Langmuir 2004, 20, 3933-3939
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Mixed Micelles of Fluorocarbon and Hydrocarbon Surfactants. A Small Angle Neutron Scattering Study M. Kadi,*,† P. Hansson,‡ and M. Almgren† Department of Physical Chemistry, Uppsala Biomedical Centre, P.O. Box 579, SE-751 23 Uppsala, Sweden, and Department of Pharmacy, Uppsala Biomedical Centre, P.O. Box 580, SE-751 23 Uppsala, Sweden
M. Bergstro¨m Department of Chemistry, Surface Chemistry, Drottning Kristinas va¨ g 51, Royal Institute of Technology, SE-100 44 Stockholm and YKI, Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden
Vasil M. Garamus GKSS Research Centre, Max-Planck Strasse, 21502 Geesthacht, Germany Received December 19, 2003. In Final Form: February 19, 2004 Mixtures of the partly fluorinated cationic surfactant HFDePC (N-(1,1,2,2-tetrahydroperfluorodecanyl)pyridinium chloride and deuterated headgroup) with C16TAC, hexadecyl-trimethylammonium chloride, have been investigated using small angle neutron scattering with contrast matching. Earlier results from this system suggested that a demixing occurred, into two coexisting populations of micelles, hydrocarbonrich and fluorocarbon-rich, respectively. The present results could be explained by one type of mixed micelles with an inhomogeneous distribution of fluorinated and hydrogenated surfactants within the micelles although a demixing cannot be definitely excluded.
Introduction The possible demixing in mixtures of fluorinated and hydrogenated surfactants have received a lot of attention in recent years. The fluorinated surfactants have chemical and physical properties that are different from those of normal hydrocarbon surfactants.1-4 The nonideal net repulsive interactions between hydrogenated and fluorinated chains lead to macroscopic phase separation in mixtures of alkanes and fluoroalkanes with sufficiently long carbon chains.5 The conditions for a demixing into two different populations of micelles in aqueous mixtures of fluorocarbon and hydrocarbon surfactants has been a matter of debate. A number of different techniques have been tried in order to prove the coexistence of two different micelle types, for instance cmc measurements,6-11 fluorescence spectroscopy,11-17 NMR,18-23 gel filtration,24 ultracentrifugation,25 light,25 and neutron scattering.26,27 * To whom correspondence should be addressed. † Department of Physical Chemistry, Uppsala Biomedical Centre. ‡ Department of Pharmacy, Uppsala Biomedical Centre. (1) Fletcher, P. D. I. In Specialist Surfactants; Robb, I. D., Ed.; Blackie Academic and Professional: London, 1997; p 104. (2) Kissa, E. Fluorinated Surfactants and Repellents; Hubbard, A. T., Ed.; Marcel Dekker: New York, 2001. (3) Monduzzi, M. J. Curr. Opin. Colloid Interface Sci. 1998, 3, 467. (4) Shinoda, K.; Hato, M.; Hayashi, T. J. Phys. Chem. 1972, 76, 909. (5) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365. (6) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984. (7) Esumi, K. Colloids Surf. A: Physicochem. Eng. Aspects 1994, 84, 49. (8) Ben Goulam, M.; Moatadid, N.; Graciaa, A.; Marion, C.; Lachaise, J. Langmuir 1996, 12, 5048. (9) Arai, T.; Takasugi, K.; Esumi, K. J. Colloid Int. Sci. 1998, 197, 94. (10) Tamori, K.; Kihara, K.; Esumi, K.; Meguro, K. Colloid Polym. Sci. 1992, 270, 927. (11) Asakawa, T.; Amada, K.; Miyagishi, S. Langmuir 1997, 13, 4569. (12) Almgren, M.; Wang, K.; Asakawa, T. Langmuir 1997, 13, 4535.
