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Langmuir 1989,5, 728-733
Micelle Size Determined by Electron Spin Resonance and Fluorescence Spectroscopy Goran Wikander* and Lennart B.-A. Johansson Department of Physical Chemistry, University of UmeP, S-901 87 Umeh, Sweden Received September 21, 1988. In Final Form: December 29, 1988 The size of micelles formed by potassium octanoate (KC8) and potassium dodecanoate (KC12) in water was studied by means of electron spin resonance (ESR) and fluorescence-quenchingspectroscopies. The fluorescence-quenching experiments gave aggregation numbers of KC12 ranging between 52 and 69, when the surfactant concentration was increased from 5% to 30% by weight. The aggregation numbers of the KC8 system could not be evaluated due to perturbation of the micelles by the quencher, benzophenone. An analysis of the ESR data assuming that the spin label (5-doxylstearic acid) moves isotropically as in a solvent yields unphysically low values of the hydration radii for both of the micellar systems. However, an extended model applied on the KC12 system agrees very well with the radii calculated according to Tanford and those extracted from the aggregation numbers. This model accounts for the local fast motion of the spin label and its translational motion in the aggregates as well as the rotational motion of the micelles. We conclude that an appropriate analysis of ESR line shape must account for the locally fast and slow motions of the probe molecules solubilized in amphiphile aggregates.
Introduction Surfactant or amphiphilic molecules are characterized by a hydrophilic head group and a hydrophobic tail. The tail is a hydrocarbon chain of varying length, while the other moiety is an electroneutral or positively/negatively charged species. Above a certain concentration of the surfactant in water, the critical micelle concentration (cmc), these molecules form aggregated structures called micelles. Micelles are rapidly fluctuating aggregates that can be regarded as primitive precursors of lyotropic liquid crystalline phases. The fluctuations are due to the residence time of an individual amphiphile in a micelle. This quantity displays a variation with the length of the amphiphile, but it is longer than nanoseconds.l Different spectroscopic methods me commonly used for determining the micellar size. A review where the advantages and the drawbacks of these different techniques are considered has recently been publisheda2 Sijderman et al. have investigated the size of amphiphile aggregates of different systems by means of NMR relaxet al. have studied the ation m e a s ~ r e m e n t a .Di ~ ~Meglio ~ variation of the radii of nonionic micelles as a function of temperature by means of electron spin resonance (ESR) spectrosc~py.~In a recent paper a combined study of small-angle X-ray scattering (SAXS) and ESR measurements was carried out on aqueous solutions of sodium deoxycholate. The hydrodynamic radius, the shape, and the aggregation number of the micellar aggregates were then determined.s Another method which gives information about the aggregation number is fluorescence quenching experirnenta?-l0 The method works very well, as long as the distribution and photophysics of the (1)Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffman, H.; Kielmann, 1.; Ulbricht, W.; Zana, R.; Lang, J.; Toudre, C. J. Phys. Chem. 1976,80,905. (2)Surfactant Solutions New Metho& of Inuestigation; Zana, R.,Ed.; Surfactant Science Series Vol. 22, Marcel Dekker: New York, 1987. (3)Walderhaug, H.; M e r m a n , 0.;Stilbs, P. J.Phys.Chem. 1984,88 16.5.5.
(4)Saderman, 0.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J. Phys. Chem. 1985,89,3693. (5) Di Meglio, J. M.; Paz, L.; Dvolaitaky, M.; Taupin, C. J. Phys. Chem. 1984,88,6036. (6)Eeposito, G.; Giglio, E.; Pavel, N. V.; Zanobi, A. J. Phys. Chem. 1987,91,356. (7)Almgren, M.; Lbfroth, J.-E. J. Colloid Interface Sci. 1981,81,486. (8)Malliaris, A.; Lang, J.; Zana, R. J. CoEloid Interface Sci. 1986,110, "0"
,401.
(9)Infelta, P.P.Chem. Phys.Lett. 1979,61,88. (10)Atik, S.S.;Nam,M.; Singer, L. A. Chem. Phys.Lett. 1979,67,75.
fluorescent probes in the aggregated surfactant systems fulfill certain criteria. An illuminating discussion of these criteria is given in ref 7 and 8. By combining the two probe methods, ESR and time-resolved fluorescence quenching, it is possible to cover the same time scale, viz., the nanosecond time domain, with two different techniques. In the present paper, results from a combined ESR and fluorescence quenching investigation on potassium octanoate (KC8) and potassium dodecanoate (KC12)micellar solutions are presented. To our knowledge a combined study of this kind has never been published before. However, a combined ESR and NMR study on liquid crystalline phases was recently presented from this laboratory."
