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Foam Films Stabilized with Dodecyl Maltoside. 2. Film Stability and Gas Permeability RM Muruganathan,† R. Krastev,* H.-J. Mu¨ller, and H. Mo¨hwald Max-Planck Institute of Colloids and Interfaces, Am Mu¨hlenberg 1, Golm/Potsdam, 14476 Germany ReceiVed February 7, 2006. In Final Form: July 10, 2006 The gas permeability and stability of foam films stabilized by n-dodecyl-β-D-maltoside (β-C12G2) were determined. The permeability coefficient (K, cm/s) and the mean film lifetime were measured as a function of the surfactant concentration. The films are less permeable than those stabilized by other surfactants at comparable conditions. The permeability coefficient decreases with increasing surfactant concentration. It does not show a remarkable dependence on the salt concentration. Stable Newton black foam films (NBFs) are formed above a surfactant concentration of 3.9 × 10-6 M β-C12G2 in the presence of 0.2 M NaCl. The theory of nucleation hole formation in NBFs was applied to describe the observed dependencies of the permeability and film stability on the surfactant concentration. The theory gave satisfactory relation to the experiment.
Introduction surfactants1
Sugar-based “natural” are gaining growing environmental awareness. They are of low toxicity, biodegradable, and are widely used in protein solubilization and membrane studies.1,2 Foams are important in daily life and technology. Many of the properties of the foams depend on the properties of the thin liquid lamellae, which separate the foam bubbles, that is, the foam films.3,4 Series of works on thin liquid films stabilized with sugar-based surfactants have been published dealing mainly with glucoside (one sugar ring) surfactant.5-10 n-Dodecyl-β-Dmaltoside (β-C12G2) is a sugar-based nonionic surfactant. Its hydrophilic headgroup consists of two sugar rings connected via an ether bond. Precise disjoining pressure/thickness measurements using the thin film pressure balance technique on foam films stabilized by β-C12G2 have been reported recently by Stubenrauch et al.10 In a previous paper,11 we also reported on some basic properties of β-C12G2-stabilized foam films. The present work summarizes results on the permeability and stability of foam films stabilized by the same surfactant. Many studies have been performed to investigate foam stability in short and long time periods.3,4 Short-term stability is governed by the dynamics of foam formation and drainage of the films, * Corresponding author. Tel: ++49(0)331 567 9232. E-mail:
[email protected]. † Present address: Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, FL 32306. (1) Holmberg, K. Curr. Opin. Colloid Interface Sci. 2001, 6, 148. Hill, K. V.; von Rybinski, W.; Stoll, G. Alkyl Polyglycosides; VCH: Weinheim, Germany, 1997. (2) Lopez, O.; Cocera, M.; Parra, J. L.; de la Maza, A. Colloid Polym. Sci. 2001, 279, 909. (3) Exerowa, D.; Kruglyakov, P. Foam and Foam Films; Elsevier: Amsterdam, 1998. (4) Prud’homme R.; Kahn, S. Foams; Marcel Dekker: New York, 1996. (5) Waltermo, A.; Claesson, P. M.; Simonsson, S.; Manev, E.; Johansson, I.; Bergeron, V. J. Colloid Interface Sci. 1996, 183, 506. (6) Bergeron, V.; Waltermo, A.; Claesson, P. M. Langmuir 1996, 12, 1336. (7) Waltermo, A.; Claesson, P. M.; Simonsson, S.; Manev, E.; Johansson, I.; Bergeron, V. Langmuir 1996, 12, 5271. (8) Waltermo, A.; Manev, E.; Pugh, R.; Claesson, P. M. J. Dispersion Sci. Technol. 2001, 15, 273. (9) Liljekvist, P.; Kjellin, M.; Eriksson, J. C. AdV. Colloid Interface Sci. 2001, 89-90, 293. (10) Stubenrauch, C.; Schlarmann, J.; Strey, R. Phys. Chem. Chem. Phys. 2002, 4, 4504. (11) Muruganathan, RM.; Krustev, R.; Mu¨ller, H.-J.; Kolaric, B.; Klitzing, R. v.; Mo¨hwald, H. Langmuir 2004, 20, 6352.