In an earlier paper, mixtures of cetyltrimethylammonium chloride and a partly fluorinated cationic surfactant, N-(1,1,2,2-tetrahydroperfluorodecanyl)pyridinium chloride, were studied.18 From NMR diffusion measurements, together with time-resolved fluorescence quenching and cryo-TEM, strong indications of two coexisting micelle populations were found. From NMR 19F line width measurements, it was furthermore suggested that a segregation occurred within the micelles.18 With increasing temperature, an increased mixing was observed. Demixing into coexisting micelles of different composition has been suggested by others to occur in this surfactant mixture.12,28 Asakawa et al.28 suggested a demixing into two micelle (13) Muto, Y.; Esumi, K.; Meguro, K.; Zana, R. J. Colloid Interface Sci. 1987, 120, 162. (14) Asakawa, T.; Okamoto, T.; Miyagishi, S. J. Jpn. Chem. Soc. 1997, 46, 777. (15) Asakawa, T.; Saruta, A.; Miyagishi, S. Colloid Polym. Sci. 1997, 275, 958. (16) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1996, 12, 1204. (17) Asakawa, T.; Miyagishi, S. Langmuir 1999, 15, 3464. (18) Kadi, M.; Hansson, P.; Almgren, M.; Furo, I. Langmuir 2002, 18, 9243. (19) Carlfors, J.; Stilbs, P. J. Phys. Chem. 1984, 88, 4410. (20) Asakawa, T.; Imae, T.; Ikeda, S.; Miyagishi, S.; Nishida, M. Langmuir 1991, 7, 262. (21) Clapperton, R. M.; Ottewill, R. H.; Ingram, B. T. Langmuir 1994, 10, 51. (22) Guo, W.; Guzman, E. K.; Heavin, S: D.; Li, Z.; Fung, B. M.; Christian, S. D. Langmuir 1992, 8, 2368. (23) Barthe´le´my, P.; Tomao, V.; Selb, J.; Chaudier, Y.; Pucci, B. Langmuir 2002, 18, 2557. (24) Asakawa, T.; Miyagishi, S.; Nishida, M. Langmuir 1987, 3, 821. (25) Haegel, F. H.; Hoffmann, H. Prog. Colloid Polym. Sci. 1988, 76, 132. (26) Burkitt, S. J.; Ottewill, R. H.; Hayter, J. B.; Ingram, B. T. Colloid Polym. Sci. 1987, 265, 628. (27) Caponetti, E.; Chillura Martino, D.; Floriano, M. A.; Triolo, R. Langmuir 1993, 9, 1193.
10.1021/la036410t CCC: $27.50 © 2004 American Chemical Society Published on Web 04/17/2004
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populations containing mole fractions 0.89 and 0.17 of the fluorinated surfactant, respectively. In the present contribution, we have used small angle neutron scattering with contrast matching for further investigations of this system. By varying the H2O/D2O ratio of the solvent, the contrast of either the hydrocarbon or the fluorocarbon surfactant can be matched. Contrast matching with SANS has earlier been used for studying mixtures of fluorinated and normal surfactants with relatively short hydrophobic tails. Mixtures of ammonium decanoate and ammonium perfluoro-octanoate were found to form mixed micelles, but the possibility of segregation within these micelles was discussed.26 The mixture of sodium perfluorooctanoate and sodium dodecanoate is another system that has been studied using SANS with contrast matching.27 Also in this case only one population of mixed micelles was found in the solution. It should be pointed out that, to minimize the effects of intermicellar interactions, the measurements in the present study were performed at lower total surfactant concentrations than in the previous paper.18 Experimental Section Materials. The cationic fluorocarbon surfactant HFDePC (N(1,1,2,2-tetrahydroperfluorodecanyl)pyridinium chloride), with the pyridinium headgroup deuterated, was a gift from Prof. Asakawa (Kanazawa University, Japan). The synthesis has been described earlier.28 C16TAC (cetyltrimethylammonium chloride) was prepared from the bromide salt (Serva, analytical grade) by ion exchange. Cryo-TEM. The technique has been described in detail elsewhere.29,30 Within a chamber of controlled temperature and humidity, a drop of the sample solution was placed on a copper grid covered by a perforated polymer film. Excess liquid was removed by blotting using a filter paper. The samples were thereafter vitrified by quick freezing in liquid ethane and transferred to a Zeiss 902A transmission electron microscope. The temperature was kept low during the entire procedure to prevent sample perturbation and the formation of ice crystals. Light Scattering. Static light scattering (SLS) measurements were carried out with a BI-200SM goniometer system connected to a BI-9000AT digital correlator from Brookhaven Instruments and a water-cooled Lexel 95-2 laser with maximum power of 2 W and wavelength 514 nm. The samples were measured at 25 ( 0.2 °C. SLS experiments were performed at 29 different angles in the range of 15° e θ e 155°, corresponding to values of the scattering vector modulus q in the range of 4.26 × 10-4 Å-1e q e 33.2 × 10-4 Å-1. For each angle, five individual measurements were performed and subsequently averaged. The data were then set to absolute scale intensities using toluene as a reference standard. Small Angle Neutron Scattering. The SANS measurements were performed at the GKSS Research Centre, Geesthacht, Germany.31 Three different instrumental settings (sample-todetector distance was varied from 0.7 to 4.5 m) were used. Experimental data were collected in the interval of 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 Å is the neutron wavelength) from 0.01 to 0.25 Å-1. All measurements were performed at 25 °C. The data were corrected for background scattering and put on an absolute scale by dividing with the known scattering spectrum of pure H2O. (28) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1995, 11, 478. (29) Dubochet, J.; Adrian, M.; Chang, J. J.; Homo, J. C.; Lepault, J.; McDowall, A. W.; Schultz, P. Q. Rev. Biophys. 1988, 21, 129. (30) Bellare, J. R.; Davis, H. T.; Scriven, L. E.; Talmon, Y. J. J. Electron Microsc. Technol. 1988, 10, 87. (31) 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.
