2112
Langmuir 1991, 7, 2112-2116
Counterion Effect on the Immiscibility of Fluorocarbon and Hydrocarbon Surfactants in Mixed Micelles Tsuyoshi Asakawa,* Tomohiro Fukita, and Shigeyoshi Miyagishi Department of Chemistry and Chemical Engineering, Faculty of Technology, Kanazawa University, Kanazawa 920, Japan Received January 18, 1991. I n Final Form: May 10, 1991 We examined the influence of the addition of lithium chloride or diethylammonium chlorideon micellar miscibility. The miscibility of fluorocarbon and hydrocarbon surfactants in a micelle was evaluated by the micellar pseudophase diagram, i.e., mixture cmc’s and second cmc’s. The addition of LiCl induced an increase of immiscibility in the micelle. The micellar size was rather large with the addition of LiCl and was further increased by the mixing of lithium perfluorooctanesulfonate (LiFOS) and lithium dodecyl sulfate (LIDS). Molecular theory was attempted to describe the nonideal mixtures of fluorocarbon and hydrocarbon surfactants. The calculation also indicated the existence of two kinds of mixed micelles and micellar growth by mixing the fluorocarbon and hydrocarbon surfactants.
Introduction The miscibilities of fluorocarbon and hydrocarbon surfactants have been reported by several inve~tigators.l-~ Shinoda indicated the coexistence of two kinds of mixed micelles and described the condition of the immiscibility in detail.2 The prediction of miscibility was made by applying regular solution theory to the pseudophase separation micelle. There is a quit lot of work in the literature on mixed micelles, but few studies of about the counterion effect on the immiscibility of mixed micelles. Micellar immiscibility has been evaluated by mixture cmc curves, surface tension, NMR spoectroscopy, etc. The formation of mixed micelles is governed mainly by hydrophobic and electrostatic interactions. Surfactants associate to form aggregates of various sizes, depending on the amount of added salts and the counterion species. The hydrophilic groups and counterions also play a significant role in the formation of mixed micelles, but the variation of miscibility caused by such effects has not been examined in mixed fluorocarbon and hydrocarbon surfactant systems. Minimizing the electrostatic repulsion between hydrophilic groups should induce the increase in ordered packing of hydrophobic chains in the micelle. The “phobic” interaction between fluorocarbon and hydrocarbon chains (dueto the weak interaction of fluorocarbon and hydrocarbon chains as compared to their selfinteractions) would be expected to be characterized in such a case. Hoffmann et al. reported the influence of various ions on the micellar properties of fluorocarbon surfactants.8 Conductivity measurements gave unusually low dissociation degrees for dimethylammonium ion in contrast to rather high dissociation degrees for lithium ion. Kinetic measurements using relaxation techniques also gave unusual results, indicating micellar growth induced by the dimethylammonium counterion. The size of the mixed micelle provides important (1) Muker’ee, P.; Yang, A. Y. S. J. Phys. Chem. 1976,80, 1388. (2) Shmoda, K.; Nomwa, T. J. Phys. Chem. 1980,84, 365. (3) Funamki, N.; Hada, S. J. Phys. Chem. 1980,84, 736. (4) Kamrath, R. F.; Franeee, E. I. Znd.Eng. Chem. Fundam. 1983,22, 230. (5) Harada, S.; Sahara, H. Chem. Lett. 1984, 1199. (6) h k a w a , T.;Johhn,K.; Wagishi, S.;Nishida,M.Langmuir 1985, I , 347. (7) Aaakawa, T.; Mowi, M.; Miyagishi, S.;Nishida, M. Langmuir 1989, 5, 343. (8) Hoffman,H.;Ulbricht, W.;Tageeeon,B.Z.Phys. Chem. 1978,113, 17.