while long-term stability depends on the properties of the equilibrium foam films. The rupture of the films leads to the coalescence of the bubbles. The transfer of the gas between the bubbles (Ostwald ripening) is another factor that influences the foam stability. Despite a host of investigations of foam films, measurements of the gas permeability are relatively rare. The first measurements of the gas permeability of the foam films were performed in the middle of the 20th century.12,13 Detailed investigations of the basic relations between the gas permeability of the foam films and the thermodynamic parameters of the system have been performed over the past 20 years. The influence of the film thickness, the surfactant adsorption density, the surfactant chain length, and the temperature on the gas permeability of the foam films have been reported.14-16 Recently, it was shown17 that measurements of the gas permeability of the foam films also deliver valuable information about the structure and the interactions in the thin layers, where the surface forces are operative. The foam films consist of an aqueous core with thickness h2 covered on both sides with a monolayer of adsorbed surfactant molecules with thickness h1.3,18,19 Equilibrium foam films with a uniform thickness are easily obtained from solutions of surfactants. If the surfaces are charged, the diffuse electrostatic double layers on both surfaces cause repulsion, and common black films (CBFs) are formed at the end of the draining process at low concentrations of electrolytes. Their thickness varies from a few nanometers to hundreds of nanometers and decreases with the addition of electrolytes. At high concentrations of electrolyte, the diffuse electrical double layers are suppressed, and very thin Newton black foam films (NBFs) are formed. They essentially consist of only two surfactant monolayers and form a bilayer. For a review of the properties of the foam films, see refs 3, 4, 18, and 19. (12) Brown, A. G.; Thuman, W. C.; McBain, J. W. J. Colloid Sci. 1953, 8, 508. (13) Princen, H. M.; Mason, S. G. J. Colloid Interface Sci. 1965, 20, 353. (14) Nedyalkov, M.; Krustev, R.; Kashchiev, D.; Platikanov, D.; Exerowa, D. Colloid Polym. Sci. 1988, 266, 291. (15) Nedyalkov, M.; Krustev, R.; Stankova, A.; Platikanov, D. Langmuir 1992, 8, 3142. (16) Krustev, R.; Platikanov, D.; Stankova, A.; Nedyalkov, M. J. Dispersion Sci. Technol. 1997, 18, 789. (17) Krustev, R.; Mu¨ller, H.-J. Langmuir 1999, 15, 2134. (18) Sheludko, A. AdV. Colloid Interface Sci. 1967, 1, 391. (19) Ivanov, I. B., Ed. Thin Liquid Films; Marcel Dekker: New York, 1988.
