QuasielasticLight Scattering from Micellar Solutions
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
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(6) A. G. Evans, J. C. Evans, and E. H. Godden, J . Chem. SOC. 6 ,546 (1969). (7) A. G. Evans, J. C. Evans, P. J. Ems, C. L. James, and P. J. Pomery, J. Chem. SOC. B , 1484 (1971). (8) 0. R. Stevenson and J. G. Conceptcion,J . Phys. Chem., 76, 2176 (1972). (9) G. R. Stevenson and J. G. Conceptcion, J . Am. Chem. SOC.,95, 5692 (1973). (10) F. Jachimowicz, G. Levin, and M. Szwarc, J. Am. Chem. SOC.,99, 5977 (1977). (11) G. J. Hoijtink, E. De Boer, P. H. Van der Meij, and W. P. Weijland, Red. Trav. Chim. Paw-Bas. 75. 487 (1956). (12) J. Jagur-Grodzinski,M: Feld, S. L.'Yang,'and M. Szwarc, J . Phys. Chem., 69, 628 (1965). (13) G. R. Stevenson and I. Ocasio, J. Am. Chem. Soc., 98, 890 (1976).
Acknowledgment. The financial support of our studies by the National Science Foundation is gratefully acknowledged. References and Notes (1) H. C. Wang, G. Levin, and M. Szwarc, J. Am. Chem. Soc., 99, 5056
(1977). (2) M. Szwarc, "Carbanions, Living Polymers, and Electron Transfer Processes",Wiley-Interscience, New York, N.Y., 1968. (3) C. Carvajal, K. J. Tolle, J. Smid, and M. Szwarc, J. Am. Chem. Soc., 87, 5548 (1965). (4) P. Chang, R. V. Slates,and M. Szwarc, J. Phys. Chem., 70, 3180 (1966). (5) A. G. Evans and J. C. Evans, J . Chem. SOC. B , 271 (1966).
Deduction of Micellar Shape from Angular Dissymmetry Measurements of Light Scattered from Aqueous Sodium Dodecyl Sulfate Solutions at High Sodium Chloride Concentrations Charles Y. Young,' Paul J. Mlssel, Norman A. Mazer, George B. Benedek, Department of Physics, Center for Materials Science and Engineering, and Harvard-MIT Program in Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
and Martin C. Carey Department of Medicine, Harvard Medical School, Division of Gastroenterology, Peter Bent Brigham Hospital and Harvard-MIT Program in Health Sciences and Technology, Boston, Massachusetts 021 15 (Received January 30, 1978) Publication costs assisted by the National Science Foundation
From measurements of the angular dissymmetry and autocorrelation function of laser light scattered from 2 g/dL aqueous solutions of sodium dodecyl sulfate (SDS) in 0.6 M NaCl, we have deduced both the mean radius of gyration, R,, and mean hydrodynamic radius, R h , of SDS micelles over a wide temperature range (15-85 "C) including the supercooled region below the critical micellar temperature (cmt). Above 40 "C, values of the angular dissymmetry function, d(O), defined as the ratio of scattered intensities Z(0)/Z(180° - 0) (30" 5 0 5 go"), are less than 1.05 implying that R, is smaller than 100 A. Below 40 "C, d(0) values increase appreciably as the temperature is lowered and R, is found to increase from 121 8, at 30 "C to 380 A at 15.7 "C, indicating a substantial growth of micellar size. This growth is also reflected by an increase in the R h values from 101 to 195 A. A deduction of micellar shape is made by comparing the measured dependence of R, on R h with theoretical calculations, assuming either spherical, disklike or rodlike micellar growth. The data are found to be in excellent agreement with the predictions based on a rodlike micellar shape, a finding which confirms the previous conclusion of Mazer et al.