0743-7463/91/2407-2112$02.50/0
information for characterizing such a micellizationprocess, but there are only a few works that deal with the size of the mixed micelles. Nagarajan developed the molecular theory and calculated not only the mixture cmc and the average micelle composition but also the average micelle size in mixed-surfactant ~ y s t e m s .Interesting ~ results on how the micellar size varies with the composition of the surfactant mixture and on the occurrence of azeotropy were also presented. Burkitt et al. investigated mixed micelles of fluorocarbon and hydrocarbon surfactant systems by the small-angle neutron-scattering method.I0 They indicated that mixed micelles were cylindrical in shape and proposed that segregation between fluorocarbon and hydrocarbon surfactants in the micelle would occur. In this paper, the micellar miscibilities of fluorocarbon and hydrocarbon surfactants were evaluated by the micellar pseudophase diagrams. We shall give much attention to the influence of the addition of salts (diethylammonium chloride and lithium chloride) on the micellar immiscibility. The mixture cmc was determined by the conductivity method, and the second cmc was evaluated by the surface tension method and/or the fluorescence probe method using 1-anilinonaphthalene-8-sulfonate. Moreover, we applied Nagarajan’s molecular theory for the nonideal mixture of fluorocarbon and hydrocarbon surfactants in order to investigate whether the coexistence of two kinds of mixed micelles with different compositions and sizes could be illustrated or not.
Experimental Section Materials. Lithium perfluorooctanesulfonate(C$1,SO&i, LiFOS),lithium perfluorononanoate(CeFl+200Li,LiPFN),and lithium dodecyl sulfate (C12HmSO&i,LIDS) were prepared by the same procedures as reported pre~iously.~ 1-Anilinonaphthalene-8-sulfonate (Cl&eN20&
ANS; Wako Pure Chemical
Ind., Ltd.) and auramine (C17HzlNaHC1, Kanto Chemical Co., Inc.) were used aa received. The other reagents were of guaranteed grade. Measurements. Conductivity measurements were carried out using a conductivity meter, Model CM-20s (TOAElectronics Ltd.). Fluorescence spectra of ANS and auramine were recorded on a Hitachi 204-5fluorescence spectrometer. The fluorescent M ANS and 1.0 X 1W M probes were prepared as 6.3 X auramine as reported previously? All experiments were performedat 25 OC. Surfacetensionwas measuredby the wihehy (9) Nagarajan, R. Langmuir 1985,1,331.
(10) Bwkitt, S. J.; Ottewill, R. H.; Hayter, J. B.; Ingram, B. T. Colloid Polym. Scr. 1987,265,628.
0 1991 American Chemical Society
Langmuir, Vol. 7, No. 10,1991 2113
Immiscibility of Mixed Micelles
Immiscible region
0
Concentration /mM
2 4 6 Concentration /mM
0
0.2 0.4 0.6 0.8 1.0 Mole Fraction of LiPFN
Figure 1. Specificconductivityvs concentrationof LiPFN,LiDS, and their equimolar mixture: (a) LiDS (01,LiPFN (A),a = 0.5 (m) in the absence of DEA, (b) LiDS (01, LiPFN (A), a = 0.5 ( 0 ) in 5 mM DEA.
Figure 2. cmc’s of mixtures of LiPFN and LiDS. The plotted
technique (Kyowa Kagaku surface tension meter, Model A-3). Relative viscosity was measured at 25.0 f 0.03 “C using a Ubbelode-typecapillary viscometer. The relative viscosity is given by q, = pt/p&,, where t (to) is the flow time of surfactant solution (solvent), and p (PO)is the density of solution (solvent). The density of solutions was measured by the use cif Ostwald pycnometers of 5- and lO-cms capacities.
