Langmuir 1992,8, 3020-3026
3020
Equilibrium Measurements of Oscillatory Disjoining Pressures in Aqueous Foam Films V. Bergeron and C. J. Radke' Earth Sciences Division, Lawrence Berkeley Laboratory, and Department of Chemical Engineering, University of California, Berkeley, Berkeley, California 94720 Received April 2, 1992. In Final Form: July 23, 1992 Disjoining pressure isothermsare measured for single, isolated foam films stabilized with sodium dodecyl sulfate above the critical micelle concentration (cmc). The measured isotherms exhibit an equilibrium oscillatory component that extends out to film thicknesses as large as 50 nm. The oscillations originate from surfactant structuring within the film and are responsible for the multiple black films extensively studied by Perrin in 1918. We find that as film thickness decreases, the slopes and peak heights of the oscillations increase for each subsequent black film encountered. The discrete changes in film thickness observed at each black film transition range from 6 to 10 nm and are a function of the ionic strength and surfactant concentration. Pressures required to rupture the multiple black films are several orders of magnitude lower than the finalfilm-rupturepressure. Finally, the oscillatory form of the disjoiningpressure permitsquantitative interpretation of the stepwise thinningbehavior observed in films containing surfactant above the cmc.
Introduction Thin-liquid soap films have been used extensively in the past to study a variety of phenomena. The first recorded studies of soap films were made by Hooke' and Newton2in the late seventeenth century. They employed soap bubbles to investigate the reflections, refractions, and colors of light. In doing so they were the first to document the so-called black and multiple black films that occur in foam films that are too thin to produce interference colors (400nm). Two centuries later Reinold and Rucker? following the work of Plateau, studied soap films to determine 'the radius of molecular action". This was accomplished by investigating the effect film thickness has on surface tension. Their results led them to conclude that thin-film forces become sensible a t distances of approximately 50 nm. These experiments are the forerunner to modern day disjoining-pressure measurements. The disjoining pressure, II, was first introduced by Derjaguin and O b u ~ h o v .II ~ is the excess pressure, acting normal to a film interface, which results from the overlap of molecular interactions between the interfacial layers. This pressure, which is a function of the film thickness, can be either positive (disjoining) or negative (conjoining). The classical description of the thin-film forces that .~ generate these pressures is known as DLVO t h e ~ r y This theory combines two types of interaction forces: electrostatic repulsive forces, which tend to stabilize films, and London-van der Waals dispersion forces, which are typically responsible for destabilizing films. DLVO theory, however, cannot account for the stepwise-thinning (otherwise known as stratification or multiple black) behavior
* Author to whom correspondence should be addressed.
(1) Hooke, R. In The History of the Royal Society of London; Brich, T., Ed.; London, 1757; Vol. 3, p 29. (2) Newton, I. BookII, Obs.17-19. In Opticks, Based on the 4th ed.; London, 1730; Dover: New York, 1952; p 214. (3) Reinold, M. A.; Rkker, A. W. Philos. Trans. 1886, 177.2, 627. (4) Derjaguin, B. V.; Obuchov, E. Acta Physicochim. URSS 1936,5, 1. (5) Derjaguin, B.; Churaev, N. V.; Muller, V. M. In Surface Forces; Kitchener, J. A,, Ed.;Consultants Bureau: New York, 1987, p 293.
