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Langmuir 1996, 12, 1336-1342
Disjoining Pressure Measurements for Foam Films Stabilized by a Nonionic Sugar-Based Surfactant Vance Bergeron* Groupe Colloids, Service de Chimie Moleculaire, Centre d’Etudes de Saclay, 91191 Gif sur Yvette, France
Åsa Waltermo and Per M. Claesson Laboratory for Chemical Surface Science, Department of Chemistry, Physical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden, and Institute for Surface Chemistry, P.O. Box 5607, S-114 86 Stockholm, Sweden Received July 17, 1995. In Final Form: November 20, 1995X Disjoining pressure isotherms for foam films made from a nonionic surfactant, octyl β-glucoside, are measured at different surfactant concentrations, ionic strengths, and solution pH values. Below the cmc an electrostatic double-layer repulsion is present and dominates the long-range interaction. The decay length of the forces agrees with the expected Debye length and the measured long-range interactions are consistent with solutions to the nonlinear Poisson-Boltzmann equation using constant charge conditions. The deduced surface charge densities increase with pH and ionic strength but decrease with increasing surfactant concentration. At, or just above, the cmc, surfactant covers the interface and suppresses the charge sufficiently to induce a transition from a common black film to a Newton black film. Ultimately, the film stability is determined by both surface forces and elasticity. Combining both, via an overall film tension, leads to a general expression for the film elasticity.
Introduction Foams play a decisive role in a variety of fields and their properties are of both technical and fundamental interest. Since foam is made of thin liquid films separated by gas, its stability is ultimately determined by the strength of these individual films. Foam lifetimes are governed by film rupture and/or interbubble gas diffusion across the films. Therefore a fundamental understanding of foam relies on a detailed knowledge of the films isolating the dispersed gas phase. Several different mechanisms affect film rupture but the initial concern is liquid drainage out of the film. Hence, properties that influence hydrodynamic flow within the film, such as bulk and surface viscosity, or surface elasticity (Gibbs Marangoni phenomena) are important. Moreover, changes in free energy associated with film thinning will also effect fluid flow. These include molecular interactions that create repulsive forces between the interfaces and impede or completely arrest drainage. Similarly, increases in film area are also associated with unfavorable changes in free energy and tend to resist local thinning fluctuations and contribute to film stability.1 Conversely, attractive forces across the film will also arise (i.e., van der Waals forces), which promote drainage and cause film rupture. Excluding bulk viscosity, all of the properties effecting film stability depend on the surface active components (surfactants) adsorbed at the interface. Therefore the type (e.g., cationic, anionic, nonionic, or amphoteric) and quantity of surfactant will determine the important mechanisms involved in film stabilization. It is also important to note, that since all of the film-stabilization mechanisms rely on the same fundamental property, surfactant adsorption, they are inherently interdependent. Thus, changes in surfactant adsorption will affect more than just one film property and simple correlations with a particular property may not always help identify the important mechanisms that govern a film’s stability. * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, February 1, 1996. (1) Vrij, A.; Overbeek, J. Th. G. J. A. Chem. Soc. 1968, 90, 3074.
Nevertheless, for solutions without polymer additives, bulk flow effects are normally unimportant after the first few hundreds seconds of a film’s lifetime, and stability for extended periods is controlled by the molecular interactions that arise when the two film interfaces are in close proximity. For thin liquid films (i.e., foam, emulsion, etc.) these interactions are quantified by the excess pressure created normal to the film interfaces, and normally termed the disjoining pressure.2 Since these interactions depend on the distance between the interfaces, the disjoining pressure is measured as a function of the film thickness to create so-called disjoining pressure isotherms. These isotherms can be used to determine directly the individual film stability and are valuable for understanding fundamental aspects of intermolecular forces.3 In the later regard, they are analogous to “surface force” studies.4 Previous measurements of foam-film disjoining pressure isotherms have concentrated on ionic surfactant systems;5-8 however Kolarov et al.9 measured isotherms for two different nonionic poly(oxyethylene) surfactants. Results from their study reveal that foam films containing nonionic surfactant can actually be stabilized by repulsive electrostatic interactions. Since then several experimental investigations on isolated foam films from nonionic surfactant solutions have confirmed that electrostatic forces are present,10-13 and the results have been interpreted using the classical DLVO theory under constant charge conditions. However, the origin of the interfacial (2) Derjaguin, B.; Obuchov, E. Acta Phys. U.R.S.S 1936, 5, 1. (3) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. In Surface Forces; Kichner, J. A., Ed.; Consultants Bureau: New York, 1987. (4) Israelachvili, J. In Intermolecular and Surface Forces, 2 ed.; Academic Press, Inc.: San Diego, CA, 1991. (5) Exerowa, D.; Kolarov, T.; Khristov, Khr. Colloids Surf. 1987, 22, 171. (6) Bergeron, V.; Radke, C. J. Langmuir 1992, 8, 3020. (7) Bergeron, V.; Fagan, M. E.; Radke, C. J. Langmuir 1993, 9, 1704. (8) Aronson, A. S.; Bergeron, V.; Fagan, M. E.; Radke, C. J. Colloids Surf., A 1994, 83, 109. (9) Kolarov, T.; Cohen, R.; Exerowa, D. Colloids Surf. 1989, 42, 49. (10) Barneveld, P. A.; Scheutjens, J. M. H. M.; Lyklema, J. Colloids Surf. 1991, 52, 107. (11) Manev, E. D.; Pugh, R. J. Langmuir 1992, 47, 2253. (12) Waltermo, A° .; Manev, E.; Pugh, R.; Claesson, P. J. Dispersion Sci. Technol. 1994, 15, 273. (13) Cohen, R.; Exerowa, D. Colloids Surf., A 1994, 85, 271.