calculation of micelle composition, the pseudophase separation regions are 0.25-0.90 in the absence of salt, 0.240.90 in 5 mM DEA, and 0.23-0.90 in 10 mM DEA. Thus, the hydrocarbon-richmicelles solubilizedthe fluorocarbon surfactant somewhat more than the fluorocarbon-richmicelles solubilizedthe hydrocarbon surfactant. This mutual solubility behavior in micelles resembles that observed by Burkitt et al. for a mixture of ammonium decanoate and ammonium perfluorooctanoate.1° As shown in Figure 2, the immiscible region does not change significantly with increasing DEA concentration. The addition of DEA suppresses the electrostatic repulsion between hydrophilic groups in micelles, thereby inducing close and/or ordered packing. Such a situation would scarcely influence the mutual immiscibilityof fluorocarbon and hydrocarbon surfactants in the first formed micelles at the cmc’s. At 20 mM DEA concentration, the mixture cmc’s were determined by the surface tension method and second cmc’s were evaluated by the ANS fluorescence probe method. The variation of ANS fluorescence intensity gaves the second cmc as reported previ~usly.~The abrupt increase in fluorescence intensity indicates the formation of hydrocarbon-rich micelles. When the splitting of micelles occurs, the second cmc values are given by material balances.7
Results and Discussion Mysels and Otter reported the determination of cmc’s of a surfactant mixture by electrical conductivity.11 They observed a gradual change in the conductivity above the mixture cmc and pointed out that this behavior corresponds to a change in the composition of mixed micelles and monomers. Mukerjee and Yang (in ref 9) investigated the differential conductance in fluorocarbon and hydrocarbon surfactant systems. They observed an abrupt change in the differential conductance curve far above the mixture cmc and suggested that the second inflection point is evidence of the appearance of a second type of mixed micelle. In the present study, the conductivity method was used to measure the cmc’s of several mixtures of fluorocarbon and hydrocarbon surfactants. Figure 1 shows the specific conductivity as a function of total surfactant concentration (LiPFN, LiDS, and their equimolar mixture) in both the absence and presence of diethylammonium chloride (DEA). The inflection point correspondingto the cmc decreased upon addition of DEA as expected. When SIand SZwere used to denote the slopes of the conductivity vs concentration curves below and above the cmc, respectively, the Sz/Sl ratio was previously shown to be the index of counterion dissociation of micelles.8 Here we find that in the absence of DEA the &/SIratio of LiPFN is larger than that of LiDS (LiPFN, 0.56; LiDS, 0.43). This suggests that the dissociation degree of the lithium ion of LiPFN micelles is larger than that of LiDS. However,the &/SI ratio of LiPFNdecreases considerably with increasingDEA concentration (LiPFN, 0.29 in 5 mM DEA, 0.14 in 10 mM DEA; LiDS, 0.47 in 5 mM DEA, 0.47in 10mM DEA). This suggests preferential binding of the DEA ion to LiPFN micelles. We could not detect the second inflectionpoint in the conductivity curve of the LiPFN-LiDS mixtures. Figure 2 shows the experimental mixture cmc values of LiPFN-LiDS systems as a function of mole fraction of LiPFN along with calculated cmc curves. The latter were performed by the group contribution method as reported previously.6 This method predicts that two kinds of mixed micelles will be formed in the solution. From the (11) Myeels, K.J.; Otter, R. J. J. Colloid Sci. 1961,16, 462.
points are experimental values. The solid and dotted-dashed lines are cmc and micellar composition curves, respectively, calculated from the group method in the absence of DEA (a), 5 mM DEA (A), 10 mM DEA (m).
cmc2 =,C
(XF- X,)/(XF
- a)
cmcz = ,C (Xu - X H ) / ( a- Xw)
(1)
(2)
where XM and CM are the composition and concentration under the azeotropic conditions, Xp and XH are the compositions of fluorocarbon surfactant in fluorocarbonrich and hydrocarbon-rich micelles, respectively, and a is the composition of fluorocarbonsurfactant in the mixture. The larger value of cmcz in eqs 1and 2 leads to the second cmc. The micellar pseudophase diagram is shown in Figure 3. The cusp of the mixture cmc curve (a= 0.34in 20 mM DEA) is shifted to left compared to that in the absence of DEA (a = 0.61). The hydrocarbon-rich micelle first appears at the left side of the cusp of the mixture cmc curve. The fluorocarbon-rich micelle first appears at the right side of the cusp of the mixture cmc curve. Both fluorocarbon-rich and hydrocarbon-rich micelles, which are mutually saturated with each other, coexist within the region between the second cmc curves. That is, the coexistence region of the two kinds of mixed micelles is shifted to the left compared to that in the absence of DEA. The observed second cmc’s were described by the splitting
Asakawa et al.
