262
R. J. VETTER
MICELLE STRUCTURE IN AQUEOUS SOLUTIOSS OF COLLOIDAL ELECTROLYTES’ R . J. VETTERa
Chemistry Department, University of Wisconsin, Marlison, Wisconsin Received August 8, 1946 INTRODUCTION
Two hypotheses, one by McBain (19) and the other by Hartley (8), have been developed t o explain the behavior of aqueous solutions of colloidal electrolytes. Both points of view state that the unusual concentration dependencies of properties such as osmotic pressure, equivalent conductivity, density, and others result from the aggregation of large organic ions to form colloidal micelles. The two hypotheses differ in the structural details ‘and properties of the micelles, and in the nature of the equilibrium between micelles and simple ions. The purpose of this paper is to contribute t o the discussion of micellar structure with the aid both of new experimental observations and of a reexamination of a few observations published by other investigators. The colloidal electrolyte chosen for study was the sodium salt of sulfonated di(2-hexyl) succinate, which is known commercially as .kerosol hI.4. This compound is characterized by having its hydrophilic ionizing group at approximately the mid-point of the molecule. I t was of interest for this reason because most of the work in this field had been confined to electrolytes in which the hydrophilic group is at the end of a linear chain structure. Experimental measurements were made of the density and viscosity behavior of Aerosol MA in aqueous solutions and also of the rate of diffusion in aqueous sodium chloride solvents. The measurements were extended over an appreciable range of concentration. Several papers (6, 20) describing some of the solution properties of Aerosol MA have appeared since the work reported here was initiated. They show that the “Aerosol”-type compounds are colloidal electrolytes, and that the ‘*Aerosols” and other branched-chain compounds differ from members of the straightchain type in the degree t o which certain properties depend upon chain length (21). EXPERIMESTAL
Purification of Aerosol MA A commercial sample was obtained which contained about 1 per cent impurities, these being chiefly water and about 0.1-0.2 per cent sodium sulfate.s The 1 Presented a t the Twentieth National Colloid Symposium, which was held a t Madison, Wisconsin, May 28-29, 1946. This paper is based on a thesis submitted by R. J. Vetter t o the Faculty of the University of Wisconsin in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1944. Z Present address: E. I. du Pont de Nemours & Co., Inc., Richmond, Virginia. 3 The sample and its analysis were obtained through the kindness of Mr. C. A . Sluhan of the American Cyanamid and Chemical Corporation.
MICELLE STRUCTURE I N COLLOIDAL ELECTROLYTES
'
263
inorganic impurities were removed by filtration of a purified-dioxane solution followed by evaporation a t 100°C. with the ultimate use of high vacuum. The resulting material was white and odorless; it was stored over phosphorus pentoxide at room temperature. The use of a more elaborate procedure has been described ( 6 ) but it was not felt justified, because Aerosol RIA undergoes carboxy-ester hydrolysis in aqueous solution.
Preparation of solutions .ill solutions were prepared by weight, other than those for diffusion studies, and the .lerosol h1.1 was allowed to dissolve at room temperature. Solutions used for density and viscosity measurements were made with freshly boiled, double-distilled conductivity water. The aqueous sodium chloride solvents used for diffusion measurements contained ordinary distilled water and Baker's analyzed salt. Turbidity developed several hours afier preparation in salt-free solutions containing less than 2.2-2.5 per cent Aerosol MA. More concentrated solutions remained clear for months, but on dilution below 2.2-2.5 per cent a t any time after several hours' aging they immediately became turbid. With aqueous sodium chloride solvents the Aerosol IUA concentration at which turbidity appeared decreased with increasing salt concentration. The effects of turbidity and aging on density and viscosity were indetectably small; their effect on diffusion behavior is described belo\\. -1plausible explanation for the appearance of turbidity is that water-insoluble 2-hesanol is formed by ester hydrolysis, for it is known that the pH of an Aerosol MX solution gradually decreases with time. I n a sufficiently concentrated solution the colloidal micelles present solubilize the alcohol but in a more dilute solution, Lvhere colloid does not exist, the alcohol separates into a finely divided second phase which causes turbidity. This second phase is presumably stabilized by the emulsifying action of the detergent. The effect of sodium chloride on the concentration dependence of turbidity is associated with the ability of added salt t o reduce the critical concentration for micelle formation (see below). For density measurements each solution was prepared directly from detergent and water and was used within 24 hr. after preparation. For viscosity measurements all but three solutions were prepared by dilution of a more concentrated solution. Referring to the order given in table 3, the first seven, the next two, and the last twelve solutions form the three dilution series. I n several of these solutions, the solute had been dissolved for as long as 1 meek. For diffusion measurements separate solutions of Aerosol X A and sodium chloride, prepared by weight, and water were mixed volumetrically. The volumetric mixing was the more convenient for insuring equal concentrations of sodium chloride in the two solutions employed in the differential-diffusion measurements. Some of the aqueous Xerosol solutions mere allowed to stand as long as 2 weeks prior t o w e , but no aging effect could be detected within limits of experimental error.
