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Connect the Drops: Using Solids as Adhesives for Liquids Edward J. Stancik and Gerald G. Fuller* Department of Chemical Engineering, Stanford University, Stanford, California 94305 Received January 23, 2004. In Final Form: April 26, 2004 Colloidal particles are shown to be capable of developing adhesion between liquid phases through a bridging mechanism by which intervening, micrometer-scaled, fluid films are stabilized. Particle dynamics leading to the assembly of the stabilizing structure are discussed. Models for the resulting adhesive force are developed from considerations of both interface shape perturbation and the force applied by surface tension on an individual particle. Finally, predictions from these models are compared to direct measurements of the forces that arise during the separation of adhering interfaces. Such comparisons lead to a novel method for determining the three-phase contact angle inherent to particles residing at fluid interfaces.
The ability of colloidal particles to stabilize emulsions has led to a renewed interest in their behavior at fluid interfaces. Pickering1 was first to show that emulsions could be stabilized by solid particles alone, and such systems are now frequently referred to by that name. Early work2 recognized that a primary factor governing the character of these emulsions is the three-phase contact angle at which the particles reside on the droplet surfaces. Generally, if a particle is hydrophobic, the contact angle measured with respect to the aqueous phase is greater than 90°, and most of the particle body will reside in the oil phase. Such particles are best able to stabilize waterin-oil emulsions, in which they can form a thick protective layer around the water droplets in the system. The converse is true for hydrophilic particles, which best stabilize oil-in-water emulsions. More recent studies3,4 concerning the stability of Pickering emulsions have confirmed the importance of particle wetting behavior and also revealed the effects of additional parameters including particle concentration, size, and size distribution. Particle interactions are also known to influence emulsion stability, and a number of studies have sought to understand the mesostructures formed by particles adsorbed to fluid interfaces when attractive5 or repulsive6 forces are dominant. Additional work7,8 has sought to understand the effects of surface flows on these structures. The relevance of particle interactions to emulsion stability is made clear from an understanding of the dynamics resulting when two suspended droplets9 approach each other. The main process governing these dynamics is the drainage of the intervening thin film of fluid that resists coalescence. More specifically, a pressure gradient is required to drive the radial flow of this fluid from between the droplets. Depending on their approach * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Pickering, S. U. J. Chem. Soc. 1907, 91, 2001. (2) Finkle, P. J. Am. Chem. Soc. 1923, 45, 2780. (3) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21-41. (4) Tambe, D. E.; Sharma, M. M. Adv. Colloid Interface Sci. 1994, 52, 1-63. (5) Robinson, D.; Earnshaw, J. Phys. Rev. A 1992, 46, 2045-2054. (6) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Langmuir 2000, 16, 1969-1979. (7) Stancik, E. J.; Hawkinson, A. L.; Vermant, J.; Fuller, G. G. J. Rheol. 2004, 48, 159-173. (8) Hoekstra, H.; Vermant, J.; Mewis, J. Langmuir 2003, 19, 91349141. (9) Klaseboer, E.; Chevaillier, J. P.; Gourdon, C.; Masbernat, O. J. Colloid Interface Sci. 2000, 229, 274-285.
speed, the pressure between the drops can become significant enough to flatten droplet curvature or even invert curvature from a convex to a concave shape over the approach area. Such an inverted shape is often referred to as a dimple and appears simply as a depression on the droplet surface. Finally, drop features in the areas where the intervening film is thinnest, frequently near the rims of dimples when approach velocities allow their formation, will be accentuated by van der Waals attractions and eventually lead to coalescence. Surfactants, which are often used to stabilize emulsions, add complexity to these phenomena primarily by providing a mechanism10 for the development of Marangoni stresses on the droplet interfaces. Essentially, the draining film hydrodynamically couples with surfactant molecules on the surfaces of the droplets and carries them away from the area of closest approach. Marangoni stresses, arising from the resulting gradient in interfacial concentration, attempt to counter the developing inhomogeneity by refilling the depleted area with surfactant. This surface flow couples with the fluid in the thin film and slows the drainage process. An alternate description of this effect considers that the mobility of the droplet interfaces decreases with increasing surfactant concentration. As a result, the boundary condition influencing the velocity gradient within the draining film transitions from one that is highly fluid to one that is significantly rigid, thus providing more resistance to flow. The presence of colloidal particles on the surface of a coalescing droplet has recently allowed direct observation of these interfacial dynamics.11 In this letter, we report the outcome of the special case where the stabilizing particles are wet primarily by the fluid film residing between a droplet and a flat fluid interface. The flat interface in the model system was generated by floating decane over an aqueous solution of 10 mM NaCl in a clean polystyrene dish. A droplet of the same aqueous solution was then brought into proximity with this interface via a capillary tube maneuvered by a computer-controlled, micrometer-driven xyz stage. A 90° bend in the capillary allowed the creation of a horizontal cantilever to which a force transducer was attached for the purpose of measuring the interaction of the drop with the flat interface. Spherical polystyrene particles (Interfacial (10) Yeo, L. Y.; Matar, O. K.; De Ortiz, E. S. P.; Hewitt, G. E. J. Colloid Interface Sci. 2003, 257, 93-107. (11) Stancik, E. J.; Kouhkan, M.; Fuller, G. G. Langmuir 2003, 20, 90-94.
