Oct., 1062
MICELLE PHASE OF CALCIUM DINONYLNAPHTHALENE SULFONATE
1843
THE MICELLE PHASE OF CALCIUM DINONYLNAPRTHALENE SULFONATE IN TL-DECANE BY FREDERICK M. FOWKES* Shell Development Company, Emeryville, California Received March I$, 186.9
In n-decane a t 25" calcium dinonylnaphthalene sulfonate (CaDNNS) forms a saturated molecular solution a t concentrations less than 10-8 mole/liter. Solute in excess of this concentration is in the form of micelles with an axial ratio of 2 averaging 12 molecules each. Interfacial tension measurements a t the decane/Ca( NOa)z solution interface show the chemical potential OF CaDNNS to be constant from 10-6 to 10-3 mole/liter. This means that the micelles are a separate, though soluble, phane of CaDNNS. This is in contrast to the previously accepted hypothesis that micelles equilibrate with dissolved molecules according to the mess law principle.
Introduction Micellar equilibria have been studied primarily in aqueous solutions of ionized detergents such as the sodium alkyl. sulfates, where the effect of concentrationl or added salt2 has been explained by use of the mass law equations. Hutchinson proposed ithat in these systems the micelles may be treated better as a separate phase in equilibrium with molecularly dispersed solute having a chemical potential independent of the amount of micelle phase present. 3 Micelles in non-aqueous media are hardly representative of all micelles, but it is certainly of interest to see whether these equilibrate by mass law equations or as a separate phase. Several investigators have reported on the properties of these in which the polar "heads" form the clenter of the micelle and the hydrocarbon "tails" are in contact with the solvent. Theory.-- If micelles are a separate but soluble phase in equilibrium with a saturated molecular solution, the chemical potential of the latter must remain constant no matter how much solute is in the micellar phase. Any measure of the chemical potential of the solute could be used to determine whether it is changed by changing ratios of micellar to molecular dissolved phase. Interfacial tensions between the decane solutions of CaDNNS and 1 M aqueous Ca(NO& have been used in this study. If CaDNNS associates in n-decane to form nmers according to the mass law principle nCaDNNS (CaDNNS),
where f is the activity coefficient of the molecularly dispersed sulfonate and fm is the activity coeffi* Sprague Electric Co., North Adams, Mass. (1) K. Durham, "Surface Activity and Detergency," The Maomillan Co., London, 1961, Chapter 2. (2) M. L. Corrin and W. D. Harkins, J . A m . Chem. Soc., 69. 683 (1947). (3) E. Hutchinson, A. Inaba, and L. G.Bailey, 2. phgsik. Chem., 6 , 344 (1955); E. Hutchinson and K. Shinoda, J. Phys. Chem., 6 6 , 577 (1962). (4) S.M. Nelson and R. C. Pink, J . Chem. Soc., 1744 (1952). (5) M.B. Mathews and E. Hirschhorn, J . Colloid Sci., 8 , 86 (1953) (61 C. R. Singleterry, J . A m . 0 2 1 Chemists' Soc., 82, 446 (1955). (7) M. van der Waarden, J . Colloid Sci.. 5, 448 (1950). (8) J. G. Honig and C. R. Singleterry, J . Phys. Chsm., 58, 201 (1954). (9) S. Kaufman and C. R. Singleterry, J . Colloid Sci.. 10, 139 (1955). (10) S. Kaufman and C. R. Singleterry, ibid.. 12, 465 (1957).
cient of the micelles. When [(CaDNNS),] >> [CaDNNS], the total concentration C is negligibly different than [(CaDNNS),]. Then d In [CaDNNSIf =
-n1 d In Cfm
(2)
The interfacial tension between the decane solution and the 1 M Ca(N03)2is governed by the Gibbs absorption equation
-2.3kT dYow -_ __ d log [CaDNNSIf A
(3)
where yow is the interfacial tension and A the area per molecule in this interfacial film. Combination of equations 2 and 3 gives drow - -2.3kT -d log Cfm nA
(4)
for the change of yowwith C well above the critical concentration for micelle formation if the mass law is valid. Experimental Details Materials.-Dinonylnaphthalene was prepared by aluminum chloride-catalyzed alkylation at 60" using fractionally distilled I-a-nonenes derived from trimerization of propylene. A heart cut of the dinonylnaphthalene fraction was then sulfonated with Sulfan B a t -8" and titrated to neutralization with sodium hydroxide. Isopropyl alcohol extraction was used to separate NaDNNS from the unsulfonated oil, and the calcium salt was prepared by contacting with concentrated CaC12 solutions. The molecular weight was found by sulfate ash determinations to be 930, as compared with the theoretical value of 958. Presumably a small amount of dealkylation occurred during sulfonation. CaDNNS is quite hygroscopic; consequently i t was freezedried from benzene solutions, pumped out a t room temperature at less than 1 mm. pressure, and the resulting fluffy powder dissolved in dry solvent, Phillips 99 mole yo ndecane, which was dried with molecular sieves. Reagent grade Ca(NO& was used in doubly distilled water. Diffusion coefficients were measured at 25" in the Spinco Electrophoresis-Diffusion apparatus, using schlieren optics. Concentration differences of 2 g./l. were used and the coefficients were calculated from the time dependence of the second moments; the latter were calculated with a Bendix computer programmed for second moments by S. J. Rehfeld. Sedimentation coefficients were determined a t 25' with the Spinco Analytical ultracentrifuge using schlieren optics at the higher concentrations and ultraviolet absorption mole/liter. optics at Intrinsic viscosity [v] and partial specific volume F were measured at 25' by normal analytical methods. Interfacial tensions were measured at 25' by the pendant drop method. At the higher concentrations equilibrium was attained rapidly but at concentrations of less than 10-4
FREDERICK M. FOWKES
1844
Vol. 66
mole/liter more than an hour was required. To speed this process drops were purposely made large originally and then partly retracted into the syringe to compress the adsorbed film. I n these drops interfacial tensions lower than equilibrium were obtained but these rose rapidlyto the equilibrium values. Apparently there is a lower energy barrier to deemption than adsorption in these monolayers. Pressure-area relations of an insoluble monolayer on 1 hf CaClz were measured at 25" with an automatic. recording film balance" by Dr. R. C. Nelson. This will be reported in more d@ail later. From this isotherm it is estimated that A = llOA.Z/molecule at 50 dynes/cm.