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R . J. VETTER
Density measurements Two pycnometers were used, one a 60-cc. OstwaldSprengler type and t h e other a 26-cc. instrument of the type described by Tennent and Vilbrandt (28). Measurements were made a t 25.00"C. i 0.01". Precautions were taken with respect to rinsing and wiping the pycnometers prior to weighing, temperating in the balance case, double weighings, the buoyant effect, use of a similarly constructed counterweight for the pycnometer (second type only), sensitivity of balance, and calibration of weights. Weighings were reproducible t o &O.l mg. The partial specific volumes of the Aerosol MA were calculated by a modification of the second (graphical) method of Lewis and Randall (18). The volume of the solution per gram of water was computed for each concentration, and the difference between adjacent values was divided by the difference in concentrations expressed as fractions. The values of partial specific volume thus obtained were assigned to the means of the two concentrations. This method has the advantage of simplicity and the disadvantage that very small errors in the data are greatly magnified. I t is also an integral rather than a differential method.
Viscosity measurements Viscosities were measured in an Ostwald viscometer at 25.00'C. f 0.02". The flow time for water was 375.1 sec. The viscometer was calibrated with water and two sucrose solutions; it was found that the kinetic-energy correction amounted t o less than 1 part in 1000 and it was therefore neglected.
Difusion measurements Rates of diffusion were measured at 25.00'C. f 0.02" in an all-glass cell of the type described by Svedberg (26), with the aid of the scale-line displacement method of Lamm (16). In all experiments the solute was allowed to diffuse from a more t o a less concentrated solution. RESULTS
Partial specific volume The data show that two transition ranges of concentration exist in ,which the partial specific volume changes abruptly and between which it remains constant. This behavior is illustrated in figure 1;the experimental density data are given in table 1 and the derived values of partial specific volume in table 2. The concentration a t which the first transition sets in has been called the "critical concentration for micelle formation" and is about 1.0 per cent Aerosol MA. This value agrees with the result of Haffner, Piccione, and Rosenblum (6), who found a sharp downward break in the equivalent conductivity-concentration curve at 1.1 per cent Aerosol MA. The first transition range appears to extend to about 2.5 per cent, but since an integral rather than a differential method was used to calculate partial specific volume, it is probable that the transition range is somewhat narrower than indicated by figure 1,
li
265
MICELLE STRUCTURE I N COLLOIDAL ELECTROLYTES
FIG.1. The variation of the partial specific volume with concentration in aqueous solutions of Aerosol MA a t 25%.
TABLE 1 Density data and derived quantities f o r Aerosol M A in water at 26.00"C. & 0.01" CONCESPBATION
1
DENSITY (ABOLUTE)
1
VOLUME OF SOLUTION P E R G R A M OF H'ATER
weigh1 per cent
O.Oo0
0.475j* 0.6094 0.6909* 0.9308" 1.21g6* 1.4487 1.8710 2.3293 2.4167 3.5992 4.5890 5.666s 6.7581 7.5342 9,4794
LC.
0.99704 0.99806 0.99823 0.99848
0.99897 0.99949 0.99995 l.oOO86 1.00169 1.00190 1.00401 1.00597 1.00796 1.01005 1.01139 1.01508
1.00296 1.00673 1.00786 1.00849 1.01043 1.01287 1.01475 1.01819 1.02213 1.02282 1.03319 1.04188 1.05170 1.061810 1.06930 1.08831
* Values obtained in the 60-cc. Ostwald-Sprengel pycnometer. The second transition range begins at about 4.5 per cent. Although the data are not extensive enough a t higher concentrations t o show the attainment of a second range of constant partial specific volume, they indicate a trend in this
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R. J. VETTER
direction. Hess, Philippoff, and Kirssig (13) found two transition ranges of concentration in measuring the densities of aqueous solutions of an homologous series of soaps, provided themolccnlc contained six or more carbon atoms. They found also that the appearance of long-spacing x-ray diffraction began a t the same concentration where the second transition of partial specific volume set in. These investigators regard this concentration as a second critical point. The lack of agreement in figure 1 between the curve and the points at 5.13 and 6.21 per cent can be accounted for by an error in estimating either the density or the concentration of but one solution, that a t 5.GG7 per cent. A change of eithcr 15 parts per 100,093 in density or 2 parts per 1000 in concentration would bring thc two points in figure 1 to close coincidence with the curve as drawn. TABLE 2 Partial specific volume of Aerosol MA in water CONCENTPATION
I
at 25.00OC.