10.1021/la049778e CCC: $27.50 © 2004 American Chemical Society Published on Web 05/14/2004
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Figure 1. Illustration of experimental geometry by which a force transducer (A) measures interfacial interactions as a capillary holding a water droplet (B) is lowered to the interface (C) between decane and a 10 mM NaCl solution. Particles are adsorbed to the fluid interfaces and observed through a 10× objective (D). Computer-controlled, micrometer-driven actuators (E) are used to position the stage on which the force transducer and capillary rest.
Figure 2. Micrographs showing the transition from a crystalline-like order to an aggregated state when particles assume a bridging geometry between the two aqueous phases. Particle interfacial concentration is approximately 10%. The scale bar represents 50 µm.
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Figure 3. Illustration of particle behavior as a thin film of decane (B) drains from between two aqueous phases (A). Particles (a) initially at equilibrium (b) begin to interact with those on an approaching interface before (c) finally making contact and subsequently aggregating in a bridging geometry.
Figure 4. Micrographs of contact angle measurements in which (a) a water droplet in a bath of decane or (b) a decane droplet in a bath of water is observed as it wets a surface spin-coated with polystyrene from the studied particles dissolved in chloroform. Note that the actual contact angles with the surface were measured to be 129° for the water drop and 49° for the decane drop, each reproducible within 1°. Because these values should sum to 180° in the absence of hysteresis, the data suggest that the aqueous phase wets the particles at an angle of 130 ( 2°.
Dynamics Corp.) with a mean diameter of 3.1 µm were then added to the flat interface using a working dispersion of 5.0 × 108 particles/mL suspended in a solution of 20% isopropyl alcohol in deionized water (specific resistance 18.2 MΩ‚cm, Millipore). More specifically, small droplets of the working dispersion were injected into the oil phase from which they were forced into contact with the aqueous phase by gravity. This contact subsequently led to coalescence of the droplets with the aqueous phase and release of the particles at the oil-water interface. To create colloid-covered droplets, the tip of the capillary tube, which was filled with a 10 mM NaCl solution, was then brought into contact with the aqueous subphase. Upon withdrawal of the capillary, a colloid-laden aqueous bridge was created that subsequently broke to leave a colloid-laden droplet attached to the capillary. This provided a convenient method for creating the system shown in Figure 1 with equal particle concentrations on the two interfaces. As the droplet is brought back into contact with the flat interface, the mesostructure formed by the particles transitions from one that exhibits crystalline-like ordering to one that is strongly aggregated as shown in Figure 2. The crystalline structure results from ionizable sulfate groups on the surfaces of the particles that become negatively charged when they are brought into contact with the aqueous phase. Because these groups do not become ionized on the portion of the spheres that are in contact with the oil phase, an asymmetry in the charge distribution results and gives rise to a repulsive dipoledipole interaction between the particles.12 In addition, it has been shown13 that trapped water molecules can allow some charges to remain at the particle-oil interface where
