Langmuir 1987, 3, 729-735
Assuming AI to be equal to A, gives us the possibility to calculate G from the combined t and T-A measurements.
Irreversible Processes The approach presented in the above could also contribute to the description of irreversible processes. Especially the squeeze-out effect could be treated well with the clustering mechanism. For squeeze-out effects, irreversible horizontal parts of the T-A curves are typical. Introducing clustering we could explain this behavior by assuming that there exists a modification of a certain cluster (“F”-cluster) containing F molecules which can disappear in the water below the surface layer. Thus we exclude squeeze-out in which molecules move to above the water-air interface. When the surface compression is performed slowly, once the clustering is gone so far that “F”-clusters appear by clustering, these clusters would transform into soluble clusters and disappear into the water causing a horizontal part in the T-A curve.
729
When the compression is going too fast, it might occur that not all the “F”-clusters are transformed into the soluble form and that bigger clusters are formed. This would lead to the return of the negative slope of the r A curve. A quantitative description of this phenomenon is the purpose of further work of our group.
Conclusions and Discussion We dealt with surface pressure-area (a-A) curves starting from the existence of clusters in the monolayer. Thereto we introduced the equilibrium clustering constant K. With this single parameter, however, we did not succeed in explaining plateaux in the (a-A) curves. The explanation was successful upon assuming that for larger clusters (exceeding m molecules) the equilibrium clustering constant differs from K. The resulting plateaux are more pronounced at high values of m. In addition a parameter G is introduced, accounting for the difference in specific area between molecules in large clusters and molecules in small clusters. With this theoretical description dif€erent phenomena encountered in 7r-A measurements can be coped with without introducing phase transitions.
Micellar Solubilization of 1-Pentanol in Binary Surfactant Solutions: A Regular Solution Approach C. Treiner,* A. Amar Khodja, and M. Fromon Laboratoire d%lectrochimie, U.A. 430 CNRS, Universite Pierre et Marie Curie, BAT.F., Paris 75005, France Received October 1, 1986. In Final Form: January 20, 1987 The partition coefficient P of 1-pentanol between micelles and water has been determined in the cases of a variety of mixed-surfactant solutions in the whole surfactant composition range by using gas chromatography. The following systems have been studied: (I) lithium dodecyl sulfate (LiDS) + lithium perfluorooctanesulfonate (LiFOS); (11) sodium dodecyl sulfate (SDS) + poly(oxyethy1ene) (23) dodecyl ether (POE23);(111) SDS + poly(oxyethy1ene) (4) dodecyl ether (POE4); (IV) sodium decyl sulfate (SDeS) + trimethyldecylammoniumbromide (Cl&r). The solubilizationof the solute in the mixed-surface solutions is calculated from the regular solution theory (applied to a three-component solution) by using the interaction parameter 6 deduced from the same theory as applied to the case of a binary surfactant solution. A positive departure from partition ideality is observed for system I; an almost ideal behavior is observed for system I1 and a larger departure from ideality for system 111; a strongly negative deviation from ideality is displayed with system IV. Thus the sign and magnitude of 0 govern the variation of P with micelle composition only in cases I and IV. In these binary surfactant solutions, 1-PeOH must be distributed throughout the micellar structure; however, in systems I1 and 111, the experimental results suggest a preferential solubilization in the mixed-micelle hydrocarbon core. An application of these findings to microemulsion formulations is suggested. Difficulties with the notion of micellar volume are outlined.
Introduction One of the main uses of surfactants concerns the solubilization in aqueous solutions of otherwise scarcely soluble compounds. A single surfactant can seldom practically achieve this purpose so that two or more surfactants are often needed. This situation is found most often in emulsion technology’ but is of more general concern. For emulsions, the HLB scale serves as a useful semiquantitative tool for the choice of a proper mixture of surfactants to emulsify a given oil; however, not much is known about the solubilization properties of mixed surfactants in homogeneous solutions. A few isolated examples may be
* To whom all correspondence should be addressed. 0743-7463/87/2403-0729$01.50/0
found in the literature concerning micellaP4 or microemulsion solution^.^-^ A great deal of interesting theoretical work has been performed recently on the properties of non ideal mixed surfactant solutions.&l* These studies have prompted us (1) Encyclopedia of Emulsion Technology; Becher, P., Ed.; Marcel Dekker: New York, 1985; Vol. 2. (2) Nishikido, N. J. Colloid Interface Sci. 1977, 60,242. (3) Tokiwa, F.;Tsujii, K. Bull. Chem. SOC.Jpn. 1973, 46, 1338. (4) Treiner, C.;Vaution, C.; Miralles, E.; Puisieux, F. Colloids Surf. 1985, 14, 285. (5) Shincda, K.; Kuneida, H. J. Colloid Interface Sci. 1973, 42, 381. (6) Koukounis, C.;Wade, W. H.; Schechter, R. S. SOC.Pet. Ing. J . 1983, 23, 301. ( 7 ) Haque, 0.; Scamehorn, J. F. J. Dispersion Sei. Technol. 1986, 7, 129.
0 1987 American Chemical Society
Treiner et al.
