Langmuir 1999, 15, 4579-4583
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Imaging Ellipsometry/Reflectometry for Profiling the Shape of a Deformable Droplet as It Approaches an Interface D. G. Goodall,† G. W. Stevens,‡ D. Beaglehole,§ and M. L. Gee*,† Departments of Chemistry and Chemical Engineering, University of Melbourne, Parkville 3052, Victoria, Australia, and Department of Physics, Victoria University of Wellington, New Zealand Received November 2, 1998. In Final Form: March 9, 1999 The application of imaging ellipsometry/reflectometry to study the system of an oil droplet approaching a silica surface in a continuous aqueous medium is described for the first time. Imaging ellipsometry/ reflectometry is shown to be capable of accurately determining changes in the profile of a droplet as film drainage occurs between a droplet and an interface. The technique has the advantages that it is sensitive to the measurement of both thick and thin films and yields a film profile in real time without the need to scan across the surface. It is shown that imaging ellipsometry/reflectometry provides a valuable alternative to interferometric and photometric techniques, which have previously been employed to study a system of this type. The approach of a squalene droplet to a silica surface in a continuous aqueous phase was investigated. The droplet was observed to dimple on approach to the silica plate. The shape of the droplet evolved from a dimpled to flattened profile. The equilibrium film thicknesses and film drainage data obtained were observed to be dependent upon electrolyte concentration because of double-layer interactions between the droplet and the silica surface.
Introduction This paper describes a new application of the technique of imaging ellipsometry/reflectometry to the monitoring of changes in droplet profiles as they approach an interface. Compared to other techniques, imaging ellipsometry/ reflectometry has the advantage of high vertical resolution, enabling the study of both thick and thin films. Consequently, the entire film drainage process between a droplet and an interface may be monitored up until the point at which film rupture occurs. Additionally, the entire droplet profile is sampled simultaneously; there is no need to scan across the surface as with other techniques that can only give a film thickness at one point at a time. The incorporation of sampling time differences between successive points on the droplet surface, as occurs with scanning techniques, are therefore eliminated when imaging ellipsometry/reflectometry is used, thereby ensuring accurate determination of the droplet profile at any given time. The advantages of imaging ellipsometry/reflectometry as a real time profiling technique are valuable to our understanding of the factors that influence coalescence phenomena and stability in emulsion systems. Emulsion instability is a direct result of droplet coalescence and eventual phase separation. This is an undesirable process in emulsion products such as margarine, sauces, and paints as it essentially reduces the product’s shelf life and quality. When two droplets approach each other in an emulsion system, a thin liquid film forms between the two droplets.1 The rate at which this film thins is the rate at which the liquid drains from the gap between the two droplets. When * To whom correspondence should be addressed. † Department of Chemistry, University of Melbourne. ‡ Department of Chemical Engineering, University of Melbourne. § Victoria University of Wellington. (1) Jeffreys, G. V.; Davies, G. A. Recent Studies in Liquid-Liquid Extraction; Pergamon Press: Oxford, 1971.
the film becomes sufficiently thin, ∼100 nm, the effects of van der Waals and electrostatic forces become significant. In stable emulsion systems, the film will thin to an equilibrium thickness at which point no further thinning of the intervening fluid between the droplets occurs. This equilibrium thickness is dependent upon the magnitude of the disjoining pressure in the film, which in this case acts to stabilize the film. If the system is unstable, the film continues to thin to what is termed the critical thickness, at which point an instability develops, the film ruptures, and the two droplets coalesce. The shape of the drop/film as film drainage occurs depends on the deformability of both the droplet and the interface. The extent of deformation that is incurred is dependent on a number of physical properties such as viscosity of the continuous phase, interfacial tension, the size of the droplet, and the density difference between the two phases. Earlier work2,3 has shown that when an initially spherical droplet approaches a surface, the film between the droplet and the surface drains, allowing the film to thin. However, the rate of drainage of the film is not everywhere uniform. The outer regions of the film are relatively thick because of the spherical shape of the droplet, whereas the center of the film is relatively thin since it corresponds to the closest point of the droplet to the surface. Therefore, drainage from the periphery of the film is opposed by only a small viscous drag compared to the viscous drag opposing drainage from the thinner, central film area. Drainage from the film periphery is initially greater than the drainage from the central region of the film and so excess liquid is “trapped” at the film’s center. Thus, the droplet acquires a “dimple”-type shape. Dimpling is particularly pronounced if the droplet is approaching a nondeformable surface. Beyond this point, a positive Laplace pressure resulting from the reverse (2) Allan, R. S.; Charles, G. E.; Mason, S. G. J. Colloid Sci. 1961, 16, 150. (3) Platikanov, D. J. Phys. Chem. 1964, 68, 3619.