observed in dynamic thinning studies on films containing surfactants above the critical micelle concentration (cmc). Johonnott6 and Perrin7 were among the first to study multiple black behavior in thin-liquid foam films. Since then several studies have addressed this phenomenon."" Stepwise-thinning behavior has also been observed in emulsionla and pseudoemulsion films (asymmetric gas/ water/oil f i i P for a variety of surfactant solutions.These numerous works indicate that stratification in free liquid films containing surfactant above the cmc is quite universal. Our objective is to quantify the thin-film forces in stratifying films by measuring the disjoining pressure isotherm for a free thin-aqueous foam film containing sodium dodecyl sulfate above the cmc. Previous studies on stratifying films have focused on the dynamic thickness transitions that occur as the films thin under an imposed capillary pressure. In contrast to these kinetic studies, we control the capillary pressure and probe the equilibrium film thickness as a function of imposed pressure. Careful manipulation of the capillary pressure permits direct measurement of the disjoiningpressure isotherms for films that show multiple black behavior. (6) Johonnott, E. S. Philos. Mag. 1906,11, 746. (7) Perrin, J. Ann. Phys. 1918, 10, 160. (8)Rickenbacher, W. Kolloid Chem. Beih. 1916,8, 139. (9) Wells, P. V. Ann. Phys. 1921, 16, 69. (10) Dewar, J. In Collected Papers ofsir James Dewar Vol.XI; Dewar, L., Ed.; Cambridge, 1927, p 1170. (11) Bruil, H. G.; Lyklema, J. Nature, Phys. Sci. 1971,233, 19. (12) Friberg, S.;Linden, E.; Saito, H. Nature 1974,251, 494. (13) Keuakamp, J. W.; Lyklema, J. In Adsorption at Interfaces; ACS Symposium Series 8; Mittal, K. L., Ed.; American Chemical Society: Washington, DC, 1975; p 191. (14) Manev, E.; Proust, J. E.; Ter-Minassian-SaragaColloid Polym. Sci. 1977, 255, 1133. (15) Manev, E. D.; Sazdanova, S. V.; Rao, A. A.; Wasan,D. T. J. Dispersion Sci. Technol. 1982, 3, 435. (16) Nikolov, A. D.; Wasan, D. T. J . Colloid Interface Sci. 1989,133, 1. (17) Nikolov, A. D.; Wasan,D. T.; Denkov, N. D.; Kralchevsky, P. A.; Ivanov, I. B. h o g . Colloid Polym. Sci. 1990, 82, 87. (18) Manev, E. D.; Sazdanova, S. V.; Wasan, D. T. J.Dispersion Sci. Technol. 1984,5, 111. (19) Bergeron, V.; Radke, C. J. InPhysical Chemistry of Colloids and Interfaces in Oil Production; Toulhoat, H., Lecourtier,J., Ede.;Editions Techinip: Paris, 1992; Vol. 1.
0743-7463/92/2408-3020$03.00/0Q 1992 American Chemical Society
Langmuir, Vol. 8, No. 12, 1992 3021
Disjoining Pressure Isotherms in Foam Films
Pr
/Ill -4- -
Figure 3. Schematic of low pressure film holder.
surfactant solution I
I
Figure 1. Schematic of porous-disk film holder and cell. Camera
Hg-Xe Arc lnmp (heat fliteredl
~
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PWS
r------I 1 I
I I I
!
I
Pressure Transducer
&
Vibration Isolation Table
!
\
Syringe Pump
Strip-cherl recorders
Figure 2. Schematic of experimental apparatus.
Apparatus and Experiments Apparatus. To construct disjoining pressure isotherms, we utilize the porous-plate technique, first developed by Myselsm and later refined by Exerowa et al,21*22 Single, thin-liquid films are formed in a hole drilled through a fritted glass disk which is fused to a 4-mm capillary tube, as shown in Figure 1. The film holder is then enclosed in a 200-cm3hermetically sealed Plexiglas cell with the capillary tube exposed to a constant reference pressure. As sketched in Figure 2, the cell is mounted on a pneumatic vibration-isolation system (Newport StableTop TXT series) and thermostated to within 0.1 "C. The gas pressure in the cell is regulated with a syringe pump manually operated through a precise micrometer drive. Manipulation of the cell pressure alters the imposed pressure on the film (i.e., the capillary pressure) and sets the disjoining pressure. Once equilibrium is established, the film thickness is measured interferometrically. A video camera is mounted on the microscope to permit visual inspection of the film. At equilibriumand in the flat portion of the film, the disjoining pressure is equal to the capillarypressure. The capillarypressure, P,, is simply the difference between the gas pressure, P,, and the bulk liquid pressure, PL,in the Plateau-border region=
P, = P*- PL= n (1) This relation, together with a force balance over the cell pictured in Figure 1,provides the working equation for the measurement of n n=P,-Pr+--Apghc 2u where P r is the external reference pressure, u is the equilibrium (20) Myaels, K.J.; Jones, M. N. Discuss. Faraday SOC.1966,42,42. (21) Exerowa, D.; Scheludko, A. Chim. Phys. 1971,24,47. (22) Exerowa, D.; Kolarov, T.; Khristov, K. H. R. Colloids Surf. 1987, 22, 171. (23) Toshev, B. V.; Ivanov, I. B. Colloid Polym. Sci. 1975,253, 558.
