Langmuir 1996, 12, 3399-3403
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Kinetic Study of Sodium Decyl Sulfate Solutions by the Capillary Wave Method B. A. Noskov* and D. O. Grigoriev Chemical Faculty, St. Petersburg State University, 198904 St. Petersburg, Stariy Petergof, Russia Received October 17, 1995. In Final Form: April 15, 1996X The capillary wave method has been applied to aqueous solutions of sodium decyl sulfate (SDes). The damping coefficient increased monotonically with concentration below the critical micelle concentration (cmc) and decreased in the micellar region. This behavior is different from the results for solutions of sodium dodecyl sulfate (SDS), where a single local maximum of the damping had been observed at concentrations far less than the cmc. The difference can be explained with the help of the theory of surface viscoelasticity, which has been developed recently. For dilute solutions the experimental data agree with the theory based on the assumption that the adsorption kinetics is controlled by diffusion in the bulk phase. At concentrations higher than the cmc a more complex theory taking into account the micellization process has been applied. In this case the only adjustable parameter was the characteristic time of the slow stage of micellization. The values of this quantity, thus obtained from the experimental data, reasonably agree with the results of independent measurements.
Introduction The methods of relaxation spectroscopy are now being rather extensively used to study the kinetics of different physical and chemical processes in the surface layer of surfactant solutions. Among them the method of transverse surface (capillary) waves is one of the most elaborate. Some possibilities of this experimental technique have been demonstrated recently in the course of experimental studies of adsorption kinetics at the air-water interface1-5 and dynamic properties of insoluble monolayers.6-9 However, from the point of view of the physical chemistry of surfactant solutions, investigation of different processes in the bulk phase is not less important. The surface layer is an example of the nonautonomous phase, and relaxation of mechanical stresses caused by propagation of surface waves is connected with the kinetics of relaxation processes in the bulk phase, e.g. the kinetics of micellization. As a consequence, the dynamic surface properties of micellar solutions can be connected with the kinetic coefficients of the processes of formation and disintegration of micelles. This connection was made theoretically for the first time by Lucassen.10 A more elaborate theory based on the two-stage model of the micellization kinetics11 was published several years ago by one of us12 and a little later by a Bulgarian group.13 The first experimental findings corroborating the theory were obtained for solutions of decyl- and dodecylpyridinium bromides with the help of the capillary wave X
Abstract published in Advance ACS Abstracts, June 1, 1996.
(1) Noskov, B. A.; Vasil’ev, A. A. Kolloidn. Zh. 1988, 50, 909. (2) Stenvot, C.; Langevin, D. Langmuir 1988, 4, 1179. (3) Noskov, B.; Anikieva, O. A.; Makarova, N. V. Kolloidn. Zh. 1990, 52, 1091. (4) Noskov, B. A. Colloids Surf., A 1993, 71, 99. (5) Jiang, Q.; Chiew, Y. C.; Valentini, J. E. J. Colloid Interface Sci. 1993, 155, 8. (6) Earnshaw, J. C.; Winch, P. J. J. Phys.: Condens. Matter 1990, 2, 8499. (7) Miyano, K.; Tamada, K. Langmuir 1993, 9, 508. (8) Sakai, K.; Takagi, K. Langmuir 1994, 10, 802. (9) Noskov, B. A.; Zubkova, T. U. J. Colloid Interface Sci. 1995, 170, 1. (10) Lucassen, J. Faraday Discuss. Chem. Soc. 1975, 59, 76. (11) Anniansson, E. A. G.; Wall, S. N. J. Phys. Chem. 1974, 78, 1024. (12) Noskov, B. A. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1989, N2, 105. (13) Dushkin, C.; Ivanov, I.; Kralchevsky, P. Colloids Surf. 1991, 60, 235.