0.01"
PARTIAL SPECIFIC VOLUME
w i g h t per c t d
cc. per grom
0.0Q-1.0 1.33 1.54 1.66 2.10 2.14 3.01 4.09 5.13 6.21 7.15 8.51
0.800 0.820 0.817 0.815 0.859 0.818 0.877 0.878 0.912 0.926 0 965 0.977
Viscosity Thc relative viscosity-concentration curve, figure 2, shows a break a t 1.1 per cent Aerosol MA, in agreement with the density and cited conductivity measurements. The general shape of the curve is quite similar t o that found generally for aqueous solutions of colloidal electrolytes (23) ; the gentle upward curvature with relative viscosities above about 1.1 is the result of mutual interference between colloidal particles in motion during flow. The absence of a second break in the curve corresponding t o that found with density measurements is suggested but not proven because the measurements do not extend to high enough concentrations. The experimental viscosity data are given in table 3.
Di$usion It was necessary to measure the rate of diffusion by the differential rather than the integral method because turbidity appeared at low concentrations of
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MICELLE STRCCTURE IP; COLLOIDAL ELECTROLYTES
Aerosol MA which made it difficult, or impossible, t o measure the displacement of the scale lines. Aerosol 1 I X diffused in a manner which closely approximated that theoretically expected for free diffusion, as can be seen from figure 3, in which “normalized” diffusion cun-es are compared vith the theoretical curve (16). Deviations oc-
FIG.2. The variation of the relative viscosity with concentration in aqueous solutions of Aerosol M.4 a t 25°C. TABLE 3 Viscosities of aqueous solulions of Aerosol MA relative to water at 25.00”C. CONCEMPAIION
wri6hl per cant
0.000 0 709, 1.0549 1.3130 1.6526 1.849, 2.0364 2.297s 2.5480
2.7754 a.inil
+C
0.02”
RELATIYE VISCOSITY
*(eight $er cent
1.021s 1.0318 1.0133 1.05ge 1.0689 1. 0764 1.091, 1.103, 1.114~ 1.1353
I
3.3868 3.6199 3.4232 3.709, 3.9969 4.3490 4.71& 5.0928 5.4531 ;.a475 6.3761
1.1502 1.1644 1.1532 1,170, 1.190s 1.214, 1.238e 1,265, 1.291, 1.320, 1.3617
curred in that the maximum height of the cuwe was slightly greater than ideal and also in that the curves were slightly skewed. The degree of skewness increased the lower the concentration of the less concentrated solution. From the shape of the “normalized” curves it is probable that calculation of the diffusion coefficient by the method of slope and area would yield too lorn a value and that use of the method of (second) moments would give too high a value. It was
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R . J. VETTER
found that in all but two of sixteen experiments this order was obtained, and it is considered that the average of the values given by the two methods is more nearly correct than either of the two separately. In most of the experiments the two methods gave values which agreqd to within 10 per cent, so the average may be regarded as accurate t o about 5 per cent or less. The turbidity appearing at low concentrations of the less concentrated solution began in the cell a t a level slightly above the diffusion boundary and continued on into the remainder of the dilute solution. With increasing time the boundary of the turbid region receded away from the diffusion boundary. Attending the appearance of turbidity, the form of the diffusion curve changed in the manner
5 FIG.3. The variation of the scale-line displacement with distance in the diffusion cell for the differential-diffusion behavior of Aerosol MA in aqueous sodium chloride solutions. The curve represents the ideal behavior in free diffusion and the various sets of points represent “normalized” experimental curves taken at varioue times after formation of the boundary.
shown by figure 4. This curve was obtained 12 hr. after the diffusion boundary was formed between 1.0 and 0.5 per cent solutions of Aerosol -MA in 0.128 N sodium chloride. The anomalous shape of this curve was probably the result, first, of the separation of 2-hexanol in the less concentrated solution and second, of its progressive solubilization as Aerosol MA diffused into the turbid region. Three factors were found t o affect the rate of diffusion in clear solutions: ( f ) the average Aerosol MA concentration of the two solutions used in the experiment; (2) the difference between the detergent concentrations of the two solutions; (3) the concentration of sodium chloride. The first factor was studied systematically a t one constant set of values for the second and third variables,
MICELLE STRKCTKRE IS COLLOlDAL ELECTROLYTES
269
but only a few other experiments were made which show trends in the effects of these wriables separately. The effect of varying the first factor while keeping the other two constant is t o cause an initial decrease of diffusion coefficient with increasing concentration.
DISTANCE IN C E L L
FIG.4. The anomalous diffusion behavior of Aerosol MA at low concentrations in differential-diffusion experiments. The solid curve is that obtained experimentally, and the dotted curve is that t o be expected in the absence of turbidity.