2114 Langmuir, Vol. 7, No.10,1991 5
I
0
2 0
I
I
0.2 0.4 0.6 0.8 1.0 Mole Fraction of LiPFN
Figure 3. Micellar pseudophasediagram of LiPFN-LiDS in 20
mM DEA. The solid and the dashed lines are calculated cmc and calculated second cmc curves (XF= 0.75, XM = 0.34, CM = 1.62mM),respectively: mixture cmc’sby surface tension method (a),second cmc’s by ANS fluorescence method (m).
0.2 0.4 0.6 0.8 1.0 Mole Fraction o f FC Surfactont
0
Figure 5. Relative fluorescence intensity of auramine vs mole fraction of fluorocarbon surfactantain mixtures: 20 mM LiPFNLiDS in 0.1 M LiCl (a),20 mM LiPFN-LiDS in 20 mM DEA (A),20 mM LiPFN-LiDS in 1.0M LiCl (B), 20mM LiFOS-LIDS in 1.0 M LiCl (v).
I LiC1. Bendedouch and Chen indicated that the LiDS mi-
c
A
1 .o
0
0.2 0.4 0.6 0.8 1.0 Mole Fraction of FC Surfactant
Figure 4. Relative viscosity vs mole fraction of fluorocarbon Surfactants in mixtures: 20 mM LiPFN-LiDS in the absence of salt (a),20mM LiPFN-LiDS in 20mMDEA (A), 20mMLiPFNLiDS in 1.0 M LiCl (m), 20 mM LiFOS-LiDS in 1.5 M LiCl (v). of micelles when XF was equal to 0.75. This increase in misibility of fluorocarbon-rich micelles as compared to the predicted miscibility (XF= 0.90) at the cmc might be caused by the hydrophobicity of the DEA ion. The dissociation degree of the DEA ion from fluorocarbonrich micelles is rather low compared to that from hydrocarbon-rich ones. That is also supported experimentally by the conductivity measurements of diethylammonium perfluorononanoate solution (S2/S1 = 0.06). The strong binding of the DEA ion to fluorocarbon micelles would probably be due to hydrogen bonds and/or hydrophobic interaction. Therefore,the fluorocarbon-richmicelles with hydrophobic DEA ion would preferentially solubilize the hydrocarbon surfactant. Next, we evaluated the micellar growth and the microviscosity in micelles upon addition of DEA or LiCl and attempted to determine the relation between micellar growth and miscibility in micelles. Figure 4 shows the variation of the relative viscosity of fluorocarbon and hydrocarbon surfactant solutions. The viscosity of LiPFNLiDS solutions in the absence of salt is close to 1 and is almost constant in all regions. The viscosity of LiPFN is markedly increased by the addition of DEA or LiC1, while that of LiDS remains closeto 1. The viscositiesof LiPFNLiDS mixtures in 20 mM DEA increase with increasing mole fraction of LiPFN. This indicates that the micellar growth of fluorocarbon-rich micelles is probably due to the counterion binding of DEA to the micellar surface. In the case of LiC1, the viscosity of a LiPFN solution increases considerably at LiCl concentrations above 0.5 M. When the LiCl concentration is 1.0 M (Figure 4), it is expected that the shape of the LiPFN micelle would depart from spherical. Ap abrupt increase in viscosity was observed for LiDS and LiFOS solutions above 1.2 M
celle in aqueous LiCl solutions could be represented as a prolate ellipsoid according to their small-angle neutronscattering experiments.12 Thus, the salt-induced increase in viscosity could be caused by the variation from sphere to ellipsoid. The viscosities of LiPFN-LiDS mixtures in 1.0 M LiCl showed behavior similar to those in 20 mM DEA, while those of LiFOS-LiDS mixtures in 1.5 M LiCl increase drastically at low mole fractions, reach a maximum at a = 0.3, and decrease only slightly thereafter. The results suggest micellar growth by mixing of LiFOS and LiDS in high LiCl concentration. So-called electroviscous effects would surely be released by the sufficient addition of LiC1. Figure 5 shows the variation of the fluorescenceintensity of auramine in fluorocarbon and hydrocarbon surfactant mixtures. The intensity in water (lo) was used as a standard. The increase of fluorescence intensity is known to reflect the increase of effective microviscosity felt by auramine in its mi~roenvironment.’