ACTIVITY COEFFICIENT OF SURFACE-ACTIVE SUBSTANCES
107
T H E ACTIVITY COEFFICIEXT OF SURFACE-ACTIVE MATERIALS IK AQUEOUS SOLUTIONS' HAROLD M . SCHOLBERG
Central Research Department, Minnesota Mining &. Manufacturing Company, St. Paul, Mannesota Received August 82, l@@
Because, up to the present time, no satisfactory method has been available for estimating the activity coefficient of surface-active substances in aqueous solutions, the far too common practice has been to ignore the question. The standard methods for the determination of the activity of a solute, such as change in vapor pressure or osmotic pressure of the solvent, are of questionable value because the presence of micelles raises the effective molecular weight of the solute to too high a value to allow any degree of precision. The experiments outlined in this paper are an attempt to show that surface tension measurements can be used to determine the activity coefficients of surface-active materials. The method allows a considerable increase in accuracy, for it is in the very dilute regions that surface tension measurements show the greatest changes. It is believed that the arguments in this paper lend, in addition, to a clearer understanding of the Gibbs adsorption equation. Many attempts have been made to verify the Gibbs adsorption equation. Donnan and Barker (2), Harkins and Gans (4), and McLewis and Patrick (9) reported fairly good agreement, although in all these tests the experimental value of the amount adsorbed tended to be larger than the theoretical value. McBain and his coworkers (8) stated that, with the exception of nonylic acid, the amounts adsorbed in all cases greatly exceeded those calculated with the aid of the Gibbs equation. Lately much work has been reported on the determination of the point, or concentration, corresponding to the beginning of micelle formation. The change in the absorption spectrum of a cyanine dye, as developed by Harkins and his coworkers (l),gives good results. Surface pressure measurements are here shown to provide a good method for the determination of the critical point. EXPERIMENTAL
Figures 1 and 2 show typical curves obtained for Duponol OS, Triton NE, Duponol 80, Tergitol No. 7, Tergitol No. 4, and Tergitol No. 8. Figure 3 shows the data on sodium cetyl sulfate taken from the paper by Nutting and Long (10) and also the curve for hexanolamine oleate. The surface pressure of solutions of wetting agents was determined as a function of the logarithm of the concentration. The solution whose surface pressure was to be determined was sealed into a test tube. The distance from the bottom of the meniscus to where it came in 1 Presented a t the Twenty-third National Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the American Chemical Society a t Minneapolis, Minnesota, June 6-8, 1949.
108
HAROLD M. SCHOLBERG
LOG CONC., p r / r O O q r ~ O
FIG.1. Surface tension measurements on Tergitol No. 4, Tergitol S o . 7, and Tergitol No. 8
r----
60
F I G 2. . Surface tension measurements on Duponol OS, Triton K E , and Duponol 80. On the Duponol OS curves represents fresh solutions run on December 12, 1946 and 0 represents the same solutions run on January 31, 1947.
contact with the wall of the test tube was measured with a traveling microscope. The value of the capillary constant, u2 = 2u,/pg, was read from a calibration curve of u2 against h, the height of the meniscus, prepared from a series of pure
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ACTIVITY COEFFICIEKT O F SURFACE-ACTIVE SUBSTANCES
M-
CSODIUM
-60
ETYL SULPHATE 70,
40.C
I
20-
>d 0 -
i
E
410-
20
0 5
3
-4
2
0
DISCUSSION
The break in the surfacc. pressure curves is contrary to what the Gibbs equation would lead us to expect, for this discontinuity says that as the film pressure is increased the area per molecule increases, and this can hardly be allowed. It can be reconciled, however, if we call the part of the curve below the critical break point and its extrapolation above that point, as shown by the dotted lines, the activity curve. The difference between the two curves a t a given surface pressure is then the logarithm of the activity coefficient. The justification for this is given below. Let us suppose that two different wetting agents are dissolved in \yater and that at the same activity of the solute, the drop in surface tension is the same in both solutions. Let us further suppose that wetting agent A gives a surface film that obeys the simple gas law; that B gives a solid film, as, for instance, stearic acid spread on dilute hydrochloric acid. For simplification we also set the condition that the solutions are sufficiently dilute so that the amount of wetting agent a t the solution-air interface due to adsorption at the interface is much greater than the amount which would be at the interface if there were no adsorption.