10.1021/la981543d CCC: $18.00 © 1999 American Chemical Society Published on Web 05/25/1999
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curvature of the droplet drives further drainage of the fluid trapped in the central dimple region. Accurate modeling of the droplet profile as film drainage occurs has to date been unsuccessful because of the complexity of the coalescence process and also the lack of experimental data in both the thin and thick film regimes. Imaging ellipsometry/reflectometry is a means of addressing this experimental deficiency. Many investigators have employed the technique of interferometry4-10 to examine profile changes of a droplet or bubble approaching a surface. Interferometry, although capable of determining droplet profiles with a relatively small degree of error, is restricted to the study of film thicknesses greater than those at which rupture occurs. Additionally, interferometry cannot give the droplet profile, in its entirety, in real time. The profile is obtained by performing a series of interferometric film thickness measurements at various points along the droplet as the film drains and/or accumulating such data for a series of different droplet experiments. Imaging ellipsometry/ reflectometry does not suffer from either of these experimental limitations. Imaging ellipsometry is an optical technique in which changes in polarization of light due to reflection from a film-covered surface are analyzed in terms of thickness and refractive index of the film. This technique has previously been employed to investigate profiles of siloxane oil droplets spreading on glass, silica and mica11, protein patterning on silica surfaces12 and domains of surfactant monolayers at an air/water interface.13 The application of imaging ellipsometry/reflectometry to study the system of an oil droplet approaching a hydrophilic, negatively charged silica plate in a continuous aqueous medium is described in this paper. The ionic strength of the continuous phase was varied over the range 10-5-10-3 M NaCl, and equilibrium film thicknesses and drainage data for these systems are reported. Experimental Section Theory of Ellipsometry/Reflectometry. Ellipsometry14 is a polarimetric technique which involves the measurement of changes in polarization of monochromatic light upon reflection from a film-covered surface. Information regarding refractive indices and thicknesses of thin films for a variety of systems can be determined from these changes in polarization. As mentioned previously, ellipsometry has the ability to measure thicknesses of thin films. From film thickness measurements at various points along an interface at which a droplet is approaching, a profile of a droplet as film drainage occurs can be built up. In a substrate/film/droplet system (Figure 1), such as the ones of interest in this project, an incident beam, plane polarized in nature, is reflected and refracted at the substrate/film interface. The refracted portion of the light undergoes internal reflection within the film and, as a result, suffers a phase change, β, in relation to the light reflected at the substrate/film interface. β is related to the thickness of the film, d, and the film’s refractive (4) Burrill, K. A.; Woods, D. R. J. Colloid Interface Sci. 1969, 30, 511. (5) Fisher, L. R.; Mitchell, E. E.; Hewitt, D.; Ralston, J.; Wolfe, J. Colloids Surf. 1991, 52, 163. (6) Burrill, K. A.; Woods, D. R. J. Colloid Interface Sci. 1973, 42, 15. (7) Horn, R. G.; Bachmann, D. J.; Conner, J. N.; Miklavcic, S. J. Langmuir 1996, 12, 4197. (8) Aveyard, R.; Binks, B. P.; Cho, W.-G.; Fisher, L. R.; Fletcher, P. D. I.; Klinkhammer, F. Langmuir 1996, 12, 6561. (9) Joye, J.-L.; Miller, C. A. Langmuir 1992, 8, 3083. (10) Hewitt, D.; Fornasiero, D.; Ralston, J. J. Chem. Soc., Faraday Trans. 1993, 89, 817. (11) Beaglehole. D. J. Phys. Chem. 1989, 93, 893. (12) Reiter, R.; Motschmann, H.; Orendi, H.; Nemetz, A.; Knoll, W. Langmuir 1992, 8, 1784. (13) Jin, C.; Jansson, K.; Arwin, H. Rev. Sci. Instrum. 1996, 8, 67. (14) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarised Light; Elsevier North-Holland Inc.: New York, 1977.