I
le10
FIG.5 . The variation of the differential-diffusion coefficient with concentration of Aerosol MA in 0.257M sodium chloride, Diffusion coefficients calculated by the method 01 and the method of area and slope ( D A . 8 ) . The concentration difference moments (D”) between the two solutions is 0.5 per cent Aerosol.
This is followed by a concentration region in which the diffusion coefficient is constant. At sufficiently high concentrations there is indication that the diffusion rate again falls off with concentration. This behavior is shown in figure 5 ,
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R. J. VETTER
the points of which are marked with an asterisk in table 4. The initial fall, followed by a region of constant diffusion coefficient, is in agreement with the observations of Hakala ( 7 ) , Lamm (17), and Hartley and Runnicles ( l l ) ,who measured the diffusion rate of various straight-chain colloidal electrolytes in the presence of swamping electrolyte. Increasing the concentration of swamping electrolyte was studied a t two average concentrations of Aerosol ILL The results show that the diffusion coefficient decreases with increasing salt concentration. From experiments 1 and 2 and experiments 6 and 7 in table 4 it is seen that at 0.75 per cent .lerosol TABLE 4 ueous sodium chloride solutions at 25°C.
The differential diffusion of Aerosol .MA in NO.
1
c
SaCl
CI
D.”
Y
2a. , , . , . . , . . 2b.. . . . . . . . . 3 . . . . . . . . . . . i. 4. .......... 5. . . . . . . . . . . 6a... . . . . . . .
6b.. . . . . . . . . 7. . . . . . . . . . . .
12a 12b
I
0.75 0.75 1.00 1.25 1.25 1.50 1.50 1.50
250 2 50
, I
1.00 1.00 1.00 1.25 1.50 2.00 2.00 2.00 2.00 2.00 2.00 2.25 2.50 2.75 300 3.00
0.50 0.50 0.50 0.75 1.00 0.50 1.00 1.00 1.00 1.50 1.50 1.75 2.00 2.25 2.00 2.00
,
0.180 0.257 0.257 0.257 0.257 0.257 0.23 0.257 0.514 0.257 0.257 0.257 0.257 0.257 0.386 0.386
29.9 21.6 19.5 16.4 14.6 16.7 15.3 16.4 13.8 14.0 14.0 13.4 14.2 12.9 8.2 8.2
23.3 19.6 li.8 16.7 14.4 15.0 15.1 14.8 13.9 13.5 (16.9) 13.2 12.8 7.8 7.9
26.6 18.8* 16.5,* 14.5* 15.8 15.4 13.8&* 13.4’ 13.7* 12.&* 8.0
c , and c2 are the concentrations of colloidal electrolyte in the more and in the less concentrated solutions, respectively; c is the average of these two. Aerosol M A concentration is given in weight per cent and that of the sodium chloride in normality. D’ and DAss are the diffusion coefficients in lo-’ cm.l per second as calculated by the methods of second moments and of area and slope, respectively. * Points plotted in figure 5.
MA the diffusion coefficient is more sensitive t o addition of salt than a t 1.50 per cent. The effect of increasing the difference between detergent concentrations of the two solutions seems t o be dependent on the absolute values of the concentrations, but the data a t hand do not present a clear picture. Comparing the result of experiment G with the diffusion coefficient t o be expected from figure 5 and also comparing experiments 4 and 5 , it is seen that increasing the concentration difference increases the rate of diffusion. There is some uncertainty connected with this point, because on this basis it would be expected that experiment 6 should shoiv a larger value of diffusion coefficient than experiment 4. At higher
JIICELLE STRTCTURE IS COLLOIDAL ELECTROLTTES
271
concentrations of Aerosol 11.1 increasing the concentration difference and the salt concentration together causes a decrease in the rate of diffusion, as is apparent from experiments 11 and 12. For reasons outlined below, it seems probable that either one of these factors separately would have had the same effect, although t o a lesser extent than both together. DISCUSSIOS
Some insight as t o the average size, shape, and weight of colloidal particles can be obtained from a combination of diffusion, viscosity, and density data (27c). I n general, the estimation of molecular-kinetic parameters from these measurements is accompanied by some uncertainty, for several reasons.. First, a model for the colloidal structure need be assumed which is amenable to mathematical analysis of its hydrodynamic properties. Second, with models other than spheres, the effects of shape and solvation have not been separated (2). Third, hydrodynamic analyses of concentration effects have not been surcessful beyond very dilute solutions except for the case of spherical particles. Fourth, the calculation of particle weights from the above measurements involves transposition from the volume to the weight basis with the aid of the partial specific volume, the assumption being that this quantity is an estimate of the density of the colloidal phase. With the exception of the last factor, thcse uncertainties are greatly reduced if there is evidence t.hat the colloidal particles are spherical in shape. The shape of the particles, or micelles, in aqueous colloidal electrolyte systems is thought by Hartley t o be spherical. He believes also that the radius of the spherical micelle is constant over a range of concentrations above a critical concentration for micelle formation and that the radius is approximately eqiial t o the stretched-out length of the aggregating chain ions. McBain, on the other hand, suggests that two colloidal micelles eo-exist, the one being a small spherical micelle and the other a larger lamillar structure whose over-all shape is, presumably, not spherical. The two types are in equilibrium with simple ions and with each other. The size of the lamillar micelle increases gradually nith concentration and is believed to be responsible for the diffraction of x-rays which is observed at higher concentrations. The various facts nhich support these two points of view have been reviewed in detail elsewhere (8,9, 19). Seither of these two theories, nor any of the various modifications of them which have been suggested (12, 25), is capable cf explaining adequately all the experimental observations. McBain has not discussed a second critical concentration, although he estends his analysis to concentrations beyond this point. Hartley has not attempted to explain the x-ray diffraction observed, which occurs only at concentrations above the second critical concentration (12, 25) ; for this reason, his theory can be regarded only as an explanation of the facts below this concentration. The measurements reported in this paper d o not extend appreciably beyond the second critical concentration, and the interpretations t o follow are confined t o concentrations below this point. It is shown that with this restrict,ion a