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HAROLD M. SCHOLBERG
Gibbs’s equation may be written as: lo-’’ dAu -= 2.303kT d log U: This may be integrated thus:
2.303kT Vnder the conditions above
/
dAU
=
/
r
d log a2
r = -1 4
and equation 2 may be written
where k = the gas constant per molecule, T = the absolute temperature, Au = the surface pressure of the solute, a2 = the activity of the solute, F = the molecules per square h g s t r i m adsorbed a t the interface, and A = the area per molecule in square Angstroms. Equation 3 was integrated for the tv-o solutions mentioned above, assuming a surface tension lowering of 20 dynes per centimeter and log u2 = - 2 as the starting point. In figure 4 curve A is for the gaseous film ( A u A = k T ) , and curve B is for the stearic acid, solid-type film. The point of this example is to show that the two extreme types of surface films give curves which, to a rather high degree of accuracy, will extrapolate above 20 dynes substantially the same and almost in a straight line when the variables are log a? and Au. By the nature of Gibbs’s law, the slope of these curves must always increase as the surface pressure increases. This last statement may be amplified as follows: Suppose the surface pressure continued to increase but the slope of the curve became less positive. This would mean that the amount adsorbed at the interface was decreasing, which is the same as saying that the area per molecule in the surface film becomes greater as the film pressure rises. Also as long as the film pressure is increasing with increasing concentration, the activity must) increase for, if it did not, the area per molecule would become either zero or negative. None of these later possibilities are possible and we may consider ourselves justified in extrapolating these curves smoothly as long as the surface pressure is increasing. We now make the assumption that below the discontinuity in the surface pressure-log concentration curves the concentration is substantially equal to the activity. This assumption is justified by the fact that the concentrations of wetting agents are, in all cases, very low. Furthermore, if the activity were considerably less than the concentration in this region, the calculated values of the area per molecule at close packing at the interface, using the value of the slope at the break point taken from the concentration curve, would be low. These
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ACTIVITY COEFFICIENT O F SURFACE-ACTIVE SUBSTANCES
values of area (see table 1) are in all cases consistent with similar values obtained from film balance data.
FIQ.4 . Curves obtained with two extreme types of surface films TABLE 1 Area per molecule at the point of discontinuity WETIUZG AGENT
I
Tergitol No 7 Tergitol Xo 4 Tergitol S o 8 Duponol OS Triton S E Duponol 80 Hexanolamine oleate Sodium cetyl sulfate
1
A s
36.2 26 0 30 5 12 8 15 5 32 2 46 7 21 9
The log activity coefficient is obtained by subtracting the log concentration from log activity a t any given surface pressure. The discontinuity in the surface
112
HAROLD 111. SCHOLBERG
pressure-log concentration curve probably corresponds to the beginning of micelle formation, while the maximum in the curve corresponds to the end of micelle formation. Duponol OS and hexanolamine oleate both shoiv a maximum in the surface pressure curve. It may be that this represents a region of unstable equilibrium and that measurements on old solutions would not show a maximum. Measurements of the solutions of Duponol OS after standing about two months seemed to indicate that this was so (see figure 2). An illustration of this procedure is the case of hexanolamine oleate. The activity coefficients, calculated from the surface pressure curve in figure 3, are
FIG.5 . -4ctivity coefficientsfor hexanolamine oleate: 0 ,d a t a on freezing-point lowering; e , surface tension d a t a .
shown in figure 5 , together with the activity coefficients calculated from the data of McBain (3), which are based on the lowering of the freezing point. The agreement between the two methods is rather striking, particularly in view of the fact that the work iyas done in different laboratories on different samples of soap. The point -4 in figure 3 is the critical point for micelle formation, according to McBain (3). The data from surface pressure measurements have been used in plotting figure 5 only up to the maximum of the surface pressure curve, since beyond the maximum, in the regions of higher concentration, we do not know what the activity is. However, a slope of - 1 would mean that the activity is a constant in that region, and this is a probable conclusion from the surface tension data. It is possible that the ideas given here may help to explain the maxima which are found in the surface pressure curves of many substances.
