650
C. BOTRI~, V. L. CRESCENZI AND A. MELE
is in good .agreement with the 2.9kT estimated by another approach.ls (2) The c.m.c. values of sodium dodecyl sulfate and sulfonate, 0.0081 and 0.0095 mole/l., are close to those of non-ionic surfactants containing a Cs hydrocarbon chain. Thus, the surface activity of non-ionic surfactants with octyl as the hydrophobic group is similar to that of ionic surfactants with dodecyl as the hydrophobic group, provided that the hydrophilic groups of the non-ionic surfactants are not very large. (3) The c.m.c. value of octyl glucoside (0.025 mole/l.) is about 100 times larger than that of polyoxyethylene dodecyl ether (0.00025 mole/l.) , although the hydrophilic groups are nearly the same size. Therefore, the energy required to transfer one methylene group from a hydrocarbon medium (13) K. Shinoda, Bull. Chem. SOC.Japan, 26, 101 (1953). (14) .J. T h . G. Overbeek and D. Stigter, REC.lvav. chin., 76, 1203 (1950). (15) I
a0 #,*.'l,,
LO 102.
Fig. 2.-Experimental activity coefficient yexas a function of the molarity of sodium lnuryl sulfate (NaLS).
interpolated from the curves of Figs. 2 and 3, are reported in the fourth column of Table I. From these results it appears that membrane electrodes may offer a new useful technique to determine the c.m.c. in detergent solutions. A qualitative approach to this method was outlined by Kolthoff, et al.,? some years ago, but to the best of our knowledge no further work has been carried out along this line. As mentioned in the experimental part, the membrane potential determinations mere carried out following two alternative procedures. While the two methods have provided equivalent results regarding the values of the c.m.c., the general trend of the y-conceiitration curves below the c.m.c. was found to be dependent markedly upon the procedure followed. Lower values of the activity coefficients were obtained by using the dilution method, (7) C. W. Carl, W. F. Johnson and I. M. IColthoff, THISJOURNAL,
sa,
636 (1948).
C. B O T R V. ~ , L. CRESCENZI AND A. MELE
652
Vol. 63
views, that above the c.m.c. any addition of detergent merely increases the number of micelles. Both the concentration of monomers and the number of monomers per micelle are considered constant. With these conditions and by formal separation of the contribution of the unmicellized and micellized molecules, the experimental activity of counterions may be expressed as a = r(Co
where
+
(1)
aCm)
CO = c.m.c.
-
c co = micelle concn. Cm = n a y
n
= degree of dissociation of micelles = activity coefficient of counterions = number of monomers
C = concn. of detergent 0."
0.5
15
f.0
2.0
Lin t i r i o ~ ,
Fig. 3.-Experimental activity coefficient yes as a function of the molarity of sodium laurate (NaL) and laurylamine hydrochloride (LAH).
0.25
0.50
0.75
1.00
co/c. Fig. 4.-Experimental activity coefficient yezas a function of CO/Caccording equation 2: --- sodium lauryl sulfate (NaLS); - - - -, sodium laurate (daL); . . . . laurylamine hydrochloride (LAH).
Thus far, no satisfactory explanation may be adduced. False equilibria and formation of small clusters of detergent molecules may account for this peculiar effect. These hypotheses can only be convalidated by a further and more careful study. Binding of Counterions in Micelle Solutions.With regard to the change of the activity coefficient with concentration, it may be observed that below the c.m.c. the behavior of detergent molecules is not very different from that typical of uni-univalent electrolytes. The departure from the behavior which might be predicted by direct application of the Debye-Huckel theory can be ascribed to the tendency of detergent molecules to give small aggregates below the c.m.c. Actually in the case of sodium lauryl sulfate, dimerization is claimed to occur up to 50% at the critical micelle concentration8; perhaps for sodium laurate and laurylamine hydrochloride the situation is similar. Immediately above the c.m.c., the y-concentration curves show a steep decrease which is clearly consistent with the assumed nature of the micelles in solution. The high charge density on the surface of micelles exerts a strong electric field on the counterions, which therefore are attracted strongly. Using our experimental data, we have made an attempt to evaluate the extent of the binding of counterions by micelles. For this purpose we have assumed, in agreement with generally accepted (8) P. Mukerjee, Abstracts of the Meeting Soo., Miami, April, 1957.
of the American Chem.
It follows from (1) that the experimental value of the activity coefficient is yex
= ay
+ r[Co/C(1 -
(2)
CY)]
In Fig. 4 a plot of 7%against Co/C is shown for the three detergents studied. In each case, a linear relationship is obtained indicating that both y and a may be considered practically constant in the range of concentration investigated. By extrapolating Co/C = 0, the values of ay have been obtained (see first column of Table II), and in turn assuming y to be equal to the experimental value at the critical micelle concentration (second column of Table 11) approximate values of a have been calculated for each case (third column of Table 11). From the number n of monomers per micelle and the value of a,the number of charges z, per micelle has been calculated (fourth column of Table 11). In the last column of the same table, the values of the degree of dissociation a evaluated from the data given in the literature (light scattering and electrophoresis) also are shown. TABLE I1 Compd.
oy
Y at c.m.c.
a
n
a,
ZC
lit.
