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Dynamic Surface Properties of Solutions of Phosphine Oxides: A Capillary Wave Study
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
188, 9–15 (1997)
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Dynamic Surface Properties of Solutions of Phosphine Oxides: A Capillary Wave Study B. A. NOSKOV,* D. O. GRIGORIEV,*
AND
R. MILLER† ,1
*Institute of Chemistry, St. Petersburg State University, St. Petersburg-Stariy Petergof, Russia; and †Max-Planck Institute of Colloid and Interface Science, Berlin–Adlershof, Federal Republic of Germany
Received February 2, 1996; accepted September 3, 1996
In the past two decades, this quantity was investigated many times theoretically (1–6) and was determined experimentally (5–10). An overview is given, for example, in (11). However, attention was paid mostly to comparatively simple systems, such as, solutions of surfactants at concentrations below the CMC (1–4, 6–9), elastic and viscoelastic insoluble monolayers (2, 4, 10), and systems containing mixtures of insoluble and soluble surfactants (4, 5). Although micellar solutions are more interesting from the point of view of applied problems, information about dynamic surface properties in this region in general, and information about the dynamic surface elasticities at concentrations above the CMC, in particular, are relatively scarce (12). The dynamic surface elasticity of micellar solutions was first determined by Lucassen (13). However, the developed theory was based on a simplified single-step model of the micellization process. A more elaborate theory based on the two-step model of Aniansson and Wall (14) and takes into account diffusion of both monomers and micellar aggregates has been published recently (15–17). However, to check this theory and to determine experimentally the dynamic surface elasticity of micellar solutions proved to be a difficult task. Apparently, the main reason is that the characteristic times of the micellization correspond to frequencies which are difficult to investigate using the usual methods of relaxation spectrometry of liquid surface layers. For example, the first attempts to apply the capillary wave method to micellar solutions failed—the damping coefficient and, consequently, the dynamic surface elasticity did not depend on the concentration above the CMC (9, 18). Moreover, Kao et al. (19) even argued that the wave methods cannot be used for micellar solutions. Recently, we have shown that the last statement is not true, in general. A significant decrease of the damping coefficient was discovered for solutions of some ionic surfactants at concentrations above the CMC, and the dynamic surface elasticity of micellar solutions was calculated (20–22). These experimental data were used to calculate the character-
The characteristics of capillary waves on the surface of aqueous solutions of dimethylalkyl phosphine oxides have been measured as a function of frequency and surfactant concentration. The damping coefficient for solutions of dodecyldimethyl phosphine oxide increased with concentration, passed through a local maximum below the CMC, and was independent of concentration above the CMC. For solutions of decyldimethyl phosphine oxide, a second maximum is observed at the CMC and the damping decreases considerably in the micellar region. This effect can be explained by an influence of the micellization kinetics on the dynamic surface elasticity and was not observed earlier for solutions of nonionic surfactants. The results are used to calculate the characteristic time of the slow step of the micellization process. q 1997 Academic Press
Key Words: capillary wave damping; surface rheology; nonionic surfactants; exchange of matter; micelles.
INTRODUCTION
It is well known that nonequilibrium mechanical properties of solutions of surfactants do not comprise only the dynamic surface tension. The behavior of a system with a free interface at any moment is determined in the general case by the whole of its preceding history. However, if deviations from the equilibrium are not large or one is interested only in the behavior close to a steady-state (quasisteadystate), in order to describe the dynamics of the system it is sufficient to determine, besides the surface tension, a set of dynamic surface elasticities. Moreover, if the system does not contain polymers or insoluble surfactants, it is possible to neglect the surface shear elasticity and viscosity and the transverse surface viscosity in most situations. As a result, the only additional characteristic in comparison with the equilibrium case is the complex dilational dynamic surface elasticity which depends on the frequency of disturbances of the system (1–3). 1
To whom correspondence should be addressed. 9
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istic time of the slow step of the micellization (21, 22). The obtained values were in reasonable agreement with data obtained in independent studies on the bulk properties of micellar solutions. However, the calculations mentioned above are not of high accuracy. It is well known that the charge of micelles influences the kinetics of their formation and dissolution and even the mechanism of these processes, in some cases, can be different for ionic and nonionic surfactants ( 23 ) . On the other hand, the theory of Aniansson and Wall ( 14 ) and the theory of the dynamic surface elasticity of micellar systems ( 15 – 17 ) are related only to solutions of nonionic surfactants. Therefore, an experimental verification of the obtained relationships must be realized first for nonionic systems. In this work, the capillary wave method is applied to solutions of dimethylalkyl phosphine oxides. These substances are chemically stable in aqueous solutions and can be purified easily. The surface properties of solutions of dimethylalkyl phosphine oxides were investigated in detail at concentrations below the CMC. The dependence of surface tension on concentration is described by a Frumkin equation (24) and the adsorption process is determined by a simple diffusion mechanism (25). The present paper describes the basic features of the theory of dynamic surface properties of micellar solutions. Experiments with a capillary wave technique are presented and the results are interpreted in terms of the dynamic surface dilational elasticity. The data also allowed us to calculate the kinetic characteristics of micellization. THEORY
In the general case of a nonequilibrium system, the tensor of surface tension and its isotropic part s depend on the area S of a surface element under consideration. However, in order to determine the quantity s at the moment t 0 , it is not sufficient to define a value of the surface at t Å t 0 . The surface tension is determined by the character of changes of the area in the preceding time (t õ t 0 ), and consequently, is a functional of the quantity S(t). If the deformation of the surface (extension or contraction) is small, this functional can be considered as linear and the following general presentation can be used (15) ds Å
*
t
G(t 0 t )(ddS( t )/d t )d t,
[1]
0`
where ds Å s 0 s0 , ds / s0 ! 1, dS Å S 0 S0 , dS/S0 ! 1; the subscript zero corresponds to the undisturbed state, G is the surface function of relaxation, t is ‘‘dummy variable’’ and ds Å ds(t). Application of the Fourier transformation to Eq. [1] leads to a linear relation between Fourier images
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( ds )v Å 1 ( v )( dS)v ,
[2]
where 1 ( v ) Å 1r ( v ) / i1i ( v ) is the complex dynamic surface elasticity
1r Å G 0 / v
*
`
G( h )sin( vh )d h,
0
1i Å v
*
`
G( h )cos( vh )d h.