Introduction In a previous study, we employed quasielastic light scattering spectroscopy (QLS) to investigate the size and shape of sodium dodecyl sulfate (SDS) micelles formed in aqueous NaCl solutions a t detergent concentrations well above the critical micellar concentration (cmc).'~2In the presence of 0.6 M NaCl, the mean hydrodynamic radius of the micelles, R h , was found to increase dramatically from a minimum value of 25 8, a t high temperatures ( 4 5 "C) to 168 8, a t 18 "C, a temperature at which the micellar phase was supercooled several degrees below the critical micellar temperature (cmt = 25 "C in 0.6 M NaCl). From the dependence of the scattered light intensity measured at a fixed angle on R , we further concluded that the increase in micellar size was consistent with growth of the micelles from a minimum spherical shape of hydrated
* Correspondence and Reprint Requests should be addressed to Charles Y. Young, MIT 13-2018, Cambridge Mass. 02139. 0022-3654/78/2082-1375$01 .OO/O
radius 25 8, into long prolate elliposids (rods) having a semiminor axis of 25 A. In light of existing controversies as to whether the shape of large nonspherical micelles is rodlike or d i ~ k l i k ewe ,~~ considered that additional experimental information on the shape of the large SDS micelles would be useful. In addition to measurements of R h , another quantity which may be used to characterize the size and shape of micelles is the mean radius of gyration, R,, which can be deduced from the angular dissymmetry of the scattered light intensity. For a given value of R h , R , will have different values for particles of different shape. Thus different relationships will exist between R h and R , depending on the shape of the micelles. Hence, measurements of both quantities can be employed to distinguish between the possible shapes of large micelles. In this paper, we report experiments in which R h and R g of SDS micelles are measured in 2 g/dL solutions a t various temperatures (15-85 "C) in 0.6 M NaCl. These 0 1978 American Chemical Society
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The Journal of Physical Chemistry, Vol. 82,
No.
Young et ai.
12, 1978
measurements confirm our previous conclusion that the shape of large SDS micelles is rodlike.
Materials and Methods A. Reagents and Solutions. The SDS used was the same high quality gel electropheresis grade material (Bio-Rad Laboratories, San Diego, Calif.) used in the previous study. This material gave a single spot on thin layer chromatography, indicating the absence of organic alcohols. Furthermore, it was also free of titratable and solubilized impurities as indicated by potentiometric titration and surface tension measurements.' The sodium chloride and water purification procedures were identical with that used in the previous study. B. QLS Measurements. QLS was used to obtain the mean diffusion coefficient ( D ) of the SDS micelles. The apparatus, cell filling methods, temperature control, and cumulants data analysis of the autocorrelation function were identical with those employed earlier.' From D , we deduced Rh using the following equation8 Rh =
kTl6nqB
(1)
where k is Boltzmann's constant, T is the absolute temperature, and q is the solvent viscosity. Experimental and theoretical results discussed in detail previously' suggest that the Rh values deduced from this equation will not be substantially affected by intermicellar interactions under the conditions of the present experiment. C. Dissymmetry Measurements. The intensity of light scattered from a solution of macromolecules will become measurably greater in the forward direction relative to the backward direction as the radius of gyration of the macromolecule, R,, exceeds -1/20 the wavelength of the incident light.g It can be shown quantitatively that the intensity I ( 8 ) scattered a t an angle 8 is related to the intensity scattered in the forward direction I ( 0 ) according to the approximate formulag
which is valid for K(O)R,C 1. K(8),the magnitude of the scattering wave vector, is given by 47~sin ( 0 / 2 ) K ( 0 )= (3)
In
where X is the wavelength of the incident light in vacuo and n is the index of refraction of the scattering medium. Although it is possible to directly measure I(8) as a function of 8, such measurements are complicated by slow drifts in the incident light intensity, the necessity for a solid angle correction, and the effects of stray scattering from sample cell walls. However, these complications can be overcome by directly measuring the dissymmetry function d(8) defined in eq 4 as the ratio of the intensity of light scattered a t supplementary angles 8 and 180" - 8. d(e) = 1(e)/1(180"- e ) (4) We therefore employed the apparatus shown schematically in Figure 1 to measure d(8) as a function of 8. As shown in Figure 1, the He-Ne laser beam (Spectra Physics 124A laser, X 6328 A) is split and routed in such a way as to allow the beams to travel identical paths in the sample cell but from opposite directions. A rotating beam chopper alternately allows only one of the two beams to pass a t a given time. The time frame in which the two beams alternate is of the order of 4 ms. The light which is alternately being scattered from the solution at 8 and 180" - 8 is imaged onto the surface of a photomultiplier
P1
.."\
p-T
A
'--zi sritchino circuit
cank
Figure 1. Apparatus used to measure angular dissymmetry of scattered light intensity, d(8). Laser light is split into two equal intensity light beams by beam splitter, BS1. Mirrors M1, M2, and M3 are used to route the beams so that they travel in exactly opposite directions. Lenses L1 and L2 focus the beams into the sample cell (SC) and the beam at the center of the cell is imaged onto a pinhole PHI by lens L3. A motorized chopper allows only one of the two beams to pass through the sample at one time. Depending on the direction of travel of the beam, either one of the two photodiodes P1 and P2 is activated by part of the beam split off by BS2. The signals from these photodiodes are used to trigger the electronic switching circuit which directs the photopulses from the photomultiplier tube PMT into the appropriate channel (corresponding to either I ( 0 ) or 1(180° - 0)) of a two-channel counter. The ratio of the number of photopulses in these channels is then displayed on a digital meter as the dissymmetry d(8).