10.1021/la0603673 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/05/2006
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A measure of the gas permeability of a foam film is the permeability coefficient K (cm/s)12,13,20 defined by
dN ) -KS∆Cg dt
(1)
Here, N is the number of moles of gas that permeate through the film, t is the time, S is the area of the film, and ∆Cg is the concentration difference of the gas on both sides of the film. Taking the film structure into account, a detailed expression for the permeability was proposed by Princen et al.:13
K)
D wH h2 + 2Dw/kml
(2)
Here, Dw is the diffusion coefficient of the gas in the aqueous core of the film, H is the Ostwald coefficient of the solubility of the gas in the aqueous solution, and kml is the permeability coefficient of a single surfactant monolayer. The film aqueous core thickness h2 . 2Dw/kml for thick films, and the permeability is characterized by the transport properties of the gas through the aqueous core. The film permeability increases with decreasing film thickness, whereas the thickness of the monolayers remains constant in this regime. If h2 < 2Dw/kml, the gas permeability is governed by the permeability of the adsorbed monolayers by kml. Different mechanisms for the permeation through surfactant monolayers and their advantages to explain the foam film permeability are proposed in the literature.16,20-23 Only a limited number of surfactants have been used in the investigation of the gas permeability of foam films so far. The present work shows results on the gas permeability of foam films stabilized by β-C12G2. The dependencies of the gas permeability on the surfactant concentration, the salt concentration, and the temperature are shown. Air was used as the permeating gas in all experiments. The contact angle between the foam film and the bulk solution was measured as a function of the salt concentration. The permeability experiments were performed at a slightly increased pressure. This changes the balance of the interaction forces in the film, and the measurement of the contact angle under those conditions supplied information about this change. Another insight in the film structure was obtained by measurements of the lifetime of NBFs as a function of the surfactant concentration. Experimental Section Materials. The nonionic surfactant β-C12G2 (Glycon Biochemicals, Germany), the same as that used in ref 11, was used without further purification. Previously measured surface tension/surfactant concentration (σ/CS) dependence did not show a minimum near the critical micelle concentration (cmc), indicating the absence of surfaceactive impurities. The cmc for the salt-free surfactant solution is 1.70 × 10-4 M β-C12G2, as shown in refs 10 and 11. The addition of 0.2 M NaCl to the surfactant solutions causes a minor shift of the cmc to 1.70 × 10-4 M.11 Sodium chloride (NaCl) (Merck, Germany) was roasted at 600 °C for 5 h to remove surface-active contaminations. An Elga Labwater (Germany) purification setup was used to purify the water for the preparation of the solutions. The specific resistance of the water used was 18.2 MΩ cm, the pH was 5.5, and the total organic carbon value was less than 10 ppb. The surfactant solutions were prepared by dilution of a concentrated stock solution 12 h before the experiment and were stored at room temperature. (20) Barnes, G. T. AdV. Colloid Interface Sci. 1986, 25, 89. (21) Kashchiev, D.; Exerowa, D. Biophys. Biochem. Acta 1983, 732, 133. (22) Barnes, G. T.; Hunter, D. S. J. Colloid Interface Sci. 1990, 136, 198. (23) Princen, H. M.; Overbeek, J. Th. G.; Mason, S. G. J. Colloid Interface Sci. 1967, 24, 125.
Figure 1. Time dependence of the film permeability at 25 °C and constant surfactant and electrolyte concentration, Cβ-C12G2 ) 1 × 10-3 M and CNaCl ) 0.2 M.
Methods Film Permeability. The “diminishing bubble” method described earlier in detail14,24 was used to measure the film permeability. A small floating bubble with radius R ) 100 µm is formed on the surface of the investigated solution. It is observed from the bottom by using a reflected light microscope. On the top of the bubble, a foam film is formed, and its radius (r) is observed simultaneously with a second microscope. The gas pressure in the bubble is higher because of the capillary pressure, which varies during the experiment, typically from 700 to 1000 Pa. This overpressure causes permeation of gas through the thin foam film. As a consequence, the bubble shrinks, and R and r decrease with time (t). The permeability coefficient K was calculated using the relation
] ∫ r dt)
8 K ) (Pat/2σ)(R04 - Rt4) + (R03 - Rt3) ( 9
[
t 2
0
-1
(3)
where, Pat is the atmospheric pressure, R0 and Rt are respectively the values of R at the beginning (t ) 0) and at the end (t ) t) of the experiment. The integral in the denominator of eq 3 was numerically evaluated using the procedure described in ref 24. The precision of the method is (0.002 cm/s. A detailed description of the method is given in the Supporting Information. All presented K values are arithmetical mean values from more than 10 single experiments. Film Formation and Equilibration. The experiments started shortly after the formation of the bubble. The dependence of the film permeability on the time period after the film formation was studied in detail. The radii of the bubble and the film were recorded for 180 min. The permeability coefficient was calculated for successive 20 min intervals. The result is given in Figure 1. It shows no dependence of the gas permeability on the time (the oscillations are within the limits of the experimental error). This proves that foam films keep their equilibrium properties throughout the experiments, even when the bubble shrinks. Film Lifetime. The experiments were performed in a manner similar to that described earlier.25 Foam films were formed from a biconcave drop of surfactant solution in the ScheludkoExerowa ring cell.3,18 The formation of the film and its rupture were observed using video-enhanced microscopy. The films thin under the action of the capillary pressure and the disjoining (24) Krustev, R.; Platikanov, D.; Nedyalkov, M. Langmuir 1996, 12, 1688. (25) Nikolova, A.; Kashchiev, D.; Exerowa, D. Colloids Surf. 1989, 36, 339.