[3]
0
We assume here that G Å G0 / G(t) or the quantity G consists of a constant component and a component that depends on time, ( dS)v and ( ds )v are the corresponding Fourier transformations, h is the ‘‘dummy variable’’. The function 1 ( v ) represents a fundamental property of the interface. It can be related to the equilibrium thermodynamic characteristics of the interface and the kinetic coefficients of the processes in the surface layer. The most general expressions for 1 ( v ) can be obtained with the help of nonequilibrium thermodynamics (2, 3). It is noteworthy that the theory of surface viscoelasticity cannot be constructed by analogy with the corresponding three-dimensional theory. The surface layer is a nonautonomous phase and the quantity 1 depends on the exchange of surfactants between the continuous bulk phases and the interface and consequently depends on the kinetic coefficients of chemical and physicochemical processes in these phases in the presence of surfactants. Apparently, the most important effect is connected with the micellization. Although the surface activity of micelles is close to zero and the changes of equilibrium surface tension with concentration usually do not exceed the limits of accuracy of conventional experimental methods, the modulus of the dynamic surface elasticity can change abruptly when the concentration exceeds the CMC (21, 22). The expansion (compression) of a surface element leads to adsorption (desorption) of the surfactant. If any adsorption barrier is absent, the adsorption rate is determined by the rate of transport of surfactant molecules from the depth of the bulk phase to the surface, or in other words, by the rate of diffusion of surfactant molecules in the bulk phase. Micelles can completely change the mechanism of monomer transfer to the interface and consequently can lead to significant changes in the dependency of the dynamic surface properties on surfactant concentration. In the general case of the nonequilibrium micellar system it is necessary to consider N equations of diffusion for the bulk phase, where N is the number of different aggregates in the solution (N @ 1). However, it is possible to simplify the problem significantly for some important situations. One can assume that the micellization goes on as a consecutive addition (separation) of one monomer (14)
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Ai 01 / A1 S0 Ai
[4]
ki
(here Ai denotes a micelle with the aggregation number i, A1 denotes a monomer, k i/01 and k i0 are the kinetic coefficients of the aggregation and separation reactions) and can consider the time scale comparable with the characteristic time of the slow stage of the micellization process. Then the N diffusion equations are reduced to only two relations (15, 16), Ìdc1 c1dcm dc1 Å D1Ddc1 0 / t2 Ìt ncmt2 Ìdcm (c1 / » s 2 … cm ) dcm Å DmDdcm 0 Ìt n 2 cmt2 /
(c1 / » s 2 … cm ) dcm , nc1t2
[5]
where c1 and cm are the concentration of monomers and micelles, D1 is the diffusion coefficient of monomers, Dm is the mean diffusion coefficient of micellar aggregates, n is the mean aggregation number, and » s 2 … is the dispersion (standard deviation) of the size distribution of micelles. The quantity t2 Å R1 (c1 / » s 2 … cm )n 02
[6]
is the relaxation time of the second stage of the micellization process (the establishment of the equilibrium number of micelles in the process of dissolution (formation) of micelles) R1 Å (i (k i0 ci ) 01 is the kinetic resistance of the process of disintegration (formation) of micelles, the summation corresponds to the region of the minimum in the size distribution of aggregates. The function which describes such a distribution has two maxima corresponding to the monomers and average size micelles regions, respectively. The deep minimum in between corresponds to premicellar aggregates. The summation is made just in this region in between. To determine the dilational dynamic surface elasticity it is necessary to solve a boundary problem for a system of equations of the dynamics of liquid and of diffusion (2, 3, 15). The boundary conditions at the interface are the equations of momentum and mass conservation. If the applied disturbances are small and the relations [5] are used, the solution of the problem is obtained without any fundamental difficulties. However, in the considered case of micellar solutions, the resulting expressions are rather cumbersome (15). For the present purposes it is sufficient to use only the particular forms corresponding to the case when the surfactant exists in the solution mainly in the form of micelles (n 2 (c1
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/ » s 2 … cm ) 01 cm @ 1) and the adsorption kinetics is purely diffusional
1r Å 0 1i Å
1 / p(q 0 1) 1 / 2 Ìs Ì ln G [1 / p(q 0 1) 1 / 2 ] 2 / p 2 (q 0 1)
Ìs p(q / 1) 1 / 2 , Ì ln G [1 / p(q 0 1) 1 / 2 ] 2 / p 2 (q 0 1)
[7]
where G is the adsorption, p Å ( ÌG / Ì c1 ) 01 (2v 2t2 /D1 ) 01/2 , and q Å (1 / v 2t 22 ) 1/2 . When t2 r ` the relations (7) reduce to well-known equations for solutions of surfactant without micelles (26). The most elaborate experimental methods used for the determination of the dynamic surface elasticity 1 are based on the application of surface waves. In this case, one usually measures the damping coefficient a and the wavelength l. These two quantities are connected with the longitudinal surface elasticity 1I by the dispersion equations (26) ( rv 2 0 sk 3 0 rgk)( rv 2 0 mk 21I ) 0 1I k 3 ( sk 3 / rgk) / 4irmv 3k 3 / 4m2v 2k 3 (m 0 k) Å 0,
[8]
where k Å 2p / l / ia, r is the liquid density, m is the viscosity, g is the gravitational acceleration, m2 Å k 2 / ivr / m, and Re m ú 0. For solutions of surfactants, the surface shear viscosity is negligible compared with the surface dilational viscosity 1i / v. Thus, the longitudinal surface elasticity reduces to the surface dilational elasticity 1 and the relations [7], [8] describe completely the propagation of linear transverse and longitudinal surface waves in the micellar solution. EXPERIMENTAL
The characteristics of capillary waves were measured with the help of the electromechanical method based on the principle of the dynamic condenser. One condenser armature was a thin metal plate with the thickness less than half of the wavelength. The other armature was the investigated liquid surface. Waves were excited by an electromechanical vibrator fed from a low-frequency electric generator. Propagation of capillary waves causes the capacity of the condenser to oscillate and as a result an alternating electric current appears in the circuit. Measurements of the amplitude and the phase of the electric signal allowed us to determine the damping coefficient and the length of capillary waves. A detailed description of the experimental apparatus has been presented elsewhere (8, 21). The equilibrium surface pressure was measured by means of the Wilhelmy plate technique using a roughened platinum plate. Decyldimethyl phosphine oxide (C10DMPO) and dode-
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cyldimethyl phosphine oxide (C12DMPO) were purchased from Gamma-Service Dr. Schano (Berlin, Germany) with a purity necessary for interfacial studies and used as received. All the solutions were prepared immediately before the measurements. Fresh twice-distilled water was used for these purposes. An all-Pyrex apparatus and alkaline permanganate were employed in the second stage of distillation. All the measurements were carried out at 20.07 { 0.57C. All the investigated systems fulfilled the standard criterion of surfactant purity, the absence of a minimum in the surface tension isotherm in the region of the CMC. Moreover, after the mechanical equilibrium in the system was established ( about a minute ) the time changes of the surface tension, the wavelength, and the damping coefficient did not exceed the error limits for both surfactants at all concentrations with the exception of the region of dilute solutions of C12DMPO. Thus, the adsorption equilibrium is established at the time less than a minute. This fact indicates the absence of contaminations with high surface activity ( 27 ) . Nevertheless, the surface of all solutions was purified before the measurements with the help of a moving barrier and Pasteur pipette ( 8, 28 ) . Slow changes of the surface properties with time were observed only for dilute solutions of C12DMPO (c õ 10 05 mol/liter). However, this effect is not connected with any influence of contaminations but is caused by the high surface activity of the surfactant having a slow adsorption rate which is corroborated by calculations of the characteristic diffusion time of C12DMPO (24). In the following only the results of measurements for solutions with an adsorption time less than several minutes are presented.
