the properties of detergent solutions. i. molecular weights determined by light-scattering...

THE PROPERTIES OF DETERGENT SOLUTIONS. I. MOLECULAR WEIGHTS DETERMINED BY

LIGHT-SCATTERING MEASUREMENTS

Eric Hutchinson

Department of Chemistry, Stanford University

Received February 8, 195.4

ABSTRACT It is pointed out that all published results to date for light-scattering experiments

on detergent solutions have been interpreted by a method which implicitly treats these solutions as being nonelectrolytes. Reasons are presented for believing that the molecular weight or degree of association is best determined by experiments in which a large excess of neutral salt is added to the detergent solution.

Debye has applied his treatment of light scattering to solutions of col- loidal electrolytes (l), and similar applications have been made by Anacker (2) and Hutchinson (3). Hermans (4), Doscher and Mysels (5), and Hutch- inson (6) have extended this treatment to take account of the fact that colloidal electrolytes are, in fact, electrolytes and that due attention must be paid to the question of gegenions and added salts in evaluating the so- called molecular weight of micelles from light-scattering data.

In particular Doscher and Mysels have deduced that

HCZ* __ = 7

&* (1 + P>

where H = the conventional scattering constant; c2* = the concentration of solute in grams per milliliter;

Mz* = the micelle molecular weight; T = the absolute turbidity of the solution; and p = the net charge on the micelle when the gegenions are uni-

valent. In the presence of excess electrolyte, p tends to zero, and Doscher and Mysels have concluded that, at the CMC of the colloidal electrolyte, the latter provides sufficient of its own simple ions for the condition 13 --+ 0 to be satisfied and that, consequently, extrapolation of the HQ*/T curve to t.he CMC yields a close approximation to the true value of M2*. I propose to show that this is not so.

Debye’s treatment (1) leads to the result

Hey.* 1 an -=-- 7 RT dcg*’

191

192 ERIC HUTCHINSON

in which x is the osmotic pressure of the solution. In applying this to solu- tions of alkylammonium halides Debye has treated these as if the solute were a nonelectrolyte, writing,

I have recently shown (6) that for a solution of a pure colloidal electrolyte in the absence of salt,

Hc2 Mn

27 = g1 + 3!L

a log cz 141

where c2 = the concentration of solute in gram formula weights per milliliter ;

MS = the gram formula weight of the solute; g1 = the osmotic coefficient of the solvent.

The model for this derivation is that of a‘uni-univalent electrolyte in ex- tremely dilute solution.

Dr. Marjorie Void (7) has developed a treatment of micelle behavior on the basis of a model which essentially treates a micelle A,G, as a weak electrolyte,

AnG, + (A,G,& + Gf g (AnGn9)= + 2G” S, etc.

This treatment embraces considerable generality as to the possible varia- tions of the association factor T, and leads to the same model as the author’s in dilute solution.

Dr. Void has shown that all available osmotic data are consistent with the hypothesis that the micelles carry a fixed ratio of gegenions to colloidal electrolyte ions, and deduces that

at71 m+----= a log cz 4(1 - r) + +c ag

2

where r = the ratio of gegenions per single colloidal electrolyte ion; ci = the concentration in moles per liter of the species (LLG,-J-~; d = the concentration in moles per liter of the species AG.

The summation in Eq. [5] is to be carried out over all permissible values of T and i.

Assuming for simplicity that in a given solution n has only a single value (as seems justified by the apparent monodispersity of colloidal micelles (8)), we have, from Eqs. [4] and [5],

Hcz Mz -=((l- 7

where cn is the concentration of the unique colloidal ion now presumed to be formed in solution.

PROPERTIES OF DETERGENT SOLUTIONS. I 193

But dc,/dci = I/n where n is the association factor;

. . . Hc2Mz - (1 - r) + ;. 161 7 This equation is almost identical with Eq. [I].

Dr. Void’s treatment implies that r remains constant under given condi- tions, and hence Hc2M2/7 should be constant. This is not observed to be the case, but, in view of the fact that the concentrations of the various species have been equated to their activities, this is not surprising.

