942
NOTES
gregate t o form micelles. Below the c.m.c. it generally has been assumed that, in the absence of hydrolysis, such electrolytes consist of simple ions though the suggestion has been made from time to time that aggregation occurs below the c.m.c. We have made accurate measurements of the electrical conductivity of aqueous solutions of sodium dodecyl sulfate at 25’ a t concentrations below the c.m.c. domi to 4 X M in order to investigate the extent of aggregation of anions to form dimers or small pre-micelles which, alone, presumably would increase the conductivity, or of association to ion pairs which would decrease the conductiyity. The results have been analyzed in the light of the theory of electrolytic conductance given by FLIOSS and Onsager , 2
0.0
\
-0.1
+ii 8C
Vol. 66
-0.2
-0.3
-0.4
0.5
1.0
1.5
4112.
Figure 1.
log y& was found to be =kO.OOl over a range of 0.1 to 1.2 m and .tO.OlO up, to 2.0 m. This value of A,’ corresponds to 1.84 A. for (2, the mean distance of closest approach. Use of the further extended Debye-Huckel equation with the added term of B, did not give a better fit after the proper adjustment of Am’ and B. i l s is expected for ammoniuni salts, the value of B is much lower than the values for the alkali halides, which range between 3.5 and ~ to indicate 6.2 8. The small value of B T V O L I ~seem that other important effects are present in addition to the very low hydration energies of the cation and anion. The logs of the mean molal actiyity coefficients of ammonium perchlorate along with some other 1-1 electrolyte~l~ are plotted in Fig. 1. It can be seen that the plot is slightly lower than that of ammonium nitrate, as m s expected. The L. L. line represents the Debye-Huckel limiting slope. (13) Reference 1, pp. 479-480.
CONDUCTIT’ITY OF SODIUM DODECYL SULFATE SOLUTIONS BELOW THE CRITICAL MICELLE CONCEKTRBTION BY G. D. PARKITT AND 8.L.
SMIT€ll
Department of Chemistrg, linzversity o f ATottingham, Kottzngham, Endand Recezved October 16, 1.961
Colloidal electrolytes such as sodium dodecyl sulfate shorn a more or less abrupt discontinuity in physical properties over a relatively short concentration range termed the critical micelle concentration (c.m.c.). Above this concentration it is well established that the amphipathic ions ag(1) A t the time of this vork a t the College of Technology, Northampton, England.
Experimental The sodium dodecyl sulfate was a pure sample kindly supplied by Thomas Hedley & Co., Ltd., having a purity of 99.9% as determined by partition end-point titration.8 It was purified further by a liquid/liquid extraction technique.* The water used was obtained from an ion exchange column and, equilibrated with air, had a conductivity 1.1 X 10-aohm-l cm.-l. Conductivities were measured on a conventional 1000 cycles/sec. bridge incorporating a Wagner earth using resistance boxes of 0.05% grade. The cell, similar in design t o that of Flockhart and Graham,6 was of 400 ml. capacity and required 50 ml. to cover the electrodes. Dilution additions were by weight and concentrations calculated from measured densities. Equilibrium was reached about 30 min. after dilution. Resistances were taken after about 1 hr. and remained constant for a t least 7 days.
Results and Discussion The results are shown in Fig. 1 by a plot of A us. c X lo3 which is of the form expected for a 1:l strong electrolyte. Both the internal consistency and the agreement between the three overlapping series of measurements were -0.05%. Fuoss and Onsager2 give for an unassociated 1:1 electrolyte (neglecting a small viscosity term) A = Ao - SC‘/Z-j- EC log c JC (1) where X is the Onsager limiting slope, E is a function of .io and the solvent properties, and J is a function of do,the solvent properties, and the ion size parameter “a” For an associated electrolyte this becomes
+-
A =
A0
- SC‘/Zy ’ / z f ECy IOg cy
+
JC+y
- KaCyf’h
(2)
Treating the sodium dodccyl sulfate as a simple unassociated 1:l electrolyte do was found from the data by a Shedlovsky extrapolation6 so that X and E could be calculated and eq. 1 applied. A plot of -1 SC’/~- Ec log c us. c (Fig. 2 ) is straight up t o concentrations very close to the c.m.c., after which an abrupt change is obvious. The slope, J , of the portion below the c.m.c. is $95, which corresponds to a value for “u” of 5.0 A. This is rather less than the aT-erage value of 5.5 8.found’ for this electrolyte in dioxane-water mixtures a t lower dielectric constants with appreciable values of the
+
(2) (a) R. M.Fuoss and L. Onsager, J . Phvs. Chem., 61,868 (1957); (b) R. M. Fuoss and L. Onsager, sbzd., 62, 1339 (1958). (3) T.Barr, J. Oliver, and W. V. Stubbings, J . 8 o c . Chem. Ind.. 67, 45 (1948). (4) S.P. Harrold, J. CoElozd Sez., 15, 280 (1980). (6) B. D. Flockhart and E. Graham, %bad.,4,367 (1949). (6) T.Shedlowky, J . Am. Chem. Soc., 64, 1405 (1932). (7) G.D.Parfitt and A. L. Smith, awaiting publication.