S0743-7463(95)00880-8 CCC: $12.00
method.14-16 The damping coefficient decreased abruptly after the cmc (critical micelle concentration), thus indicating an influence of the slow stage of the micellization process on the dynamic surface properties. However, first attempts to discover this effect for micellar solutions of anionic surfactants were unsuccessful3 and the role of the sign of charged hydrophilic groups in the surfactant molecule remained to be elucidated. To solve this problem we chose aqueous solutions of sodium decyl sulfate (SDeS) as the object of this study. For this system we can expect that the exchange of monomers between micelles and the surrounding aqueous phase is faster than that for solutions of SDS which were studied before17,18 and an influence of the micellization kinetics on the dynamic surface properties is more probable. In a subsequent part of this work the principle relations between dynamic surface properties and the kinetic coefficients of relaxation processes are presented. Then the main features of the experimental methods are described. In the final part of the work we represent experimental results which are used afterward to calculate the relaxation time of the slow stage of the micellization process. Theoretical Considerations Static and dynamic surface properties are related to characteristics of capillary waves of small amplitude propagating along the liquid-air interface by the following dispersion equation19
(Fω2 - σk3 - Fgk)(Fω2 - mk2) - k3(σk3 + Fgk) + 4iFηω3k3 + 4η2ω2k3(m - k) ) 0 (1) where F is the liquid density, η is the liquid shear viscosity, k ) 2π/λ + iR, λ is the wavelength, R is the damping coefficient, ω is the angular frequency, g is the gravitational acceleration, m2 (14) Noskov, B. A.; Grigoriev, D. O. Prog. Colloid Polym. Sci. 1994, 97, 1. (15) Grigoriev, D. O.; Noskov, B. A.; Semchenko, S. I. Kolloidn. Zh. 1993, 55, 45. (16) Grigoriev, D. O.; Krotov, V. V.; Noskov, B. A. Kolloidn. Zh. 1994, 56, 637. (17) Inoue, T.; Shibuya, Y.; Shimozawa, R. J. Colloid Interface Sci. 1978, 65, 370. (18) Diekman, St. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 528. (19) Hansen, R.; Ahmad, J. In Progress in Surface and Membrane Science; Danielli, J. F., Ed.; Academic Press: New York and London, 1971; Vol. 4, p 1.
© 1996 American Chemical Society
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) k2 + iωF/η, (Re(m) > 0), σ is the surface tension, and ) r + ii is the complex longitudinal dynamic surface elasticity. The quantity characterizes both reversible (elastic) and dissipative (viscous) surface properties and can be presented as a sum of two terms describing a response of the system to dilational and shear deformations. The latter contribution can be neglected for systems containing only soluble conventional surfactants, and the former one can be calculated with the help of irreversible thermodynamics.20 Below the cmc for systems containing a single surfactant the following expression can be used20
)
(
∂σ 1+ ∂ ln Γ
)
1
(2Dω )
1 + iωτ + (1 + i)
1/2
(2)
∂Γ ∂c
where τ ) (R˜ + β˜ c/Γ∞)-1, R˜ and β˜ are the kinetic coefficients of the desorption and adsorption, respectively, Γ is the adsorption, Γ∞ is the saturation adsorption, D is the diffusion coefficient of the surfactant in the bulk phase, and c is the subsurface concentration. Note that in this case the dynamic surface elasticity is determined mainly by the kinetic coefficients of the adsorption process. Measurements of the surface wave characteristics allow us to calculate with the help of eq 1 and then to determine the adsorption mechanism by means of eq 2. For micellar solutions the dynamic surface elasticity depends also on the kinetic coefficients of micellization.12 In this case periodic compressions (expansions) of the surface lead to adsorption (desorption) of the surfactant and consequently to local perturbations of the concentration of monomers in the subsurface layer. If the characteristic time of the micellization process is comparable with the period of external perturbations, formation or destruction of micelles influences the rate of adsorption (desorption) and, consequently, the dynamic surface elasticity. One can expect that this influence is most important for frequencies comparable with the reciprocal time of the slow stage of the micellization process (τ2-1)11
τ2-1 ) R ˜ -1(c1 + 〈σ˜ 2〉cm)-1n2
(3)
where c1 and cm are the concentrations of monomers and micelles, respectively, n is the mean aggregation number, 〈σ˜ 2〉 is the dispersion of the micellar size distribution, and R ˜ is the kinetic resistance of the micellar disintegration (formation). When most of the surfactant molecules belong to micelles,
n2(c1 + 〈σ2〉cm)-1cm . 1
(4)
the dynamic surface elasticity can be presented as12
)-
{
(
)(
)
iDsk βc1 2 iω ∂σ 1 + iD1 R + 1k + ∂ ln Γ ω Γ∞ D1 D1τ2
[ (
ωβ 1 -
)
(
)]}
Γ iω 1 + ωD1 k2 + Γ∞ D1 D1τ2
1/2
1/2 -1 -1
× (5)
where D1 is the diffusion coefficient of monomers in the bulk phase and Ds is the surface (two-dimensional) diffusion coefficient. Expression 5 can be simplified if the adsorption kinetics is determined by diffusion of the surfactant in the bulk phase
D1β-1[-iω/D1 + (D1τ2)-1]1/2 , 1 - Γ/Γ∞
(6)
This inequality restricts the kinetic coefficient β from below. In the considered case both terms inside the brackets have the same decimal order of the value and 1 - Γ/Γ∞ is a small but finite number somewhere between 0.1 and 0.01 (this is a typical case when adsorption below the cmc is described by Langmuir or Frumkin isotherms). Then β-1 < 0.01/(D1ω)1/2 or if we use the following estimates, D1 = 10-9 m2/s and ω = 103 s, β > 0.1 s/m, which corresponds to purely diffusion adsorption kinetics.21 (20) Noskov, B. A. Kolloidn. Zh. 1982, 44, 492. (21) Chang, C.-H.; Frances, E. I. Colloids Surf., A 1995, 100, 1.