~J*The dependence of fluorescence intensity on mixed composition generally resembles that of the viscosity in Figure 4. That is, the microviscosities are almost constant in all regions a t low LiCl concentration (0.1 M LiCl),whereas they are increased by increasing the LiPFN composition at high LiCl concentration (1.0 M LiC1) or 20 mM DEA. At high LiCl concentration (1.0 M LiC1) in LiFOS-LiDS, the microviscosities of the mixture are larger than either of the individual surfactants. Micellar growth generally attends ordered packing in micelles following an increase in microviscosity. Therefore, these results also indicate micellar growth by the addition of salts or by mixing as described above. The rigid fluorocarbon chain might afford the ordered packing of hydrocarbon chains in micelles, which could then result in increasing the micellar size in the LiFOS-LiDS mixture. We again dealt with the micellar miscibility of fluorocarbon and hydrocarbon surfactants at high LiCl concentrations. Figures 6 and 7 show the micellar pseudophase diagrams of LiPFN-LiDS in 1.0 M LiCl and LiFOS-LiDS in 1.5 M LiC1, respectively. These cmc’s and second cmc’s were determined by surface tension and ANS fluorescence probe methods. Two inflection points were observed in surface tension vs total concentration plots. Similar behavior was also reported for LiFOS-LiTS system by Tajima.16 The mixture cmc’s are well described by the calculated curve (solid, the group method), and the (12) Bendedouch, D.; Chen, S.-H. J. Phys. Chem. 1984,88,648. (13)Oetar, G.; Nishijima, Y. J. Am. Chem. SOC.1956, 78, 1581. (14) Kobayashi, Y.; Niehimura, M. J. Biochem. (Tokyo) 1972,71,276. (15) Tajima, K. Nippon Kagaku Zasshi 1985,1832.
Langmuir, Vol. 7, No. 10, 1991 2115
Immiscibility of Mixed Micelles
0
0.2 0.4 0.6 0.8 1.0 Mole Fraction of LiPFN
Figure 6. Micellar pseudophasediagram of LiPFN-LiDS in 1.0 M LiCl. The solid and dashed lines are calculated cmc and calculated second cmc curves (XH= 0.05, XF= 0.90,Xu = 0.66, Cm = 0.62 mM), respectively: mixture cmc's by surface tension method (e),second cmc's by surface tension method (A), second cmc's by ANS fluorescence method (u). II
-
chains from water to mixed micelles. In Nagarajan's work, the hydrophobic effect term ( A p w )was obtained from a linear combination of components of two different hydrocarbon chains. However, in a fluorocarbon and hydrocarbon mixture, the excess Gibbs energy arising from the immiscibility should be considered in this term. The second term represents the interfacial energy between the micellar core and water. u is the interfacial tension (50 dyn/cm for hydrocarbon-water and 56.5 dyn/ cm for fluorocarbon-water).16 The interfacial tension of a fluorocarbon and hydrocarbon mixture was assumed to be additive. a is the surface area per molecule at the micellar core, and a0 is the surface area shielded from contact with water and equal to the cross-sectionalarea of a polar head group (ap). a was calculated according to the procedure as reported by Nagarajan. The molecular volume ( V H )of a h drocarbon chain was evaluated by VH = 27.4 + 26.9nc ( 3 ) (nc, number of carbon). The molecular volume of a fluorocarbon chain ( V F )was assumed to be 1.5 time3 VH based on partial molar volumes by density measurements. The length of the h drocarbon chain was evaluated by LH = 1.50 + 1 . 2 6 ~( ) and that of fluorocarbon chain by LF = 1.25 + 1.25nc (A). The molecular constants and parameters of surfactants (LiDS, LiFOS, LiPFN, and DEA-PFN) are summarized in Table
K
K
1.17-19
0
0.2 0.4 0.6 0.8 1.0 Mole Fraction of LiFOS
Figure 7. Micellar pseudophasediagram of LiFOS-LiDS in 1.5 M LiCl. The solid and dashed lines are calculated cmc and calculated second cmc curves (XH 0.05, Xp = 0.90,X u = 0.43, C u = 0.24 mM), respectively: mixture cmc's by surface tension method (e),second cmc's by surface tension method (A), second cmc'a by ANS fluorescence method (u).