130 Langmuir, Vol. 3, No. 5, 1987 to investigate the solubilization properties of various mixtures of surfactants using one of the simplest of these theoretical approaches: the regular solution theory (RST).l9 This theory was used12-14to calculate the composition of mixed-surfactant solutions using activity coefficients with a single empirical interaction coefficient W. More sophisticated (and realistic) models have been used which show that the composition of the mixed micelles as calculated by the RST (whose shortcomings are well recognized) are essentially ~ 0 r r e c t . I ~ The advantage of using the RST in the present context is that the theory has been applied to the prediction of the solubility of neutral apolar solutes in binary so1vents.20,z1 It has been shown that as a first approximation the solubility of such a solute may be predicted provided that the solubility of the solute in each pure solvent is known as well as an empirical solvent solvent interaction coefficient, This interaction coefficient is formally the same as the one used in the activity coefficient relationships for the binary surfactant systems; thus the RST could in principle be applied to the solubility of a nonpolar solute in a mixed surfactant system with no extra adjustable parameters and with only the same restrictions as with the binary surfactant systems (without solute). In fact the deficiencies of the theory as applied to classical ternary liquid solutions are known. In general it predicts solubilities of nonpolar solutes larger (in absolute values) than the experimental ones;z1however, the calculation of the solubility of a solute in a mixed-surfactant solution from a detailed physical model seems still a distant goal. Furthermore one of the main features of the RST is that it provides a simple test of the suitability of the theory as a base to further refinements. If the interaction parameter W is positive, then the solubility in the mixed solution should be larger than that predicted by the ideal additivity law. If W is negative, then the solubility should be less in the mixture than that predicted by the ideal law. We have shown recentlyz2that the solubility (in fact the partition coefficient between the micellar solution considered as a pseudophase and water) of l-pentanol was effectively larger in micellar solutions of two mixed binary surfactant solutions, namely, sodium decyl sulfate (SDeS) + sodium perfluorooctanoate (PfONa) and sodium dodecyl sulfate (SDS) + sodium perfluorooctanoate solutions, than in either of the pure micellar solutions, in agreement with the prediction of the RST. The partition coefficients of the solute in each pure surfactant solutions were close to each other, so the partition coefficient in the mixed-surfactant solutions passed through a maximum.
+
(8)Clint, J. H. J. Chem. Soc., Faraday Trans I 1975,71, 1327. (9)Nishikido, N.; Imura, Y.; Kobayashi, H.; Tanaka, M. J . Colloid Interface Sci. 1983,91,125. (10)Rathman, J. F.;Scamehorn, J. F. Langmuir 1986,2, 354. (11) Hall. D.G.:Huddleston. R. W. Colloids Surf. 1985.13. 209. (12)Rubingh, D: N. In Solution Chemistry of Surjactants; Mittal, K., Ed.; Plenum: New York, 1979;Vol. 1. (13)Holland, P. M.; Rubingh, D. N. J . Phys. Chem. 1983,87,1984. (14)Kamrath, R. F.;Franses, E. I. Ind. Eng. Chem. Fundam. 1983, 22. 2.111 --, - -. (15)Nagarajan, R. Langmuir 1985,1,331. (16)Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, M. Langmuir 1985,I , 347. (17)Osborne-Lee, I. W.; Schechter, R. S.; Wade, W. H.; Barakat, Y. J . Colloid Interface Sei. 1985,108, 60. (18)Mivaeishi, S.; Ishibai, Y.; Asakawa. T.; Nishida, M. J. Colloid Interface Sc; 1985,103, 164. (19) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. In Regular and Related Solutions; Van Nostrand-Rheinhold: Princeton, NJ, 1970. (20)O'Connell, J. P.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1964, 3,347. (21)O'Connell, J. P. IChE J . 1971,17,658. (22)Treiner, C.; Bocquet, J. F.; Pommier, C. J.Phys. Chem. 1986,90, 352.
The empirical parameter W was positive in these cases due to the well-known phobicity effect of hydrogenated and fluoro moieties.lg The calculated partition coefficients were larger than the experimental ones as with classical liquids and the polar character of the solute did not seem to introduce further difficulties. These findings seemed interesting enough to envisage an extension of the study to the investigation of various mixed-surfactant systems: two anionic + nonionic systems (with the same slightly negative W values and very different chain length), one mixed anionic + cationic system with very negative W value, and finally a binary system of hydrogenated and perfluorated anionic surfactants with again a positive W value. The solute is 1-pentanol (1PeOH), a model compound in many studies on micellar solutions and on microemulsions (as a cosurfactant). We used a gas chromatographic method for the determination of the partition coefficients.
Materials and Technique T h e sources of the surfactants were as follows: SDS, SDeS, and lithium dodecyl sulfate (LiDS) were from Merck and used without purification. T h e cmc's of the surfactants in water a t 25 "C were 0.0081, 0.0317, and 0.0085 mol/kg, respectively, as deduced from conductance measurements. This was considered as the purity criterion. LiFOS, a gift from PCUK, had a cmc of 0.0064 m ~ l / k g . ~ ~ Trimethyldecylammonium bromide (C,,Br) was obtained from Eastman Kodak and recrystallized 3 times from pure acetone (cmc = 0.066 mol/kg). T h e two poly(oxyethy1ene) dodecyl ether surfactants used had 23 (POE23) and 4 (POE4) oxyethylene groups, respectively. They were both from Aldrich. HPLC analysis in the case of the liquid POE4 showed a symmetric distribution around 4.0 oxyethylene groups. T h e cms's were determined from surface tension experiments and found equal to 0.000 065 and 0.000 04 mol/kg for POE23 and POE4, respectively. 1-Pentanol was a product of Fluka (purum). The gas chromatograph was from Girdel (Model 3000) and was equipped with a gas-flame detector. The temperature of the oven was in the range 130-160 O C . Helium, the carrier gas, was used a t a flow rate of 12 mL/min. The column was described before."
