Langmuir 1993,9,1193-1200
1193
Fluorinated, Protonated, and Mixed Surfactant Solutions: A Small-Angle Neutron Scattering Study E. Caponetti,' D. Chillura Martino, M. A. Floriano, and R. Triolo Dipartimento di Chimica Fisica, Universith di Palermo, V. Archirafi 26, 90123 Palermo, Italy Received May 4,1992. In Final Form: February 9,1993 Contrast matching experimentshave been performed on aqueoussolutionsof sodiumperfluorooctanoate, sodium dodecanoate, and a mixture of the two surfactants. Moreover, sodium dodecanoate has been studied as a function of the concentration. Previous findings in several mixed fluorocarbon-hydrocarbon syetems indicated the coexistence of two different kinds of micelles, one rich in hydrocarbon and the other in fluorocarbon surfactant; on the contrary, because of the existence of a unique and well-defined contrast match point, the present data indicate the formation of mixed micelles having the same composition and a very narrow size distribution, at least at the composition examined. This has been confiied by fitting the experimental patterns with a model baaed on the above-mentioned hypothesie: the structure function has been calculated by means of the rescaled mean spherical approximation usin a screened Coulombic potential plus hard sphere repulsion; the particle form factor has been calculatedusing several different models. Among the modelstested, a core plus shellprolateellipsoid model gave the best fib. The aggregation number found for the mixed micelles was intermediate between those of the two single surfactant micelles, while the degree of counterion dissociation was lower than each of them.
Introduction With an increase in the concentration of surfactant molecules, made with hydrophilic and hydrophobic portions, in aqueous solution, a sudden change in most of the solution properties can be observed at a critical micellar concentration (cmc). This change is related to the formation of aggregates in which the contact between the hydrophobic portion of the molecules and water is minimized, while, at the same time, the hydrophilic interaction is maximized. These aggregates are highly dynamic entities, though stable enough to be detected using different techniques. Micellar solutions formed from amixture of two or more surfactants are of considerable interest from both practical and fundamental viewpoints. Mixtures of ionic and nonionic Surfactants have been studied by Bucci et al.lt2 Other authors considered mixtures of surfactants differing in the length of the hydrocarbon chain- or having different head groups6or isomeric ~ o n t e n t .So ~ far, most studies on mixed surfactants have focused on the cmc of the system in order to discuss the miscibility of components.2A8.9 Mixed systems of hydrocarbon and fluorocarbon surfactants are of considerable interest because of the difference in their thermodynamic parameters of micellization. The main focus is on whether hydrocarbon and fluorocarbon Surfactants combine to form mixed or homogeneous micelles; the result could depend on the chain length, the head group, and the counterion. So far the behavior of these systams has been explained in terms of _
_
_
_
~
~
~
nonideal mixing, which determines the coexistence of two kinds of mixed micelles, one rich in hydrocarbon, the other in fluorocarbon s u r f a ~ t a n t s . ~ JThese ~ J ~ conclusion have been reached by studying these systems with various methods,*15 but the structural studies, reported in the literature, are surprisingly scarce. In this paper we describe a study on a mixed surfactant system formed by sodium perfluorooctanoate (C7F15' COONa) andsodiumdodecanoate(CllH&OONa). c7F15' COONa was chosen since it has been studied by different authors.16J7 The protonated surfactant was chosen because it is known that the cmc values of fluorocarbon surfactants are close to those of hydrocarbon surfactants whose carbon atoms chain is 1.5 times longer;lg this has been attributed to the difference in the free energy of transferring the 4F2- and 4 H 2 - from the aqueous environmentto the micellar state. It is interesting to note that the volume of the two molecules is about the same, 364 A3 for the hydrogenatedsurfactant and 384 A3 for the perfluorinated one. We have used small-angle neutron scattering (SANS) coupled with the external contrast variation technique. It is well-known that in "two-phase" systems, such as a micellar solution, both inter- and intraparticle scattering contribute to the measured SANS intensity. As a consequence, important information about particles size and shape, the distribution of particles sizes, and the nature and the strength of interparticle interactions can be inferred. Moreover, because of the substantial difference in coherent scattering length densities between hydro-
~
(1) Rubmgh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.;Plenum: New Yolk, 1979; p. 337. ( 2 ) Bucci, 5.;Fagotti, C.; De Giorgio, V.; Piazza, R. Langmuir 1991,7, 824. (3) Malliaris, A.; Binana-Limbele, W.; Zana, R. J. Colloid Interface Sci. 1986, 110, 114. (4)BorMly, S.; Cser, L.; Vase, S.; Ostanevich, Yu. M. J. Appl. Cryatallogr. 1991,24,747. (5) Velbquez, M. M.; Costa, S. M. B. J. Chem. SOC.,Faraday Trans. 19%0,86,4043. (6) Rathman,J. F.; Scamehom, J. F. J. Phys. Chem. 1984,88,5807. (7) Zana, R.; Muto, Y.; Esumi, K.; Meguro, K. J . Colloid Interface Sci. 1988.123.602. ( 8 ) Clht, J. J. Chem. SOC.1975, 71, 1327. (9) Asakawa,T.; Mouri, M.; Miyagishi, S.;Niehida, M. Langmuir 1989, 5,343.