Experimental Section Potassium octanoate (KC8)and potassium dodecanoate (KC12) were synthesized at our laboratory according to a procedure outlined in ref 12. 5-Doxylstearic acid was purchased from Molecular Probea Inc. and was used without any purification. The label was dissolved in chloroform-methanol (21 vol/vol). A suitable amount of the label was transferred to glass vials. The solvent was pumped off under an N2atmosphere. Appropriate amounts of amphiphile and water were added to the thoroughly dried label. Thereafter, the glass vials were sealed off. The samples were thoroughly mixed by repeated centrifuging at 40 "C for several days. They were stored for equilibration during some days. Small amounts of the samples were sucked into glaas capillary tubes, sealed off, and thereafter run on the ESR spectrometer. The label/amphiphile ratio was always kept at 1/103 on a molar basis. All ESR spectra were registered at 25 "C with a Varian Model E-109 X-band (9 GHz) spectrometer by using an E-238 (TMllomode) cavity. Temperature regulation was achieved by means of a Model V-6040 variable-temperature regulator. The spectrometer was interfaced to a Zenith-111-32 PC similar t o the procedure outlined by Lipscomb and Salo.l3 Computer simulations for ESR line shape analysis were performed on a Cyber 180/75 at the computer centre of the University of Umel.
Pyrene for the fluorescencemeasurements was obtained from Fluka (melting point 429 K) and was recrystallized 3 times from diethyl ether. Samples were made by preparing two identical solutions containing the appropriate amount of the actual sur(11)(a) Wikander, G.; Lindblom, G.; Arvidson, G.; Bumell, G. Presented at the 2nd Chianti Workahop on Magnetic Resoaance; San Miniato, Italy, June 1520,1987.(b) Wikander, G.; Eriksson, P.-0.; Lindblom, G.; Burnell, E.; Kristoffersson, J.; Stael von Holstein, J., to be submitted. (12)Johansson, L. B.-A.; Lindblom, G. Liq. Cryst. 1986,I, 53. (13)Lipscomb, J. D.; Salo, R. W. Computer-Enhanced Spectroscopy 1986, 1, 11.
0743-7463I89 12405-0728$01.50I O 0 1989 American Chemical Societv
Langmuir, Vol. 5, No.3, 1989 729
Micelles by Electron Spin Resonance
Table I. Correlation Times, sa and sC, According to Eq 2, for the Spin Probe 6-Doxylstearic Acid in Micellar Phases of Potassium Octanoate (KCS) and Potassium Dodecanoate (KC12) in Aqueous Solutionsa KC8
10 15 20 25 30 35 40
0.75 0.79 0.85 0.94 0.99 1.16 1.43
0.65 0.68 0.73 0.81 0.84 0.96 1.11
KC12
6.2 6.3 6.5 6.7 6.8 7.1 7.4
6.5 6.6 6.8 7.0 7.1 7.5 8.1
1.16 1.34 1.37 1.48 1.49
1.52 1.78 1.90 2.17 2.44
10.9 11.4 11.5 11.8 11.8
11.9 12.5 12.8 13.4 13.9
"REand Rc are the estimated radii of the spherical micelles according to eq 3. factant in triply distilled water. To both of these solutions a weighed amount of pyrene was added. The molar ratio of the surfactant to pyrene was approximately 105/l. To one of these solutionsa weighed amount of benzophenone (Aldrich99+% Gold label) was added so that the molar ratio of surfactant/(pyrene + benzophenone)was approximately 100/1. The solutions were equilibrated for a couple of days under gentle shaking at 25 "C. Time-resolvedsingle photon counting fluorescence was monitored on a PRA system 3000 (Photochemical Research Assoc., Inc., London, Ontario, Canada). The excitation source was a thyratron gated flash lamp (Model 510 C) filled with deuterium gas and operating at 25 kHz. The excitation and emission wavelengths were selected by interference fiiters centered at 332.8 and 398.8 nm, respectively. The deconvolution software (DECAY V 3.0 a) used was developed by PRA. The samples were not degassed but sealed in quartz capillary tubes and thermostated to the measuring temperature to within 1 O C .
