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Disjoining Pressure and Film Tension in Comb-Graft Copolymer-Stabilized Oil Films M. R. Anklam,* D. A. Saville, and R. K. Prud’homme TRI/Princeton and Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544 Received February 16, 1999. In Final Form: June 24, 1999 Thin, supported decane films stabilized with comb-graft copolymers were studied as models of polymeric surfactant stabilized water-in-oil emulsions. The stabilizing polymeric surfactant (“polysoap”) was composed of a poly(dimethylsiloxane) backbone with hydrophobic alkyl and hydrophilic ethylene/propylene oxide grafts with a total molecular weight of 62 000. Electrical compressive stresses were imposed on the films, and their thicknesses were determined from measurements of capacitance and optical interference. The theory for the interpretation of capacitance versus applied electric field in terms of disjoining pressure was developed. Sessile drop measurements of interfacial tension were used to infer a polymer coverage of 1.7 nm2/molecule. Dynamic light scattering measurements showed hydrodynamic diameters of 6 nm at 5.2 wt % of the polymer in decane. The measured film thicknesses ranged from 32 to 62 nm over a compressive force range of 0-1400 Pa. The films were remarkably thick and compressible compared to films formed from simple surfactant or lipid systems. The films displayed compressive moduli ranging from 1000 to 6400 Pa. The film properties were relatively insensitive to the surfactant concentration and moderately sensitive to polymeric surfactant purity. The observed thicknesses are shown not to arise from interfacial electrostatic effects or van der Waals forces but from steric interactions. The observed thicknesses are consistent either with strongly stretched chains adsorbed at the interface or with multichain aggregate structures at the interface.
Introduction Many water-in-oil (w/o) emulsions are stabilized by macromolecules or particulates that provide a mechanically strong film to prevent coalescence in the absence of electrostatic repulsive forces. The structures of films stabilized by polymeric surfactants and the behavior of these films during compression as the polymers resist approach of the interfaces are of particular interest. The goal of this study was to investigate the disjoining pressure and compressibility of comb-graft copolymer-stabilized oil films. Studies on w/o emulsions and oil films stabilized with polymeric surfactants are few, and the relevant studies present little information on the film structure and stability. Aston et al.1 measured film thickness for oil films stabilized with various concentrations of B246, a block copolymer, but the measurements were made at an unknown capillary pressure. It is not clear how the thicknesses of these films would change under compression. Lyklema and van Vliet2 examined poly(vinyl alcohol)stabilized aqueous films and present disjoining pressure isotherms (disjoining pressure as a function of thickness) for films stabilized with polymers of various molecular weights. This appears to be the most thorough study of fluid interfaces stabilized by polymer. In related studies, Bergeron et al.3 and Exerowa et al.4 studied stabilizing forces in polymer-containing thin foam films. Clark et al.5 * Present address: Department of Chemical Engineering, RoseHulman Institute of Technology, 5500 Wabash Ave., Terre Haute, IN 47803. (1) Aston, M. S.; Herrington, T. M.; Tadros, T. F. Colloids Surf. 1989, 40, 49. (2) Lyklema, J.; van Vliet, T. Discuss. Faraday Soc. 1978, 65, 25. (3) Bergeron, V.; Langevin, D.; Asnacios, A. Langmuir 1996, 12, 1550. (4) Exerowa, D.; Sedev, R.; Ivanova, R.; Tadros, T. F. Colloids Surf. 1997, 123-124, 277. (5) Clark, D. C.; Coke, M.; Mackie, A. R.; Pinder, A. C.; Wilson, D. R. J. Colloid Interface Sci. 1990, 138, 207.