dCTIVITY COEFFICIENT OF SURFACE-ACTIVE SUBSTAKCES
113
Because it was thought that the observed break in the surface pressure curve might be due to impurities in the sample, a search was made of the literature to find a material which exhibited the break point, which was very probably pure, and fcr which activity coefficient data existed. Figure 6 shows the data for ethyl alcohol taken from the International Critical Tables. Curve X shows the curve of surface pressure (6) us. logarithm of the mole fraction; curve B shows the par-
i
FIG.6. Ethyl alcohol-water Bolutions. Curve A , curve of surface pressure us. logarithm of the mole fraction; curve B , curve of partial pressure of alcohol vapor os. the logarithm of the mole fraction.
tial pressure ( 5 ) of alcohol v:tpor v s . the logarithm of the mole fraction. Activity coefficients for alcohol cannot be calculated by this method, for the coefficient deviates from 1 in the low-roncentration region. The coincidence of the break points offers confirmation of the method developed here. It also indicates that the method has rather wide applicability. Since ethyl alcohol-water mixtures show a maximum in the viscosity-concentration curve at the criticnal concentration ( i )it, is tempting to interpret the break point as micelle formation. However, if such a micelle did exist, it would be extremely dilute.
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F. E. BARTELL AND CHARLES G . DODD
These data show why the attempts to verify the Gibbs absorption equation have given high values except in the case of nonylic acid, where extremely dilute solutions were used. Presumably the measurements in this case were made at concentrations below the critical. SUMMARY
1. A method has been suggested for the determination of the activity coefficient of surface-active materials at low concentrations in water solutions. 2. Data are presented to show that the method has wide applicability. 3. The apparent lack of applicability of the Gibbs adsorption equation to such systems is shown to be due to large variations in the activity coefficient of dissolved surface-active material. (1) (2) (3) (4)
REFERENCES CORRIN,M. L., KLEVENS, H . B., A N D HARKIXS, W. D . : J. Chem. Phys. 14, 216 (1946). DONNAN, F. G., AND BbRKER, J. T.: Proc. Roy. SOC.(London) A86, 557 (1911). GONICK, E., AND MCBAIN,J. W.:J . Colloid Sci. 1, 127 (1946). HARKINS,W. D., AND GANS,D . hI.: Colloid Symposium Monograph 6, 40 (192i);
6.36 (1928). ( 5 ) International Critical Tables, Vol. 111, p. 290. JIcGraw-Hill Publishing Company, New York (1928). (6) International Critical Tables, Vol. IV, p. 467. hlcGraw-Hill Publishing Company, S e w York (1928). (7) International Critical Tables, Vol. V, p. 22. hIcGraw-Hill Publishing Company, S e w York (1929). (8) MCBAIN,J. W., AND DAVIES,G. P.: J. Am. Chem. SOC.49, 2230 (1927). (9) MCLEWISAND PATRICK, W. A , : Phil. Mag. 1908 and 1909 (10) KUTTISG,G. C., LONG,F. A , , A N D HARKIXS, VI. D . : J. Am. Chem. SOC.62,1496 (1940).
SURFACE ARE-AS OF CRYSTALLIKE CARBOS AKD CARBIDE POWDERS AS MEASURED BY T H E ADSORPTIOS OF KITROGEKl, * F. E. BARTELL
AND
CHARLES G. DODD'
Department of Chemistry, University of Michigan, Ann Arbor, Michigan Received August BB, 1949
The problem of measuring specific surface areas of finely divided solids has been attacked quite successfully in recent years by methods involving treatments 1 Presented a t the Twenty-third National Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the American Chemical Society a t Minneapolis, Minnesota, June 6-8, 1949. * The data presented in this paper are from a dissertation submitted by Charles G. Dodd t o the Horace H. Rackham School of Graduate Studies of the University of Michigan in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1948. a Present Address: Petroleum Experiment Station, U.S. Bureau of Mines, Bartlesville, Oklahoma.