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R. J . VETTER
slight modification of the Hartley picture is better able t o explain the facts than is the McBain viewpoint. The constancy or the variability of micelle size in the range between the first and second critical concentrations is a pertinent test of the Hartley and McBain theories. Three lines of evidence may be cited-namely, diffusion, osmoticpressure, and viscosity measurements-to show that micelle size is constant in this range. The diffusion behavior of colloidal electrolytes may be used to estimate micelle size only if the measurements are made in the presence of sufficient swamping electrolyte t o eliminate the small-ion charge effect (11, 27a). Such measurements have been made by Hartley and Runnicles ( l l ) ,Lamm (17), Hakala (7) and the writer, as reported in the present paper. All of these investigators found that after an initial range in which the diffusion coefficient decreased with increasing concentration, another range followed in which the diffusion coefficient was constant. This behavior indicates constancy of micelle size, micelle shape, and degree of solvation in this second range of concentrations if these three factors do not change simultaneously in such a manner that they neutralize their separate effects. Thiz latter possibility seems highly improbable. The McBain and Brady analysis of the osmotic pressures of colloidal electrolyte systems (21) indicates that the number of molecules per micelle (the aggregation number) depends only on the structural type of the aggregating molecules and not on their molecular length. McBain and Brady make the following statement:
+
“Consider reactions of the type aA bB = A.Ba for different substances a t molalities m and m‘ and m”,etc., such that a,the fraction of total A in the complex, has the same value for all. Then g likewise will be the same provided that the equilibrium constants are functionally the same even if in general numerically different, that is, if a and b are the same for all the substances.”
They support this statement with experimental evidence. Assuming its validity, one may conclude either that a true equilibrium between simple ions and micelles does occur, in which event the aggregation number and hence the micelle size is constant with concentration, or that the concentration dependencies of the parameters a and b are functionally the same for all substances of the same structural type. The former possibility seems more probable. The intrinsic viscosity of colloidal solutions is regarded as a measure of either the size (14) and/or the shape (24) of the colloidal units, depending on the model chosen. With an ellipsoid of revolution as model, for which a sphere is a unique case, constancy of intrinsic viscosity indicates constancy of shape as well as degree of solvation. This model may be assumed as a close approximation t o colloidal electrolyte micelles, in view of the diffusion work cited above. It is clear that if colloid does not exist below a critical concentration for micelle formation, the ordinary method of plotting reduced viscosity‘ against concentration and taking the intercept on the ordinate axis as the intrinsic viscosity will The reduced viscosity is the quantity q,Jc
MICELLE STRUCTURE I N COLLOIDAL ELECTROLYTES
273
not apply. The analyses of Grindley and Bury (5) and of Wright and Tartar (29) indicate that the concentration of simple ions reaches an approximate saturation value at the first critical concentration; hence, the solution at this concentration may be taken as the solvent for the colloidal micelles. Theintrinsic viscosity characterizing the micelles can then be evaluated by computing the viscosities of solutions more concentrated than the critical concentration relative to that of the latter solution and at the same time subtracting the critical from the higher concentration values. Upon applying this adjusted viscosity analysis to the mertsurements of Wright and Tartar (29), who studied aqueous solutions of sodium dodecyl sulfonate, it is found that the intrinsic viscosities at 40°, 50°, GO”, and 70’C. are 10.3, 10.4, 10.1, and 10.0, respectively. This is to say that the intrinsic viscosities are independent of temperature within experimental error. This result seems readily understandable on the basis of a spherical micelle whose radius is controlled by the length of the aggregating molecule, but is difficultly reconcilable with the suggestion of an equilibrium between two considerably different types of micelle, especially since the critical concentration is temperature dependent. From the considerations outlined above, it is concluded that a single spherical micelle of constant size exists in the region between the first and second critical concentrations. The mass-action treatment of Grindley and Bury (5) indicates that micelle formation begins at a critical concentration and that micelle size increases to a maximum over a short transition range of concentration. The amount of solvent kinetically associated with the spherical micelles can be