second cmc's are close to the calculated curve (dashed, eqs 1 and 2) if the splitting of micelles occur between X H = 0.05 and X F = 0.99. The results of second cmc's suggest almost perfect demixing. The addition of LiCl suppresses the electrostatic repulsion between hydrophilic groups, leading to more ordered packing of the hydrophobic chains in the micelles. The "phobic" interactions between fluorocarbon and hydrocarbon chains were characterized as compared to their self-interactions. We were further interested in the micellar growth by mixing of LiFOS and LiDS and tried to apply Nagarajan's molecular theory for the mixed systems as follows? The equilibrium size distribution of the aggregates can be calculated from the following relation. XnA,nB = X A ~ ~exp[-(&A,&' X B ~ ~
- ~ A P A ' - n@B")/kTI
(3) where X"A,,,Bis the mole fraction of aggregates containing n~ and ng molecules of surfactants A and B in the total solution including water, X Aand X Bare the mole fractions of monomeric surfactants A and B, and CL,,A,,,B~, PA', and p ~ ' are the standard chemical potentials of aggregates and monomers A and B, respectively. The standard Gibbs energy difference was written by (P,,A,,,B"- nAPAo - nBPBo)/kT= nApm
+
na[a - (nAaoA + n ~ a o ~ ) / n ] / knTIn- [ 1 - (nAapA+ nBapB)/na] + (nio,e2fl/2ekTr)[(l + Kai)/(l + KUi + Kr)l+ [ n A In (nAVA/(nAVA+ nBVB)) + nB In (nBvB/(nAvA + nBVB))I ( 4 ) The first term accounts for the transfer of hydrophobic
The third term accountsfor the steric repulsions between the hydrophilic groups. The electrostatic interactions at the micellar surface was estimated by the fourth term. The term was evaluated for spheres of radius P and nion charges on the micellar surface. fl is a constant value that accounts for the inadequancies of the Debye-Hiickel approximation and is assumed to be the dissociationdegree of counterion. ai is the radius of counterion, c is the dielectric constant of a given electrolyte solution (water, 78.51,and K is the reciprocal Debye length. The last term accounts for the entropy of mixing the two surfactants in the micelle. To begin with, we dealt with the calculation of single fluorocarbon surfactant systems and estimated the hydrophobic effect accounting for the transfer of a fluorocarbon chain from water to a fluorocarbon micelle core. The term was obtained by fitting the cmc values of fluorocarbon surfactants. The calculated average aggregation numbers of LiFOS, LiPFN, and DEA-PFN are 67, 59, and 78, respectively. The calculated cmc's of LiFOS, LiPFN, and DEN-PFN are 7.0,10.7,and 3.1 mM compared to experimental values of 7.1, 10.6, and 3.1 mM, respectively. The increase in aggregation number of DEA-PFN was predicted because the low dissociation degree of the counterion (B = 0.04) contributed to the suppression of the electrostatic repulsion term. Next, we treated the calculation of fluorocarbon and hydrocarbon surfactant mixtures. The concentrations, in mole fraction units, are expressed by contour lines in Figure 8. They are also shown three-dimensionally against the aggregationnumbers of LiFOS and LiDS in Figure 8. The major problem for calculation was the lack of a suitable estimation of A ~ H F .The APW was approximated by the equation A p m = -2.6X2 + 0.15X - 17.55 (X is the composition of fluorocarbon surfactant in the micelle), which gives reasonable aggregation numbers and partially mixed micelles. As shown in Figure 8, the coexistence of two kinds of mixed micelles was also predicted by the ~
~
(16) Handa, T.; Mukerjee, P. J. Phys. Chem. 1981,85, 3916. (17) Hasted,J. B. J. Chem. Phys. 1948,16, 11. (18) Stigter, D.J. Phys. Chem. 1974, 78,2480. (19) Ruckenstein, E.; Beunen, J. A. Lmgmuir 1988,4,77.
2116 Langmuir, Vol. 7,No. 10, 1991
Asakawa et al.
