W. L. COURCHENE
1870
Micellar Properties from Hydrodynamic
by W. L. Courchene The Procter & Gamble Company, M i a m i Valley Laboratories, Cincinnati, Ohio (Received February 6 , 1964)
46239
Intrinsic viscosities, sedimentation coefficients, and diffusion constants have been used to determine the size, shape, and hydration of nonionic (dimethyldodecylamine oxide) and anionic (sodium dodecyl sulfate) surfactant micelles. From these data it is concluded that the micelles are small, spherical, and highly hydrated (contain -40’% water by volume) in dilute solution. A model for the micelle is postulated and shown to be in agreement with the experimental data.
Few measurements have been made of the hydrodynamic properties of micelles where the results have been used to deduce size, shape, or hydration. Kushner, et uL11-3 measured viscosity as a function of concentration for a number of detergents but concluded that hydration of the micelle was an important factor only for a commercial nonyl phenol-ethylene oxide condensate which gave a high intrinsic viscosity. Tyuzgo4 used diffusion coefficients and Stokes’ law to calculate hydration for several salts of fatty acids. Other workers5 also used diffusion coefficients to calculate hydration of a series of methoxy polyoxyethylene decanoates and dodecanoates assuming the particles were spherical. Vetter6 used several pieces of hydrodynamic data to deduce that micelles of Aerosol MA contained water, while Hakala7 ignored hydration to conclude from hydrodynamic data that micelles of sodium dodecyl sulfate were ellipsoidal. On the other hand, Stigter, Mysels, and Williams* compared diffusion data with light scattering molecular weights to conclude that sodium dodecyl sulfate micelles were hydrated if a spherical shape vias assumed. I n order to clarify some of these apparently conflicting results, a numbel of hydrodynamic measurements were made on micellar solutions of very pure nonionic and ionic surfactants and the size, shape, and hydration of the micelles were determined from these data.
Experimental Viscosity. The viscosities of the solutions were measured at 30.00 f 0.02” using an Ostwald-Fenske viscometer with a flow time for water of about 220 sec. The Journal of Physical Chemistry
Flow times were measured to 0.01 sec. with a stop watch. The average deviation for five to seven measurements of a single solution did not exceed =t0.07 sec. The viscometer was calibrated with distilled water and 10% glycerine and the usual equation, = Apt Bp/t, was used to calculate the viscometer constants. The absolute viscosity and density of water a t 30” were taken to be 0.007976 poiseg and 0.99568 g./ml.,Io respectively. The viscosity and density of the glycerine solution were taken to be 0.01024 poise and 1.01927 g./ml., respective1y.l’ The surface tension correction, arising from the difference in shape of the nieniscus in the upper and lower bulbs of the viscometer, mas ignored. This is possible because the quantity of interest is the viscosity of the solution relative to the viscosity a t the critical micelle concentration, and the surface tension of these solutions was constant above the
+
(1) L. M. Kushner, B. G. Duncan, and J. I. Hoffman, J . Res. Natl. Bur. Std., 49, 85 (1952). (2) L. M. Kushner and W. D. Hubbard, J . P h y s . Chem., 5 8 , 1163 (1954). (3) L. M. Kushner, W. D. Hubbard, and R. A. Parker, J . Res. Arutl. Bur.. Std., 59, 113 (1957). (4) K. Tyuego, Kolloid-Z., 175, 40 (1961). (5) K. Shinoda, T. Nakagawa, B. Tamamushi, and T. Isemura, “Colloidal Surfactants,” Academic Press, New York, N. Y . , 1963, p. 117. (6) R. J. Vet.ter, J . Phys. Chem.. 51, 262 (1947). (7) N . V. Hakala, Thesis, University of Wisconsin, 1943. (8) D. Stigter, R. J. Williams, and K. Mysels, J . Phys. Chem., 59, 330 (1955). (9) J. R. Coe and T. D. Godfrey, J . A p p l . Phys., 15, 625 (1944). (10) L. W. Tilton and J. K. Taylor, J . Res. Natl. Bur. Std., 18, 205 (1937). (11) M . L. Sheely, Ind. Eng. Chem., 24, 1060 (1932).
