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Anomalous Damping of Capillary Waves in Systems with Insoluble Monolayers of Alkyldimethylphosphine Oxides B. A. Noskov,† D. O. Grigoriev,† and R. Miller*,‡ Institute of Chemistry, St. Petersburg State University, Universitetskiy pr. 2, 1989084 St. Petersburg, Petrodvoretz, Russia, and Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489, Berlin-Adlershof, Germany Received April 24, 1996. In Final Form: September 4, 1996X Anomalously high damping of capillary waves has been discovered for systems with insoluble surface films of N-alkyldimethylphosphine oxides in the transition region from a heterogeneous to a continuous monolayer. This effect is probably caused by capillary wave scattering at two-dimensional cavities of a gaseous phase in the condensed monolayer phase (two-dimensional bubbles).
Introduction It is well-established nowadays that the damping of capillary and capillary-gravity waves (ripples) plays a key role in the dissipation of energy of the sea surface. Thereby a strong influence of insoluble surface films, of natural or human origin, on interactions between the ocean and the atmosphere can be explained.1 On the other hand, capillary waves can be successfully applied to investigate dynamic properties and the structure of insoluble monolayers on liquid subphases. In early works capillary wave propagation along a homogeneous surface had usually been considered,2-4 now a lot of attention is paid to heterogeneous surface films.5-14 Recently it has been shown that measurements of capillary wave properties allow information to be obtained about the macroscopic film structure which has been obtained before only by optical methods.6-11 Characteristics of capillary waves are sufficiently sensitive to surface viscoelastic properties only at not too large values of the modulus of dynamic surface elasticity (|| e 20 mN/m). Thus the main attention was paid to capillary wave investigation in the coexistence region of a gaseous phase and more densely packed two-dimensional phase where the static surface elasticity is close to zero.611,14,15 If the denser phase is liquid-condensed, the results of different authors qualitatively agree. The behavior of †
St. Petersburg State University. Max-Planck-Institut fu¨r Kolloid- und Grenzfla¨chenforschung. X Abstract published in Advance ACS Abstracts, December 15, 1996. ‡
(1) Alpers, W.; Hu¨hnerfuss, H. J. Geophys. Res. 1989, 94, 6251. (2) Lucassen-Reynders, E. H.; Lucassen, J. Adv. Colloid Interface Sci. 1969, 2, 347. (3) Hansen, R. S.; Ahmad, J. In Progress in Surface and Membrane Science; Danielli, J. F.; Rosenberg, M. D.; Cadenhead, D. A., Eds.; Academic Press: New York, 1971; Vol. 4. (4) Miyano, K. In Light Scattering by Liquid Surfaces and Complementary Techniques; Langevin, D., Ed.; Marcel Dekker: New York, 1992. (5) Noskov, B. A. Izv. AN SSSR, Ser. MZhG 1991, 1, 138. (6) Miyano, K.; Tamada, K. Lamgmuir 1992, 8, 160. (7) Miyano, K.; Tamada, K. Langmuir 1993, 9, 508. (8) Tamada, K.; Miyano, K. Jpn. J. Appl. Phys. 1994, 33, 5012. (9) Lee, K. Y.; Chou, T.; Chung, D. S.; Mazur, E. J. Phys. Chem. 1993, 97, 12876. (10) Wang, Q.; Feder. A.; Mazur, E. J. Phys. Chem. 1994, 98, 12720. (11) Sakai, K.; Takagi, K. Langmuir 1994, 10, 802. (12) Chou, T.; Nelson, D. R. J. Chem. Phys. 1994, 101, 9022. (13) Chou, T.; Lucas, S. K.; Stone, H. A. Phys. Fluids 1995, 7, 1872. (14) Noskov, B. A.; Zubkova, T. U. J. Colloid Interface Sci. 1995, 170, 1. (15) Kretzschmar, G.; Li, J. B.; Miller, R.; Motschmann, H.; Mo¨hwald, H. Colloids Surf., A 1996, 114, 277.