examined aqueous films stabilized with proteins and investigated protein diffusion and displacement.6 Others have investigated the macroscopic stability of emulsions stabilized by polymers.7-9 Studies on thin oil (lipid) films as models for biomembranes are numerous. Many of the relevant references deal with the thickness and structure of these films as measured either electrically or optically and with the effects of solvent and chain length.10-16 Others have examined the compression of lipid films due to an electric field.10,17-23 These films appear to thin in an electric field, and this probably arises by squeezing out solvent,17 as lipids are believed to be rigid. In some cases, the capacitance was found to be proportional to the square of the voltage.19,20 All of these studies show that the films (6) Wilde, P. J.; Clark, D. C. J. Colloid Interface Sci. 1993, 155, 48. (7) Chattopadhyay, A. K.; Shah, D. O.; Ghaicha, L. Langmuir 1992, 8, 27. (8) Clayfield, E. J.; Wharton, D. G. In Theory and Practice of Emulsion Technology; Smith, A. L., Ed.; Academic Press: London, 1976; p 217. (9) Bohm, J. T.; Lyklema, J. In Theory and Practice of Emulsion Technology; Smith, A. L., Ed.; Academic Press: London, 1976; p 23. (10) Andrews, D. M.; Manev, E. D.; Haydon, D. A. Spec. Discuss. Faraday Soc. 1970, 1, 46. (11) Dilger, J. P. Biochim. Biophys. Acta 1981, 645, 357. (12) Cherry, R. J.; Chapman, D. J. Mol. Biol. 1969, 40, 19. (13) Hanai, T.; Haydon, D. A.; Taylor, J. Proc. R. Soc. A 1964, 281, 377. (14) Rovin, Y. G.; Pivovarov, N. Y.; Bageveev, I. A. Kolloidn. Zh. 1976, 38, 1005. (15) Taylor, J.; Haydon, D. A. Discuss. Faraday. Soc. 1966, 42, 51. (16) Fettiplace, R.; Andrews, D. M.; Haydon, D. A. J. Membr. Biol. 1971, 5, 277. (17) Requena, J.; Haydon, D. A.; Hladky, S. B. Biophys. J. 1975, 15, 77. (18) White, S. H. Biophys. J. 1970, 10, 1127. (19) White, S. H.; Thompson, T. E. Biochim. Biophys. Acta 1973, 323, 7. (20) White, S. H. Biochim. Biophys. Acta 1970, 196, 354. (21) Wobschall, D. J. Colloid Interface Sci. 1972, 40, 417. (22) Benz, R.; Janko, K. Biochim. Biophys. Acta 1976, 455, 721. (23) Berestovsky, G. N.; Gyulkhandanyan, M. Z.; Ivkov, V. G.; Razhin, V. D. J. Membr. Biol. 1978, 43, 107.
10.1021/la9901581 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/07/1999
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were bilayers which behave as nearly ideal capacitors (see below) and film thicknesses were approximately the length of two lipid molecules (∼3-5 nm). This paper presents a study of the disjoining pressure, compressibility, and structure of polymer-stabilized oil films. Measurements of the disjoining pressure and film contact angles are made using electrical capacitance and electric field induced compression on single-oil films in aqueous electrolyte solution. Optical interference measurements are used to observe film thickness variations. We begin with a brief derivation of the thermodynamics of thin films with applied electric fields to determine the disjoining pressure and contact angle relationships. We then present the experimental results on film thickness. Finally, we comment on the polymer aggregation and assembly that would be consistent with the experimental observations. Electric Field Effects Capacitance/Disjoining Pressure Measurements. The thickness of an oil film can be determined from measurements of the film capacitance, provided the conductivity of the film is small compared to the surrounding aqueous phase. The specific capacitance (capacitance per unit area) is
C ˆ )
0 h
(1)
where 0 is the permittivity of free space (8.854 × 10-12 F/m), is the dielectric constant of the film, and h is the thickness of the film. The film thickness can be ascertained, given the dielectric constant of the oil phase, by measuring the capacitance (electrically) and the film area (optically). When a voltage is imposed across the film, a compressional force per unit area,
FE )
2 C ˆ V2 0V ) 2h 2h2
(2)
is produced; V is the applied voltage. As the compression force increases, the disjoining pressure in the film grows to balance the forces on the film interfaces; i.e.,
Π ) Pc + FE
(3)
where Π is the disjoining pressure and Pc is the capillary pressure at the film meniscus. In this way, disjoining pressure-film thickness isotherms are obtained using an electric field to compress the film and measure thickness. If the field is large, the applied voltage can induce rupture. Our studies of rupture in polymer-stabilized oil films are presented elsewhere.24 Thermodynamics of Thin Films. Requena and Haydon25 and Pethica and Hall26 described the behavior of thin films with an applied electric field, and the thermodynamic relationships for thin films in the absence of an electric field have been developed by a number of researchers.27-31 We extend the treatment of a thin film (24) Anklam, M. R.; Saville, D. A.; Prud’homme, R. K. Colloid Polym. Sci., in press. (25) Requena, J.; Haydon, D. A. J. Colloid Interface Sci. 1975, 51, 315. (26) Pethica, B. A.; Hall, D. G. J. Colloid Interface Sci. 1982, 85, 41. (27) Toshev, B. V.; Ivanov, I. B. Colloid Polym. Sci. 1975, 253, 558. (28) Eriksson, J. C.; Toshev, B. V. Colloids Surf. 1982, 5, 241. (29) de Feijter, J. A.; Rijnbout, J. B.; Vrij, A. J. Colloid. Interface Sci. 1978, 64, 258. (30) Derjaguin, B. V. Colloid J. 1991, 53, 861.