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Figure 1. Reflection and refraction of plane polarized light in a substrate/film/droplet system. index, n2, via the following expression:
β ) 2π (d/λ)(n1 - n2 sin2 φ1)1/2
(1)
where λ is the wavelength of the incident monochromatic light, φ1 is the angle of incidence, and n1 is the refractive index of the substrate. The Fresnel reflection coefficients15 of the resultant reflected beam are
Rp ) (rp12 + rp23e-2βi)/(1 + rp12rp23 e-2βi)
(2)
Rs ) (rs12 + rs23e-2βi)/(1 + rs12rs23e-2βi)
(3)
where r12 and r23 are the Fresnel reflection coefficients at the 1-2 and 2-3 interfaces, respectively. Ellipsometry determines the ratio of the complex Fresnel reflection coefficients for p and s components as given by eq 4, viz
F ) Rp/Rs ) tan ψe-i∆
(4)
where tan ψ ) |rp12|/|rs12| and ∆ ) δrp - δrs, δrp and δrs being the phase shifts experienced upon reflection for the p and s components, respectively. For the case in which unpolarized light is incident at the substrate/film interface, film thicknesses can be obtained from measuring the intensity of the light reflected from the sample surface. The ratio of the intensity of the reflected light to the intensity of the incident light is commonly known as reflectance, R, and is given by eq 5:
R ) (Rp + Rs)/2
(5)
Apparatus and Procedure. Measurements of droplet profiles for the system of an oil droplet rapidly expanded toward a silica substrate in a continuous aqueous medium were made using a Beaglehole Instruments imaging ellipsometer. The arrangement of the fundamental components of the imaging ellipsometer is shown in Figure 2. Details of the microscopic imaging ellipsometer are briefly outlined below. Specifics of the instrument, however, are described elsewhere.16 The imaging ellipsometer, although similar in concept to a conventional ellipsometer, differs in that a quartz halogen lamp (50 W, 12 V, 5 A) with a beam area of 1 cm2 is employed instead of the usual laser light source of beam area 1 mm2. A condensing lens and an objective lens as well as a CCD detector are also inserted in the optical lineup to provide the microscopic imaging. This combination allows sensitive, simultaneous sampling of the entire droplet profile at any one time. Experimentally, a silica prism is placed to seal on top of a glass cylindrical cell (Figure 3) filled with the fluid of the continuous phase (aqueous solution) and located at the ellipsometer axis. Droplets are formed from a stainless steel capillary tip which is positioned 2 mm from the silica/aqueous interface. The capillary is connected to a gastight syringe contained in a dispenser which provides volume control. The optical components, (15) Born, M.; Wolf, E. Principles of Optics; Pergamon Press: Oxford, 1990. (16) Beaglehole, D. Rev. Sci. Instrum. 1988, 12, 59.
Ellipsometry/Reflectometry of a Deformable Droplet
Figure 2. Schematic representation of the components of the imaging ellipsometer: F, filter (600 nm); P, polarizer; R, retarder; CL, collimating lens; OL, objective lens.