they can make a significant contribution to interparticle repulsion because of an absence of screening by counterions in the oil phase. The aggregated structure develops when the particles actually make contact with the opposing interface as illustrated in Figure 3. Initially, the particles are at the equilibrium spacing determined by their interfacial concentration and the dominant interparticle repulsions. As the two interfaces come into proximity, the droplets begin to flatten as a result of the pressure driving film drainage. The dimple profile is not able to fully develop, however, before the particles on one interface begin to interact with those on the opposite interface. This is supported by measurements (see Figure 4) suggesting that the particles meet the aqueous phase at a contact angle of 130°, from which it can be calculated that they protrude 2.5 µm into the oil phase when adsorbed to a fluid interface. Note that this length scale is a magnitude greater than that at which van der Waals forces will act to accentuate a dimple shape in these systems.14 Thus, the particles will align into the interstices of the opposing lattice and eventually make contact with its associated fluid interface. This geometry eliminates any asymmetry in charge distribution that can give rise to dipole-dipole repulsion and reduces the oil-particle interfacial area, from which trapped charges can exert a Coulombic force. As a result, capillary forces15 dominate the particle interactions and induce aggregation. The most remarkable effect of the bridging geometry11,16 attained by the particles is observed when the droplet is
(12) Pieranski, P. Phys. Rev. Lett. 1980, 45, 569-572. (13) Aveyard, R.; Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Horozov, T. S.; Neumann, B.; Paunov, V. N.; Annesley, J.; Botchway, S. W.; Nees, D.; Parker, A. W.; Ward, A. D.; Burgess, A. N. Phys. Rev. Lett. 2002, 88, 246102-246102.
(14) Chen, J. D.; Slattery, J. C. AIChE J. 1982, 28, 955-963. (15) Danov, K. D.; Pouligny, B.; Kralchevsky, P. A. Langmuir 2001, 16, 6599-6609. (16) Ashby, N. P.; Binks, B. P.; Paunov, V. N. Chem. Commun. 2004, 436-437.
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Figure 5. Micrograph showing adhesion between aqueous phases and perturbation to interface shape as a droplet (a) makes contact with the flat interface and is (b) subsequently withdrawn. The solid line fitting the interface shape is from eq 2. The scale bar represents 500 µm.
pulled away from the flat fluid interface after this aggregation as shown in Figure 5. It is quite apparent that the particles are able to generate an adhesion between the two aqueous fluid phases. An understanding of the forces contributing to the adhesion can be garnered from geometric considerations similar to those made for ringshaped devices, or Du Nouy rings, used to measure surface tension.17 Essentially, balancing surface tension and the hydrostatic pressure associated with raising a fluid into one that is less dense, as a function of radial position, leads to an equation of the form
[x
1 d r r dr
dh/dr 2
1 + (dh/dr)
]
)
∆Fg h γ
(1)
where r is the radial position, h is the height of the flat interface above its equilibrium value, ∆F is the density difference between the two fluid phases, g is the acceleration due to gravity, and γ is the surface tension of the particle-coated oil-water interface. Note that this is the equation of capillarity, published by Laplace in 1805, expressed in a form that accounts for the rotational symmetry of the system.18 For elevations that are small relative to the capillary length, defined by λ ) (γ/∆Fg)1/2, solution leads to
K0(r/λ) h ) h0 K0(R/λ)
(2)
where h0 is the height at which the aggregate is raised above the equilibrium level of the flat interface, K0 is the modified Bessel function of the second kind of order zero, and R is the radius of the particle aggregate. The solid line included in Figure 5 confirms that this analysis is able to model the perturbation to interface shape due to the adhesion. If a sufficient force is applied to the droplet, however, the bridging particles will be pulled from one interface such that adhesion is lost. The force exerted on the aggregate can be calculated by methods similar to those used to determine interface shape perturbation, but in this case by summing contributions from hydrostatic pressure and surface tension at the aggregate rather than balancing them over the entire interface:
(x
F ) ∆FgπR2h0 - 2πγR
dh/dr
)|
1 + (dh/dr)2
(3) r)R
(17) Maijgren, B.; Odberg, L. J. Colloid Interface Sci. 1982, 88, 197203. (18) Kralchevsky, P. A.; Nagayama, K. Particles At Fluid Interfaces And Membranes: Attachment Of Colloid Particles And Proteins To Interfaces And Formation Of Two-Dimensional Arrays; Elsevier Science B. V.: Amsterdam, 2001.