Kadi et al.
Small Angle Neutron Scattering Data Analysis Model Fitting. A quantitative estimate of the geometrical structure of the micelles could be obtained by means of fitting our small-angle scattering data to either a model for ellipsoids of revolution or a model for polydisperse rigid rods.32 The scattering cross-section for a monodisperse collection of interacting anisotropic particles can be expressed in the following way:
[
dσm(q) 〈F(q)〉02 ) ∆Fm2 Vm2Nm〈F2(q)〉0 1 + 2 (S(q) - 1) dΩ 〈F (q)〉 0
]
(1)
where ∆Fm is the difference in scattering length density per unit mass solute between particles and solvent, Vm is the volume of the particles, and Nm is the concentration of particles. For an ellipsoid of revolution, the orientational averaged form factor is obtained by means of integrating over the square of the amplitude
F(q,r) )
3[sin(qr) - qr cos(qr)] (qr)3
(2)
where r(a,b,θ) ) (a2 sin2 θ + b2 cos2 θ)1/2, to yield33
〈F2(q)〉0 )
∫0π/2 F2[q,r(a,b,θ)] sin θ dθ
(3)
〈F(q)〉0 is obtained in an analogous way by integration over the amplitude. To account for interactions between the micelles the decoupling approximation34 in eq 1, valid for particles with small anisotropy, was used together with a structure factor S(q) derived by Hayter and Penfold35 from the OrnsteinZernike equation and the rescaled mean spherical approximation (RMSA),36 with a soft repulsive potential between two macroions surrounded by a diffuse double layer of counterions as calculated from the PoissonBoltzmann theory. In some of the samples, the micelles were seen to be rather long and the corresponding data were fitted with a model for polydisperse cylinders. To avoid unreasonably long computation times, we have simplified the model by means of separating the form factor due to the length of the micelles Plength(q) and the corresponding one due to the particle cross section Pcs(q). Hence, we have used the following scattering cross-section valid for particles with a length much larger than the cross-section dimensions37
dσm(q) ) ∆Fm2Plength(q)Pcs(q)Vm2Nm dΩ
(4)
The form factor Pcs(q) for a circular cross-section with radius r is given by
Pcs(q) )
(
)
2B1(qr) qr
2
(5)
where B1(x) is the Bessel function of first order. Since qmax ) 0.25 Å-1, it was not possible to obtain any additional (32) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171. (33) Guiner, A. Ann. Phys. 1939, 12, 161. (34) Kotlarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (35) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 409. (36) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651.
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information by using a two-shell model or assuming an elliptical cross-section in the analysis. The scattering function for polydisperse rigid rods can be written as follows:
Plength(q) )
∫Nrod(L)L2Srod(q,L) dL ∫Nrod(L)L2 dL
(6)
where the number density of the length L of the micelles, Nrod(L), is assumed to follow a Schultz distribution. The form factor for an infinitely thin rod is given by38
Srod(q,L) ) 2Si(qL) -
4 sin2(qL/2) (qL)2
(7)
where
Si(x) )
∫0x sint t dt
(8)
The polydispersity of the rod-shaped micelles were accounted for by setting the relative standard deviation to σL/〈L〉 ) 0.7, i.e., somewhere between what is expected for infinitely small rods (σL/〈L〉 ) 0) and infinitely large rods (σL/〈L〉 ) 1). Moreover, since it is difficult to take into account, interparticle interference effects were neglected in the analysis using the model for polydisperse rods. Throughout the data analysis corrections were made for instrumental smearing.39,40 For each instrumental setting, the ideal model scattering curves were smeared by the appropriate resolution function when the model scattering intensity was compared with the measured one by means of least-squares methods. The parameters in the model were optimized by means of conventional leastsquares analysis.41 Model Independent Approach: Indirect Fourier Transformation. Data analysis by indirect Fourier transformation (IFT)42 was performed on the 2 wt % samples at q > 0.02 Å-1 where the effects of intermicellar interactions are negligible. This yields the scattering at zero angle (dσm(0)/dΩ) and the radius of gyration without any presumptions regarding particle size and shape. The radius of gyration is given by
∫0D ) D 2∫0
max
2
Rg
Results and Discussion
p(r)r2 dr
max
Figure 1. (a) Scattering intensity as a function of scattering vector for a sample with X(C16TAC) ) 0.5 at two different solvent compositions, X(D2O) ) 0.05 and X(D2O) ) 0.67. Total surfactant concentration was 2 w% in 100 mM NaCl. The results from fits with models for oblate ellipsoids are also shown. (b) Scattering intensity as a function of scattering vector for samples with X(C16TAC) ) 0 and X(C16TAC) ) 1 in pure D2O. Total surfactant concentration was 2 w% and the concentration of NaCl 100 mM. The results from a fit with a model for oblate ellipsoids (X(C16TAC) ) 1) and with a model for polydispers rods (X(C16TAC) ) 0) are also shown.
