Effect of Headgroup Size on Permeability of Newton Black Films

the foam films, keeping the size of the hydrophobic part constant (C12) and varying the size of the ... size, but the contact angle remains small and ...
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Langmuir 2005, 21, 12222-12228

Effect of Headgroup Size on Permeability of Newton Black Films RM. Muruganathan,*,† H.-J. Mu¨ller, H. Mo¨hwald, and R. Krastev Max-Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany Received September 1, 2005. In Final Form: October 10, 2005 Gas permeability and thin-film interferometry are used as a tool to elucidate the orientation of polymeric headgroups in free-standing foam films. Nonionic polyoxyethylene (EO) surfactants were used to stabilize the foam films, keeping the size of the hydrophobic part constant (C12) and varying the size of the hydrophilic (EO numbers) part. The effect of headgroup size on the gas permeability of Newton black foam films was studied. Thickness, contact angle, and surface tension were measured to understand the permeation mechanism. Increase of film thickness and surface tension was observed while increasing the headgroup size, but the contact angle remains small and constant. Upon increasing the headgroup size, the permeability decreases showing that the headgroups provide a resistance to permeation. For smaller headgroups, the permeability follows a linear dependence on the film thickness, whereas for larger headgroups, the permeability essentially deviates from linearity. We use the conventional “coil model” of the EO chains to explain the observed results providing a detailed picture of the orientation of this important molecule in a confined volume of foam films.

Introduction Surfactants are prevalent in consumer products, biological systems, and industrial processes.1 One of the characteristic features of surfactants is their tendency to adsorb at interfaces in an oriented fashion. Consequently, a molecular level understanding of how surfactants adsorb and orient at surfaces has ramifications for many of the economic, health, and environmental issues of today. This adsorption has been studied to determine2 (1) the concentration of surfactant at the interface, since this is a measure of how much of the interface has been covered (and thus changed) by the surfactant, and because the performance of the surfactant in many interfacial processes (e.g., foaming, detergency, emulsification) depends on its concentration at the interface; (2) the orientation of the surfactant at the interface, since this determines how the interface will be affected by the adsorption, that is, whether it will become more hydrophilic or hydrophobic; and (3) the energy changes, ∆G, ∆H, and ∆S, in the system, resulting from the adsorption, since these quantities provide information on the type and mechanism of any interactions involving the surfactant at the interface and the efficiency and effectiveness of its operation as a surfaceactive material. Besides the scientific interest of the adsorption of nonionics, the structure of the adsorbed layer of nonionic polymeric surfactants3 is also of industrial relevance due to the fact that the structural moieties in those surfactant molecules and their orientation at the interface are essential for systems such as foams that are stabilized by surfactants. The behavior of such uncharged polymeric surfactants at an interface is largely dependent on the molecular characteristics of the polar headgroup * Corresponding author. E-mail: [email protected]. † Present address: Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida 32310. Fax: +1-850-644 8281. (1) New products and applications in surfactant technology; Karsa, D. R., Ed.; Sheffield Academic Press: Boca Raton, FL, 1998. (2) Rosen, M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1989. (3) Nonionic Surfactants, Physical Chemistry: Surfactant Science Series; Schick, M. J., Ed.; Marcel Dekker: New York, 1987.