Basic Considerations Modeling of ESR Line Shapes. For fast motions of nitroxide radicals on the ESR time scale, i.e., when the correlation time, TR, is less than lo-" s, the ESR spectrum of the radical is insensitive to the rate of the molecular motion. In this time domain, the ESR spectrum consists of three narrow lines with equal intensity. For slower motions, i.e. for rotational correlation times in the range lo-" s < T R < s, the three hyperfine lines become differentially broadened. This is due to an incomplete motional averaging in the g and A tensor anisotropies. In the Redfield limit, the inverse of the spin-spin relaxation time, (T2,m)-1,can be written14Js (T2,m)-1 = A Bm Cm2 (1)
+
+
The f i i t term contains contributions from the anisotropies of the g and A tensors, static terms due to unresolved proton hyperfine coupling, instrumental broadening, and relaxation due to the presence of oxygen in the solutions. The B and C factors are functions of the g and A tensor elements of 14Nand the rotational correlation time of the molecule. m, finally, is the magnetic spin quantum number of the nitrogen nucleus (0,fl). The correlation time, TR, of an isotropically tumbling nitroxide molecule can be expressed by the recursion f ~ r m u l a s ' ~ J ~ J ~
TC
= 5.95 X lO-'OAB(O)[
(')"
1-1
+
(")" I+1
- 2 1 (2b)
AB(0) is the width of the central line (in Gauss).
Io,
(14) Freed, J. H.; Fraenkel, G. K. J. Chem. Phys. 1963, 39, 326. (15) Kivehon, D. J. Phys. Chem. 1969,33, 1094. (16) Schreier,S.; Polnaszek, C. F.; Smith,I. C. P. Biochim.Biophys. Acta 1978,515, 375. (17) Hemminga, M. A. Chem. Phys. Lipids 1983,32, 323.
and Il are the intensities of the different lines. For an isotropic rotational motion of the label, TB = TC = q+ Equation 2 is only valid for fast motion, i.e., for T being shorter than approximately 3 ns. A difference between T B and TC indicates an anisotropic rotational motion and/or an ordering of the spin label. From eq 2 it is possible to determine the rotational correlation time for the label directly from the experimental spectra. The calculated values of T B and T~ for 5-doxylstearic acid in the KC8 and KC12 systems are given in Table I. Assume that the spin label is rigidly attached to a micelle that performs an isotropic tumbling motion. For Brownian rotational diffusion, the correlation time, TR, can be estimated from the Debye-Stokes-Einstein equation T R = 4rvR3/3kT (3) R is the hydrodynamic radius of the aggregate, t is the viscosity of the solvent, k is the Boltzmann constant, and T is the temperature. In this particular case, T R = T B = TC. Hence by combining eq 2 and 3 it is then possible to estimate the hydrodynamicradius of a micelle. The results from such a calculation on the KC8 and KC12 systems are given in Table I. Another approach is the "two-step model", which appears to be more realistic from a physical point of view. This model was originally developed for NMR applications.18 In this model, the motions of the spin label are separated into a fast and a slow part. The motion of the micelle is considered as slow and independent of the local rapid motions of the label. The rotational motion of the micelle can be treated isotropically, at least for a spherical aggregate. However, the rotational motions of the label should be considered as anisotropic since the local environment of the aggregate is anisotropic. In an extended model, the rotation about the z-axis (the long axis) of the label is very fast, while motions perpendicular to the z-axis are slow. This local anisotropic motion leads to a partial averaging of the anisotropy in the g and A tensors of the label. By multiplying the g and A tensor with a local order parameter of the label, we account for the local averaging of the g and A tensors. The local order parameter of the label is obtained from measurements when the label is solubilized in a lamellar liquid crystalline phase. The local interaction between the label and its environment is considered to be the same in the micellar and lamellar phases of the same kind of amphiphile. The local order parameter, S, is defined as19
s = (All' - A,')/[A,, - f / 2 ( A x x + A,)1 All' = 1/2C(a?)Ai, A,'
(4)
= 1 / 2 C ( 1 - ( $ ) ) A i , and Aii are
(IS)(a) WennerstrBm, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974,6,97. (b) WennerstrBm, H.; Lindman, B.; SBderman, 0.;Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. SOC.1979,101, 6860. (19) Mason, R. P.; Polnaszek, C. F.; Freed, J. H. J.Phys. Chem. 1974, 78, 1324.