Figure 1. Schematic representation of the capillary wave generation and detection system. In this case the following expressions for the real r and the imaginary i components of the dynamic surface elasticity can be derived from eq 5
r ) -
i )
1 + p(q - 1)1/2 ∂σ ∂ ln Γ [1 + p(q - 1)1/2]2 + p2(q - 1)
p(q + 1) ∂σ ∂ ln Γ [1 + p(q - 1)1/2]2 + p2(q - 1)
(7)
(8)
where p ) (∂Γ/∂c1)-1(2ω2τ2/D1)-1/2 and q ) (1 + ω2τ22)1/2. Therefore, after determination of the dynamic surface elasticity with the help of the capillary wave method one can apply eqs 7 and 8 to calculate τ2 and to obtain information about the slow stage of the micellization process.
Experimental Procedures The damping coefficient and the wavelength of the capillary waves were measured by means of an electromechanical technique, using a capacity wave probe1,14 (Figure 1). The main features of the experimental technique consist of the following. The capillary waves were created by a mechanical generator 1, made of thin capillary tubes. The generator oscillated perpendicular to the liquid surface under the action of an electrodynamic vibrator 2, fed from a low-frequency electric generator 3. The receiving probe 4 was a dynamic air condenser formed by a stainless steel plate, with a thickness smaller than half of the wavelength, and the surface of the liquid. The alternate electric current induced in the circuit by oscillations of the liquid surface was proportional to the vibration amplitude. This signal was amplified by an electrometer unit 5 and a selective unit 6, and compared in phase relationship to the input signal of the electrodynamic vibrator with the help of an oscillograph 7. The circuit included also a grounded platinum electrode 8 immersed in a rectangular silica trough 9. The voltage of the electric signal was measured as a micromanipulator 10 moved the vibrator relative to the fixed wave probe. Successive measurements of the amplitude and the phase of the signal allowed us to determine the damping coefficient and the wavelength with accuracies of about 0.2% and 5%, respectively. All the experiments were carried out at 20.0 ( 0.5 °C. Equilibrium surface pressure was measured by means of the Wilhelmy plate technique. The viscosity of the solutions was determined by means of a capillary viscometer.
Kinetic Study of Sodium Decyl Sulfate Solutions
Figure 2. Damping coefficient as a function of frequency for SDeS solutions at concentrations of 20.0 mol/m3 (curve 1) and 1.78 mol/m3 (curve 2).
SDeS was prepared by the reaction between decanol and chlorosulfonic acid and subsequent neutralization of the obtained decylsulfuric acid by NaOH. The synthesis was performed according to the method described by Abramzon.22 SDeS was purified in two stages. At first the substance was washed by hexane in a Soxhlet extractor for several hours to remove the remains of long chain alcohols. After drying, SDeS was recrystallized four times from ethanol. The degree of purification was controlled by means of the standard criterion of purity of surfactant solutions: absence of a minimum on the surface tension isotherm in the region of the cmc. All the solutions were prepared immediately before the measurements. Fresh double-distilled water was used for these purposes. An all-Pyrex still and alkaline permanganate were used in the second stage of distillation. In spite of the preliminary purification of the surfactant and water, the surface properties of the solutions still varied slowly with time, presumably because of the hydrolysis of SDeS. Similar behavior had been observed earlier for solutions of SDS;3 however, for SDeS solutions this time dependence was more pronounced. Therefore, the liquid surface was cleaned additionally of insoluble and slowly desorbing impurities using a sweeping barrier and a Pasteur pipet attached to a vacuum pump.1,3 Before the measurements of wave characteristics were started, the surface had been purified several times, and the purification was subsequently repeated every 30 min. During this time, the variations of the capillary wave parameters were within the accuracy of the measurements. Results and Discussion Figure 2 shows the measured damping coefficient for two solutions of SDeS as a function of the frequency ν ) ω/2π. The R vs ν dependencies are almost linear. Some distortions may be noticed only at higher concentration. However, the investigated domain of the damping spectrum is too narrow in comparison with the transitional region from the pure elastic behavior of the adsorbed film (ν f ∞) to the state of zero dilational resistance (ν f 0). (22) Abramzon, A. Surfactants. Synthesis, Analysis, Properties, Applications; Chimia: Leningrad, 1988 (in Russian).
