736
J. Phys. Chem. 1980, 84, 736-744
to the fact that &(t)now contains more than one relaxation time. These values of T,”, are also plotted in Figure 15 vs. a. Further it should be pointed out that there are very asymmetric micelle distributions still satisfying the condition for a single relaxation time. Therefore experimental situations can exist where a single relaxation time is present and the plot 1/7 vs. a is curved a t least in the neighborhood of the cmc. In conclusion of this section we can say that it is necessary to move very far from the condition for a single relaxation time in order to obtain a relaxation spectrum containing a substantial contribution to the fast process from more than one relaxation mode.
Natural Science Research Council is gratefully acknowledged.
Supplementary Material Available: Calculation of the concentration dependence of 4; values, further material on eigenvectors and their properties, the movements of AB, the time developments of a whole relaxation process and the amplitudes, equations describing T ( & ) for large deviations from equilibrium, and the distribution function, rate constants, and 4; values for the case treated in section 10 (20 pages). Ordering information is available on any current masthead page. References and Notes (a) E. A. G. Aniansson and S.N. Wall, J . Phys. Chenr., 78, 1024 (1974); 79, 857 (1975); (b) “Chemical and Biological Applications of Relaxation Spectroscopy”, E. Wyn-Jones, Ed., Reidel, New York, 1975, pp 223-238. R. Folger, H. Hoffmann, and W. Ulbricht, Ber. Bunsenges. Phys. Chem., 78, 986 (1974); E. A. G.Aniansson, S. N. Wall, M. Almgren, H. Hoffmann, I.Kieimann, W. Ulbricht, R. Zana, J. Lang, and C. Tondre, J . Phys. Chem., 80, 905 (1976). (a) S.-K. Chan, U. Herrmann, W. Ostner, and M. Kahlweit, Ber. Bunsenges. Phys. Chem., 81, 60 (1977); (b) ibid., 81, 396 (1977); 82, 380 (1978); S.-K. Chan and M. Kahlweit, ibid., 81, 1294 (1977). (a) 6. W. Gear, “The Automatic Integration of Stiff Ordinary Differential Equations”, Proceedingsof the I.F.I.P. Congress, 1968; (b) Harwell Subroutine Library, compiled by M. J. Hopper, Theoretical Physics Division U.K.E.A. Research Group, Atomic Energy Research Establishment, Harweli, Didcot, England, 1973. (a) “International Mathematical and Statistical Libraries, Inc.”, 4th ed,1974, Houston, Texas. (b) J. H. Wilkinson and C. Reinsch, “Linear Algebra”, Springer-Verlag, West Berlin, 1971. M. Almgren, E. A. G. Aniansson, and K. Holmaker, Chem. Phys., 19, 1 (1977). S.Wall, Thesis, Goteborg, 1977. H. Hoffmann,R. Nagel, G. Platz, and W. Ulbricht, Co/ioU Polym. Sci., 254, 812 (1976). E. A. G. Aniansson, Ber. Bunsenges. Phys. Chem., 82, 981 (1978). E. A. G. Aniansson and S.Wall, Ber. Bunsenges. Phys. Chem., 81, 1293 (1977).
11. Final Remarks All computer calculations show that the flow analogy underlying the theoretical treatment correctly predicts the character of the relaxation processes sketched in section 2. The proper approximations suggested by this analogy for the analytical solution of kinetic eq 3-5 are found to yield very accurate results. Thus the relaxation times predicted for the slow process agree with the numerical solutions to within 1%. The agreement is even better when the minimum in k;AB is deeper. The replacement of differences by derivatives in the treatment of the fast process is found to be remarkably accurate even for very narrow micelle distributions. Finally, it should by now be abundantly clear that the notion of Chan et aL3 of an s independence of the [& values in the micellar region during the slow process is entirely erroneouslo as is, consequently, also the expression for the slow relaxation time deduced therefrom.
Acknowledgment. The financial support by the Swedish
Coexistence of Two Kinds of Mixed Micelles‘ Norlakl Funasaki” and Sakae Hada Kyoto College of Pharmacy, Yamashina-ku, Kyoto 607, Japan (Received February 26, 1979; Revised Manuscript Received August 8, 1979) Publication costs assisted by the Kyoto College of Pharmacy
The surface tension y of mixed fluorocarbon (NF) and hydrocarbon (STS) surfactants was measured in 0.01 and 0.05 M sodium chloride solutions, and two kinds of mixed micelles were found to coexist in equilibrium. The micellar composition x, was determined from the surface tension data on NF-STS solutions above the cmc. In the relation between the y at the cmc and xm, a plateau region was observed, and both ends of this region represent the mutual solubility of NF and STS in the mixed micelles. The cmc vs. monomeric composition curve breaks where two micellar phases coexist. In the relation between the y at the cmc and the composition of adsorbed monolayers on aqueous solution, there was no plateau region, indicating the complete miscibility of NF and STS in the adsorbed monolayers. From the temperature dependence of mutual solubilities in 0.01 M sodium chloride solution, the critical solution temperature was shown to exist in the NF-STS comicellar system. This fact demonstrates that micelles have a character of a liquid like phase. A quantitative analysis based on regular solution theory was made in an attempt to explain the relations of cmc to the monomeric and micellar compositions as well as the temperature dependence of the mutual solubility. The major reason for the partial miscibility of NF and STS in the mixed micelles may be the phobicity of the fluorocarbon and hydrocarbon chains in the mixed micelles. The change of electrostatic energy with comicellization, albeit a minor factor, should be taken into account.