estimated by comparing the intrinsic viscosity with the value 2.5, which has been shown to be characteristic of unsolvated spheres (3, 4). This is conveniently effected by computing the “hydrodynamic volume” of Kraemer and Sears (15). The intrinsic viscosity of Aerosol MA in aqueous solution is found to be 4.05; hence the “hydrodynamic volume” is 4.05/2.5 = 1.G2. This value indicates that a.bout 38 per cent of the volume of the colloidal unit is kinetically associated solvent. Indirect evidence for an appreciable degree of solvation may be inferred from the variation of partial specific volume xith concentration. Over the range of concentration studied it increases by more than 20 per cent of its value in very dilute solutions; in view of the fact that the fusion of salts involves a volume change of about 10 per cent (1) it seems highly improbable that a change in excess of 20 per cent for Aerosol MA can be accounted for on the basis of its space requirements alone. Rather it suggests that the formation of micelles is attended by a change in the structure of the solvent, that is, by an interaction between micelles and solvent. The radius of spherical colloidal particles can be calculated from the diffusion coefficient with the aid of the Stokes equation (27b). A comparison of the radius found by this method with that predicted for the model proposed is a test of the validity of the model. The longest chain leading away from the sulfonic group in Aerosol MA contains seven methylene groups and one carboxy-ester linkage, the length of which, including the sulfonic group, is 15 A. if one takes 109” 28’ as the angle between all atomic bonds. Assuming the amount of associated
274
R . J . VETTER
solvent, as estimated from the “hydrodynamic volume,” to be layered on the exterior of the micelle, the predicted radius is 17.G A . The value of the diffusion coefficientin the range 1.50-2.25 per cent Aerosol 11.1 in 0.257 S sodium chloride is 13.8 X lo-’ cm.* per second, which yields the value 17.3 A. for the radius of the micelle. The effects on diffusion coefficient of si\ amping electrolyte concentration and the difference in Aerosol X I concentrations of the two solutions used in the experiment were mentioned above. They present pertinent questions regarding the characterization of the colloidal micelle by the diffusion coefficient chosen in the preceding paragraph. The effectP of varying the concentration difference were observed with solutions in the neighborhood of the critical concentrations where the size of the micelle is changing nith concentration. Similarly, the effects of varying swamping electrolyte concentration can be associated 11it11 changes in the critical concentrations due t o addition of more salt (8, 19). I t is clear, assuming Hartley’s point of vien, that in order t o estimate the size of the micelle, both solutions used in the diffusion experiment must be in the range of fullv formed micelles. From inspection of figure 5 , the experiments at 1 75, 2.00, and 2.25 per cent Aerosol MA in 0.257 .V sodium chloride seem t o meet this requirement. From the constancy of the diffusion coefficient, it may be inferred that the salt \vas present in sufficiently high concentration t o eliminate the smallion charge effect; additional evidence for this statement is supplied by the measurements of Hakala ( i ) ,nho studied the diffusion coefficient of sodium lauryl sulfate as a function of snamping electrolyte concentration. The very close agreement between the observed and calculated values for the radius of Aerosol NAmicelles is probably fortuitous. First, the value of “hydrodynamic volume” calculated pertains t o salt-free solutions, whereas the diffusion coefficient was measured in salt solution. If the viscosities had been measured in the latter solution, it is probable that the “hydrodynamic volume” would have been reduced, because the effect of salt is t o reduce the eiectroviscous effect (2). Second, it seems improbable that the paraffin-water interface in the micelle should be perfectly sharp, as is implied by assuming exterior layering of the associated solvent. Rather it seems more probable that water penetrates the micelles in the neighborhood of the interface. Both these factors tend t o reduce the expected radius of the micelle below the value 17.6 A , , but it is evident from the length of the aggregating molecule that the loiver limit is 15.0 A. Experimental e ;idence suggesting penetration of water within the micelles of straight-chain colloidal electrolytes may be cited by comparing the “hydrodynamic volume” of sodium dodecyl sulfonate with that t o be expected on the basis of the diffusion coefficient of the closely similar sodium lauryl sulfate. Hakala’s measurements ( 7 ) of the latter compound indicate a (spherical) micelle radius which is about 20 per cent greater than the maximum length of the molecule, leading t o an expected “hydrodynamic volume” of about 1.7 on the basis of exterior layering of the associated solvent. \$’right and Tartar’s viscosity measurements (29) show that the “hydrodynamic volume” of sodium dodecyl sulfonate is actually 4.0, 51 hich is to sap that solvation accounts for 75 per cent
MICELLE STI!TCTTPC
I S COLLOID.IL