Figure 3. Schematic representation of the imaging ellipsometer experimental cell. located on two motorized, rotatable arms, are arranged for reflection from the silica/aqueous interface. In a typical experiment, a droplet is rapidly expanded from the capillary tip, thus pressing up toward the silica prism plate, and measurements are taken to determine the profile of a droplet as film drainage occurs. The time resolution for these experiments is ∼1 s, which allows for accurate monitoring of the changes in the profile of the droplet as it continually approaches the surface. In an ellipsometric measurement, light is initially passed through a filter (600 nm) before being polarized at 45° to ensure that the amplitudes of the p and s components of the light are of equal value. The light is then passed through a retarder which introduces a desired phase shift between the p and s components. A lens then converges the resultant beam which is reflected from the sample surface. The reflectance pattern is then passed through an objective lens and a second retarder resulting in a microscopic image which is captured by a CCD detector. By varying the polarization of the incident light, two images can be obtained using the imaging ellipsometer, one polarized and one unpolarized in nature. The polarized picture gives the image of the coefficient of ellipticity over the sample surface, and the unpolarized picture gives the image of the intensity of the light reflected from the sample surface. The imaging ellipsometer therefore has the adaptability to be run in either ellipticity or reflectance mode, hence having the ability to study both thin and thick films. Materials. The two immiscible fluids used in these experiments were squalene (droplet phase) and water (continuous phase). Squalene (C30H50) was obtained from Sigma Aldrich Chemical Co. Pty. Ltd. (98+%) and was used without further purification. The water used in the experiments was produced using a Milli-Q filtration system. Sodium chloride was obtained from Ajax Chemicals (99.9+%).
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Figure 4. Droplet profile data for the system of a squalene droplet approaching a hydrophilic silica plate in a continuous medium of 10-3 M NaCl (pH ) 6.8). The equilateral dispersing prism made of fused silica (refractive index ) 1.458) was supplied by Ealing optics. The prism was removed of impurities first by light scrubbing with a warm solution of Extran 100, followed by thorough rinsing with Milli-Q water. The prism was then further treated with a hot ammonical peroxide solution (two parts hydrogen peroxide, one-part water, one-tenth ammonia) before copious rinsings with Milli-Q water. The capillary was soaked in Extran 100 for ∼12 h and rinsed with Milli-Q water before being immersed in a hydrofluoric acid wash (60% water, 35% concentrated nitric acid, 5% hydrofluoric acid), followed by repeated rinsings with Milli-Q water. The syringe casing was washed in an Extran solution (∼2 h, nitric acid washed (∼12 h) before numerous rinsings with Milli-Q water. All other glassware and fittings were scrubbed and soaked in an Extran solution for ∼12 h, rinsed with Milli-Q water, and then soaked in concentrated base (NaOH). The glassware and fitting were then finally rinsed numerous times with Milli-Q water. Solution conditions for all experiments were set such that the silica plate had an overall negative charge. Thus, for all experiments, the aqueous phase was set to a pH of 6.8 using a dilute NaOH solution. Droplet profiles and film drainage was hence monitored at this pH but as a function of electrolyte concentration (10-3, 10-4, and 10-5 M NaCl).