NaLS 0.124 0.76 0.16 80. 13 0.18" NaL .16 .51 .31 .. .. LAH .10 .67 .15 133b PO O.llb a J. N. Phillips and K. J. Mysels, THIS JOURNAL, 59, 325 (1955). M. E. McBain and E. Hutchinson, "Solubilization," Academic Press, Inc., New York, N. Y., pp. 232-235. C Z = an.
..
The agreement is very satisfactory, particularly in view of the approximations in the above treatment and of the many restrictive hypotheses made in order to estimate the z values from light scattering and electrophoresis. The high binding properties toward their own counterions and the practical invariance of the degree of binding shown by micelles in detergent solutions has been suggested to compare micelles with polymeric electrolytes. It is apparent from the results of this investigation that micelles and the coiled macroions which are present in solution of polyelectrolytes, show many common features. Micelles, in fact, may be considered as spheres with a charge distribution on the surface, comparable in size and shape-though to a smaller degree-with coiled polyelectrolytes.
May, 1959
A convenient approach to the problem of binding by micelles will be considered here on the basis of a simple theory that has been proved already to be successful. when applied to other polyelectrolytes. For this purpose, a simplified picture of micelle solutions was assumed. Micelles were considered as spheres covered with n ionizable groups (n = number of monomers per micelle) of radius a corresponding to the hydrocarbon chain length of the monomers. The monomers present in solution at a practically constant concentration (c.m.c.) were assumed to play the role of “added salt.” Both radius and number of ionizable groups per micelle were considered independent of micelle concentration. Therefore, an evaluation of the binding of counterions by micelles has been made by means of the relation In
1 - a CY
653
A MODELOF ACTIVECARBON
+mk’+
= In
3. (YP(1 1-6 +
tJ1’8)
(3)
proposed by Oosawa for spherical polyelectrolytes,10 where m is the number of added ions. The parameter p is related to the charge n on the spherical ion and its dimension a according to e is the p = - ne2 DkTa
(4)
charge, D the dielectric constant and k and T have the usual meaning. d is the volume fraction of the micelles and it is proportional to the micelle concentration according t o 4
Cm
N
6 3 ra3i V Cm = k
(5)
N = Avogadro number V = total volume a and n have the meaning as in (4)
Equation (3) has been applied to NaLS, a compound of well defined properties and structure. Values of a have been calculated for NaLS in the absence of extraneous ions (m = c.m.c.) and (9) F. Ascoli, C. BotrB, V. L. Crescenzi, A. M. Liquori and A. Mele, t o be published.
(10) F. Oosawa. J. Polymer Sci., 23, 421 (1957).
for NaLS in the presence of NaCl 0.02 M (m = c.m.c. 0.02). The parameters introduced in (3) are listed in Table I11 and the linear plots obtained are shown in Fig. 5.
+
o.,
(.I
I.,
I.?
‘.O
I.8
I.6
I.‘
I.>
UI
I.d.,“.‘,,”,O~
Fig. 5.-Degree of dissociation (Y versus the molarity of sodium lauryl sulfate as calculated according to equation 3. The points represent the values of (Y from the yea's.
TABLE I11 a,
mc X
A. n 108 P NaLSa 18.5 80 0.80 32.0 NaLS-NaCI. 0.02 Nb 21.0 94 2.39 33.1 * J. N. Phillips and W. J. Mysels, THISJOURNAL, 59, 325 (1955). b D DStigter . and W. J. Mysels,.ibid., 59, 45 (1955). m in the absence of added NaCl is assumed equal to the concentration of detergent a t the c.m.c. Compd.
The points on the curves represent the value of CY as obtained according to relation 2 from the experimental data. The agreement between theory and experiments is quite satisfactory; furthermore, the effect due to the addition of NaCl on the degree of dissociation is correctly verified by the theory. Acknowledgments.-The authors are greatly indebted to Prof. A. M. Liquori for helpful suggestions and stimulating discussions. This work was sponsored and financially supported by Colgate-Palmolive Company, New York, which is gratefully acknowledged.
A MODEL OF ACTIVE CARBON’ BY W. F. WOLFF Research Department, Standard Oil Company (Indiana), Whiting, Indiana Received J u l y 14, 1068
A model for the structure of active carbon and a mechanism for the formation of such a structure is proposed. According to this view, the micropore structure of conventional active carbons is formed by a random oxidative attack on individual graphitic planes. A mathematical treatment based on this model defines a structure consistent with the available experimental data.
Introduction Two steps common to the preparation of active carbons are carbonization and activation.2 In the first step, organic matter is pyrolyzed to give a carbonaceous residue, or ((char.” In the activation step, a gaseous oxidant is commonly used to de(1) Presented in part before the Division of Physical and Inorganic Chemistry at the 133rd meeting of the American Chemical Society, San Francisco, California, April, 1958. (2) J. J. Ilipling, Quart. Reus., 10, l(1956).
velop a pore structure in the char. Carbons used for gas adsorption are activated by steam through the endothermic water-gas reaction. Gas-adsorbent carbons apparently have a layer structure,a with a micropore system consisting of molecular-size fissures4 developed during the activation step. Typically, about half of the carbon is consumed during this step. The size and (3) P. H. Emmett, Chem. Reus.. 43,09 (1948). (4) FV. F. Wolff, THISJOURNAL, 62, 829 (1958).
