432
Ki%G SHINODA
group of atoms in general) has an effect on the value of A for a given species of peripheral atom. The essential identity of the A values for the hydrocarbon series and for the amine series when the peripheral atoms are all H indicates that a central group composed of C and N atoms is equivalent to a central group composed entirely of C atoms. A central group composed of C and 0 is apparently not quite equivalent to one composed of C alone, since A for the entire molecule of alcohols and ether is larger than A for the hydrocarbons. The A values increase in order of increasing atomic numbers for the peripheral atoms
Vol. 59
Postulations.-A theoretical basis may be given equation 1. I n the quantum theory of dispersion it is shown that the polarizability a of an atomin a stationary electric field is given by
where (ex), and Y, are the electric moment and the characteristic frequency associated with the transition from the ground state to state m. As a postulate for the situation in molecules the polarizability a might similarly be the sum of such terms. Consider the case of a molecule composed of a central group of atoms essentially completely surAtom in a A-value, rounded by a single species of atoms. As a second moleoiile e.v. X cm.8 X lO-r4 postulate it is assumed that there is a series of valH 8.8 ues of Y for the molecule which are pi degenerate F 17.8 when p i is the number of peripheral atoms of kind i c1 30.3 per molecule. Assuming further that the main The value of la’ = 37 X e.v. X ~ m per . S~ contribution t o this series of Y values may be approxatom is out of order. A-value for oxygen, obtained imated by a single transition and that hv for this e.v. X cm.s. This is transition is approximately the first ionization poas la for H20, is 18.8 X also above but close to the A-value of the neighbor- tential of the molecule, equation 2 for these special ing atom, F, in the periodic table. molecules becomes These correlations allow the calculation of ionizaCY = 2pi(ex)*,/I (3) tion potentials of fluorocarbons for which, other than CF4,there are no measured values. The ratio I is the first ionization potential of the molecule, and of ionization potentials of fluorocarbons to those of (ex),,, is the magnitude of the dipole associated with hydrocarbons of the same carbon skeleton is in the the postulated single transition. If (ex), is a conrange 1.3 to 1.6. A contrast of this magnitude in stant for various molecules having the same kind of the ionization potential of non-polar substances can peripheral atoms, Ia vs. p i should be a straight account14 for a significant part of the non-ideal be- line through the origin of slope 2 ( e ~ ) , ~= Ia/pi. havior of solutions containing both a fluorocarbon Thus A in equation 1becomes 2 ( e ~ ) , ~ . and a hydrocarbon. Acknowledgment.-The author benefited from discussions of this work with Dr. J. H. Simons. (14) T.M.Reed, THISJOURNAL,68, 425 (1955). ’
THE CRITICAL MICELLE CONCENTRATIONS I N AQUEOUS SOLUTIONS OF POTASSIUM ALKYL MALONATES BY K6z6 SHINODA Department of Physical Chemistry, Faculty of Engineering, Yokohama National University, Minamiku, Yokohama, Japan Received November 1.3, 1964
The critical micelle concentrations (CMC) in aqueous solutions of homologous surfactants which possess two carboxyl radicals at one end of their hydrocarbon chain have been determined by the visual color change of dye, absorption spectrum of dye, solubilization and surface tension. Relation between the logarithm of the CMC of aqueous potassium alkyl malonates and the number of carbon atoms in hydrocarbon chain, m, is linear and the slope of the line is 0.51. Relation between the logarithm of the CMC versus m under the condition of definite concentration of counterions is also linear, and the slope of this line is 1.07. This value is nearly equal to the slope (1.08) between log CMC versus m in the case of fatty acid soaps. Accordingly the environmental energy change a t the micelle formation er methylene radical is given as about 1.08kT. The effect of added univalent salts on the CMC has also been measured. kelations between the logarithm of CMC and the logarithm of the total concentration of counterions, log C8, in all alkyl malonates investigated are linear, and the slopes of these lines are 1.12 within experimental error. This slope is just twice the mean slope 0.56 in the case of fatty acid soaps. This may result from the fact that the alkyl malonic acid ion is a bivalent anion, while the fatty acid ion is univalent.