(LO) Tamori, K.; Eeumi, K.; Meguro, K. J. Colloid Interface Sci. 1991, 142. 236. (11) Muto, Y.; Esumi, K.; Meguro, K.; h a , R. J . Colloid Interface Sci. 1987, 120, 162. (12) Kalyanasundaram, K. Langmuir 1988,4,942. (13) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976,80, 1388. (14) Fisicaro,E.;Pellizzetti, E.; Bongiovanni,R.; Borgarello, E. Colloid Surf. 1990,48, 259. (15) Burkitt, S. J.; Ottewill, R. H.; Hayter, J. B.; Ingram, B. T. Colloid Polym. Sei. 1987, 266, 628. (16) Burkitt, S . J.; Ottewill, R. H.: Havter, J. B.: Inmam, B. T. Colloid Polym. Sci. 1987, 285, 619. (17) Berr, S. S.; Jones, R. R. M. J. Phys. Chem. 1989,93, 2555. (18) Bezzobotnov, V. Yu.; Borbbly, S.; Cser, L.; Faragb, B.; Gladkih, I. A.; Ostanevich, Yu. M.; Vass, Sz. J. Phys. Chem. 1988,92,5738. (19) Shinoda, K.; Hato, M.; Hayashi, T. J. Phya. Chem. 1972,76,909. ~
0743-746319312409-1193$04.00/0 0 1993 American Chemical Society
1194 Langmuir, Vol. 9,No. 5, 1993 carbon and fluorocarbon chains, this technique can be very useful in studying one species in the presence of the other. In a contrast study the scattering density of the DzO-HzO mixture can be varied from that of pure DzO, 6.40 X cm-2,to that of pure HzO, -0.56 X 10-locm-2. The difference in scattering length densities of the two surfactants implies that, if the two species micellized separately, it would be possible, by the use of appropriate D20-Hz0 ratio, to “see” each one independently, i.e. the one while the other is at zero contrast (a point in which scattering length density of the DzO-HzO mixture is equal to that of the surfactant, that is the match point); hence nonzero scattering intensities would be expected at the two match points. On the other hand, if mixed micelles were formed, while scattering would occur at the contrast match point of each species, there would be another contrast at which complete matching would be achieved. Any study on a mixed surfactant system requires information on the single surfactant behavior, such as the trend of aggregate dimension, the shape, and the internal structure of the micelles as a function of the monomeric concentration. Therefore, to get information on the internal structure of the micelles, we have performed scattering measurements on both surfactants and on their mixture at different DzO-HZOvolume ratios. The CTF15COONa SANSconcentration study has been done by Beer at al.;17hence,we have performed scatteringmeasurements as functions of concentration only for CllH23COONa in DzO.
Experimental Section Materials. Sodium perfluorooctanoate was prepared by neutralizing perfluorooctanoic acid (Fluka A.G. product) with sodium hydroxide (Merck Suprapur). Sodium dodecanoate was purchasedfrom Sigma. Before use, the products were dried under vacuum for 72 h. D20 was an Aldrich product (99.8 atom % D) while HzO was conductivity-grade water. Solutions used in the concentration study were prepared by weight in approximately 2-mL quantities; for contrast measurements stock solutions of each surfactant in D2O and HzO were mixed in such a way as to obtain the required DzO-HzO and hydrocarbon-fluorocarbon surfactant molar ratios. The samples were sealed with a Teflon septum cap and stored at room temperature until use. Composition. The mixture of the two surfactants has been studied in five DzO-HzO solutions with a 99,75,50,24, and 0% (v/v) D20 content; C7F15COONa and CllH23COONa concentrations were 0.33 and 0.16 M, respectively. Their concentrations have been chosen so that they gave comparable scattered intensities when studied separately. C7F15COONa contrast data have been obtained from five 0.33 M D20-H20 solutions with a 99,75,48,24and 0% (v/v) DzO content. CllH23COONacontrast data have been obtained from five 0.16 M D20-H20 solutions with a 99,75,50,26,and 0% (v/v) DzO content; CllH23COONa concentration study has been done, using DzO as solvent, as the following molar concentrations: 0.16, 0.25, 0.32, 0.46, 0.53. SANS Measurements. Experiments were performed on the 30-m (source to detector) SANS instrument of the National Center for Small Angle Scattering Research (NASCASR) at the High Flux Isotope Reactor (HFIR) in Oak Ridge, TN. A position-sensitive detector subtending an area of 64 cm x 64 cm was used to record the scattered neutrons. The sampleto-detector distance was 150 cm. The neutron wavelength was X = 4.75 A, with a spread AX/X = 6%. With this setting the modulus of the scattering vector Q, defined by the expression Q = 4r(sin @)/A (28 being the scattering angle) ranged between 0.048 and 0.35 A - I . The solutions were placed in quartz spectrophotometer cells of 1 and 2 mm path lengths. The temperature of the specially built cell holder was maintained at 25.0 i 0.2 OC by circulating fluid from an external bath.