730 Langmuir, Val. 5, No. 3, 1989
Wikander et al. 1 I
I/ I! I
-
2All
Figure 3. ESR spectrum of Bdoxyhtearic acid solubilized in the
lamellar phase of potassium octanoate (KC8)/H20/decanol (50/23/27 wt %) at 25 O C . The total scan range is 80 G.
Figure 1. ESR spectra of 5-doxylstearic acid solubilized in
micelles of potassium octanoate in water, at different concentrations (percent by weight). The total scan range is 50 G.
Figure 2. ESR spectra of 5-doxylstearic acid solubilized in micelles of potassium laurate in water, at different surfactant concentrations (percent by weight). The total scan range is 80 G.
principal components of the hyperfine coupling tensor of the label. aii are direction cosines (i = x , y, z ) , and the brackets denote time averages. S is determined from the ESR spectrum of the probe in a lamellar phase according to (5) S = All - A,/[Az, - l/z(Axx + Ayy)l(a,'/ao) (20) Seelig, J. In Spin Labeling. Theory and Applications; Berliner, L. J., Ed.; Academic Press: New York, 1976; Chapter 10.
Alland A, are defined as shown in Figure 3. a,,' = 1/3(Axx + A, + A,) and a. = l/JAll 4- 2AJ. a(/ao is a correction due to differences in the polarity, a,,' is obtained from an analysis of the principal components of the A tensor in a single crystal, and a. is the corresponding value obtained for the lamellar phase. Further details concerning this correction are given in ref 19. A simulation of the line shape is needed to obtain the slow correlation time of the label, 7:. We have used a computer program similar to that developed by Polnaszek and Freed.21 In this program the stochastic Liouville equation is solved for a Brownian rotational reorientation of the probe in an isotropic medium. A symmetrical rotational diffusion tensor is used (R,,= RL),and the label is assumed to be confiied in a spherical aggregate. The g values from ref 22 were used in the simulations. However, the elements of the A tensor have been scaled similar to the procedure outlined by Meirovitz and Freed.23 The corrected elements of the A and g tensors have been multiplied by the experimentally determined order parameter, s. This procedure then accounts for the local averaging of the anisotropy in g and A tensors as mentioned above. Fluorescence Quenching. The quenching of pyrene due to the formation of excimers or quenchers such as benzophenone has been used in determinations of the aggregate size of rnicelles?-'O Recently, the self-quenching of pyrene in a cubic liquid crystalline phase yielded information about the aggregate size.24 The decay of the photophysics of pyrene solubilized in micelles is monoexponential, with a lifetime of about 200 ns. Adding a quencher as benzophenone causes the fluorescence decay to become more complicated. Usually a rapid initial decay is observed followed by a monoexponential decay, which is often equal to the fluorescence emission of the monomer. Provided that the migration of pyrene or its quencher is slow on the time scale of fluorescence, it may be shown that the fluorescence decay depends on the mean number of quenchers per aggregate (X), the quenching rate constant k,, and the monomer lifetime as9J0 F ( t ) = F(0) exp(-t/Tf - (8)[1 - exp(-k,t)]) (6) The aggregation number, N, can be calculated from (8) ([amphiphile] - cmc) N= (7) [pyrenel (21) Freed, J. H. In Spin Labeling. Theory and Applications; Berliner, L. J., Ed., Academic Press: New York, 1976; Chapter 3. (22) Gaffney, B. J.; McConnell, H. M. J. Magn. Reson. 1974, 16, 1. (23) Meirovitch, E.; Freed, J. H. J. Phys. Chem. 1984,88, 4995. (24) Johansson, L. B.-A.; Sgerman, 0. J.Phys. Chem. 1987,91,5275.
Langmuir, Vol. 5, No. 3, 1989 731
Micelles by Electron Spin Resonance
-20
0
20
I
40
,
-20
numa
m
!