Langmuir, Vol. 12, No. 14, 1996 3401
Figure 3. Concentration dependency of the wavelength for solutions of SDeS at the frequency 180 Hz. The broken curve represents results of calculations according to eqs 1, 2, 9, and 10.
Figure 4. Concentration dependency of the damping coefficient for solutions of SDeS at the frequency 200 Hz. The curves represent results of calculations according to eqs 1, 2, 9, and 10: τ ) 0 (broken curve); τ ) 0.01 s (dotted curve).
For pure diffusional relaxation this transition corresponds to a change of frequency of as much as five decimal orders.12 Therefore, the dependencies of capillary wave properties on concentration prove to be more useful for kinetic investigations of surfactant solutions. Figures 3 and 4 show the measured characteristics of capillary waves for solutions of SDeS as a function of the logarithm of concentration at the frequencies 180 and 200 Hz, respectively. The results are qualitatively the same in the entire investigated region of frequency (70-520 Hz). The wavelength is mainly determined by the equilibrium surface tension, and as a result the λ vs lg c dependency is similar to the surface tension isotherm: below the cmc (=35 mol/m3) the wavelength decreases monotonically, and in the micellar region all changes are comparable with the error limits (Figure 3). The concentration dependence of the damping coefficient is more complex. Unlike solutions of surfactants with higher surface activity, where a local maximum has been discovered below the cmc,1-4 the damping increases monotonically in this concentration region (Figure 4). The nonmonotonous behavior of the R vs c curve for dilute solutions follows from the analysis of the dispersion
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equation (eq 1) if the modulus of the surface elasticity is higher than about 0.15σ.19 However, in the case of SDeS we can observe in this region only a bending point and, therefore, it is necessary to assume low values of the quantity ||. It means according to eq 2 that τ and the characteristic time of the diffusion process (∂Γ/∂c)2/D are smaller than the wave period, and consequently, all relaxation processes are relatively fast. As in the case of solutions of dodecyl- and decylpyridinium bromides14-16 the damping coefficient goes through a maximum at the cmc (Figure 4). A slow increase of the damping at concentrations significantly higher than the cmc (after a local minimum in the case of SDeS solutions) is observed for most surfactants and can be exlained by the corresponding growth of the viscosity of the bulk phase.3,14-16 However, a decrease of the damping immediately after the cmc was not discovered for solutions of other anionic surfactants.23 This effect clearly indicates an influence of the micellization kinetics on the damping coefficient and, consequently, on the dynamic surface elasticity of SDeS solutions. The essential advantage of the capillary wave method as compared with experimental techniques, devised to study the adsorption kinetics and based on large deviations from the equilibrium, is the possibility to describe the experimental situation theoretically with the help of a linear boundary problem.4,19 As a consequence simple algebraic relations can be used to calculate the kinetic coefficients of the relaxation processes. In the concentration region below the cmc it is possible to determine the adsorption mechanism. For this purpose the experimental dependencies R vs lg c and λ vs lg c were compared with the results of calculations according to eqs 1 and 2. To calculate the derivatives ∂Γ/∂c and ∂σ/∂ ln Γ, corresponding to the equilibrium, the following relations have been used
bc )
ϑ exp(-2aϑ) 1-ϑ
σ ) σ0 + n˜ Γ∞RT[ln(1 - ϑ) + aϑ2]
(9) (10)
where ϑ ) Γ/Γ∞, R is the gas constant, T is the temperature, σ0 is the surface tension of the solvent, b is the adsorption equilibrium constant, a is the parameter of interactions in the surface layer, and n˜ ) 2 for an ionic surfactant if it is a 1:1 electrolyte. The diffusion coefficient D was determined according to the Nernst-Einstein equation from the experimental values of the electroconductivity24 and was equal to 6.5 × 10-10 m2/c. The roots of the dispersion equation were determined by the Newton-Raphson technique. At the beginning of the calculations the parameters a, b, and Γ∞ were varied to get agreement between the calculated λ vs lg c dependency and the corresponding experimental data. The parameter τ almost does not influence the wavelength and at this stage of calculation it was equal to zero, which corresponds to a pure diffusion adsorption mechanism. At the second stage all the parameters a, b, Γ∞, and τ were varied and an agreement was obtained between both the calculated curves R vs lg c and λ vs lg c, and the experimental results for concentrations below the cmc. The optimum set of parameters was a ) 0.95, b ) 0.065 m3/mol, Γ∞ ) 4.2 × (23) A local maximum of the damping coefficient at the cmc was observed also for alkaline solutions of sodium caprinate.3 However, the absolute values of the damping coefficient were unusually high and the complex behavior of this system did not allow clear interpretation. (24) Haffner, F.; Piccione, G.; Rosenblum, C. J. Phys. Chem. 1942, 46, 662.