(9) p(r) dr
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 estimated to 65 Å from the results of the model dependent fittings. In some cases, 60 Å was used for Dmax, since it gave better results, i.e., a stable and smooth solution for the p(r) function which after Fourier transformation is fitted to the experimental scattering data. (37) Pedersen, J. S.; Schurtenberger, P. J. Appl. Crystallogr. 1996, 29, 646. (38) Neugebauer, T. Ann. Phys. Leipzig 1943, 42, 509. (39) Pedersen, J. S. Journal de Physique IV (Paris) Colloqium C8 1993, 3, 491. (40) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321. (41) Bevington, B. R. Data Reduction and Error Analysis for Physical Sciences; McGraw-Hill: New York, 1969. (42) Glatter, O. In Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Ed.; Academic Press: London, 1982.
Small-Angle Neutron Scattering. The SANS measurements were performed at two different total surfactant concentrations, 0.5 wt % and 2 wt %. The molar fraction of C16TAC to HFDePC was varied between 0 and 1. The 2 wt % samples were prepared in three different solvents with the following weight fractions of D2O: X(D2O) ) 0.05, the calculated match point for the hydrocarbon surfactant, X(D2O) ) 0.67, the calculated match point for the fluorinated surfactant, and X(D2O) ) 1, where both surfactants are visible. The 0.5 wt % samples were prepared in pure D2O. Additional measurements of pure C16TAC and HFDePC at different contrasts were performed. All solutions contained 100 mM NaCl. The scattering data for two of the samples are presented in Figure 1a, showing that the curves measured for a sample with X(C16TAC) ) 0.5 and a total surfactant concentration of 2 wt % at different contrasts are represented by the same shapes. It suggests that the observed aggregates are similar in size and shape. At the contrast match point of C16TAC (X(D2O) ) 0.05) one should observe the scattering only from HFDePC and at contrast matching of HFDePC (X(D2O) ) 0.67) one should observe
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Kadi et al.
Table 1. Results from Model Dependent Fittingsa
Table 2. Results Obtained from IFT Analysisa
X(D2O)
X(C16TAC)
w%
a/Å
b/Å
X(D2O)
X(C16TAC)
Rg/Å
(dσm(0)/dΩ)/cm-1
1 1 1 1 1 0.67 0.67 0.67 0.67 0.05 0.05 0.05 0.05 1 1 1 1 1
0 0.25 0.5 0.75 1 0.25 0.5 0.75 1 0 0.25 0.5 0.75 0 0.25 0.5 0.75 1
2 2 2 2 2 2 2 2 2 2 2 2 2 0.5 0.5 0.5 0.5 0.5
R ) 15 31 31 31 32 30 31 32 32 21 35 34 32 R ) 17 33 31 32 32
〈L〉N ) 56 16 18 19 19 13 15 17 19 55 13 13 17 〈L〉N ) 46 14 17 18 20
1 1 1 0.67 0.67 0.67 0.05 0.05 0.05 0.35
0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75 0.5
20.065 ( 0.12 19.36 ( 0.21 20.0 ( 0.2 18.55 ( 0.52 18.1 ( 0.22 18.7 ( 0.3 21.22 ( 0.20 20.65 ( 0.2 20.1 ( 0.7 21.6 ( 0.3
1.067 ( 0.007 1.65 ( 0.02 2.86 ( 0.04 0.174 ( 0.004 0.56 ( 0.01 1.11 ( 0.02 0.83 ( 0.01 0.48 ( 0.01 0.137 ( 0.005 0.143 ( 0.005
a The values of D max, the maximum dimension of the particles, were estimated from the model dependent fittings.
a The data were fitted with a model for oblate ellipsoids with half-axes a > b or prolate ellipsoids with half-axis a < b or with a model for polydisperse rigid rods with number average length 〈L〉N and a circular cross-section of radius R.