Introduction Surfactants (detergents) possessillg a hydrocarbon chain are well-known to be completely miscible in mixed mic e l l e ~ . The ~ * ~critical micelle concentration (cmc) of mixtures of two surfactants which possess the same head group 0022-3654/80/2084-0736$01 .OO/O
and which have hydrocarbon chains that differ in length is well explained on a thermodynamic b a s i ~ . ~Studies t~ on two surfactants with different head groups have also been done.4 Recently, a few systems of two surfactants, one of which 0 1980 American Chemical Society
Coexistence olf Two Kinds of Mixed Micelles
possegses a hydrocarbon chain and the other of which possesses a fluorocarbon chain, have been reported to have a limited mutual solubility in the mixed micelleab7In these systems, anomalous relations between the cmc and the monomeric ~omposition,~ as well as between the differential electric conductance and total surfactant concentration, have been observed,6 and the mutual solubility has been determined from surface tension data.7 This limited solubility in the mixed micelles may be ascribed mainly to the phobicity between the fluorocarbon and hydrocarbon chain^,^-^ as seen in bulk phases.8 To determine the mutual solubility in mixed micelles, one must obtain the composition of mixed micelles by methods such as electric conductance, pNa, and surface t e n s i ~ n As . ~ already discussed, the surface tension method may be most suitable for the purpose of our inve~tigation.~ Since micelles generally show liquidlike properties, the critical solution temperature is expected to exist for mixed fluorocarbon and hydrocarbon surfactants, as is seen for some liquid--liquid mixtures.8 A similar phenomenon may occur in monolayers adsorbed at the air-water interface. Such observations have been reported for spread monolayersgbut not for adsorbed monolayers (st the air-water interface. The present work deals with the surface tension of aqueous solutions of mixtures of Neos Ftergent (NF),'O a fluorocarbon surfactant, and sodium tetradecyl sulfate (STS), a hydlrocarbon surfactant, in the presence of 0.01 or 0.051M soldium chloride. Using the values of crnc and surface tension, we determined the micellar composition. A region in which the surface tension remained unchanged with the micellar composition was observed, and both ends of this region represent the mutual solubility in the mixed micelles. From the temperature dependence of mutual solubilities, the critical solution temperature was shown to exist in the NF-STS comicellar system. Furthermore, both surfact,ants were completely miscible in the mixed monolayers adsorbed a t the air-water interface. The mutual solubility in the mixed micelle was discussed from the standpoint of thermodynamics, taking into account the phobicity between the fluorocarbon and hydrocarbon chains in the mixed micelles.
Experimental Section Materials. NFlO was donated by Neos Co. and recrystallized three times from acetone. STS was synthesized by the sulfation of 1-tetradecanol (Tokyo Kasei Organic Chemicals Co., 99% or more) with concentrated sulfuric acid and recrystallized several times from ethanol, after extraction with diethyl ether, until the surface tension minima had disappeared. The sodium chloride (Merck) was purified by extraction with diethyl ether and adsorption with active charcoal. The ion-exchanged water was twice distilled just before use. Method. 'The surface tension was measured by the Wilhelmy method, the details of which have already been reported.ll The temperature of all solutions was maintained constant within 0.1 "C of the specified temperature. All surfactant solutions contained 0.01 or 0.05 M of sodium chloride and were used within 6 h after preparation. Results Surface Tension us. Surfactant Concentration Curve. The surface tension y of pure NF and STS in water decreased above the cmc. The addition of 0.01 or 0.05 M sodium chloride, however, kept the value constant, as shown in Figure l a for NF (curve a). A similar observation has already been reported for hexadecyltrimethylammonium bromidea4Hence, all the present work was done in
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980 737
Y
C
.-0
'
-3.5
~
-3.0
-2.5
log Ct(Ct,rnol/L) al
25:\ : 5 23-
'c
VI
(b)
";, t
21 -
log CNF(CNF#mol/L) Figure 1. (a) Typical plots of surface tension against the logarithm of total surfactant concentration at 30 OC where the overall mole fraction, xSTS,of STS is kept constant: curve a, xSTS= 0;curve b, xSTS= 0.097; cutve c, xmS= 0.649. (b) Typical plots of surface tension against the logarithm of NF concentration at 30 O C where the total STS concentration, CsTs(mol/L), is kept constant: curve d, CsTs= 2.01 X curve f, CsTs= 7.60 X curve e, CsTs = 5.75 X
the presence of 0.01 or 0.05 M sodium chloride. Curves b and c shown in Figure l a represent typical plots of surface tension against the total surfactant concentration Ct, where the overall mole ratio of STS and NF was kept constant. Curve b appears to have one kink point whereas curve c has two. On the other hand, in Figure l b the surface tension is plotted against the logarithm of the total NF concentration, CNF,where the total STS concentration is kept constant. At a high STS concentration (curve d), the surface tension decreased more rapidly above the cmc (point N) than below the cmc, as shown by the broken line. At a low STS concentration (curve e), the value decreased more slowly above the cmc (point H)than below the cmc, remained constant at 18.61 dyn/cm within points K and M, and increased asymptotically to that of the pure NF solution with further increases in NF concentration. A t a further low STS concentration (curve f), the surface tension slightly increased above the cmc. No surface tentiions of NF-STS mixtures in 0.05 M sodium chloride solution at 30 "C decreased below 18.61 dyn/cm. The open circles shown in Figure 2 represent plots of surface tension at the cmc against the monomeric mole fraction, q,STS, of STS. These circles are taken from the first kink point in Figure 1,a and b, viz., at a constant mole ratio and a constant STS concentration, and lie along a curve, viz., curve b. The open circles shown in Figure 3 represent plots of cmc's against the monomeric mole fraction of STS, which are taken from the first kink point in Figure 1. In the cmc vs. XbSTS curve of this figure, a maximum and a kink point (E) are observed. A few systems have already been reported to have a maximum C ~ C . ~ , ~ Micellar Composition. Following our method already r e p ~ r t e d , ~one J l can obtain the micellar composition from surface tension data. With this method, it is assumed that for a constant composition of mixed micelles the surface tension remains constant regardless of the number of
738
The Journal of Physical Chemistry, Val. 84, No. 7, 1980
Funasaki and Hada
TABLE I: Amount of Adsorption at the Air- Water Interface ~ N F ~ ~ l't X X
XbSTS
Y, dyn/cm
0.004 0.095 0.168 0.247 0.385 0.488 0.627 0.744 0.755 0.841 0.901
18.80 18.64 18.66 18.73 18.84 19.00 20.81 23.80 24.17 26.61 28.40
cSTS,
1
mmol/L 0.0076 0.0196 0.0367 0.0575 0.1024 0.1435 0.1833 0.2014 0.2035 0.2162 0.2238
I
0
0.2
0.4
0.6 mole fraction of STS
1.o
0.8
Flgure 2. Plots of surface tension at the cmc against the mole fraction of STS in adsorbed monolayers (curve a), in monomers (curve b), and in micelles (curve c). I
I
L
0
0.2
0.4 0.6 mole fraction of STS
I
i
0.8
1
Flgure 3. Plots of cmc against the mole fraction of STS in monomers (curve a) and in micelles (curve b).