,
surface tension of the solution, r is the radius of the capillary tube, Ap is the density differencebetween the aqueous surfactant solution and the gas, h, is the height of the solution in the capillary tube above the film, and g is the gravitational constant. Each term on the right side of eq 2 is measured independently providing a direct determination of n. When n is large (-1 kPa) the last two terms in eq 2 are negligible, and the pressure difference, P, - P r , is sufficient to evaluate n. In this case,P, is referenced to atmospheric pressure, PA,and II is simply the excess gas pressure in the cell. This excess pressure is readily gauged with standard water or mercury manometers depending on the pressure range of interest. Values of II less than 100 Pa prove much more difficult to measure. The first obstacle to overcome is fluctuations in the atmospheric reference pressure. When variations in the room pressure (e.g., from doors opening and closing) are significant relative to the magnitude of n, then the reference pressure can no longer be taken as constant over'a period long enough for the film to reach equilibrium. This difficulty is overcome by referencing the pressure to a humidified steel chamber (- 1m3) which isolates the film from atmospheric pressure disturbances. The differentialpressure, P,- P,, is then measured with a sensitive draft-range differential pressure transducer from Omega (Model PX750-06DI) with an accuracy of 0.5 Pa. At low values of II all of the terms in eq 2 must be very carefully evaluated. The pressure jump in the capillary tube, 2u/r, is determined by measuring the capillary radius with a Kandon micrometer caliper while the surface tension of the surfactant solutionis obtained by the Wilhelmy-platetechnique. The height needed for the liquid head correction in the capillary tube is determined with a Wild cathetometer (Model KM-274) to within 30 pm. In this measurement, the film height is precisely located by using the measured workingdistance of a microscopeobjective focused on the center of the film. By use of these techniques, the disjoining pressure can be measured to within a precision of A1 Pa. The maximum and minimum capillary pressures obtainable with the porous-plate technique are determined by the geometric characteristics of the porous holder. To prevent imbibition of the gas phase, the maximum imposed capillary pressure muat not exceed the entry pressure for the porous disk. Therefore disks with smallerpores are required for higher capillarypressures (Corning, Chemglass, and Ace Glass, Inc.). The minimum capillarypressure is determined by the meniscus curvature when the film is first generated. This curvature is set by the dimensions of the hole used to support the film. Larger meniscus radii correspond to smaller capillary Pressures. Figure 3 demonstrates that capillary pressures can be minimized &e., the meniscus radii increased) by lowering the aspect ratio, L/D, of the hole used to form the film. Here L represents the hole depth while D corresponds to the hole diameter. With LID > 1and for a zero contact angle between the meniscus and disk, the minimum capillary pressure is set by the radius of the hole (Po, = 2u/blI,). However, with LID < 1the angle of contact at the hole edge is greater than zero when the film is first formed. This in turn produces a larger meniscus radius and a lower capillary pressure. We manufacture low aspect ratio holes by tapering the porous disk to create a very small hole depth, -0.1 mm, while maintaining the hole diameter at approximately 2 mm. These dimensions permit formation of films at capillary pressures as low as 15 Pa without susceptibility to bowing under the influence of gravity. Cell operation at these low capillary pressures, however, requires porous disks with relatively large pore sizes (10-20 pm radii) to minimize flow resistance and allow unimpeded access of the surfactant solution to the film.
