size of the hydrophobic parts of the surfactants is most important for the width and the degree of nonideality. For the three systems of this study the width was largest in the nonionic case, suggesting this system to be close to critical conditions. For the ionic systems, SDeS/SPFO in 200 mM NaCl and LiDS/LiPFN in 200 mM LiCl similar widths were suggested by the fitting to the SANS data, in spite of the fact that the surfactants in the latter are larger. Although the low quality of the data for the former system suggests that the width has been overestimated in that case, the change of counterion is probably also important. Both the nonionic and the cationic systems with surfactant sizes similar to LiDS/LiPFN give broader distributions. The 19F chemical shift measurements are complementary to the SANS studies, providing information on the average local environment of in this case the CF3 group of the fluorinated surfactant. This information is independent of the distribution of surfactants over the micelles. The density of neighbors depends on the average number of nearest neighbors of each kind, and also on the local density. In fluorocarbon-hydrocarbon mixtures where the excess volumes are particularly large this nonideality

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must be taken into account. We used data from fluorocarbon-hydrocarbon mixtures to estimate the effect in the mixed micelles and found it to explain a very substantial part of the deviation from the ideal mixing behavior; the rest of the deviation was ascribed to a preference for like neighbors. The results show a clear increase in the preference for like neighbors with the size of the systems, the nonionic system being most nonideal. Even in this system the preference was clearly below what would be expected for critical systems, in contrast to the results from the SANS study. It is possible that the excess volume effect is substantially smaller for the surfactant mixtures than for similar hydrocarbon/ fluorocarbon mixtures so that the preference for like neighbors was severely underestimated in the evaluations. Comparing published results on nonideality of alkane/ perfluoroalkane mixtures;we focused on the critical temperature;with the contrast variation SANS results for all micellar systems studied at the GKSS Research Centre in Geeshacht it is clear that the surfactants must have much larger hydrophobic parts than the alkanes in order to reach critical conditions. Since already the introduction of polar end groups in the alkanes reduces the critical temperature strongly, this is not necessarily a sign of an effect from micelle formation. Acknowledgment. We are indebted to professor Bengt J€onsson, Lund University, for a discussion of the obstruction factors for diffusion in charged systems, and to professor H. Maeda, Fukuoka University, for enlightening discussions on several aspects of this work. The Swedish Research Council (VR) supported this work. The SANS investigations were supported by the European Commission under the sixth Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures, Contract No RII3-CT-2003-505925. Supporting Information Available: Text, tables, and figures giving details of the self-diffusion studies, results obtained from generalized indirect Fourier transform analysis for all systems, Stuhrmann plots for all systems, and direct modeling fits to SANS data for LiDS/LiPFN and the nonionic system. This material is available free of charge via the Internet at http://pubs.acs.org.

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