FIG. 2. The dependency of the wavelength on the concentration of decyldimethyl phosphine oxides at n Å 180 Hz (1), n Å 270 Hz (2), and n Å 380 Hz (3). Lines represent results of calculations.
RESULTS AND DISCUSSION
The characteristics of capillary waves were measured in the frequency region from 120 up to 520 Hz. Figure 1 shows as an example the damping coefficient as a function of frequency n for solutions of C12DMPO at three different concentrations. For both surfactants at all concentrations the dependencies a( n ) can be approximated by straight lines. This fact can be explained by a relatively restricted interval of the investigated frequencies. The region of dynamic surface properties changes spans over several orders of magnitude even when only a single relaxation process is assumed and can be investigated only with the help of several experimental methods (15). The wavelength with a precision of a few percents can be predicted with the help of the Kelvin equation (the equation [8] at 1 Å 0 and m Å 0) 2pn 2 0
FIG. 1. The dependency of the damping coefficient on the frequency for solutions of dodecyldimethyl phosphine oxides at c Å 0.00001 mol/ liter (1), c Å 0.0001 mol/liter (2), and c Å 0.0005 mol/liter (3).
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g 4p 2s 0 Å 0, l rl 3
[9]
and consequently depends on the dynamic surface elasticity only weakly. The function l (log c) is determined by the surface tension and the shape of the corresponding curves is close to the shape of the surface tension isotherms (Figs. 2 and 3). The lines in Figs. 2 and 3 are the dependencies l (log c) calculated from the Kelvin equation. Small deviations from the experimental data are caused by systematic experimental errors, i.e., registration of capillary wave parameters. The values of the CMC for solutions of C10DMPO (3.3 1 10 03 mol/liter) and C12DMPO (3 1 10 04 mol/liter), determined from these curves, agree with the results obtained from surface tension measurements (24).
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FIG. 3. The dependency of the wavelength on the concentration of dodecyldimethyl phosphine oxides at n Å 180 Hz (1), n Å 270 Hz (2), and n Å 380 Hz (3). Lines represent results of calculations.
In contrast, the damping coefficient of capillary waves is determined mainly by the dynamic surface elasticity and the dependency a( log c ) turns out to be significantly more complex. This curve for solutions of C 10DMPO ( Fig. 4, n Å 200 Hz, for other frequencies the results are qualitatively the same ) have two local maxima. The first maximum corresponds to the point where the wave numbers of the transversal and longitudinal component of the capillary wave are equal, k t Å kl , and is observed for all systems where the modulus of the dynamic surface elasticity increases with concentration and exceeds the value 0.16s ( 29 ) . For solutions of C12DMPO, the corre-
FIG. 5. The dependency of the damping coefficient on the concentration of dodecyldimethyl phosphine oxides at n Å 200 Hz. The line represents results of calculations.
sponding region of concentrations turns out to be inapproachable for experimental investigation because of the too slow establishment of the adsorption equilibrium. Figure 5 shows only the experimental results at concentrations close to the CMC, where the adsorption rate is sufficiently fast. Note that in this region the maximum in the a( log c ) curve, if it exists, is on the order of the experimental error. At concentrations less than the CMC, the dependency a(log c) can be calculated with the help of Eq. [8] and corresponding expressions for the dynamic surface elasticity (9, 18, 20–22). In this case, it is necessary to know the parameters a, b, G` of the equation of state and of the Frumkin adsorption isotherm
FS
s Å s0 / RT G` ln 1 0
bc Å
G G`
D S DG /a
G exp(2aG / G` ), G` 0 G
G G`
2
[10]
[11]
where R is the gas constant, T is the temperature, and s0 is the surface tension of the solvent. The regression analysis of the experimental dependency l (log c) (9, 18, 20–22) gives the following values of the parameters C10DMPO C12DMPO FIG. 4. The dependency of the damping coefficient on the concentration of decyldimethyl phosphine oxides at n Å 200 Hz. Lines represent results of calculations at t Å 0 (solid) and t Å 1 s (dashed).
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a b, m3/mol G` 1 1006, mol/m2
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0.5 180 3.8
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NOSKOV, GRIGORIEV, AND MILLER
FIG. 6. The dependency of the characteristic time of the slow stage of the micellization of decyldimethyl phosphine oxide on the total concentration of the surfactant.