the scattering only from C16TAC. The fact that the shape of the curves are similar for X(D2O) ) 0.05 and X(D2O) ) 0.67 can be explained by: (i) demixing into C16TAC-rich and HFDePC-rich micelles having the same size and shape or (ii) formation of mixed micelles. A demixing into pure C16TAC and pure HFDePC micelles can be rejected since these micelles give different scattering curves (Figure 1b). This is supported by the results from the model fittings shown in Table 1. All of the data were best fitted with a model for oblate ellipsoids of revolution (a > b), except for pure HFDePC in X(D2O) ) 0.05 that was best fitted with a model for prolate ellipsoids of revolution (a < b) and pure HFDePC, 0.5 and 2 wt %, in D2O that were best fitted with a model for polydisperse rods. The lengths given in Table 1 are number averages (〈L〉N) for polydisperse rods. For the assumed Schultz distribution with a relative standard deviation of σ/〈L〉N ) 1 the weight average length, 〈L〉W, is equal to 2〈L〉N. The weight average lengths in 0.5 and 2 wt % HFDePC are hence 92 and 112Å, respectively. On the other hand, for 2 wt % HFDePC in X(D2O) ) 0.05, the form factor of a prolate ellipsoid, with half-axis a ) 21 Å and b ) 55 Å, gave the best fit. Note that the average lengths obtained for the polydisperse rods are apparent lengths, since interactions between the micelles were not accounted for. Because of this, the real lengths of the rods are expected to be longer than the values obtained from the fittings. The scattering curve for 2 wt % HFDePC in D2O (Figure 1b) clearly shows that these micelles are elongated. Hence, it seems as if the HFDePC-micelles are larger in D2O than in X(D2O) ) 0.05. This observation will be further discussed below. The pure C16TAC micelles were best fitted with a model for oblate ellipsoids, giving essentially the same results in X(D2O) ) 1 and X(D2O) ) 0.67. It is worth noticing here that in an earlier study of pure SDS and DTAB micelles the SANS-data were, somewhat surprisingly, best fitted with a model for oblate ellipsoids.43 The radius of gyration and the scattering at zero angle obtained from the IFT analysis are presented in Table 2. The values of the uncertainties of the scattering at q ) 0 in Table 2 are only statistical errors. Of course, some systematic errors due to the normalization procedures are larger (in the order of 5%). (43) Bergstro¨m, M.; Pedersen, J. S. Phys. Chem. Chem. Phys. 1999, 1, 4437.
Figure 2. Scattering intensity as a function of scattering vector for a sample with X(C16TAC) ) 0.5 at three different solvent compositions, X(D2O) ) 0.05, X(D2O) ) 0.35, X(D2O) ) 0.67, and X(D2O) ) 1. Total surfactant concentration was 2 w% and the concentration of NaCl 100 mM. The solid lines represent the results from the IFT analysis.
As an example, in Figure 2, the experimental data for a sample with X(C16TAC) ) 0.5 in three different solvents, X(D2O) ) 0.05, 0.67, and 1 (total surfactant concentration 2 wt %), is shown together with the fitting results from the IFT analysis. At zero angle, the form factor is equal to unity irrespective of particle shape, and the scattering is described by
dσm(0) ) (Fj - Fs)2Vm2NmS(0) dΩ
(10)
where S(0) is the structure factor at q ) 0. Within the interval of q (q > 0.02 Å-1) analyzed by IFT, the effect of S(q) is negligible taking into account the low concentration of micelles and the screened electrical interactions. Hence, S(0) is close to 1 in eq 10. Fj is the average scattering length density of the micelles and Fs is the scattering length density of the solvent. The square root of the zero scattering intensity is plotted versus solvent composition for three samples with different molar ratios of C16TAC to HFDePC in Figure 3. For Fs > Fj, the values are plotted with negative signs. For completely mixed micelles, straight lines, with the zero crossing points moving along the x axis as the composition of the micelles is changed, are expected. If two different populations of noninteracting micelles were present in the solution, the scattered intensity at zero angle would be a sum of two terms (eq 10), and it would not equal zero at any solvent composition provided that the scattering densities of the two micelles are different.26
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Figure 3. Square root of the scattering at zero angle plotted vs solvent composition for three samples with X(C16TAC) ) 0.25, X(C16TAC) ) 0.5, and X(C16TAC) ) 0.75. Total surfactant concentration was 2 w% and the NaCl concentration 100 mM. Table 3. Experimental and Calculated Values of Gj, the Average Neutron Scattering Length Densities of the Micelles, the Squared Radius of Gyration at Infinite Contrast, and the Parameter r X(C16TAC)
Fj(exp)/ 1010cm-2
Fj(calc)/ 1010cm-2
Rg,02/ Å2
R/ 10-6
0.25 0.5 0.75
2.82 ( 0.07 1.92 ( 0.07 0.47 ( 0.14
2.98 ( 0.07 1.87 ( 0.07 0.90 ( 0.07
425 ( 5 384 ( 5 387 ( 6
84 ( 14 100 ( 13 21 ( 17