and its structure, orientation, solvation, and interaction with adjacent surfactants. Recent developments of interface specific techniques allowed the orientation of surfactants at the interface to be measured and interpreted.4 For example, sumfrequency generation spectroscopy and second-harmonic generation spectroscopy are useful tools to measure the tilt angle, gauche defects, and orientation of the hydrophobic tail part of the surfactant.5 Although these studies have provided information about the ordering of the alkyl chains and the surrounding interfacial water structure, results from neutron reflectivity and X-ray diffraction are used to interpret the headgroup hydration, orientation, and configuration.6 Though most of these techniques are employed in single surfactant monolayer adsorbed at the air/water interface, over the past few years, several different methods emerged to investigate the structure within thin-liquid films at their interfaces. The most common and perhaps the simplest technique used for determining structure in thin-liquid films is the thin-film interferometer. The primary measurement in this case is the film thickness (and changes therein) which was then used to infer specific structural information of the film.7,8,9 Similarly, but at a much higher resolution (i.e., smaller length scales), X-ray and Neutron reflectivity and confocal micro-Raman spectroscopy are used to gain detailed knowledge of the molecular organization in the film and at its interface.10,11 Here, we use a different strategy to elucidate the orientation of polymeric headgroups in a (4) Structure-Performance Relationships in Surfactants, 2nd ed.; Esumi, K., Ueno, M., Eds. Marcel Dekker: NewYork, 2003. (5) Vidal, F.; Tadjeddine, A. Rep. Prog. Phys. 2005, 68, 1095. (6) SPIE Proceedings Vol. 2547 Laser Techniques for Surface Science II Hicks, J. M., Ho, W., Dai, H., Eds.; SPIE Press: San Diego, CA. (7) Exerowa, D.; Kruglyakov, P. Foam and Foam Films; Elsevier: Amsterdam, 1998. (8) Thin Liquid Films; Ivanov, I. B., Ed.; Marcel Dekker: New York, 1998. (9) Stubenrauch, C.; Klitzing, R. J. Phys.: Condens. Matter. 2003, 15, R1197. (10) Stubenrauch, C.; Albouy, P.-A.; Klitzing, R. v.; Langevin, D. Langmuir 2000, 16, 3206. (11) Krastev, R.; Gutberlet, T.; Gupta, M.; Mishra, N. C. Unpublished data.

10.1021/la052389f CCC: $30.25 © 2005 American Chemical Society Published on Web 11/22/2005

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confined volume such as foam films for reasons discussed below. Foam films are thin liquid lamellae that separate foam bubbles.12 In foam films, two identical monolayers of surfactants are separated by a thin aqueous core. Permeability of gases through a foam film is highly sensitive to small changes that occur in the film structure.13 Therefore, the transport properties of the film will be different for different orientations of the surfactant molecules at the film surfaces. In this paper, we use gas permeability as a tool to identify the orientation of polyoxyethylene headgroups in a confined volume of foam films. Nonionic dodecyl-j-oxyethylene glycol monoether (C12Ej) surfactants are used to stabilize the foam films. 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.14,15 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. Recently, it has been shown13 that measurements of gas permeability of the foam films deliver valuable information about the structure and the interactions in the thin layers, where the surface forces are operative. The influences of the film thickness, the surfactant adsorption density, the surfactant chain length, and the temperature on the gas permeability of the foam films have already been reported.16,17,18,19 In this paper, we show the effect of surfactant headgroup size on the foam film permeability. The foam films consist of an aqueous core with thickness haq covered on both sides with a monolayer of adsorbed surfactant molecules with thickness hml.7,20 These films are easily formed from solutions of surfactants. Equilibrium films with a uniform thickness are obtained. If the surfaces are charged, the diffuse electrostatic double layers on both surfaces cause repulsion. At a low concentration of electrolytes, common black films (CBF) are formed at the end of the draining process with an aqueous core of a few nanometers to hundreds of nanometers in thickness. The thickness decreases with the addition of electrolytes. At a high concentration of electrolytes, the diffuse electrical double layers are compressed, and very thin Newton black foam films (NBF) are formed. They essentially consist of only two surfactant monolayers, which are adsorbed onto each other and form a bilayer. For a review of the properties of the foam films, see the literature in ref 21 as well as refs 7 and 8. A measure of the gas permeability of a foam film is the permeability coefficient K (cm/s)14,15 defined by

dN ) -KS∆Cg dt

(1)

