Langmuir 1994,10, 3279-3289
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Measurements of Hydrophobic and DLVO Forces in Bubble-Surface Interactions in Aqueous Solutions William A. Ducker,? Zhenghe Xu,* and Jacob N. Israelachvili* Department of Chemical Engineering, and Materials Department, University of California, Santa Barbara, California 93106 Received March 17, 1994. In Final Form: May 31, 1994@ The forces between hydrophilic and hydrophobic silica particles and an air bubble were measured in pure water and in NaCl solutions using an atomic force microscope. In addition to the expected doublelayer and van der Waals forces, strong long-range attractive forces were also observed. A long-range attraction was also measured between a hydrophilic silica particle and a hydrophobic silica plate. A gas bubble thus behaves like a hydrophobic surface. The long-ranged attractive component of the force disappeared when the anionic surfactant sodium dodecylsulfate (SDS) was added to the solution. This effect is explicable in terms of surfactant adsorption at the hydrophobic interfaces which renders them hydrophilic. A “thermodynamic”model is proposed that appears to be consistent with these and previous force and wetting experiments on hydrophobic surfaces. It is also demonstrated that a nonzero water contact angle on clean hydrophilic silica and similar hydrophilic surfacescan arise from DLVO forces alone and is not necessarily an indicationof surface contamination or some hydrophobic component in the force.
Introduction Most experimental measurements of surface forceshave focused on interactions between two solid surfaces in controlled gaseous or liquid environments or between amphiphilic and polymer surfaces in liquids. Here we shall be concerned with the interactions between a gas bubble and various solid surfaces in aqueous salt solutions. While we can expect the same types of forces to occur, such systems are of particular interest because of the following: (1)A liquid surface is much more deformable than a solid surface and can change shape dramatically in response to a surface force. Furthermore, since the surface-tension-controlledenergetics of a liquid surface are quite different from the elasticity-controlled energetics of a solid surface, these interaction-induced deformations can also be qualitatively different. (2) Measuring the interactions between a vapor phase and a solid phase across a liquid phase allows us to further examine two important but still poorly understood forces in water: the hydrophobic and hydrophilic forces. (3)The interaction is “asymmetric”(the two interacting surfaces are different), allowing for the measurement and theoretical testing of the electrostatic and van der Waals forces between dissimilar surfaces. (4) There is rapid diffusion across the liquid-gas interface and relatively high mutual solubility of the two phases, allowing for true thermodynamic equilibrium to be attained for the liquid phase. The interactions between particles and air bubbles in aqueous solutions are also of special technological interest because they dictate the process of froth fl0tation.l In this process, mineral particles of varying surface chemistry are selectively separated on the basis of their different affinities for and capture rates by bubbles. Since this is the process whereby most of the world’s minerals are separated, much attention has focused on understanding t Current address: Department of Chemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand. * Currentaddress: DepartmentofMining and Metallurgy,McGill University, Montreal, Quebec,Canada. Abstract published in Advance ACS Abstracts, July 15,1994. @
(1)Leja, J. Surface Chemistry ofFroth FZotution;Plenum: New York, 1982.
A. Bubble-particle aggregate
B. Hydrophobicsurface (0 zz 90)
C. Hydrophilic surface (0 = 0)
D. Relevant properties
Figure 1. Schematicbubble-surfaceconfigurations considered in this work. (A) Gas bubble rising in water, trapping hydrophobic particles on its way (thebasic mechanism of “froth flotation”). (B) Air bubble in water subtending a contact angle 8 on a partially hydrophobic surface (full hydrophobicity generally requires that 8 > 100’). (C)Air bubble on hydrophilic or very weakly hydrophobic surface (fullhydrophilicity usually requires that 8 = 0’). (D) Bubble, solution, and surface properties that are important in determining the interaction forces between bubbles and surfaces in water: refractive index ( n ) ,dielectric constant( E ) , surface energy ( y ) , surface potential (q)and charge (a),elastic stiffness of surface (&), radius of bubble (r),viscosity of liquid (q).
and controllingthe interactions between colliding particles and bubbles.’ The equilibrium stability of a bubble-particle aggregate in water (Figure 1A) is determined by a balance between the forcesofwetting (the contact angle, 8,defined in Figure 1B,C) and the forces of gravity on the particle and bubble. But in practice, the capture rate is also important. The capture rate is determined by the longer-ranged colloidal
0743-7463/94/2410-3279$04.50/00 1994 American Chemical Society
3280 Langmuir, Vol. 10, No. 9, 1994 Detector
Ducker et al.