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of the micelle volume. I n order t o retain the proposed micelle model, it seems necessary t o assume that polvent penetrates the paraffin portion of the micelle t o an appreciable extent. If this is the case, it is probable that the density distribution of solvent xithin the micelle decreases with depth of penetration and that the core of the micelle is practically pure paraffin in nature. This picture represents a slight modification of the point of view of Hartley, iyho suggests that the paraffin-water interface estends over the length of, say, two water molecule diameters 19). The difference between the contributions of solvent t o the micellar volumes of MA and sodium tlodecyl sulfonate. 38 and 7 5 per cent, respectively, is probably associated with the difference in structure between the two molecules. The radius of the herosol micelle is determined by the length of the longer of two chains leading away from the ionic group, but the shorter chain is also imbedded in the micelle. I t is clear that the presence of the shorter chain will reduce the volume of solvent xhich can cluster around the ionic group, and, on the basis of t h e structure proposed above, it should also reduce the volume within the micelle xvhich might othervise be available for penetrating solvent. Were it not for the fact that the aggregation numbers of straight-chain and branched-chain electrolyte differ (21), it irould be easy to test the validity of this esplanation with the data at hand for the tn-o compounds. Further evidence for the Hartley micelle, as modified ahove, is suggested by the \\-ark of l\IcBain and ,Johnson (22), n-ho studied the solubilization of the water-insoluble dye Orange OT in aqueous solution by four potassium soaps. The results show that for soaps containing eight, ten, twelve, and fourteen carbon atoms, respectiye1 the amounts of dye solubilized per mole of soap are in the proportions 1:2.14 4 8 : ll.61.5 McBain and Brady’s analysis (21) indicates that the aggregation numliers of these four soaps are equal, and from this it follows that the above proportions give directly the relative amounts of dye solubilized per micelle. I t seems generally accepted that in solubilization of the type stuaiecl by NcBain anti Johnson the dye dissolves in the paraffinic interior of the micelle (10, 19). To account for the quantitative data cited ahove it is necessary that a proposed structure for the micelle enable one to correlate the chain length of the soap molecules with the effective paraffinic volume of the micelle. .kccording t o the modified Hartley structure it folloivs that the effective paraffinic nature of the micelle diminishes with distance from the center because of the attendant increasing frequency of witer molecules. The volume of the effective paraffinic portion should consequently be proportional to the third paver of an adjusted chain length of the soap molecule. By a process of trizl and error it was found that if the number of carbon atoms per soap molecule in the above series were reduced by three and the resulting series 5 , 7 , 9, and 11 raised t o the third power, the volumes obtained are in the proportions l : 2 . i 4 : 5.83: 10.65. Considering the approximate nature of the treatment, these ratios are in good agreement ivith those found experimentally by 1tcBain and Johnson. The original figures have been modified at the suggestion of Sister Agnes Green.
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Objections to the micelle structure outlined might be raised on the grounds that penetration of mater within the micelle would reduce the decrease of free interfacial energy attending micelle formation. While this may be true, penetration of water would also reduce the repulsion betmen the like-charged ionized groups on the surface of the micelle. The aggregation number of Aerosol MA micelles may be estimated approximately with the aid of the diffusion coefficient, partial specific volume, and “hydrodynamic volume” on the basis of the modified Hartley micelle. The equation relating aggregation number with these parameters is: Aggregation number = TrD/HLM where 1- = volume of micelle, D = density of aggregating ions in micelle, H = “hydrodynamic volume,” and M = molecular weight of Aerosol MA There are several approximations involved in the use of this equation. The one perhaps of chief concern is that the partial specific volume is assumed t o be a measure of the density of the detergent molecules in the colloidal phase. It was indicated above that the magnitude of the change in this formal quantity strongly suggests that a change in the structure of the solvent attends micelle formation. If this is the case, the observed partial specific volume of the solute is not a true estimate of the density of the colloidal phase. In this connection, Adams (1) has shown how the solute density can be estimated with the aid of pressure-density-concentration studies. Several other approximations enter because both the density and the viscosity measurements were made in salt-free solutions, whereas the Affusion coefficient pertains t o salt solutions of the detergent. Considering the fact that a 5 per cent error in estimating the diffusion coefficient causes a 16 per cent error in the calculated micellar volume, the writer is inclined t o the viewpoint that the errors involved in the approximations mentioned n ill not seriously reduce, in the relative sense, the precision of estimating the aggregation number. Using the values 17.3 A. for the micelle radius, 1.62 for the “hydrodynamic volume,” 0.8% for the partial specific volume, and 388 4 for the molecular xeight of the Aerosol MA, one obtains the value 23 6 for the aggregation number. SUMMARY 8
1. Measurements of the densities and viscosities of aqueous solutions of purified Aerosol R l h have been carried out over an appreciable concentration range. The diffusion behavior of Aerosol 31A micelles in aqueous sodium chloride solutions has also been investigated. 2. The “critical concentration for micelle formation” in aqueous solution is about 1.1 per cent Aerosol A L A , and the probable existence of a second critical concentration a t about 5 per cent in aqueous solution is indicated. 3. The diffusion coefficient and the partial specific volume are constant in a concentration range between the first and second critical points.