(12) Ter Minassian-Saraga, L.; Vincent, B.; Adler, M.; Barraud, A.; Churaev, N.; Eaton, D.; Kuhn, H.; Misono, M.; Platikanov, D.; Ralston, J.; Silberberg, A.; Zemel, J. Thin Solid Films 1996, 277, 7. (13) Krustev, R.; Mu¨ller, H.-J. Langmuir 1999, 15, 2134. (14) Brown, A. G.; Thuman, W. C.; McBain, J. W. J. Colloid Sci. 1953, 8, 508. (15) Princen, H. M.; Mason, S. G. J. Colloid Interface Sci. 1965, 20, 353. (16) Nedyalkov, M.; Krustev, R.; Kashchiev, D.; Platikanov, D.; Exerowa, D. Colloid Polym. Sci. 1988, 266, 291. (17) Nedyalkov, M.; Krustev, R.; Stankova, A.; Platikanov, D. Langmuir 1992, 8, 3142. (18) Krustev, R.; Platikanov, D.; Stankova, A.; Nedyalkov, M. J. Dispersion Sci. Technol. 1997, 18, 789. (19) Muruganathan, RM.; Krustev, R.; Ikeda, N.; Mueller, H.-J. Langmuir 2003, 19, 3062.

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. Earlier work of Exerowa et al.22 confirms that the foam stability is not related to the bulk properties of the surfactants, such as micelle formation, but is dependent on the surfactant adsorption and orientation. This indicates that the change in the headgroup size should have a certain influence on the surfactant adsorption and/ or orientation of the headgroups at the interface and hence on the gas permeability which is very sensitive for such changes at the adsorption surfaces. In this paper, we show that the hydrophilic EO groups provide a measurable resistance for gas permeation. Experimental Section Materials. A set of polyoxyethylene surfactants, i.e., C12Ej where j ) 5-9, were purchased from Fluka with more than 98% purity and used without any further purification. C12E18 was synthesized, at the MPI-KG by Dr. G. Czichocki. Sodium chloride (Merck, Germany) was heated at 600 °C for 5 h to remove surfaceactive contaminations. An Elga Lab water (Germany) purification setup was used to purify the water for the preparation of the solutions. The specific resistance of the used water is 18.2 MΩ cm, the pH is 5.5, and the total organic carbon (TOC) value is less than 10 ppb. Methods. Permeability. Gas permeability was measured by using the diminishing bubble method.16 Basically, in the diminishing bubble method, a small freely floating bubble is formed at the air/solution interface. The radius of the bubble, Rb, and the radius of the film formed on the top of the bubble, r, as a function of time, t, are measured simultaneously. Then the permeability coefficient, K, is calculated from the following relations:16

] ∫ r dt)

8 K ) (Pat/2σ)(R04 - Rt4) + (R03 - Rt3) ( 9

[

t 2

0

-1

(2)

where, Pat denotes the atmospheric pressure and σ is the solution surface tension. R0 is initial radius of the bubble at time 0, and Rt is the final radius of the bubble at time t. In the present work, the atmospheric air was used as a permeating gas. The investigated solution was placed in a small Teflon vessel with a diameter of 1 cm. The small radius of the vessel allows the formation of a convex surface. A tiny floating bubble with radius Rb of 100 µm was formed under the surface of the investigated solution. The bubble floats to the surface and at the contact a foam film with radius r is formed on top of the bubble. Because of the curvature of the solution, the surface of the bubble was fixed in its center. It was observed from the bottom in reflected light by using an inverse microscope. The film formed on top of the bubble was observed simultaneously with a second specially developed microscope in transmitted light. Both microscopes are coaxial which allows simultaneous observation of the radius of the bubble and the radius of the film. The experiments were started shortly after the formation of the bubble. The radii of the bubble and also the radii of the film were recorded, and the permeability coefficient was calculated for successive 20 min intervals. The numerical evaluation has been performed using the calculation procedure described in ref 23. The precision of the method is (0.002 cm/s. All presented K values are arithmetical means of more than 10 single experimental values. The sample standard deviation is shown as error bars on the graphs. The scatter of the experimental values is less than 3% of the mean value. Film Thickness. The ring cell of Scheludko and Exerowa7,24 was used for the microinterferometrical measurement of the (20) Sheludko, A. Adv. Colloid Interface Sci. 1967, 1, 391. (21) Muruganathan, RM.; Krustev, R.; Mu¨ller, H.-J.; Kolaric, B.; Klitzing, R. v. Langmuir 2004, 20, 6352. (22) Exerowa, D.; Khristov, K.; Penev, I. Foams; Academic Press: London, 1976. (23) Krustev, R.; Platikanov, D.; Nedyalkov, M. Colloids Surf. A 1996, 123-124, 383. (24) Scheludko, A.; Exerowa, D. Colloid J. 1959, 165, 148.