10-6 mol/m2, and τ ) 0. The broken lines in Figures 3 and 4 represent the results of calculations, and at c < 1.3 mol/ m3 the agreement with experimental data is reasonably good if one takes into account the accuracy of measurements and calculations. Note that in a narrow concentration region close to the cmc the deviation of the calculated damping coefficient from the experimental results is somewhat higher than the error limits. Similar but slighter deviations were observed earlier for solutions of decylpyridinium bromide.14 Apparently, at present it is impossible to distinguish between several possible explanations of this discrepancy. At first an influence of the hydrolysis can not be completely excluded because the surface rheological properties may be more sensitive to impurities than the surface tension. Then, as Stenvot and Langevin pointed out,2 eqs 9 and 10 can be insufficient for a description of the equilibrium surface properties. At last the premicellar aggregation can occur close to the cmc, and this phenomenon is not taken into account in our theory.12 It is noteworthy that this discrepancy cannot influence the main conclusion that the adsorption kinetics is determined by diffusion of the surfactant in the bulk phase. Indeed, any deviations of the quantity τ from zero can only make worse the agreement between experimental and calculated R vs lg c curves. As an example, Figure 4 shows the concentration dependence of the damping coefficient calculated at the same values of a, b, and Γ∞ but at τ ) 0.01 s (the mixed adsorption mechanism). The determined diffusional adsorption mechanism justifies application of eqs 7 and 8 to concentrations exceeding the cmc. It is well-known that most changes of the static surface properties with the concentration above the cmc are comparable with experimental errors. If the same assumption is made for the dynamic surface properties and only changes of properties of the bulk phase are taken into account, then calculations according to eqs 1, 2, 9, and 10 allow us to determine the R vs lg c dependency in the micellar region. An increase of the concentration is accompanied by a slow increase of the damping (Figure 4, the broken curve after the cmc). The difference between the calculated and experimental values exceeds several times the error limits. Application of eqs 7 and 8 allows us to avoid this discrepancy. We assume that the derivatives ∂σ/∂ ln Γ and ∂Γ/∂c do not change above the cmc and in this case the dynamic surface elasticity becomes a function only of a single parametersτ2. Then a variation of this quantity allows us to get agreement between the values of the damping coefficient calculated according to eq 1 and the experimental results. At this moment it is necessary to emphasize an important consequence of the theory of dynamic surface properties of micellar solutions.12,13 Although this theory is based on the assumption that equilibrium surface properties are constant above the cmc and it considers only infinitesimal deviations from the equilibrium, dynamic surface properties can change significantly with concentration in the micellar region. This feature follows from the fact that the surface layer is a nonautonomous phase which hardly manifests itself at equilibrium but has important consequences for nonequilibrium properties.12,20 The dilational dynamic surface elasticity essentially depends on the processes in the bulk phase. Experimental data presented in this work confirm the main results of the theory.12,13 The values of τ2 obtained with the help of the algorithm that has been described above are presented in Table 1. This table contains also some results of the relaxational studies of the bulk phase of SDeS solutions.17,18
Kinetic Study of Sodium Decyl Sulfate Solutions
Langmuir, Vol. 12, No. 14, 1996 3403
Table 1 this work
other studies
c, mol/m3
10-3 τ2, c
c, mol/m3
60.0 80.0 100.0 120.0 160.0
0.60 0.40 0.47 0.60 1.00
ref 17 33.8 ref 18 39.0 44.5 53.0 69.0 84.0 106.0 125.0 150.0 200.0
10-3 τ2, c 0.20 0.30 0.24 0.27 0.36 0.55 0.95 1.25 2.20 3.70