These results are close to the values determined from the surface tension data (24). Small differences, probably, are connected with different methods of measurements. Figure 4 shows also the dependencies a(log c) calculated for D1 Å 6 1 10 010 m2 /s and for values of the relaxation time of the pure adsorption process t corresponding to the pure diffusion mechanism ( t Å 0) and to the pure kinetic mechanism ( t Å 1 s). Far from the CMC (c õ 0.5 mol/ m 3 ), both calculated curves are close to each other (this is characteristic for solutions of high surface active surfactants (9)) and simultaneously agree with the experimental data. Small deviations can be observed only in the region of the first maximum, where the calculated a values are shifted slightly along the concentration axis relative to the results of measurements. Deviations of this kind were observed earlier for solutions of ionic surfactants which can apparently be explained by an insufficient accuracy of the description of the surface properties by Eqs. [10] – [11] for dilute solutions (18, 20, 21). It is noteworthy that the calculated and experimental values of a that correspond to the local maximum are selfconsistent. If the surface activity is not high, measurements of the characteristics of capillary waves permit us to find the adsorption mechanism easily using the value of the damping coefficient in the region of the first maximum (9, 18, 20–22). Any differences in the adsorption mechanism cause differences in the damping coefficient much higher than the error limits. In the considered case, these differences are small and a conclusion about the adsorption mechanism can be obtained from the analysis of the damping in the concentration region close to the CMC. Thus, we can conclude that the C10DMPO at concentrations below the CMC adsorb purely diffusion-controlled as in this concentration region the curve for a purely kinetic-controlled
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mechanism deviates significantly from the experimental curve. For solutions of C12DMPO both curves are close to each other in the whole concentration region and therefore a definite conclusion about the adsorption mechanism is impossible from capillary wave damping experiments. A diffusion-controlled adsorption mechanism of alkyldimethyl phosphine oxides at the liquid–gas interface below the CMC was determined also earlier by measurements of the dynamic surface tension (25). Thus, it is obvious to assume that any adsorption barrier is also absent for micellar solutions of these surfactants. Then Eq. [7] can be used for the analysis of the a(log c) dependency. For C12DMPO concentrations above the CMC the damping coefficient does not change within the error limits (Fig. 5). This behavior is characteristic for many surfactants at frequencies corresponding to externally excited capillary waves (9, 18) and signifies that micelles do not take part in the mass exchange between the surface layer and the bulk phase at compression (expansion) of the interface. Actually, from the constancy of the a value it follows that 1r , 1i are constant also and an application of Eq. [7] immediately gives t2 @ v 01 . Therefore, the surface deformations are so fast that micelles have not enough time to disintegrate or aggregate and the diffusion process occurs as in the solution without micelles. Another behavior of the damping coefficient is observed for solutions of C10DMPO. In the region of micellar solutions, a starts decreasing quickly and the CMC corresponds to an absolute maximum of damping (Fig. 4). Such features have been observed earlier only for solutions of ionic surfactants with relatively low surface activity (20–22) and it gives evidence of the influence of processes of micelle disintegration and formation. Above the CMC, parameters like
FIG. 7. The dependency of the real and imaginary parts of the dilational dynamic surface elasticity of solutions of decyldimethyl phosphine oxide on the concentration at n Å 200 Hz.
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r, m, s, and l do not change significantly and therefore any change in the damping parameter a of the dispersion equation [8] must be caused by a change in the complex dynamic elasticity. Any decrease in a must correspond to a decrease in the components of the complex elasticity. According to the theory of dynamic surface properties, this is only possible if t2 £ v 01 , i.e., if the formation and dissolution of micelles influence the exchange of matter between the surface and the bulk phase. Thus, C10DMPO is the first investigated nonionic surfactant that allowed the discovery of the influence of the micellization kinetics on the damping coefficient of capillary waves, and consequently, on the dynamic surface elasticity. Application of Eqs. [7] and [8] permits us then to calculate the relaxation time of the slow stage of the micellization process (22). Figure 6 shows the calculated dependency of t2 on the total surfactant concentration. The values of the derivatives ÌG / Ìc ¸ Ìs / Ì ln c, used in the course of the calculations, were determined at c Å CMC. The quantity t2 monotonically decreases with the concentration and this dependency apparently is determined by the dependency of the kinetic resistance on the concentration. The quantities » s 2 … and n can depend on concentration also which makes an application of Eq. [6] difficult. However, if we exclude a region close to the CMC, where an application of Eq. [7] is not justified, the determined values of t2 for solutions of C10DMPO are more precise than the values obtained earlier for ionic surfactants (22), where the electric charge of micelles was not taken into account. To our knowledge, no data on the micellization kinetics of alkyldimethyl phosphine oxides have been published, so we cannot compare the relaxation times obtained from these measurements of surface properties with those from properties of bulk phase. The obtained results allowed us to calculate the real and imaginary parts of the complex dynamic surface elasticity of solutions of C10DMPO. Figure 7 presents results at n Å 200 Hz. Below the CMC, both curves go through a maximum that is typical for most of surfactants at frequencies of about 100 Hz (22). In conclusion, it is noteworthy that in this work for the first time the micellization kinetics of nonionic surfactants was investigated with the help of the capillary wave method. Application of this method to kinetic studies of surfactant solutions turns out to be sufficiently successful if the surface activity of the surfactant is not too high. For solutions of higher surface active substances other methods of the relaxation spectrometry of the surface layer must be used, for
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example, the method of longitudinal surface waves (6) or the method of oscillating bubble method (30) or others (11). ACKNOWLEDGMENT This work was financially supported by the European Union (INTAS 93-2463).