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thickness and the contact angle of the film. A detailed description of the cell and the experimental procedure are presented in ref 25. Microscopic films with a radius of r ) 0.25 mm formed in a glass ring with a radius of R ) 2 mm were studied. The thickness of the film is determined by the equilibrium between the disjoining pressure and a small known capillary pressure, Pc ) 2σ/R. Pc varies between 30 and 40 Pa at the conditions of our experiments.26,27 The film thickness has been calculated from the measured intensities of the light reflected from the film using the method proposed by Scheludko.20,24 This is the thickness of a homogeneous film with a refractive index equal to the refractive index of the solution from which the film is formed. Contact Angle. The topographic method7,28 was used to measure the contact angles. This method is based on the determination of the radii of the Newton interference rings when the film is observed in reflected monochromatic light. Knowing the film thickness, the contact angle was calculated from

tg2θ ) B2 - 4A(C - h/2)

(3)

where

A)

l 2x1 - x2 ; 2x1x2 x2 - x1

2

B)

l x2 - 2x1 ; 2x1x2 x2 - x1

Figure 1. (a) Thickness (b) Contact angle of C12Ej type surfactants stabilized foam films with various EO sizes. The solid line is a guide for the eye. Csurfactant ) 2(cmc); CNaCl ) 0.1 M; T ) 22 °C.

λ l C) ;l) 2 4n

x1 is the distance between the first and the second Newton ring, and x2 is the distance between the first and the third Newton ring. λ ) 456 nm is the wavelength, and n is the refractive index of the solution (a detailed description of this method with the picture showing Newton rings around the film is given in our earlier paper21). The process of film formation and its equilibrium behavior were recorded by a video camera. Data acquisition was performed using a PC equipped with a frame grabber, Flash point 128 (Integeral Technologies, Inc., Indiana, USA). The film size and the width of the Newton rings were evaluated by an image processing program, Image Pro Plus (Media cybernetics, Maryland, USA). x1 and x2 were determined by averaging the data obtained from four measurements with successive 30° rotation around the center of each film as it is described in.21 Surface Tension. The surface tension of the solutions was measured by using the du Nou¨y ring method utilizing a Lauda (KM5) tensiometer with an accuracy of (0.1 mN/m. The surface tension was measured at least 20 times for each surfactant concentration. To compare the permeability of different surfactant stabilized foam films, in each case the concentration of surfactant was fixed as 1.5 × 10-4 ( 0.5 × 10-5 mol/L. Those concentrations are two times above the critical micelle concentration (cmc). The cmc values for these surfactants varies between 6.6 × 10-5 mol/L and 7.4 × 10-5 mol/L, the precise values are taken from ref 3 and summarized in the appendix in Table A1 (given in the Supporting Information). 0.1 M NaCl was added into each test solution to prepare the NBFs.29 The experiments were carried out at 22 °C. The solutions were equilibrated in the thermostated apparatus for at least 1 h before measurements.

Results Figure 1a shows the film thickness as a function of number of EO units, nEO, at a constant surfactant concentration of 2(cmc). The thickness of the foam film increases upon increasing the number of EO units, and at higher EO units (>EO14), the thickness tends to reach (25) Krustev, R.; Mueller, H.-J.; Toca-Herrera, J. L. Colloids Polym. Sci. 1998, 276, 518. (26) There is a large difference in the capillary pressure between the ring cell (Pc ) 30-40 Pa) and the diminishing bubble (Pc ≈ 700 Pa) but this difference does not affect the film thickness in the present study, since we always have Newton black films whose thickness is not affected by the external parameters such as pressure or salt concentration. (27) Muruganathan, RM.; Krustev, R.; Mueller, H.-J.; Moehwald, H. Langmuir Submitted. (28) Kolarov, T.; Scheludko, A.; Exerowa, D. Trans. Faraday Soc. 1968, 64, 2864. (29) Mu¨ller, H. J.; Rheinla¨nder, T. Langmuir 1996, 12, 2334.