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4. A micelle-structure hypothesis has been proposed for the concentration range between the first and second critical points which is a modification of the spherical-micelle picture of Hartlep. The modification is that solvent penetrates the micelle t o an extent which depends on the distance from the center of the micelle. 5 . I n the concentration range between the first and second critical points Aerosol MA micelles contain about twenty-four detergent molecules bvhich, on a volume basis, constitnte about 62 per cent of the micelle, the remainder being solvent. The writer wishes t o express his gratitude to Professor J. W.Williams, under whose direction this work \vas carried out. REFERESCES (1) ADAMS,L . H . : J. Am. Chem. Soc. 63, 3769 (1931). (2) COHN,E . J . , AND EDSALL, J. T.: Proteins, A m i n o Acids and Peptides, p. 522. Reinhold Publishing Corporation, Xew York (1943). (3) EIRICH,F.: Kolloid-Z. 74, 276 (1936). (4) EIRICH,F . : Kolloid-Z. 81, 7 (1937). J . , AND BURY,C. R . : J. Chem. SOC.1929, 679. (5) GRINDLEY, (6) HAFFNER, F. D . , PICCIONE, G . .4., AND ROSENBLUM, c . : J. Phys. Chem. 46, 662 (1942). (7) HAKALA, S . V . : Dissertation, University of Wisconsin, 1943. G. S.: Aqueous Solutions of Parafin-Chain Salts, Actualit& scientifiques et (8) HARTLEY, industrielles No. 387. Hermann et Cie., Paris (1936). (9) HARTLEY,G. S.: Kolloid-Z. 88, 22 (1939). (10) HARTLEY, G . S.: “Solvent -4ction of Detergent Solutions”, in Wetling and Detergency. Chemical Publishing Company, Inc., New York (1937). (11) HARTLEY, G . S., AND RUKKICLES, D. F.: Proc. Roy. SOC.(London) A168,420 (1938). (12) HESS,K . : Fette u. Seifen 49, 81 (1942). (13) HESS,K . , PHILIPPOFF, W., A N D KIEGSIG, H . : Kolloid-Z. 88, 40 (1939). M. L.: J. Phys. Chem. 42,911 (1938); 43,439 (1939). (14) HVGGINS, (15) KRAEMER, E. O., A N D SEARS,G . R . : J. Rheol. 1, 231 (1930). 0.:Xova Acta Reg. SOC.Sci. Upsaliensis 4, S o . 6, 10 (1937). (16) LAMM, (17) LAMM, 0 . :Kolloid-Z. 98, 45 (1942). (18) LEWIS,G. S . , A N D RANDALL, M.:Thermodynamics and the Free Energy of Chemical Substances, p. 36. McGraw-Hill Book Company, Inc., Xew York (1923). (19) RIcB.41K, J. W . : In Alexander’s Colloid Chemistry, Vol. 5 . Reinhold Publishing Corporation, Kew York (1944). (20) MCBAIN,J. W., AND BOLDUAK, 0. E. A , : J . Phys. Chem. 47, 94 (1943). (21) MCBAIN,J. W., AND BRADY, A . P.: J. Am. Chem. SOC.66, 2072 (1943). (22) MCBAIN, J . W., AND JOHNSON, K. E . : J. Am. Chem. S O C .6 6 , 9 (1944). W.: Viskosrdt der liolloide. J. W. Edwards, .4nn Arbor, Michigan (1944); (23) PHILIPPOFF, originally published in Germany in 1940. (24) SIMHA,R . : J. Chem. Phys. 13, 188 (1945). (25) STAUFF,J.: Kolloid-Z. 89, 224 (1939). (26) SVEDBERG. T.: Zsigmondy Festschrift (Erg. Bd. zu Iiolloid-Z. 361, p. 53 (1925). (27) SVEDBERG, T., A N D PEDERSES,K . 0.: The LUacentrifuge, Oxford Gniversity Press, Oxford and Kew York (1940) : (a) p. 23; (b) p , 38; ( e ) p. 42. (28) TENNENT, H. G . , AND VILBR.ASDT, C. F.: J. Ani. Chem. Soc. 65,424 (1943). (29) WRIGHT, K . A . . ASD TARTAR, H. I-.:J. Am. Chem. Soc. 61, 2 4 (1939).
