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Notes Temperature Dependence of the Gas Permeability of Foam Films Stabilized by Dodecyl Maltoside R. M. Muruganathan, R. Krustev,* N. Ikeda, and H. J. Mu¨ller Max-Planck Institute of Colloids and Interfaces, Am Mu¨ hlenberg 1, D-14476 Golm, Germany Received October 22, 2002. In Final Form: December 19, 2002
Introduction Despite the host of investigations of foam films, measurements of the gas permeability of the films are relatively rare. Nevertheless, it has been shown that such measurements deliver valuable information not only about the long-term stability of foams and the transfer of matter between different phases, but also about the structure and the interactions in the foam films.1-5 Only a limited number of surfactants have been used in the investigation of the gas permeability of foam films so far. Sugar-based surfactants represent a class of surfaceactive substances with growing importance and application. They can be made from renewable materials, and they possess favorable properties for application in different fields.6 To our knowledge, studies about gas permeability of foam films stabilized with such surfactants have not been reported until now. The properties of the foam films and foams are summarized in several monographs and reviews.7-9 The foam films consist of a thin aqueous core covered on both sides with a monolayer of adsorbed surfactant molecules. These films are easily formed from solutions of surfactants. After formation, the initial thick film thins by drainage of the solution due to the capillary pressure in the meniscus and the interactions between the two film surfaces. Equilibrium films are obtained with a uniform thickness. If the surfaces are charged, the diffuse electrical double layers at both surfaces cause repulsion. At a low concentration of electrolytes, equilibrium films are formed at the end of the draining process with an aqueous core with a thickness from a few nanometers to hundreds of nanometers. At * Corresponding author. E-mail:
[email protected]. Telephone: 49 (0) 331/567 9232. Fax: 49 (0) 331/567 9202. Mailing address: 14424 Potsdam, Germany. (1) Princen, H. M.; Mason, S. G. J. Colloid Interface Sci. 1965, 20, 353. (2) Nedyalkov, M.; Krustev, R.; Kashchiev, D.; Platikanov, D.; Exerowa, D. Colloid Polym. Sci. 1988, 266, 291. (3) Nedyalkov, M.; Krustev, R.; Stankova, A.; Platikanov, D. Langmuir 1992, 8, 3142. (4) Krustev, R.; Platikanov, D.; Nedyalkov, M. Colloids Surf., A: Physicochem. Eng. Aspects 1996, 123-124, 383. (5) Krustev, R.; Mu¨ller, H.-J. Langmuir 1999, 15, 2134. (6) Stubenrauch, C. Curr. Opin. Colloid Interface Sci. 2001, 6, 160. (7) Ivanov, I. B., Ed. Thin Liquid Films; Marcel Dekker: New York, 1988. (8) Exerowa, D.; Kruglyakov, P. Foam and Foam Films: Theory, Experiment, Application; Studies in Interface Science; Elsevier: Amsterdam, 1998. (9) Prud’homme, R. K., Kahn, S., Eds. Foams; Marcel Dekker: New York, 1996.
high concentration of electrolytes, the diffuse electrical double layers are compressed and very thin Newton black foam films (NBFs) are formed. They consist essentially of two surfactant monolayers. A measure of the gas permeability of a foam film is the permeability coefficient K (cm/s),1,10 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. The inverse quantity of the permeability is called resistance. Then the relation between the permeability through the two covering adsorption layers of the film and the aqueous core is1
2 1 1 ) + K kml kw
(2)
Here kml is the permeability through a single surfactant monolayer and kw is the permeability through the central aqueous core. In a NBF there is no core, and the permeability is governed by the permeability of the two surfactant monolayers:1
K ) kml/2
(3)
It has been shown that the permeability of the foam films depends on the properties of the surfactant molecules and on their packing density at the film surface.4,5,11 Because of the simple relation (eq 3) between the permeability of the whole film and that of the monolayers, information about the structure of the film adsorption layers can be obtained from measurements of the permeability of the NBF. The permeability kml depends on the adsorption density of the surfactant in the film adsorbed monolayers. These monolayers are in contact and in thermodynamic equilibrium with the monolayers that cover the surface of the bulk phase, which surrounds the film. Then, the adsorption density of the surfactant molecules at the interface of the bulk phase governs to a high extent the adsorption density in the film forming monolayers. Many investigations on the permeability of Langmuir and Gibbs monolayers have been performed in the past.12 The theoretical models which describe the monolayer permeability can be applied also to the permeability of the film monolayers which constitute the NBF.11 In our present investigation we studied the temperature dependence of the permeability of foam films stabilized with the commercially available nonionic sugar-based surfactant n-dodecyl-β-D-maltoside (β-C12G2). This sur(10) Brown, A. G.; Thuman, W. C.; McBain, J. W. J. Colloid Sci. 1953, 8, 508. (11) Krustev, R.; Platikanov, D.; Stankova, A.; Nedyalkov, M. J. Dispersion Sci. Technol. 1997, 18, 789. (12) Barnes, G. T. Adv. Colloid Interface Sci. 1986, 25, 89.