Although the theory leading to Eq. [3] cannot be extended to cover cases in which added salt is present, except by making simplifying assumptions about the supposed ideality of the added salt in the absence of colloidal electrolyte, yet with reasonable accuracy Eq. [6] may still be applied. It may be anticipated that the effect of added salt is to cause r -+ 1, i.e., to make the micelle virtually uncharged. Then, and only then, does the Debye result give the correct value for n. It is noteworthy that in all cases reported the addition of salts brings the plot down to much more constant values.

From the results of conductance studies on pure colloidal electrolyte qolutions (9) it may be deduced with certainty that, in the absence of added salts, r is appreciably less than unity, and that, in consequence, we have to deal with charged micelles. Consideration of osmotic coefficients and elec- trical conductance data suggests that with solutions for which n NN 100 the value of T may lie between 90/100 and 99/100. It follows from this that at a concentration some ten times greater than the CMC the total ionic population is only very slightly greater than that at the CMC. If the nonconstancy of Eq. [6] for solutions containing no added salt is due to the dependence of the activities of the various species on ionic population, e.g.,

Hc2M2 _ acz + bC22 + ***>,

r

it follows that the correct value of the quantity in the first brackets is ob- tained by extrapolation of Hc2M~/r to zero concentration, and not to the CMC as suggested by Debye (1) and by Doscher and Mysels (5).

In the presence of added salts r -+ 1, and thus the effect of ionic popula- tion on the activity of the micelle may be expected to be negligible, as ap- pears to be the case. Alternatively, even if the micelle still bears a charge in the presence of added salt the ionic population is so little affected by the contribution due to the colloidal electrolyte that, over the range studied, no dependence of activity on the concentration of colloidal electrolyte will be perceptible.

It becomes obvious that the interpretation of these light-scattering data is far from simple. In Fig. 1 I have replotted Debye’s data for dodecyl- amine hydrochloride (1). If we assume that r = 1 in 0.0457 M NaCl solu-

194 ERIC HUTCFIINSON

0.0457 MOLAR NaCl

0 01 0.02 0.03

CONCENTRATION IN GRAMS/ML

FIG. 1. Plot of Hc~Ms/T against concentration for dodecylamine hydrochloride, taken from the results of Debye (1).

tion, the value of n obtained is approximately 133. The extrapolated curve for pure dodecylamine hydrochloride gives a value of about 0.016 for the quantity l/n + (1 - T). To interpret this one need not assume that n has changed. If n remains 133, a value of T = 132/133 corresponding to a micelle bearing a single charge would satisfy the result. It is therefore im- proper to assume that addition of salt necessarily changes the size of the micelle (1).

Clearly, since Eq. 161 contains two unknowns, we cannot obtain the size of a micelle from light-scattering data, any more than we can derive the size from freezing-point depression, except for uncharged micelles. All that we can do is to obtain a minimum value for n-a value which may be very much smaller than the true value.

Contrary to the idea that the addition of salt causes a change in the size of the micelle, it appears more reasonable, until further information be- comes available, to assume that the effect of added salt is solely on the value of r. Some justification for this procedure may be adduced from ex- periments on solubilization. The solubilizing power of a micelle toward a nonpolar material may be expected to be more or less independent of the charge of the micelle. Harkins (lo), has shown that in solutions of concen- trations not more than about five times that of the CMC, the increased solubilizing power of potassium laurate due to added salt may be ascribed to the depression of the CMC and the consequent formation of more of the same micelles as were present before the salt was added. More convincing, however, is the evidence that experiments on the effects of added salts on

PROPERTIES OF DETERGENT SOLUTIONS. I 195

the conductance of dodecylamine hydrochloride (9) show no signs of a change in the size of the micelle. The association factor of approximately 133 is in good accord with values obtained by diffusion and X-ray dif- fraction (8).

