2078
L. SHEDLOVSKY, C. W. JAKOB, AKD M. B. EPSTEIN
0.03
I vf 0.10 M
7-
1.05
1.10
1.15
1
MOLE . 7 LOWER HOMOLOG
0
100 87.5 75 50 25
i
o
0
O
0
I
I
e 0
0.06
--_ CMC
0.10 0
v€ 1.02 104 1.06 108 1 Fig. 6.-( -log f) vs. c‘/? for mixtures of sodium decyl and dodecyl sulfates (upper plot) and of sodium dodecyl and tetradecyl sulfates (lower plot). Reference curves are given for NaC1.
non-micellar electrolyte to tzhe observed activities. For mixtures, in place of the constant c.m.c. used with a single electrolyte, the concentration of non-micellar material, c,, is substituted and the activity becomes .fc
=
fX(CN
$-
- CN))
where Q is the degree of dissociation of the sodium ions by the micelles. Then f/”f\V
=
Q
+
(1 - a)
The experimental data are plotted in Fig. 5 in the form f/fw us c,/c. The otherwise widely separated and curved lines for the mixtures are brought together as a fairly close series of straight lines, which for the model implies that the extent of the dissociation is constant for each mixture over the range measured. The values of a estimated from the intercepts are given in Table I. For pure C12, BotrB, Crescenzi, and Melel found a to be 0.16 and Philips and RSyselsgestimated 0.18 from light scattering and electrophoresis. Our value is somewhat higher for CIS. Mean Activity Coefficients below the C.m.c.-A graph of -log f us. cl/? (Fig. 6) for the two series can be compared with the corresponding activity coefficients for a uni-univalent electrolyte (NaC1). Because, for point charges, the Debye-Huckel limiting equation for a strong electrolyte may be written -log f = Xcl/?, the ratio log f ~ B ~ l / lwas ~ g calculated f employing the c.m.c. and the same concentration for the SaCI, using reported coefficients for the latter.6 This calculated ratio (Table I) provides an indication of interactions in addition to those present in SaC1. The pure Cloand mixtures of Clo and ClZcontaining 87.5, 75, and 50 mole % Closhow relatively small differences from ITaCl. On the other hand, for all the other mixtures, the ratio becomes progressively smaller with increasing amounts of higher homolog. I n Fig. 6, it is seen that the divergence between - log f values for the mixtures and for S a C l persists to concentrations well below the c.m.c. Mysels and Kaparranlo concluded that the conductivity of C1, did not indicate the marked dimerization for (9) J. K, Philips and K. J. Mysels, J . Phys. Chem., 59, 325 (1955). (10) R. J. Mjsels and P. Kapauan, J . Collozd Scs., 16,481 (1961).
Vol. 67
dilute solutions which had previously been reported for Clz.ll A different interpretation for the data of ref. 11, was offered by van Voorst Vader,12namely, that either large ion-size or a combination of large ion-size and a minor degree of dimerization could account for the conductivity. Some of the effects which we have described for the activity coefficientswould be expected if Clzand CI4,but not Clo, favor the formation of dimers, but the direction of these effects cannot be accounted for by the Falkenhagen corrections for ion size. Acknowledgments.-Dr. R. A. Bauman very kindly prepared the sample of C14especially for this work. We also are grateful for instructive discussions with Professor A. M. Liquori and Mr. J. V. Schurman.