REFERENCES 1. Miller, R., Loglio, G., Tesei, U., and Schano, K.-H., Adv. Colloid Interface Sci. 37, 73 (1991). 2. Noskov, B. A., Kolloidn. Zh. 44, 492 (1982). 3. Noskov, B. A., Kolloidn. Zh. 45, 689 (1983). 4. Jiang, Q., Valentini, J. E., and Chiew, Y. C., J. Colloid Interface Sci. 174, 268 (1995). 5. Jiang, Q., O’Lenick, C. J., Valentini, J. E., and Chiew, Y. C., Langmuir 11, 1138 (1995). 6. Bonfillon, A., and Langevin, D., Langmuir 10, 2965 (1995). 7. Stenvot, C., and Langevin, D., Langmuir 4, 1179 (1988). 8. Noskov, B. A., and Vasyliev, A. A., Kolloidn. Zh. 50, 909 (1988). 9. Noskov, B. A., Colloids Surf. 71, 99 (1993). 10. Noskov, B. A., and Zubkova, T. U., J. Colloid Interface Sci. 170, 1 (1995). 11. Dukhin, S. S., Kretzschmar, G., and Miller, R., in ‘‘Studies of Interface Science’’ (D. Mo¨bius and R. Miller, Eds.), Vol. 1. Elsevier, Amsterdam, 1995. 12. Chang, C.-H., and Franses, E. I., Colloids Surf. 100, 1 (1995). 13. Lucassen, J., Faraday Discuss. Chem. Soc. 59, 76 (1975). 14. Aniansson, E. A. G., and Wall, S. N., J. Phys. Chem. 78, 1024 (1974); J. Phys. Chem. 79, 857 (1975). 15. Noskov, B. A., Izv. Akad. Nauk SSSR. Mekh. Zydkosty i gaza 2, 105 (1989). 16. Noskov, B. A., Kolloidn. Zh. 52, 509 (1990); 52, 796 (1990). 17. Duschkin, C., Ivanov, I., and Kralchevsky, P., Colloids Surf. 60, 235 (1991). 18. Noskov, B. A., Anykieva, O. A., and Makarova, N. V., Kolloidn. Zh. 52, 1091 (1990). 19. Kao, R. L., Edwards, D. A., Wasan, D. T., and Chen, E., J. Colloid Interface Sci. 148, 247 (1992). 20. Grigoriev, D. O., Noskov, B. A., and Semchenko, S. I., Kolloidn. Zh. 55, 45 (1993). 21. Noskov, B. A., and Grigoriev, D. O., Prog. Colloid Polym. Sci. 97, 1 (1994). 22. Noskov, B. A., and Grigoriev, D. O., Langmuir 12, 3399 (1995). 23. Kahlweit, M., Pure Appl. Chem. 53, 2069 (1981). 24. Lunkenheimer, K., Haage, K., and Miller, R., Colloids Surf. 22, 215 (1987). 25. Miller, R., and Lunkenheimer, K., Colloid Polym. Sci. 264, 357 (1986). 26. Lucassen, J., and Hansen, R. S., J. Colloid Interface Sci. 23, 319 (1967). 27. Mysels, K. J., and Florence, A. T., J. Colloid Interface Sci. 43, 577 (1973). 28. Lunkenheimer, K., and Miller, R., Tenside Deterg. 16, 312 (1979). 29. Earnshaw, J. C., and McCoo, E., Langmuir 11, 1087 (1995). 30. Wantke, K.-D., Lunkenheimer, K., and Hempt, C., J. Colloid Interface Sci. 159, 28 (1993).
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Dynamic Surface Properties of Solutions of Phosphine Oxides: A Capillary Wave Study B. A. NOSKOV,* D. O. GRIGORIEV,*
AND
R. MILLER† ,1
*Institute of Chemistry, St. Petersburg State University, St. Petersburg-Stariy Petergof, Russia; and †Max-Planck Institute of Colloid and Interface Science, Berlin–Adlershof, Federal Republic of Germany
Received February 2, 1996; accepted September 3, 1996
In the past two decades, this quantity was investigated many times theoretically (1–6) and was determined experimentally (5–10). An overview is given, for example, in (11). However, attention was paid mostly to comparatively simple systems, such as, solutions of surfactants at concentrations below the CMC (1–4, 6–9), elastic and viscoelastic insoluble monolayers (2, 4, 10), and systems containing mixtures of insoluble and soluble surfactants (4, 5). Although micellar solutions are more interesting from the point of view of applied problems, information about dynamic surface properties in this region in general, and information about the dynamic surface elasticities at concentrations above the CMC, in particular, are relatively scarce (12). The dynamic surface elasticity of micellar solutions was first determined by Lucassen (13). However, the developed theory was based on a simplified single-step model of the micellization process. A more elaborate theory based on the two-step model of Aniansson and Wall (14) and takes into account diffusion of both monomers and micellar aggregates has been published recently (15–17). However, to check this theory and to determine experimentally the dynamic surface elasticity of micellar solutions proved to be a difficult task. Apparently, the main reason is that the characteristic times of the micellization correspond to frequencies which are difficult to investigate using the usual methods of relaxation spectrometry of liquid surface layers. For example, the first attempts to apply the capillary wave method to micellar solutions failed—the damping coefficient and, consequently, the dynamic surface elasticity did not depend on the concentration above the CMC (9, 18). Moreover, Kao et al. (19) even argued that the wave methods cannot be used for micellar solutions. Recently, we have shown that the last statement is not true, in general. A significant decrease of the damping coefficient was discovered for solutions of some ionic surfactants at concentrations above the CMC, and the dynamic surface elasticity of micellar solutions was calculated (20–22). These experimental data were used to calculate the character-
The characteristics of capillary waves on the surface of aqueous solutions of dimethylalkyl phosphine oxides have been measured as a function of frequency and surfactant concentration. The damping coefficient for solutions of dodecyldimethyl phosphine oxide increased with concentration, passed through a local maximum below the CMC, and was independent of concentration above the CMC. For solutions of decyldimethyl phosphine oxide, a second maximum is observed at the CMC and the damping decreases considerably in the micellar region. This effect can be explained by an influence of the micellization kinetics on the dynamic surface elasticity and was not observed earlier for solutions of nonionic surfactants. The results are used to calculate the characteristic time of the slow step of the micellization process. q 1997 Academic Press
Key Words: capillary wave damping; surface rheology; nonionic surfactants; exchange of matter; micelles.