Figure 2. Surface tension of C12Ej type surfactants with various EO size. The solid line is a guide for the eye. Csurfactant ) 2(cmc); CNaCl ) 0.1 M; T ) 22 °C.

a plateau value. Complementary contact angle between the film and its meniscus as shown in Figure 1b reveal constancy irrespective of the number of EO units present in the foam film. The surface tension values, which are necessary for the contact angle calculations, of the EO surfactant solutions show that there is a slight increase in the surface tension between C12E5 and C12E9 and a notably high value of the surface tension for C12E18 (Figure 2). The gas permeability through the foam film was measured at the same conditions (i.e., similar surfactant and salt concentration and temperature) as were the film thickness and contact angle measurements. Films stabilized with a low number of EO chains show high permeability compared to those with a high number of EO chains. The systematic decrease of film permeability upon increasing the number of ethylene oxide units is given in Figure 3. Discussion Film Thickness vs Headgroup Size. Figure 1a shows a systematic increase of film thickness upon increasing the EO numbers from 5 to 18. The thickness difference between EO5 stabilized (6.8 nm) and EO9 stabilized film (9.3 nm) is about 2.7 nm. This is an increase of 40%, in other words, 0.7 nm per EO group, whereas the thickness difference between the films stabilized by EO9 and EO18 is about 1.7 nm. This is a difference of 20% or 0.2 nm per EO group. Measured film thicknesses are usually attributed to the two distinguished parts of the foam films (i) monolayer thickness (hml) and (ii) aqueous core thickness (haq). The thickness of the monolayer depends on the

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Figure 3. Permeability of C12Ej type surfactants stabilized foam films with various EO sizes. Csurfactant ) 2(cmc); CNaCl ) 0.1 M; T ) 22 °C.

size of the adsorbed surfactant molecules (hml ) htail + hhead). In the present study, the htail remains the same; that is, the approximate length of a single CH2 unit is about 1.25 Å, and all of the surfactants used in this study consist of 12 CH2 units which results in a contour length of the tail of htail ) 15 Å. Therefore, the measured increment in the film thickness originates either from hhead or from haq. When the number of EO units is increased, the volume of the EO region also increases. This not only expands the area per molecule at the interface but also increases the thickness of the film. An approximate estimation for the degree of expansion of the headgroups while increasing the number of monomer units can be made by calculating the Flory radius30

RF ) lN3/5

(4)

where N is the number of monomer units and l is the length of a single monomer unit. In this work, the unit length is kept constant i.e., l ) 0.35 nm (CH2CHO) and the variable is N which is the number of EO units. The theoretically estimated thickness of a single adsorbed monolayer upon increasing the number of EO units is summarized in Table 1. The deviation between the measured and theoretical film thicknesses increases as the size of the headgroup increase. When estimating the theoretical film thickness, we assume a constant aqueous core thickness of haq ) 2 nm; for example, if the theoretical hml for C12E5 is 2.1 nm, foam film has two monolayers therefore 2hml ) 4.2 nm. The difference between the measured film thickness and the theoretical bilayer thickness is about 2 nm that should come from the central aqueous core that separates the two adsorbed monolayers. This 2 nm thick central aqueous core is always there irrespective of the number of the EO units that are present in the adsorbed surfactants. This is confirmed by the simultaneous contact angle measurements. A contact angle is a direct measure for the film interactions (∆gf) and disjoining pressure (Π) in the film.31 The contact angles are measured between the film and its meniscus, and they are sensitive to changes in the interaction in the film. The specific film interaction free energy ∆gf is a convenient quantity for studying the interaction forces, and it is evaluated from the measured contact angle and the surface tension of the bulk solution32 f

∆g ) 2σ(cos θ - 1)

(5)