SOTES
May, 1962
943
which the Onsager limiting slope is drawn. Such an extrapolation naturally gives overwhelming weight t o the least accurahe data at greatest dilution where the solvent correction is stated to be 10-40%. In this work the maximum solvent correction is rather less than 4%. I n a recent investigation9 of sodium dodecyl sulfate belom the c.m.c. by e.m.f. measurements it was found that dimerization was at most small and the results are, in fact, in good agreement with a zero dimerization constant. We conclude, therefore, that there seems no reason to postulate that sodium dodecyl sulfate below its critical micelle concentration is other than a 1:1 strong electrolyte. (9) F. van Voor-Jt Vader, Trans. Faraday Sac., 51, 110 (1961).
60
0
6 8 10 103. Fig. 1.-Equivalent conductivity of solutions of sodium dodecyl sulfate (c in moles 1.-1): , Onsager tangent.
2
4
c
x
-
T H E NATURE OF THE BINDING OF COUKTERIONS 03 CHARGED COLLOIDS AND RIACROMOLECULES BY PASUPATI MUKERJEE Indtan Association for the Cultivation of Soence, Jadavpur, Calcutta-8% India Received October l Y , 1961
Various different kinds of investigations, such as counterion activity determination, conductivimetry, and transport studies leave little doubt that for highly charged colloids such as polyelectrolytes and micelles of association colloids a large fraction of the counterions remains bound to the colloidal particles, strongly enough to form part of the kinetic entity. B question of some importance in the theoretical study of ion-binding and the energetics of these species concerns the nature of 72.8 , , , , , , , , this binding, i.e., is it entirely non-specific binding arising out of the strong electrical forces or are 0 2 4 6 8 there perhaps more specific forces such as covaIent c x 103. Fig. 2,-Plot of A + - Ec log c us. concentration for forces involved? Recent studies using Raman sodium dodecyl sulfate ( c in moles l.-l). spectra’ and nuclear magnetic resonance2 suggest that the binding is non-specific. The purpose of association constant KA. At low values of K A with y , the degree of dissociation, nearly unity it this note is to show that an equilibrium method, would need alirnost impossibly precise data to involving the use of partial molal volumes, P, is a separate the Jc term from the K A q f 2 A term. The useful general method for studying this question. The method is applied to a micellar system and a difference between the two “a” values would be polyelectrolyte. accounted for by a K A of about 0.5. The basis of the method can be derived from the Thus, in water, a t concentrations below the properties of simple electrolyte^.^ For these, at c.m.c. sodium dodecyl sulfate has been found to infinite dil_ution, V’s are strictly additive, beigg the behave as a simple 1:l electrolyte. The appreciable formation of dimers or larger aggregates would sums of V’s of: individual ions, so that AV, the cause deviations from eq. 1 which have not been difference in V of two electrolytes of the same charge-type with one ion in common, is independent observed. of the nature of the c_ommon ion. The conceiitraI n the work of Mukerjee, Mysels, and Dulin8 on sodium dodecyl sulfate and other similar electro- tion dependence of I/ for strong electrolytes can lytes the conductivity data are explained in terms be expressed over a wide range as P = Vo S d e of dimer formation below the c.m.c. to account for where Vois the value at infinite dilution and X is a equivalent conductivities well above the Onsager constant characteristic of the electrolyte. An limiting slope. Although the latter work preceded important property of X is that its values also are the Fuoss-Onsager theory, a footnote points out reasonably additive with respect to individual ions, that the higher terms introduced by this theory particularly for 1:1 electrolytes. As a result, even would not account for the observed deviations. a t fairly high concentrations, in spite of consider11) S. Lapanje end s. A. Rice, J . Am. Chem. Soc., 83, 496 (1961). However, the analysis of these workers starts by an (2) L. Kotin and RI. Nagasawa, ibtd., 83, 1026 (1961). plots to obtain ho from extrapolation of A us.
\ ,I
+
(8) P. Mukerjee, K. J. Mysels, and C. I. Ilulin, J . Phys. Chem., 62, 1390 (1958).
(3) E. 8. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold Publ. Gorp., Nev York,
N. Y.,
1958.