Figure 1. Control volume for the thermodynamic analysis of a thin emulsion film.
by Eriksson and Toshev28 to include an applied electric field using the system sketched in Figure 1. Electrodes in the conducting electrolyte phase surrounding the film perform electrical and mechanical work by charging the film interface and causing film compression. The electric field in the electrolyte phase vanishes due to high conductivity, and the field in the meniscus is also assumed negligible due to the large separation of the interfaces. Accordingly, the film is treated as an ideal, parallel-plate capacitor. In the curved meniscus region at the edges of the film, the pressure difference across the water-oil interface is
Pd - Pm ) Pc
(4)
where Pd is the pressure in the conductive aqueous phase, Pm is the pressure in the meniscus, and Pc is the capillary pressure. We proceed by minimizing the free energy, including electrical work, in the flat region. The energy of a capacitor ˆ V2/2, where Af is the area of the capacitor. In addition is AfC to the P dV work, the work done to the system is that necessary to charge the film and change its area. This must equal the change in the energy of the capacitor
dw ) -
1 1 d(AfC ˆ V2) ) - V2 d(AfC ˆ ) - AfC ˆ V dV 2 2
(5)
The differential free energy of a small control volume at the film interface (assuming constant temperature, voltage, and area) is
dF ) PdAf dh -
PN f
2 1 V 0Af Af dh + dh 2 h2
(6)
where PN f is the component of stress in the film acting normal to the interface. When the free energy is minimized with respect to the film thickness, the equilibrium normal stress is
PN f ) Pd +
2 1 V 0 ) Pd + FE 2 h2
(7)
Equations 4 and 7 along with the definition of disjoining pressure give
Π ≡ PN f - Pm ) Pc + FE
(8)
which is identical to the result obtained using a force balance on the interfaces (eq 3). Note that the disjoining (31) Rusanov, A. I. In Research in Surface Forces; Derjaguin, B. V., Ed.; Consultants Bureau: New York, 1971; Vol. 3; p 103.
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pressure is the extra pressure (above the external fluid pressure) necessary to stabilize the film. Similarly, minimization of the free energy of a small control volume on the border between the film and meniscus regions gives a balance of stresses tangential to the film interface. With h and volume constant, the differential free energy for changing the film area is
dF ) Pmh dAf - PTf h dAf
(9)
where PTf is the component of the stress in the plane of the film interfaces. When the energy is minimized with respect to film area, eq 9 reduces to
PTf ) Pm
(10)
The pressure in the meniscus is equal to the uniform tangential stress in the thin film. Extending the method of Eriksson and Toshev28 to include the electrical energy terms, the differential Helmholtz free energy of the film (at constant temperature) may be written as T dFf ) -PN f Af dh - Pf h dAf + 2σf dAf + 1 µi dNi - d(AfC ˆ V2) (11) 2 i
∑
where σf is the film interfacial tension, µi is the chemical potential of species i, and Ni is the number of moles of i in the film. This can be combined with Equations 7, 8, and 10 to give
dFf ) -PcAf dh - Pm dV + 2σf dAf +
∑i µi dNi - Cˆ AfV dV -
C ˆ V2 2
C ˆ V2 2
∑i µi dNi - Cˆ AfV dV
dAf (12)
(13)
where σb is the interfacial tension between bulk phases, γ is the film tension, and θ0 is the contact angle where the extrapolated meniscus interface meets the film midplane. Effective film and film interfacial tensions can be written which represent tensions measured from contact angles:
γeff ) γ -
C ˆ V2 2
(14)
σeff ) σf -
C ˆ V2 4
(15)
and
Thus, eq 12 could be rewritten as (32) de Feijter, J. A. In Thin Liquid Films: Fundamentals and Applications; Ivanov, I. B., Ed.; Marcel Dekker: New York, 1988; p 1.