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Langmuir, Vol. 12, No. 5, 1996 1337 pressure in the cell is then regulated by a syringe pump which allows us to change the capillary pressure imposed on the film. As shown by Bergeron and Radke,6,17 this capillary pressure can be related to the disjoining pressure, Π, in a plane-parallel film by the following expression
Π ) Pg - Pr +
Figure 1. Schematic drawing of a Thin-Film Balance.
charge and the exact nature of all the forces acting in foam films stabilized by nonionic surfactants and how these forces are influenced by the nature of the surfactant and by additives are still unknown. Moreover, except for Kolarov et al.9, previous works only measure a single point on the disjoining pressure isotherm, which severely limits the amount of information available. Therefore, to gain more insight about thin-liquid films stabilized with nonionic surfactants, we measure the full disjoining pressure isotherms for foam films made from a nonionic sugar-based surfactant, octyl β-glucoside. Octyl β-glucoside, C8β, is a simple nonionic surfactant containing a small glucose headgroup with a relatively short hydrocarbon chain, C8. This surfactant was chosen not only for its simplicity but also for its industrial importance. Sugar-based surfactants have low toxicity, biodegrade easily, and are widely used in membrane research. Furthermore, Waltermo et al.12 have recently reported that octyl β-glucoside foam films display electrostatic forces similar to those observed for nonionic poly(oxyethylene) surfactants. Hence, in this work we measure the complete disjoining pressure isotherms for octyl β-glucoside under various solution conditions to gain further insight into the origin and nature of the forces that stabilize octyl β-glucoside foam films. We also relate these measurements to film stability and show how they compare to previous nonionic foam-film measurements. Experimental Section Materials. Octyl β-glucoside, C8β (n-octyl β-D-glucopyranoside), was obtained from Sigma and carefully stored in a moisturefree environment below 0 °C. No minimum in the surface tension versus concentration curve was observed and the surfactant was used without further purification. Sodium hydroxide (NaOH) and hydrochloric acid (HCl) were purchased from Merck while potassium hydroxide (KOH) was obtained from Eka Nobel. Potassium bromide (KBr), pro analysi grade, was also supplied by Merck, and to drive off organic contaminants, it was roasted at 500 °C for 24 h before use. Finally, all solutions were prepared with water, pretreated by a Milli-RO 10PLUS unit followed by a Milli-Q PLUS185 unit and final micropore filtration. Methods. The surface tensions are determined by the Du Nou¨y ring method, utilizing a surface tension/contact angle meter, Sigma 70, from KSV Instruments Ltd. Measurements of the pH were performed with a PHM portable pH meter from Radiometer. Disjoining pressure isotherms are measured with a Thin-Film Balance, TFB, based on the original design of Mysels and Jones.14 This device, sketched in Figure 1, imposes a capillary pressure on the film, which in equilibrium is balanced by the disjoining pressure. Single thin-liquid foam films are formed in the hole drilled through a fritted glass disk, onto which a glass capillary is fused. This solution-permeable film holder is placed in a gastight measuring cell with the free end of the capillary tube exposed to a reference pressure (i.e., atmospheric pressure). The gas (14) Mysels, K. J.; Jones, M. N. Discuss. Faraday Soc. 1966, 42, 42.