The intensity according to eq 10 would then have a finite minimum value close to Fj ) Fs (if the volume of both types of micelles were the same the minimum would occur where Fj, average over both types of micelles, equals Fs). In a plot as in Figure 3, there would then be a jump, at Fs ) Fj, from a positive value to the same value with negative sign. The few data points in Figure 3 do not rule out this possibility. Furthermore, an inhomogeneous contrast of the mixed micelles would produce similar deviations from straight lines. The scattering length densities of the micelles were determined from the zero crossing points, since for dσm(0)/dΩ ) 0, the value of Fs is equal to the average value of the scattering length densities of the micelles. The values of Fj obtained from the plots are presented in Table 3. These experimentally determined values of Fj were found to be in agreement with the calculated values for mixed micelles with a composition equal to the total composition of the sample, at least for X(C16TAC) ) 0.25 and 0.5 (Table 3). The experimental value for X(C16TAC) ) 0.75 is very uncertain. The scattering from this sample in X(D2O) ) 0.05 was very low and only two points were used in the fit. A sample with X(C16TAC) ) 0.5 (2 wt %) was also measured at a solvent composition of X(D2O) ) 0.35, corresponding to the calculated match point for completely mixed micelles. The result is shown in Figure 2 together with the scattering observed for samples with the same surfactant composition at solvent compositions X(D2O) ) 0.05, X(D2O) ) 0.67 and X(D2O) ) 1. Some scattering could in fact be observed also in X(D2O) ) 0.35. Scattering at this solvent composition can be produced either by different populations of micelles coexisting in the solution or by mixed micelles with an inhomogeneous distribution of surfactants within the micelles. If we consider the first case, for completely demixed micelles, assuming that the volume of the micelles are equal, the absolute intensity
would be approximately two times lower than for X(D2O) ) 0.05 and X(D2O) ) 0.67. The observed absolute intensity is much lower than this (four to five times). Assume instead that the demixing results in two populations of micelles with the fraction of fluorinated surfactant equal to 0.89 and 0.17, respectively. We then find that 46% of the micelles would be of the former type, and the rest of the latter. The scattering at the matching point would then be a fraction 0.33 of the scattering with either X(D2O) ) 0.05 or 0.67, as compared to the ratio of the measured values of 0.25-0.30 (Table 2). Evidently, the experimental results are not in accord with a demixing as clear as that suggested by Asakawa et al.28 One can argue, however, that the demixing in systems of relatively small micelles is less strict and that there is instead a broad distribution of micelle compositions.44 This would occur if a pair of demixed micelles are only marginally more stable than the mixed ones. If the distribution could be described in a first approximation with three populations, a mixed micelle population in addition to the two demixed populations, then the mixed one should comprise about 25% of the total to explain the observed scattering at the match point. As discussed above, the results could also be explained if there were only one population of micelles present and the scattering at X(D2O) ) 0.35 was a result of mixed micelles with some kind of inhomogeneous internal structure. Strictly speaking, there are three contributions to scattering at X(D2O) ) 0.35: (i) the scattering from internal inhomogenities within the micelles, (ii) the scattering from some “residual contrast” between the actual average neutron scattering length density and the solvent with composition X(D2O) ) 0.35, and (iii) scattering due to a composition variation within the population of micelles. A residual contrast could result from a composition of the micelles that differed from that assumed, due to substantial concentrations of free surfactants in the aqueous pseudo phase. In our case, however, a surfactant concentration of 2 wt % corresponds to 33.1 mM HFDePC or 62.7 mM CTAC, and the cmc values at 100 mM NaCl are as low as 0.2 and 0.7 mM, respectively. The difference between the analytical composition and the composition of the micelles would then be at most of the order of 1% and can be safely ignored. The radius of gyration squared, obtained from the IFT analysis, is shown in Figure 4 as a function of the reciprocal of the contrast for the same three samples as in Figure 3. The relation between the radius of gyration and the contrast is described by the Stuhrmann equation45
Rg2 ) Rg,02 +
β R ∆F ∆F2
(11)
where Rg,02 is the square of the radius of gyration at infinite contrast and is commonly referred to as the radius of gyration of shape. The coefficients R and β are defined by
∫ Ff(r)r2 dr
(12)
∫ Ff(r1)Ff(r2)(r1r2) dr1 dr2
(13)
R ) V-1 β ) V -2
Ff(r) is the fluctuation of the scattering length density within the particle: F(r) ) Fj + Ff(r) where F(r) is the scattering length density of the particle at the point r. To account for the internal structure of the mixed micelles, F(r) was approximated by a core surrounded by a spherical (44) Barzykin, V. A.; Almgren, M. Langmuir 1996, 12, 4672. (45) Stuhrmann, H. B.; Fuess, H. Acta Crystallogr. 1976, A32, 67.