The low contact angle values (≈1.5°) indicate that the

repulsion between the headgroups is very strong; whereas, the constant contact angle values (Figure 1b) imply that there is a constant interaction in the film irrespective of the size of the surfactant headgroup. Table 2 shows that the specific film interaction free energy remains unchanged for all of the EO surfactants stabilized foam films. This means that there is a constant interaction in the film irrespective of the size of the headgroup; that is, the aqueous core thickness remains constant upon moving from C12E5 to C12E18. Flory theory of flexible chain molecules30 delivers a proportionality to the square root for the end-end distance and the radius of gyration of randomly coiled chains. Plotting against the square root of the degree of ethoxylation vs measured film thickness (shown in Figure 4) yields a part which linearly depends on each other and the other part which has no linear relationship. The part which shows the linear relationship is in agreement with Florys theory of flexible chain molecules which predicts the coil structure of the EO chains. The deviation from the linear relationship indicates that at high EO numbers the chains are more extended in the direction of the film interior29 than given by the random coil conformation. From the results of thickness and the contact angle measurements, we infer that the volume of the headgroups from the two adsorbed monolayers expand laterally while increasing the number of EO units, but the monolayers always keep the normal distance between them. The expansion scales with the number of EO groups which means that no condensation of the chains is observed. If this is true, then the gas permeability through these films should be influenced only by the film thickness. Influence of Over-All Film Structure on K. Taking the film structure into account, a detailed expression for the permeability is used15

K)

DaqH haq + 2Daq/kml

(6)

Here Daq 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. There are two limiting cases to describe the permeability. It is either governed by the central aqueous core or by the adsorbed monolayers. Case 1, for thick films, i.e., 2Daq/kml , haq, the permeability is characterized by the transport properties of the gas through the aqueous core

K)

DaqH haq

(7)

In this regime, the film permeability increases with decreasing film thickness, whereas the thickness of the monolayers remains irrelevant. Case 2, for thin films, i.e., haq , 2Daq/kml, the permeability is governed by the permeability of the adsorbed monolayers by kml

K)

DaqH 2Daq/kml

(8)

(30) Flory, P. J. Statistical Mechanics of Chain Molecules; Wiley: New York, 1969. (31) De Feijter, J. A.; Vrij, A. J. Colloid Interface Sci. 1978, 64, 269. (32) De Feijter, J. A.; Rijnbout, J. B.; Vrij, A. J. Colloid Interface Sci. 1978, 64, 258.

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Table 1. Estimated Size of Polar and Nonpolar Parts of the Used Surfactants

surfactant

measured film thickness h ) 2 hml + haq h (nm)

polar group sizes estimated using eq 4 hhead (nm)

estimated size of the nonpolar group htail (nm)

theoretical hml (nm)

theoretical h (nm)a

C12E5 C12E6 C12E7 C12E8 C12E9 C12E18

6.79 ( 0.49 7.34 ( 0.21 7.45 ( 0.32 8.45 ( 0.15 9.33 ( 0.54 11.0 ( 0.41

0.60 0.64 0.67 0.70 0.73 0.92

1.5 1.5 1.5 1.5 1.5 1.5

2.10 2.14 2.17 2.2 2.23 2.42

6.20 6.28 6.34 6.40 6.46 6.84

a

Assuming a constant aqueous core thickness haq ) 2 nm.

Table 2. Measured Surface Tension, Contact Angle, and Specific Film Interaction Free Energy for Various EO Surfactants surfactant

surface tension (mN/m)

C12E5 C12E6 C12E7 C12E8 C12E9 C12E18

28.65 28.8 29.5 29.2 29.5 33.9

contact angle (degree) 1.31 ( 0.40 1.44 ( 0.33 1.38 ( 0.31 0.94 ( 0.40 1.27 ( 0.45 large error

∆gf (mJ/m2) 0.015 0.018 0.017 0.010 0.015

It is easy to understand the permeability in terms of resistance which is the inverse of the permeability, 1/K. Then the relation between the permeability of the whole film and the permeability of the two covering adsorption layers of the film and the aqueous core is15,33

1 2 1 + ) K kml kaq

(9)

Here, kaq ) Daq/haq is the permeability of the central aqueous core. In our case, we have NBFs where the central aqueous core is very thin and negligible in size.7 Therefore, we assume that the two surfactant monolayers are adsorbed onto each other; that is, the headgroups are in direct contact. Now we can omit the term 1/kaq from eq 9, to obtain