micelles. As a result of this assumption, the surface tension of a pure surfactant must be constant above the cmc. This assumption seems justified under the present conditions where the system contains an excess electrolyte. From the material balance of STS in the system, one can obtain the mole fraction, xdm, of STS in micelles from eq 1, where xSTS is the overall mole fraction of STS, viz., XmSTS = (CtXSTS - cmcxbfYl"l')/(Ct- cmc) (1)
+
moles of STS/(moles of NF moles of STS). When two kinds of mixed micelles coexist, the averaged composition of the micelles is calculated from this equation. When applying this equation, one measures the surface tension of a solution with an xSTS composition and at a ca. tenfold higher Ct concentration over the cmc. The monomeric composition, xbSTS,corresponding to this measured surface tension value is interpolated on curve b of Figure 2. Next, the crnc corresponding to this XbSTS value is read from curve a of Figure 3. Thus, one can calculate an XS,TS value by substituting these values into eq 1. Under the present conditions, the deviation of micellar composition from the overall value was ca. 5% or less, A t the compositions less than XE shown in Figures 2 and 3, xS,TS was less than XSTS, whereas above the xE, x,STS was greater than xSTS. The solid circles shown in Figures 2 and 3 represent the plots of the micellar mole fraction of STS thus calculated against the surface tension and the cmc, respectively. In Figure 2, it can be seen that the surface tension remains constant at 18.61dyn/cm within the micellar compositions of X A and xB. This constant surface tension indicates the coexistence of two kinds of mixed micelles with the com-
10 , mol/ cm2 2.08 2.04 2.03 2.01 2.00 1.98 1.95 1.88 1.88 1.33 0.90
1010,
mol/
cm2 2.13 2.18 2.34 2.54 2.86 3.04 3.17 3.23 3.24 3.27 3.28
xaSTS
0.023 0.064 0.132 0.209 0.301 0.349 0.385 0.418 0.420 0.593 0.726
positions of xA and xB. A similar procedure has been employed to determine the miscibility of lipids in spread monolayers at the air-water interfacesg Composition of Adsorbed Monolayers at the Air- Water Interface. In the presence of ionic surfactant DM and uni-univalent salt MX, the Gibbs adsorption equation is written as -dy/RT = rDd In CD + rx d In Cx + rM d In CM ( 2 ) where the activities of all ionic species are assumed to equal the concentrations, When the adsorption of co-ions M is neglected, viz., rM = 0, and the salt concentration C, is kept constant, eq 2 is simplified below the cmc to12 -1
When applying a similar consideration to the system of two surfactants, NF and STS, one can obtain the total surface excess, rt,at a constant CNF/CSTS from eq 4 and
the surface excess of NF, FNF,a t a constant C s ~ from s eq 5. The terms of Ct/(Ct t C,) in eq 3 and 4 and of C,/(Ct
+ C,) in eq 5 were negligible, since the present system contained an excess sodium chloride. The total surface excess I't at the cmc can be calculated by substituting the slope of the y vs. log Ct curve, a t the cmc in Figure la, into eq 4. The surface excess of NF, rNF, at the cmc can be calculated by substituting the slope of the y vs. log CNFcurve, a t the cmc in Figure lb, into eq 5. These values are shown in part in Table I. By the divided circles in Figure 2 , the surface tension at the cmc is plotted against the mole fraction, X ~ S T S of , STS in the adsorbed monolayer. As is evident in curve a, the surface tension changed continuously with the composition of the mixed monolayer, indicating that the phase separation does not occur in the adsorbed monolayer of NF and STS. Coexistence of Two Kinds of Mixed Micelles. Figure 4 shows the relation between the total surfactant concentration and the overall mole fraction of STS, being separated into four regions I-IV by the solid lines. There are no micelles in region I. In region I1 there are NF-rich micelles, whereas in region IV STS-rich micelles are present. In regions I1 and IV, the compositions of coex-
The Journal of Physical Chemistry, Vol. 84, No. 7, 798Q 739
Coexistence of Two Kinds of Mixed Micelles
TABLIE11: Values of Cmc for NF, Mutual Solubilities X A and XB, X E , cmcE, and Molecular Area of Adsorbed NF at Different TemDeratures and Sodium Chloride Concentrations
cs
T , "C
_____ 30 0 30 0 34 0 37 5 40.7 42 0 50.0
mmol/L
XA
XB
50
0.188 0.555 0.600 0.631 0.668 0.690 0.182
0.056 0.065 0.102 0.130 0.164 0.189
0.117
10 10 10 10 10 10
xA
20
-2.5
mmol/L
ANF, A2/molecule
-
0.470 0.424 0.359 0.275 0.234
0.102 0.113 0.154 0.168 0.225 0.209
0.208 0.617 0.708 0.755 0.837 0.855
78 12 73 77 83 86
.
XB
.
.
.
.
Ii
I
h
CmCE 7
XE
C ~ ~ N F ,
7
mmol/L
ti C
i? -3.51
\
0
2
c
3
5 0.0
I
-4.0;
0.2
0.4
0.6
0.8
1
overall mole fraction of STS Figure 4. Coinicellization diagram displayed as a function of total concentratlon and overall mole fraction of STS in 0.05 M sodium chloride solution at 30 'C: region I, no micelles; region 11, NF-rich micelles: region HI, two kinds of mixed micelles; region IV, STS-rich micelles. The broken lines represent the asymptotes at infinite total concentration.
0
0.2 0.4 mole fraction of STS
Figure 5. Surface tensions plotted against the micellar (solid circles) and monomeric (open circles) compositions in 0.01 M sodium chloride solution at different temperatures. I
f
isting monoiiners and micelles change with the total concentration. In region 111, two kinds of micelles with the compositions xAand xB coexist with monomers, with the composition of point E. The total moles of NF-rich micelles and SI'S-rich micelles, on a monomer basis, are (C, - CE)(XB - XSTS)/(XB - XA) and (Ct - CE)(XSTS- XA)/(XB x A ) , respectively. The boundary line between regions I1 and I11 is determined by the condition where two kinds of mixed micelles (zmSTS = xA)coexist with monomers (cmc = CE and XbSTS = xE). From the material balance of STS, ct = (xE - xA)CE/(XSTS - xA) (6) Analogously, the boundary line ( x ~ T s= XB, cmc = CE, and XbSTS :3 xE) between regions I11 and IV is calculated from Ct = (XB - XE)CE/(XB- XSTS) (7) Mysels13 used expressions equivalent to eq 6 and 7 and produced a inicellization diagram similar to Figure 4. Temperature Effects on Mutual Solubility in Mixed Micelles. In the presence of 0.01 M sodium chloride, also, the surface tension for pure STS (30 " C ) and NF (30.0, 34.0, 3'7.5, 40.7, and 50.0 " C ) remained constant above the cmc. For NF-STS mixtures in 0.01 M sodium chloride solution, the relation between the surface tension and the micellar composition was determined a t different temperatures, in the same way as was done in the case of 0.05 M sodium chloride solution (Figure 2). Figure 5 shows typical data; the open circles depict those against the mole fraction of SI'S in monomers, and the solid circles depict those tigainsit the micellar composition. Since the total concentration used to determine the micellar composition was much higher than the cmc, the micellar composition agreed with the overall value within 5%. Thus, in Figure 5, the micellam composition at 50 O C is taken to equal the overall value.