Laser
bubble
........
Air bubble
bubble
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....
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Figure 2. Schematic figure of the experiment for measuring the forces between silica particles and bubbles. A bubble is constrained within a hydrophobic template so that the force can be measured without lateral or vertical motion of the threephase line. The silica sphere is attached to a cantilever spring, which is the usual force sensor in a commercial AFM. The length of the cantilever was 120 or 200 pm, corresponding to spring constants K, of 0.11 and 0.04 N m-l, respectively.
and hydrodynamic forces operating during the approach of the particle and bubble (Figure 1D). These include equilibrium forces, such as the van der Waals, electrostatic double layer, hydration, and hydrophobic forces, and nonequilibrium forces such as viscous forces. Viscous forces are particularly important when the separation between the particle and bubble reaches nanometer dimensions. Until recently is has been difficult to make direct measurements of the forcesbetween small particles during collisions; these forces can now be measured by attaching a particle to the force-sensing cantilever spring of a conventional atomic force microscope (AFM) and bringing it toward another solid surface or a liquid-vapor interf a ~ e . In ~ ?this ~ paper, we describe the forces between a hydrophilic silica particle of radius -3 ,um and an air bubble of radius -250 ,um (Figure 2). All measurements were performed in the regime where there is no velocity dependence of the measured force, so that in the final analysis we could ignore the effects of viscous forces. Gravitational forces could also be ignored for the small particles used. The most commonly considered case of colloidal forces is the “symmetric” system, i.e., a system of identical particles. In that case, the van der Waals force between any two particles is always attractive and the doublelayer force is always repulsive. Stability is thus dependent on the relative strength of these opposing forces. In the more general case of an “asymmetric” system, e.g., a system of dissimilar particles, both the van der Waals and double-layer forces may be attractive or repulsive: The net DLVO force may thus be purely attractive, purely repulsive, or the sign and gradient may vary in a complex way as a function of distance. (2) Chan, D. Y. C.; Horn, R. G.J . Chem. Phys. 1985,83,5311-5324. (3) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature (London) 1991,353,239-241. (4)Butt, H.-J. Biophy. J . 1991, 60, 1438-44. Also, manuscript submitted for publication. ( 5 ) Vigil, G.; Xu, Z.; Steinberg,S.;Israelachvili, J. J . Colloid Znterface Sci. 1994,165,367-385.
-2.5 nm
Figure 3. Schematic figures of the interaction systems examined. (A) Hydrophilic silica particle and air bubble in water. (B)The same as (A)but in the presence of sodium dodecyl sulfate which adsorbs only at the water-air interface. (C) Hydrophilic particle and hydrophobic OTS-coated silica surface in water. (D)The same as (C)but in the presence of sodium dodecyl sulfate which adsorbs as shown. Bubble radii were typically r = 200-300 pm, and particle radii were R = 3-5 pm. The distance S is defined as the closest distance between the particle and bubble surfaces.
For the interaction between a silica particle and an air bubble in water, the nonretarded van der Waals force is expected to be The double-layer force is somewhat more difficult to calculate because of uncertainty in the exact magnitude of the electrostatic potential of the air-water interface ( q b in Figure 1D). Previous work has shown that q b % -15 mV for an air bubble’ and that q, % -60 mV for the silica-water i n t e r f a ~ e .We ~ would thus expect the double-layer force to be repulsive a t long-range then, depending on the charge regulation mechanism, repulsive or attractive a t shorter-range-the latter in the more likely case of surfaces interacting close to constant potential. The repulsive van der Waals force is expected to dominate a t very short range, aided by any repulsive hydration or steric force.5 Thus we expect the net interaction to be repulsive over most separations with a possible attractive region a t intermediate separations of a few nanometers, that is, we expect water either to wet silica (6 = 0) or to have a small contact angle (6 -= 5”) which is indeed what is commonly observed. Our experiments reveal the presence of a strong attractive force between air bubbles and hydrophilic silica particles (Figure 3A) which cannot be explained by DLVO forces alone. The range of the force is comparable to that previously observed between (solid) mica surfaces made hydrophobic by adsorption of and between a hydrophobic and a hydrophilic surface.1° This similarity is perhaps not surprising since the air-water interface (6) Hough, D. B.; White, L. R. Adv. Colloid Znterface Sci. 1980,14, 3-41. (7)Usui, S.;Sasaki,H.; Matsukawa, H. J . Colloid Znterface Sci. 1980, 8i,ai-84. (8) Israelachvili, J. N.; Pashley, R. M. Nature 1982,300, 341. (9) Claesson, P. M.; Blom, C. E.; Herder, P. C.; Ninham, B. W. J. Colloid Interface Sci. 1986, 114, 234-242. (10)Tsao, Y. H.; Evans, D. F.; Wennerstrom, H. Langmuir 1993,9, 779-785.