10.1021/la020870p CCC: $25.00 © 2003 American Chemical Society Published on Web 03/01/2003
Notes
Langmuir, Vol. 19, No. 7, 2003 3063
factant consists of two glycoside rings connected by an ether bond to the alkyl chain. Stable foam films are formed from the solutions of this surfactant. Air was used as permeating gas. The results are compared with the temperature dependence of the adsorption density of β-C12G2 at the interface with the bulk phase at the cmc, determined by the surface tension measurements. This allows us to obtain additional insights into the mechanism of the gas permeation. Experimental Section Materials. n-Dodecyl-β-D-maltoside was purchased from Glycon Biochemicals, GmbH (Luckenwalde, Germany) and used without further purification. The surface tension/concentration dependence does not show a minimum near the cmc, indicating the absence of surface-active impurities. Sodium chloride (Riedelde Haaen) was roasted at 600 °C for 5 h to remove surface-active contaminations. The solutions were prepared by using Millipore water (pH 5.5). The formation of stable foam films requires densely packed monolayers of the amphiphile at the film surfaces.8,13 Because of that, all foam film experiments were conducted at constant surfactant concentration, 0.001 M, which is about 8 times the cmc for pure β-C12G2.14 Methods. The film permeability was measured using the “diminishing bubble” method described earlier.2,15 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 than that in the free space 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, which separates the interior of the bubble from the free atmosphere above. As a consequence, the bubble shrinks and R and r decrease with time. The permeability coefficient K was calculated from the experimental time dependencies of the film and bubble radii by15
] ∫ r dt)
8 K ) (Pat/2γ)(R40 - R4t ) + (R30 - R3t ) ( 9
[
t 2
0
-1
(4)
Here, Pat is the atmospheric pressure and γ is the solution surface tension, measured separately, R0 and Rt are the values of R at the beginning (t ) 0) and at the end (t ) t) of the experiment, respectively. The numerical evaluation of eq 4 has been performed using the calculating procedure described in ref 15. The precision of the method is (0.002 cm/s. Since the experiments are highly sensitive toward temperature, much attention was given to maintain the temperature. Room temperature was maintained as 25 °C ((0.5 °C) for all the measurements. An external Pt100 thermosensor was kept near the solution/air interface and adjacent to the diminishing bubble. A high precision circulation thermostat (Phoenix P1 Circulator, Thermo Haake, Karlsruhe, Germany) coupled with the sensor maintained the temperature with the precision (0.05 °C. All presented K values are arithmetical means from more than 10 single experimental values. The sample standard deviations are shown as error bars in the figures. The film thickness was measured using the microinterferometric method as described earlier.16-18 After the experimental cell was closed, a biconcave drop was formed in a glass ring. The cell was allowed to equilibrate for at least 2 h. This time is required (13) Exerowa, D.; Nikolov, A.; Zacharieva, M. J. Colloid Interface Sci. 1981, 81, 419. (14) Liljekvist, P.; Kjellin, M.; Eriksson, J. C. Adv. Colloid Interface Sci. 2001, 89-90, 293. (15) Krustev, R.; Platikanov, D.; Nedyalkov, M. Langmuir 1996, 12, 1688. (16) Krustev, R.; Mu¨ller, H.-J.; Toca-Herrera, J. L. Colloid Polym. Sci. 1998, 276, 518. (17) Frankel, S. P.; Mysels, K. J. J. Appl. Phys. 1966, 81, 3725. (18) Bergeron, V.; Waltermo, A.; Claesson, P. M. Langmuir 1996, 12, 1336.
Figure 1. Thickness of foam films prepared from 0.001 M solutions of β-C12G2 as a function of the NaCl concentration at 25 °C. The values are obtained from the experimental equivalent solution thickness using the three-layer model of the film. for the saturation of the interior of the cell with the vapor of the solution and for the equilibrium of the adsorbed surfactant monolayers. The films were formed by applying a comparatively small capillary pressure of 35 Pa. We observed that the film thickness is smaller when equilibrium conditions are not established. The value of the measured thickness was constant with time once the film had reached its state of equilibrium. The surface tension of the solutions was measured by using a Lauda (KM5) tensiometer with an accuracy of (0.1 mN/m. In all the surface tension experiments the temperature was kept constant within (0.1 °C.