micellar mole fraction of STS Figure 6. Temperature dependence of mutual solubility in mlxed NF and STS micelles in 0.01 M sodium chloride solution. The dot-dash llne is calculated from eq 13 and 14, and the broken line passes through the midpoint of the mutual solubility limits.
The limits of the plateau region in the surface tension vs. micellar composition curve shown in Figure 5 represent the mutual solubility in the mixed NF-STS micelles. In Table 11, the mutual solubilities, X A and xB, thus obtained are shown together with the composition of the coexisting monomers, viz., XE and CE. As the temperature is raised, the plateau region becomes narrower and vanishes at 50 " C ; at this temperature, NF and STS are completely miscible in the mixed micelles. In Figure 6, the mutual solubilities thus obtained are plotted against the temperature. In the region surrounded by the solid line, two kinds of mixed micelles coexist. In the remaining region, there is one kind of mixed micelle present. This mutual solubility diagram resembles that for bulk liquid-liquid mixtures.* This observation, therefore, demonstrates that micelles are close to the liquid phase.
740
Funasaki and Hada
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980
0
01
0.2
0.3
monomeric mole fraction of STS Figure 7. Plots of cmc against the monomeric mole fraction of STS in 0.01 M sodium chloride solution at different temperatures ( O C ) : curve a, 42.0; curve b, 40.7; curve c, 37.5; curve d, 34.0; curve e, 30.0. The arrows indicate points corresponding to composition xE shown in Table 11.
The broken line is drawn through the midpoint of the solubility limits to accurately determine the critical point. The intersection of the solid and broken lines gave a critical solution temperature of 42.3 "C and a composition of XmSTS = 0.210. In Figure 7 , the cmc value near xE, which is the mole fraction of monomers coexisting with two kinds of mixed micelles, is plotted against the monomeric mole fraction of STS at different temperatures. As the temperature is raised, the break at point E becomes less sharp. This behavior corresponds to the decrease of mutual solubility with increasing temperature (Figure 6). In Table 11, the molecular area of adsorbed NF, calculated from eq 3 by using the surface tension vs. concentration curve, is included. Increases in temperature result in the expansion of the N F film. By substituting the values of the compositions of coexisting monomers and two mixed micelles (CE, xE, x A , and xB) into eq 6 and 7 , we can draw the temperature dependence of the region in which two mixed micelles coexist, viz., region 111; Ct > (xE - zA)CE/(XSTS- xA) and Ct > (xB - XE)CE/(XB - XSTS). In Figure 8, region I11 is depicted as a function of overall mole fraction, total surfactant concentration, and temperature. The temperature vs. composition curve at infinite concentration corresponds to data in Figure 6. Analysis of Surface Tension vs. Surfactant Concentration Curves. The broken lines in Figure l a were calculated fromll eq 8, where the monomeric and micellar
ct = cmc(xbSTS - xmSTS)/(xSTS - XmSTS)
overall mole fraction of STS Figure 8. Two-micellar region depicted as a function of total concentration, overall composition, and temperature in 0.0 1 M sodium chloride solution.
within points K and M, and at point M it enters into region 11; here the STS-rich micelles disappear. During this process, the number of kinds of mixed micelles initially increases from one to two and finally decreases to one. Thermodynamics of Comicellization of NF and STS. Hydrocarbon surfactants are completely miscibile in the mixed micelles, and at least some binary systems of hydrocarbon and fluorocarbon surfactants exhibit the partial immiscibility in the mixed micelles."' Hence the partial immiscibility of NF and STS in the mixed micelle should be explained, as the principal factor, in terms of the phobicity between the fluorocarbon and hydrocarbon chains, as already reported in the case of bulk fluorocarbon-hydrocarbon m i ~ t u r e s . ~ J ~ Hildebrand and Scott8 depicted the phase diagram of binary systems of liquid fluorocarbon and hydrocarbon mixtures and made an analysis on the basis of the regular solution theory. Shinoda also has explained cmc values on the basis of a phase separation model of micelle formation.2 A combination of these theories yields In c b l = -Kgl In (Cbl + Cb2 + C,)A2+ In xml
+
(8)
compositions, q,STS and xmSTS,corresponding to the measured surface tension value are interpolated on curves b and c of Figure 2 and the cmc value corresponding to this XbSTS value is read from curve a in Figure 3, respectively. Since the overall composition of curve b in Figure 1is close to that of point E in Figure 2, the surface tension above the cmc remains constant at 18.61 dyn/cm, as if the mixture were a compound. At total concentrations higher than the concentration of point G on curve c (since two kinds of mixed micelles coexist with monomers at the concentration CE), the surface tension shows a constant value of 18.61 dyn/cm. The broken line shown in Figure 1b was calculated fromll eq 9, where the micellar composition and monomCNF CbNF + (CSTS - CbSTS)XmSTS/XmNF (9) eric concentrations corresponding to the measured surface tension value are read from Figures 2 and 3. Curves d and e move from region I to IV shown in Figure 4 at points N and H, respectively. Curve e is in region I11
In these equations, the first term on the right-hand side represents the contribution of electrostatic potential of mixed micelles and the second and third terms represent those of the entropy and enthalpy of mixing in micelles. The last term, Kmi,and K,, are constants which are determined from the salt concentration dependence of cmc's for the pure surfactant i. The A value is the mean molecular area of surfactants at the micellar surface, q is the ratio of molal volumes of two surfactants, viz., V2/V,, and is the solubility parameter of (probably hydrophobic chain of) the surfactant i. In the application of eq 10 and 11 there are several uncertainties in the estimation of A, q, V,, and 6, (Table 111). Figure 9 depicts typical examples of calculations. In the present experiment, since an excess electrolyte is added, viz., C, >> Chi, the value of (Cbl + Cb2 + C,) was approximated as (C, + 0.3) mmol/L. Component 1 denotes STS.
