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Surface Dilational Viscoelasticity of C14EO8 Micellar Solution Studied by Bubble Profile Analysis Tensiometry V. B. Fainerman,† J. T. Petkov,‡ and R. Miller*,§ Medical Physicochemical Centre, Donetsk Medical UniVersity, 16 Ilych AVenue, 83003 Donetsk, Ukraine, UnileVer R&D Port Sunlight, Quarry Road East, Bebington, CH63 3JW, U.K., and Max-Planck-Institut fu¨r Kolloid- and Grenzfla¨chenforschung, Am Mu¨hlenberg 1, 14424 Potsdam, Germany ReceiVed December 28, 2007. ReVised Manuscript ReceiVed March 27, 2008 The experimental dependences of viscoelasticity modulus and phase angle as a function of frequency for various C14ΕΟ8 concentrations at the critical micelle concentration (cmc) of 7 µmol/L and far above the cmc (up to 70 × cmc) were studied using the buoyant bubble profile analysis method. With increasing C14EO8 concentration the viscoelasticity modulus decreases and the phase angle increases. At the highest surfactant concentrations, the phase angle was more than 45°. For the theoretical description of the equilibrium surface tension isotherm and the limiting elasticity modulus, a combined theoretical model was used considering surface reorientation and molecular compression. To analyze the experimental dependencies of the viscoelasticity modulus and phase angle on frequency, a model proposed by Joos for fast micellar kinetics was applied. This theory agrees well with the experimental data of the viscoelasticity modulus obtained for all concentrations of the studied nonionic surfactant C14EO8.
Introduction Many modern technologies depend on the optimum use of surfactants, while the applied concentrations are often above the critical micelle concentration (cmc) and special effects are directly related to the presence of micelles. The formation and dissolution of micelles or the release or incorporation of single molecules are controlled by the relaxation times of slow and fast dissociation processes. The presence of micelles in the bulk have an impact on the adsorption kinetics and hence the dilational elasticity. The first work on this subject was published by Lucassen more than 30 years ago.1,2 This topic was further discussed in many subsequent publications.3–21 The state-of-the-art in micelles dissociation * Corresponding author. E-mail:
[email protected]. † Donetsk Medical University. ‡ Unilever R&D Port Sunlight. § Max-Planck-Institut fu¨r Kolloid- and Grenzfla¨chenforschung.
(1) Lucassen, J. Faraday Discuss. Chem. Soc. 1975, 59, 76. (2) Lucassen, J.; Giles, D. J. Chem. Soc. Faraday Trans 1 1975, 71, 217. (3) Fainerman, V. B. Kolloidn. Zh. 1981, 43, 94. (4) Miller, R. Colloid Polym. Sci. 1981, 259, 1124–1128. (5) Fainerman, V. B. Kolloidn. Zh. (Russ.) 1981, 43, 717; Kolloidn. Zh. (Russ.) 1981, 43, 926. (6) Joos, P.; van Hunsel, J. Colloids Surf. 1988, 33, 99. (7) Noskov, B. A. Fluid Dynamics 1989, 24, 251. (8) Noskov, B. A. Kolloidn. Zh. (Russ.) 1990, 52, 509. (9) Dushkin, C. D.; Ivanov, I. B. Colloids Surf. 1991, 60, 213. (10) Dushkin, C. D.; Ivanov, I. B.; Kralchevsky, P. A. Colloids Surf. 1991, 60, 235. (11) Fainerman, V. B.; Makievski, A. V. Colloids Surf. 1993, 69, 249. (12) Garrett, P. R.; Joos, P. Colloids Surf. A 1994, 90, 149–154. (13) Patist, A.; Axelberd, T.; Shah, D. O. J. Colloid Interface Sci. 1998, 208, 259–265. (14) Joos, P. Dynamic Surface Phenomena; VSP: Dordrecht, The Netherlands, 1999. (15) Zhmud, B. V.; Tiberg, F.; Kizling, J. Langmuir 2000, 16, 2557–2565. (16) Danov, K. D.; Valkovska, D. S.; Kralchevsky, P. A. J. Colloid Interface Sci. 2002, 251, 18–25. (17) Liao, Y. C.; Basaran, O. A.; Franses, E. I. AIChE J. 2003, 49, 3229–3240. (18) Frese, C.; Ruppert, S.; Sugar, M.; Schmidt-Lewerkuehne, H.; Wittern, K. P.; Fainerman, V. B.; Eggers, R.; Miller, R. J. Colloid Interface Sci. 2004, 267, 475–482. (19) Nyrkova, I. A.; Semenov, A. N. Macromol. Theory Simul. 2005, 14, 569–585. (20) Colegate, D. M.; Bain, C. D. Phys. ReV. Lett. 2005, 95, 198302-1198302-4. (21) Song, Q.; Couzis, A.; Somasundaran, P.; Maldarelli, C. Colloids Surf. A 2006, 282-283, 162–182.