Forces in Bubble-Surface Interactions may also be considered to be hydrophobic. For comparison we also measured the force between a hydrophilic silica particle and an air bubble in the presence of sodium dodecyl sulfate (Figure 3B). This anionic surfactant does not adsorb on silica but does adsorb at the air-water interface rendering the solution-side hydrophilic." Finally, we also investigated the force between the same hydrophilic silica particle and a chemically hydrophobized solid surface in the presence and absence of surfactant (Figure 3C,D).
Materials and Methods Force-Distance Measurements. Forces were measured using a Digital Instruments Nanoscope I1 atomic force microscope12 (Santa Barbara, CA). With this instrument, forces are determined from the motion of a laser-beam reflected from the back of a microfabricated silicon nitride cantilever (Figure 2). The cantilever spring constant K,was determined by two different methods, which yielded the same results: measurement of the loaded and unloaded resonant frequency,13p d measurement of the deflection under a known weight.14 Springs with K. values in the range 0.045-0.105N m-l were used in these experiments. Samples were moved relative to the cantilever spring using a piezoelectric tube scanner to which the sample was attached. A description of how the measured force curves were analyzed is given elsewhere,l5 but we note that it is necessary to first calibrate the spring deflection (measured in arbitrary units by the AFM position-sensitive detector) in terms of distance. Most previous experiments have involvedsolid materials that are much stiffer than the cantilever spring. The spring deflectioncan thus be simply calibrated once the surfaces are in contact by moving the piezoelectric support by a known distance and measuring the resulting deflection. In the present case the spring and bubble can have similar stifhesses so that the calibration must be done separately (before or after the force measurements) by pressing the particle against a rigid surface, e.g., of mica or silica. Force measurements on bubbles must also consider the deformations ofthe bubble throughout an interaction, even before contact is made. For example, in response to an attractive force the bubble deforms so as to decrease the particle-bubble separation, while a repulsive force acts to increase the separation. Ignoring the influence of finite bubble stifhess leads to errors in estimating the surface separation. Similarly, a naive calibration of the spring deflection with the particle (or tip) in contact with the bubble produces correct distances but overestimates the force. We have accounted for the bubble deformation by calibrating the cantilever by pushing it against a stiff surface (described above) and again when it is pushed against the (deforming) bubble. In this way, the bubble stiffness and the force-distance relationship could be independently calculated. Preparationof Hydrophilic Silica Particle Surfaces. A silica particle (Polysciences,Inc., Warrington, PA) was attached to the end of a cantilever spring as previously d e ~ c r i b e d .The ~ radii of these particles, R, were between 3 and 5 pm (Figure 2). Immediately prior t o each experiment the silica sphere was cleaned by exposure to a water plasma generated by a dc field. The procedure was designed to remove adsorbed organic contaminants and to create a high density of hydrophilic silanol groups (Si-OH) on the surface. The contact angle of water on an oxidized silicon wafer treated in the same manner was found b be less than 5". Measurements performed on silica spheres which had been cleaned by exposure to UVirradiation for 45 min yielded the same results as those using the plasma-treated particles. These surfacs are termed "hydrophilic" even though the water contact angle on them may be finite. Preparationof Hydrophobic Surfaces. Hydrophobicsilica surfaces were prepared from silicon wafers (Semiconductor Processing Co., Boston, MA). A 100 nm thick Si02 film was grown on the silicon wafer by exposure to an oxygen atmosphere (11)Tajima, K,; Muramatsu, M.; Sasaki, T. Bull. Chem. SOC.Jpn. 1970,43,1991-1998. (12)Binnig,G.;Quate, C.;Gerber,G.Phys.Reu.Lett. 1986,56,930-