Figure 6. Plot showing agreement between a measured force profile (0) during drop withdrawal and values obtained by substitution of aggregate height into eq 4 (solid line), which was derived from consideration of interface shape, surface tension, and hydrostatic pressure.
Note that the first term in this equation accounts for the cylinder of fluid directly beneath the aggregate while the second term accounts for the influence of surface tension as it supports the fluid outside of this area. Equation 3 can be evaluated through substitution of eq 2 for the height profile and, at elevations that are small relative to the capillary length, yields
[
F ) ∆FgπR2h0 1 +
2K1(R/λ)
]
(R/λ)K0(R/λ)
(4)
where K1 is the modified Bessel function of the second kind of first order. As shown in Figure 6, even in the absence of adjustable parameters, forces obtained by the substitution of measured aggregate heights, h0, into eq 4 agree well with experimentally determined force profiles. Note that, over time, these heights differed from and were less than the linear displacement of the capillary, which was raised at a constant rate, because of deformation of the droplet shape by the adhesion force. While consideration of interface geometry during drop withdrawal allows development of eq 4, the ultimate force required to break the adhesion between the drop and the flat interface can also be derived from the vertical force exerted by surface tension on a particle as it is moved perpendicular to a fluid interface:19,20
FP ) γ cos(π - θ - R)(2πa cos R)
(5)
Here, a is the radius of the particle and θ is the threephase contact angle with respect to the aqueous phase. An additional term, R, refers to the angle formed between the line connecting the center of the particle to the point where it makes contact with the fluid interface and the direction parallel to the unperturbed interface. By these definitions, the first term in eq 5 determines the component of the surface tension acting perpendicular to the interface while the second term determines the length of the contact line through which the surface tension exerts an influence on the particle. Differentiation with respect to R allows determination of the magnitude of the maximum force
|FP| ) 2πγa cos2(θ/2)
(6)
that develops when a single particle is removed from the interface such that it is engulfed by the oil phase. This leaves only the number of particles contributing to the total force to be determined. A plot of the ultimate force attained during drop withdrawal for aggregates of various radii, as shown in Figure 7, makes clear that a linear (19) Scheludko, A.; Toshev, B. V.; Bojadjiev, D. T. J. Chem. Soc., Faraday Trans. 1 1976, 72, 2815-2828. (20) Nutt, C. W. Chem. Eng. Sci. 1960, 12, 133-141.
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Figure 7. Plot of the measured force required for adhesive failure between the drop and the flat interface for aggregates of various sizes.
Figure 8. Plot of contact angles determined from eq 8 using measurements of the force required for adhesive failure between the drop and the flat interface.
dependence exists between the two. Thus, the number of particles
angles determined from force measurements fall near 130° measured by the method shown in Figure 4. This confirms the validity of eq 8 as a model for determining the force for adhesive failure in these systems. From the complementary standpoint, it provides a method for determining contact angles for particulate systems, for which measurement by other means can be somewhat difficult. Also, it should be noted that, in contrast to methods that rely on a comparison of eqs 4 and 8, contact angles determined through direct force measurements are valid even when the generated adhesion results in a large perturbation to interface shape. Last, because eq 8 does not depend on particle size, it provides a simple method for determining contributions from line tension in these systems as well.
NP )
2πR 2a
(7)
contributing to the force includes only those that exist on the perimeter of the aggregate where the adhesion between the two aqueous phases is supported. This is analogous to the proportionality that exists between the adhesive force and the contact line of pressure-sensitive tape as it is peeled off a solid surface. Multiplying eqs 6 and 7 leads to a model for the ultimate adhesive force that can be supported by the particles between the aqueous phases:
F ) 2π2γR cos2(θ/2)
(8)
By substituting experimentally determined maximum adhesive forces into eq 8, it is possible to calculate the three-phase contact angle at the particle surface. This provides an alternate approach to that of Ashby et al.16 who suggest that a comparison of eqs 4 and 8 can be used to determine the value. Figure 8 illustrates that contact
Acknowledgment. The authors thank Peter Kralchevsky and Clayton Radke for useful discussions and Bernard Binks for sharing ref 16. We also gratefully acknowledge NSF/CTS-0085114, NATO PST.CLG.978728, Unilever, and the Center on Polymer Interfaces and Macromolecular Assemblies for funding this research. LA049778E