Results and Discussion Experimental Procedure. The experiments were performed as follows: 1-PeOH was solubilized in pure water or in a water + salt solution in a 500-mL flask immersed in a thermostat at 25 f 0.02 O C . A stream of helium gas was gently blown on the solution surface at a rate of approximately 50 Ml/min. A set of 3-5 chromatograms were taken, the peak areas being determined by an electronic integrator. The pure solid surfactant was then poured into the solution or added through a Hamilton syringe in the case of the liquid POE4 and a new set of chromatograms taken. The second surfactant was then added to the solution by successive amounts until the mole fraction of surfactant 2 was around 0.6. Then the same procedure was adopted with surfactant 2 as the pure surfactant. The two sets of r e s u l t s o v e r l a p p e d nicely in all cases studied. The partition coefficient (the ratio of solute mole fraction in the micellar and in the aqueous phases) was calculated from the expression24 P= (Ao/A)((l - A/Ao)55.5)/(C, - C, + C N E ( 1 - A/Ao)) (1) ~
(23)Treiner, C.; Chattopadhyay, A. K. J . Colloid Interface Sci. 1984, 98, 447. (24)Fromon, M.; Chattopadhyay, A. K.; Treiner, C. J . Colloid Interface Scc. 1984,102, 14.
Solubilization of 1-Pentan01 in Binary Surfactants
Langmuir, Vol. 3, No. 5, 1987 731
where A and A" represent the areas under the peaks in the Table I. Partition Coefficient P (Mole Fraction Scale) of 1-PeOH in the Mixed-Surfactant System LiDS (a = 0) + presence and in the absence of surfactant, respectively, LiFOS whose total concentration is CT, CNE is the 1-PeOH concentration, C, is the concentration of surfactant monoa X" P a X@ P mers, a quantity which, for a single surfactant is identical 0.0 0.0 900 0.597 0.64 940 with the critical micelle concentration; for a mixed sur0.0258 0.01 890 0.623 0.67 920 0.0645 factant C, and the cmc might be very different from one 0.03 940 0.700 0.81 820 0.106 0.06 1010 0.787 0.90 750 another. It is the case with the mixed SDS + nonionic 0.11 1020 0.181 0.827 0.93 730 systems. Here, the monomer surfactant concentration with 0.298 0.25 1070 0.883 0.96 670 the highest cmc will increase above the cmc, whereas the 0.355 0.33 1090 0.969 0.99 610 monomer surfactant concentration with the lowest cmc will 0.414 0.41 1040 1.0 1.0 650 remain constant or may even d e ~ r e a s e . ~ 0.520 0.55 990 In the present cases (SDS + POE23 and SDS + POE4) The z values were calculated (eq 2) at different total surfactant the following procedure was adopted: the dodecyl sulfate concentrations (see text). monomer concentration was calculated knowing the stoichiometric concentration of each component, the micelle Table 11. Partition Coefficient of 1-PeOH in the composition as a function of total surfactant concentration Mixed-Surfactant System SDS (a = 0) + POE23 (see below), and the cmc of the binary surfactant solutions. a X P a X P The nonionic monomer concentration was considered 0.0 0.0 785 0.451 0.47 480 negligibly small as the smallest nonionic surfactant con0.0124 0.0147 740 0.500 0.52 500 centration was at least 10 times the cmc. In the other cases 0.0466 0.062 670 0.600 0.62 490 studied, the monomer surfactant concentration was cal0.1007 0.127 565 0.700 0.71 450 culated above the mixed-surfactant cmc. 0.1792 0.22 540 0.800 0.81 460 0.350 0.37 500 1.0 1.0 460 Equation 1 is based on the pseudophase model and 0.366 0.39 480 assumes that Henry's law applies to the vapor pressure of the solute in the micellar solution and in water. This raises Table 111. Partition Cofficient of 1-PeOH in the question of the exact meaning of the concentration of Mixed-Surfactant Systems solute in the pseudomicellar phase. The present experia X P a X P mental technique avoids the problem by assuming that the POE23 (a = 0) + POE4 vapor pressure (the peak area) is proportional to the solute 0.0 0.0 460 0.654 0.66 360 concentration (see the Appendix). 0.174 0.18 440 0.732 0.74 380 It was verified that under our experimental conditions 0.387 0.39 410 1.0 1.0 280b (below 0.03 mol/kg of 1-PeOH), P may be considered as 0.512 0.51 340 a real thermodynamic constant, i.e., does not change with SDS (a = 0) + POE4 solute concentration. Above approximately 0.05 mollkg 0.0 0.0 785 0.115 0.16 600 this is no longer valid. 