tube which is mounted on a rotatable platform, enabling 8 to be varied from 30 to 150". A second beam splitter is used in conjunction with two photodiodes (Pl, P2) to detect the direction in which each beam enters the sample cell. Signals from the photodiodes trigger an electronic switching circuit and direct the photomultiplier pulses into the proper channel of a two-channel pulse counter. The dissymmetry is then displayed on a digital meter as the ratio of the number of photopulses in the two channels, which corresponds to the ratio of the scattered intensities. Since scattered light from both beams has the same correction for solid angle, suffers the same stray scattering, and is measured over very short time scales (-4 ms), this apparatus avoids the experimental difficulties outlined above for the direct mea!urements of I(8). Moreover, although micellar interactions can affect the absolute values of the scattered intensity, to a first approximation, such effects will be independent of scattering wave vectorg and will therefore cancel in the dissymmetry function. By substituting eq 2 and 3 into eq 4, one can show that d(0) is approximately related to R, in the following way: (5)
Thus, from the slope of d(8) vs. cos 8, the value of R, can be obtained. The validity of the linear approximation given in eq 5 was tested in the following way. According to Debye and A n a ~ k e r ,the ~ form factor, I(e)/Z(O) for long rods of negligible diameter is calculated to be
where K(0) is the scattering wave vector and L is the length
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Quasielastic Light Scattering from Micellar Solutions
1377
-
1.75
-
1.20
-
0
195
380
0
130
255
-
A 72
-
h
0
0
0
0.2
0.4
0.6
cose
0.8
0.4
0.6
cos e
0.8
1.0
Flgure 3. Plots of dissymmetry d(8) vs. cos 8 for 2 g/dL SDS solutions in 0.6 M NaCl at 40, 20, and 15.7 "C. Note a progressive increase in the slope as temperature is lowered.
1.0
Figure 2. Plots of dissymmetry d(O) vs. cos 8 for long rods of 1000, 1500, and 2000 A in length. Dotted lines are obtained by the linear approximation (eq 5) and the solid lines are calculated by taking the ratio of form factors (eq 6) at supplementary angles. A wavelength of 6328 A and refractive index of 1.33 were used in the calculations.
of the rod. In Figure 2 the dissymmetry calculated using eq 6 is compared to the linear approximation (eq 5) taking R to be L/&. Deviations in the linear dependence of dt8) vs. cos 0 begin to become appreciable for rods having a length of 2000 8, ( R = 577 A), thus fixing an upper limit on the validity of the linear approximation. Similar calculations for disks and spheres show that the linear approximation is also valid for R, less than ~ 6 0 A. 0 On the other hand, particles with R, less than 100 A would produce a dissymmetry less than 1.05, too small to be measured reliably, thus fixing a minimum detectable limit. From Figure 2, it should be noted that even in the case of slight departure from linearity, the radius of gyration can still be obtained from the average slope of d(8) vs. cos 6.
When the apparatus was tested on a nearly monodisperse solution of latex spheres of know size (450 f 30 A radius) lo the experimentally deduced R, values were within 5% of the predicted value, attesting to the reliability of the apparatus and the validity of eq 5. In the case of polydisperse solutions, such as a micellar solution, the slope of d(0) vs. cos 8 provides a mean radius of gyration denoted by 17,. It can be shown that R , is related to the radius of gyration of each species by the following equation:
E, = (ZCiMiR,,i2/XCiMi)'/2
0.2
(7)
where Ci is the concentration (w/v) of the ith micellar species having molecular weight M , and radius of gyration Rg,l. From this equation, it also follows that the background scattering from detergent monomers and added electrolyte will have an imperceptible effect on the measured R values as the concentrations and molecular weights of taese species are negligibly small. R e s u l t s and Discussion QLS and angular dissymmetry measurements were conducted on 2 g/dL SDS solutions in 0.6 M NaCl over
z,
TABLE I : Experimental Values of and fig Measured from 2 g/dL SDS Solutions at Various Temperatures in 0.6 M NaCl Concentration' -
T," C
-
Rh,A
Rg,A
85 70 55 40 30 25 22 21 19 18.1 18 15.7
25 32 45 72 101 130 145 150 163 170 170 195