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Figure 4. Radius of gyration squared plotted vs the reciprocal of the contrast for three samples with X(C16TAC) ) 0.25, X(C16TAC) ) 0.5, and X(C16TAC) ) 0.75. Total surfactant concentration was 2 w% and the NaCl concentration 100 mM. The solid lines are the least-squares fits of eq 11 to the experimental data.
shell. The parameter R is positive if the shell has a higher (neutron scattering) density than the core and negative if the core has a higher density than the shell. Parameter β describes the displacement of the center of mass as a function of contrast and is zero for the shell-model we are assuming for mixed micelles. The parameters Rg,02 and R obtained by fitting Rg2 versus contrast by eq 11 are given in Table 3. Parameter R was found to be positive and equal to 100 × 10-6 for the sample with X(C16TAC) ) 0.5, suggesting that the fluorocarbon surfactant is enriched in the outer shell of the micelles. The theoretical value of R was calculated, assuming completely mixed micelles, for the mixture with X(C16TAC) ) 0.5. The minimum and maximum radii of the core were calculated as the length of a nonextended and extended C16 chain, respectively. The total radius of the micelle was calculated from the molecular volumes of the heads and tails. This gave for the minimal possible size of the core a value of 40 × 10-6 for the parameter R and for the maximal possible size of the core a value of 60 × 10-6 for R. For these limiting cases, the theoretical value of R is lower than the experimental value, supporting our suggestion about enrichment of the fluorinated surfactant in the outer shell of the micelles (Table 3). The studied micelles are slightly anisotropic (Table 1), which should be taken into account in the calculation of the theoretical value of R. If one takes the minor axis as 15 Å and the other axis as 30 Å, the value of R will be 60 × 10-6; that is, it is still within the range of values possible for spherical geometry. In Figure 5, p(r), the pair distribution function, is plotted versus r for the samples with X(C16TAC) ) 0.5 in the three different solvents. The lowest maximum of p(r) is observed for X(D2O) ) 0.05. The higher maximum values for X(D2O) ) 0.67 and 1 point to a higher scattering contrast in the core of the particles in these solvents (X(D2O) ) 0.67 and 1) than in X(D2O) ) 0.05. This is in line with the assumption of an enrichment of the fluorocarbon surfactant in the outer shell of the micelles and an enrichment of C16TAC in the micellar core. The results could also be understood if there were a demixing, and the fluorocarbon rich micelles were somewhat larger than the hydrocarbon rich micelles. It was earlier proposed that an intramicellar phase separation occurs in this mixture, based on results from
Kadi et al.
Figure 5. Pair distribution function, p(r), plotted vs r for a sample with X(C16TAC) ) 0.5 in three different solvents, X(D2O) ) 0.05, X(D2O) ) 0.67, and X(D2O) ) 1. Total surfactant concentration was 2 w% and the NaCl concentration was 100 mM.
NMR measurements.18 To explain the results obtained by 19F-line width measurements, a model was required that explained the fact that the fluorine atoms closest to the headgroup experienced a larger change in molecular environment upon exchange than the fluorine atoms at the end of the tail. The only plausible explanation was a micelle with hydrocarbon and fluorocarbon rich domains. That such micelles may exist had already been suggested by others.26,46 In the neutron scattering study of the mixture of ammonium decanoate and ammonium perfluoro-octanoate also a single mixed micelle was observed.26 It was found that the size and shape of the micelles were essentially independent of sample composition within the range of molar ratios of APFO to AmDec of 2:1 and 1:2. A model for the cylindrical micelles with the rigid perfluorooctanoate chains packed side by side in a helical conformation, and the flexible decanoate chains accommodated in rows between them was suggested. Mixed micelles with intramicellar segregation were suggested to form in mixtures of ammonium perfluorononanoate and ammonium dodecyl sulfate.46 Two possible models have been presented to explain the results. The first is a mixed micelle with angular separation of the surfactants allowing for pure hydrocarbon and fluorocarbon sites. The other possibility was a mixed layered micelle with radial separation of the surfactants. The earlier NMR results supported the first model, whereas the SANS data of the same system in the present study has been discussed in terms of a layered micelle. These models are not necessarily conflicting, however. Different averaged contrasts of core and shell regions may very well result from an arrangement of the surfactants in different angular domains, e.g., as in the model of Fromherz.47 A strict core-shell separation of the fluorinated and the hydrogenated surfactants is not implied. Moreover, such a separation would have been evident in the scattering data collected at the solvent match point for C16TAC. Also these data were best fitted with the model for oblate ellipsoids, indicating that the two surfactants mix to a significant degree in the micelles. Light Scattering. To cover a wider q range, static light scattering measurements were performed on three of the (46) Kamogawa, K.; Tajima, K. J. Phys. Chem. 1993, 97, 9506. (47) Fromherz, P. Chem. Phys. Lett. 1981, 77, 460.