0.015 780 0.147 0.21 600 0.0087 Finally a special problem arose with the SDS POE4 0.0159 0.026 760 0.405 0.44 460 system. The nonionic surfactant is poorly soluble in water 0.031 0.050 740 0.500 0.52 460 so that 1-PeOH solubilization measurement in the pure 0.080 710 0.592 0.61 410 0.051 0.090 0.13 630 0.695O 0.70 380 aqueous surfactant solution was not possible. Thus mixed solutions of POE4 + POE23 surfactants were prepared. Surfactant solubility limit. *Value obtained by extrapolation. This system behaves almost ideally as far as solute solubilization was concerned so that a linear extrapolation of were not obtained. As they are necessary for the P callog P values vs. mixture composition to pure POE4 soluculation according to eq l , the following procedure was tions was possible from the POE4 + POE23 results. adopted. Micellar Composition. The stoichiometric composiThe cmc for a mixed surfactant system in absence of tion a is the practical scale in our experiments; however, added electrolyte is related to the micellar composition x the only physically meaningful scale is the micellar comby the r e l a t i ~ n s h i p ~ ~ position x , which may be different from a,the difference C,(l+K%)= c1(l+KdflX + C2(1+Kdf2(1 -x) (5) between these two variables being a function of the quantity CT - C,. The parameter x can be calculated where Kg is an additive interaction parameter which is above the cmc8 by using the following relationship: equal to 0.60 for the LiDS + LiFOS system;ls P was equal x = (-(c~ - A) + ((c, - A)' + ( ~ ~ C T A ) ~ / ~(2) ) ) / ~ Ato 2.218 in the present mixed system. For a given x value, the cmc can be calculated by eq 5 and the necessary rewith lation between x and a may be obtained through Rubingh's expression which is valid only at the cmc: A = f2C2 - flC1 P = 1n [(Cm4/(ClX)I/(1 - x)2 (6) C1and C2 are the cmc of each surfactant in pure water; the activity coefficient of each monomer within the mixed The value of 0 was equal to -2.6 in the case of the SDS micelle is given by the RST: + POE23 ~ y s t e m .A~ value of -3.912 was adopted for the SDS + POE4 system and of -13.213 for the SDeS + CloBr f2 = exp((W/Rnx2) (3) binary in presence of 0.05 mollkg of NaBr. fl = exp((W/RT)(l (4) The results are presented on Tables I-IV. The accuracy of the P values is of the order of 5 % . Some literature data where WIRT is equal to in Rubingh's article.12 are available for 1-PeOH in a few single aqueous surfactant The P values for the four systems under consideration solutions. In the case of SDS one finds P = 690 by a have been obtained from surface tension (SDS + nonionics4J2and SDeS + C10Br13)or from fluorine spectroscopy (25) Shinoda, K.; Nomura, T. J. Phys. Chem. 1984, 84, 365. data (LiDS + LiFOS).ls In the latter case the cmc values (1
+
a
732 Langmuir, Vol. 3, No. 5, 1987
Treiner et al.
Table IV. Partition Coefficient of 1-PeOH in the Mixed-Surfactant System Cl@r (CY = 0) SDeS in 0.05 mol/ka NaBr
+
~~
LY
X
P
a
X
P
0.0 0.00136 0.0029 0.0145 0.0298 0.0561 0.106 0.182
0.0 0.00035 0.007 0.034 0.06 0.10 0.16 0.23
520 520 520 440 440 380 310 280
0.300 0.659" 0.758" 0.841" 0.909" 0.975" 1.0"
0.33 0.65 0.74 0.81 0.88 0.96 1.0
260 350 360 400 460 530 610
L
-.-. -..- - _ _ _ _ _ _- -_- fP = -26
300.
" Turbid region. 1
1-
_---__
*..\.
I
00
-
X
_ e
-
a5
1.0
Figure 2. Partition coefficient of 1-PeOHbetween micellar phase and water as a function of mixed-micelle composition, SDS + POE23; dotted lines, eq 10; ideal mixing, 0 = 0.
J pz2.1
12001
I
\ 600. 1
0
05
X
10
-
Figure 1. Partition coefficient of 1-PeOHbetween micelles and water as a function of mixed-micelle composition,LiDS + LiFOS; dotted line, eq 10. method based on Krafft point m e a s ~ r e m e n t sP, ~=~ 722 deduced from a gas chromatograph method,%and P = 760 from the present study. The agreement is satisfactory. Finally an indirect method of partition determination based on the measurement of the rate of change of surfactants cmc's upon addition of alcohols was proposed by Nishikido et aLZ7for the case of poly(oxyethy1ene)dodecyl ether compounds. The surfactants used had 6,11,20, and 41 oxyethylene groups. The results recalculated according to the present definition of a partition coefficient were the following for 1-PeOH: 160, 160, 380, and 450, respectively. Nishikido's data are in reasonable agreement with ours in the case of POE23 ( P = 460 in the present work) but somewhat too small for the lower surfactant homologues ( P = 280 as deduced from the present work for POE4).