Experimental Results Table I shows the sedimentation coefficients which extrapolate to so = 2.54 =t0.07 X sec. for dry systems; larger values were obtained in the presence of moisture. The partial specific volume of CaDKNS in n-decane at 25' was 0.882 i 0.002 ml./g. The intrinsic viscosity [ q ] is 0.0254 g./dl. or 0.0288 ml./dl. This corresponds to an axial ratio of 1.9 if rod-shaped and 2.1 if diskshaped.12 From these values the ratio of the frictional coefficient to the frictional coefficient of non-solvated spheres f/f0 is found to be 1.038 for rods and 1.047 for disks.13 These values of so and f / f o give the gram-micellar weight M as 11,000 i 300. This corresponds to an average of 11.8 TABLE I SEDIMENTATION AND DIFFUSIONCOEFFICIEKTS FOR CaDNNS I N n-DECANE AT 25" Concn., D &/I. sec. (Xs'lola) cm.*/sec. '(x 100) 20 2.07 .. 10 2.36, 2.26 .. 9 ... 1.17 7 1.15 5 2.35, 2.45 1.16 3 .. .. 1.21 I 1.32 0.01 2.47 ..
....
. . I . . . .
. ..
. . e . . . .
i 0.3 molecules/micelle.
The diffusion coefficients shown in Table I extrapolate a t infinite dilution to Do = 1.43 x 10-6, which together with the value of go gives M = 12,240 f 400; this corresponds to 13.1 & 0.4 molecules/micelle. A proposed structure for a 12-molecule micelle with axial ratio 1.8 is shown in Fig. 1. This aggregation number is definitely larger than the 5 reported previously in fluorescence depolarization measurements of Rhodamine B solubilized by CaDNNS in benzeneV8 It was suspected that this dye may have reduced the aggregation number because of interaction with the polar groups, so some leuco-Rhodamine B was added to a CaDNNS solution and centrifuged with schlieren optics. It was found that the schlieren peak sediments nearly twice as fast as the red color of the relatively few micelles with solubilized dye; the sedimentation coefficient for the latter was sec. at a total concentration of 5 g./l. 1.6 X of CaDNNS. The equilibrium interfacial tensions of n-decane solutions of CaDNNS versus 1 M Ca(NO3)z at 2 5 O are shown in Table I1 at concentrations from (11) M. J. Schick, J. Polgmer Sci., 26, 465 (1957). (12) R. Simha, Proceedings International Congress Rheology, Amsterdam, 1948, Vol. 11, p. 70. ( 1 3 ) T. Svedberg and K. 0. Pedersen, "The Ultracentrifuge," Q x ford Press, New York, N. Y.,1940,p. 41.
Fig. 1.-A model of the CaDNXS micelle in agreement with sedimentation and viscosity measurements. Methyl groups in upper right diagram are shown as open circles.
to low6mole/l. The values at all concentrations are 0.93 f 0.09 dyne/cm., with no significant concentration-dependence of interfacial tension. TABLE I1 EQUILIBRIUM INTERFACIAL TENSIOKS OF CaDNNS SOLUTIONS I N n-DECANE AT 25 Concn., moles 11.
Interfacial tension, dyneslcm.
Av. f std. dev., dynedom.
10" 10-6
0.85,0.97,1.08,1.10 .85, .92, .97,0.99 .83, .85, .95,1.00 .89, .89
1.oozto.11 0.93f .06 -91 zk .08 .89
10-4 10-8
0.93 f 0.09
Discussion If the mass law were to govern the equilibrium between CaDNNS molecules and micelles the slope of interfacial tension versus log c would be as shown in equation 4
drew d log cfm
-
-2.3kT - -960 X nA 12 x 110
x
1010
-0.73 dyne/cm. The value of f m is nearly constant at all concentrations as shown by the values in Table I of the diffusion coefficient. If the mass law applied, a 2.2 dynes/cm. fall of interfacial tension would be found from to 10-3 mole/l., 25 times the standard deviation. Thus, the constancy of interfacial tension is strong evidence that these micelles act as a separate soluble phase in equilibrium with a saturated solution of CaDNNS molecules of very lorn concentration (below mole/l.). Similar results have been obtained with NaDSNS and SH,DNSS solutions in n-decane. Acknowledgment.-The interfacial tension mea