Langmuir, Vol. 10,No. 9,1994 3281 for 2 h at 1000 "C. The maximum peak to valley roughness of this film over a region of (300nm)2was 1.5 nm, and the mean roughness was 0.15 nm. The surface of the wafer was made hydrophobic by chemisorbtion of a self-assembled monolayer of octadecyltrichlorosilane (OTS) as follows: The silica wafer was first treated with a water plasma to clean the surface and increase the density of silanol groups. It was then immersed in a 1mM solution of OTS in dehydrated bicyclohexly for 6 min. The surface emerged dry from this solution and was rinsed for several minutes in chloroform to remove any unadsorbed OTS. The advancing and receding contact angles ofwater on the OTS-modified surface were 115" and 113",respectively. The high contact angle and small degree of hysteresis indicate a high density of chemically reacted OTS molecules. The contact angle was unchanged after soaking in water or chloroform for several days, showing that the OTS layer is also very stable-as expected for a covalently bound monolayer. An OTS film prepared in the same way on quartz (instead of silica)was shown to be 2.5 nm thick by neutron scattering,16indicating a single layer of OTS. These films have been the subject of much recent study17 particularly the mechanism of the binding reaction and the degree of covalent attachment to solid surfaces. Preparation and Attachment of Air Bubble. The geometry of the interaction between the silica sphere and bubble is shown schematically in Figure 2. Air bubbles of radii r % 250 pm were formed from laboratory air and constrained within a hydrophobic template which prevented the three-phase line from moving laterally or vertically. The hydrophobic template was made by gluing a thin (-50pm) mica sheet with a 200pm radius hole to a hydrophobic silica surface. The template thus consisted of a small hydrophobicpocket within a large relatively hydrophilic sheet. After this template was placed in water, a small bubble was spontaneously transferred from a microsyringe onto the hydrophobic pocket where it remained attached as shown in Figure 2. Bubbles trapped in this way were stable for many hours. In contrast, bubbles produced by an alternative setup where the bubble was connected directly to a syringe during measurement proved to be quite unstable. Preparation of Aqueous Solutions. Deionized water was distilled once, then passed through a commercial Milli-Q system containingion-exchange and charcoal stages. Solutionsof sodium dodecyl sulfate were prepared using Sigma brand SDS (99%) without further purification. Solutions of NaCl were prepared from Aldrich brand NaCl(99.999%)which was heated to 500 "C for 5 h to remove organic contaminants.
Results and Analysis Particle-Bubble Forces in Water (Figure 3A). Figure 4 shows the measured force between a hydrophilic silica particle and an air bubble in pure water a t pH 6. At large distances, D > 50 nm, the force is constant (the apparently sinusoidal variation in force is due to optical interference, shown more clearly in the inset, and does not represent a true force). At the position marked J in the figure, there is a sudden inward jump of the particle to a new equilibrium position marked E. During the jump, the cantilever undergoes rapid, nonequilibrium motion toward the bubble until a strong repulsive force is experienced. The strong repulsive force is reversible and has a constant gradient, and we assume that it is due to the deformation of the bubble from its equilibrium configuration when in contrast with the partice. This deformation probably occurs over the whole bubble surface. The stiffness of the bubble, &, can be simply calculated from the slope of the measured force t o the left of point E in Figure 4; assuming that the bubble and cantilever act as two springs in series as illustrated in Figure 2, the measured stiffness K, is given by
922
1--.
(13)Cleveland, J.P.; Manne, S.; Bocek, D.; Hansma, P. IC Rev.Sci. Instrum. 1993,64,1-3. (14)Senden, T.J.; Ducker, W. A. Langmuir 1994,10,1003. (15)Ducker, W.A.;Senden,T. J.; Pashley, R. M. Langmuir 1992,8, 1831-1836.
(16)Smith, S.Private communication. (17) Angst, D. L.; Simmons, G. W. Langmuir 1991,7,2236-2242.