40
Bluss
K C g , 4 0 % w/w
9
-, 1-90
-20
0
20
7
40 QKISS
Figure 4. Experimental and simulated (dotted lines) spectra for Bdoxylstearic acid at two different concentrations of potassium octanoate (10%and 40% by weight) and potassium dodecanoate (5% and 30% by weight) in water.
Results Analysis of ESR Data. The ESR spectra of 5doxylstearic acid solubilized in micellar solutions of KC8 and KC12 at different concentrations are displayed in Figures 1 and 2. For both of the systems it appears that the line shape of the label is broadened differentially. However, the motion of the label is still in the fast to intermediate time domain as concerns the ESR time scale. The motion of the label is slower in the KC12 system as compared to the KC8 system. This can be judged from the broader line width of the central line. Furthermore, the shape of the low- and high-field lines of the KC12 system appears to be more asymmetric compared to those in the KC8 system. The binary system KC8-H20 does not form any lamellar phase. However, by adding decanol, a lamellar phase can be found in the ternary system.25 The order parameter of the label was determined for several different compositions. The average value of S is 0.53 (cf. Table 11). The binary system KC12-H20 forms lamellar phases only at high temperatures.26 Therefore, we determined S at elevated temperatures and extrapolated ow results to 25 OC. There is no straightforward relation between the order (25) Ekwall,P.; Mandell,L.; Fontell, K. J. Colloid Interface Sci.1969, 31, 508. (26) McBain, J. N.; Sierichs, W. C. J. Am. Oil. Chem. SOC.1948,25, 221.
Table 11. Order Parameters, S, of 5-Doxylstearic Acid in Lamellar Phases of Potassium Octanoate (KC8)/H20/Decanol and Potassium Dodecanoate (KC12)/Hz0 at Various Compositions and Temperatures" sample sample S t , "C comp, wt % S t , OC comp, w t % KC8/HzO/Decanol 20/42/38 0.54 25 50/23/27 0.53 25 30133137 0.54 25 55/25/20 0.49 25 40126134 0.54 25 85/15
80/20
0.37 0.38 0.38 0.39 0.40 0.41 0.38 0.38 0.39
KC12/Hz0 70 60 55 50 45 40 70 60 50
"For KC8/HzO/decanol, 0.45 0.02.
*
80120 74/26
0.40 0.42 0.37 0.37 0.37 0.38 0.39 0.40
45 40 65 60 55 50 45 40
s = 0.53 k 0.02. For KC12/Hz0, s =
parameter and the temperature. However, Seelig27*28 has shown that, at least for lamellar systems doped with 5doxylstearic acid, the order parameter decreases almost (27) Seelig, J. J. Am. Chem. SOC.1971, 93, 5017. (28) Axel, F.; Seelig, J. J. Am. Chem. SOC.1973, 95, 7972.
132 Langmuir, Vol. 5, No. 3, 1989
Wikander et al.
Table 111. Results from the Line Shape Simulations of 5-Doxylstearic Acid in Micellar Phases of Potassium Octanoate (KCS) and Potassium Dodecanoate (KC12)in WaterO amphiphile wt, 70 R, X lo", s-l G T:, ns r X lolo, m KC8 10 2.2 16.4 0.760 0.50 16.7 0.737 0.50 15 2.3 2.4 17.1 0.695 0.50 20 17.4 0.662 0.50 25 2.5 18.4 0.571 0.50 30 2.9 19.7 0.482 0.55 35 3.5 20.3 0.446 0.55 40 3.7
80
KC12 0.60 0.65 0.70 0.75 0.75 0.80
20
5 10 15 20 25 30
0.319 0.300 0.281 0.255 0.226 0.193
5.2 5.6 5.9 6.5 7.4 8.7
21.0 21.5 22.1 23.0 24.0 25.5
O R , denotes the rate of rotational reorientation for 5-doxylstearic acid. ( T2)-I denotes the line width. The rotational correlation times (7:) and the radii of aggregates ( r ) are under the assumption of spherical micelles according to eq 8.