Caponetti et al. Table I. Volumes, V,and Scattering Length Densities, p, of G r o u ~ s hydration 10%bi,o cm V,*A3 W O p , om-2 numbep groups -CH3 -0.457 54.3 -0.842 26.9 -0.309 -CHz -0.0832 -CF3 2.345 73.7 3.18 -CF2 1.785 44.9 3.97 37.02 4.93 11 -coo1.825 Na+ 0.363 3.81 9.53 13 30.2 6.34 1.915 Dz0 30.05 -0.56 H20 -0.168 a b = isotopically averaged coherent scattering length. Reference 21. References 22-24. Reference 25. Scattering from sampleswas corrected for detector background and sensitivity, empty cell scattering, and sample transmission. The corrected intensities were converted to radial-average intensities vs Q and absolute differential cross sections, dZ(Q)/ dQ, were computed from calibration based on the known scattering from pure HzO. The software used in this data reduction was developed by staff members of NCSASR. The resulting dZ(Q)/dQversus Q are shown in Figures 1,2,3, and 9. Conductance Measurements. Electrical resistance measurements were performed at 25 OC with a calibrated ac bridge at a frequency of 2 kHz and a flow microcell with unplatinized electrodes in a constant temperature bath controlled within 0.01 OC.
Analysis of the Scattering Data Theory. In the absence of multiple scattering, the measured intensity, for an arbitrary mixture of particles, is proportional to the coherent elastic differential scattering cross section per unit volumzodefined as
(F,ixj
(1) dI;(Q)/dQ= bibjexp[iQ(ri - rj)l) which is a s u m of amplitude weighted phase shifts over all atoms in the sample; i and j may refer to atoms in the same particle or in different particles and bi and bj are the isotopically averaged scattering lengths of nuclei i and j whose positions relative to an arbitrary origin in the same are ri and rj. In the simplest assumption that the sample contains a monodispersepopulation of spherical scatterers, eq 1can be rearranged in a simple formz1
dZ(Q)/dQ= NpP(Q)SCQ) (2) where Npis the particle number density, S(Q)is the static structure factor, and P(Q) is the intraparticle factor. The modulus of Q has been used because of the symmetry of the system. S(Q)specifies the correlation between the centers of different particles, and it is the Fourier transform of the radial distribution function g(r) for the mass centers of the particles. P(Q)containsinformationconcerningthe single particle, such as dimension, size, and internal structure. Surfactants in solution can form micelles of different shapes depending on the their concentration, on the length and the nature of the hydrophobic chain, and on the nature and the structure of the polar head. Usually, at concentrations close to the cmc, the shape of these aggregates is spherical, while, by increasingthe concentration, changes of shape can occur, leading to ellipsoidal, disklike, or cylindrical shapes. In the case of ionic surfactants, part of the counterionsare “bound”to the surface of the micelle, (20) Guinier, A.; Fournet, G. Small-Angle Scattering of X-ray; John Wiley: New York, 1955. (21)Caponetti, E.; Triolo, R. Adu. ColloidZnterface Sci. 1990,35,235.
Langmuir, Vol. 9, No.5, 1993 1195
Fluorinated, Protonated, and Mixed Surfactant Solutions
Table 11. Results from Two (Sphere) or Three Parameters Fits to SANS Data of Sodium Perfluorooctanoate in HzO Using the Models Described in the Text. [Cd1&0ONal = 0.33 M, Bk = 0.93 cm-1a ~
model sphere prolate ellipsoid oblate ellipsoid polydispersesphere
Z,ue
v
B
11.9 .+ 0.4* 12.3 0.3* 12.4*0.3* 12.2 0.31
38.1 i 0.3* 39.0 .+ 0.2. 39.1 i 0.2* 38.9 0.2*
0.31 0.31 0.32 0.31
* *
*
€
1.2
* 0.1*
0.8* 0.1*
~~
al,A 14.1 14.6
zs
a2,A 19.8 22.3 (3
70) X 1@*
1@“p
R,A
micelles/A3
rl
x
20.7 20.9 20.9 20.9
7.97 7.79 7.78 7.81
0.18 0.18 0.18 0.18
5.8 3.9 4.0 4.0
Bk = incoherent scattering plus machine background; 2 = micelle apparent charge; v = aggregation number; 0 = degree of counterion dissociation; e axial ratio; a1 = core minor semiaxis; 02 = core major semiaxis; Zs = breadth parameter of the Schulz distribution function; R = radius of the sphere, whose volume is equivalent to the ellipsoid or to the weight average particle size; Np= particle number density; rl = volume fraction of the dispersed phase; x = square root [(sum of the squares of weighted residuals)/(number of point minus number of parameter plus one)]. * parameter adjusted in the fit procedure. 0.6,
E
v
2.0
-
1.5
-
. sa
1.0
,
,
-
,
,
0
v
9
24 0.5
0.0 0
0.1
0.2
0.3
0.4
Q (k’) Figure 1. Three-parameter fit of experimental SANS external contrast data for sodium perfluorooctanoate with results shown in Table In: symbols, experimental values; lines, calculated intensities. The inset shows an enlarged view of the runs at low intensity. The incoherent scattering and machine background have been subtracted in the fib, but not in the figure. Each run is identified by the corresponding % (v/v) DzO content.