Introduction On the micelle of colloidal electrolytes, there have been done many investigations during the past forty years.1-4 It has become clear that (1) G. 8. Hartley, “Aqueous Solutions of Paraffin-Chain Salts,” Hermann et Cie., Paris. 1936. (2) J. W. McBain, “Colloid Science,” Reinhold Publ. Corp., New York, N. Y.,1950. (3) W. D. Harkina, “The Physical Chemistry of Surface Films,” Reinhold Publ. Corp., New York, N. Y., 1952. (4) Per Ekwall, J . Colloid Sci., Supplement, 1, 66 (1964).
colloidal electrolytes show all the phenomena of colloids and exhibit a remarkably varied behavior which, however, has been shown to be subject t o quantitative control and to be perfectly reproducible. These experimental results impress that the micelle formation is a thermodynamically reversible process and the micellar solution obeys the phase rule for heterogeneous equilibrium.6 Especially in ( 5 ) J. W. h4cBain, R . D. Vold and M. J. Vold, J . AM. Chem. Soo., 60, 1866 (1938).
May, 1955
CRITICALMICELLECONCENTRATIONS IN POTASSIUM ALKYLMALONATE SOLUTIONS 433
Materials recent years the mechanism for the formation of micelle, association number and shapes of micelle Alkyl bromides have been prepared by the bromination have become clear by the investigations on the crit- of aliphatic alcohols with sodium bromide and concenical micelle concentration (CMC) of various colloidal trated sulfuric acid. Alkyl malonic acid diethyl esters have synthesized by the addition of malonic acid diethyl electrolytes under various condition^,^-'^ X-ray been ester to the alkyl bromides under the existence of sodium small angle ~ c a t t e r i n g * ~and - ~ ~light ~ c a t t e r i n g , ~ O - alcoholate. ~~ Alkyl malonic acid diethyl esters have been etc. After all, it is to be expected that scores of sur- saponified with alkali in alcohol and then acidified to alkyl factants aggregate into a micelle directing their malonic acids. These acids have been recrystallized two in benzene. Solution of potassium alkyl malonate hydrocarbon chains end-to-end and side-by-side times has been prepared by the similar procedures as in the case of and their polar groups toward the water, forming fatty acid soap. Aliphatic alcohols, alkyl bromides and oblate spheroidal double layer. On the other hand alkyl malonic acid diethyl esters have been purified by a theoretical equation of the CMC,25which is de- fractional distillation through a 50-cm. lass packed column. melting points or boiling points o f alkyl malonic acids rived from equating the chemical potentials of long- The and related compounds are shown in Table I. 2-Nitrodichain electrolytes in the micelle and that in the soluhenylamine is a product of Daiichi Pure Chemicals Co., tion, has explained many experimental results co- f t d . herently. It is apparent from this equation that TABLE I the charges on the polar group play an important Malonic acid diethyl Malonia role on the properties of surfactants. In order to Alkyl ester acid radical B.P., O C . a t Mm. m.p., "C. comment the anticipations derived from the theoretical equation of the CMC, the following experiOctyl 130-134 3 111 ments are needed: the systematic investigation of Dodecyl 165470 2 121-121.5 (1) the effect of added salts on the CMC,8v9(2) the Tetradecyl 196-200 4.5 122 123 effect of added alcohols on the CMC,l0J1 (3) the Hexadecyl 0.15 112.6-113 174-184 CMC of soap m i x t u r e ~ , l ~etc. - ~ ~ These investigaOctadecyl 185-200 0.2 119-121 tions had already been carried out, showing good Experimental Results agreement with the theory, but they were restricted to substances which possess one polar radical a t one The determination of the CMC has been perend of the hydrocarbon chains. formed by the change in color and spectrum of pinConsequently it has become important and inter- acyanole and the break in surface tension-concenesting to investigate the substances which possess tration and solubilization-concentration curves. two or three polar-ionic radicals a t one end of the (1) The Effect of Chain Lengths on the CMC.hydrocarbon chains, t o obtain the new knowledge The values for the CMC of the potassium alkyl on the micelle. In this purpose, the experiments malonates from the octyl malonate to the octadecyl of the alkyl malonic acids, which are considered malonate as determined by the change in color are the most convenient compounds for the theoretical shown in column 2 of Table 11. treatment, are eagerly demanded. The present investigation has been undertaken TABLE I1 to measure the CMC of aqueous solutions of a se- T H E CMC OF POTASSIUM ALKYL MALONATES (MOLES/L.) ries of potassium alkyl malonates, RiCH(COOK)2: Methods of the determination of CMC Viaual color Surface especially the relation of log CMC versus the numchange, tension. Mol. formula 25' 200 ber of carbon atoms in the hydrocarbon chain of alkyl malonates in case no salts added and under RaCH( COOK)I 0.35 0.30 the condition of definite concentration of counterRioCH(COOK)z .13" ... RizCH( C0OK)z .048 ,048 ions, and the effect of added salts on the CMC of the R&H( COOK)* ,017 ,019 respective potassium alkyl malonate.