Bergeron and Radke
3822 Langmuir, Vol. 8, No. 12,1992 Film thicknesses are determined by the microinterferometric technique, first developed by Scheludko,’ in conjunction with video microscopy. Heat-filtered white light from an Oriel 200-W Hg-Xe arc lamp is conducted via a fiber optic cable to a specially equipped reflected-light microscope (cf. Figure 2). After reflection from the film at normal incidence, the light passes through a beamsplitter where it is transmitted both to a digital 5000 Panasonic video camera and to fiber optic probes (EG&GGamma Scientific Model 700-10-34A & 37A) located in the microscope oculars. The probes have different aperture diameters and provide measurements on spot sizes of 15and 45 pm at the center of the film. To provide independent verification of the film thickness, reflected intensities from two different wavelengths of light (i.e., 546 and 665 nm) are monitored simultaneously with thermoelectrically cooled (Products for Research Model TE-104) lowlight-level photomultiplier tubes (RCA C3103402). The signal from the photomultipliers is then processed using digital photometers from Pacific Instrumente (Model 124). The refractive index of the solutions is determined using an Abbe refractometer. Optical thicknesses are then calculated from the reflected intensities using the equations derived by Scheludko and Platikanovz6.26
h, =
($-)
arcsin
{+
A 1 (4R/(1- R)2)(1 - A)
where A = (Z-Z-)/(Z,,-Z&,&is t h e f i i thicknesscalculated assuming a homogeneous refractive index equal to the bulk solution value (i.e. n = 1.33), X is the wavelength of light, and R = (n- l)z/(n l)z.Z is the instantaneous value of the reflected intensity while I,, and Z b correspond to the last interference maximum and minimum values. Subsequent application of the three-layered model to account for surfactant layers at the interfacez7provides a measurement of the total film thickness including the surfactant tails. We designate this thickness ash. The thickness of the aqueous core can be estimated from & by subtracting the 2.4-nm contribution from the two surfactant layers. Independent measurements of the film thickness with the two different wavelengths agree to within 10.5 nm. Materials. Kodak electrophoresis grade (>99%) sodium dodecyl sulfate (SDS)is used as received. Surface tension versus concentration measurements reveal that the purity is high (no evidence of a minimum in the tension versus concentration plot) when the samples are first prepared, but, as the solutions age over a period of days, they show signs of degradation.% This observation is consistent with recent work by Mysels.28 The cause of the degradation is the slow hydrolysis reaction, known to occur in SDS solutions at nonalkaline conditions,m$lproducing dodecan01 as an impurity. Therefore, when SDS is used, careful monitoring of the solution age, or special precautions, such as those outlined by Kekicheff et al.,3z should be taken to obtain reliable data. Analytical grade sodium chloride (NaCl) is obtained from Mallinckrodt. Prior to use, the NaCl is oven roasted at 500 OC for several hours to drive off any organic contaminante. All of the solutions are prepared with distilled water that was further purified with a four-stage Milli-Q reagent grade water system from Millipore. Procedure. The film holder is saturated with surfactant solution to provide a continuous liquid connection between the porous disk and the attached capillary tube. The experimental cell, which contains excess solution located close to the film to ensure vapor-liquid equilibrium, is then assembled with the film holder situated under an optical window that is treated with a
+
(24) Scheludko, A. Kolloid 2.1957, 155, 39. (25) Scheludko, A.; Platikanov, D. Kolloid 2. 1961, 175, 150. (26) Scheludko, A. Proc. Kon.Nederl. Akad. Wetensch., Ser. B 1962, 97.
(27) Duyvis, E. M. Thesis, Utrecht, 1962. (28) Bergeron, V. Ph.D. Thesis, University of California, Berkeley, in preparation. (29) Mysels, K. J. Langmuir 1986,2,423. (30) Muramatau, M.; Inoue, M. J. Colloid Interface Sei. 1976,55,80. (31) Nakagaki, M.; Yokoyama, S. J. Pharm. Sci. 1985, 74, 1047. (32) Kekicheff, P.; Grabielle-Madelmont, C.; Ollivon, M. J. Colloid Interface Sci. 1989, 131, 112.
12
A
k?