forming what is called the “Stern layer”, whereas the remaining counterions are localized at greater distances from the surface of the micelle, in what is called the “GouyChapmann electric double layer”. C,F&OONa External Contrast Study. We started to analyze the five CTF15COONa 0.33 M solutions, at different D20-HzO composition, using the monodisperse in core plus shell spherical model used by Beer et del7 their study of sodium perfluorooctanoate micelles as a function of concentration. In this model, which is the most common one for micellar structures, a core of hydrophobicmaterial, where the fluorocarbon chains are confined, is surrounded by a shell containing the head groups, a fraction of counterions, and the water hydration molecules. For this model the single particle scattering function is given by where VI, R1, and p1 are the volume, the radius, and the scatteringlength density of the core, respectively, subscript 2 indicates the same quantities for the shell, and subscript s denotes the solvent; the scattering amplitude, Fo,is given by the relation ~ , ( x )= 3(sin x
- x cos x ) / x 3
The scattering length densities for the various groups were computed from atomic scattering length22and from volume^^^^^ reported in the literature. Both quantities (22) Bacon, G. E. In Neutron Diffraction,3rd ed.;Clarendon: Oxford, 1975; p 38. (23) Tanford, C. In The Hydrofobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, 1973.
are summarized in Table I together with the hydration numbers26used in building up the micelle structuremodel. The static structure factor was computed by means of the rescaled mean sphericalapproximation(RMSA) using a screened Coulombic potential plus hard sphere repul~ i ~ Innthis. one-component ~ ~ ~ ~ macrofluid ~ model the counterions and solvent molecules are treated as a continuousneutralizing background which determinesthe screeningin the system; neglectingthe finite size of sodium counterions, the value of the micellar charge must be considered to some extent an apparent charge. To reduce the number of fitting parameters for each run a Q independent term, Bk, which includes the incoherent scattering and the machine background, has been evaluated in the Porod region of the scattering curve from the slope of @[dX(Q)/dQlvs @. After the Bk terms have been subtracted, the experimentalscattering absolute intensities have been analyzed by fitting the experimental intensities to eq 2. The aggregation number, v, and the micellar charge, 2,were used as fitting parameters. R2 can be obtained once v is known: R2 = (3~Vmod4a)l/~, where Vmo, is the volume of the monomer; it includes the fluorocarbon chain, the headgroup, the fraction of the counterions, 1 - B, computed from v and 2, and the hydration water. R1 is obtained from v and the volume of fluorocarbon chain. For all D20-H20 compositions the cmc in pure H2O (0.036 M)19 has been used. By use of the core plus shell sphericalmodel, satisfactory fits were obtained, but in the high Q range computations gave oscillations not observed in the experimental data. Since such oscillations can be smoothed by introducing either anisotropy or polidispersity, polydisperse spheres and monodisperseprolate and oblate ellipsoidmodels were tested. In the presence of polydispersity and particle anisotropy the expressions of the differential cross section become more complex. Nevertheless, assuming that there is no correlation between position and size (in the case of polydisperse sphericalparticles) and between position and orientation (in the case of monodisperse anisotropic particles), the decoupling approximation holds, and the absolute intensity can be computed by adding a new term in eq 2 dX(Q)/dQ= NpS(Q)I(F(Q))12 + NP[W(Q)I2) - l(F(Q))l21(3) The ellipsoids of revolution are described by three semiaxes, a, a, and b = ac; the axial ratio e being greater ~~
~
(24) Immirzi, A,; Perini, B. Acta Crystallogr., Sect. A 1972, 33, 216. (25) Millero, F. J. In Water and Aqueous Solution; Horne, R. A. Ed.; Wiley Interscience: New York, 1972; Chapter 13, p 519. (26) Rutgers, A. J.; Hendrikx, Y. Trans. Faraday SOC.1962,58,2158. (27) Aahcroft, N. W.; Lekner, J. Phys. Reu. 1966, 145, 83. (28) Hayter,J. B.; Penfold, J. Mol. Phys. 1981,42,109;J. Chem. SOC., Faraday Trans.1 1981, 77, 1851.
1196 Langmuir, Vol. 9,No. 5, 1993
Caponetti et al.
Table 111. Results from Threeparameter Fits to SANS Contrast Data of Sodium Perfhomoetanoate U l h g the Monodisperse Core + Shell Prolate Ellipsoid Model. [C7Fl&OONa] = 0.33 Ma
Bk,cm-l
% DzO (v/v) 99 75 48 24
2,ue 0.05 10.5h 0.5* 0.25 12.2 0.43 11.9h 0.9* 0.66 12.4* 0.3* 0 0.93 12.3* 0.3' a See Table I1 for an explanation of symbols.
V
B
6
38.1 i 0.4* 39.2 39.5* 0.7* 39.2 f 0.3* 39.0f 0.2*
0.27 0.31 0.30 0.31 0.31
1.3 f 0.1* 1.3 1.4 f 0.2* 1.3 f 0.1* 1.2 A 0.1*
al,A 13.2 13.5 13.2 13.6 14.0
a2,A
R,A
103N,, micelles/&
18.9 19.2 18.8 19.3 19.8
20.9 21.0 21.0 20.9 20.9
8.12 7.84 7.78 7.83 7.97
x 6.7 1.4 2.2 3.9
* parameter adjusted in the fit procedure.