r
1 0.0
X
10
05
c
Figure 3. Partition coefficient of 1-PeOHbetween micellar phase and water as a function of mixed-micelle composition, SDS + POE4; dotted lines, eq 10; ideal mixing, 0 = 0. I
Discussion It has been shown beforemthat the Henry's law constant for a nonpolar gas in a binary mixed solvent may be calculated by the expression In H , = x In HI (1 - x ) In Hz - Px(l - x ) (7) where the H's are Henry's constant in the mixed solvent and each pure solvent. 0 is the same interaction parameter as appearing in eq 3,4, and 8. In terms of the gas mole fraction solubility z , eq 7 becomes In z, = x In z1 + (1 - x ) In z2 + Bx(l - x ) (8) Applying the pseudophase model with the partition coefficient defined as
+
p = Z(",l,2)/ZW
(9)
(26) Hayase, K.; Hayano Bull. Chem. SOC.Jpn. 1977,50, 83. (27) Nishikido, N.; Moroi, Y.; Uehara, H.; Matuura, R. Bull. Chem. SOC.Jpn. 1974, 47, 2634.
Figure 4. Partition coefficient of 1-PeOHbetween micellar phase and aqueous 0.05 M NaBr solution as a function of mixed-valence
composition, SDeS + CloBr; dotted line, eq
10.
m, 1,2, and w refer to the solubility in the mixture, in each pure micellar solution and in water. Replacing in eq 8, one gets In P, = x In PI + (1 - x ) In P2 + Px(1 - x ) (10) In eq 10, x refers to the composition of the mixed micelles. For reasons noted before, x is close to a in the mixed ionic + nonionic systems because of the relatively high surfactant concentrations employed and their low cmc values. A general observation is of interest on considering Figures 1-4. The P = f ( x ) profiles resemble the plots rep-
Solubilization of 1 -Pentan01 in Binary Surfactants resenting the cmc variation with surfactant composition: a maximum with the hydrogenated + fluorinated system% as in Figure 1, a decrease followed by a leveling off with the anionic/non ionic systems4 as in Figures 2 and 3, and rapid changes at both ends of the diagram as for the cationic anionic system of Figure 4. This general result follows from an examination of eq 6 and 10. Equation 10 predicts that the variation of P with x should be governed by the sign and magnitude of the p parameter, Le., by the type of interactions between the two mixed surfactants. We shall examine the results of the different mixed systems successively and then summarize our essential findings. We recall that throughout this paper, the term mixed micelle is applied to the aggregates formed by two different surfactants. 1. LiDS + LiFOS. This mixed hydrogenated + fluorinated system behaves identically with the SDS + PfONa and SDeS + PfONa binaries studied before.22 A positive deviation is observed as a consequence of the positive value of the interaction parameter 0. The calculated P values are larger than the experimental ones. As noted in the Introduction section, this behavior as been observed for apolar gases in mixed solvents and therefore cannot be considered as due to the peculiarities of the micellar system. In a series of recent papers, Amidon et al.29have used the same approach for the prediction of the solubility of drugs in mixed solvents but with a more sophisticated treatment of the activity coefficient of each solvent based on Wohl’s equations. Furthermore they have added an empirical solute + solvent interaction term. Such refinements are certainly necessary with the present system as well, although they will be of a more complicated nature. The structure of the mixed micelles formed by perfluorinated and hydrogenated surfactants has been the subject of recent debate^.^&^^ According to the RST, two types of mixed micelles of different composition should coexist when 0> 2. This is called a demixing effect. The 0values of the mixed-surfactant systems studied were for SDeS PfONa, +1.8;25for SDS + PfONa, and, for LiDS + LiFOS, +2.2.18 However, the consequences of such a demixing effect on the P = f ( x ) profile depends on too many unknown parameters to be usefully discussed. 2. SDS + POE23 and SDS + POE4. The situation appears more complicated in the mixed anionic nonionic systems than in the previous mixtures as shown on Figures 2 and 3. A series of observations should be made. The P = f ( x ) profile is similar for the two mixed-surfactant systems and differences appear essentially when comparison is made with the prediction of the RST. Furthermore, we note again that the predicted values are lower than the experimental ones as observed with classical fluids in almost all the surfactant composition range. The ideal line has also been drawn on Figures 2 and 3. In fact, P = f ( x ) follows this line in the whole composition domain for SDS POE4 and remains only close to it in the nonionic-rich surfactant domain for the SDS + POE23 system. It is interesting to recall that some years ago Nakagawa and I n ~ u had e ~ deduced ~ from light-scattering experiments a number of physical parameters for the system SDS +
+
+
+
+
(28) Carlfors, J.; Stilbs, P. J . Colloid Interface Sci. 1985, 103, 332. (29) Williams, N. A.; Amidon, G. L. J. Phurm. Sci. 1984, 73, 14. (30) Mukerjee, P.; Yang, A. Y. S . J. Phys. Chem. 1976,80, 1388. (31) Funasaki, N.; Hada, S. J . Colloid Interface Sci. 1980, 78, 376. (32) Mukerjee, P.; Handa, T. J . Phys. Chem. 1981,85, 2298. (33) Nakagawa, T.; Inoue, H. J . Chem. SOC.Jpn., Pure Chem. Sect. 1957, 78, 636.