kinetics theory and the influence of micelles on the adsorption dynamics and dilational rheology were presented in recent reviews.22–26 When surfactant molecules adsorb at the interface, the concentration of monomers in the subsurface decreases and a concentration gradient of monomers results. Such a molecular distribution is not in local equilibrium with micelles in the bulk, which react and release single molecules (fast micellar kinetics) or even completely disintegrate (slow micellar dissolution), in order to re-establish the local equilibrium. This change in the local micelle concentration generates in turn a concentration gradient of micelles that initiates a diffusion process of micelles. Hence, the adsorption of surfactants at an interface generates a diffusion process of monomers and micelles and a disintegration of micelles. All these processes are directed toward the re-establishment of equilibrium for the whole system: locally in the bulk between monomers and micelles and close to the interface between monomers in the subsurface and at the interface. In rheological experiments, i.e., when the surface layer is periodically compressed and expanded around the equilibrium state, we also meet the situation that molecules desorb from the interface, increasing the local concentration of monomers such that micelles have to either take up molecules or form new micelles. In this case, diffusion fluxes of monomers and micelles from and to the interface exist, depending on the respective situation at the interface.1,6–8,14,23,24 New instrumentations for dilational rheology based on harmonic oscillations of drops or bubbles work in a broad frequency range and represent an excellent methodology to study the effect of micellar dynamics (22) Eastoe, J.; Dalton, J. S. AdV. Colloid Interface Sci. 2000, 85, 103–144. (23) Noskov, B. A.; Grigoriev, D. O.; Fainerman, V. B.; Mo¨bius, D.; Miller, R. (Eds.) Adsorption from micellar solutions. In SurfactantssChemistry, Interfacial Properties and Application, Studies in Interface Science; Elsevier: New York, 2001; Vol. 13, pp 402-510. (24) Noskov, B. A. AdV. Colloid Interface Sci. 2002, 95, 237–293. (25) Danov, K. D.; Kralchevsky, P. A.; Denkov, N. D.; Ananthapadmanabhan, K. P.; Lips, A. AdV. Colloid Interface Sci. 2006, 119, 1–16. (26) Danov, K. D.; Kralchevsky, P. A.; Denkov, N. D.; Ananthapadmanabhan, K. P.; Lips, A. AdV. Colloid Interface Sci. 2006, 119, 17–33.
10.1021/la704058y CCC: $40.75 2008 American Chemical Society Published on Web 06/03/2008
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on interfacial properties, such as the viscoelastic modulus and phase angle.27–32 In the present work, bubble and drop profile analysis tensiometry is used to study the dilational rheology of C14EO8 micellar solutions. The target is the evaluation of the models derived by Lucassen1 and Joos,14 respectively, for describing the rheological behavior of surface layers formed from micellar solution with various micelle dissolution mechanisms and the analysis of the mechanism valid for C14EO8 micelles. It is shown by comparison of experimental results with model calculations that there is a satisfactory agreement between our data and the theory of Joos.14
Experimental Section The experiments were performed with two different versions of a bubble/drop profile analysis tensiometer (PAT-1 and PAT-2P, SINTERFACE Technologies, Germany), the principle of which was described in much detail elsewhere.28,33,34 The temperature of the measuring glass cell (volume V ) 20 mL) was kept constant at 25 °C. In this study we used a buoyant (oblate) bubble formed at a Teflon capillary with a tip diameter of 3 mm. To study the dilational elasticity, after having reached the adsorption equilibrium, the buoyant (oblate) bubble was subjected to harmonic oscillations with frequencies between f ) 0.005 and 0.2 Hz. Due to the wetting behavior, the oscillating bubble arrangement provided more stable results as compared to oscillating drops. The substance studied was the oxyethylated surfactant C14ΕΟ8 (from Sigma Chemical), and it was used without further purification. The solutions were prepared using Milli-Q water.