(16)
If additional film area is formed by a stretching process at constant T, µi, P, V, and h and the free energy found from integration over the film area is differentiated and subtracted from eq 16, a Gibbs-Duhem relation is obtained:
0 ) -Pc dh + h dPm - 2 dσeff -
∑i (Ni/Af) dµi - Cˆ V dV
(17)
At constant voltage and bulk interfacial tension, this reduces to
2 dσeff ) -Pc dh
(18)
which for zero applied voltage reduces to the widely used relation32
2
( ) ∂σf ∂h
) -Π
T,Pm,µi
(19)
Note that if the voltage is nonzero, then the capillary pressure is not equal to the disjoining pressure. The relationship between film tension, γeff, and film interfacial tension, σeff,27,32 modified to account for capacitive energy effects, gives
γeff ) 2σeff + Pch
(20)
By using this relationship, one obtains for constant chemical potential, pressure, and temperature
ˆ V dV dγeff ) -C
It is clear that any measurable “tension” of the film is actually a combination of film tension and capacitive energy. This effect must be included in the relationship between interfacial tension, contact angle, and film tension32 as
2σb cos θ0 ) γ -
dFf ) -PcAf dh - Pm dV + 2σeff dAf +
(21)
as was obtained by Requena and Haydon25 and Pethica and Hall26 (the latter authors have an additional constraint of constant disjoining pressure). With an applied voltage, the difference between the interfacial tension and the true film tension is related to the specific interaction free energy, ∆f(h),32 but the difference between the interfacial tension and the measurable or effective film tension is not. Nonetheless, although contact angle measurements at nonzero voltages do not yield free energy values, they do provide information about the interfacial tension and capacitance as described below. Also, the use of the effective tensions is illuminating since contributions to the decrease in the measured film tension from capacitive energy effects and ion adsorption are emphasized. Contact Angles. A contact angle is observed where a meniscus or a lens meets the interface of the film. This contact angle (in the absence of an electric field) provides information about the film’s free energy of formation.32 When a voltage is applied across an oil film, the lateral tension in the film decreases, and therefore, the contact angle increases to balance the tangential stress.25 To explore the effect of an electric field on the tension and the surface charge for an oil film, Requena and Haydon25 used chemical potential arguments based on the Gibbs adsorption equation to show that
-(dγ/dV)T,p,µ ) q
(22)
where q is the induced surface charge per unit area. This is identical to eq 21 if the capacitance replaces q/V and the effective film tension replaces the film tension, γ. Upon
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Figure 2. Chemical structure of the Abil polymeric surfactant. Neither the molecular weights of the various groups or the distribution is known.
integration,
∫γγ dγ ) ∫VVCˆ V dV
-
0
0
(23)
where γ0 is the tension at the reference voltage, V0. The relationship between the contact angle, film tension, and interfacial tension32 follows from the force balance
γ ) 2σb cos θ0
(24)
(see also eqs 13 and 14). If the specific capacitance is independent of voltage, which holds for incompressible lipid films,25 eq 19 can be integrated to yield
ˆ /4σb)(V2 - V02) cos θi - cos θE ) (C
(25)
where σb is the bulk interfacial tension and θi and θE are the contact angles at the film midplane at V0 and V, respectively. The contact angle for a lens has been measured interferometrically by Dimitrov.33 For small lenses, the lens surface is spherical and the radius is determined by finding the minima and maxima in reflected light intensity along a line bisecting the lens’ interferometric pattern. It has been suggested that the capillary pressure of a lens may affect the measurement of a contact angle.34 However, the film tension is constant across the film, so from eq 24, the contact angles should be constant as well. Line tension effects are expected to be negligible but will be apparent if contact angles depend on the lens diameters. Materials and Methods Film Components. The polymeric surfactant Abil EM-90 (Goldschmidt) is a comb copolymer with a poly(dimethylsiloxane) backbone and grafted hydrophobic and hydrophilic chains, cf. Figure 2. The Abil surfactant was chosen for this work due to its large size (>10 000 MW) and remarkable ability to stabilize water-in-oil emulsions.35,36 Decane (99+% Sigma) was used as a solvent, and the aqueous phase consisted of 1.0 M KCl (99.99+% Aldrich) in Picopure water. Salt and solvent were used as received. The Abil was used at concentrations of 0.52% and 0.058% (w/w) in the oil phase. For the thin film experiments, the oil phase and the aqueous phase were preequilibrated by gently pouring the oil over the aqueous phase and allowing the phases to remain in contact for at least a week. The polymer was purified by washing eight times with acetone (2:1 vol acetone: polymer). GPC-light scattering yielded a number-average molecular weight of 17 000 and a polydispersity (33) Dimitrov, A. S. Colloids Surf. 1990, 47, 299. (34) Requena, J.; Billett, D. F.; Haydon, D. A. Proc. R. Soc. London, Ser. A 1975, 347, 141. (35) Sela, Y.; Magdassi, S.; Garti, N. Colloids Surf. A 1994, 83, 143. (36) Garti, N.; Aserin, A. Adv. Colloid Interface Sci. 1996, 65, 37.
