1390
PASUPATI MUKERJEE, KAROL J. MYSELSAND C. I. DULIN
Vol. 62
DILUTE SOLUTIONS OF AMPHIPATHIC IONS. I. CONDUCTIVITY OF STRONG SALTS AND DIMERIZATION1 BY PASUPATI MUKERJEE, KAROL J. MYSELSAND CYRILI. DULIN Department of Chemistry, University of Southern California, Los Angeles 7, California Received September 18, 1067
The equivalent conductivity of pure sodium lauryl sulfate has been determined from the c.m.c. to the highest accessible dilutions. The A us. c< plot, while almost linear, has a slope which cannot be that of a simple 1:1 electrolyte. Qualitative arguments point to the reversible formation of a more conducting dimer LSz- by the amphipathic LS- ion and this hypothesie accounts quantitatively for the available data. The similarly anomalous conductivities of highly dilute solutions of the lithium salt are also in quantitative agreement with this explanation. An important consequence of these findings is that the intermicellar liquid is not formed by monovalent ions but by a mixture of mono- and divalent ones. Thus the concentration of simple ions is not e ual to the stoichionietric concentration a t the c.m.c. The reversible formation of the dimer is ascribed to an equilibriumsetween the increasing electrostatic repulsion between the heads and the decreasing interfacial energy as the hydrocarbon tails join.
The most outstanding property of amphipathic ions-characterized by a hydrophilic charged “head” and a hydrophobic hydrocarbon (%ail))is their tendency to form large aggregates, the micelles, above a certain rather sharply defined concentration, the critical micelle concentration or c.m.c. Because of the unique purity and thermodynamic stability of these colloids, much effort has been, and is being, expended in the study of the structure of these micelles and of forces responsible for it. Recently, emphasis has been placed on the extrapolation of measurable properties of micelles to their infinite dilution, Le., to the c.m.c., and on the structural interpretation of the extrapolated value in terms of interaction of the colloidal ion with the small ions surrounding This approach by-passes the much more formidable problem of interpreting, in addition, the inter; action of colloidal ions with each other. It depends critically, however, on a knowledge of the nature of the simple electrolyte present a t the c.m.c. In the absence of added salt this electrolyte consists of amphipathic ions and their counterions. Even in the presence of added salt the amphipathic ions are always present and contribute to the over-all interaction. Thus detailed knowledge about the behavior of the amphipathic ions, aside from its intrinsic interest, is valuable for an understanding of the equilibrium between small ions and micelles. It has been recognized for some time that amphipathic ions with carboxyl heads which are present in ordinary soap, hydrolyze extensively in dilute solutions to form more or less soluble products and thus render any interpretation difficult. Hence salts of strong amphipathic acids and bases, such as the alkyl quaternary ammonium salts and the alkyl sulfonates and sulfates, have become the preferred subjects of study. Sodium lauryl (dodecyl) sulfate or NaLS has been studied extensively,a-Din this Laboratory in particular. (1) Based in part on the Ph.D. thesis of P. Mukerjee, University of Southern California, 1957, and presented a t the Kendall Award Symposium honoring P. J. W.Debye a t the Miami Meeting of the A.C.S., April, 1957. (2) P. Debye, THIS JOURNAL, 53, 1 (1949). (3) D. Stigter and K. J. Mysels, ibid., 69, 45 (1955). (4) D. Stigter, R. J. Williams and K. J. Myaels, %‘bid., 69, 330
(1955).
( 5 ) W. Prins and J. J. Hermans, Proc. Ron. Ned. Akademie van Wettenschafe‘cr,B59, 162 (1956). (G) R. J. Williams, J. N. Phillips and K. J. Mysels, Trans. Faraday Soc., 61, 728 (1955).