Theory For premicellar solutions or for micellar solutions in which the disintegration of micelles does not take place, the dilational elasticity can be calculated from the expression (see refs 1, 6, 14, 35, 36)
ε(iω) ) ε0[1 + (1 - i)ζ]-1
(1)
where ζ ) (ωD/2ω), ε0 ) -dγ/d ln Γ is the limiting (high frequency) elasticity, Γ is the adsorption, γ is the surface tension, c is the bulk surfactant concentration, ωD ) D(dΓ/dc)-2 is the characteristic frequency for a diffusion relaxation, and ω ) 2πf is the angular frequency of the generated oscillation of area A at frequency f. The viscoelasticity ε(iω) is taken here as a complex number where the real part is called the storage modulus equal to the dilational elasticity, and the imaginary part is called the loss modulus, representing the dilational viscosity. Equation 1 can be transformed into expressions for the viscoelasticity modulus ε and phase angle φ between stress (dγ) and strain (dA): (27) Benjamins, J.; Cagna, A.; Lucassen-Reynders, E. H. Colloids Surf. A 1996, 114, 245. (28) Loglio, G.; Pandolfini, P.; Miller, R.; Makievski, A. V.; Ravera, F.; Ferrari, M.; Liggieri, L. Drop and bubble shape analysis as tool for dilational rheology studies of interfacial layers. In NoVel Methods To Study Interfacial Layers; Mo¨bius, D., Miller, R., Eds.; Elsevier, Amsterdam, 2001, pp 439-484. (29) Wantke, K. D.; Fruhner, H. J. Colloid Interface Sci. 2001, 237, 185–199. ¨ rtegren, J.; Wantke, K. D.; Motschmann, H. ReV. Sci. Instrum. 2003, (30) O 74, 5167–5172. (31) Ravera, F.; Ferrari, M.; Liggieri, L. Colloids Surf. A 2006, 282-283, 210–216. (32) Benjamins, J.; Lyklema, H.; Lucassen-Reynders, E. H. Langmuir 2006, 22, 6181–6188. (33) Fainerman, V. B. Zholob, S. A. Petkov, J. T. Miller, R. Colloids Surf. A 2008, in press. ¨ FW (Engl. Version) 2004, 2–10. (34) Miller, R.; Olak, C.; Makievski, A. V. SO (35) Lucassen, J.; van den Tempel, M. Chem. Eng. Sci. 1972, 27, 1283. (36) Lucassen, J.; Hansen, R. S. J. Colloid Interface Sci. 1967, 23, 319.
|ε| ) ε0(1 + 2ζ + 2ζ2)-1/2 φ ) arctan[ζ/(1 + ζ)]
(2)
The theoretical equations for the modulus ε(iω) for various micelle dissociation mechanisms were derived in refs 1, 6– 8, 14, 23, 24. In the present study, a very simple expression is used, obtained by assuming fast micellar kinetics under the condition that the constant of fast micelle dissociation kf is very large (kff∞, see eq 10.57 in ref 14): -1
ε(iω) ) ε0[1 + (1 - i)ζ√(1 + β)(1 + Rβ) ]
(3)
where β ) (c0 - ck)/ck, R ) Dm/D ≈ 0.25, ck ) cmc, c0 is the total surfactant concentration, and D and Dm are the diffusion coefficients of surfactant monomers and micelles, respectively. From a formal point of view, eq 3 is identical to eqs 1 and 2, provided that the diffusion coefficient D for monomers is replaced by the so-called effective diffusion coefficient of monomers D*, as proposed by Joos:6,14
D* ) D(1 + β)(1 + Rβ)
(4)
In ref 1, rheological equations for the slow process of micelle dissociation were derived (complete micelle dissolution). Under the condition ksf∞, they have the same form like eqs 3 and 4; however, instead of β they contain the parameter mβ, with m being the micelle aggregation number. It was shown by Danov et al.26 that eq 4 describes the diffusion processes in micellar solutions for a time range exceeding the time of fast micelle dissociation. At the same time eq 4 with the parameter mβ instead of β can be used in a time range significantly longer than the time of the slow micelle dissolution process, as demonstrated in ref 26. Thus, for the description of the dilatational viscoelasticity modulus of micellar solutions