Figure 3. Schematic diagram showing the thin film apparatus. of 2.45 for the unpurified Abil EMG, while the purified product has a number average molecular weight of 62 000 and a polydispersity of 1.2.37 Thin Film Apparatus. Figure 3 shows the thin film apparatus based on the design of Requena et al.,34 which allows application of an electric field across the film and interferometric observation of the film using reflected light. A hole to support the film (1-mm diameter) is drilled into the bottom of a cup made of Kel-F (AIN Plastics). The edges around the hole are tapered to make the hole as thin as possible (∼0.6 mm). The lateral small capillary has a diameter of 0.013 in. Oil is delivered to the support hole through Teflon tubing (Cole-Parmer, size to fit over 16 gauge needle) inserted into the side of the cup and sealed by an O-ring and a nylon screw with a hole drilled through the center. Teflon tubing connects to a dual-syringe system (2-mL Gilmont micrometer syringe, GS 1200, and 25-µL Hamilton threaded plunger syringe, Model 1702T PLT) for coarse and fine adjustment of the volume. The cup is immersed in aqueous solution in a reservoir machined from 1-in.-thick acrylic with an optical glass bottom (Escoproducts, 3-in.-diameter fused silica) mounted using RTV rubber and a Delrin support ring. In the final configuration, the oil film separates two electrically isolated aqueous phases, one inside the film holder cup and the other in the external reservoir. Ag/AgCl electrodes are used to apply electrical signals across the film. Tilt stages reduce stray reflections from the optical window. A plug inside the cup prevents reflections from the surface of the aqueous phase from interfering with optical measurements. Finally, the entire system (light source, film holder, and microscope) is surrounded by a Faraday cage and mounted on an optical table. The acrylic reservoir and film holder are mounted above an inverted microscope (Mitutoyo Finescope FS 50, APO 10, and APO 20 objectives with f ) 200). Monochromatic light from a mercury arc lamp (Oriel Model 6281 with Model 8500 power supply) with a monochromatic filter (λ ) 546 nm, Oriel) is directed into the side of the microscope and internally reflected through the objective and onto the lens (see Figure 3). The interference reflections are observed using a CCD camera (Sanyo VDC 3800) (37) Personal communication with M. Long at Helene-Curtis, 1996.
Comb-Graft Copolymer-Stabilized Oil Films attached to the microscope. Images are viewed on a monitor (Panasonic CT-1383Y) and either recorded on a S-VHS recorder (Panasonic AG-7350) or sent directly to the computer (Power Macintosh 7100/80) and captured using a frame grabber (Data Translation Quick Capture). NIH-Image software is used to measure the intensities and sizes. Electronics and Voltage Application. The electrical potential across the film is generated with a Dagan 3900A integrating patch clamp with 3901 headstage, 3910 expander, and X10 bath connector. Ag/AgCl electrodes were formed by electroplating using the method of Keller.38 The patch clamp system measures capacitance by imposing a 5-mV peak-to-peak, 100-Hz triangle wave across the film and measuring the resultant square current wave. The applied voltage signal and measured current signal were verified using an oscilloscope (LeCroy 9400). The patch clamp was also used to apply steady voltages for contact angle measurements. Capacitance Measurements. For the capacitance measurements, films were formed slowly to minimize the inclusion of lenses. Also, unless otherwise noted, films were formed at the voltage of interest, and the voltage was kept constant. Capacitance measurements were taken 5-20 min after the film was formed once a steady capacitance value was reached. The film area was measured using image analysis with NIH-Image software. The reported capacitance values represent averages from two or more films (formed hours apart) with multiple measurements made to ensure steady state. Contact Angle Measurement. The contact angle measurement involved forming a film rapidly at a moderate voltage (typically 200 mV) so as to include lenses. The voltage could then be adjusted as necessary. From the video image, the contact angle was measured from the interference rings. The reported contact angles represent averages of two or more lenses (typically four) from at least two different films (formed hours apart). For an applied voltage of 100 mV or larger, contact angles achieved steady