Results To find out the conditions for formation of the very thin bilayer NBF, the thickness of films prepared from 0.001 M solutions of β-C12G2 as a function of the salt concentration up to 0.5 M NaCl was measured at 25 °C. The film thickness values obtained from the experimental results using the three-layer model17 are presented in Figure 1. The shape of the dependence is similar to those for other nonionic surfactants.18 At very small salt concentrations, thick films are formed. This shows that films stabilized by the nonionic surfactant β-C12G2 exhibit some electrical double-layer repulsion, in agreement with the results shown in the literature.8,18-20 Increasing the concentration of NaCl leads to a sharp decrease in the film thickness, which reaches a plateau value of 5.7 nm above CNaCl ) 0.05 M. We identify these films as NBFs. Their thickness is similar to that obtained by other authors.21 It shows that the film consists of two adsorbed surfactant layers with a thickness of around 2 nm (htail ≈ 0.96 nm and hhead ≈ 1.14 nm) and an aqueous core of around 1 nm. This aqueous core is assumed to represent the hydration water of the surfactant headgroups. The permeability measurements were performed at 0.2 M NaCl concentration, which ensures the formation of NBFs in the range of the experimental conditions. We assume that the higher capillary pressure (700-1000 Pa) at which the films are exposed in the permeability measurements does not change their thickness. A basis for this assumption is that in the case of NBFs the applied external pressure cannot change the film thickness. This behavior is experimentally confirmed for β-C12G2 by Stubenrauch et al.21 (19) Marinova, K. G.; Alargova, R. G.; Denkov, N. D.; Velev, O. D.; Petsev, D. N.; Ivanov, I. B.; Borwankar, R. P. Langmuir 1996, 12, 2045. (20) Persson, C. M.; Per Claesson, M. Langmuir 2000, 16, 10227. (21) Stubenrauch, C.; Schlarmann, J.; Strey, R. Phys. Chem. Chem. Phys. 2002, 4, 4504.
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Notes
Table 1. Film Permeability (K), Monolayer Permeability (Kml), and β-C12G2 Adsorption Densitya as a Function of the Temperature temp, °C
K cm/s
Kml cm/s
film thickness, nm
ads‚density,a mol/m2
15.0 20.0 22.0 25.0 28.0 30.0 35.0
0.018 0.013 0.011 0.009 0.012 0.016 0.018
0.036 0.026 0.021 0.018 0.024 0.032 0.036
5.13
4.08 × 10-6
5.14
4.25 × 10-6
5.66
3.75 × 10-6
a
Adsorption density at the cmc.
barrier theory of the monolayer permeability.11 Following Barnes and La Mer,22 it is
K ) C exp(-∆Gq/RT)
(5)
where ∆Gq is the activation free energy of the permeability. ∆Gq can be divided into three terms related to the changes in the energy ∆Uq, the entropy ∆Sq, and the area per surfactant molecule ∆Aq:
∆Gq ) ∆Uq + π∆Aq - T∆Sq
(6)
Then eq 5 will be written as
ln K ) (ln C + ∆Sq/R) - (∆Uq + π∆Aq)/RT
Figure 2. Dependence of the monolayer permeability kml (according to eq 3) on the temperature for foam films prepared from a solution of 0.001 M β-C12G2 and 0.2 M NaCl.
The gas permeability and the thickness of NBFs, obtained from a solution of 0.001 M β-C12G2 and 0.2 M NaCl, were measured as a function of the temperature in the range from 15 to 35 °C. The results are presented in Table 1. The permeability coefficients are smaller compared to those of other already investigated surfactants.2,4,11 However, the values are above the resolution of the method, and all effects are significant. The lowest film permeability was measured at 25 °C. The dependence of the monolayer permeability kml (according to eq 3) on the temperature is presented in Figure 2. The monolayer permeability decreases, and the film thickness is constant upon increasing the temperature in the range from 15 to 25 °C. There is a well-pronounced kink point in the permeability at 25 °C, after which kml continuously increases with the temperature up to 35 °C, although a slight increase in the film thickness is observed as well (see Table 1). This behavior differs essentially from that of other surfactants. It was shown in the earlier works3,4,11,15 that the gas permeability of the foam films increases with the temperature. The average energy of the gas molecules increases with increasing temperature. Then the number of molecules that possess the necessary energy to overcome the energy barrier (in our case the foam film) increases. This leads to the experimentally observed increase in the rate of permeability shown in the literature. Earlier investigations2 have demonstrated that the permeability of a surfactant monolayer at the surface of a foam film depends on the adsorption density of the surfactant molecules. The permeability of a single adsorbed surfactant monolayer can be explained from the point of view of the theories of the gas transport through monolayers spread onto aqueous substrates. The permeability of the film monolayers was successfully described by the energy
(7)