Similarly, unpublished data of the author for the effect of added salts on light scattering by sodium dodecyl sulfate solutions lead to an association factor of about 80, in good accord with diffusion and X-ray data (8).

It thus seems best to use light-scattering measurements to determine the size of micelles in fairly concentrated salt solutions, where the micelles are nearly uncharged, and to interpret the apparently smaller association in the absence of added salt in terms of the ionization of the micelle.

Some correlation of the light-scattering data with the results of conduc- tance experiments may be made as follows. Above the CMC the solution may be considered to contain simple ions and charged micelles, and the specific conductance may be evaluated by the method suggested by van Rysselberghe (11). If we assume for simplicity that there is only one kind of micelle containing n units and possessing a charge m, and assume further that the concentration of solute in the aggregated form is (cZ - c#), where cZo is the CMC value, the specific conductance K of the solution is given by

K= [71

where I, = the equivalent conductance of the micelle-forming ion, and I, = the equivalent conductance of the gegenion.

writing K” = (~2~/1000) (I, + E,), where K” is the specific conductance at the CMC,

K - K” = “;o&f’ (mZ, + m2n-‘Zm).

Hence,

K - K” c2 - cy?

= kn (ml, $ m2n-'1,). M

From the work of Ralston and Eggenberger (9) and Lottermoser and Puschel (12) the slopes of K - K”/c2 - c20 may be obtained for dodecyl- amine hydrochloride and sodium dodecyl sulfate. Using the values of n obtained from light scattering in the presence of salt, viz., about 133 and 80, respectively, one may calculate that the charge m is about +15 for dodecylamine hydrochloride micelles and about -14 for sodium dodecyl sulfate micelles. Putting the appropriate values of (1 - r), calculated from these values, into Eq. [6], we have

He2 M2 ___ = iis+ iii

cz 0.11 7

196 ERIC HUTCHINSON

for dodecylamine hydrochloride, and

Hcz M2 7

= &, f ; w 0.18

for sodium dodecyl sulfate. It is noteworthy that although the Hc2M2/7 plots for these compounds do not yield constant values, particularly in the neighborhood of the CMC, as they should according to Eq. [6], yet the curve for sodium dodecyl sulfate (6) tends to a value of 0.2 in more con- centrated solutions (concentrations some fifty times the CMC), and there is some indication that in the case of dodecylamine hydrochloride, where the results extend only to some fifteen times the CMC, a limiting value of Hc2M2/r is reached, somewhere between 0.05 and 0.1.

The surprisingly good agreement which thus obtains between the light- scattering data and X-ray and diffusion data on the one hand, and between the light-scattering data and the conductance data on the other, supports the hypothesis that the size of the micelle is, in fact, unchanged by the addition of salt, and that the light-scattering data obtained in salt-free solutions give information on the charge rather than the size of the micelle.

REFERENCES

1. DEBYE, P., J. Phys. & Colloid Chem. 63, 18 (1949). 2. ANACBER, E. W., J. Colloid Sci. 8, 402 (1953). 3. HUTCHINSON, E., Technical Report g1 O.N.R. Contract NGONR 25130. 4. HERMANS, J. J., Rec. traa. chim. 68, 859 (1949). 5. DOSCHER, T. M., AND MYSELS, K. J., J. Chem. Phys. 19, 254 (1951). 6. HUTCHINSON, E., Technical Report #3 O.N.R. Contract N6ONR 25130. 7. VOLD, M. J., J. Colloid Sci. 6, 506 (1950). 8. PHILIPPOFF, W., Discussions Faraday Sot. No. 11, 96 (1951). 9. RALSTON, A. W., AND EGGENBERGER, D. N., J. Am. Chem. Sot. 70, 980 (1948).

10. HARKINS, W. D., et al., J. Chem. Phys. 16, 496 (1947). 11. VAN RYSSELBERGHE, P., J. Phys. Chem. 43, 1049, (1939). 12. LOTTERMOSER, A., AND PUSCHEL, F., Kolloid-2.63,175, (1933).