B. C. BENNION,L. K. J. TONG, L. P. HOLMES, AND E. M. EYRING
3288
Kinetics of Sodium Lauryl Sulfate Micelle Dissociation by a Light-Scattering Temperature-Jump Technique1 by B. C. Bennion,2L. K. J Tong,3L. P. Holmes, and E. M. Eyring Department of Chemistry, University of Utah, Salt Lake City, Utah 84119
(Received February $8,1960)
The time-dependent intensity of white light scattered at a right angle to the incident beam has been measured following a rapid 9" temperature jump in aqueous solutions of sodium lauryl sulfate. A rate constant for the dissociation of a first monomer anion from the micelle has been deduced from the concentration-dependent relaxation time measured in the millisecond time range. Introduction It is well known that the intensity of light scattered by colloidal particles is a function of particle size and shape. Most measurements of scattered light intensities in colloidal solutions have had as their objective the discovery of the equilibrium properties of the colloid. We report here instead a study of a colloidal system in which relaxation times, T, and a specific rate of micelle dissociation are deduced from the time dependence of scattered white-light intensity measured a t an angle of 90" to the incident beam and subsequent to a precipitous 9" temperature rise in the aqueous sample solution. The micelles are formed from sodium lauryl sulfate (NaLS) and the resulting rate constant is valid a t 35". The rate of micelle dissociation has, in general, only been estimated heretofore as being very fast.4 The one recently successful quantitative study of a similar systhe dissociation rate of dodecylpyridinium iodide micelles in aqueous solution, also required Eigen's temperature-jump relaxation technique.6 However, Kresheck, et aLj5made the more conventional measurement of time dependence of light-absorbance changes rather than scattered light intensities. Experimental Section We used the following chemicals: Eastman dodecyl sodium sulfate (NaLS), mp 213-215", reagent grade sodium nitrate, and distilled, deeminized, boiled water. Our Joule-heating temperature-jump apparatus closely resembles that of Hammes and Fasella' modified for single-beam operations except for the following features. The light source was a PEE( 110 mercury arc lamp rather than a tungsten lamp. No monochromator was used because it severely limited the scattered-light intensity. The lucite sample cell has 0.5 cm diameter cylindrical entering and exit light paths of lucite at 90" to one another. The barrel of the exit cylinder was painted flat black to prevent entry of spurious light rays to an additional 2-cm lucite rod carrying the scattered light to the glass envelope of a shielded 1P28 photomultiplier tube. Chemical relaxations following a 9 T h e Journal of Physical Chemistry
1" temperature jump were measured for a series of solutions 1.75 X loF3to 4.0 X M in NaLS. Each solution was also 0.1 M in NaN03 to ensure rapid heating. The initial sample temperature was 26" and the reported relaxation times are for 35 f 1". Blank solutions of aqueous NaN03 were run to verify that scattered light (and not artifacts such as stray electromagnetic fields) was responsible for the relaxations observed. The precision of our experimental relaxation times is approximately f15%. The critical micelle concentration (cmc) of sodium lauryl sulfate has been determined in the presence of 0.1 M NaCl as 1.6 X M at temperatures close to our final temperature of 35" .9,10 Because our experimental conditions were somewhat different, we determined the cmc of KaLS in aqueous 0.1 M NaN03 at 35" by exploiting the fact that both the absorbance and fluorescence of acridine orange vary considerably when NaLS micelles are present or absent. With a concentration of M acridine orange and 0.1 M NaN03 in each 5X of twelve solutions of varying NaLS concentration, the absorbance was measured at 496 mp on a Beckman DB spectrophotometer and plotted against total detergent concentration (see Figure 1). Results and Discussion While the ordinate of Figure 1 clearly does not repre(1) Supported in part by Grant AM 06231 from the National Institute of Arthritis and Metabolic Diseases. (2) NDEA Graduate Trainee, 1966-1969. (3) Eastman Kodak Co., Rochester, N. Y . (4) P. Mulrerjee, Advan. CoZZoidInterfac. Sci., 1,241 (1967). (5) G. C. Kresheck, E. Hamori, G. Davenport, and H. A. Scheraga, J . Amer. Chem. SOC.,88,24G (1966). (13) M . Eigen and L. DeMaeyer, "Technique of Organic Chemistry," Vol. VIII, Part 11,S. L. Friess, E. S. Lewis, and A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1963, p 977 ff. (7) G. G. Hammes and P. Fasella, J . Amer. Chem. SOC.,84, 4644 (1962). (8) G. G. Hammes and J. I. Steinfeld, ibid., 84,4639 (1962). (9) E. Matijevic and B. A. Pethica, Trans. Faraday SOC.,54, 587 (1958). (10) K. Shigehara, Bull. Chem. SOC.Jap., 39,2332 (1966).