2γ - ∆Fghc r
(1)
where Pg and Pr are the gas and external reference pressures, respectively, γ is the surface tension of the solution, r is the radius of the capillary tube, ∆F is the density difference between the aqueous surfactant solution and the gas, hc is the height of solution in the capillary tube above the film, and g is the gravitational constant. Each term on the right side of eq 1 is measured independently, providing a direct measurement of Π. Film thicknesses are measured via Sheludko’s microinterferometric technique15,16 in conjunction with video microscopy. White light from a 100-W halogen lamp is passed through a heat filter and focused at normal incidence onto the individual foam film formed in the porous-plate holder. Reflected light from the film is then split and sent to a CCD video camera and a fiber optic probe placed in the microscope ocular. The video camera documents film drainage throughout the experiment while light from the fiber optic is filtered (λ ) 546 nm) and analyzed with a sensitive photomultiplier tube. The so-called “equivalent” film thickness is then calculated from the standard Scheludko interferometric equation which assumes a constant refractive index across the film15,16
heq )
( )
λ arcsin 2πnw
x
1+
∆ 4R(1 - ∆)
(2)
(1 - R)2
where ∆ ) (I - Imin)/(Imax - Imin), heq is the equivalent film thickness, λ is the wavelength of light, R ) (nw - 1)2/(nw + 1)2, and nw is the refractive index of the surfactant solution. I is the instantaneous value of the reflected intensity while Imax and Imin correspond to the last interference maximum and minimum values. This equivalent thickness is slightly thicker than the true film thickness, h, because the surfactant adsorption layers at each film interface have a higher refractive index than the aqueous core. To correct for this difference we adopt the following multilayer correction factors, derived by Duyvis18
h ) heq - 2hhc
(
) (
nhc2 - nw2 nw2 - 1
- 2hpg
)
npg2 - nw2 nw2 - 1
(3)
where hhc is the thickness of the surfactant hydrocarbon tails at the interface and hpg is the surfactant’s polar headgroup thickness. These values are calculated from the volume of the hydrocarbon chain and the polar headgroup, together with the area per molecule at the interface, which we evaluate from surface tension data using Gibbs’ adsorption equation. nhc and npg are the refractive indexes for the hydrocarbon tails and polar head groups and are assigned values of nhc ) noctane ) 1.397 and npg ) nglucose ) 1.510. Finally, the thickness of the film’s aqueous core, haq, can be determined by subtracting the thickness of the adsorbed layers from the total film thickness evaluated in eq 3
haq ) h - 2(hhc + hpg)
(4)
Disjoining pressure isotherms are generated by measuring the equilibrium film thickness after applying a fixed capillary pressure to the film. Equilibrium conditions for the C8β films are reached after 10-90 min depending on the magnitude and change of the imposed capillary pressure. Systematic changes to the capillary pressure by altering the gas cell pressure, Pg, allow us to map out the entire repulsive (positive) branch of the disjoining pressure isotherm (negative capillary pressures cannot be imposed with the porous-plate method). The disjoining (15) Scheludko, A. Kolloid Z. 1957, 155, 39. (16) Scheludko, A. Adv. Colloid Interface Sci. 1967, 1, 391. (17) Bergeron, V. PhD Thesis, University of California, Berkeley, 1993. (18) Duyvis, E. M. Thesis, Utrecht, 1962.
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Figure 2. Surface tension for C8β in water (×) and in 5 mM KBr (O) as a function of surfactant concentration. The dotted line is calculated according to the Szyszkowski equation and the dashed line is fitted to a polynomial of second degree. The inset shows the Gibbs elasticity as a function of surfactant concentration. The calculation of the elasticity is based on a third order polynomial fit of γ versus ln Γ.
Bergeron et al.
Figure 3. Adsorption isotherm for C8β calculated from the surface tension as a function of surfactant concentration.
pressures are then plotted against the film’s aqueous core thickness, haq, to facilitate theoretical comparisons. All of the isotherms that we report are measured at 21 ( 1 °C and they were reproduced at least once and in some cases several times. Additional experimental details can be found elsewhere.6,17
Results Surface Tension Results. Figure 2 contains surface tension versus surfactant concentration data for C8β in water and for C8β in a 5 mM KBr solution. The two lines in the figure represent a second order polynomial fit (dashed line) to the data and a fit using the Szyszkowski equation (dotted line).19 Both fits appear to agree with the measured surface tension isotherm equally well at surfactant concentrations above 0.2 mM; however, when surface tension data are used to calculate molecular adsorptions20 and surface elasticities,21 it has been demonstrated recently that polynomial fits, instead of classical adsorption isotherm models, give better results. From Figure 2 we determine a cmc of ∼20 mM, in agreement with literature values, and note that the surface tension isotherm does not display a dip, indicating that no surface active impurities are present. Furthermore, as seen in the figure, the addition of 5 mM KBr has no effect on the surface tension isotherm, implying that KBr does not influence C8β adsorption at the air-water interface. After applying Gibbs’ adsorption equation, we find at the cmc the surfactant saturated interface has a molecular area of 0.36 nm2. The Gibbs elasticity, , is also determined from the surface tension isotherm by applying, ) -Γ dγ/dΓ, where Γ is the surfactant surface excess and γ is the bulk surface tension. The calculated elasticities as a function of the bulk surfactant concentration are shown in the inset in Figure 2, while the full adsorption isotherm is displayed in Figure 3. Disjoining Pressure Results. Changing Surfactant Concentration. Figure 4 displays the disjoining pressure (19) Szyszkowski, B. Z. Phys. Chem. 1908, 64, 385. (20) Simister, E. A.; Thomas, R. K.; Penfold, J.; Aveyard, R.; Binks, B. P.; Cooper, P.; Fletcher, P. D. I.; Lu, J. R.; Sokolowski, A. J. Phys. Chem. 1992, 96, 1383. (21) Jayalakshmi, Y.; Ozanne, L.; Langevin, D. J. Colloid Interface Sci. 1995, 170, 358.