It has been assumed generally that in the absence of hydrolysis, the amphipathic ions behave as simple monovalent ions up to the c.m.c. This is the simplest assumption and could be well defended, on balance, in view of some supporting experimental evidencelo-12 despite clear danger signs, shown particularly by some work of McBain’s school which revealed appreciable deviations from ideality below the c.m.c.13J4 The difficulty of obtaining dependable data at high dilutions and of finding an alternative quantitative interpretation also argued acceptance of the simplest picture. The work to be reported in this series shows that the behavior of dilute solutions of amphipathic ions, especially of LS-, requires the existence of a reversible equilibrium between the LS- ion and its dimer LS2--. With Na+ and Li+ ions these give strong, completely ionized, salts, but with Ag+ and with quaternary ammonium ions there is some weakness. The suggestion that dimers are present in dilute solutions of these compounds is not new. Kraus and c ~ - w o r k e r s ~ ~have J ~ J ~advocated their irreversible formation in some higher cationics. The reversible, equilibrium formation has been postulated several times on various grounds, either as the only aggregation step prior t o micelle formationl7-l9 or as one of the stages toward “small” or “ionic’) micelles.2o Yet the arguments advanced appear not to have been strong enough to influence the general course of thought in the field. This may well be because most, if not all, evidence for reversible dimerization came from the study of alkali soaps of fatty acids where hydrolysis and pre(7) J. N. Phillips and K. J. Mysels, THISJOURNAL, 59, 326 (1955). (8) K. J. Mysels and C. I. Dulin, J. Colloid Sei.,10, 461 (1955). (9) P. Mukerjee and K. J. Mysels, J. A m . Chem. Soc., 7’7, 2937
(1955). (10) (11) (12) (13)
P. F. Grieger and C. A. Kraus, ibid., 71, 1455 (1949). D. W. Kuhn and C. A. Kraus, ibid., 7 2 , 3676 (1950). A. B. Scott and H. V. Tartar, ibid., 65, 692 (1943). M. E. L. McBain, W.B. Dye and 9. A. Johnston, ibid., 61, 321
(1939).
(14) M. E. L. McBain, J . Colloid Sci., 10, 223 (1955). (15) E. J. Bair and C. H. Kraus, J . Am. Chem. SOC.,7 3 , 1129 (1951). (16) M. J. McDowell and C. A. Kraus, ibid., 7 3 , 2173 (1951). (17) J. Stauff, Kolloid Z . , 96, 244 (1941). (18) G. Jander and W. Weitendorf, Z . angew. Chem., 47, 197 (1934). (19) P. Ekwall, ibid., 80, 77 (1937). (20) J. W. McBain, “Colloid Science,” D. C. Heath and Co., Boaton, Mass., 1950; P. Ekwall, Rolloid Z . , 92, 41 (1940).
yl
Nov., 1958
DILUTE SOLUTIONS OF AMPHIPATHIC IONS
cipitation make the interpretation very involved and uncertain. Our purpose is to present evidence from the study of non-hydrolyzing ions that the presence of dimers is quantitatively necessary and sufficient to account for the available facts; that they are present in substantial proportions (so that they must be taken into account in any rigorous interpretation) , and that while they make some calculations much more complicated, they clarify many aspects of this field. Because of the importance of dimerization in the interpretation of the properties of micelles, because of the light it sheds on interionic forces in solution and because of certain disturbing coincidences which will be discussed later, it was desirable to obtain several independent lines of evidence for this picture. The present paper gives the original argument based on the conductivity of the strong salts while the following papers deal with transference work, the conductivity of the weak salts, and a reinterpretation of some literature data which all support our point of view. The emphasis on conductance is due to two factors: its outstanding accuracy in dilute solutions and the reliability of the Onsager interpretationz1 for the same region. Experimental Materials.-The NaLS was prepared and periodically recovered by the method already described .8 LiLS proved to be too Boluble for repeated recrystallization. It was prepared according to a general method, described elsewhere,l2 by careful turbidimetric titration of AgLS with LiCl in alcohol, separation of the silver chloride, and evaporation of the alcohol. The LiLS sample was recrystallized once from fresh 95% ethanol. Its purity was estimated to be about 99.9%, the rest being inorganic salts. The water used was either commercial distilled water equilibrated against carbon dioxide in air, or water distilled from alkaline permanganate solutions, purified further by passage through an ion-exchange column, and equilibrated against carbon dioxide. The former type of water gave a solvent correction of 2-3 X 10-8 ohm-' and the latter 0.8-1.8 X 10-6 ohm-'. The latter water was used for all the work in the most dilute region (