Coexistence of Two Kinds of Mixed Micelles
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980 741
i
0.41
0
02
04 06 mole fraction of STS
08
1
Figure 9. Comparison of the theories for the cmc vs. composition relations in 0.05 M sodium chloride solution at 30 "C: solid lines, model I; broken lines, model 11; dot-dash lines, model 111; open circles, monomeric composition; solid circles, micellar composition.
10 and 11, the shape of the cmc vs. composition curves markedly changed. Thus, further theoretical studies are required. Analysis of Critical Solution Temperature. Hildebrand and Scott collected the phase diagram of liquid-liquid mixtures and analyzed the results on the basis of the regular solution theoryas The mutual solubility between nonpolar liquids is symmetric when plotted against the volume fraction instead of the mole fraction, and this fact strongly supports their theory. According to the regular solution theory? the mutual solubility between the primed and unprimed phases is given for the binary system by
TABLE 111: Estimated Values of Parameters in 0.05 M NaCl at 30 " C A , A'/
6,
v,
K , molecule (cal/mL)''* mL/mol M , 0.656 50 8.0a 282b 316.4 260' NF 0.645 78 6d 344e 626.2 C,F,,COOH 5.7f 227.5b 414.1
surfactant ._ -I STS
Value at 25 " C for n-hexadecane taken from ref 8. Micellar molal volume a t 25 "C taken from ref 14. ' Molal volume of the tetradecyl group calculated from ref 15. Roughly estimated from solubility parameters (25 "C) of analogous compounds given in ref 8. e Taken to equal 227 5 x 626.2/414.1. Value at 25 "C for perfluor0.n-heptane taken from ref 8 and 16. a
Model I ( q = I , V1(& - 8J2 = 1040 cal, and A = constant). The solid lines in Figure 9 are calculated by employing values of Vl = 260 mL and - 621 = 8.0 - 6 = 2 and predict cmc values higher than those observed. In this model the micellar and monomeric compositions are noted to coincide at the maximum cmc, thus differing from other models, When V1(6, - 62)2 is greater than 2RT, the phase separation occurs. Then, the calculated cmc values, however, were much higher than the observed values. Model 11 ( q = 1, V1(& - 8J2 = 1040 cal, and A from eq 12). As Tablle I11 shows, the molecular area occupied at the air-sodium chloride (0.05 M) solution interface differs with the two surfactants. Hence the surface charge density a t the micellar surface is expected to differ in the micelles of the two surfactants. The broken lines are calculated, assuming that the molecular area at the air-water interface is proportional to that at the micellar surface and that the mean area of mixed micelles can be written as the average of the areas of the pure surfactants:
A = xmlA1 + xrn2A2 (12) Model 111 (q = 0.564, V1(6, - &J2 = 1946 cal, and A = constant). Equations 10 and 11 can also be used in the case where two kinds of mixed micelles coexist in equilibriums Using the values of observed mutual solubilities, one can obtain values of q = 0.564 and V1(6, = 1946 cal. Substitution of these values into eq 10 and 11yielded the dot-dash lines shown in Figure 9. As in evident in comparisons of the observed values (Figure 3) with the model calculations (Figure 9), the discrepancy between theory and experiment is not much improved by the alternative choice of the q and V1(6, - 82)2 values. Such may be attributed to the approximation of eq 10 and 11 dealing with electrostatic energy and to the inadequate assignment of the surface charge density. In fact, when we employed the observed molecular area of the mixed adsorbed monolayers (Table I) as the A value in eq
Here the charge effects of mixed micelles are neglected. A t the critical solution temperature, TO81l7
RTc = 2xrnlxrn2q2V1(61- 6d2/(xrn1 + xrn2d3 (15) xrnl
= (1- (1 - q
+ q2) 1'2) /( 1
- q)
(16)
If we can apply the above theory to the mixing of the hydrophobic chains of NF and STS in the mixed micelle, we obtain q = 0.393 and V1(al = 1724 cal by substituting the observed T, and xml values at T, into eq 15 and 16. Furthermore, when assuming that the values of q and V1(6, do not depend on the temperature, we obtain the dot-dash line in Figure 6 by substituting these values into eq 13 and 14. On the other hand, Table I11 shows the estimated values of A, a t 30 "C, Vi and 6i at 25 " C for NF, STS, and perfluoro-n-octanoic acid. From V1(& - &J2 = 1724 cal and V1 = 260 mL, wie can obtain 16, - = 2.6 (cal/mL)1/2. This value is in rough agreement with the estimated value shown in Table 111, when the temperature dependence of VI, q, and 6iis taken into account. This fact suggests that the principal factor for the partial miscibility of NF and STS appears to be the repulsive force between the hydrophobic chains in the mixed micelles. However, the great differences between the q values calculated from eq 16 and estimated from Table 111, as well as between the solid and dot-dash lines shown in Figure 6, suggest the participation of some alternative factors. The molal volumes in eq 13-16 may be regarded as the effective ones, since the shape of NF and STS molecules are considerably differentS8 Moreover, change in the electrostatic energy with comicellization of NF and STS should be taken into account, since the micelles of pure NF and STS will have different surface charge densities. The molecular area of NF and STS adsorbed at the airwater interface was different and depended on the temperature (Tables I1 and 111).