than 1 for prolate and less than 1 for oblate ellipsoid. The scattering of asymmetricparticles must take into account all orientations with respect to the neutron beam, thus
" -
-
2.0
h
-
1.5
. 2
-2 h
being the cosine of the angle between the direction of the long dimension and the scattering vector, Ui = Q[ei2ai2 ai2(1 - pz)]0.5. In the case of polidispersity the following expressions were used
p
+
I(F(Q))IZ =
01.0
0.5
0.0
0.1
0.2
0.3
0.4
Is,"F(Q)f(Rs)MI2
where f(Rs) is the S ~ h u l zdistribution ~~ of radii first proposed by Aragon and Pe~ora.~O f ( ~ , =) (ZS+
exp[-(Zs
+ I)XI/
Rr(zs + 1) zs> -1 X being Rs/R and r ( Z s + 1)representing the r function
o
0.16M
of argument 2s + 1. The breadth parameter, Zs, characterizes the distribution and is a function of the mean radius and of the variance u:
2s = [ l - (u/R)21/(u/R)2 In both the asymmetric particles and the polydisperse spheres cases, the structural factor used in the fit of d2(Q)/dn to eq 3 is that computed for a sphere of size equivalent to the ellipsoid or to the (weighted) average particle size. Using the polydispersity model and the ellipsoid model, we introduced in the fit procedure an additional adjustable parameter, 2s or t alternatively, assuming that the axial ratios are the same for the core and the shell. The introduction of anisotropy and polydispersity improves the agreement between the experimental data and the computed intensities in the high Q region; it does not change the value of the fitting parameters appreciably. As an example, results obtained by the four models are reported in Table I1 for the solution in pure HzO where the contrast between the particles and the solvent is higher. As it can be noticed the difference in the x is small (x is square root [(sum of the squares of weighted residuals)/ (numberof point minus number of parameter plus one)]). The high value of Zs obtained from the fit indicates that the system is essentially monodisperse. From the values of e we can conclude that, at this concentration, we are dealing with a system of nearly spherical monodisperse particle^.^^ (29)Schultz, G.J. Z Phys. Chem., Abt. B 1939, 43, 25. (30)Aragon, S.R.;Pecore, R. J. Chem. Phys. 1979, 64, 2395. (31) Caponetti, E.;Floriano, M. A.; Di Dio, E.; Triolo, R. Submitted
to J . Appl. Crystallog.
"0
0.1
0.2
0.3
0.4
Q (A') Figure 3. Three-parameter fit of experimental SANS concentration data for sodium dodeconate with results shown in Table V symbols, experimental values; lines, calculated intensities.
Since the best x has been obtained for the monodisperse core plus shell prolate ellipsoid model, the comparison between the experimental data and computed intensities obtained using this model, for all the D20-H20 compositions, are shown in Figure 1. The curve corresponding to 75 96 (v/v) DzO is flat; on this case the contrast is about zero and, hence, we are very close to the match point. Since in this condition it is not possible to fit the experimental data to any model, the intensity related to this composition has been simulated using the mean value of the fitting parameters obtained for the other runs. It is important to notice that the simulation is able to reproduce the experimental data. In Table I11 the results of the least-squares fitting procedure are reported. The fact that the fitting parameters are about the same for all the solvent mixtures, except
Fluorinated, Protonated, and Mixed Surfactant Solutions
Langmuir, Vol. 9, No. 5, 1993 1197
Table IV. Three Parameter Fits to SANS Contrast Data of Sodium Dodecanoate Using the Monodisperse Core + Shell Prolate Ellipsoid Model. [CllH&OONa] = 0.16 Ma % DzO (v/v) 99 75 50 26 0
B c al,A 0.08 15.2 f 0.4* 57.0 0.3* 0.27 1.3 f 0.1. 14.9 0.29 15.2 15.1 0.8' 56.5 f 0.6* 0.27 1.2 *0.1* 0.48 15.6f 0.6* 57.6 0.4* 0.27 1.3* 0.1' 15.1 0.71 15.3 56.0 f 2* 1.3 14.9 0.27 0.97 15.3 57.0 0.27 1.3 15.0 See Table I1 for an explanation of symbols. * parameter adjusted in the fit procedure.
Bk,cm-I
Z, ue
R,A
az,A 21.6 21.9 21.8 21.6 21.7
Y
*
23.7 23.6 23.8 23.5 23.7
1@Np
x
miceiies/A3 2.37 2.38 2.34 2.37 2.32
4.0 4.8 1.8 1.4
Table V. Results from Three Parameter Fits to SANS Concentration Data of Sodium Dodecanoate Using the Monodisperse Core + Shell Prolate Ellipsoid Model.
C,M Bk,cm-l Z, eu V B c al,A 0.16 0.08 15.2 0.4* 57.0*0.3* 0.27 1.3i 0.11 14.9 0.25 0.10 15.5 0.2* 60.8* 0.2* 0.25 1.6f 0.1* 14.3 0.32 0.12 15.9 0.1* 0.25 1.5f 0.1* 14.8 63.2f 0.1* 0.46 0.10 14.1 f 0.4* 67.8*0.3* 0.21 1.8f 0.12 14.3 0.53 0.15 11.3f 0.6* 70.3* 0.3* 0.17 1.6 f 0.1* 15.0 See Table I1 for an explanation of symbols. * parameter adjusted in the fit procedure.
