Oct., 1963
STUDYOF pKa
OF
AQUEOUSSOLUTIONS OF SODIVM DECYLSULFATES
2075
STUDY OF pNa OF AQUEOUS SOLUTIONS OF SODIUM DECYL, DODECYL, AND TETRADECYL SULFATES BY E.M.F. MEASUREMENTS BY L. SHEDLOVSKY, C. W. JAKOB, AND M. B. EPSTEIN Colgate-Palmolive Research Center, Colgate-Palmolive Company, iVew Brunswick, S . J. Received March 8, 1963 Electromotive force measurements were made with sodium-respopsive glass electrodes and saturated KCl, calomel electrodes on mixtures of sodium alkyl sulfates. Two solution pairs were studied: sodium decyl and dodecyl sulfates and sodium dodecyl and tetradecyl sulfates. Critical micelle concentrations were selected from plots of p y a us. log c. The procedure of Mysels and Otter was used to establish the non-micellar concentrations in the micellar solutions of mixtures. The extent of the dissociation of sodium counterions by the micelles was estimated from the reduced data. From the activity coefficients strong interaction below the critical micelle concentration was inferred for all the mixtures except those containing more than 25 mole Y, c f sodium decyl sulfate.
The present investigation examines the behavior of aqueous solutions of mixed colloidal electrolytes by means of electromotive force (e.m.f.) measurements based on a sodium-responsive glass electrode. Botr6, Crescenzi, and Mebe’ carried out similar measurements for solutions of a few single colloidal electrolytes by using cationic organic membranes. In their discussion they treated the micelles as polyelectrolytes. It often is convenient to treat micellar solutions of colloidal electrolytes as a system of quasi-phases, one, an aqueous or non-micellar medium, within which a second, the micelles, is distributed. Lange2 recognized that in a micellar system, which contains two surface active Eiolutes, the critical micelle concentration (c.m.c.) varies with the relative amounts of the two solutes and that the locus of the c.m.c. was a kind of phase boundary of the aqueous medium. On the basis of a theoretical model, Mysels and Otter3 recently employed conductivity measurements to obtain the boundary of the mixed micelles and the tie lines to the aqueous medium; they discussed also the thermodynamics of the system. It is implicit in their treatment that it may be applied to other intensive properties. We have used e.1n.f. measurements both to establish the composition of the micelles and to extend the treatment of BotrB, Crescenzi, and Mele to mixed systems. Experimental Electromotive Force Measurements.-These were made with glass electrodes responsive to sodium and a saturated KCl, calomel half-cell. We are indebted to Professor Eisenman, who supplied bulbs made of XAS 11-18 glass4 with which initial measurements were made. All of the data reported here were obtained with a Beckman Cationic Electrode XQ.78137. Insufticiept reproducibility of potentials a t the outset was substantially eliminated by the use of a MacInnes-Belcher calomel haif-cell and 3-way stopcock assembly6 in place of fibre or sleeve-type calomel electrodes. This permitted formation of a fresh, uncontaminated liquid junction for each measurement. Potentials promptly read after formation of the jpnction were reproducible on a given solution to 0.1 my. (0.0017 pNa unit). Delay of more thanafew seconds, except in the more dilute solutions, led to slow precipitation a t the liquid junction and lowering of the potentials by as much as 1 mv. in a minute. The liquid junction was re-formed repeatedly for each solution to obtain a value for the poteptial. Currently the use of a potassium-free salt bridge is being examined. We consider, however, that variations in potential a t the liquid junction may also accompany the use of 0.1 N NaC11 in place of saturated KCI. The balance of the circuit included a (1) C. Bot&, 7,‘. L. Crescenzi, and A, Nele, J . P h y s . Chem., 63, 660 (1959). (2) H.Lange, i’~oZload-ZeztachrP~~, 131, 96 (1953). (3) K. J. Mysele and R. J. Otter, J . Colload Scz., 16, 462, 474 (1901). (4) G. Eisenman, D. 0. Rudin, and J. V. Casby, Science, 126,831 (1957). (5) D. A. Maolnnes and D. Belcher, Ind Eng. Chem., Anal. Ed., 6 , 199 (1933).
Keithley 2008 electrometer connected directly to the glass rlectrode and a Rubicon precision potentiometer. Values of 2.303RTIF taken on NaCl solutions of known mean activity6 were within 0.1 mv. of the theoretical value for the temperature of the run. 811 measurements were made a t known temperatures between 23 and 26”. Electromotive force values on experimeptal solutions were converted to pNa by use of the Eo and 2.303RTIF values which were obtained with NaCl solutions. It is necessary that the liquid junction potentials be the same for experimental and NaCl solutions for a valid conversion. Both the formation of micelles (which resemble polyelectrolytes) and the precipitation may alter this relation. Materials.-The sodium n-decyl sulfate sample ( “ C d ’ ) is described elsewhere.’ The sodium n-dodecyl and n-tetradecyl sulfates (“C12” and ‘‘C14’’) were prepared from 99.8 and 99.5% normal alcohol8 purchased from the Applied Research Laboratories and Lachat Chemicals, Inc., respectively. No corrections* for p H in the calculation of p y a values were necessary as the solutions of these materials gave neutral pH.