Langmuir, Vol. 3, No. 5, 1987 733 POE23 in 0.4 mol/kg NaCl solution. For example, the effective charge of the mixed micelles ( q / e ) ,where q and e have their usual meaning, decreases from 29 in aqueous SDS solutions (a= 1)to 7 for a = 0.6 and remains constant thereafter before dropping to 0 for a = 0. The constant domain corresponds essentially to that for which P = f ( x ) decreases ideally to the pure nonionic solution. Electrostaticlo and molecular15models of mixed surfactant cmc calculations have recently shown that the variation of cmc in the mixed anionic + nonionic systems is essentially due to surface electrostatic effects. Furthermore the interaction of a poly(oxyethy1ene) chain with a sulfate head group has been estimatedMas equal to about -40 kJ/mol, a rather important energetic change suggesting weak complex formation. Figures 2 and 3 show clearly that the same conclusions apply to the solubilization phenomenon, again as suggested by eq 7 and 10. The specific effect due to the polar character of 1-PeOH does not seem to introduce a distortion on the P = f ( x ) profile; this effect must be either small or could probably be taken care of by a constant solute + solvent interaction term. Such a procedure would, however, not be worthwhile at the present time. The interaction coefficient p is certainly not a constant in the whole range of surfactant composition when the total surfactant concentration greatly exceeds the cmc. It is only so within the RST model which may only be considered an acceptable approximation because of the difficulty of the precise determination of the interaction ~0efficient.l~ The study by Nishikido2 on the solubility of an anionic dyestuff, yellow OB, in mixed systems of manganese dodecyl sulfate and various dodecyl poly(oxyethy1ene) surfactants (POE6, POE29, POE49) is of special interest here. This author found that for longer oxyethylene chain length the dye solubility in the binary surfactant mixture was somewhat larger than for the ideal mixture. Although the value of the /3 parameter is not known for these systems, it should be negative as with all SDS nonionic systems studied, a result which seems to contradict the prediction of eq 10. However, it must be pointed out that yellow OB is a very large molecule which upon solubilization within the micellar structure might be greatly modified. In the RST formalism, one would postulate that the value of the 0parameter changes with dye molecule penetration. The direction of that change will most likely be toward less negative p values as there will be less contacts between both type of surfactant molecules. These considerations indicate the limits of applicability of eq 10 to be mixedsurfactant aggregates. The average number of 1-PeOH molecules per micelle N , can be estimated in the case of the SDS + POE23 system under our experimental conditions. Knowing again from light-scattering data the number N of monomers per mixed micelle, the total amount of solute and the peak areas in the presence and in the absence of surfactant, N,, is found equal to around 5 throughout most of the micelle composition range, down from about 20 in pure SDS solutions. These values are somewhat underestimated because the light-scattering experiments were performed in the presence of 0.4 mol/kg of NaC1, thus increasing the number of monomers per mixed micelle at high SDS micellar content. 3. SDeS + CloBr. The last case studied concerns a mixture of a cationic and an anionic surfactant in the presence of 0.05 mol/kg of NaBr. Upon addition of a given amount of any surfactant component to the other, the
+
(34) Moroi, Y.; Nishikido, N.; Saito, M.; Matuura, R. J. Colloid Interface Sci. 1975, 52, 356.
734 Langmuir, Vol. 3, No. 5, 1987
Treiner et al.
solution becomes slightly turbid. Upon further addition an unstable emulsion is formed a t total surfactant concentration well exceeding the cmc. The experiments were performed over the slightly turbid region only. As p is very negative (-13.2), the calculated P values approach zero around x = 0.5. The experimental P values decrease very drastically as eq 10 predicts at both ends of the binary diagram; within the region defined by 0.05 C x C 0.92, the calculated P values are much smaller than the experimental ones; as noted before, this is a general characteristic of eq 10 for a negative P interaction coefficient. Note also that the rate of change of P with surfactant composition is slightly larger in the anionic-rich region than in the cationic-rich one. This situation reflects the profound electrostatic changes occurring at the mixed-micellar surface where most 1PeOH molecules are supposed to be located (the palisade layer). 4. General. The discussion of the experimental results has so far been limited to comparisons with the prediction of eq 10. This approach could be misleading. One of the main differences being a binary classical solvent and the mixed-surfactant micelles is that one may consider in the former case that all portions of the solvent molecules have essentially the same probability of contact with the solute molecules. This is not totally correct as preferential solvation effects, especially when ions are concerned, will change that probability through a modified radial distribution function. The situation is even more complicated in a micellar solution. The location of a polar solute molecule depends on the charge and/or the polarity of the surfactant and the solute. The protection of drugs against hydrolysis according to the charge of the ionic micelles in which they are solubilized is a clear example of this effect.35 On the other hand, Praipaitrakul and King%have shown that the solubility of a hydrocarbon gas in anionic and cationic ionic micellar solutions depends on the hydrocarbon chain length of the solute and the surfactant but not on the surfactant ionic charge. This is due to the hydrocarbon gas preferential solubilization in the micellar hydrocarbon core. Insofar as the nonideal contribution to solubilization in eq 10 is reflected (as with the micelliiation process) only on surface changes, one may predict that the solubility of an apolar gas should follow the ideal behavior in mixedsurfactant systems such as the anionic + nonionic and the anionic + cationic ones. On the other hand, the solubility of an apolar hydrocarbon molecule should be highly nonideal in the case of the hydrogenated fluorinated surfactant mixture, as the solute molecule should solubilize in the apolar core of the mixed micelles and therefore participate in the repulsion interaction between hydrocarbon and fluorocarbon moieties. The complexity of the solubilization behavior of a polar molecule such as 1-PeOH follows, if correct, from the above analysis. In the hydrogenated + fluorinated system, the interaction coefficient governs semiquantitatively the solubilization behavior of 1-PeOH; thus the solute should be considered as partly located in the mixed hydrocarbon + fluorocarbon micellar core where the repulsion interaction takes place. With the ionic + nonionic systems, 1-PeOH follows rather closely the ideal mixing law for the SDS + POE4 system which may only mean that the solute is
+
(35) (a) Mitchell, A.G. J.Pharm. Pharmucol. 1964,16,43. (b) Lattes, A. In Galenica No. 5; Puisieux, F., Seiller, M., Eds.; Techniques et documentations: Paris, 1983. (36) Praipaitrakul, W.; King, A. D., Jr. J. Colloid Interface Sci. 1985, 106,186.