MICELLAR PROPERTIES FROM HYDRODYSAMIC DATA
critical micelle concentration. The filling temperature correction, arising from the difference in temperature between the solution when the viscometer is filled and the temperature a t which the viscosity is determined, was avoided by allowing each solution to come to temperature equilibriuni in the viscometer a t the temperature of the measurements. When equilibrium had been reachcd (151-30 min.) the volume of the solution was adjusted in the viscometer. Density and Partial Specific Volume. Densities were measured with a 25-ml. pycnometer a t 30.00 f 0.02". I n all cases, plots of density us. concentration were linear above the critical micelle concentration up to the maximum concentration (l'%)used in these studies. Partial specific volumes (g) were calculated by standard methods. l 2 Ultracentrifugation. Sedinieiitation runs for each of the solutions were made a t 30" using a Spiiico Rlodel E ultracentrifuge equipped with a rotor temperature indicator (RTIC) and phase plate Schlieren optics. Sedimentation coefficients were determined in the usual mannerI3 from plots of In XH us. time, where XE was calculated from the maximal ordinate of the peak position. Diffusion Measurements. The self diffusion coefficients were determined by the open-ended capillary met hod using radiotagged dimet hyldodec ylaiiii ne oxide (C14) and sodium dodecyl sulfate (S39, Details have been previously described. Materials. Dimethyldodecylaniine oxide (DCI2AO) (both tagged and untagged) was taken from batches made in this laboratory whose preparation and purity have been previously described. l5 The dimethyloctylamine oxide (DCsAO) was prepared the same way. TO prepare sodiuni dodecyl sulfate (SDS), dodecyl alcohol (99.3% by gas chromatography) *6 was sulfated in ethylene dichloride-dioxane with liquid SO3, neutralized with sodium hydroxide, and the unsulfated alcohol extracted with petroleum ether. The freezedried product was recrystallized from ethyl alcohol and twice from an ethyl alcohol-water (80-20%) mixture. Since small amounts of residual dodecyl alcohol can cause a minimum in the surface tension curve, the material was further purified by the method of Harrold.'? S o surface tension niinimuiii was observed in fresh solutions. P5-Labeled SDS was prepared by sulfating the same dodecyl alcohol with S3j chlorosulfonic acid. Thereafter, the preparation was the same as with the unlabeled material. Solutions. Stock solutions of the surfactants were prepared on a weight/volunie basis using doubly distilled water in calibrated glassware. Dilutions mere
1871
made from the stock solutions using calibrated glassware. All amine oxide solutions were pH > 7 . This means only nonionic surfactant was present.
Results In agreement with the practice suggested by Kushnerl and Debye,lg infinite dilution for the micelles was taken to be the critical micelle concentration (c.m.c.). Relative viscosities were calculated using the viscosity a t the c.m.c. for the "solvent" viscosity. Figures 1-3
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Z
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4
'p
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,
0.1
I
0.2
I
I
I
I
I
0.3 0.4 0.5 0.6 0.7 0.8 0.9
C-C
M
I
0.1
C (gms/IOOml)
Figure 1. Reduced viscosity ctirve for dirt~ethj,lt~octec~yltlmine oxide in water at 30".
.03 J
J
1
1
!
0.1 0.2 0.3 0.4
,
1
!
!
1
0.5 0.6 0.7 0.0 0.9
1.0
C - C M C (gms/IOOml) Figure 2. Reduced viscosity curve for sodium dodecyl sulfate: X, in water; 0 , in 0.2 m SaCl at 30". (12) G. N. Lewis and M. Randall, "Thermod~nainics," McGrawHill Book Co., Inc., New, l-ork, N. T., 1923, 11. 38. (13) H. K. Schachman, "Tltracentrifugation in Biochemistry," 1959. Academic Press, New 7iork, N. T., (14) J. Wang, J . Am. Chcm. SOC.,73, 510 (1951). (15) D. G. Kolp, R . G. Laughlin, F. E'. Krause, and R. E. Zimmerer, J . P h y s . Chem., 67, til (1963). (16) Conditions: column. 30% polyethylene glycol-diglycolate polyester 011 00/80 Chromosorb in a 200 X 0.63 e m . 0.d. copper tube: column temperature 154': 51.3 nil. of He carrier gas/min. (17) S.1'. Harrold, J . Colloid Sei., 15, 250 (1960). (18) K. W. Herrmann, J . Phys. Chrnz., 6 6 , 29.5 (1962) (19) P. Debye, J . Colloid Sci., 3, 4 0 i (1945).
Volume 68, A'umber 7
J u l y , 1964.
W. L.COURCHENE
1872
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r c ._ m
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[email protected]?-
8
1
3
3
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1
.2
.4 .6 .8 CONCENTRATION ( g m S / 1 0 0 m l )
I
'(h .04
'
I
I
1
I
2
3
t
IO
Figure 4. Sedimentation data for dimethyldodecylamine oxide in water at 30".