** *
80
I
I
I
I
R,A
az,A 21.6 20.8 21.5 20.9 22.0
23.7 24.3 24.6 25.4 25.8
1@Np
miceiiea/A3 2.37 3.72 4.59 6.34 7.18
x 4.0 5.0 3.9 9.5 9.3
I
60
ir
40
20
0 0.4
0.5
0.6 0.7 0.8 (C cmc)li4 M l i 4
-
0.9
1
Figure 4. Aggregation number against the one-fourthpower of the micellized surfactant concentration: A, sodium dodecanoate, this paper; 0, sodium perfluorooctanoate, ref 17; 0, sodium octanoate, ref 32. 0.00
the 75% (v/v) D20, indicates that the model is able to describe well the micellar structure of the surfactant. CllHzaCOONa External Contrast and Concentration Study. Both the experimental SANS data sets obtained as a function of the concentration, C, in DzO (C ranging between 0.16 and 0.56 M)and at a fixed CllH23' COONa concentration (0.16 M)using five different D2OH2O compositions, have been analyzed using the same procedure followed in the analysis of sodium perfluorooctanoate contrast data. For all DzO-HzO compositions the cmc in pure H2O (0.027 M)le has been used. At low concentrationsno appreciable differencebetween the results obtained by the four models used has been observed. On increasing the concentration, the micelles grow and the monodisperse core plus shell spherical model gives poorer fits than the other models, implying a departure from sphericity. Figure 2 shows the experimental contrast data and the computed intensities obtained by using the monodisperse core plus shell prolate ellipsoid model. The data set in pure H20 has been reproduced successfully using for the parameter the mean values obtained from the three run at higher DzO content. The 26% (v/v) DzO run has been fitted by fixing e and 2 and adjusting Y. The good agreement between the concentration experimental data and the computed intensities,shown in Figure 3, implies that the model is able to take into account the
1
I
0.02
0.04 Q2
0.06
0.0s
(A-2)
Figure 5. log[dZ(Q)/dQ]against Q2for sodium perfluorooctanoate external contrast data: symbols, experimental values; lines, linear fit obtained in the 0.0204.035 Q2range. Numbers abovethe curves identifythe corresponding % (v/v) D20 content. The scale refers to the 0% (v/v) DzO. The other runs are shifted 1, 3, 5, and 6 units, respectively, for reason of clarity.
behavior of the system also at higher concentration than the one related to the contrast study. In Tables IV and V, for the contrast and the concentration data, respectively,we report the results of the leastsquares fitting procedure only for the monodisperse core plus shell prolate ellipsoid model. The mean value of the core minor semiaxis, al, is consistent with the length of the hydrocarbon fully extended chain (15.4 A). This correspondencehas been observed in other systems32where the particles grow in such a way that a spherical core, whose radius is equal to the length of the hydrocarbon fully extended chain, is not able to contain all the hydrocarbon chains, so that the particles elongate in one direction. A plot of the aggregation number versus the concen, in tration of micellized surfactant, (C- c m ~ ) l /is~shown (32) Caponetti, E.; Causi, S.;De Liai, R.; Floriano, M.A.; Milioto, S.; Triolo, R. J. Phys. Chem. 1992, 96,4950.
Caponetti et al.
1198 Langmuir, Vol. 9, No. 5, 1993 1 0 ' ~p, (an")
-0.56
0.82
I
I
I
1
I
0
20
40
60
80
100
-1
0.00
2.19
4.94
3.57
6.32
%(v/v) D,O
0.04
0.02
0.06
0.08
Figure 8. [dZ(Q=O)/dQ]1/2 against the % (v/v) [lower scalel and ps [upper scale]: 0, sodium perfhorooctanoate;A, sodium dodecanoate; 0, their mixture; lines, linear fits.
QZ (.;6-*)
I
Figure 6. log[dZ(Q)/di?]against Q2 for sodium dodecanoate external contrast data: symbols,experimentalvalues; lines,linear fit obtained in the 0.010-0.025 Q2 range. Numbers above the curves identify the corresponding % (v/v) D20 content. The scale refers to the 0% (v/v) D20. The other runs are shifted 1, 2, 3, and 4 units, respectively, for reason of clarity.
I 1.0
2.0
-
1.5
-
01.0
.
-
-E
I I
h
. s h
I
I
-
0.1
0.2
0.3
v
Y
Oa5
0.0;
3
t
-
050 75
99 _-
0.4
Q (k')
2
aw
Figure 9. Three-parameters fit of experimental SANS external contrast data for the sodium perfluorooctanoate/sodiumdodecanoate mixture with results shown in Table VI1 symbols, experimentalvalues;lines,calculatedintensities. The inset shows an enlarged view of the runs at low intensity. The incoherent scattering and machine background have been subtractedin the fits, but not in the figure. Each run is identified by the corresponding % (v/v) DzO content.
v
3
g 1
-1
0
-1 -2
I
I
-3 0.00
0.04
0.02 Qz
I 0.06
0.08
(A-')
Figure 7. log[dZ(Q)/di?] against Q2 for sodium perfluorooctanoate/sodium dodecanoate mixture external contrast data: symbols, experimental values; lines, linear fit obtained in the 0.020-0.035 Q 2 range. Numbers above the curves identify the corresponding 5% (v/v) D20content. The scale is related to the 0% (v/v) DzO. The other runs are shifted 2, 4, 5, and 6 units, respectively, for reason of clarity. Figure 4. In the same figure we also report literature data of Y for sodium o c t a n ~ a t e(cmc ~ ~ = 0.4 M) and sodium perflu~rooctanoatel~ obtained in DzO and HzO, respectively. T h e aggregation numbers of all the surfactants follow a linear trend. Plotting aggregation numbers versus the one-fourth power of the concentration has been suggested by proposing a simple model of micelles formation.'E This model is based on a n energetic balance between the hydrophobic (monomer-monomer) interaction and the intra- and intermicelles electrostatic inter(33) Hayter, J. B.;Zemb, T.J. Chem. Phys. Lett. 1982, 93, 91.