The agreement between the two data sets is reasonably good if one takes into account that the corresponding experimental techniques are based on measurements of the surface and the bulk properties, respectively. However, the character of the concentration dependency of τ2 agrees less with the experimental data. The main difference corresponds to the concentrations exceeding slightly the cmc. In this region the system does not meet the condition described in eq 6 and application of eqs 7 and 8 can lead to mistakes. Besides, these equations correspond strictly only to solutions of nonionic surfactants. An accounting of dissociation of surfactant molecules can influence the shape of the τ2 vs c curve but, apparently, does not influence the order of the value. The obtained results allows us to calculate the real and the imaginary parts of the complex dynamic surface elasticity (Figure 5). The calculated dependencies |r|(1g c) and |i|(1g c) are essentially nonmonotonous. Below the cmc both curves go through a maximum which is connected with the different concentration dependencies of the two multipliers on the right side of eq 2. The equilibrium factor ∂σ/∂ ln Γ increases with concentration, and the kinetic factor changes in the opposite direction. It is interesting that the maxima of the damping coefficient and of the surface elasticity correspond to different concentrations. In general the damping coefficient is a nonmonotonous function of the modulus of surface elasticity: in the region where || = 0.15σ an increase of || is accompanied by a local maximum of R.19 However, in the case of SDeS solutions, apparently, there is another cause of this peculiarity. A strong decrease of the surface tension is accompanied by an increase of the damping coefficient, and this trend preponderates the influence of the surface elasticity. In the micellar region the dependencies |r| vs lg c and |i| vs lg c have a minimum which is connected with nonmonotonous character of the relaxation time τ2. Note that the observed increase of |r| and |i| (after the minimum) corresponds to the concentration region where the viscosity of the bulk phase begins to change also. Although this effect is taken into account in the course of calculations, it can lead to some reduction in the accuracy of the calculated components of the surface elastivity. On the other hand an increase of the viscosity of the bulk phase can indicate changes of the shape and of the aggregation number of micelles. In this case the theory of dynamic surface properties12,13 cannot be applied. Nevertheless, we present the values of surface elastivity
Figure 5. Concentration dependency of the absolute values of components of the complex dynamic surface elasticity for solutions of SDeS at the frequency 200 Hz: r (solid curve); i (broken curve).
in this region as rough estimates because of their importance. Indeed, recent studies of the foamability of micellar solutions have shown that strong changes of this property can be connected with corresponding changes of the dynamic surface elastivity.25,26 Conclusions We make the following main conclusions from this investigation of the effects of SDeS on the capillary wave characteristics at the air-water interface: 1. Below the cmc the damping coefficient increases monotonically with the concentration. Comparison with the results of diffusion theory shows that the adsorption kinetics is controlled by diffusion of the surfactant in the bulk phase. 2. At the cmc the damping coefficient goes through a maximum, thus indicating an influence of the micellization kinetics on the dynamic surface properties of SDeS solutions. For solutions of anionic surfactants this effect was discovered for the first time. 3. The calculated values of the characteristic time of the slow stage of the micellization agree with the data obtained in the course of conventional studies of the bulk phase. This result can be considered as an experimental confirmation of the theory of surface viscoelasticity developed earlier for micellar solutions. On the other hand it means that the method of capillary waves not only can give information about surface properties and adsorption kinetics but also can be used for investigation of relaxation processes in the bulk phase. Acknowledgment. We thank S. S. Levichev for the preparation of the surfactant. This work was done with financial support from the Russian Foundation of Fundamental Research (Project nos. 93-03-5478 and 96-03-34046a). LA9508809 (25) Oh, S. G.; Klein, S. P.; Shah, D. O. AIChE J. 1992, 38, 149. (26) Garrett, P. R.; Moore, P. R. J. Colloid Interface Sci. 1993, 159, 214.