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pressure. At the high salt concentrations used in the present work, the final result was the formation of NBFs11 via the appearance of black spots in the initial thicker film. These spots grow and finally cover the whole film. The film expands shortly (in less than a second) at that moment. The lifetime of an NBF is defined as the time between the end of the short expansion and the moment of the film rupture.25 The radius of the film after the expansion was always constant (0.22 mm). The moment of the film rupture was observed on a TV screen and measured with a stopwatch with the precision of the human reaction. Individual lifetimes were measured from the moments of the film formation up to 300 s. Films that were stable for more than 300 s were counted as highly stable. Each experiment was repeated 50 times for good statistics. Contact Angle Foam Film/Meniscus. The diminishing bubble method allowed for the measurement of the contact angle θ formed at the transition between the foam film and the bulk solution. The following formula, based on simple geometrical relations (see Figure 1 SI in the Supporting Information), gives the relation between the experimentally measured bubble radius and film radius and the contact angle:3,26,27
2θ ) arcsin
2FgR3 r - arcsin R 3rσ
Figure 2. Dependence of the mean lifetime (τ) on the β-C12G2 concentration for NBFs with a radius of 0.22 mm, obtained in the presence of 0.2 M NaCl at 25 °C. The solid line shows the theoretical fit according to eq 8.
(4)
Here, F is the density of the solution, and g is the acceleration due to gravity. Temperature Control. The temperature of the different experiments was kept constant with a precision of (0.05 °C using a high-precision circulation thermostat, coupled with a Pt100 sensor placed in the experimental cells. The room temperature was also kept constant with a precision of (0.5 °C.
Results and Discussion Film Permeability and Lifetime as a Function of the Surfactant Concentration. Experiments at different surfactant concentrations were performed at a constant NaCl concentration of 0.2 M. The salt concentration ensured the formation of NBFs.11 A preposition for a successful gas permeability experiment is the stability of the foam film for at least 30 min, which is the time window for the experiment. The mean lifetimes (τ) of foam films prepared from β-C12G2 solutions in a wide range of surfactant concentrations were measured at a constant temperature of 25 °C. The film stability versus the β-C12G2 concentration is shown in Figure 2. The dependence demonstrates the formation of stable films above the concentration of 3.9 × 10-6 M β-C12G2. The dependence of the foam film permeability on the β-C12G2 concentration, which was varied in the range above the concentration necessary for the formation of stable films, is shown in Figure 3. The experiments were performed at two temperatures: 25 and 35 °C. The permeability was constant in the range of higher β-C12G2 concentrations. The foam films were much less permeable in this concentration range (K ≈ 0.012 cm/s) compared to the permeability of foam films stabilized with other surfactants at similar conditions13-16 (e.g., K ≈ 0.033 cm/s in the case of NBFs from sodium dodecyl sulfate). The permeability increased steeply at surfactant concentrations around and below the cmc. It also increased with increasing temperature, that is, the whole K(CS) curve for a higher temperature was placed above the corresponding curve for a lower temperature. This temperature dependence is expected, as discussed in ref 28. (26) Nedyalkov, M.; Platikanov, D. Abh. Akad. Wiss. DDR 1985, 1N, 123. (27) Dimitrov, D. C. R. Acad. Bulg. Sci. 1977, 30, 269. (28) Muruganathan, R. M.; Krustev, R.; Ikeda, N.; Mu¨ller, H.-J. Langmuir 2003, 19, 3062.