Table VI. Particle Scattering Length Densities Obtained from the Match Points, pmp, Compared with Those, po Calculated for Dry Micelles Using Data in Table I under the Assumption that Mixed Micelles Are Formed in the Mixed System svstem perfluorooctanoate dodecanoate perfluorooctanoate-dodecanoab
Pmp,
Pc,
10-6 cm-*
10-6 cm-2
4.29 0.14 3.01
0.22 2.80
3.97
actions. As it can be noticed, the lower the cmc the higher is the aggregation number, in agreement with increasing hydrofobicity. It can be stated that the perfluorocarbon surfactant forms bigger micelles than the ones formed by the hydrocarbon surfactant having the same number of carbon atom in the chain but smaller than the ones formed by the hydrocarbon surfactant having a chain of equal volume.
CllH2&OONa-C~Fl&OONa External Contrast S t u d y . Looking at the flat scattering intensity of the two surfactant mixture in the 60% (v/v) DzO solution (see Figure 9), it is clear that we are very close to a match point. Since the corresponding scattering density value
Fluorinated, Protonated, and Mixed Surfactant Solutions
Langmuir, Vol. 9, No. 5, 1993 1199
Table VII. Results from Three Parameter Fits to SANS Contrast Data of Sodium Dodecanoate and Sodium Perfluorooctanoate Mixed System Using the Monodisperse Core Shell Prolate Ellipsoid Model. [C7F1EOONal = 0.33 M; [CllH&OONa] = 0.16 Ma
+
% DzO (v/v) 99 75 50 24 0
Bk,cm-1
Z, ue
UHF
B
0.10 0.31 0.46 0.68 0.90
6fl* 6 * 2* 6.8 7 f 22 8 * 1*
52.9f0.4* 53.5f 0.6* 51.9 50.8* 0.6* 50.4h 0.3*
0.12 0.11 0.13 0.13 0.17
t
1.8fO.11 1.8f 0.1* 1.6 1.5h 0.1* 1.3f 0.1*
103~,,
al,A
az,A
R,A
micelleslA3
x
13.2 13.4 13.8 13.9 14.6
19.3 19.6 20.1 20.4 21.2
23.7 23.8 23.5 23.3 23.1
8.84 8.67 8.94 9.06 9.8
10 4.8 2.3 3.0
U H F = sum of sodium dodecanoate and sodium perfluorooctanoate monomers in the micelle. See Table I1 for an explanation of other symbols. * parameter adjusted in the fit procedure.
Table VIII. Results from Three Parameter Fits to SANS Contrast Data of Sodium Dodecanoate and Sodium Perfluorooctanoate Mixed System Using the Core + Shell Polydisperse Spheres Model. [C,F&OONa] = 0.33 M, [CllHz&OONa] = 0.16 Ma 103~,, % Dz0 (v/v) Bk,cm-1 Z, eu UHF B Z, R,A micelles/A3 X 99 0.10 10 31 47 i 21 23.5 9.97 21.5 0.22 158 f 80* 75 0.31 10 4* 47 f 21 0.22 134 f 71* 22.5 9.83 7.5 24 0.68 7 f 41 49 '2 0.14 614 f 1300* 23.0 9.38 2.3 0 0.90 9 f 1* 49 f 1* 0.19 540 f 500* 22.8 9.35 3.2
*
*
a UHF = sum of sodium dodecanoate and sodium perfluorooctanoate monomers in the micelle. See Table I1 for an explanation of other symbols. * parameter adjusted in the fit procedure.
is far from those of the two homogeneous micelles, this is an indication that a unique type of micelles is present in solution. It is known that, for entities whose scattering density is uniform, and when the particle number density is low enough so that S(Q)is about 1, the square root of the extrapolated intensities a t zero scattering angle (Q = 0) can be plotted versus the scatteringdensity of the medium to determine the point where the scattering density of the solvent matches that of the particles. Micelles formed by ionic surfactants usually do not have uniform scattering density, moreover they are charged so that even at low concentration the interaction peak, present in the scattering curve, can interfere with the extrapolation of d2(Q)/dfl. To verify the possibility of using the above-mentioned procedure in our experimentalconditions,before analyzing the surfactants mixture contrast data, we followed the procedure to obtain the scattering density of the two homogeneous micelles. Figures 5 and 6 show the plots of the log of experimental intensities (the term Bk having been subtracted) against Q2for C7F15COONa and CnH23COONa, respectively. The corresponding Q2 ranges used, in the linear fit, for obtaining extrapolated intensities a t Q = 0 were 0.02-0.035and 0.01-0.025 A-2. These ranges are above the theoretical Guinier limit,34 but when deviations from spherical symmetry are observed, the validity of the Guinier approximation is extended well above the theoretical limit.34 The square root of the extrapolated intensities at Q = 0 are reported against percent (v/v) D20 in Figure 8. By a linear fit we have calculated the D&-H20 volume ratios corresponding to scattering length densities equal to that of the particles; results are shown in Table VI together with the micelle scattering densities, computed from data in Table I. The good agreement between the experimental and the computed scattering length densities of the two homogeneous micelles indicates that the method used gives acceptable results even in the actual experimental conditions; hence we have analyzed the mixture contrast data in the same way. Figure 7 shows the plots of the log of (34) Caponetti, E.; Lizzio, A.; Triolo, R.; Compere, A. L.; Griffith, W. L.; Johnson, J. S., Jr. Langmuir 1989, 5, 357.