KINETICSOF
W 9
00
SODIUMLAURYLSULFATEMICELLEDISSOCIATION
L
I
I
I
I
I
2
3
4
c0
,
3289
M
Figure 1. Plot of light absorbance measured on a Beckman DB spectrophotometer at 496 mp us. total molar sodium lauryl sulfate concentration, CC,in aqueous 6.1 M NaNOs a t 35". A smooth curve has been drawn through the experimental circles.
sent a true absorbance due to the complication of fluorescence, this plot permits an approximation of the critical micelle concentration under our experimental conditions. The major break in the plot corresponds to M. In Figure 2 we a cmc of approximately 1.3 X have plotted 7-l) the reciprocal of the observed relaxation time, ws. Co,the total molar concentration of NaLS. The value of Co corresponding to 7-1 = 0 in this plot suggests a very similar cmc of 0.95 X low3M. It is M the 7-l vs. Co interesting that at Co values above plot is no longer linear, a result also observed for aqueous dodecyl pyridinium iodide.K We fitted our kinetic data of Figure 2 to the expression derived by Kresheck, et ~ l . for , ~ the mechanism in which a series of" reversible steps leads to the formation of micelles (An) from monomers (A) kl?
A + A s A z ka
(1)
h a
Az i- A
ka
A3
(2) (3)
Here n is the average number of monomers per micelle, and it is presumed that the distribution of aggregation numbers about this average is sharply peaked. ReacAk e A, were assumed by tions of the type Aj Kresheck, et aZ.,5 to be negligible. Their fundamental assumption that the last reaction step is slow compared with all previous steps permits the derivation of the reciprocal relaxation time
+
+
where Co = [A] n[An], and T is the usual relaxation time determined from the oscilloscope trace. [A] is the equilibrium monomer concentration which increases with Co until the cmc is reached. Beyond this point, added monomer results in the formation of more mi-
i
OO
I
2
3
4
cot tu3M
Figure 2. Plot of reciprocal relaxation times, 7-1, determined by the light-scattering temperature-jump technique us. total molar sodium lauryl sulfate concentration, CO,in aqueous 0.1 M NaNOa at 35". The straight line is a least-squares fit of the experimental points.
celles, leaving the monomer concentration essentially unchanged. Consequently, for any Co in the range of our study, the monomer concentration [A] is assumed constant and identical with the cmc. Thus, at 7-l = 0 we have Co = [A] cmc, and from Figure 2 we obtain the kinetic approximation to the cmc of 0.95 X low3M mentioned above. If the number of monomers per micelle, n, is known, the rate constant ICn,,+l of micelle dissociation can be calculated. According to several independent studies,11-13 n for NaLS decreases slightly with increasing temperature, but increases with increasing counterion concentration. We have used n = 95 which is an average of the data11-13 obtained a t 21' and 25' for NaLS in aqueous 0.1 M NaC1. With this value of n, the relaxation data of Figure 2, and eq 5 we calculate ICn,n-I = 5.3 sec-l. Kresheck, et ~ i l . reported ,~ a ICn,,+l = 50 sec-I for aqueous dodecylpyridinium iodide at 22". It may be advantageous to use light-scattering rather than light-absorbance detection in relaxation method kinetic studies of many other colloidal systems in which the introduction of a dye would otherwise unnecessarily complicate the kinetics. Thus we have also observed millisecond-time-range chemical relaxations in 2.3 X M yeast alcohol dehydrogenase solutions ( 2 5 O , pH 7.5, ionic strength 0.2 M adjusted with phosphate buffer) and in 401,by weight aqueous solutions of Knox gelatin (25O, pH 7.7) using the present light-scattering temperature-jump technique. (11) J. N.Phillips and K. J. Myaels, J. Phps. Chem., 59, 326 (1955). (12) H.F. Huisman, Proc. Koninkl. Ned. Akad. Wetenschap., B67, 388 (1964). (13) M. F.Emerson and A. Holtser, J. Phps. Chem., 69,3718 (1965).
Volume 73,Number 10 October 1969