I
lot1
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I
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0.009 M SDS
Present Work (24°C) 0 Mysels&Jones
0
0
10
s! X
l o
C
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Thickness, h (rim)
Figure 4. Disjoining pressure isotherm for 0.009 M SDS. commercial antifoggingagent. Once assembled,the temperature control jacket around the cell is activated to 24 10.1 OC and several hours are provided to establish equilibrium. A biconcave lens is formed in the film holder, and the pressure in the cell is varied to produce a series of thin f i i whose thicknesses define the last interference maximum (I-) and minimum (I-) needed in eq 3. This process is repeated several times before and after every experiment to ensure highly accurate I,, and 1- values. Intensity readings after rupturing the f i e are also taken to verify the stray reflections from the holder are negligible. After the interference extrema are defiied, the pressure in the cell is carefully set to the desired value. The reflected intensity is monitored continuously during this process, and once the film establishes equilibrium, the intensity and pressure are recorded. Repeating this procedure by gradually increasing or decreasing the pressure allows us to map out the entire disjoining pressure isotherm. Additional experimental details are available in the thesis of Bergeron.z8
Results and Discussion Low Surfactant Concentrations. Figure 4 represents the isotherm obtained for a fresh (1 day old) 0.009 M SDS solution. This concentration is quite near the cmc (0.008 M). Our data in the dark squares compare favorably with those in the open circles obtained by Mysels and Jones.2O Stable films are found in the thickness range from 20 to 11.6 nm. At approximately 13 nm, a strong repulsive branch in the isotherm stabilizes the f i i to pressures greater than 70 kPa. Films observed in this thickness region are referredto as common black films (CBF). Their stability is attributed to electrostatic repulsive forces generated by overlapping double layers in the interfacial regi~n.~ A similar comparison is made in Figure 5. In this case the ionic strength of the solution is increased by adding NaCl (0.18M) to a fresh 0.001 M SDS solution. These concentrations produce a solution that corresponds to the c ~ c The . ~isotherm ~ depicted contains three sets of data: the present work (closed squares), data from Mysels and Jones (open circles), and recent data by Exerowa et al.22 (open triangles). Although Mysels and Jones operated at slightly different conditions (0.0017M SDS and 0.18 M NaCl), good agreement is found among all the data. Figures 4 and 5 reveal that at higher ionic strengths the CBF is encountered at much smaller thicknesses (-8 versus 11 nm) and the slope of the isotherm in this region increases. Both effects result from the increased elec(33) de Feijter, J. A. Thesis, Utrecht, 1973.
Langmuir, Vol. 8, No. 12, 1992 3023
Disjoining Pressure Isotherms in Foam Films
0.001 M SDS 0.18 M NaCl
00 0
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g
h
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Present Work (240C)
o Mysels & Jones
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Exerowa et al.
1
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1 2i 150
0
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Thickness, h (nm) Figure 5. Disjoining pressure isotherm for 0.001 M SDS in a 0.18 M NaCl solution.
trostatic screening caused by the addition of electrolyte consistent with DLVO theory. Another important difference between the two isotherms in Figures4 and 5 is the existence of a second stable branch created by the addition of salt. In Figure 5, when the pressure exceeds 100 kPa, the film undergoes an abrupt transition in thickness from 7 to 4.5 nm. The stable black film formed in this thinner region is designated a Newton black film (NBF) (also known as a Perrin or second black film). Although NBF transitions have been extensively i n ~ e s t i g a t e dthe , ~forces ~ ~ ~ which give rise to their stability remain unclear.n Various explanations include hydration, steric, undulation, and protrusion f o r ~ e s . ~However, ~,~~ direct evidenceto distinguish among these forcesis lacking, leaving the issue u n r e s ~ l v e d . ~ ~ The transition between the CBF and the NBF in Figure 5 is discrete because films a t the intervening film thicknesses are thermodynamically unstable. de V r i e ~es-~ ~ tablished that free films are unstable whenever the slope of the isotherm is positive (i.e., d n / d h > 0). Hence, the gap observed in the isotherm of Figure 5 corresponds to a region with a positive slope in n(h). High Surfactant Concentrations. The disjoining pressure isotherm for a film generated from a fresh 0.1 M SDS solution is displayed in Figure 6. A t this concentration the solution is well above the cmc but is still within the spherical micellar region of the phase diagram.32 The abscissa (pressure axis) of the isotherm is split into two separate ranges. In the upper portion of the isotherm the pressure scale matches the one used previously in Figures 4 and 5. Observations in this region are similar to those made for the 0.009 M SDS solutions in Figure 4. However, for the increased ionic strength a t 0.1 M SDS commonblack-film formation occurs a t a slightly reduced thickness (-10 nm). A NBF does exist for this system a t higher pressures, but we have not characterized it quantitatively. The pressure scale in the lower portion of Figure 6 is expanded to reveal four discrete branches in the isotherm (i.e., transitions) that occur a t disjoining pressures below 100 Pa. Somewhat similar stepwise transitions in a (34) Jones, M. N.; Mysels, K. J.; Scholten, P. C. Tram. Faraday SOC. 1966,62,1336. (35) Exerowa, D.; Nikolov,A.; Zacharieva, M.J. Colloid Interface Sci. 1981,81, 419. (36) Ninahm, B. W. Chem. Scr. 1985,25,3. (37) Israelachvili, J. W.; Wennerstrom, H. Langmuir 1990, 6, 873. (38) Parsegian, V. A.; Rand, R. P. Langmuir 1991, 7, 1299. (39) de Vries, A. J. Recueil 1958, 77, 441.