linearly with increasing temperature. The order parameters obtained a t different temperatures and compositions of KC12-H20 are given in Table 11. The mean value of the extrapolated order parameter at 25 OC was 0.45. In the first run, the best fits between simulated and experimental spectra were judged by visual inspection. The values obtained from these "best" fits were then used as input values in the least-squares fits. The results from our line shape simulations are displayed in Table I11 (see also figure 4). The slow correlation time, T,", is assumed to depend on two different contributions. These are the rotation of the aggregate, expressed by the Debye-Stokes-Einstein equation (c.f. eq 3), and the diffusion of the probe over the curved surface of the micellar aggregate, T>, which is equal to r2f 6D for spherical aggregates. r is the radius of the sphericaf micelle; D, is the lateral diffusion coefficient of the probe. It is assumed that D , Dsdaht: 1/T," = l / T C R + 1 / T C L (8) The translational diffusion coefficient of the surfactant is not known for micelles. However, it has been measured for the cubic liquid crystalline phase of KC8-HzO. The corrected value due to geometrical considerations for the rodlike structure of the cubic phase (multiplication by a m2 s-l.% (In ref 29a, a value of factor of 3) is 9.4 X D = 8.8 X lo-" m2 s-l is reported. Later, ErikssonBb has remeasured this quantity with more powerful equipment. The result from this latter determination, corrected for geometry, is the figure given above.) The lateral diffusion coefficient for the system KC12-HzO is 5.3 X lo-" m2 s-l, as determined by Johansson et From eq 8 it is now possible to calculate radii of the micellar aggregates through an iterative procedure. The correlation times T," (from the line shape simulations), the diffusion coefficient of the amphiphile, and the viscosity Pa s) were used as input values. of water (0.89 X Obtained radii of the micelles are given in Table 111. Analysis of Fluorescence Quenching. Pyrene was solubilized in micelles of KC12. The micellar concentration (29) (a) Lindblom, G.; WennerstrBm, H. Biophys. Chem. 1977,6,167. (b) Eriksson, P.-O., unpublished data.
70
60
CI
CI CI
50 40
30
0
20
10
30
40
Potassium dodecanoate W % Figure 5. Aggregation numbers ( N ) of potassium dodecanoate (KC12) in water as a function of the surfactant concentration (percent by weight).
varied from 5% to 30% by weight in two seta of samples of KC12. In the first set, the pyrene concentration was kept at a molar ratio 1/106. In a second set, the concentration of benzophenone was kept at 1/102 while the pyrene concentration was the same as in the first set of samples. The time-resolved fluorescence was monitored pairwise for samples with the same amphiphile concentration. From a graphical comparison of the decay curves and eq 6 , we can calculate (X).The mean aggregation number is then easily calculated from eq 7 since ( X ) and the concentration of amphiphile and quencher, as well as the cmc value, are known. The results are presented in figure 5. The KC8 micellar system was also investigated as a function of the amphiphile concentration. We found that the slow decay of the photophysics in the quenched system, i.e., those micelles containing benzophenone, was faster than that of the unquenched system. This indicates either a migration of benzophenone between the micelles or a perturbation of the KC8 micelles. Migration appears, however, to be a less probable explanation since we do not observe such an effect in the KC12 system. A perturbation is not unexpected since micelles formed by KC8 are relatively small as compared to the size of a pyrene and a benzophenone molecule.
Discussion In this section we compare our results with those previously obtained on similar systems. The radius of the hydrophobic interior (r,) of a micelle is, according to Tanford3I rc = 1.5 1.265nC(A) (9)
+
n, denotes the number of carbon atoms in the alkyl chain. From eq 9, r, of the KC8 and KC12 micelles become 10.4 and 15.4 A, respectively. Contributions from the carbdxylic group and the hydration layer must also be taken into account. By adding 3.5 A to the value obtained from eq 9 we obtain a value that should be compared to those obtained from the ESR and fluorescence data. This corresponds to a hydrodynamic radius of 13.9 and 18.9 A, respectively. If we compare these values with those calculated from ESR experiments and analyzed according to eq 2, we find a poor agreement, as shown in Table I. The (30) Johansson, L. B.-& Siiderman,0.;Fontell, K.; Lindblom, G . J. Phys. Chem. 1981,85, 3694. (31) Tanford, C. J. Phys. Chem. 1972, 76,3020.