Figure 3. Film gas permeability as a function of the β-C12G2 concentration at two different temperatures and at a constant electrolyte concentration of 0.2 M NaCl. The solid lines denote the theoretical curves fitted to the experimental points for CS < cmc according to eq 6.
The two surfactant layers that form the film strongly interact with each other in the case of bilayer NBFs. Then the monolayers do not behave as single layers, and the foam film permeability needs special models to be explained. A model that successfully describes the permeability and the stability of NBFs as a function of the surfactant concentration from a single point of view is the nucleation theory of the fluctuation formation of holes developed by Kashchiev and Exerowa.3,21 The experimentally established sharp increase in permeability with decreasing surfactant concentration was in favor of the permeability through fluctuationformed holes of molecular vacancies. According to the theory, the film is considered to be populated by microscopically small holes consisting of i ) 1, 2, 3, and so forth vacancies of surfactant molecules. The gas transfer across the bilayer film occurs simultaneously through its hole-free area as well as through holes with different size. K is a sum of the area-weighted permeability coefficients Ko of the hole-free bilayer and Ki of the holes of i vacancies:
So
K ) Ko
S
∞
+
Si
Ki ∑ i)1 S
(5)
Ko is called the coefficient of background permeability, characterizes the permeability of a bilayer without any holes, and does not depend on the surfactant concentration; S is the total area of the film, Si is the overall area occupied by the holes of
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size i, and So ) S - ∑i Si is the hole-free film area. This area is accepted to be very close to the whole area of the film. If the permeability obeys Fick’s law, then the coefficients Ko and Ki may be represented as Ko,i ) D0,i/h, where D0,i is the bulk diffusion coefficient through the defect-free film area (index 0) or through the holes that consist of i vacancies (index i). Earlier studies20 on the permeability through insoluble monolayers and foam films23 show that usually Fick’s law is not obeyed. The permeability is not a linear function of the surfactant chain length, but D varies with the number of CH2 groups in the hydrophobic part of the surfactant molecules.20 Thus, it is more suitable to describe the results as permeability instead of diffusion. The area Si may be determined using the nucleation theory of the hole formation. Then K may be presented as a function of the surfactant concentration CS by14 ∞
K ) Ko +
aiCs-i ∑ i)1
(6)
Here, ai is defined as14,21
ai ) KiiCie exp(-Pi/kT), with Pi ) (4πA)1/2κi1/2
(7)
Ce is the critical equilibrium concentration at which the NBF and a large two-dimensional phase of vacancies are in a thermodynamic equilibrium, Pi is the work necessary for the formation of the perimeter of a hole in the film with line tension κ at the three-phase contact between the hole and the surrounding film, and A is the area per surfactant molecule. Equation 6 expresses the dependence of K on the surfactant concentration in a general form. It shows that K increases with decreasing CS on account of the permeability through the holes in the bilayer. According to theory, this is due to the decrease in the work necessary to form a hole at lower CS values on the increased number of holes. The permeability decreases with increasing CS because the number of holes diminishes. At a certain threshold concentration Ct, K becomes equal to Ko, and further increase of CS does not change K, that is, K ) Ko at CS > Ct. The statistical treatment of the K(C) data for each temperature was done using equations such as eq 6, including Ko and all possible combinations of the summands with i ) 1, 2, 3,... up to 6. The following criteria of reliability were used: (i) the sum s (Kl - K/l ) should be minimal, (K/l is the calculated value ∑l)1 corresponding to the measured Kl value, and s is the number of experimental points); (ii) the ai values should be positive; (iii) the ai value should be much greater than its calculated error. The theoretical equations were fitted only to the experimental points for CS < cmc. This is the range where the monomer surfactant concentration changes and K depends on CS. The solid lines in Figure 3 were calculated according to the statistical treatment. The fitted theoretical curves coincide