values in 30 s to 1 min. For lower voltages, longer times (5-10 min) were required for steady values to be achieved. Film Formation. The film experiments began by placing the Kel-F cup into the aqueous reservoir followed by expression of oil into the hole region. The excess oil was removed with a syringe to clear the 1-mm hole of oil (i.e., allow a continuous path for the aqueous phase). Oil was then slowly expressed into the hole using the syringes until oil filled the entire region and the aqueous phases were separated. A film was formed by withdrawing oil until the two interfaces came into contact and a particular film diameter was set. Unless otherwise noted, measurements were made 1 h or more after the first interface was formed. Time was measured both from the first injection of oil (age of experiment) and from each injection of oil subsequent to film rupture (film age). Interfacial Tension. The sessile drop technique used to measure interfacial tension employed the Boyce et al. algorithm.39 Before forming a drop, the phases were preequilibrated. Then drops were made by placing a small quantity of the aqueous phase onto a Kel-F base in a cuvette filled with the oil phase. The drops were imaged from the side using an Olympus stereomicroscope (SZ-Tr) (8× magnification eyepiece and variable magnification body) connected to a CCD camera (Sanyo). Interfacial tension was monitored for 24 h. Dynamic Light Scattering. Dynamic light scattering measurements were made with a Brookhaven Instruments goniometer and correlator. Cleaning Procedure. All components were washed thoroughly with detergent and water followed by multiple rinses with deionized water. A penultimate wash in a chromic acid/ sulfuric acid mixture removed any adsorbed materials. This was followed by a thorough deionized water rinse.
Results and Discussion Interfacial Tension. Temporal changes in the interfacial tension between Abil solutions and 1.0 M KCl show that the adsorption and rearrangement processes for (38) Keller, S. L. Ph.D. Thesis, Princeton University, 1995. (39) Boyce, J. F.; Schurch, S.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1984, 9, 307.
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Figure 4. Interfacial tension-time for Abil in decane solutions against 1.0 M KCl (after preequilibration). Different data points represent different drops.
Figure 5. Interfacial tension as a function of the logarithm of the concentration for solutions of purified Abil in decane against 1.0 M KCl solutions.
polymer at the interface were quite slow (Figure 4). Typically, surfactants take seconds (or minutes) to reach equilibrium; the Abil surfactant requires hours (>10 h for the purified material). The effects of impurities can be seen from the tension values for the unpurified Abil solutions. With these solutions, the interfacial tension went through a minimum and then increased. Presumably, this was caused by the displacement of low molecular weight species by higher molecular weight compounds. Purified Abil did not display this behavior. Instead, the purified polymer solution showed a gradual decrease of interfacial tension; it took significantly longer to reach a steady value. The interfacial tension-concentration relation for the purified Abil in Figure 5 is based on tension values after 22-24 h of aging. The problem in determining the surface excess concentration from interfacial tensionconcentration measurements is that, as pointed out by Fleer et al.,40 the surface excess concentration values determined for polydisperse systems may be in error. For purified Abil, the surface excess concentration in the steepest region of the diagram gives an estimate of adsorption, viz., ∼1 molecule/1.7 nm2. The decrease of -dσb/d ln C in Figure 5 indicates aggregation or interfacial rearrangement of polymer, often observed with polymers at interfaces. (40) Fleer, G. J.; Stuart, M. A. C.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London, 1993.
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Figure 7. Image of an early film from 0.058% purified Abil showing dark spots. This image was taken about 30 min after the formation of the film. The spots do not grow significantly with time.
Figure 6. Images from the draining of a film from 0.52% Abil in decane under a large applied voltage (∼500 mV). The voltage is applied in b, and the thick regions re-form into lenses. When the voltage is removed in f, the lenses can be seen to change shape by increasing in diameter.