3282 Langmuir, Vol. 10,No. 9,1994
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Figure 4. Raw data showing the interaction between a hydrophilic particle and a bubble in water (Figure 3A). The
horizontal axis showsthe measured distanceD that the particle moves relative to the undeformed bubble surface. The zero of distance, D = “O”, has been arbitrarily placed near where a strong repulsive force is measured. The inset shows the data over a longer distance, and demonstrates the presence of interference fringes which may appear as a repulsive force at small separations if not corrected for. so that the bubble stiffness is Kb
(2-(2 1)
1) where C h is the cantilever deflection per unit sample translation when pushed against a hard surface and c b is the cantilever deflection per unit sample translation when pushed against the bubble. A typical bubble stiffness in pure water calculated from this equation is Kb = 0.065 f 0.005 N m-l. As mentioned in the Introduction, it is reasonable to assume that the bubble will deform due to surface forces even before it makes contact with the particle (see the inset to Figure 5 for the case of attractive forces). If we assume that the bubble stiffness, &, is uninfluenced by the interaction with the particle, we can calculate the deformation of the bubble (D- S )due to the “real” surface forceF(S) at a separation S. The measured force-distance curve F(D)of Figure 4 can then be transformed into a F ( S ) plot giving the force as a function of particle-bubble separation, S. This is shown in Figure 5. Note that in Figure 4, the distance between the start and end of the arrow (fromJ to E) of -25 nm is not the real jump distance. The real jump distance is given by the horizontal line (of constant force)connectingthe jump distance with the point at which it cuts the dotted curve (from J to E’) or -50 nm, which is the value shown in Figure 5. The difference between these values is entirely due to the spring and bubble deflection. The finite contact angle also affects the measured jump distance. This is not taken into account in Figure 5 and will be considered later. This transformation is not entirely satisfactory for two reasons: (i) we have assumed that the stiffness of the bubble is unaffected by the presence of the particle (we have only measured that it is constant after it contacts the particle);(ii)we have implicitly assumed that the shape of the bubble is constant during the interaction. Experiments by Fisher et al.l8J9 show that a large bubble approaching a flat surface deforms due to viscous as well -
(18)Fisher, L. R.; Mitchell, E.; Hewitt, D.; Ralston, J.; Wolfe, J. Colloids Surf. 1991,52, 163-174. (19) Hewitt, D.; Fornasiero, D.; Ralston, J.; Fisher, L. R. J . Chem. SOC.,Faraday Trans. 1993,89,817-822.
-50
“0”
50 100 Separation, S (nm)
150
200
Figure 5. Measured force between a hydrophilic particle and a gas bubble. This shows the same data as in Figure 4,but now
the deformation of the bubble has been taken into consideration, so that the horizontal scale shows the deduced separation S between the particle and bubble. In this conversion, we have assumed that the stiffnessof the bubble is constant throughout the interaction. The closed points extending beyond the top of the graph indicate that the force continues to be repulsive at higher loads, and the open circles at negative forces show that stable positions are also possible at negative loads. The inset shows the relationship between S,the true surfaceseparation, and D, the measured distance between the particle and hypothetically undeformed bubble surface. as surface forces so that the air-solid separation does not decrease in a simple way with radial distance from the axis of symmetry. This effect should be much smaller in the experiments reported here because (1)the radius of the particles is small and thus the viscous force opposing film drainage is very small and (2)the small bubbles used in our experiments are relatively stiff. It is important that the bubble be as stiff as possible so that most of the strain occurs in the spring (the measuring device) rather than in the bubble (the deformation of which we have not monitored). It is for this reason that we used bubbles with the smallest experimentally convenient radii. Having noted these assumptions, we see from Figure 5 that there is a large attractive force between the particle and the bubble starting a t a separation of about 44 nm and a strong repulsive force between them a t small separations which, most likely, is an indication that the particle and bubble are in “contact”. Unfortunately, the technique does not allow us to determine the absolute separation, S, between the particle and bubble surfaces. It is possible that there is still a thin “wetting” film of water on the particle surface, as illustrated schematically in Figure lC,in which case the steep repulsion at “contact” can be understood in terms of the large energy cost associated with squeezing out the water film. If there is still a film of finite thickness So at the highest load applied, this value must be added to S in Figure 5. The same procedure would need to be performed for all subsequent F ( S ) curves to give the real water gap thickness. Thus, all quoted S values probably underestimate the true surface separation in water. The strong long-range attractive force in Figure 5 is somewhat more dificult to rationalize. The first possibility we wish to consider is whether the apparently large distance a t which the instability occurs indicates a rupturing of the thick water film followed by its rapid thinning until no water or only a thin “wetting” film remains. Referring to Figure 6, the distance Do = R(1cos 6 )by which the particle penetrates the bubble can be calculated from the particle radiusR and the contact angle 6. The particles were too small to measure their contact angles directly, but for a silica sheet prepared in the same
Forces in Bubble-Surface Interactions
Langmuir, Vol. 10,No. 9,1994 3203 0
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Figure 6. Schematic figure showing the cantilever spring