Discussion Mixed Micelles. Mukerjee and Mysels estimated the mutual solubility in mixed micelles of sodium dodecyl sulfate and perfluorooctanoic acid in the absence of in-
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The Journal of Physical Chemistry, Vol. 84, No. 7, 1980
TABLE IV: Surface Tension vs. Total Concentration Relation for NF-STS Mixtures Above the Cmc at 30 "C
cs,
ct,
Yobsd,
Ycalcd I
mmol/L
xSTS
mmol/L
dyn/cm
dyn/cm
50
0.544
50
0.097
10
0.113
0.318 0.341 0.378 0.222 0.292 0.624 0.794
19.40 19.26 19.02 18.62 18.61 18.41 18.41
19.38 19.23 19.05 18.62 18.61 18.41 18.41
organic salts, by sufrace tension measurement^.^ Although the details of the analysis have not been reported, these authors seem to assume a priori that the total monomer concentration, viz., cmc, should be a maximum when two mixed micelles coexist, as shown by the dot-dash lines in Figure 9. Our results, however, were inconsistent with this assumption, as shown in Figures 3 and 7. The same phenomenon was observed in other systems.18 This assumption appears to hold for nonionic fluorocarbon and hydrocarbon surfactants,18 When two kinds of mixed micelles coexist, the surface tension of solutions above the cmc must remain constant regardless of the total surfactant concentration, Ct, and the overall mole fraction, xSTS. The surface tension of solutions with a composition of xSTS = 0.544,at which the cmc value has a maximum as depicted in Figure 3, is shown as a function of the total concentration in Table IV. This table clearly shows that the surface tension decreases with increasing total concentration. The calculated surface tension values shown in this table were calculated in the same manner as the broken lines in Figure la. As Figure 9 shows (dot-dash line), the cmc vs. monomer composition curve must break where two mixed micelles coexist. As shown in Figure 3, however, the cmc vs. XbSTS curve did not break a t the composition showing a maximum cmc. Such a break, as shown in Figures 3 and 7, was observed at point E, where two mixed micelles coexist and the cmc does not show a maximum. Furthermore, this break became less sharp with elevation in temperature, as shown in Figure 7. As shown in Table IV, the surface tension of solutions with composition XE remained constant above the cmc, as expected when two mixed micelles coexist. As shown in Figure 9 (solid and broken lines), when only one kind of mixed micelle is present, the cmc vs. monomer composition curve does not break even at a maximum cmc. This is observed in Figure 3. Thus, the composition of monomers with which two kinds of mixed micelles coexist is XE. Mukerjee and Yang reported the cmc vs. monomer composition curve for sodium laurate (SL) and sodium perfluorooctanoate mixtures.6 Although not discussed by these authors, a break similar to that seen in Figure 3 is observed at XbSL 0.65 in the cmc vs. monomer composition curve. Furthermore, the cmc vs. monomer composition curve, calculated by Mysels under an assumption, breaks at the point where two kinds of mixed micelles coexist, and the curve shows no maxima.13 For two-component liquid mixtures (mainly nonpolar and almost spherical molecules) including fluorinated compounds, the composition a t T, can be accurately predicted by the regular solution the~ry,~tl' viz., eq 16. Our results on the NF-STS comicellar system are considerably different from those predicted by the regular solution theory, thus suggesting the participation of alternative factors.
Funasaki and Hada
The present system contains four components-water, sodium chloride, NF, and STS. In the present analysis, however, mixed micelles are regarded as being composed of two surface active ions; the contributions of water, counterions, and co-ions were neglected. Such analysis appears to be successful in systems of hydrocarbon surfactants possessing the same head group (ionic and nonionic) and similar alkyl chain^.^,^ Whether or not there is If water in the interior of micelles is controversial.KJ9~20 water is entrapped in micelles, inorganic ions such as sodium and chloride ions may be solubilized in the water. At least, water21and counterions are bound to the micellar surface. In such a case, mixed micelles may be treated as a four-component system. As the theory of micelle formation, phase-separation and mass-action models have been p r ~ p o s e d In . ~general, ~~~~~~ the analysis by phase-separation models seems to be simpler, though less rigorous, than that by mass-action models. For instance, the existence of the critical solution temperature in comicellar systems, as is shown in Figure 6 , appears to support the former models, but a rigorous analysis of the mutual solubility in mixed NF-STS micelles, at least, required the improvement of eq 10 and ll, based on a phase-separation model. An analysis based on mass-action models will require knowledge of unknown parameters such as association constants and aggregation numbers. A recent theoryz3based on the thermodynamics of small systemsz4 improved phase-separation models. This theory, however, has not been developed for ionic surfactants. The electrostatic free energy terms in eq 10 and 11should be essentially applied to flat surfaces, and the relationship of cmc to the surface charge density has not been experimentally verified, though there are some applicationsq2 The existence of the critical solution temperature demonstrates that micelles are close to the liquid phase. However, the interior of micelles of hydrocarbon surfactants probably does not possess a microenvironment identical with that of liquid hydrocarbon^.^^^^^^^^^^^ For instance, oxygen solubility on a mole fraction basis is only 10 X in sodium dodecyl sulfate micelles as compared to 21 X in pure nonane.20>26This difference is rationalized by the presence of water in micelle interiors20 or by the presence of the Laplace pressure which stems from the interfacial tension at a curved micelle-water interface.26 Furthermore, the free energy of micellization shows the odd-even alternation with the variation of the hydrocarbon chain length,25which is frequently observed in the properties involved in the solid having a hdyrocarbon chain. Thus, the micelle interior is not identical with, although it is close to, that of liquid hydrocarbons. As discussed above, there are several reasons which may explain the disparity in properties between nonionic liquid mixtures (particularly forming regular solution) and mixed micelles. Probably charge effects are most important. As shown in Table I1 (30 "C),the mutual solubility depends on the salt concentration. For the NF-STS comicellar system, the critical solution temperature and micellar mole fraction of STS at this temperature considerably increased by increasing the salt concentration.18 Moreover, NF and a nonionic hydrocarbon surfactant were completely miscible in the mixed micelles.ls These effects of salt concentration and surfactant charge type seem to be explicable in terms of charge effects of mixed micelles. In comicellar systems of NF with sodium alkyl sulfates, the critical solution temperature and the micellar mole fraction of NF at this temperature greatly increased with increases in the alkyl chain length.18 These results are, at