A
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100
K 50
0 0
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Thickness, h (nm) Figure 6. Disjoining pressure isotherm for a foam film stabilized with 0.1 M SDS.
0.1 M SDS
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Figure 7. Disjoining pressure in the low pressure region of the 0.1 M SDS isotherm. Arrows indicate the directionof the pressure scans.
disjoining pressure isotherm have been reported for multicomponentfoam filmswhich contain phmpholipids.a The three branches in Figure 6 extending out beyond 20 nm represent force barriers generated by amphiphilic structuring in the film while the thinnest branch a t 16 nm marks the low pressure extension of the CBF. Separation distances between the branches are on the order of 10nm, and the influence of the surfactant structuring can be detected a t rather long ranges (>50 nm). A portion of the data in this region is reproduced in Figure 7 to provide more detail. Two types of data are identified in Figure 7. Open squares represent data obtained upon increasing the cell pressure while filled squares correspond to data collected after pressure decreases. Arrows in the figure reinforce this distinction. They also indicate that branch-to-branch transitions occur only in the increasing pressure direction. With a decrease of the capillary pressure to zero along any (40) Exerowa, D.; Lalchev, 2.Langmuir 1986,2,668.
Bergeron and Radke
3024 Langmuir, Vol. 8, No. 12, 1992
branch the film spontaneously separates into a biconcave lens. We infer that the local minima in the II curve occur a t negative values that are not accessibleusing the porousplate technique. Each datum represents a stable film that is kept at a constant pressure and thickness for at least 20 min. This requires constant surveillance of the film from a video monitor for over a 20-h period, spending approximately 5 h probing each branch. Since the radius of the film is sensitive to minute pressure changes, the visual observations from the video monitor confirm that a constant capillary pressure is maintained on the film. The overlap of the data points, together with the ability to scan the pressure reproducibly up and down each branch of the curve for an indefinite amount of time, verifies the (metastable) equilibrium behavior of these films. The first stable amphiphilic layer for the 0.1 M SDS isotherm is encountered a t approximately 50 nm. Because of the very low pressures involved a t this thickness, extremely careful pressure adjustments are required to prevent premature transition to the next stable layer. These adjustments are made possible by inserting dead volume on the high pressure side of the cell. A 200-cm3 glass chamber is placed inline between the syringe pump and the measuring cell to permit microadjustments to the pressure. The pressure can then be gradually increased until a critical region in the isotherm is reached, at which point pressure fluctuations initiate the transition to a new stable film thickness (i.e., the transition to the next branch in the isotherm). When the critical pressures for two consecutive transitions are similar (see for example the 40 to 30 nm branches in Figure 7), two transitions can occur in quick succession if disturbances are large enough. This problem is compounded by the complicated dynamics of local hole(@formation and expansionduring the transition process. Jimhez-Laguna et provide a detailed description of this transition. The scenario outlined there is repeated for each amphiphillic layer encountered. Although not in the context of a disjoining pressure isotherm, Johonnott6 was the first to describe the origin of the multiple black films as arising from “alternating molecular forces of attraction and repulsion as we pass from one black film to the next”. Keuskamp and Lyklemal3 later explained multiple black films as originating from undulations in the Gibbs free energy of the film as it changes in thickness. Two theories have emerged to account for these undulations in the free energy: repeating units of surfactant b i l a y e r ~ , ~ ~ Jor~ *a ~cubic O lattice of ordered micelles.42 More recently has used density functional theory for micellar solutions to calculate disjoining pressures that evidence oscillatory behavior, consistent with the experimental observations. However, neutron reflection experiments, a t the air-water interface of an SDS solution, by Lee et al.& suggest that bilayer and micellar models may not be mutually exclusive. Figure 8 suggests a possible scenario. Here we illustrate a gradual transition from micellar domains at relatively thick films to bilayer-like structures when the film becomes thinner. Unfortunately, the periodicityof the observed oscillations, 10 nm, which can be accounted for by combining twice
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(41) Jimbnez-Laguna, A. I.; Bergeron, V.; Radke, C. J. Submitted for publication in Langmuir. (42) Nikolov, A. D.; Kralchevsky, P. A.; Ivanov, I. B.; Wasan, D. T. J. Colloid Interface Sci. 1989,133, 13. (43) Laso, M. Ph.D. Thesis, University of California, Berkeley, in preparation. (44) Lee, E. M.; Simister, E. A.; Thomas, R. K.; Penfold, J. Colloq. Phys. 1989,50, 75.