before (dotted)and afier (solid)the jump into contact with the bubble. There are two effects which could lead to incorrect estimates of thejump distance: (1)the air bubble deformsunder the applied load; (2) there is a finite contact angle 8 between the particle and bubble. In the latter case, the particle will penetrate the bubble by a small amount, DO= R ( l - cos e), which will change the position of zero separation on contact. The following is a list of some representative values of the contact angle and the corresponding corrected jump distances (forR = 3 pm) (6 (deg),DO(nm),S (nm)): 0, 0,44.0;1,0.5,43.5; 5, 11.4,32.6; 10,45.0,0. way, the contact angle is always less than 5". Some representative penetration distances Do are given in the caption to Figure 6 for various 8 values. Although the penetration distances are too small to account for the measured instabilities, they cannot be ignored and must be subtracted from all measured D values to obtain the real surface separation distance S (to which we must still add So if a wetting film remains). Assuming a maximum contact angle of 5",we see that the maximum value that must be subtracted from the measured jump distance DJ to obtain the real jump distance SJ due to this mechanism is -11 nm, significantly less than the measured jump distance of 44 nm. When part of the particle moves from the liquid phase into the gas phase, there is also a gravitational force due to the change in the buoyancy. Although the gravitational force is always acting downward (toward the bubble in the geometry used here), the change in this force acts in the same way as a repulsive force between the particle and bubble. However, this force turns out to be very small: the force required to move the entire particle into the bubble is only 0.003 nN, or about one-third of our force resolution. In comparison, the buoyancy force on the bubble is much larger (because of the larger radius) but is effectively included in the measured stiffness Kb. Comparison of Measured Force Curves with DLVO Theory. We now consider in more detail the theoretically expected DLVO force between the hydrophilic silica particle and the bubble. A theoretical nonretarded Hamaker constant of A = -1.0 x J was calculated by Hough and White6 for the interaction between silica and air in water. This van der Waals force is repulsive. We have calculated the full retarded and screened van der Waals force using the program of Grabbe.20 The force is about 10% higher than was calculated by Hough and White at small separations, e.g., A = -1.16 x J at 10 A, but decreases more rapidly with increasing separation because of retardation and ionic screening effects. (20)Alexis Grabbe kindly provided us with a program to calculate double-layer and van der Waals forces. The double-layer force is calculated using an exact numerical solutionto the Poisson-Boltzmann equation and the van der Waals force is calculated from Lifshitz theory and includes retardation.
-2.0
-3 E; L."
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20 30 40 Separation, S (nm)
50
60
Figure 7. Calculated values20 for the DLVO interaction
between a silica particle and gas bubble in water. The force is the sum of a repulsive van der Waals force and an attractive double-layerforcecalculated for constant surface potential using an exact numerical solution.34The potential of the particle q s is assumed to be 60 mV and the bubble potentials ?#b were varied from 0 to 25 mV. The arrows show the positions where we would theoretically expect the surfacest o jump into contact. The position at which the jump was actually measured is also shown, and is seen to be greater than the maximum computed DLVO force. The inset shows that at small separations the repulsive van der Waals force eventually dominates, i.e., the limiting interaction as S 0 is always repulsive. The energy minima at S = SOM 1.5nm give rise to small but finite contact angles of water on silica, as quantified in the Discussion (Table 2).
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The double-layer force can be calculated if the surface potential of the particle and bubble and the nature of the charge regulation are known. Previous AFM force measurement~ on~similar silica particles gave a fitted surface potential of -60 mV in M NaCl solutions and a doublelayer interaction lying between constant charge and constant potential. The measured zeta potential of air bubbles in water is about -15 mV for bubbles of radius 0.5 mm and increases for smaller bubble^.^ Estimates of the surface potential yield a slightly higher figure of -25 f 10 mV.21 The potential is thought to arise from the selective adsorption of anions and OH- ions from solution,22which are known to be less water soluble than cations due to their larger size. The large variations in the reported potentials of bubble surfaces and the total ignorance of the charge regulation mechanism do not allow us to accurately compute the theoretically expected doublelayer force. However, it is reasonable to suppose that in the absence of strongly surface active ions, the bubble surface should regulate close to constant potential. Thus, even though the surface potential and charge of the bubble at large separations are negative, under the influence of the approaching silica particle, the bubble surface charge may change sign, resulting in an attractive double-layer force. The maximum possible attractive force for two surfaces that are both negative at large separation occurs when the surfaces maintain constant surface potential. Figure 7 shows the expected bubble-particle DLVO interaction curves computed for qs= -60 mV and a variety of bubble-surface potentials, q b , each calculated at constant potential. The curves show that the force becomes more attractive as q b falls, with maximum attraction occurring when ?#b = 0 (positive values for q b were not (21) Farrell, J.R.; McTigue,P. J.EZectroanaZ.Chem. 1982,139,3756. (22) Davis, J. T.; Ridel, E. K. ZnterfaciaZ Phenomenon: Academic Press: New York, 1961; p 148.