C-C M C (gms/IOOml)
Figure 3. Reduced viscosity curve for dimethyloctylamine oxide in water a t 30". I.5
I
show plots of reduced viscosity ( v s p l c - c.m.c.) us. x 1.3 concentration. These plots can be extrapolated to inI.2 finite dilution (the c.ni.c.) to obtain the intrinsic viscosity ( [VI) for the micelles. The critical micelle concentrations used for these systems had been previously I determined from light scattering measurements18~20 0.2 0.4 0.6 0.8 1.0 CONCENTRATION gm /100ml) and some of them were also obtained from diffusion measurements. The agreement between methods was Figure 5 . Sedimentation data for sodium dodecyl sulfate good. in 0.2 m KaCl a t 30". Figures 4 and 5 show the sedimentation data for the systems studied. Infinite dilution has again been taken efficient. These two lines will intersect a t l / c = 1/ as the c.m.c. and the curves have been extrapolated to c.m.c. and thus provide a means for determining the the c.m.c. to obtain the sedimentation coefficient a t incritical micelle concentration. Figures 6 and 7 show finite dilution (So). S o t e in Fig. 4 that the sedimentathese plots for DClzAO and SDS in 0.2 m SaC1. tion coefficients are negatiGe because the density of the Discussion micelles is less than that of water. The treatment of diffusion data to obtain the diffusion The intrinsic viscosities (Fig. 1-3) are not very large coefficient for the micelles has been previously decompared to the 0.025 dl./g. expected for spherical scribed.16 It was shown that particles on the basis of Einstein's theory. There were indications from light scattering dissymnietry that the micelles in these systems were small since no where co and D orefer to the single detergent ione, c,,, dissymmetries larger than one were observed. Thus and D , to the micelles, and c and D to the bulk conthese micelles are certainly not elongated rods or long centration and the apparent diffusion coefficient. Since prolate ellipsoids. The intrinsic viscosity is related to the shape and volume of the micelles2' by c = co cm v)
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1
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+
NvVh
then
D
=
D,
+c
co -(Do - Dm)
Below the c.m.c., c = co and D , = 0, SO D = DO. Above the c.ni.c., co is nearly a constant (cg c.m.c.). Thus a plot of the observed D us. l / c will consist of two straight lines; one intersects the ordinate at D,, the micellar self-diffusion coefficient, and one is parallel to the abscissa a t D = Do, the monomer self-diffusion coThe Journal of Physical Chemistry
=
E
where N is Avogadro's number, Vh is the volume of the hydrated particle, M is the molecular weight, and v is a shape factor which depends upon the axial ratio of the particles (2.5 for spheres). I n order to determine the (20) K. W. Herrmann, unpublished work. (21) H. A. Scheraga and L. hlandelkern, J . A m . Chem. SOC.,75, 179
(1953).
hfICELL.4R PROPERTIES FROM
1873
HYDRODYNAMIC DATA
tering are 17,300 for DC1~A0,18 and 26,800 for sodium dodecyl sulfate in 0.2 m sodium chloride.22
'C
M C =-!-
:0.029 35.0
gmxl
Table I : Hydrodynamic Data for Micelles SO System
SDS(0 2 m NaC1) DCn.40
'I 20
40
60
80
100
(dxm)
Diffusion data for sodium dodecyl sulfate in 0.2 m NaCl a t 30". Figlire 6.
7 6 V
$5 V
W
4
0 x3 n
2 1
B
DE,
[?I
(10-18)
( X 10-6)
M
( X 106)
1.34 0.0345 1.17 0.880 24,900 2.12 -1.01
0 0495 1 . 1 0 1.12
20,300 2.13
It is apparent from Table I that the experimental pvalues are in excellent agreement with that calculated for spherical particles (2.12 X lo6). This means the micelles in these systems must, be sinall and spherical (or very close to spherical) in dilute solutions such as those examined here. Since the micelles are spherical, one can return to the equation for intrinsic viscosity, substitute 2.5 for V , and calculate the hydrated volume of the micelles. Values calculated in this way are given in Table 11. It is also possible to estimate the anhydrous volunie (V,) one would expect for these same particles, since V , = M g / N . Although this equation has been used to obtain Ti, it should be noted that the identification of a real volume with a partial specific volume cannot really of V , calculated in this way are be j ~ s t i f i e d . ~Values ~ given in Table 11. A comparison of these with the hydrated volumes, also given in Table TI, yields an estimate of the amount (volume yo)of water associated with the micelles. Table I1 : Amount of Water Associated with Micelles
Figure 7. Diffusion data for dimethyldodecylamine oxide in water at 30'. Detergent
size and shape of the micelles, it is necessary to have another piece of hydrodynamic data. This is provided by the sedimentation coefficient. Scheraga and hlandelkern have shown how this can be used, together with molecular weight, to obtain a function p which can be compared to theoretical values to determine the shape of the particles. Table I lists the sedinientation constants, intrinsic viscosities, diffusion coefficients, partial specific volumes, and molecular weights for the two systems measured, along with the calculated value of @ for these systems. The molecular weights which were calculated from the sedimentation and diffusion data are in agreement with those obtained from light scattering measurements. Values from light scat-
SDS (HzO) SDS ( 0 . 2 m NaC1)
DCizAO DCsAO
,
Hydrated volume, cc. x 10 -19
Anhydrous volume, cc. x 10 -19
% RzO
0.574 0.731
0.167 0.392
(1
..