Micelles by Electron Spin Resonance
calculated radii are too small, as compared to the expected values of 13.9 and 18.9 A, respectively. From Table I, it is also seen that the TB and TC values are different. This indicates that the motions of the label are anisotropic. The difference between the T values is rather small for the KC8 system but more pronounced for the KC12 system. Hence, the correlation times cannot be obtained directly by the Debye-Stokes-Einstein relation. If we consider the hydrodynamic radii, obtained from calculations using the "two-step model", the agreement is much more convincing (see Table 111). In two previous investigations performed by Zemb and co-workersg,32t93micelles of sodium octanoate have been studied by means of neutron small-angle scattering and light scattering. They found that the hydrodynamic radii of the micelles varied between 12 and 14 A. If we compare our radii of the KC8 micelles, neglecting the effects of different counterions with their radii, our values appear to be slightly higher. Our analysis gives values on the hydrodynamic radii ranging between 16 and 20 A, when the amphiphile concentration is increased from 10% to 40% by weight. There is a reasonably good agreement at low concentrations between our results and those obtained according to Tanford's formula. The discrepancy at higher concentrations is most likely due to a growth of the micelles. This is compatible with the formation of a hexagonal phase at 47 wt % For the KC12 system, radii between 21 and 25 A are obtained when the surfactant concentration is increased from 5% to 30% by weight. The lower value is slightly larger than that of 18.9 A, predicted by means of Tanford's formula. How do these radii compare with those calculated from the aggregation number investigations? Fluorescencequenching results yield aggregate numbers in the range 52-69 (cf. Figure 5). By using group contributions to the volume of an amphiphilic molecule, viz., VCH.~ = 49, VCH.~ = 28," and v ~ f=i 12 A3,%it is possible to calculate the hydrodynamic radius of the micellar ag-
.
(32) Hayter, J. B.; Zemb, T. Chem. Phys. Lett. 1982, 93,91. (33) Zemb, T.:Drifford, M.,Havoun, M.: Jehanno, A. J. Phvs. Chem. 1983,87,4524. . (34) Jbnseon, B. Ph.D. Thesis, University of Lund, 1981. (35) Israelachvili, J. N. Intermolecular and Surface Forces with Applications to Colloidal and Biological System; Academic Press: London, 1985; Chapter 7.
Langmuir, Vol. 5, No. 3, 1989 733 gregates. The hydration number per amphiphile is taken to be 9, which appears to a reliable upper limit.3s The values found from this calculation vary in the range 18-19 A. On the average, these values should be increased by 2 A due to the carboxylic group of the amphiphile. These values, ranging between 20 and 21 A, agree rather well with those obtained from the extended line shape analysis (cf. eq 8). Furthermore, another factor of importance is the influence of the order parameter on the analysis of ESR spectra. An increase of the order parameter of KC12 from 0.45 to 0.50 yields a decrease of the T," values of about 1 ns. This leads to radii in the range 19-24 A, which is in even better agreement with values obtained from the aggregation numbers. The increasing radii and aggregation numbers with increasing KC12 concentration strongly suggests that the micelles grow. However, we cannot exclude effects due to perturbations caused by probe molecules in the KC8 micelles. Hence, the radii of the unperturbed ensemble of KC8 micelles, at low concentrations of the amphiphile, might differ somewhat from the values accounted for in Table 111. The cubic crystalline phase of NaCgoctanewater has recently been investigated by NMR relaxation measurem e n t ~ . ~ 'I t is suggested that the phase consists of hemisphere-capped cylinders with an axial ratio of 21.% The correlation time characterizing the translational motion about the aggregate long axis was found to be 3.3-3.6 ns. These numbers are close to those of :T (cf. Table 111) obtained at concentrations above 30% by weight KCB. This suggests that the KC8 micelles grow into cylinders above 30% by weight KC8.
Acknowledgment. We are grateful to Eva Vikstrom and Karin Stjernholm for valuable technical assistance and to the Swedish Natural Science Research Council for financial support. Registry NO. KC8, 764-71-6; KC12,1012465-9; 5-doxyLstearic acid, 29545-48-0; pyrene, 129-00-0; decanol, 112-30-1. (36) Lindman, B.; WennerstrBm, H. Phys. Rep. 1979,62,1. (37) Saderman,0.;Henriksson, U. J. Chem. SOC.,Faraday Trans. 1 1987,83, 1515. (38) Fontell,K.; Fox,K. V.; Hansson, E. Mol. Cryst. Liq. Cryst. 1985, 1, 9.