3284 Langmuir, Vol. 10, No. 9, 1994
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Table 1. Force Curve Parameters in Various NaCl Solutions (SpringStiffness: & = 0.04 N/m)
theoretical jump-in distances, S (nm) $b=
solution water 10-3MNaCl M NaCl
qb=
OmV -15mV 33 19
20 8
?+!t,=
measured
jump distances, S
jumps jumps in(nm) out
-25mV
&15%
hm)
18 no instability
80 80 40
3.5
3.0 1.5
considered). In this case the bubble surface should undergo an instability at a separation of S = 15 nm. If we assume constant charge boundary conditions, the double layer force is monotonically repulsive at all separations for any negative bubble potential, resulting in even worse agreement between theory and experiment. Thus, if we sum the maximum jump expected due to dewetting (11nm) with the maximum jump due to the DLVO force (15 nm), we would expect that the instability would occur at a separation of D = 26 nm. The fact that we measure the instability a t D = 44 nm indicates that there is a strong additional attractive force. Further Measurements of the Force Instability in Bubble-Particle Interactions. To further test a possible contribution of an attractive double-layer force a t these large separations, we measured the forces in and M NaCl salt solutions which is expected to decrease the range of the double-layer force by more than an order of magnitude. A spring which was less stiff (K, = 0.04 N m-l) than the bubble (Kb= 0.065 N m-l) was used to increase the accuracy of these measurements. In all cases, the instabilities occurred at separations greater than 40 nm where the DLVO force was effectively zero. Thus, the whole force curve could be parameterized simply by F % 0 up to the jump-in position on approach, and the jump-out (adhesion) force when the applied load was reversed to separate the surfaces. The results are tabulated in Table 1. Table 1also shows the separation a t which the instability is predicted by DLVO theory. Not only are the calculated separation distances less than those measured but the measured forces do not even follow the qualitative prediction that the instability should occur at M NaCl solution. This implies smaller separations in that the maximum possible attractive double-layer force, even if present, makes a negligible contribution to the overall force which is even more attractive. This force increases in gradient suddenly at some large separation of S x 30 nm and it appears to be only weakly sensitive to the ionic strength of the solution (for 1:l electrolytes). A n oscilloscope(Tectronix) was used to investigate the force in the region just before the instability in greater detail, the aim being to accurately measure the extra attractive force before the jump instability. Using this instrument, we were able to accurately record the forcedistance curve with a distance resolution about 20 times better than with the commercial Nanoscope I1 AF'M software. We could not detect any systematic cantilever deflection (in the background of the oscillations shown in Figure 4) right up to the jump. Time-Dependent Effects. Although this investigation concentrates primarily on the equilibrium forces which are not velocity dependent, we would like to comment here that the forces measured showed an unusual velocity effect that is not normally observed when a solid particle approaches a solid surface. When a spherical particle approaches a solid surface, there is a repulsive viscous force that increases with the velocity of approach. For micrometer-sized particles in water, this force is usually very small a t speeds below about 2pm s-l. At a similar speed, we observed that the force on a particle
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Separation, S (nm) Figure8. Interaction between a silica sphere and an air bubble in 3 mM sodium dodecyl sulfate solution. The force is monotonically repulsive and fits well to a calculated DLVO curve with constant unequal potentials of 50 and 60 mV and a decay length of 5.5 nm. approachinga bubble underwent oscillations,even at large separations (-1 pm). Somehow, the motion of the sphere is reflected back from the bubble, perhaps by causing transverse hydrodynamic waves on the bubble surface. All experiments reported here were performed at speeds slower than those where this interesting effect was observed. Bubble-Particle Forces in Sodium Dodecyl Sulfate Solutions (Figure3B). The measured interaction between a hydrophilic silica particle and bubble in 3 mM SDS solution (cmc = 8 mM23)is shown in Figure 8. The force is monotonically repulsive and reversible at all loads up to about 3 mN m-l. At greater