eq 2 can be used. In this case, we have to assume that c0 ) cmc for c0 > cmc, and instead of D we use an effective diffusion coefficient D* for the monomers, as given by eq 4. The limiting elasticity ε0 ) -dγ/d ln Γ and the derivative dΓ/dc which enter eqs 1 and 2 can be determined from the equation of state and adsorption isotherm at c ) cmc. Therefore, it is very important to describe this isotherm accurately close to the cmc. It was shown recently that the whole set of experimental data available for C14EO8 solutions up to the cmc, including dynamic and equilibrium surface tension, adsorption values, and dilational rheology, is described in the best possible way by a combined reorientation/compression model.33 This model assumes the ability of the oxyethylene group to be adsorbed at the solution/ air interface at low surface coverage and to be partially desorbed with increasing surface pressure, leading to a reorientation of the EO groups. In addition, the model accounts for the internal compressibility of the monomolecular interfacial layer in the state of minimum molar area, realized, for example, by a change in the tilt of the hydrocarbon chains. The reorientation model was described in detail elsewhere,33,37,38 and assumes that two orientations of adsorbed (37) Fainerman, V. B.; Kovalchuk, V. I.; Aksenenko, E. V.; Michel, M.; Leser, M. E.; Miller, R. J. Phys. Chem. 2004, 108, 13700–13705. (38) Kovalchuk, V. I.; Miller, R.; Fainerman, V. B.; Loglio, G. AdV. Colloid Interface Sci. 2005, 114-115, 303–313. (39) Lin, S. Y.; Lee, Y. C.; Shao, M. J.; Hsu, C. T. J. Colloid Interface Sci. 2003, 244, 372. (40) Lee, Y. C.; Stebe, K. J.; Liu, H. S.; Lin, S. Y. Colloids Surf. A 2003, 220, 139–150. (41) Zholob, S. A.; Makievski, A. V.; Miller, R.; Fainerman, V. B. AdV. Colloid Interface Sci. 2007, 134-135, 322–329. (42) Access to software packages is free of charge via http://www.sinterface.com or http://www.mpikg.mpg.de/gf/miller/. (43) Miller, R.; Fainerman, V. B.; Mo¨hwald, H. Surf. Detergents 2002, 5, 281–286.
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surfactant molecule coexist at the surface, with different molar areas ω1 and ω2 (for definiteness we assume ω1 > ω2). Assuming ideal enthalpy and entropy of mixing of the surface layer, the equations of state and adsorption isotherm read37,38
Π)b2c )
RT ln(1 - θ) ωS
(5)
Γ2ωS
(6)
(1 - θ)ω2/ωS
where Π ) γ0 - γ is the surface pressure, R is the gas law constant, T is the temperature, θ ) ωSΓ is the surface coverage, γ0 is the surface tension of the solvent (water/air surface tension), and b2 is the adsorption equilibrium constant in state 2. The total adsorption Γ and mean molar area ωS are defined by
Γ ) Γ1 + Γ2
(7)
ωSΓ ) θ ) ω1Γ1 + ω2Γ2
(8)
and the ratio of adsorptions in the two possible states of the adsorbed molecules is given by
(
Γ1 ω1 - ω2 ) exp Γ2 ωS
)( ) [
Π(ω1 - ω2) ω1 R exp ω2 RT
]
(9)
The constant R accounts for the fact that the adsorption equilibrium constant for surfactant molecules adsorbed in state 1 (with larger area) can exceed that in state 2, which results in an additional (as compared to R ) 0) increase of the fraction of states of larger area. For R ) 0, the adsorption activities b1 and b2 are identical. The combined reorientation/compression model assumes the variation of the molar area caused by a two-dimensional compressibility in state 2 with lower area according to the equation33
ω2 ) ω20(1 - κΠ)
(10)
where the proportionality factor κ is the relative two-dimensional compressibility coefficient of the surfactant surface layer, and ω20 is the molar area of the surfactant at Π ) 0.