INTRODUCTION
It is well known that nonequilibrium mechanical properties of solutions of surfactants do not comprise only the dynamic surface tension. The behavior of a system with a free interface at any moment is determined in the general case by the whole of its preceding history. However, if deviations from the equilibrium are not large or one is interested only in the behavior close to a steady-state (quasisteadystate), in order to describe the dynamics of the system it is sufficient to determine, besides the surface tension, a set of dynamic surface elasticities. Moreover, if the system does not contain polymers or insoluble surfactants, it is possible to neglect the surface shear elasticity and viscosity and the transverse surface viscosity in most situations. As a result, the only additional characteristic in comparison with the equilibrium case is the complex dilational dynamic surface elasticity which depends on the frequency of disturbances of the system (1–3). 1
To whom correspondence should be addressed. 9
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istic time of the slow step of the micellization (21, 22). The obtained values were in reasonable agreement with data obtained in independent studies on the bulk properties of micellar solutions. However, the calculations mentioned above are not of high accuracy. It is well known that the charge of micelles influences the kinetics of their formation and dissolution and even the mechanism of these processes, in some cases, can be different for ionic and nonionic surfactants ( 23 ) . On the other hand, the theory of Aniansson and Wall ( 14 ) and the theory of the dynamic surface elasticity of micellar systems ( 15 – 17 ) are related only to solutions of nonionic surfactants. Therefore, an experimental verification of the obtained relationships must be realized first for nonionic systems. In this work, the capillary wave method is applied to solutions of dimethylalkyl phosphine oxides. These substances are chemically stable in aqueous solutions and can be purified easily. The surface properties of solutions of dimethylalkyl phosphine oxides were investigated in detail at concentrations below the CMC. The dependence of surface tension on concentration is described by a Frumkin equation (24) and the adsorption process is determined by a simple diffusion mechanism (25). The present paper describes the basic features of the theory of dynamic surface properties of micellar solutions. Experiments with a capillary wave technique are presented and the results are interpreted in terms of the dynamic surface dilational elasticity. The data also allowed us to calculate the kinetic characteristics of micellization. THEORY
In the general case of a nonequilibrium system, the tensor of surface tension and its isotropic part s depend on the area S of a surface element under consideration. However, in order to determine the quantity s at the moment t 0 , it is not sufficient to define a value of the surface at t Å t 0 . The surface tension is determined by the character of changes of the area in the preceding time (t õ t 0 ), and consequently, is a functional of the quantity S(t). If the deformation of the surface (extension or contraction) is small, this functional can be considered as linear and the following general presentation can be used (15) ds Å
*
t
G(t 0 t )(ddS( t )/d t )d t,
[1]
0`
where ds Å s 0 s0 , ds / s0 ! 1, dS Å S 0 S0 , dS/S0 ! 1; the subscript zero corresponds to the undisturbed state, G is the surface function of relaxation, t is ‘‘dummy variable’’ and ds Å ds(t). Application of the Fourier transformation to Eq. [1] leads to a linear relation between Fourier images
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( ds )v Å 1 ( v )( dS)v ,
[2]
where 1 ( v ) Å 1r ( v ) / i1i ( v ) is the complex dynamic surface elasticity
1r Å G 0 / v
*
`
G( h )sin( vh )d h,
0
1i Å v
*
`
G( h )cos( vh )d h.
[3]
0
We assume here that G Å G0 / G(t) or the quantity G consists of a constant component and a component that depends on time, ( dS)v and ( ds )v are the corresponding Fourier transformations, h is the ‘‘dummy variable’’. The function 1 ( v ) represents a fundamental property of the interface. It can be related to the equilibrium thermodynamic characteristics of the interface and the kinetic coefficients of the processes in the surface layer. The most general expressions for 1 ( v ) can be obtained with the help of nonequilibrium thermodynamics (2, 3). It is noteworthy that the theory of surface viscoelasticity cannot be constructed by analogy with the corresponding three-dimensional theory. The surface layer is a nonautonomous phase and the quantity 1 depends on the exchange of surfactants between the continuous bulk phases and the interface and consequently depends on the kinetic coefficients of chemical and physicochemical processes in these phases in the presence of surfactants. Apparently, the most important effect is connected with the micellization. Although the surface activity of micelles is close to zero and the changes of equilibrium surface tension with concentration usually do not exceed the limits of accuracy of conventional experimental methods, the modulus of the dynamic surface elasticity can change abruptly when the concentration exceeds the CMC (21, 22). The expansion (compression) of a surface element leads to adsorption (desorption) of the surfactant. If any adsorption barrier is absent, the adsorption rate is determined by the rate of transport of surfactant molecules from the depth of the bulk phase to the surface, or in other words, by the rate of diffusion of surfactant molecules in the bulk phase. Micelles can completely change the mechanism of monomer transfer to the interface and consequently can lead to significant changes in the dependency of the dynamic surface properties on surfactant concentration. In the general case of the nonequilibrium micellar system it is necessary to consider N equations of diffusion for the bulk phase, where N is the number of different aggregates in the solution (N @ 1). However, it is possible to simplify the problem significantly for some important situations. One can assume that the micellization goes on as a consecutive addition (separation) of one monomer (14)
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Ai 01 / A1 S0 Ai
[4]
ki
(here Ai denotes a micelle with the aggregation number i, A1 denotes a monomer, k i/01 and k i0 are the kinetic coefficients of the aggregation and separation reactions) and can consider the time scale comparable with the characteristic time of the slow stage of the micellization process. Then the N diffusion equations are reduced to only two relations (15, 16), Ìdc1 c1dcm dc1 Å D1Ddc1 0 / t2 Ìt ncmt2 Ìdcm (c1 / » s 2 … cm ) dcm Å DmDdcm 0 Ìt n 2 cmt2 /
(c1 / » s 2 … cm ) dcm , nc1t2
[5]
where c1 and cm are the concentration of monomers and micelles, D1 is the diffusion coefficient of monomers, Dm is the mean diffusion coefficient of micellar aggregates, n is the mean aggregation number, and » s 2 … is the dispersion (standard deviation) of the size distribution of micelles. The quantity t2 Å R1 (c1 / » s 2 … cm )n 02
[6]
is the relaxation time of the second stage of the micellization process (the establishment of the equilibrium number of micelles in the process of dissolution (formation) of micelles) R1 Å (i (k i0 ci ) 01 is the kinetic resistance of the process of disintegration (formation) of micelles, the summation corresponds to the region of the minimum in the size distribution of aggregates. The function which describes such a distribution has two maxima corresponding to the monomers and average size micelles regions, respectively. The deep minimum in between corresponds to premicellar aggregates. The summation is made just in this region in between. To determine the dilational dynamic surface elasticity it is necessary to solve a boundary problem for a system of equations of the dynamics of liquid and of diffusion (2, 3, 15). The boundary conditions at the interface are the equations of momentum and mass conservation. If the applied disturbances are small and the relations [5] are used, the solution of the problem is obtained without any fundamental difficulties. However, in the considered case of micellar solutions, the resulting expressions are rather cumbersome (15). For the present purposes it is sufficient to use only the particular forms corresponding to the case when the surfactant exists in the solution mainly in the form of micelles (n 2 (c1