..
46
93
12
0.524 0.0881
0.322 0.0432
39 51
69 14
10 10
Monomers/ micelle
Hs0/ monomer
This value is 33y0 when intrinsic viscosity is corrected for electroviscous effect (see text).
Assuming a density -1 g./ml. for this water, and using the molecular weight to determine the number of (22) L. M . Kushner and W. D. Huhhard, J . Colloid Sci., 10, 428 (1955). (23) H . A. Scheraga, "Protein Structure," Academic Press, New York, N. Y., 1961, Chapter I.
Volume 68,fiumber 7 J u l y . 1964
1874
surfactant monomers per micelle, one can calculate that there are 10-12 water molecules for each surfactant molecule in the micelle. One concludes from these data that, at least in dilute solutions of these surfactants, the micelles are small, spherical, and highly hydrated. The SDS and DCI2AO are about the same chain length and the number of water molecules per monomer is found to be about the same. This suggests that a good model for the micelle is a spherical particle with a hydrocarbon interior and polar groups on the surface. A layer or two of water molecules is relatively firmly attached to the micelle and moves with it as a hydrodynamic unit. From this model one would predict that if the chain length of the surfactant were reduced and the head group kept the same, the amount of water per monomer associated with the micelle would remain constant and the volume per cent of water would be larger for micelles of the shorter chain length surfactant. The results for DCsAO (Table 11) show that this is indeed the case, since the number of water molecules per monomer is the same as that for DClzAO while the volume per cent of water has increased. The amount of water in the DCsAO micelle was calculated using an anhydrous molecular weight of 2500,'* and a partial specific volume of 1.037. A volume per cent of water of 5 1 4 3 % would be predicted from the model for micelles of this surfactant. For sodium dodecyl sulfate in water the value of intrinsic viscosity is larger than one would expect. It is well known that a large electroviscous effect is observed for this material. Boothz4has theoretically shown how to take account of this effect and Parker and W a ~ i k have shown the intrinsic viscosities for sodium dodecyl
The Journal of Physical Chemistry
W. L. COURCHENE
sulfate in water and 0.2 m sodium chloride should differ by a factor of 2.3. Thus the value 0.0765 dl./g. found for this intrinsic viscosity should be only 0.0333 dl./g. This is in fair agreement with the value ,0345 dl./g. found in 0.2 m sodium chloride and shows the hydration of SDS micelles in water is about 33% by volume and not the -7OOj, one would calculate without correction for the electroviscous effect. The model discussed here applies to the cases studied and to dilute solutions. It has been shown, for example, that micelles of CleH33(OCHzCH2)leOH in dilute solution must exist as long rods since both the light scattering molecular weight and the intrinsic viscosity are too large for spherical micelles to be present.2B It has also been postulated27 on the basis of light scattering and X-ray data that spherical micelles initially present in dilute solutions elongate as the concentration is increased. On the basis of the model postulated here, this might happen because increasing the concentration of spherical micelles uses water rapidly and it is energetically more favorable for the micelles to elongate, decrease surface/volume ratio, and thus make more effective use of the available water.
Acknowledgments. The author wishes to thank Mr.
F. P. Krause for the diffusion measurements and Mr. W. L. Gagen for the sedimentation measurements. (24) F. Booth, Proe. Roy. SOC.(London), AZ08,514 (1950). (25) R. Parker and S. D. Wasik, J . Phys. Chem., 62, 967 (1958). (26) P. H. Elworthy and C. B. Macfarlane, J . Chem. SOC.,907 (1963). ~ (27) ~ J. M. Corkill and K. W. Herrmann, J . Phys. Chem., 67, 935 (1963).