Results and Discussion The equilibrium surface tensions of C14EO8 solutions obtained from the emerging (prolate) bubble profile techniques in ref 33
are shown in Figure 1, together with values obtained in the present study mainly for micellar solutions using the buoyant (oblate) bubble method. It should be noted that equilibrium surface tensions as shown in Figure 1 were measured for C14EO8 using the emerging and buoyant bubble methods and are quite consistent with those reported in the literature.39,40 The theoretical surface tension isotherm shown in Figure 1 was calculated using eqs 5–10 with parameters given in ref 33: ω1 ) 1.0 × 106 m2/mol, ω2 ) 4.4 × 105 m2/mol, R ) 0.9, b2 ) 1.0 × 105 m3/mol, and κ ) 0.009 m/mN. It follows from Figure 1 that the cmc for C14EO8 is 7 µmol/L. The dilational rheology of C14EO8 adsorption layers for various concentrations was studied using the oscillating buoyant (oblate) bubble method at frequencies between 0.005 and 0.2 Hz and a magnitude ∆A of area oscillations of 5%. The details of the calculation procedure employed in the PAT tensiometer is explained elsewhere.41 As an example, the time dependence of surface tension γ(t) and bubble surface area A(t) during harmonic oscillations at a frequency of 0.05 Hz and magnitude 5% for a 50 µmol/L C14EO8 solution is shown in Figure 2. The results demonstrate the high quality of the experimental techniques based on buoyant (oblate) bubble profile analysis. The oscillation experiments were performed after the adsorption equilibrium was established and the results analyzed by a Fourier transformation:28
ε(iω) ) A0
F[∆γ] F[∆A]
(11)
where A0 is the initial area of the bubble surface. For the example shown in Figure 2, the viscoelasticity modulus |ε| and phase angle φ are 15.2 mN/m and 46.8°, respectively. The experimental dependencies of the viscoelasticity modulus |ε| as a function of frequency f for various C14ΕΟ8 concentrations below the cmc (c0 ) 5 µmol/L), at cmc ) 7 µmol/L, and slightly above the cmc are presented in Figure 3. With increasing micellar surfactant concentration, the viscoelasticity modulus becomes lower, caused by the essential influence of micelle dynamics on the diffusion-controlled exchange of monomers between the solution bulk and the surface layer. The theoretical curves shown in Figure 3 for c0 ) 5 µmol/L to c0 ) cmc were calculated from eq 2 using the program IsoFit.42 The obtained diffusion coefficient of monomers of 4 × 10-10 m2/s is in
Figure 1. Equilibrium surface tension isotherms of C14EO8 solutions measured by emerging bubble (0) and buoyant bubble methods (2), respectively. The curve was calculated from eqs 5–10.
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Figure 2. Time dependence of surface tension (black points) and bubble surface area (light points) during harmonic oscillations at a frequency of 0.05 Hz and a concentration of C14EO8 of 50 µmol/L.
Figure 3. Viscoelasticity module |ε| as a function of frequency f for various C14ΕΟ8 concentrations below the cmc (5 µmol/L, ]), at cmc ) 7 µmol/L (0), and above the cmc at 12 (2), 15 ([), 20 (4), and 30 µmol/L (9). Thin and thick dotted lines were calculated according to eq 2 for the cmc and 5 µmol/L, respectively; thin solid lines are calculated for c0 > cmc according to eq 3; dotted lines are calculated from eq 3 with the parameter mβ instead of β (m ) 50); the numbers correspond to concentrations given in µmol/L.
agreement with data discussed in refs 43, 44. The theoretical curves in Figure 3 for c0 > cmc were calculated according to eq 3, leading to an excellent agreement with the experimentally determined viscoelasticity modulus. At the same time, calculations from eq 3 with mβ instead of β at m ) 501,26 (shown in Figure 3 as well) give much lower values for the viscoelasticity modulus. In agreement with Danov’s theory,26 this means that in the studied frequency range, the C14EO8 micelles are subject to fast micellar kinetics with the release of single monomers, while for a slow complete micelle disintegration a possibly much lower frequency of area oscillations would be required. In Figure 4 the viscoelasticity modulus |ε| is shown as a function of frequency f for C14EO8 concentrations from 50 to 500 µmol/ L, which corresponds to 7 × cmc up to 70 × cmc. For comparison, (44) Fainerman, V. B.; Mys, V. D.; Makievski, A. V.; Petkov, J. T.; Miller, R. J. Colloid Interface Sci. 2006, 302, 40–46.
the data for a solution at cmc ) 7 µmol/L are also shown. The theoretical dependencies calculated using eq 3 agree well with the experimental data at all studied frequencies, even at the highest concentration of 500 µmol/L. This agreement indicates not only the suitability of the used model but also the high quality of rheological experiments performed using the buoyant (oblate) bubble method. Note, a modulus |ε| value of 1.0 mN/m (concentration 500 µmol/L, frequency 0.01 Hz and less) at bubble area variations of 5% corresponds to surface tension oscillations of 0.05 mN/m. The experimental error in the determination of |ε| at values aroud 1.0 mN/m does not exceed 50%, if compared with theoretical values. Hence, the error due to the dependence of surface tension on surface area28 cannot exceed 0.025 mN/m and cannot be higher than 0.1 mN/m for a bubble area variation of 20%. The experiments performed by the buoyant (oblate) bubble method have in fact shown that 20% variations in the
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Figure 4. Viscoelasticity module |ε| as a function of frequency f for various C14ΕΟ8 concentrations above the cmc [50-500 µmol/L corresponding to (7-70) × cmc] at 50 (9), 70 (]), 100 ([), 200 (2), and 500 µmol/L (∆). The thick line was calculated from eq 2 for c0 ) cmc (0); the thin lines were calculated for c0 > cmc according to eq 3. The numbers correspond to concentrations given in µmol/L.