DISCUSSION V. K. LA MER (Columbia University).-When one measures a quantity called pSa, pH or -log of any individual ion activity, he is violating the restrictions of E. A. Guggenheim [ J . Phys. Chem., 33, 842 (1929)] based on earlier statements of Willard Gibbs which in effect are that individual ion activities are hgpothetical quantities and attempts a t their measurement are alvays burdened with error. If Guggenheim strictures are carried to the limit, one should not even speak of pH. Of course this is going too far. I congratulate the speaker for checking, as well as one can, the limit of errors of principle involved in the n-ork presented. These errors are certainly small for univalent ions, for example, of pH and p y a . How far would he care t o push such measurements to such quantities as pCaII, pAlIII, and other high valence ions, particularly when the ions of opposite sign of high valence are present? A long series of solubility studies on such systems by La Mer (1924-1933) indicate that the Debye-Huckel limiting laws and the ionic strength principle were confirmed, but restricted in the generality of application by the electric-type effect [J.N. Br~nsted and V. K. La Mer, J . ,41n Chern. Soc., 46, 555 (1924), and V. K. La Mer, J . Phys. Chern., 6 6 , 973 (1962)j. Will the speaker kindly comment on these points? Almost all colloidal systems do involve ions, m-here the valence product 2 ~ often 2 ~exceeds 5 , which seems to be a limit in simple electrolyte systems. L. SHEDLOVSKY.-A “glass electrode” sensitive to divalent cations has been described by G. M. Sato, 111. E. Thompson, and A H. Truesdell [Science, 135, 1045 (1962)]. Csing such an .‘electrode” which was kindly provided by Dr. RI. E. Thompson, we found that solutions of CaC12show a linear relationship for e.m.f. us. pCa from to 10-2 iM CaCL with a slope of -30 m.v. per pCa a t 26”. The pCa of the solutions was calculated from mean activity coefficients given in the literature. These electrodes are also sensitive to monovalent cations as well as other divalent cations. For example, in the presence of sodium salts, the sensitivity to calcium is decreased. I do not know of “glass electrodes” suitable for the unambiguous determination of pRIIIr where &I111 represents a trivalent cation. As noted in the Experimental part, we converted e.m.f. to pNa by the use of Eo and 2.303RT/F values which were obtained with S a C l solutions. Our data correspond to mean activities of Na+ obtained from the literature for KaC1 solutions and not to individual activities of Na+, since the latter defy both definition and measurement. The ambiguity of individual ion activities is reflected in the liquid junction potentials. We had noted that a valid conversion of the e.m.f. to p S a depends on an equality of liquid junction potentials for the experimental and NaC1 solutions. We have no way from e.m.f. measurements of resolving the extent of any differences in these junction potentials, which may arise due particularly to the polyelectrolyte character of micellar solutions or to precipitation. The same considerations apply when pH or other p&I determinations are made by similar e.m.f. measurements. H. SCHONHORX (Bell Telephone Laboratories).-Activities of alkaline earth cations in the presence of alkali metal cations have been measured using a multilayer membrane electrode, which is far more ion specific than the ?u’a glass erectrodes. The (11) P. Mukerjee, K. J. Mysels, and C. I. Dulin. J . Phus. Chem., 62, 1390 (1958); P. Mukerjee, zbid., 62, 1397 (1958). (12) F. van Voorst Vader, Trans. Faraday Soc., 57, 110 (1961).
Oct., 1963
HYDROPHOBIC CONTRIBUTIOX TO MICELLE FORMATIOX
activities of CaClz have been determined in the presence of NaCl and KCl in the ratio of Carl/(Kf or N a f ) of 1/100. Harned’s rule has been corroborated for systems such as BaClz-KaC1, BaCkKCl, CaClz-NaC1, CaC12-KC1 in ratios of (alkali metal cation)/(alkaline earth cation) 5 100. I n principle, one could measure pX, where X could be any ionic species. The multilayer membranes are ion-selective as well as ion-specific. Anions have no effect on the transport of cationic species in the membrane phase. However, they will affect the activities of these ions in solution. L. SHEDLOVSKY.-’rhe “glass electrode” which we used to determine pNa respoiids to various monovalent cations. However, the influence of salts of divalent cations such as Ca+z is primarily a function of ionic strength. E. D. GODDARD (Lever Brothers Company).-The fractionating data are interesting and it would be useful to have con-
2079
firmatory evidence from another source. A possibility here would be the use of ultrafiltration, although complete separation of micellar from non-micellar components, of course, could not be achieved. Changes in composition with time would probably yield the required information.
L. SHEDLOVSKY.-E.Hutchinson [Z. physik Cherr,., 21, 38 1929)] has shown that after ultrafiltration of sodium decgl or sodium dodecyl sulfate solutions alone above the c.m.c., the concentration of the filtrate remained almost constant a t the critical value, while the concentration of the solution inside the nitrocellulose membranes steadily increased throughout the course of the experiment. If i t should prove to be possible to apply Hutchinson’s method to binary mixtures of homologs of alkyl sulfates, then a direct measure of non-micellar compositions will be available; thus, referring to Fig. 3, from a solution of composition B, a filtrate of composition A would be recoverable.