2 1 ) K kml

(10)

The monolayer resistance (1/kml) is influenced by the geometry of the adsorbed surfactant molecules and also the quantity of the surfactants that has adsorbed at the interface. The surfactant geometry is determined by two distinct parts in the individual surfactant molecules (1) the hydrophobic tail and (2) the hydrophilic head. In our case, all of the chosen surfactant molecule possess the same size of the hydrophobic part (C12); therefore, for the same lateral density (Γ), the resistance due to the hydrophobic part is expected to remain the same from C12E5 to C12E18. The controlled variable of this study, that is, the hydrophilic head (EO) size, might be the cause for the observed changes in the film permeability. Therefore, further discussion is restricted to the influence of the headgroup size on the various factors that can influence the film permeability, such as, film thickness, adsorption density, and conformational changes at the film surface. Adsorption Density and Film Permeability. The permeability of NBFs is governed by the adsorption density of the surfactant molecules at the film surfaces.13,27 Measurement of the bulk surface tension (surface tension of the solutions from which the films are derived) delivers (33) Barnes, G. T. Adv. Colloid Interface Sci. 1986, 25, 89.

Figure 4. Measured film thickness as a function of the degree of ethoxylation. The solid line is a guide for the eye.

the adsorbed amount of surfactant molecule at the air/ liquid interface. Figure 2 shows that there is a systematic but meagre increase of surface tension while increasing the number of oxyethylene units. This figure shows only a trend of the influence of the headgroup size on the surface tension at a particular surfactant concentration, it is not possible to derive the quantitative adsorption density values using our data. Recently, various groups have precisely measured a set of surface tension isotherms for C10Ej and C12Ej type surfactants.34,35,36 Persson et al.36 showed that the area per molecule increases while increasing the number of EO units (≈ 3 Å2/molecule for every EO unit), and the results from Karraker et al.34 reveal that the maximum adsorption (Γm) decreases while increasing the headgroup size. The neutron reflectivity experiments of Thomas, Penfold and Lu35 on various C12Ej type surfactants also exhibit a similar decrease of Γm and increase of area per molecule upon increasing the headgroup size. In Table A2 (see the Supporting Information), we summarize the area per molecules measured by various groups for C10Ej and C12Ej type surfactants. An increase in the steric repulsion between the headgroups might partly cause the drop in the adsorption density. Such a decrease in the adsorption density as shown in refs 34-36 should result in an increase of kml. On the contrary, our results in Figure 3 show that K decreases while increasing the number of EO units, suggesting that kml is not responsible for the changes in the film permeability. Film Thickness and Film Permeability. The gas permeability of foam films depends on the film thickness.7,16,37 Thicker film exhibits smaller permeabilities; decreasing the film thickness increases the film perme(34) Karraker, K. A. Ph.D. Thesis, Chemical engineering division, UC Berkeley, CA, 1999. (35) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143. (36) Persson, C. M. Ph.D. Thesis, Department of chemistry, KTH, Stockholm, 2002. (37) Krustev, R.; Platikanov, D.; Nedyalkov, M. Colloids Surf. A 1993, 79, 129.

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Figure 5. Linear fit of film permeability against the inverse of film thickness.