experimental intensities (the term Bk having been subtractet) against Q2; the Q2 range used in the fit, in this case, was 0.02-0.035A-2. The linear fit of the extrapolated intensities is shown in Figure 8; the scattering length density value corresponding to the match point is reported in Table VI together with that computed in the hypothesis that mixed micelles, with a composition equal to the stoichiometric one, are formed. Since the particles scattering length density obtained from the match point is almost equal to the computed one, we have fitted the mixed system experimental data to eq 3 using the models, previous applied to describe the homogeneous systems, with the above-mentioned assumption on the particles composition. The value of the cmc used in the fit, determined by conductivity method, was 0.038. The comparison between the experimental and the computed intensities obtained by the monodisperse core plus shell prolate ellipsoid model, which gave the lowest x , is shown in Figure 9. The good agreement, on the one hand, confirms the hypothesis on micelle composition and on the other indicates that the system is well described by the core plus shell prolate ellipsoid model. Data set whose D20-H20 ratio is very near to the match point has been successfully reproduced in the way previously described. The values of the adjusted and derived parameters obtained from the fits are reported in Table VII. In this case the aggregation number, UHF,represents the total content of the two surfactants monomers; with a the hydrogenated surfactant stoichiometric molar fraction, ~ U H is F the number of protonated monomers and (1- a)vm is the number of perfluorinated ones. Another proof for the presence of a unique type of micelle has been obtained from the polydisperse sphere model, whose results are shown in Table VIII. The very high value of Zs and its enormous error indicate that the system is essentially monodisperse (we might recall that a Schulz distribution approaches a delta function placed at Rs = R as Zs approaches infinity). In order to compare the aggregation number of mixed micelles with that of micelles formed by each surfactant at the same concentration of the mixture, we have interpolated the corresponding values from the data of
1200 Langmuir, Vol. 9, No.5, 1993 Figure 4 and we got 70.0 and 40.8 for the protonated and perfluorinated surfactant, respectively. The mean Y value of the mixed micelles, 51.9, lies between those two values. The apparent charge is smaller than for one of the singlecomponent micelles in agreement with the results of Borb6ly et aL4
Conclusion Despite previous studies in mixed fluorocarbon-hydrocarbon systems, that have claimed the coexistence of two different kinds of micelles, one rich in hydrocarbon and the other in fluorocarbon surfactant, our SANS external contrast matching experiments, performed on aqueous solutions of sodium perfluorooctanoate, sodium dodecanoate, and a mixture of the two surfactants, indicate the presence of mixed micelles having the same composition and a very narrow size distribution. The presence of a unique and well-defined match point in the external contrast data of the mixed system justifies this conclusion, which has been tested by fitting the experimental patterns with severalmodels based on abovementioned picture. The good agreement between the experimental data and the computed intensities obtained by the monodisperse core plus shell prolate ellipsoid model c o n f i i the hypothesis on micelle composition and indicates that the single particle can be well described by a prolate ellipsoid shape. The high values of the size distribution breadth parameter obtained by fitting the experimental data with a polydisperse spheres model is evidence of a nearly monodisperse system. Similar conclusionsabout the presence of mixed micelles have been reached by Burkitt et al.lS by contrastmatching experiments in a system composed of ammonium perflu-
Caponetti et al.
orooctaonate and ammonium decanoate, at pH 8.8 and an ionic strength of 0.1. They found cylindrical micelles whose aggregation number is much larger than the one observed in our system. However, a direct comparison with our results is not possible because it is known that the addition of a supporting electrolyte increasesthe particle dimension and very often changes their shape. The aggregation number found for the mixed micelles was intermediite between those of the twosingle surfactant micelles, while the degree of counterion dissociation was lower than each of them. The comparison between the aggregation numbers obtained for the sodium dodecanoate system, studied as a function of the concentration, and those of sodium octanoate and sodium perfluorooctanoate taken from literature, indicates that the perfluorocarbon surfactants forms bigger micelles than the ones formed by the hydrocarbon surfactant having the same number of carbon atom in the chain but smaller than the ones formed by the hydrocarbon surfactant having a chain of equal volume. More systematic thermodynamicand structural studies are necessary for a better characterization of the behavior of the mixed fluorinated and hydrogenated surfactant solutions,that could contribute to a better understanding of the process of micellization itself.
Acknowledgment. The authors are grateful to the Consiglio Nazionale delle Ricerche (Progetto Finalizzato Chimica Fine 11) and to the Minister0 dell'Universit8 e della Ricerca Scientifica e Tecnologica (MURST) for financial support and to NCSASR for granting the beam time for the SANS instrument at the HIFR.