well with the experimental points in the whole concentration range, even at higher surfactant concentrations where K is constant. We assume that the constant K value obtained from the horizontal part of the fitted theoretical curve is the background permeability coefficient Ko. The statistical treatment of the experimental data based on eq 6 gave positive significant a4 values at the two temperatures (Table 1). All possible combinations of other summands up to i ) 6 gave no significant values for the coefficients ai different than a4. This means that mainly the holes consisting of four molecular vacancies contribute to the increase in the permeability at low surfactant concentrations. The
Table 1. Values That Gave the Best Fit of Eq 6 to the Experimental Data K(CS) at Two Temperatures: 25 and 35 °Ca T, °C
Ko, cm/s
i
ai, cm moli/s dm3i
K4, cm/s
25 35
0.0115 0.0322
4 4
2.9 × 10-19 1.9 × 10-18
30.3 166.7
a Ko is independent of the surfactant concentration background permeability, i is the number of single vacancies constituting the holes that mostly contribute to the gas permeability at low β-C12G2 concentrations, and K4 is the permeability through these holes (see the text for the calculation details of i and K4).
population of such holes decreases upon increasing surfactant concentration until it reaches a constant value. The contribution to the film permeability of holes smaller than i ) 4 to the increase in the permeability is minor because of the low permeability coefficient through the small size holes. On the other hand, the gas flux through the larger holes (i > 4) is larger, but the number of such holes is low because the statistical probability to form larger aggregates is small. The formation of larger holes might lead to film rupture as well. The obtained a4 values allow the permeability coefficient K4 of holes formed of four surfactant vacancies to be calculated according to eq 7. The constants Ce and κ were obtained through statistical treatment of the τ(CS) dependence in Figure 2. According to the nucleation theory3,21,25 of the fluctuation formation of holes in foam bilayers, the bilayer lifetime τ depends on CS by
τ ) J exp[B ln(Ce/Cs)-1], with B ) πAκ2/2(kT)2
(8)
where J is a kinetics constant that considers the velocity of aggregation of the molecular vacancies in a hole, and κ is the line energy of the three-phase contact between the hole and the surrounding film. The experimental τ(CS) dependence was fitted with eq 8 using three fitting parameters: J, Ce, and κ. The best fit to the experimental data is shown on the Figure 2 as a full line. The calculated dependence demonstrates good agreement with the experiment. The following values for the constants at 25 °C were obtained: J ) 3.2 ( 0.6 × 10-6 (s), Ce ) 3.8 × 10-6 (M), and κ ) 1.18 × 10-11 (J/m). The area per surfactant molecule A was calculated from the experimental σ (CS) data presented in ref 11 using the Gibbs law of adsorption at a solid/liquid surface. The area per surfactant molecule was obtained to be A ) 0.39 nm2. The calculated K4 values are shown in Table 1. The values should be considered only as an estimation since they are very sensitive to the constants used for the calculation. The value at 35 °C was obtained using the Ce, κ, and A values found for 25 °C, which is an approximation. The K4 values are much larger than those of K0. The small number of holes formed by the four molecular vacancies is the only reason the film permeability increased less than an order of magnitude at low surfactant concentrations. The obtained K4 values also show wellpronounced dependence on the temperature. Film Permeability as a Function of the Electrolyte Concentration. The dependence of the film permeability on the NaCl concentration in the film-forming solution was measured at a constant surfactant concentration of 1 × 10-3 M β-C12G2 and a temperature of 25 °C. The observed dependence was weak, as shown in Figure 4. The increase in the electrolyte concentration leads to a decrease in the thickness of the CBF (see ref 11, Figure 3). Thus, according to eq 2, the permeability ought to increase upon addition of NaCl, but the experimental results do not show such a dependence. The following explanation may describe the
Foam Films Stabilized with β-C12G2
Figure 4. Dependence of the film permeability coefficient K on the NaCl concentration at a constant surfactant concentration Cβ-C12G2 ) 1 × 10-3 M and T ) 25 °C. The solid line is a guide for the eye.