ability in accordance with eq 7. The present study also reveals a similar thickness/permeability relationship. The major difference between the earlier studies and the present work is the way we change the film thickness. In ref 37, the film thickness of ionic surfactant stabilized films was changed by adding counterions thereby screening the surface charges that originate from the adsorbed ionic surfactant molecules. In the present study, the film thickness was changed by changing the nonionic surfactant headgroup size. We found that the permeability linearly changes with the thickness. The linear fit of film permeability against the inverse of film thickness is given in Figure 5. The good linear fit suggests that the thickness is the limiting parameter for the permeability but on the other hand, the linear fit for K vs 1/h does not go through the origin. This means that, in case of indefinitely thick films when 1/h is zero, the permeability is not zero, which indicates that the increase in the film thickness governs only a part of the permeability. There is a part which does not depend on the film thickness or depends differently on film thickness. Conformation and Configuration of PEO-Chain. The increase in the film thickness with the EO chain length partly explains the decrease in K, at the same time, interestingly, neither kml nor kaq directly influences K. At the moment, the reason for this is not entirely clear; however, to explain this, we propose a model of conformation and configuration changes of PEO chains at the film surfaces. There are two possible conformations for EO chains, stretched and random coil, depending on the average distance, d, between grafting sites and the Flory radius.30 The EO chain develops as random coils or mushrooms when the distance between headgroups is larger than RF, whereas the EO chain adopts a fully extended state or brush regime when the distance is smaller than RF.38 For the largest EO group (N ) 18), we estimate a headgroup size of 1.8 nm (Table 1) which cannot explain the measured film thickness of 11 nm for a coiled configuration. Hence, we must assume a brush configuration where the maximal extension would be 6 nm which is roughly half the film thickness. When the headgroup size is increased, the surface density decreases and the area per molecule increases; hence, the distance between two headgroups becomes larger at higher EO numbers. This enables the lateral repulsion between the headgroups to decrease while increasing the number of EO groups (from C12E5 to C12E18) and may result in conformational changes in the PEO chains from random coil conformation to extended brush. Figure 6 schematically shows the random coil structure of the EO headgroups in a confined area, like foam films. When the nEO units are increased. the coil size increases in the x and y directions (Figure 6 bottom). In this way,

Figure 6. Schematic diagram of a NBF stabilized by C12Ej type surfactant.

increasing the coil size increases the film thickness and decreases K. Apparently increasing the coil size decreases the film surface density which influences the film permeability. Yet another possibility is the formation of hydrogen bonding. Tortuosity of EO coils favors the formation of inter and intramolecular hydrogen bonding.39 Increasing the EO units allows the surfactants to pack at the interface in more favorable conformations, allowing formation of intralayer hydrogen bonds between the headgroups either directly or via water molecules. At some point due to the increment of hydrogen bonding there will be a gel-like network consisting of hydrated oxyethylene coils.40 Our present data do not allow to quantify the existence of the gel structure in the foam film and its influence on the film permeability. Conclusion The thickness of the NBF increases by increasing the size of the hydrophilic headgroup (number of EO chains in the polyoxyethylene surfactants), and this results in a decrease of the gas permeability. The film-meniscus contact angle and the free energy of film interaction remain constant for all C12Ej stabilized films indicating that the interactions in the film remain unchanged and there is a constant aqueous core thickness irrespective of the size of the headgroup. The adsorption density at the film surfaces decreases when the EO chain length is increased. The observed decrease in the film permeability is an apparent contradiction to the expected adsorption densitypermeability relations. This proves that the increased density of EO groups provides an additional resistance to permeation. The results are therefore interpreted taking the coil structure of the EO chains into account. Upon increasing the EO units, the size of the coil grows which increases the NBF thickness (favors the decrease of K) and decreases the air/liquid surface density (favors the increase of K). On the other hand, at higher EO numbers, the increased flexibility of the EO chain and low surface (38) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189. (39) Michaels, A. S.; Bixler, H. J. J. Polym. Sci. 1961, L, 413. (40) Diffusion in Polymers; Neogi, P., Ed.; Marcel Dekker: New York, 1996.

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density allows the surfactants to pack at the interface in more favorable extended brush conformations. Formation of inter- and intralayer hydrogen bonds between the EO units either directly or via water molecules would also favor the decrease of K while increasing the number of EO units. Acknowledgment. We thank Mrs. Emrich for assistance in the experiments and Dr. Czicocki, MPI-KGF for providing us the C12E18 surfactant. This work was

Muruganathan et al.

funded by the Deutsche Forschungs Gemeinschaft, Germany (Project No. Mu¨ 1040/9). Supporting Information Available: Critical micelle concentrations for the surfactants used in this study (Table A1). Area per molecule at the cmc for C10Ej and C12Ej type surfactants at the air/liquid interface (Table A2). This material is available free of charge via the Internet at http://pubs.acs.org. LA052389F