The area of activation ∆Aq relates the permeability to the surface pressure π ) γ0 - γ (here γ0 is the surface tension of the pure substrate). This is the area by which the monolayer must expand to form a sufficient gap between the surfactant molecules to allow the passing of the gas molecule. The value of ∆Aq becomes smaller when the packing density of the monolayer decreases,22 due to the larger free space between the molecules. The general behavior of the adsorption density is a monotonic decrease with temperature because of the enhancement of the thermal motion of surfactant molecules at the surface. This effect has already been observed for many ionic and nonionic surfactant systems.23-28 Increasing the temperature therefore should result in a larger area per surfactant molecule and, consequently, in an increase in the permeability. It has been shown5 that the adsorption density at the foam film interfaces is also influenced by the interactions in the film. It can be assumed that the absolute value of the specific interaction film free energy decreases with the temperature.29 Following the arguments in ref 5, this will lead to a smaller adsorption density as well. From the mentioned factors it has to be expected that the increase of the temperature should result only in an increase in the permeability of the foam films. The unexpected decrease of the gas permeability of foam films stabilized with β-C12G2 in the temperature range from 15 to 25 °C could be explained, if the dependence of the monolayer adsorption density on the temperature exhibits a nonmonotonic behavior. Assuming an ideal dilute solution for the surfactant in the bulk solution below the cmc, the surface density of surfactant can be evaluated thermodynamically. This assumption is more guaranteed for the aqueous surfactant solution without electrolytes. In the given case the Gibbs law of adsorption can be written
Γ1 ) -(1/RT)(∂γ/∂ ln Cs)T,p
(8)
(22) Barnes, G. T., LaMer, V. K., LaMer, V. K., Ed. Retardation of Evaporation by Monolayers: Transport Processes, 9; Academic Press: New York, 1962. (23) Barnes, G. T.; Hunter, D. S. J. Colloid Interface Sci. 1990, 136, 198. (24) Rosen, M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1989. (25) Motomura, K.; Iwanaga, S.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32. (26) Aratono, M.; Okamoto, T.; Ikeda, N.; Motomura, K. Bull. Chem. Soc. Jpn. 1988, 61, 2773. (27) Motomura, K.; Iwanaga, S.; Uryu, S.; Matsukiyo, H.; Yamanaka, M.; Matuura, R. Colloids Surf. 1984, 9, 19. (28) Aratono, M.; Shimada, K.; Ikeda, N.; Takiue, T.; Motomura, K. Netsu Sokutei 1995, 22, 131. (29) De Feijter, J. A.; Vrij, A. J. Colloid Interface Sci. 1978, 64, 269.
Notes
Figure 3. Surface tension/β-C12G2 concentration dependencies (no added NaCl) measured at three temperatures: 2, 15 °C; b, 25 °C; 9, 35 °C.
Here Γ1 is the surface density and Cs is the concentration of the surfactant. The other symbols have their usual meanings. The surface tension/surfactant concentration dependence was measured at three temperatures (15, 25, and 35 °C) in the absence of NaCl. The curves are presented in Figure 3 in the form of γ versus ln Cs plots. By using the polynomial fits to the curves in Figure 3 and applying eq 8, the surface densities at the cmc have been calculated at the three temperatures. The values are shown in Table 1. The surface density at 25 °C is larger than that at higher and lower temperatures. This result suggests a nontrivial temperature dependence of the surface density of β-C12G2. The surface density of the surfactant at the bulk surface increases slightly with increasing temperature below 25 °C, whereas it decreases above 25 °C. An increase in the
Langmuir, Vol. 19, No. 7, 2003 3065
surface density with temperature has already been observed for some nonionic surfactants of the type CnEm30 and is considered to be the result of a dehydration of the surfactant molecules. Thus, the changes which we observed in the gas permeability with temperature are parallel to the changes of the surface density of the surfactant. In summary, the changes in the permeability can be considered as a result of the competition between the increasing thermal energy of the gas and the surfactant molecules and the dehydration of the surfactant headgroups. In the temperature range from 15 to 25 °C the surfactant adsorption density increases because of the decrease in the dimensions of the surfactant headgroups due to the dehydration. This leads to a decrease in the permeability even though the energy of the gas molecules increases. Above 25 °C the surfactant adsorption density follows the general trend. It decreases with increasing temperature because of the enhancement of the thermal motion of the surfactant molecules at the interface. This leads to an increase in the film permeability supported by the increase in the energy of the gas molecules. The results of the present study underline the effect of small variations of the adsorption density in the film surfaces on the gas permeability of the foam films. To obtain quantitative relations between the packing density of the surfactant in the film surfaces and the gas permeability, further investigations are in progress. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (DFG grant No. Mu 1040/9-1). LA020870P (30) Wongwailikhit, K.; Ohta, A.; Seno, K.; Nomura, A.; Shinozuka, T.; Takiue, T.; Aratono, M. J. Phys. Chem. B 2001, 105, 11462.