Coexistence of Two Kinds of Mixed
Micelles
least qualitatively, explicable on the basis of regular solution theory. Mixed Monolayers at the Air-Water Interface. In the presence of 0.05 M sodium chloride and at 30 "C, NF and STS were Completely miscible in the adsorbed monolayers, although the surfactants were partially miscible in the mixed mice1les. Film-forming surfactants are, to our knowledge, completely miscible in their adsorbed monolayers. The thermodynamics of mixed monolayers is much more confusing than that of mixed micelle^.^^^^ By modifying the theory of Defay et aLZ7for nonionic mixed monolayers, we can obtain tentative expressions for the equilibrium of surfactants 1 and 2 between an aqueous solution and a mixed monolayer above the cmc: In c b l = - ln (Cbl + Ch2 + C,)A2 + In xal +
When we attempt to apply these equations to explain the miscibility in mixed monolayers, we encounter many uncertainties. The first term on the right-hand side of eq 17 and 18 expresses the electrostatic effect, which differs from that for micelles (see eq 10 and 11). This difference may stem from the dislparity in shape between a monolayer and a micelle. These terms for monolayers and micelles, however, neglect the discreteness of charges.28 The second term expresses the entropic effect of mixing in monolayers. Here, it is controversial whether we can neglect the contribution of water.27 The third term expresses the enthalpic effect accompanying the mixing in monolayers. Apart from the uncertainty regarding the contribution of water (neglected in eq 17 and 18),the solubility parameter in monolayers may differ from that in liquids and may depend on the phase state of monolayers. For instances, the solubility parameters olf the alkyl groups of myristic acid in a liquid-expanded film and of palmitic acid in a liquid-condensed film are estimated to be 5.7 and 7.0, respectively? whereas those of liquid long-chain alkanes are about 8.0 Therefore, we cannot use the a t 25 " C (see Table 6 values for liquids in eq 17 and 18. The fourth1 term stems from the surface free energy. Here A, is the partial molal area of component i, which corresponds to the partial molal volume in bulk solutions. This term also differentiates the miscibility in monolayers from that in bulk solutions and in micelles and depends on the surface tension of the monolayers. An accurate evaluation of the partial molal areas of NF and STS is considerably difficult, particularly in adsorbed monolayers. In spread monolayers, though most monolayers are completely miscible, some systems are reported to be partially m i ~ c i b l e :for ~ instance, oleic acid-palmitic acid, 15 O C , pH 2.0; oleic acid-stearic acid, 15 O C , pH 2.0; palmitoleyl alcoholstearyl alcohol, 25 "C, pH 5.8; and oleyl alcohol--stearyl alcohol, 25 "C, pH 5.8. Probably each of these four systems is completely miscible in liquids. The miscibility of surface-active substances does not always coincide in monolayers and liquids. According to Pagano and G e r ~ h f e l dtwo , ~ lipids in different surface phases tend to unmix in monolayers. Both adsorbed monolayers of pure NF and STS are probably liquid-condensed films, since these monolayers occupy
The Journal of Physical Chemistry, Vol. 84,
No. 7, 1980 743
relatively large molecular areas (Table 111) and show low surface tensions, viz., high surface pressures. Therefore, NF and STS may be miscible in their mixed monolayers. Conclusions The micellar composition, x, was determined from the surface tension y data on NF-STS solutions abovle the cmc. In the relation between the y at the cmc and the x,, a plateau region was observed, and both limits of this region represent the mutual solubility of NF and STS in the mixed micelles. In the relation between the y at the cmc and the composition of adsorbed monolayers on aqueous solution, there were no plateau regions present, thus indicating that NF and STS are completely miscible in the adsorbed monolayers. The concentration and composition of the sufactants at which two kinds of mixed micelles coexist were determined as a function of temperature. From the temperature dependence of mutual solubility, the critical solution temperature was shown to exist in the comicellar system of NF and STS. This fact demonstrates that micelles are close to the liquid phase. The major reason for the partial miscibility of NF and STS may be the phobicity between the fluorocarbon and hydrocarbon chains in the mixed micelles. The change of electrostatic energy with comicellization, albeit a minor factor, should be taken into account. A quantitative analysis was attempted to explain the cmc vs. composition relations and the temperature dependence of mutual solubility.
Aclznowledgment. Thanks are due to M. Ohara, Kyoto University, for assistance with the manuscript and to Dr. T. Mizuno, Neos Co., for the gift of samples of NF,, Nomenclature molal volume ratio of two surfactants, viz., V2/ VI overall mole fraction of surfactant i in the system mole fraction of surfactant i in mixed monolayers at the air-water interface mole fraction of surfactant i in monomers mole fraction of STS in monomers coexisting with two mixed micelles mole fraction of surfactant i in mixed micelles molecular cross-sectional area of surfactant i partial molal area of surfactant i in mixed monolayers concentration of surfactant i in monomers degenerate cmc, viz., total concentration of mlonomers coexisting with two mixed micelles concentration of uni-univalent salt added total surfactant concentration constant defined in eq 17 and 18 slope of log Cbi vs. log (CbL C,) plot for ionic surfactant i constant defined in eq 10 and 11 gas constant absolute temperature molal volume of surfactant i in the micellar state surface tension of aqueous solutions solubility parameter of surfactant i surface excess of species i at the air-water interface total surface excess of surfactants at the air-water interface References and Notes
+
(1) Funasaki, N.; Hada, S. Presented in part at the ACS/CSJ Chemical Congress in Hawaii, April 1-7, 1979. Preliminary findings are included in ref 7, and some data therein are corrected. (2) Shinoda, K.; Nakagawa, T.; Tamamushi, B.; Isemura, T. "Colloidal Surfactants"; Academic Press: New York, 1963; Chapter 1, (3) Funasaki, N. J . Colloid Interface Sci. 1978, 67, 384, and references cited therein.