the system changes abruptly when separate “islands” of a condensed phase form an immobile rigid structure.7,8,14,15 However, completely different results were obtained for the case of coexistence of a gaseous with a liquid-expanded phase. Miyano and Tamada discovered that capillary waves do not “see” the liquid-expanded phase up to exactly the moment when it forms a continuous homogeneous film.6,8 Lee et al. observed a gradual increase in the damping coefficient with increase of the fraction of the liquid-expanded phase.9 Moreover in ref 14 no significant changes have been observed when a liquid-condensed phase was replaced by a liquid-expanded phase. This work is a continuation of capillary wave studies of heterogeneous monolayers consisting of coexisting liquid-expanded and gaseous two-dimensional phases. Such systems can be obtained with octadecyldimethylphosphine oxide (ODPO) and eicosyldimethylphosphine oxides (EDPO) when spread on an aqueous substrate. At room temperature these substances form very stable liquid-expanded films which turn to gaseous films at zero surface pressure. Materials and Method The damping coefficient of capillary waves has been measured using a capacity wave probe. The time scale for data acquisition from the capacity sensor is between 1 s due to the inertia of the system and 10 min for transient changes. For some values of the area per molecule in the monolayer, the measurements lasted several hours to examine possible slow fluctuations of the signal. The design of the experimental setup and the experimental procedure were described in detail elsewhere.14,16,17 All measurements were performed at a frequency of 520 Hz. The surface tension was measured by the Wilhelmy technique using a roughened platinum plate. The Langmuir trough with the size of 380 mm × 140 mm × 15 mm was made of silica, and the brims were hydrophobized by purified paraffin to diminish wetting. The monolayers were spread with the help of a Hamilton microsyringe. All the measurements were carried out at 20 ( 0.5 °C. ODPO and EDPO were purchased from Gamma-Service Dr. Schano, Berlin, Germany, with a purity necessary for interfacial studies and used as received. Solutions of these substances in benzene with a concentration of 0.001 mol/L were used for spreading the monolayers. The solvent was purified beforehand by rectification. The subphase was doubly distilled water. The second distillation was carried out from a potassium permanganate solution in a Pyrex apparatus. (16) Noskov, B. A.; Vasyliev, A. A. Kolloidn. Zh. 1988, 50, 909. (17) Noskov, B. A.; Grigoriev, D. O. Prog. Colloid. Polym. Sci. 1994, 97, 1.
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Figure 1. Surface pressure isotherm of a EDPO monolayer.
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Figure 3. Dependency of the damping coefficient of capillary waves on the area per molecules for monolayers of EDPO. The results of different series of measurements are designated by different symbols. The broken line represents the results of calculations according to relations 1 and 2.
Figure 2. Surface pressure isotherm of a ODPO monolayer.
Results and Discussion Figures 1 and 2 show the dependencies of the surface pressure Π of ODPO and EDPO monolayers on the area per molecule A. The surface pressure isotherm of EDPO monolayers displays a kink at A ) 0.35 nm2 per molecule that probably corresponds to a phase transition between liquid expanded and condensed films. No peculiarities of the surface pressure isotherm of ODPO monolayers have been observed, and the region corresponding to the liquidexpanded two-dimensional phase extends up to the collapse of the film at A = 0.35 nm2 per molecule. At compression the surface pressure of monolayers of both substances begins to rise from zero very smoothly and the curves in Figures 1 and 2 do not allow determination of the moment where a continuous liquid-expanded film is formed. However, the region A > 1.0 nm2 apparently corresponds to the coexistence of liquid expanded and gaseous two-dimensional phases. The isotherms of the damping coefficient of capillary waves R for monolayers of both substances are rather close to each other (Figures 3 and 4), but on the other hand they significantly differ from the corresponding isotherms for monolayers of fatty acids.14 In the region of low surface
Figure 4. Dependency of the damping coefficient of capillary waves on the area per molecules for monolayers of ODPO. The results of different series of measurements are designated by different symbols. The broken line represents the results of calculations according to relations 1 and 2.
concentrations the damping coefficient increases slowly at compression, after then at areas close to 1.0 nm2 per molecule the fast rise of the damping can be observed and at A ) 0.9 nm2 per molecule for EDPO monolayers and at A ) 0.85 nm2 per molecule for ODPO monolayers the absolute maximum of the damping is reached. After the maximum, the damping coefficient decreases, goes through a local minimum, and begins to increases again close to the collapse point. The last region of the isotherm (after the maximum) corresponds to high values of the modulus of dynamic surface elasticity (|| > 20 mN/m). In this case the shape of R versus A curve is not sensitive to surface rheological properties, is determined at first by the surface pressure, and is similar for all investigated monolayers.9,14 However, in the region of low surface concentrations different monolayers lead to completely different results. Unlike the monolayers of dyes6 and polymers8 studied by