Film Interface
\
Bilayer-like Region
v
Micellar Domains Figure 8. Schematic representation of possible surfactant
structuring in thin-liquid foam films that show multiple black behavior.
0
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Figure 9. Disjoining pressure isotherm for a 0.1 M aged SDS solution.
the length of a surfactant molecule with a Debye atmosphere, does not differentiate between bilayers or micelle~.~~ Figure 9 reports the II(h) isotherm for a 0.1 M SDS solution aged for a period of 3 days. Comparisonto Figure 7 demonstrates that aging the solution shifts the location of the black film transitions to lower thicknesses. Apparently, the presence of dodecanol from SDS hydrolysis reduces the effectivesizeof the surfactant structures. These agingobservationsare c o n f i i e d by examiningthe location of the thinning transitions reported by Keuskamp and Lyklema.13 Their films, which contained small amounts of dodecanol, exhibit thinning transitions consistent with the location of the oscillations we measure in the aged solutions. Since our equilibrium experiments require a (45)Hayter, J. B.; Penfold, J. J. Chem. SOC.,Faraday Trans. I 1981, 77, 1851.
Disjoining Pressure Isotherms in Foam Films l
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Langmuir, Vol. 8, No. 12,1992 3025
'
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Aged 0.2 M SDS 24 "C Run #l 6 Run #2
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Aged 0.2 M SDS 0.1 M NaCl 24 "C
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* O t 40
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Figure 10. Disjoining pressure isotherm for a 0.2 M aged SDS solution.
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Figure 11. Disjoining pressure isotherm of aged 0.2 M SDS in a 0.1 M NaCl solution. 75
substantial amount of time, the remaining data to be presented are obtained with preaged solutions (typically 3 days) to guarantee solution stability over the course of an experiment. Surfactant and Electrolyte Concentrat ion Effects. When the surfactant concentration is increased to 0.2 M SDS,the isotherm obtained in Figure 10 reflects the same behavior observed previously in stepwise thinning experiments.16 Namely, more transitions (black films) are observed and the separation distances between the transitions decrease. The increased number of transitions is simply a consequence of having more surfactant available to develop organized structures. Once organized, these structures can approach one another closer because of the increased ionic screening (i.e., decreased Debye length) a t higher SDS concentrations. Using a lattice model of ordered micelles as a basis for the surfactant structuring, Nikolov and Wasan present similar arguments to explain their dynamic thinning transitions.16 Two additional observations can be extracted from Figures 9 and 10. At the higher SDS concentrations, the peak transition pressures increase while the thickness change between transitions becomes less regular. The 0.2 M SDS isotherm exhibits thickness transition intervals that change from 10 nm for the thickest films to approximately 6 nm for the thinner films. Furthermore, the locationsof the thick film transitions are less reproducible. These observations suggest differences between the amphiphilic structuring a t the various film thicknesses. One possible explanation is that diffuse micellar domains are responsible for thick film transitions while more organized bilayer-likestructures develop in thinner films (see Figure 8) It is well-known that the addition of electrolyte suppresses the stratifying behavior observed in film-thinning experiments.13J6 This fact is further supported by the data in Figure 11. In this figure, 0.1 M NaCl is added to the original 0.2 M SDS solution. Now, only one transition in the isotherm remains (marked by the dashed line) correspondingto that between the CBF and NBF discussed earlier. The disappearance of structural transitions upon addition of salt underscores their electrostatic origins. Stratification. Film thinning experiments may be performed using the same apparatus described for the equilibriummeasurements. This is achieved by subjecting
20
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(s)
Figure 12. Dynamic thinning of an aged 0.1 M SDS foam fii.