Figure 5. Phase angle φ as a function of frequency f for C14ΕΟ8 concentrations below cmc (5 µmol/L, [), at the cmc ) 7 µmol/L (0), and above the cmc at 12 (2), 15 ([), 20 (4), and 30 µmol/L (9). Theoretical curves for concentrations below 5 µmol/L (thin dotted line) and at cmc ) 7 µmol/L (thick line) calculated from eq 2 with D ) 4 × 10-10 m2/s; thin solid lines are calculated for c0 > cmc according to eq 3. The numbers correspond to concentrations given in µmol/L.
bubble area at equilibrium leads to a surface tension variation of less than 0.1 mN/m. The dependences of the phase angle φ on frequency f for the same concentrations of C14ΕΟ8 as in Figure 3 are presented in Figure 5. With increasing concentration, the phase angle φ increases up to a value of 50°, as shown in Figure 5. The theoretical dependence φ, as calculated from eq 3, predicts a maximum phase angle of 45°, in good agreement with experimental data at c0 < 2 × cmc, while at c0 > 2 × cmc the theoretical values of the phase angle are less than those from the experiment. There can be several reasons for this phase angle behavior. First, the condition kff∞ may no longer hold when the micelle concentration is increased, in agreement with the theoretical equation by Joos (see eq 10.54 in ref 14). Hence the phase angle can significantly increase (up to 90°) due to the additional relaxation process of fast micelle dissociation. Note, according to the theory presented in ref 1, there is a similar effect for the slow process of micelle
dissolution when the condition ksf∞ is not fulfilled. Second, the increase in the diffusion coefficient (especially when using an effective diffusion coefficient D*, which according to eq 3 could by increased by several orders of magnitude for c0 . cmc) could significantly influence the phase angle for oscillations of a spherical meniscus. According to the theory by Joos (see eq 8.63 in ref 14) the phase angle at low frequencies of bubble area oscillation and high diffusion coefficients can rise up to 90°. Finally, it is impossible to eliminate the influence of experimental errors (note, in particular, the above-mentioned dependence of surface tension on the bubble size), which have a relatively weak impact on the elasticity module but influence much more strongly the phase angle. For these reasons, the phase angles at large concentrations of C14EO8 micellar solutions (above 100 µmol/ L) and low frequencies can reach values of 90°-100°. Any phase angle above 90° is without physical sense, as it would correspond to a negative surface viscosity. However, at such high phase angles, their experimental determination is rather inaccurate,
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due to the very small surface tension amplitudes, so any values beyond a physical sense have to be disregarded.
Conclusions Using the surfactant C14EO8 we demonstrate how the effect of micellar kinetics on the dilatational rheological properties of adsorption layers can be experimentally studied. The experimental dependences of viscoelasticity modulus and phase angle as a function of frequency for various C14ΕΟ8 concentrations at cmc ) 7 µmol/L and far above the cmc (up to 500 µmol/L corresponding to 70 × cmc) were studied using the buoyant (oblate) bubble profile method. It is shown that the increase in C14EO8 concentration leads to a decrease of the viscoelasticity modulus and an increase in the phase angle. For the theoretical description of the C14EO8 solutions’ equilibrium surface tension isotherm and limiting (highfrequency) elasticity modulus, the so-called combined reori-
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entation/compression model33,37 was successfully applied. To analyze the experimental dependencies of the viscoelasticity modulus on frequency, the theoretical model proposed by Joos14 for fast micellar kinetics was employed. This model is based on the assumption that the equilibrium between micelles and monomers exist and involves the so-called effective diffusion coefficient of monomers. It is shown that the theory agrees well with the experimental values of viscoelasticity modulus for all the C14EO8 concentrations studied. Acknowledgment. The work was financially supported by a project of the European Space Agency (FASES MAP AO-99052) and the DFG SPP 1273 (Mi418/14-1).
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