Table I. Molecular Constants of Surfactants. molecularformula ap(Qg) /A2 ai/A a/A LIA VIAS u/dyn.cm-l 350.2 50.0 3.6 16.6 17 2.0 C12H&OJLi (LiDS) 363.9 56.5 14.3 2.0 2.3 11.3 C817SOaLi (LiFOS) C817COOLi (LiPFN) 11 2.0 2.1 11.3 363.9 56.5 363.9 56.5 11 2.8 2.1 11.3 C817COOH2N(C2H6)2(DEA-PFN) 28Cion = 78.5 20Cim (8 = 10; Cion, concentration of added salt,17 K = (cmc + Cion)'/2/(3.08 X 1 V ) at 25 OC. e =
v,
B 0.52 '
0.60 0.64 0.04
0
Q 1 0 LL10.0 1'
"
'
I
"
"
I
"
1
'
1
'
1
"
1
"
.J
"1
* L
*10 1.0
0. 9 0.8
0.7
E
0.6
3
t 0. 5
0
4.0
5 .-cr
1
0.4
0. 3
Aggregation number of LiDS 2. 0
4. 0
6. 0
8. 0
10. 0
* 10
Aggregation number of LiDS Figure 8. Size distribution of micellar aggregates vs numbers of LiFOS and LiDS at cy = 0.51 LiFOS-LiDS in the absence of salt. They were calculated by molecular theory using the parameters in Table I (6= 0.48, c = 78.5). The concentrations in mole fraction units are expressed by contour lines. The coexistence of two kinds of mixed micelles is shown threedimensionally by the inset figure.
molecular theory. The average mole fractions and aggregationnumbers of hydrocarbon-rich and fluorocarbonrich micelles were XH = 0.13,XF = 0.87 and nH+F = 71, nF+H= 84,respectively. The micellar aggregation numbers were slightly increased compared to n = 60 for LiDS and n = 57 for LiFOS in a single-surfactant system. That might result from the entropy effect of mixing of two surfactants. At high LiCl concentration, the dissociation degree of counterion (8)would decrease and the dielectric constant (e) around the polar head groups would also decrease compared to that in the absence of salt. Figure 9 shows the results for a LiFOS-LiDS mixture in 1.5 M LiCl when 6 = 0.26 and c = 48.5 are used for the calculation. The average mole fractions of hydrocarbon-rich and fluorocarbon-rich micelles are XH = 0.13 and XF = 0.87, respectively, which are close to those found in the absence of salt. That is to say, the molecular theory could not simulate the experimentally determined increase of immiscibility by added salt at the present treatments. It would be necessary to treat the difference of ordering and packing in micelles between the absence and presence of salt, which might contribute to the hydrophobic effect.
Figure 9. Size distributionof micellar aggregates with numbers of LiFOS and LiDS at cy = 0.46 LiFOS-LiDS in 1.5 M LiCI. They were calculated by moleculartheory using the parametersin Table I (8 = 0.26, c = 48.5). The concentrationsin mole fraction units are expressed by contour lines.
On the other hand, the calculated average aggregation numbers of hydrocarbon-rich and fluorocarbon-rich micelles were nH+F = 513 and nF+H = 657 at the high LiCl concentration. The micellar aggregation number of fluorocarbon-rich micelles considerably increased compared to n = 432for LiDS and n = 298 for LiFOS in a 1.5 M LiCl system. That is, the molecular theory predicts the increase in micellar aggregation number by the mixing of fluorocarbon and hydrocarbon surfactants. The present calculations illustratively indicate the Occurrence of the splitting of micelles in fluorocarbon and hydrocarbon surfactant mixtures.
Conclusion The miscibility in fluorocarbon-rich micelles is slightly increased by introducing the hydrophobic counterion (diethylammonium ion) to the fluorocarbonmicelles. A t high LiCl concentrations, evaluation of the micellar miscibility indicates almost perfect demixing. The excess counterion is known to increase counterion binding and induce access to the hydrophobic chains. The "phobic" interactions between fluorocarbon and hydrocarbon chains might be emphasized in such a case. The considerably high concentration of lithium counterion induces not only micellar growth but also further micellar growth by the mixing of LiFOS and LiDS. These results were also indicated by the molecular theory.