solubilzed in the hydrocarbon core of the binary micelle where the two hydrocarbon surfactants mix ideally. The apparent complications observed with the SDS POE23 binary might be the consequence of the important asymmetry of the system. Finally the interaction parameter describes semiquantitatively the solubilization behavior of 1-PeOH in the mixed anionic + cationic system. This implies that the solute location site should be close to the micellar surface where ion ion interactions are responsible of the highly nonideal behavior of the binary system. The main conclusion which may be drawn from these observations is that the type of solubilization behavior of a simple molecule such as 1-PeOH cannot be unambiguously predicted solely by considerations of the sign and magnitude of the interaction parameter except in extreme cases when it takes a positive or a highly negative value. If /3 is close to zero, such as with mixed cationic + nonionic ~urfactants,'~ there is a high probability that an ideal solubilization behavior will be observed with hydrophobic molecules such as aliphatic or aromatic alcohols. Although many points concerning the solubilization phenomenon in mixed surfactant systems remain at best obscure, the present approach based on the regular solution theory may have some practical applications. It is interesting to note, for example, that iri a recent study on microemulsion formation using a mixture of anionic and cationic surfactants in the presence of a co~urfactant,~' it has been observed that a hydrocarbon oil is less solubilized when mixed surfactants are used than with either pure surfactant; this experimental observation could be looked upon as an evidence in favor of the above analysis; as the above example concerned a system studied at much higher concentration of all components than in our model system, the P parameter might be a useful guideline on the micellar solubilization of apolar or slightly polar molecules in mixed-surfactant systems.
+
+
Appendix The solute concentration in the case of a molecule solubilzed in a surfactant pseudophase is an ambiguous quantity which raises the question of the meaning of a micellar volume. This is especially true in the case of nonionic surfactants with an extensive number polar groups such as POE23. The problem has been avoided in the present case by making use of the vapor-phase activity, but it should be faced if the P values were to be expressed (for practical or theoretical reasons) on a molar basis. The basic equation is P(c) = (V€I,O/V,)P(~) (11) where the indices H 2 0 and M refer to the partial molar volumes of the aqueous and micellar phases, respectively. P(c) and P ( x ) are the partition coefficients on the molar and mole fraction scales. The partial molar quantities of most of the surfactants used are known or can be estimated. For example, from the density data of Funasaki et al.,= the V value of POE23 .~~ is 1121 cm3mol-l; that of SDS is 250 ~ m ~ / m o l - ' Thus, the P(x) value of 1-PeOH should be divided by 13.9 for SDS in order to be expressed in the P(c)scale, and by 62.3 for POE23. In the case of POE4, the correction factor as deduced from density data38is only 13.3;the consequence (37) Bourrel, M.; Bernard, D.; Graciaa, A. presented at "The World Congress of Surfactants";Munich, GFR; 1984. (38) Funasaki, N.; Hada, S.; Neya, S. J.Phys. Chem. 1984,88,1243. (39) Brun, T.S.;Hoiland, H.; Vinkingstad, E. J . Colloid Interface Sci. 1978, 63,89. Ismail, A. A.; Motawi, M. M. J . Pharm. Sci. 1970, (40) Gouda, M. W.; 59, 1402.