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/ » s 2 … cm ) 01 cm @ 1) and the adsorption kinetics is purely diffusional
1r Å 0 1i Å
1 / p(q 0 1) 1 / 2 Ìs Ì ln G [1 / p(q 0 1) 1 / 2 ] 2 / p 2 (q 0 1)
Ìs p(q / 1) 1 / 2 , Ì ln G [1 / p(q 0 1) 1 / 2 ] 2 / p 2 (q 0 1)
[7]
where G is the adsorption, p Å ( ÌG / Ì c1 ) 01 (2v 2t2 /D1 ) 01/2 , and q Å (1 / v 2t 22 ) 1/2 . When t2 r ` the relations (7) reduce to well-known equations for solutions of surfactant without micelles (26). The most elaborate experimental methods used for the determination of the dynamic surface elasticity 1 are based on the application of surface waves. In this case, one usually measures the damping coefficient a and the wavelength l. These two quantities are connected with the longitudinal surface elasticity 1I by the dispersion equations (26) ( rv 2 0 sk 3 0 rgk)( rv 2 0 mk 21I ) 0 1I k 3 ( sk 3 / rgk) / 4irmv 3k 3 / 4m2v 2k 3 (m 0 k) Å 0,
[8]
where k Å 2p / l / ia, r is the liquid density, m is the viscosity, g is the gravitational acceleration, m2 Å k 2 / ivr / m, and Re m ú 0. For solutions of surfactants, the surface shear viscosity is negligible compared with the surface dilational viscosity 1i / v. Thus, the longitudinal surface elasticity reduces to the surface dilational elasticity 1 and the relations [7], [8] describe completely the propagation of linear transverse and longitudinal surface waves in the micellar solution. EXPERIMENTAL
The characteristics of capillary waves were measured with the help of the electromechanical method based on the principle of the dynamic condenser. One condenser armature was a thin metal plate with the thickness less than half of the wavelength. The other armature was the investigated liquid surface. Waves were excited by an electromechanical vibrator fed from a low-frequency electric generator. Propagation of capillary waves causes the capacity of the condenser to oscillate and as a result an alternating electric current appears in the circuit. Measurements of the amplitude and the phase of the electric signal allowed us to determine the damping coefficient and the length of capillary waves. A detailed description of the experimental apparatus has been presented elsewhere (8, 21). The equilibrium surface pressure was measured by means of the Wilhelmy plate technique using a roughened platinum plate. Decyldimethyl phosphine oxide (C10DMPO) and dode-
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cyldimethyl phosphine oxide (C12DMPO) were purchased from Gamma-Service Dr. Schano (Berlin, Germany) with a purity necessary for interfacial studies and used as received. All the solutions were prepared immediately before the measurements. Fresh twice-distilled water was used for these purposes. An all-Pyrex apparatus and alkaline permanganate were employed in the second stage of distillation. All the measurements were carried out at 20.07 { 0.57C. All the investigated systems fulfilled the standard criterion of surfactant purity, the absence of a minimum in the surface tension isotherm in the region of the CMC. Moreover, after the mechanical equilibrium in the system was established ( about a minute ) the time changes of the surface tension, the wavelength, and the damping coefficient did not exceed the error limits for both surfactants at all concentrations with the exception of the region of dilute solutions of C12DMPO. Thus, the adsorption equilibrium is established at the time less than a minute. This fact indicates the absence of contaminations with high surface activity ( 27 ) . Nevertheless, the surface of all solutions was purified before the measurements with the help of a moving barrier and Pasteur pipette ( 8, 28 ) . Slow changes of the surface properties with time were observed only for dilute solutions of C12DMPO (c õ 10 05 mol/liter). However, this effect is not connected with any influence of contaminations but is caused by the high surface activity of the surfactant having a slow adsorption rate which is corroborated by calculations of the characteristic diffusion time of C12DMPO (24). In the following only the results of measurements for solutions with an adsorption time less than several minutes are presented.
FIG. 2. The dependency of the wavelength on the concentration of decyldimethyl phosphine oxides at n Å 180 Hz (1), n Å 270 Hz (2), and n Å 380 Hz (3). Lines represent results of calculations.
RESULTS AND DISCUSSION
The characteristics of capillary waves were measured in the frequency region from 120 up to 520 Hz. Figure 1 shows as an example the damping coefficient as a function of frequency n for solutions of C12DMPO at three different concentrations. For both surfactants at all concentrations the dependencies a( n ) can be approximated by straight lines. This fact can be explained by a relatively restricted interval of the investigated frequencies. The region of dynamic surface properties changes spans over several orders of magnitude even when only a single relaxation process is assumed and can be investigated only with the help of several experimental methods (15). The wavelength with a precision of a few percents can be predicted with the help of the Kelvin equation (the equation [8] at 1 Å 0 and m Å 0) 2pn 2 0
FIG. 1. The dependency of the damping coefficient on the frequency for solutions of dodecyldimethyl phosphine oxides at c Å 0.00001 mol/ liter (1), c Å 0.0001 mol/liter (2), and c Å 0.0005 mol/liter (3).
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g 4p 2s 0 Å 0, l rl 3
[9]
and consequently depends on the dynamic surface elasticity only weakly. The function l (log c) is determined by the surface tension and the shape of the corresponding curves is close to the shape of the surface tension isotherms (Figs. 2 and 3). The lines in Figs. 2 and 3 are the dependencies l (log c) calculated from the Kelvin equation. Small deviations from the experimental data are caused by systematic experimental errors, i.e., registration of capillary wave parameters. The values of the CMC for solutions of C10DMPO (3.3 1 10 03 mol/liter) and C12DMPO (3 1 10 04 mol/liter), determined from these curves, agree with the results obtained from surface tension measurements (24).
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FIG. 3. The dependency of the wavelength on the concentration of dodecyldimethyl phosphine oxides at n Å 180 Hz (1), n Å 270 Hz (2), and n Å 380 Hz (3). Lines represent results of calculations.
In contrast, the damping coefficient of capillary waves is determined mainly by the dynamic surface elasticity and the dependency a( log c ) turns out to be significantly more complex. This curve for solutions of C 10DMPO ( Fig. 4, n Å 200 Hz, for other frequencies the results are qualitatively the same ) have two local maxima. The first maximum corresponds to the point where the wave numbers of the transversal and longitudinal component of the capillary wave are equal, k t Å kl , and is observed for all systems where the modulus of the dynamic surface elasticity increases with concentration and exceeds the value 0.16s ( 29 ) . For solutions of C12DMPO, the corre-
FIG. 5. The dependency of the damping coefficient on the concentration of dodecyldimethyl phosphine oxides at n Å 200 Hz. The line represents results of calculations.
sponding region of concentrations turns out to be inapproachable for experimental investigation because of the too slow establishment of the adsorption equilibrium. Figure 5 shows only the experimental results at concentrations close to the CMC, where the adsorption rate is sufficiently fast. Note that in this region the maximum in the a( log c ) curve, if it exists, is on the order of the experimental error. At concentrations less than the CMC, the dependency a(log c) can be calculated with the help of Eq. [8] and corresponding expressions for the dynamic surface elasticity (9, 18, 20–22). In this case, it is necessary to know the parameters a, b, G` of the equation of state and of the Frumkin adsorption isotherm
FS
s Å s0 / RT G` ln 1 0
bc Å
G G`
D S DG /a
G exp(2aG / G` ), G` 0 G
G G`
2
[10]
[11]
where R is the gas constant, T is the temperature, and s0 is the surface tension of the solvent. The regression analysis of the experimental dependency l (log c) (9, 18, 20–22) gives the following values of the parameters C10DMPO C12DMPO FIG. 4. The dependency of the damping coefficient on the concentration of decyldimethyl phosphine oxides at n Å 200 Hz. Lines represent results of calculations at t Å 0 (solid) and t Å 1 s (dashed).