Film Formation. When a film was formed rapidly, a dimple appeared and drained asymmetrically within a few seconds. A lens (or lenses) remained in the planeparallel film after drainage, cf. Figure 6f. In the absence of an electric field, this drainage process took 10-20 min. With an increase in electric field, the drainage time decreased and the lenses became smaller in diameter (effect of voltage on a lens shown in parts e and f of Figure 6). When more than a few hundred millivolts was applied across a thinning film, the thinnest regions of the film compressed within a second and the thicker regions rearranged to form lenses (Figure 6). Exceptions to this behavior occurred with films formed with the 0.058% (w/w) Abil solutions (purified and unpurified). Within the first hour of experimentation, dark spots formed within the films (Figure 7). These spots did not grow significantly over 90 min. After several hours of measurements (i.e., repeated rupture and film formation), this behavior was no longer observed, and the films thinned to a uniform thickness. Capacitance Measurements. Figure 8 shows capacitance measurements for purified and unpurified Abil solutions. The films appeared to be uniform, and only at the higher voltages (350-400 mV) were some slightly brighter spots (intensity difference barely detectable) observed. The compression (increasing voltages) and expansion (decreasing voltages) processes were reversible, and a thickness at a particular voltage could be obtained by forming a film at a particular voltage or by increasing or decreasing the voltage on a previously formed film (Figure 9). Film age did not appear to significantly alter the capacitance as long as visible thickness heterogeneities
Figure 8. Capacitance-voltage for Abil in decane films.
Figure 9. Capacitance-voltage for 0.52% Abil (purified) in decane films. Measurements while increasing voltage on one film and decreasing the voltage on another. Thickness changes by expansion and compression appear equivalent.
were not present (i.e., after about 2 h into the age of the experiment). Figure 10 shows thickness-voltage behavior for Abil films calculated from the capacitance measurements
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Langmuir, Vol. 15, No. 21, 1999 7305 Table 1. Compressive Force Parameters k/nm-1
solution
A/Pa
0.52% Abil (purified) 0.058% Abil (purified) 0.52% Abil (unpurified) 0.058% Abil (unpurified)
1.896 × 1.288 × 107 3.319 × 106 7.391 × 106 107
0.227 0.243 0.231 0.250
Table 2. Elastic Moduli, Ybl
a
solution
FE/Pa
Ybl/Pa
purified purified purified unpurified unpurified unpurified
0-200 200-600 600-1000 0-200 200-600 600-1000
1000 3500 6400 750-850a 3200 7200
Concentrations of 0.52% and 0.058%, respectively.
Figure 10. Thickness-voltage for Abil in decane films as calculated from capacitance.
Figure 12. Two possible configurations of the polymer in the film: (a) highly extended and (b) layers of aggregates.
assuming a dielectric constant of 2.1. The thickness values can be used, in turn, to convert capacitance values into the pseudo-disjoining pressure isotherms, Figure 11. Note that this is not a true disjoining pressure isotherm but rather involves the electrical compressive force alone (disjoining pressure minus the capillary pressure). Thickness values determined from capacitance measurements are an order of magnitude above those for lipid or lipidlike surfactants films. The polymer-stabilized films are highly compressible. Discussion of Film Thickness Measurements. The film thickness measurements give an interfacial layer thickness of ∼25 nm, which is considerably thicker than the molecular dimensions in solution of 6 nm measured by dynamic light scattering (see below). This suggests that either the polymer is highly extended at the surface or polymeric structures induced at the interface are the stabilizing entity. The relationship between the applied compressive force and the film thickness is shown in Figure 11 to be an exponential, Ae-kh, where h is the film thickness and A and k are fitting parameters. Decay lengths (k-1) are 4-5 nm and increase, somewhat, with concentration. Table 1 shows the values derived from the curve fitting. Elastic moduli were also estimated for the four systems. The modulus, Ybl, can be determined from the strain and the electrical force as
where δh is the change in thickness from a compressional force, FE. The moduli (given in Table 2) were independent of concentration and only slightly dependent on purification. The moduli are fairly consistent for all solutions and show a dramatic increase with compression of the films. Dynamic light scattering measurements on Abil in decane were used to determine if large objects (that could contribute to the stability and thickness of the films) were present. For the purified Abil at 5% w/w, a hydrodynamic size of 6 nm was obtained. The most interesting question arising from the observation of the thick and compressible films is what is the polymer structure(s) that leads to this phenomena. The thick films are shown not to arise from image charges at the water/decane interfaces or from ions in the decane phase as shown in Appendix A. A polymer-induced steric stabilization mechanism must be invoked. Two possibilities are shown schematically in Figure 12: the polymer adsorbed at the interface might be strongly anchored and highly extended (Figure 12a), or there might be multiple chain aggregates that lead to stabilization (Figure 12b). From the surface coverage of 1.7 nm2/molecule and the film thickness of 50 nm for two interfaces, we calculate the volume that a single anchored and extended molecule would occupy as (1.72 nm2/molecule)(25 nm) ) 43 nm3. The volume occupied by a molecule in solution is 4πRh3/3 ) 36 nm,3 since Rh was measured to be 3 nm. While these values are consistent, it would not be expected that a highly stretched polymer brush would be as compressible as the films we produce.41
h Ybl ) FE δh
(41) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989.