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differences between the surfactant hydrocarbon-water interactions in H2O and D2O because of stronger hydrogen bonding between D2O molecules. The effects on the micelles increased with increasing chain length of the surfactant. The micelles were found to be larger in D2O than in H2O. The aggregation number for 0.1 M C16TAB in water increased from 153 in X(D2O) ) 0.5 to 163 in X(D2O) ) 1. SDS micelles have also been found to be significantly larger in D2O than in H2O.49 The first observation of a solvent isotope effect on micelles was made by Mukerjee et al., who found that C10SO4Na and C12SO4Na have lower cmc’s in D2O than in H2O.50 Cryo-TEM. The micrographs in Figure 6, showing rather long threadlike micelles, were taken on (a) pure HFDePC in 100 mM NaCl and (b) a mixture of HFDePC and C16TAC at a molar ratio of 0.5. The total surfactant concentration was 2 wt %. These long threadlike micelles were not observed by neutron or light scattering. It is possible that the presence of the long micelles in the micrographs is a result of the preparation of the specimen for the cryo-TEM investigation. Surface adsorbed micelles formed on the interfaces of the thin film have been observed earlier.51 A combined cryo-TEM and scattering study showed that the longer micelles observed in the micrographs were not present in the bulk. Besides the cooling to low-temperature various adsorption effects at the very large interfacial areas of the sample toward air or the supporting polymer film may be factors important for the formation of the long micelles. Figure 6. Cryo-TEM micrographs taken on (a) 2 w% HFDePC in D2O and (b) a 2 w% mixture of HFDePC and C16TAC with X(C16TAC) ) 0.5 in D2O. Both samples contained 100 mM NaCl. Bar equals 100 nm.
2 wt % samples: pure HFDePC in X(D2O) ) 0.05 and X(D2O) ) 1 and HFDePC-C16TAC with X(C16TAC) ) 0.5 in X(D2O) ) 0.05. From partial Zimm plots we determined apparent molecular weights of the micelles to 110 kg/mol for pure HFDePC in X(D2O) ) 0.05, 287 kg/mol for HFDePC in X(D2O) ) 1 and 36 kg/mol in the mixture of HFDePC/ C16TAC (with X(C16TAC) ) 0.5) in X(D2O) ) 0.05. The aggregation numbers, calculated from the apparent molecular weights, are 190 for pure HFDePC in X(D2O) ) 0.05, 500 for HFDePC in X(D2O) ) 1, and 80 for the mixture of HFDePC/C16TAC in X(D2O) ) 0.05. Since the light scattering measurements were performed only at one surfactant concentration (extrapolation to zero concentration to eliminate effects of inter-micellar interactions was not possible), these values are somewhat smaller than the real aggregation numbers. They do indicate, however, that the pure HFDePC-micelles are larger in D2O than in X(D2O) ) 0.05, in accordance with the neutron scattering results. A solvent isotope effect has earlier been observed for C16TAB.48 In a neutron scattering and surface tensiometry study of RnTAB (n ) 12, 14, and 16), it was concluded that the solvent isotope effect is caused by small (48) Berr, S. S. J. Phys. Chem. 1987, 91, 4760.
Conclusions The main question of this investigation remains open: mixed micelles or demixing into coexisting fluorocarbon rich and hydrocarbon rich micelles. If there is a demixing, as other results strongly suggest, the distributions must be very broad and encompass a substantial fraction of mixed micelles. A much more comprehensive study using several contrasts, and investigating match points at several micelle compositions, is required to characterize the system in detail. The results in the investigated range of concentrations and compositions may be explained by only one kind of mixed micelles, but then with an inhomogeneous distribution of hydrogenated and fluorinated surfactants within the micelles, and with the fluorinated surfactants preferably located in the outer parts of the micelles and the hydrocarbon surfactants enriched in the micellar core. All of the micelles in the present study, except for pure HFDePC micelles, were best fitted with models for oblate ellipsoids. The HFDePC micelles were more elongated, and clearly larger in D2O than in H2O. Acknowledgment. Financial support from the Swedish Research Council is gratefully acknowledged. LA036410T (49) Chang, N. J.; Kaler, E. W. J. Phys. Chem. 1985, 89, 2996. (50) Mukerjee, P.; Kapauan, P.; Meyer, H. G. J. Phys. Chem. 1966, 70, 783. (51) Almgren, M.; Gimel, J. C.; Wang, K.; Karlsson, G.; Edwards, K.; Brown, W.; Mortensen, K. J. Colloid Interface Sci. 1998, 202, 222.