-
(6) H. B. Klevens, J. A m . OiE Chemist's Soc., 80, 74 (1953). 63, 130 (1948). (7) H. B. Klevens, THISJOURNAL, (8) M. L. Corrin and W. D. Harkins, J . A m . Chem. Soc., 69, 683 (1947). (9) H. Lange, K o l l o i d - Z . , 131, 66 (1951). (10) S. H.Herzfeld, M. L. Corrin and W. D. Harkins, THISJOURNAL, 64,271 (1950). (11) K. Shinoda, ibid., 58, 1136 (1954). (12) H. B.Klevens, J . Chem. Phys., 14, 742 (1946). (13) H. Lange, Kolloid-Z., 181,96 (1953). 68,541 (1954). (14) K. Shinoda, THIS JOURNAL, (15) K.Hess and H. Kiessig, Ber., 81,327 (1948). (16) J. Stauff, Kolloid-Z., 89, 224 (1939); 96, 244 (1941). (17) R. W. Mattoon. R. 8. Steams and W. D. Harkins, J . Chem. Phys., 16, 209 (1947); 16, 644 (1948). (18) W. D. Harkins and R. Mittelmann, J . Colloid Sci.. 4, 367 (1949). (19) E. W. Hughes, W. M. Sawyer and J. R. Vinograd, J. Chem. P h y s . , Id, 131 (1945). 56, 644 (1951). (20) P. Debye and E. W. Anacker, THISJOURNAL, (21) E.W. Anaaker, J. Colloid Sci., 8, 402 (1953). (22) J. J. Hermans, Rec. Irau. chim., 68, 859 (1949). (23) T. M. Doscher and K. J. Mysels, J. Chem. Phys.. 19, 254 (1951). (24) E.Hutchinson, J . Colloid Sei., 9 , 191 (1954). (25) K. Shinoda, Bull. Chem. Soc. Japan, Z6, 101 (1953).
RisCH( COOK)2 .006 .009 RisCH( C0OK)z .0023 ... This value is obtained from the intersection in Fig. 1.
Experimental procedures are described in the preceding report^.^^^'^ It has been found that the logarithm of the CMC of the homologous alkyl malonates as obtained by the visual method a t 25" fits the equation log CMC = -Kim
+ const.
(1)
where m is the number of carbon atoms in the hydrocarbon chain (number of carbon atoms in the alkyl radical plus one), and K1is the experimental constant given as 0.51. A similar relation of log CMC versus m had been noted previously for several homologous series of long-chain e l e ~ t r o l y t e s , ~and ~ - ~the ~ slope was about (26) J. Stauff, Z. physik. Chem., A188, 55 (1939). (27) G. S.Hartley, Kolloid-Z., 88,22 (1939). (28) K.Hess, W.Philippoff and H. Kiessig, ibid., 88,40 (1939). (29) A. B. Scott and H. V. Tartar, J . A m . Chem. Soc., 66, 692 (1943).
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K6zG SHINODA
0.69 in the case of fatty acid soapgu These relationships are shown in Fig. 1.
VOl. 59 I
1.4
.
I
I
I
I
5 x 1 6 ' molar plnacydnole
x'
3 1.2 a 9 s
c
1.0
0
m
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