Results and Discussion Film profiles for the system of a squalene droplet expanded toward a hydrophilic, negatively charged silica plate in a continuous medium of 10-3 M NaCl at pH 6.8 are shown in Figure 4. As the reflectance is significantly more sensitive than the ellipticity to the magnitude of the film thicknesses investigated in this work, thicknesses were obtained using the ellipsometer in reflectance mode rather than in ellipticity mode. After the expansion of the droplet toward the silica plate, the droplet initially deformed into a dimple-type shape, as seen in Figure 4. Note that typical profiles and the change in the profile of the droplet as a function of time are shown in Figure 4, but during the course of an experiment, several more profiles are obtained. As mentioned previously, this observed convex conformation of the droplet results from a faster rate of drainage in the barrier ring compared to the drainage from the central film region. It was observed that as film drainage proceeded from between the droplet and the silica surface, and near equilibrium film thickness was approached at the barrier ring, the rate of drainage in this region became increasingly retarded. Once the near-equilibrium film thickness was achieved at the barrier ring, drainage from the central film area continued, allowing the shape of the
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droplet to continually evolve from a dimpled profile to a flattened profile. This occurred at a decreasing rate until a parallel film was attained. It is suggested17,18 that organic droplets present in aqueous solution show similar characteristics to air bubbles in an aqueous environment and bear a net negative charge due to preferential adsorption of ions at the oil/aqueous interface. Speculation exists as to the actual adsorption mechanism resulting in the charging of organic droplets and air bubbles in aqueous solution. It is suggested, however, that a combination of factors contribute to this phenomenon.19,20 If charge is acquired at the oil/aqueous interface, as an oil droplet approaches a similarly charged plate, electrical double-layer repulsion exists between the droplet and surface. As observed experimentally in this study, the droplet continues to approach the surface at a decreasing rate as the double layer extending from the silica surface overlaps with that from the oil droplet. When the pressure inside the film is equal to the pressure inside the droplet, no further film drainage occurs and an equilibrium film of uniform thickness results. Film profiles were also obtained for the system of a squalene droplet expanded toward a hydrophilic silica plate in a continuous aqueous phase of both 10-4 M and 10-5 M NaCl. Profiles were similar to those shown in Figure 4, for 10-3 M NaCl. However, it was observed that the degree of dimpling was more pronounced the higher the ionic strength. This phenomenon has previously been observed by Ralston et al.10 and can be explained by considering the electrostatics of the system. As the ionic strength of the continuous phase is increased, the doublelayer interaction between the droplet and the silica plate decreases. The drainage at the barrier ring of the film increases when there is less double-layer repulsion between the two surfaces. Figure 5a shows the drainage data, that is, the film thickness at the barrier ring as a function of time, obtained for the range of salt concentrations investigated in this study. The data clearly show that drainage from the barrier ring was initially more rapid the higher the concentration of salt in solution. This is expected since, as stated above, the double-layer interaction between the droplet and the plate decreases with increasing salt concentration and so there is less resistance to the approach of the droplet to the plate.6 Note that the drainage curve for 10-5 M NaCl shows an initial rapid decrease in film thickness to about 2500 Å, followed by a slower increase. After this, drainage occurs in a manner similar to what was observed for 10-4 and 10-3 M NaCl. This unusual behavior is not real but is due to that fact that the droplet was initially brought up to the surface at too rapid a rate which lead to an initial rapid drop in film thickness. The droplet then relaxed to a position from which film drainage could occur. Rates of drainage at the central region of the droplets were measured from the time at which the barrier ring of the droplet reached its near-equilibrium position, that is, when the droplets begin evolving from a dimpled to flat profile. Figure 5b shows a log plot of the change in film thickness at the central region of the droplet as a function of time for the systems of 10-3, 10-4, and 10-5 M NaCl. The gradients of these plots are indicative of the rate of drainage. Note that the gradients of these plots are the (17) Carruthers, J. C. J. Chem. Soc., Faraday Trans. 1938, 34, 300. (18) Dickinson, W. J. Chem. Soc., Faraday Trans. 1941, 37, 140. (19) Lin, K. L.; Osseo-Asare, K. Recent Developments in Separation Science. CRC Press: Boca Raton, FL, 1986. (20) Bockris, J. O.’M.; Reddy, A. K. N. Modern Electrochemistry; Plenum Press: New York, 1970.