744
J. Phys. Chem. 1980, 84, 744-751
(4) Funasaki, N.; Hada, S. J . Ph,ys. Chem. 1979, 83, 2471, and references cited therein. (5) Mukerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, No. 9 , 239. (6) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388. (7) Funasaki, N.; Hada, S. Chem. Lett. 1979, 717. (8) Hildebrand, J. H.; Scott, R. L. "The Solubility of Nonelectrotytes"; Dover Publications: New York, 1964; Chapters 7 and 16 and Appendixes 1 and 4. (9) Pagano, R. E.; Gershfeld, N. L. J. Phys. Chem. 1972, 76, 1238. (10) The chemical structure of NF is (CFa 12 C F\
c,=c'
(CF3)zCF
\",Lo_, -
0 ,No
(11) (12) (13) (14) (15) (16) (17)
Funasaki, N.; Hada, S. Bull. Chem. SOC.Jpn. 1976, 49, 2899. MatijeviE, E.; Pethica, B. A. Trans. Faraday SOC.1958, 54, 1382. Mysels, K. J. J . Colloid Interface Sci. 1978, 66, 331. Shinoda, K.; Soda, T. J. Phys. Chem. 1963, 67, 2072. Tanford, C. J . Phys. Chem. 1972, 76, 3020. R. L. Scott, J . Am. Chem. SOC. 1948, 70, 4090. Hildebrand, J. H.; Fisher, B. B.; Benesi, H. A. J . Am. Chem. SOC. 1950, 72, 4348. Jolley, J. E.; Hildebrand, J. H. J. Phys. Chem. 1957, 61, 791. Shinoda, K.;Hildebrand, J. H. IbM. 1958, 62, 481; 1961, 65, 1885. (18) Funasaki, N.; Hada, S., unpublished results. (19) Menger, F. M.; Jerkunica, J. M.; Johnston, J. C. J . Am. Chem. SOC. 1978, 700,4676. Muller, N.; Birkhahn, J. H. J . Phys. Chem. 1967, 77, 957. SvenS, B.; Rosenholm, B. J. ColloidInterfacs Sci. 1973, 44, 495. Corkill, J. M.; Goodman, J. F.; Walker, T. Trans. Faraday
SOC.1967, 63, 768. Clifford, J. Ibid. 1965, 67,1276. (20) Menger, F. M. J. Phys. Chem. 1979, 83, 893. Acc. Chem. Res. 1979, 72, 111. (21) Mukerjee, P. J. Colloid Sci. 1964, 79, 722. (22) Overbeek, J. Th. G.; Stigter, D. Recl. Trav. Chim. Pays-Bas 1956, 75,1263. Mukerjee, P. Adv. ColloldInterface Sci. 1967, 7, 241. Anacker, E. W. In "Cationic Surfactants"; Jungermnn, E., Ed.; Marcel Dekker: New York, 1970; p 203. Tanford, C. "The Hydrophobic Effect: Formation of Micelles and Biologlcal Membranes"; WileyInterscience: New York, 1973; p 45. (23) Hall, D. G.; Pethica, B. A. In "Nonionic Surfactants"; Shick, M. J., Ed.; Marcel Dekker: New York, 1967; p 516. (24) Hill, T. L. "Thermodynamics of Small Systems"; W. A. Benjamin: New York, 1963-1964; Vol. 1 and 2. (25) Mukerjee, P. Kolloid Z. 2. Polym. 1970, 236, 76. (26) Metheson, I. B. C.; King, A. D., Jr. J . Colloid Interface Sci. 1978, 66,464. (27) Goodrich, F. C. "Proc. Int. Congr. Surf. Act., 2nd, 79571957, 7, 85. Defay, R.; Prigogine, I.; Bellemans, A,; Everett, D. H. "Surface Tension and Adsorption"; Longmans: London, 1966; Chapter 12. Lucassen-Reynders,E. H. J . Colloid Interface Sci. 1973, 42, 563. Nakagaki, M.; Funasaki, N. Bull. Chem. SOC.Jpn. 1974, 48, 2094, 2482. Funasaki, N.; Nakagaki, M. Ibid. 1975, 48, 2727. Goddard, E. D. Adv. Chem. Ser. 1975, No. 744, Chapters 3, 12, and 13. Gershfeld, N. L. Annu. Rev. Phys. Chem. 1976, 27, 349. Motomura, K.; Yoshino, S.; Fujii, K. Matsuura, R. J. Collokl Interface Sci. 1977, 60, 87. Garrett, P. R. Ibid. 1977, 62, 272. (28) Stigter, D. J . Phys. Chem. 1975, 79, 1008; 1964, 68, 3603. Fgat, G. R.; Levine, S. Adv. Chem. Ser. 1975, No. 744, Chapter 8.
Micelle Size and Shape of Sodium Dodecyl Sulfate in Concentrated NaCl Solutions Shoji Hayashi and Sholchi Ikeda" Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464, Japan (Recelved April 2, 1979; Revised Manuscript Received December 12, 7979)
Light scattering from aqueous solutions of sodium dodecyl sulfate has been measured in the presence of NaCl of different concentrations at different temperatures. In NaCl solutions more concentrated than 0.45 M, surfactant micelles fbrmed at the critical micelle concentration further associate into large micelles with increasing surfactant concentration. In 0.60 and 0.80 M NaCl at 25 "C, light scattering exhibits anomalous dissymmetry attributable to the formation of trace amounts of microgel particles. In 0.80 M NaCl at 35 "C, light scattering is normal and gives the micelle aggregation number as high as 1410 at 1.10 X g ~ m - The ~ . angular dependence indicates formation of a rodlike micelle having a length of 597 A. It is concluded that sodium dodecyl sulfate forms spherical micelles at low NaCl concentrations (10.45 M), but it associates into rodlike micelles at high NaCl concentrations when its micelle concentration is high.
Introduction Recently Mazer, Benedek, and Carey1 measured quasielastic light scattering from aqueous solutions of sodium dodecyl sulfate (SDS) in the presence of NaCl of different concentrations and found that the micelle aggregation number increases from about 80 in 0.15 M NaCl to about 1000 in 0.6 M NaCl a t 25 "C. The small micelle having an aggregation number less than about 100 has been assumed to be spherical or globular in ~ h a p e . ~However, -~ the large micelle cannot be accommodated to a globular micelle but has been assigned a rodlike shape.' The same workers together with their co-workers6further observed angular dependence of light scattering and confirmed the formation of rodlike micelles. Unfortunately it proved that the SDS samples they used were not sufficiently pure but contained considerable amounts of higher alkyl homologues.6 Furthermore, they did not examine variation of light scattering and micelle size with SDS concentration in detai1.l These workers measured light scattering at various temperatures from 11to 85 "C, but the temperatures in0022-3654/80/2084-0744$01 .OO/O
cluded the range that was considerably lower than the temperature of solubility limit or the critical micelle temperature of SDS in 0.6 M NaC1.' This fact could cast suspicion if the SDS solutions that they studied and in which they found the rodlike micelles were unstable and contained small crystallites. The formation of rodlike micelles first proposed by Debye and Anacker7i8has long been accepted with serious reservation by other worker^.^#^ In the present work we have measured light scattering from aqueous solutions of SDS in the presence of concentrated NaCl at different temperatures and examined their behavior as a function of SDS concentration at temperatures above and below its solubility limit. Conditions for preparing and clarifying SDS solutions and for lightscattering measurements have been carefully defined, and, especially, the temperatures for all these stages have been strictly regulated. A series of SDS solutions of concentrations c (g ~ m - has ~ ) been prepared by dissolving SDS solid in an NaCl solution of a given concentration, C, (M). We have found that a transition of micelle shape from sphere to rod occurs in SDS solutions of concentrations 0 1980 American Chemical Society