Figure 4. Disjoining pressure isotherms for C8β in 0.1 mM KBr solution: 2, 3 mM surfactant concentration; 0, 10 mM surfactant concentration; b, 21 mM surfactant concentration; ], 25 mM surfactant concentration. The solid lines are calculated according to DLVO theory. The arrows indicate a transition to a Newton black film (dashed line). The inset shows the DLVO fits for 10 mM C8β using different Hamaker constants: 1.85 × 10-20 J (dotted line); 3.7 × 10-20 J (solid line); 5.5 × 10-20 J (dashed line).
isotherms for four different C8β concentrations, all with 0.1 mM added KBr and at natural pH (i.e., pH ∼ 6). The two lowest concentrations shown are for 3 and 10 mM C8β, while the highest are slightly above the cmc at 21 and 25 mM. At both of the low concentrations, common black films (CBF) are formed, and in the low pressure region of these isotherms film thicknesses extend out to 80 nm. Further increases in the pressure subsequently lead to decreases in the film thickness until disjoining pressures near 3 kPa are reached. At this point, the films which are approximately 20 nm thick, rupture in a somewhat statistical fashion. That is, the exact values of the rupture pressures and thicknesses are ill-defined and depend on external disturbances. Similar to the low concentration data, the high surfactant concentration films also show a long-range com-
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Langmuir, Vol. 12, No. 5, 1996 1339
Table 1. C8β Film Data Obtained from DLVO Fitting [C8β] (mM)
[salt] (mM)
3 10 21 25 10 10 21 10 10
0.1 0.1 0.1 0.1 1 5 1 1 1
pH
6 5 9/10
κ-1 (nm)
|ψ0| (mV)
|σ0| (mC/m2)
area/charge (nm2)
30.4 30.4 30.4 30.4 9.6 4.3 9.6 9.6 9.6
57 44 21 15 48 52 16 20 48
1.6 1.2 0.5 0.4 4.1 10.1 1.2 1.5 4.1
98 138 318 452 39 16 133 106 39
ponent to the disjoining pressure isotherm. However, in these isotherms the thickest CBF films only reach 60 nm. Furthermore, upon increasing the pressure, thickness reductions follow the same slope (d log Π/dh) as the lower C8β concentration films, but instead of rupturing at 20 nm, these CBF films undergo a discrete transition to the Newton black film (NBF) state. This transition is only possible at the higher surfactant concentrations because NBF formation requires interfaces with a high surfactant coverage. The NBF films are very thin, with an aqueous core of 1 ( 0.3 nm (total film thickness 4.4 ( 0.3 nm). Hence, these films consist of two surfactant monolayers with only a small amount of water separating the headgroups. The magnitude of the disjoining pressure needed to make the NBF transition decreases with increasing surfactant concentration, and once the films enter the NBF state, no further changes in the film thickness are observed within the capillary pressure range we are able to impose. As demanded by thermodynamic considerations, these NBF films do finally rupture; however, this occurs at higher capillary pressures than for the CBF films present at low surfactant concentration. A dashed line has been drawn on the isotherm to stress this point. All of the solid curves sketched in Figure 4 correspond to model fits using DLVO theory imposing constant charge boundary conditions and the theoretical Debye length. The parameter extracted from the fits is the apparent surface charge density, σ0. These values are provided in Table 1. Furthermore, the insensitivity of the fits to our choice of a Hamaker constant is shown in the figure inset for the 10 mM surfactant concentration data set. As can be seen in Figure 4, before film rupture or transition to a NBF, very good DLVO fits are obtained. We also note that the magnitude of the double-layer repulsion decreases with increasing surfactant concentration, demonstrating a reduction in interfacial charge. Changing Electrolyte Concentration. Two examples of how the electrolyte concentration affects the disjoining pressure isotherms of C8β foam films are shown in Figures 5 and 6. In Figure 5 the surfactant concentration is held fixed at 10 mM (