135
Langmuir 1987, 3, 735-131
that of the monomer surfactant. We may apply crudely is the following: the P value of 1-PeOH is larger in POE23 this finding to micellar solubilization in the case of POE23 than in POE4 solutions when expressed on the mole fraction scale (460 and 280, respectively) but the reverse by assuming that beyond the value of 6, the EO groups do is found if the molar scale is considered (7.4 and 13.3). not participate to the solubilization process. This hypothesis is not physically unsound for the particular solute Similar situations when different concentration scales are considered are not uncommon in the l i t e r a t ~ r e . ~ ~studied ~ ~ ~ considering the close P ( x ) values with the two nonionic surfactants studied. POE23 might be considered Interpretations have been proposed which take into account the relative size and number of monomers per agthen as a hypothetical POE6 surfactant (keeping of course gregate for nonionic surfactants with the increase of the the same experimental P ( x ) value): using the correoxyethylene chain length.@ However, the specific problem sponding partial molar volume we obtain P(c) = 18.1. The to deal with is that of the ill-defined notion of the micellar P trend for POE4 and POE6 (or POE23) is now the same volume phase which might lead to calculation artifacts. An on both mole fraction and molar concentration scales, a more reasonable situation than the previous one. alternative to previous approaches is suggested below. Studies of the cmc of nonionic surfactants series with Thus one of the main advantages of gas chromatography various oxyethylene (OE) chain length^^^.^^ have lead to over other methods of solubilization determination is the the suggestion that beyond a number equal to 6, the oxdirect measurement of vapor activity in the mole fraction yethylene groups' free energy properties are identical with scale, avoiding the complex evaluation of the micellar volume phase necessary for molar basis partition coefficients. (41)Barry, B. W.; El Eini, D. I. D. J. Pharm. Sci. 1976, 28, 210. Registry No. LiDS, 2044-56-6; LiFOS, 29457-72-5; SDS, (42)Nishikido, N.; Moroi, Y.;Matuura, R. Bull. C h m . SOC.Jpn. 1975, 151-21-3; POE23, 9002-92-0; SDeS, 142-87-0; POE4, 5274-68-0; 48,1387. (43)Ray, A.; Nemethy, G. J. Phys. Chem. 1971,75,809. 1-PeOH,71-41-0; CloBr, 2082-84-0.
Dynamic Structure of a Nonaqueous Lamellar Liquid Crystal: Comparison with the Aqueous Case Stig E. Fribergt and Anthony J. I. Ward* Chemisty Department, University of Missouri-Rolla,
Rolla, Missouri 65401
David W. Larsen Chemistry Department, University of Missouri-St.
Louis, St. Louis, Missouri 63130
Received November 1, 1986. I n Final Form: January 16, 1987 The lamellar phase of sodium dodecyl sulfate/decanol/glycerol has been compared to the analogous water-based system. Results of NMR studies of deuteriated alcohol and surfactant showed the bilayer to be more disordered in the nonaqueous case than in the phase made with water. The order profiles of the two systems, however, were of the same form, implying that the same essential packing requirements applied to each case. The overall increase in dynamic disorder observed in the glycerol system is a result of a transversely more disordered bilayer/solvent interface.
Introduction Recent attention has been focused upon the associated surfactant phases formed in nonaqueous The structure and dynamics of these systems have not been characterized to the extent found for comparable aqueous systems."12 It is obvious that a direct comparison with a well-characterized aqueous system13such as waterlionic surfactant/long-chain alcohol would give insight to some of the consequences of changing the solvent. This preliminary paper presents, to the best of our knowledge, the first comparison of water- and glycerol-based lyotropic lamellar liquid crystals stabilized by a combination of an ionic surfactant (sodium dodecyl sulfate) and a long-chain alcohol (n-decanol). 2H NMR spectroscopy has been utilized to give the order parameter profiles of the bilayer interiors of both systems.
* Address correspondence to this author a t Chemistry Department, University College, Dublin, Belfield, Dublin 4, Ireland. Permanent address: Chemistry Department, Clarkson University, Potsdam, NY 13676.
Experimental Section Sodium dodecyl sulfate (SDS) from BDH Chemicals was recrystallized twice from ethanol and the n-decanol (Aldrich (1)Moucharafieh, N.;Friberg, S. E. Mol. Cryst. Liq. Cryst. 1979,49, 231. (2) Evans, D. F.; Kaler, E. W.; Benton, W. J. J. Phys. Chem. 1983,87, 533. (3) Larsen, D. W.; Friberg, S. E.; Christenson, H. J. Am. Chem. SOC. 1980.102.6565. (4)Ganzuo, L.; El-Nokaly, M.; Friberg, S. E. Mol. Cryst. Liq.Cryst. 1982. . 183. --,72 -, ~ - (5) Larsen, D. W.; Rananavare, S. B.; Friberg, S.E. J.Am. Chem. S O ~ . 1984,106,1848. (6) El-Nokaly, M.; Friberg, S. E.; Larsen, D. W. J. Colloid Interface Sci. 1984,98,274. (7) Fribera. S. E.: Liana P. Colloid Polvm. Sci. 1986,264. 449. (8) Rico, E; Lattes, A. &ouv. J. Chim. i984,8,429. (9) Rico, I.; De Savignac, A.; Ahmadzadeh, A.; Lattes, A. Presented at the International Workshop on Microemulsions, June 6-8,1984, Chemical Center, University of Lund, Lund, Sweden. (10)Tiddy, G. J. T. Phys. Rep. 1980,57,1. (11) Lindman, B.; Wennerstrom, H.,Phys. Rep. 1979,52,1. (12) Lindman, B.; Wennerstrom, H. Topics in Chemistry No. 8 7 Micelles; Springer-Verlag: Berlin, Heidelburg, New York: 1980; p 1. (13) Ekwall, P.Aduances in Liquid Crystals; Brown, G. H., Ed.: Academic: New York, 1975; p 1.
0743-7463/87/2403-0735$01.50/0 0 1987 American Chemical Society