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Miyano and Tamada, the heterogeneous films of alkyl dimethyl phosphine oxides damp capillary waves remarkably, even at A ) 2.5 nm2 per molecule when the damping coefficient is about one and a half times higher than the value for pure water (0.52 mm-1). At the same time no large fluctuations of the damping coefficient were observed in the whole region of surface concentrations for all monolayers investigated in this work. Unlike the monolayers of fatty acids investigated earlier,14 for the monolayer under study here no deviation of R from an average curve exceeds the limits of experimental accuracy ((3%) and no transition to a continuous film induced by an abrupt decrease of the amplitude of stochastic fluctuations of the electrical signal could be obtained. On the other hand at low surface concentrations the distinction between different measurements exceeds the usual error limits (Figures 3 and 4), which is probably caused by the effect of the spreading conditions on the monolayer structure. The obtained dependency R versus A can be explained if one assumes the heterogeneous film of alkyldimethyl phosphine oxides is a two-dimensional foam.6,18 In this case the equilibrium surface elasticity modulus of the whole monolayer equals to zero in the region P = 0 while the dynamic surface elasticity of some parts of the film can deviate from zero, thus leading to increased values of the damping coefficient. A transition from a foamlike to a two-dimensional gas emulsion on compression can be accompanied by an increase in the dynamic surface elasticity and, consequently, in the quantity R. However, the most important peculiarity of the experimental data can be discovered when only comparing the calculated R versus A dependency according to the dispersion equation for capillary waves4 2
3
2
2
3
(K/k)2 ) [1 - 2 inf(0)/k2]2 - [2 inf(π)/k2]2
(3)
where λ is the wavelength, Qs is the full scattering cross section, n is the surface concentration of scatterers, and f(ϑ) is the scattering amplitude which depends on the scattering angle ϑ and can be presented as a series
f(ϑ) )
∑(-i)-Ai cos jϑ
(4)
3
(Fω - σk - Fgk)(Fω - mk ) - k (σk + Fgk) + 4iFµω3k2 + 4µ2ω2k3 (m - k) ) 0 (1) Here F is the liquid density, µ is the bulk liquid shear viscosity, g is the gravitational acceleration, σ is the surface tension, ω is the angular frequency, is the complex longitudinal dynamic surface elasticity, k ) 2π/λ + iR, λ is the wavelength, m2 ) k2 - iωF/µ, and Re[m] > 0. In these calculations the values of F and µ for water were used and the quantity replaced by the surface elasticity modulus ˜ , which was determined according to the following equation
˜ ) -∂Π/∂ ln A
transverse surface viscosity (at low frequencies) has to be ruled out. Therefore the discovered deviation of experimental curves from the calculated R-values cannot be explained by the theory developed for homogeneous surface films, and one is compelled to take into account the heterogeneity of the monolayer. If a surface film is heterogeneous, a new mechanism of dissipation of capillary wave energy evolves: localized gradients of the surface properties may induce scattering of waves. Theories of surface wave scattering were developed recently.5,12,13,19 In the work of ref 5, general boundary conditions at the interface were considered. However, some assumptions related to the state of the liquid flow in the bulk phase were made. Chou and Nelson12 solved the same problem for the general liquid flow but using the Born approximation only (small fluctuations of the surface properties). Chou, Lucas, and Stone13 presented some numerical results for a particular case of the homogeneous surface elasticity. If the surface film can be presented as a two-dimensional colloidal system consisting of monosized two-dimensional particles and the scattering is weak (nQs/k , 1), the complex wavenumber k ) 2π/λ + iR has to be replaced by the effective quantity K19
(2)
The results of calculations for both investigated monolayers given as broken lines in Figures 3 and 4 are significantly lower than the experimentally obtained values in the region of the maximum in R. For fatty acid monolayers the situation was opposite.14 To reach an agreement between experimental and theoretical curves a dilational surface viscosity was assumed as an additional free parameter.14 For monolayers of alkyldimethylphosphine oxides the additional consideration of a dynamic surface elasticity with a nonzero imaginary part would lead to an even higher discrepancy. Moreover, the maximum in the calculated R value does not depend on the shape of surface pressure isotherm (if the maximum damping corresponds to surface pressures close to zero) and the largest damping coefficient is expected for a homogeneous film due to eq 1. In this case any influence of such properties as the surface shear elasticity and the (18) Moore, B.; Knobler, C. M.; Broseta, D.; Rondelez, F. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1753.
where Aj values are constant coefficients. For small circular scatterers (λ . a) it is possible to consider only the first two terms5
[
(
)]( )
iπa2 k0σ0 - k2σ k3 1- 0 4 σ m - χ/2a
A0 = -
A1 =
πk2a2 σ2 - σ 2 σ0 + σ
1-
k m (5) (6)
where a is the diameter of the scatterer, χ is the line tension of the boundary between a two-dimensional particle and the dispersion medium, the superscript zero indicates the scattering particle. Note that eq 3 takes into account the effects of multiple scattering and can be used for concentrated two-dimensional colloidal systems. The obtained equations allow us to estimate the effective damping coefficient if the parameters of the scatterers are known.19 For equilibrium liquid-expanded films, fluctuations of the surface tension cannot be large (∂σ/σ , 1) and consequently cannot lead to significant effects.5,9 Although the fluctuations of the surface elasticity modulus can be significant (|∂/| = 1), the transverse surface waves are scattered by inhomogeneities of the surface elasticity only slightly.5 A special situation arises only when capillary waves are scattered by two-dimensional cavities filled with a gaseous phase and surrounded by a more densely packed two-dimensional phase (two-dimensional bubbles).18 In this case the scattered wave contains a significant longitudinal component that leads to a sharp increase in the dissipation (19) Noskov, B. A. Kolloidn. Zh. 1996, 58, 62.
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of the surface wave energy. In other cases, the approximation given by eqs 5 and 6 becomes insufficient, and more complicated equations must be applied.5,19 The lack of information about the macroscopic structure of a film under study does not allow at present a quantitative comparison with the theory. It is important, however, that the excess damping is discovered just in the region where the theory predicts it, i.e., close to the transition from a heterogeneous to a continuous liquid-expanded
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film. A simultaneous optical and capillary wave study of these insoluble monolayers is in progress now. Acknowledgment. This work was financially supported by the European Union (INTAS 93-2463). D. O. Grigoriev is grateful for a special grant for young researchers and a grant from the DAAD (A/96/28713). LA9604083