difference between the theoretical expectations and the observed results. The capillary pressure in the microscopic bubbles studied in our measurements was around 700 Pa (bubble radius 100 µm and surface tension 35 mN/m). We showed in ref 11 that CBF films stabilized with β-C12G2 always became NBFs at a capillary pressure of around 400 Pa, irrespective of NaCl concentration. This low transition pressure is due to the weakly charged film interfaces in the case of the nonionic surfactant. Thus, because of the higher pressure in the bubbles, only NBFs were formed under our present experimental conditions. Since the thickness of the films did not depend on the salt concentration, no change in the permeability could be expected. We calculated the angle of contact between the film and the meniscus θ using the diminishing bubble method. Thus, the contact angle experiments yielded information on the interactions (see De Feijter, J. A. in ref 19, p 1) in the film, exactly at the conditions (elevated pressure) used in our permeability experiment. θ was measured as a function of the salt concentration in the range from 1 × 10-4 to 0.5 M NaCl. Contact angle values were practically constant, irrespective of the NaCl concentration (Figure 5). Our present experiment shows a difference to the earlier results when the “expansion method” was used.11 There, low values of θ, typical for the CBF, were observed at low salt concentrations. The contact angles increased upon addition of salt and reached a constant high value, typical for NBF. An important characteristic of the previous experiments was that the experiments were performed at very low capillary pressures (around 70 Pa). The constant high values of θ we obtained in the present work, using the diminishing bubble method, are similar to those that we attributed to the NBF in ref 11. This supports the argument that, because of the increased pressure in the diminishing bubble, only the thinnest NBFs were formed, irrespective of the salt concentration. Thus, no change in the film thickness could be observed and, correspondingly, the film permeability was not dependent on the salt concentration.
Conclusions The permeability of foam films stabilized by β-C12G2 was studied as a function of different thermodynamic parameters. A
Langmuir, Vol. 22, No. 19, 2006 7985
Figure 5. Dependence of the contact angle θ between the film and the bulk solution measured by the diminishing bubble method on NaCl concentration at a constant surfactant concentration Cβ-C12G2 ) 1 × 10-3 M and T ) 25 °C. The solid line is a guide for the eye.
strong dependence of the film permeability on the surfactant concentration was observed. The film permeability coefficient was constant in a wide range of β-C12G2 concentrations above the cmc, and it increased steeply at concentrations lower than the cmc. The foam films were much less permeable at high surfactant concentrations compared to the permeability of foam films stabilized with other surfactants under similar conditions. The hole-mediated theory of film permeability successfully described the experimental results. It supports the idea that the permeation through the foam films occurs upon the formation of empty places (holes) in the film monolayers. The film permeability showed a weak dependence on the salt concentration. In the case of a very weak long-range electrostatic double-layer repulsion between the film surfaces, typical for nonionic surfactants, only a small overpressure was necessary to form NBFs from the initially formed CBFs. The capillary pressure in the small bubbles studied was enough to cause such a transition. Thus, we were not able to study films with different thicknesses, but only the thinnest NBFs. The result was confirmed by parallel measurements of the contact angles between the film and the bulk solution using the diminishing bubble method at the same pressure. The observed values of the contact angle, typical for NBFs, supported the argument that, in the diminishing bubble method, irrespective of the salt concentration, only the thinnest NBFs were formed. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft under Project No. Mu¨ 1040/9. The authors sincerely acknowledge R. Emrich for assistance in the lab works. Supporting Information Available: Details describing the permeability through a single foam film. This material is available free of charge via the Internet at http://pubs.acs.org. LA0603673