Figure 11. Disjoining pressure isotherms for Abil in decane films calculated from capacitance.
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Anklam et al. Table 3. Interfacial Tensions from the Lippmann Equation solution
interfacial tension, mN/m
0.52% Abil (purified) 0.058% Abil (purified) 0.52% Abil (unpurified) 0.058% Abil (unpurified)
18.9 22.9 12.7 15.5
The Lippmann relationship, eqs 22-25, was used to determine the interfacial tension for the films (cf. Requena and Haydon25 and Rovin43). With the reference voltage, V0, set to 100 mV, the measured values of θi and θE and the measured dependence of C upon V were used to calculate the apparent interfacial tension from
2σb(cos θi - cos θE) ) Figure 13. Contact angle-voltage for Abil in decane films.
The alternative explanation involves multiple interconnected aggregates. These “flowerlike micelles” would be composed of primary units having approximately the sizes measured by DLS, which would mean that something like nine layers of micelles span the film. For very monodisperse surfactant micelles, discrete layers of micelles are observed and a thinning by shedding of single layers is observed.42 Given the polydispersity of the polymeric surfactant, it is not surprising that discrete layers are not observed during electrical compression. In support of the picture of layering, it was observed that dark spots were observed in the early stages of film development which would be consistent with films on the order of 10 nm in thickness. That the film thickness and compressibility were constant from film to film and over 1 order of magnitude in concentration is interesting and points to the role of the interface in ordering the interactions as is observed in surfactant systems where lamellar phases can be nucleated at an oil/water interface and the resulting lamellar phase acts to stabilize the emulsion. As a final note, Lyklema and van Vliet2 observed foam film thicknesses on the order of 60 nm using poly(vinyl alcohol) (MW ) 42 000). The behavior of the polymer at the interfaces and the structures of the films were not examined. Contact Angle Measurements. Figure 13 shows the contact angle as a function of voltage. The films exhibited a large change in contact angle with voltage, and the contact angles were larger at the higher Abil concentrations for the unpurified surfactant. Contact angles were smaller for the purified Abil solutions and not dependent on concentration. Thus, contact angles appeared to follow the trends observed with interfacial tension. Contact angles did not appear to vary significantly with time. Even with dark spots in the early films of the unpurified 0.058% Abil, contact angles were comparable to contact angles measured hours later. In addition, contact angles did not vary significantly from lens to lens, from film to film, or in any consistent way with the lens diameter (significant meaning that variations were small compared to the changes in contact angle when voltage is changed by 25 mV). The lenses themselves reached steady state within minutes and did not grow or drain thereafter. The lack of dependence of contact angle on lens diameter demonstrates that the contribution from line tension was negligible. Contact angles for the Abil films are significantly larger than the contact angles measured for lipid films.34 (42) Bergeron, V.; Radke, C. J. Langmuir 1992, 8, 3020.
∫VVCV dV 0
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These tensions are given in Table 3. In all cases, these values were significantly larger (by about 10 mN/m) than those obtained from the sessile drop technique; the trends (i.e., the order of increasing tension) were the same. The capillary pressure at the meniscus was estimated to be small but not insignificant in the case of the purified polymer systems. The principal radii of curvature were estimated to be 300 and 500 µm for a typical meniscus. This gives a capillary pressure of about 50 Pa for a bulk interfacial tension of 10 mN/m. However, tensions calculated from the Lippmann relationship indicate the capillary pressures for the purified Abil are higherson the order of 100 Pa. This would affect the pseudodisjoining pressure measurements by displacing the curves on the y axis. If the contact angle measurements for zero applied voltage were used to determine the free energy and the dispersion forces are assumed to be the dominant contribution to the free energy (as assumed by Requena et al. for lipid films34), then the Hamaker constant for the 0.52% purified Abil system is 5 × 10-19 J and is much larger than expected for a hydrocarbon (