Results and Discussion Selection of Critical Micelle Concentrations.-It has been commonly observed that with any given set of data ambiguity may arise in the fixing of the critical micelle concentration (c.ni.c.). That the relation between the micellar and iionmicellar material may be interpreted as a mass action equilibrium and, as a consequence, the c.m.c. in reality is of limited sharpness has been discussed. However, in the reduction of data and in the treatment of a solution as a pair of quasi-phases, selection of values seems essential and is carried out by extrapolation to an intersection of mathematical functions, preferably straight lines, fitted t o the data on each side of the c.m.c. We find that plots of mean activity (a) us. concentration (e) and of mean activity coefficient ( j ) us. c’/~are similar in appearance to the analogous plots of specific and equivalent conductance, and for the reasons given by Mysels and Otter3 this leads to differing values of c.m.c. For mixtures, however, the available straight line portioiis of the activity coefficient plot were too brief. Plots of pNa (Fig. 1 and2) appeared to be a Setter choice. In addition, there is the further consideration (assuming the Xernst equation holds for these cell chains) that the pKa is a linear function of the actual quantity measured, the electromotive force. Because different samples are involved, it is difficult to judge whether the values thus obtained (c.m.c. 111, Table I) were closer to c.m.c. I (A us. ci/’) of Mysels and Ottera than to their ( 6 ) H. S. Harned and L. F. Xims, J. A m . Chem. Soc.. 67, 1356 (1935); Soc., 44, 295 (1948); R. A. Robinson and R. H. Stokes, ibzd., 46, 612 (1949). (7) E. I. Valko and 11. B. Epstein, “Proc. 2d Intern. Congress of Surfaco Activity,” Butterworths Scientific Publications, London, 1957, p. 334.
R. H. Stokes, Trans. Faraday
I
I
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I
I
3.5
I
t
ALD
I
'I
SODIUM DODECYL TETRADECYL SULFATES
SODIUM DECYL AND DODECVL SULFATES
e , 50 c, 104 M .
100
150
Fig. 3.-g(c) us. total concentration, where g(c) is the mean activity. The upper and lower curves are for pure sodium dodecyl and tetradecyl sulfates, respectively. The middle curve is for solutions equimolar in sodium dodecyl and tetradecyl sulfates. The dashed line from the origin to D' is based on the selected c.m.c. values (c.m.c. 111). -3.0
- 1.5
-2.0
-2.5
I
log c.
Pig. l.-p?\'a
I
I
TETRADECYL SULFATES
us. log total concentration for mixtures of sodium
decyl and dodecyl sulfates. I
I
I
S O D I U M D O O E C Y L AND TETRADCCYL SULFATES
3.5
- MOL! x c-I 0 4
d
0
I
3.0
5
25
50 mole
3
- 3.0
-3.5
75
I
87
-
100
- 2.0
-2.5 log c.
Fig. 2.-pNa
vs. log total concentration for mixtures of sodium dodecyl and tetradecyl sulfates.
c.1n.c. I1 (K us. c). They found for pure Cla and for CE that c.m.c. I was 2.8% lower than c.ni.c. 11. TABLE
1
SUMMARY OF RESULTS Mole % C.m.c. I C.m.0. I1 lower (ref. 3) (ref. 3) C.m.c. homolog 108 X M. 111
log Mean .fxSc1c activity f/firaCl log! 101M.
i Clo-C12 mixtures
100 87.5 75 50 26 0
32.6 20.6 16.0 11.2 9.07 7.86
33.5
33.7
0.82 0.97 .84 .96 15.6 .86 .97 10.8 .89 .98 8.55 .86 .94 7.58 .81 .89
20.2
8.09
0.87 .79 .78 .88 .63 .41
27.8 17.0 13.35 9.60 7.39 6.14
0.30 .29 .28 .24 ,21
0.41
6.14 4.25 3.20 2.11 1.-4
.22 .18 .I8 .I7 .13
.22
C12-C1, mixtures 100 87.5 75 50 0
7 . 5 5 0.81 0 . 8 9 5.11 .83 .91 3.88 .88 .82 2.62 .81 .8:5 1.83 .79 .79
.40
.33 ,25
.l9
100
Fig. 4.-Xon-micellar concentration (e,,) us micellar and nonmicellar compositions for mixtures of sodium dodecyl and tetradecyl sulfates. Micellar points xith circles shaded on the right, left, and bottom are derived, respectively, from sclutions 87.5, 75, and 50 mole yo in sodium dodecyl sulfate.
50
2.5 2
75
yo Cln.
Distribution between Aqueous Medium and Micelles. ---RotrB, Crescenzi, and &&de1 advanced a simple model for the evaluation of the binding of counterions by micelles. Their treatment assumes among other
things that above the c.m.c. further addition of solute leads nierely to an increase in the number of micelles ; their size and the concentration of noii-micellar material remain constant, It is apparent that for a mixture of colloidal electrolytes, modification mill be necessary. In such solutions, if the ratio of the two solutes is held constant, formation of micelles is acconipanied by a fractionation between micellar and nonmicellar material which changes as the concentration is increased. The extent of aggregation for the higher member is believed greater,8 but we caniiot take account of this factor. Let lines CDE and CD'E' (Fig. 3) describe an intensive property g(c) of two pure homologs which has the characteristic that the values below the critical points D and D' lie on a common curve but above D and D' lie on parallel curyes. If g(c) follows the course CB, for a particular mixture, bIysels reasons that the absence of a sharp break and the general curvature are due to the changing composition of the micelles with concentration. He reasons further that all non-micellar solutions lie approximately on the curve CDD'. Similarly, a straight line drawn parallel to the micellar lilies (DE and D'E') for the single components will cut the line CD a t that non-micellar conreiitration (c,) which corresponds to the total solutio11 concentration (c). lye note illat. ( 8 ) H. V. Tartar, J . Collozd Sca., 14, 115 (1S59).
STUDY OF p S a
Oct., 1903
OF
:IQVEOVS SOLUTIONSOF SODIUMI ~ E C TSULFITES L
2077 ~
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LOWER HOMOLO(
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MOLE %
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to
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aiitl
31clo corrcrted for variation i n thc lion-niicellar vonccntration.
A, iiiixturcs of
sodiuiii cloclcc~yland tetradccyl sulfates; l