a biconcave lens that is first formed in the film holder to a step increasein the capillarypressure to a higher constant value. The evolution of film thickness versus time is then followed interferometrically, as previously outlined. A typical stepwise thinning curve for an aged 0.1 M SDS solution subjected to a 65-Pa capillary pressure is presented in Figure 12. Five discrete thinning steps are observed. These steps correspond to a series of multiple black films encountered as the film thins from 65 to 25 nm. A line is drawn through the transition zones to signify that this plot represents one continuous experiment. We see that the change in film thickness with each subsequent step remains roughly constant at 10 nm while the slope in the m e graduallydecreases. Similarthinning behavior has also been observed by Nikolov and Wasan a t slightly lower capillary pressures.16 The observed stepwise thinning behavior can readily be explained by the oscillatory form of the II(h) isotherm. In tangentially immobile plane-parallel films, the drainage rate is governed by the Stefan-Reynolds e q u a t i ~ n ~ ~ ~ ~ ~ (4)
where rf is the film radius, p is the bulk fluid viscosity, and t is the drainage time. The term (Pc- II(h))links the (46)Stefan, J. Sitz. Math. Natur. Akad. Wias. Wein 1874,69,713. (47) Reynolde, 0.R. SOC.London: Phdos. Trans. 1886,177,157.
Bergeron and Radke
3026 Langmuir, Vol. 8, No. 12,1992
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Figure 13. Effective disjoining pressure isotherm calculated from the thinning data in Figure 12.
thinning behavior to the disjoining pressure isotherm by providing the driving force for film thinning. Therefore, when n(h)is oscillatory and the capillary pressure is held constant, an oscillating driving force develops to produce the observed stepwise thinning. The experimentalthinning curvesprovide an alternative method for measuring n(h).The slope and thickness determined from these curves can be used with the measured value of Pc to evaluate 11 from eq 4. This procedure was first developed by Scheludko for nonstratifying films and is known as the dynamic An extensive review of the method has been recently treated by Ivanov and D i m i t r ~ v . Application ~~ of the dynamic method to the thinning data in Figure 12, using a bulk viscosity of 1 mPa*s, produces the oscillatory disjoiningpressure curve in Figure 13. Disjoiningpressures in this figure are designated as effective pressures (neff) to emphasize that they are obtained under dynamic conditions. A dashed line is sketched to provide visual continuity of the data. Comparison between the equilibrium isotherm in Figure 10 with that obtained by the dynamic method in Figure 13reveals excellent agreement between the two. To help facilitate this comparison solid rectangular regions are pictured in Figure 13 to indicate where the equilibrium data lie. Both the location and peak height of the black film transitions are reproduced quite well. This indicates that the time scale for thinning is sufficiently long to establish local equilibrium of the surfactant structures responsiblefor the transitions. We also conclude that the film remains plane-parallelwith essentiallyno-slip surfaces over the thickness range analyzed (i.e., from 65 to 25 nm). Verification of plane-parallel films is accomplished by visual observations from the video monitor and by simultaneously measuring the film thickness a t two different locations on the film. Moreover, surface tension gradients, created under flowing conditions by trace amounts of highly surface active dodecanol, are likely (48) Scheludko, A.; Exerowa, D. Kolloid 2. 1960, 168,24. (49) Ivanov, I. B.; Dimitrov, D. S. In ThinLiguidFilms,Fundamentals and Appfiations;Ivanov, I. B., Ed.; Marcel Dekker: New York, 1988; Vol. 29, p 418.
responsiblefor immobilizingthe film surfaces and creating no-slip conditions. From Figure 13 we also see that the dynamic method discloses data for negative II values. These dynamic data also reveal an additional transition at 60 nm that is not probed by the equilibrium technique. Another important feature demonstrated by the dynamic analysis is the successful application of the bulk viscosity in the thinning model. Although amphiphilic structures are clearly present in the film, their effect on flow resistance appears to be negligible. This supposition is strengthened by Lasowho calculates effective viscosities for inhomogeneous micellar films43using a local average density model.50 These calculations indicate that when micelles are assumed to be responsible for the surfactant structuring, the viscosity in the film does not significantly deviate from its bulk value.
Summary With specially constructed film holders and careful pressure isolation and control we measure disjoining pressure isotherms for thin aqueous SDS foam films down to pressures of 10 Pa. At SDS concentrations near the cmc, very good agreementwith previouslypublished results is found. For the first time n(h)isotherms are measured for foam films stabilized with surfactant well above the cmc. The low pressure region of these isotherms reveals an oscillatory structural component that is reproducible in both the increasing and decreasing pressure directions. The multiple black films that result from this component originate from surfactant structuring within the film. Magnitudes of the structural forces are low (