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a b, m3/mol G` 1 1006, mol/m2
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FIG. 6. The dependency of the characteristic time of the slow stage of the micellization of decyldimethyl phosphine oxide on the total concentration of the surfactant.
These results are close to the values determined from the surface tension data (24). Small differences, probably, are connected with different methods of measurements. Figure 4 shows also the dependencies a(log c) calculated for D1 Å 6 1 10 010 m2 /s and for values of the relaxation time of the pure adsorption process t corresponding to the pure diffusion mechanism ( t Å 0) and to the pure kinetic mechanism ( t Å 1 s). Far from the CMC (c õ 0.5 mol/ m 3 ), both calculated curves are close to each other (this is characteristic for solutions of high surface active surfactants (9)) and simultaneously agree with the experimental data. Small deviations can be observed only in the region of the first maximum, where the calculated a values are shifted slightly along the concentration axis relative to the results of measurements. Deviations of this kind were observed earlier for solutions of ionic surfactants which can apparently be explained by an insufficient accuracy of the description of the surface properties by Eqs. [10] – [11] for dilute solutions (18, 20, 21). It is noteworthy that the calculated and experimental values of a that correspond to the local maximum are selfconsistent. If the surface activity is not high, measurements of the characteristics of capillary waves permit us to find the adsorption mechanism easily using the value of the damping coefficient in the region of the first maximum (9, 18, 20–22). Any differences in the adsorption mechanism cause differences in the damping coefficient much higher than the error limits. In the considered case, these differences are small and a conclusion about the adsorption mechanism can be obtained from the analysis of the damping in the concentration region close to the CMC. Thus, we can conclude that the C10DMPO at concentrations below the CMC adsorb purely diffusion-controlled as in this concentration region the curve for a purely kinetic-controlled
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mechanism deviates significantly from the experimental curve. For solutions of C12DMPO both curves are close to each other in the whole concentration region and therefore a definite conclusion about the adsorption mechanism is impossible from capillary wave damping experiments. A diffusion-controlled adsorption mechanism of alkyldimethyl phosphine oxides at the liquid–gas interface below the CMC was determined also earlier by measurements of the dynamic surface tension (25). Thus, it is obvious to assume that any adsorption barrier is also absent for micellar solutions of these surfactants. Then Eq. [7] can be used for the analysis of the a(log c) dependency. For C12DMPO concentrations above the CMC the damping coefficient does not change within the error limits (Fig. 5). This behavior is characteristic for many surfactants at frequencies corresponding to externally excited capillary waves (9, 18) and signifies that micelles do not take part in the mass exchange between the surface layer and the bulk phase at compression (expansion) of the interface. Actually, from the constancy of the a value it follows that 1r , 1i are constant also and an application of Eq. [7] immediately gives t2 @ v 01 . Therefore, the surface deformations are so fast that micelles have not enough time to disintegrate or aggregate and the diffusion process occurs as in the solution without micelles. Another behavior of the damping coefficient is observed for solutions of C10DMPO. In the region of micellar solutions, a starts decreasing quickly and the CMC corresponds to an absolute maximum of damping (Fig. 4). Such features have been observed earlier only for solutions of ionic surfactants with relatively low surface activity (20–22) and it gives evidence of the influence of processes of micelle disintegration and formation. Above the CMC, parameters like
FIG. 7. The dependency of the real and imaginary parts of the dilational dynamic surface elasticity of solutions of decyldimethyl phosphine oxide on the concentration at n Å 200 Hz.
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r, m, s, and l do not change significantly and therefore any change in the damping parameter a of the dispersion equation [8] must be caused by a change in the complex dynamic elasticity. Any decrease in a must correspond to a decrease in the components of the complex elasticity. According to the theory of dynamic surface properties, this is only possible if t2 £ v 01 , i.e., if the formation and dissolution of micelles influence the exchange of matter between the surface and the bulk phase. Thus, C10DMPO is the first investigated nonionic surfactant that allowed the discovery of the influence of the micellization kinetics on the damping coefficient of capillary waves, and consequently, on the dynamic surface elasticity. Application of Eqs. [7] and [8] permits us then to calculate the relaxation time of the slow stage of the micellization process (22). Figure 6 shows the calculated dependency of t2 on the total surfactant concentration. The values of the derivatives ÌG / Ìc ¸ Ìs / Ì ln c, used in the course of the calculations, were determined at c Å CMC. The quantity t2 monotonically decreases with the concentration and this dependency apparently is determined by the dependency of the kinetic resistance on the concentration. The quantities » s 2 … and n can depend on concentration also which makes an application of Eq. [6] difficult. However, if we exclude a region close to the CMC, where an application of Eq. [7] is not justified, the determined values of t2 for solutions of C10DMPO are more precise than the values obtained earlier for ionic surfactants (22), where the electric charge of micelles was not taken into account. To our knowledge, no data on the micellization kinetics of alkyldimethyl phosphine oxides have been published, so we cannot compare the relaxation times obtained from these measurements of surface properties with those from properties of bulk phase. The obtained results allowed us to calculate the real and imaginary parts of the complex dynamic surface elasticity of solutions of C10DMPO. Figure 7 presents results at n Å 200 Hz. Below the CMC, both curves go through a maximum that is typical for most of surfactants at frequencies of about 100 Hz (22). In conclusion, it is noteworthy that in this work for the first time the micellization kinetics of nonionic surfactants was investigated with the help of the capillary wave method. Application of this method to kinetic studies of surfactant solutions turns out to be sufficiently successful if the surface activity of the surfactant is not too high. For solutions of higher surface active substances other methods of the relaxation spectrometry of the surface layer must be used, for
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example, the method of longitudinal surface waves (6) or the method of oscillating bubble method (30) or others (11). ACKNOWLEDGMENT This work was financially supported by the European Union (INTAS 93-2463).
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