THE HYDROPHOBIC CONTRIBUTION TO MICELLE FORMATIOX : THE SOLUBILITY OF ETHANE, PROPANE, BUTANE, AND PENTANE I N SODIUhI DODECYL SULFATE SOLUTION1 BY
ARNOLD W I S H N I A
Department o j Biochemistry, Dartmouth Medical School, Hanover. New Hampshire Received March 8, 1963
From the ratio of the solubility of the alkane in detergent solutions and in water a t different temperatures one can obtain AF, AH, and A S for the transfer of alkane from water to the SDS micelle. Such studies, using both manometric and radioactive tracer techniques, have been carried out. The parallelism between these data and the parapeters for transfer of these alkanes from water to nonpolar liquids strongly supports the hydrocarbonliquid model of the micellar interior. At 25’ AFT RAN^ per CHZis 0.8 kcal. ( - 1.7 kcal. per half-ethane). The data for AHTRANSare not as certain and cannot yet be used to predict the hydrophobic contribution to AH of micelle formation for longer chains, but it is clear from the large positive values of the entropies of transfer of the CZ-C~alkanes (17-18 e.u.) that the effect of the alkanes on the structure of water, as pictured in current theories, must be the key factor in micelle formation.
-
Introduction
It has long been realized that to obtain micelle formation in detergent solutions rather than phase separation the cohesive ]forces leading to association must be accompanied by repulsive forces in such a way that the ratio of repulsive to cohesive energies diverges as the association number n becomes sufficiently large. I n Debye’s theory”‘ the decrease in free energy arising from hydrocarbon interactions given by -nwa is eventually overcome by electrostatic repulsion growing with Debye also argued that the distribution of micellar sizes was sufficiently sharp to be represented by a single size His theory has been criticized as to its detailszb; the parallel plate model of micelles has also been modified or discarded. More recently, Hoeve and Benson3 proposed a statistical mechanical theory of micelle formation in which the repulsive forces appear as a “crowding” term depending on Che ratio of volume to surface, as well as, for ionic detergents, an electrostatic term. The interior of the micelle is treated as a hydrocarbon liquid; the rest of the cohesive forces is contained in the partition function of the monomer, which contains a (not explicitly evaluated) contribution from the so-called “hydrophobic interactions” between the water structure and the alkyl chains; finally, a term for the residual interfacial energy of the oily micellar surface is included. (1) This work was supgorted in part b y PHS Grant RG 8121 and NSF Grant G 13973. (2) (a) P. Debye, Ann. N . Y. Acad. Sei., 61, 576 (1949); (b) J. J. Hermans, Koninkl. Ned. Akad. Wetenschap. Proc., Ser. B, 68, 91 (1955). (3) C. A. J. Hoeve and G. C. Benson, J. Phys. Chem., 61, 1149 (1957). A discussion of several previous theories is included.
The largely entropic role of “icebergs4” in micelle formation has been emphasized in recent years by investigators who obtained relatively IOW heats of micellization ~alorimetrically~-~ from temperature dependence of critical micelle concentration ( C . ~ . C . or ) ~ ,from ~ vapor pressure measurements.10 This author’s own interest in hydrophobic interactions stems from studies of their role in stabilizing protein structures. The demonstration by Ross and Hudson11 that c.m.c. could be determined from the solubility of butadiene in micellar solutions led this author to investigate the solubility of propane and butane in protein soIutions.12 From a comparison with solutions of sodium dodecyl sulfate (SDS) the thermodynamic parameters for the transfer of an alkyl group from aqueous surroundings to a hydrocarbon cluster as well as other information about the protein could be derived. This paper, which also includes data for ethane and pentane, will be directed to the problem of micelle formation. The work reported here is consistent with a liquid hydrocarbon model for the interior of micelles, and will allow an estimation of the hydrophobic con(4) H. s. Frank and M. W. Evans, J. Chem. P h y s . , 13, 507 (1945). (5) E. Hutchinson and L. Winslow, J . Phys. Chem., 60, 122 (1956). (6) E. D. Goddard, C. A. J. Hoeve, and G. C . Benson. %bid., 61, 593 (1957). (7) P. White and G. C. Benson, ibid., 63, 599 (1960). (8) G. Stainsby and A. E. Alexander, Trans. Faraday Soc., 46, 587 (1950). (9) B. D. Flockhart, J . Colloid Sei., 16, 484 (1961). (10) D. Moule, P. White, and G. C. Benson, Can. J . Chem., 87, 2086 (1957). (11) S. Ross and J. B. Hudson, J . Colloid Sei., 12, 523 (1957). (12) A. Wishnia, Proc. Natl. Acad. Sci., 48, 2200 (1962).