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Figure 5. (a) Film thickness at the barrier ring as a function of time for the systems of a squalene droplet approaching a hydrophilic silica plate in continuous mediums of (() 10-3 M, (O) 10-4 M, and (4) 10-5 M NaCl. (b) Log plot of the film thickness at the center of the film for the systems of a squalene droplet approaching a hydrophilic silica plate in continuous mediums of ()) 10-3 M, (b) 10-4 M, and (4) 10-5 M NaCl.
same, within experimental error. This indicates that the drainage rate from the central film region, during the evolution of the droplet shape, is independent of salt concentration and implies that double-layer forces are inconsequential. Additionally, Figure 5b also indicates that there is a dependence on salt concentration for the time required for the barrier ring to near its equilibrium thickness. In 10-3 M salt, this time is about 300 s, in 10-4 M salt it takes 1000 s, and in 10-5 M salt it takes 2700 s. This is clearly a double-layer effect. At higher salt concentrations, the double-layer repulsion is reduced, allowing faster equilibrium, as explained above when discussing Figure 5a. When considering film drainage between a droplet and a surface, the surface interactions are important, but so too are factors which affect fluid flow. We have observed (see above) that, at high salt concentrations, the drainage rate at the barrier ring is relatively high because of the limited double-layer forces between the silica plate and the squalene droplet. We have also observed that, as a result of this higher drainage rate, the droplet deformation is more pronounced; the droplet profile has a larger degree of curvature. As a result, the Laplace pressure which drives film drainage is higher. We have also determined that a high salt concentration results in a closer approach of the droplet to the surface and so the flow of liquid confined within this gap is restricted. Thus, there are two opposing affects: the Laplace pressure which acts to promote film drainage (occurs at high salt) and spatial restriction of liquid which acts to oppose film drainage (occurs at high salt). Thus, it is possible that, regardless of salt concen-
Ellipsometry/Reflectometry of a Deformable Droplet
tration, the Laplace pressure effect is offset by the restricted fluid flow effect. It is interesting to note that, in contrast to our results, Ralston et al.10 found that drainage from the central region of an air bubble approaching a silica surface decreased with increasing ionic strength. This was explained by considering the greater resistance to fluid flow that accompanies drainage from thinner films, the film being thin as a result of reduced double-layer repulsion. No Laplace pressure effect was invoked to explain the data. However, a direct comparison between the data of Ralston et al. and ours cannot be made since the systems differ significantly. Ralston et al. investigated an air bubble which is much smaller than our squalene liquid drop. Additionally, our experiments were all performed at a pH of 6.8 to ensure a large negative potential on the surface of the silica plate. It appears that Ralston et al. have worked at natural pH and so the charge on the silica plate would have been significantly less than that in our experiments. The system investigated in the present study is stable in the sense that film drainage between the plate and the droplet continues only until the thickness of the film reaches some equilibrium value. The equilibrium film thicknesses obtained are shown in Table 1 and are observed to decrease with increasing salt concentration. Film rupture does not occur because of the repulsive double-layer forces between the plate and the droplet which act to stabilize the film. Thus, it can be concluded, as expected, that the equilibrium film thickness between
Langmuir, Vol. 15, No. 13, 1999 4583 Table 1. Equilibrium Film Thickness for 10-3, 10-4, and 10-5 M NaCl Systems ionic strength (mol/dm3)
experimental film thickness (nm)
1.0 × 10-3 1.0 × 10-4 1.0 × 10-5
75 155 244
a deformable drop and a flat plate is governed by the surface interactions between the droplet and the plate. Conclusions This paper shows that the technique of imaging ellipsometry/reflectometry is capable of following the evolution of droplet profiles as a function of time as a droplet approaches an interface. To illustrate the usefulness of this technique, we studied the system consisting of a squalene drop approaching a silica surface in a continuous aqueous phase at pH 6.8. We have monitored dimpling of the drop as a result of nonuniform film drainage and have shown that, at equilibrium, the droplet flattens such that the film is of uniform thickness. This equilibrium thickness is governed by the double-layer interaction between the drop and the silica surface. We are currently investigating the system described above more exhaustively and also intend to investigate systems in which coalescence, that is, film rupture, occurs. Acknowledgment. The authors gratefully acknowledge the financial support of the Australian Food Industry Science Centre and the Australian Research Council. LA981543D