loads, there is a small jump in of 1.0 f 0.5 nm from the position shown by the top arrow in the inset to Figure 8, and the force-distance curve is no longer reversible. When the load is then decreased, the particle-bubble separation remains unchanged until a large outward jump occurs from a negative (adhesive)force ofFIR = -6 mNm-l (lowerarrow in inset). At separations greater than 2 nm, the measured force on approach agrees well with a theoretical double-layer force calculated for constant surface potentials of -50 and -60 mV for the two surfaces, and a decay length of 5.5 nm. At smaller separations the measured force is now more repulsive than that expected from DLVO theory. The fitted potentials are in reasonable agreement with those expected from previous measurements on silica (-53 mV in M NaCl solutions) and for SDS surfaces (-55 mV in M SDS and -75 mV in M SDS a t pH 5) as measured by microelectrophoresis on bubbles in SDS solution.24 The van der Waals force is also affectedby the adsorption of a surfactant a t the air-water interface. Theoretically, the effect of adsorbing a 1.2-nm layer of hydrocarbon to the air-water interface is shown in Figure 9. The calculation was performed assuming a mean monolayer refractive index of 1.56 which is slightly higher than for pure hydrocarbon to allow for the additional contribution from the headgroups. The result ofthe adsorption changes the van der Waals force from being repulsive at all separations to becoming attractive at small separations. We thus observe that aRer adsorption of a SDS monolayer at the water-air interface, the long-range forces agree with DLVO theory and that any deviations now occur only at short range (S < 2 nm) and are now repulsive. (23)Hiemenz Principles of Colloid and Surface Chemistry; Dekker: New York, 1977; p 286. (24)Yoon, R.-H.; Yordan, J. J . Colloid Interface Sci. 1986,113,430438.
Langmuir, Vol. 10,No.9, 1994 3285
Forces in Bubble-Surface Interactions
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Separation,S (nm) Figure 9. Theoretical purely van der Waals force between a silica particle and a bubble (Figure 3B)in water calculated using the Grabbe program, which uses Lifshitz theory and accounts for retardation effects.20The force between a bubble and a silica particle in water is monotonically repulsive at separationsup to 350 nm (top curve). The separation is defined as the thickness of the water film. The lower curve shows the effect of adding 1.2 nm of hydrocarbon t o the air-water interface. Spectroscopic data for polystyrene was used but the result would be similarfor other hydrocarbons. In the presence of the thin hydrocarbonfilm,the force is attractivefrom contact up to 3 nm separation. The experimentally observedinteraction switches from attractive to repulsive on addition of a hydrocarbon layer and so cannot be explained by the action of van der Waals forces alone. d
2x10-2 M SDS E a 2 \ U
Reversible \
> 0
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U
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I
When the SDS concentration was raised to 0.02 M (well above the cmc), the principal change was that the forces were reversible up to the highest applied loads of FIR x 8 mN m-l (Figure 10). Under these circumstances we are less confident about the position of zero separation, S = 0, since it is difficult to thin the film further by applying a higher load because at high loads the bubble is more compliant than the film. However, we do observe that the measured force in Figure 10has the appropriate decay length of 2.1 nm, but the fitted potentials are dependent on where S = 0 is defined. Ifwe assume that the thinnest films achieved were in the range S = 0-2 nm, then the fitted potentials range from 20 to 30 mV for one surface and 40 t o 60 mV for the other. This may be compared with previously measured values of -34 mV for a silica M NaC13 and -75 mV for an air bubble in sphere in M SDSeZ4
Forces between a Bubble and a Hydrophobic Silica Surface. Some of the silica particles were rendered hydrophobic by the OTS reaction described in the experimental section. This configuration therefore corresponds to two hydrophobic surfaces interacting in water. When these were brought toward each other, well before any double-layer force could be measured, the cantilever spring underwent a sudden deflection well beyond the measuring limit of our device, and the entire particle and cantilever burst into the air phase of the bubble. Under these circumstances, we can observe only the large instability in the force without knowing at what particlebubble separation this occurs. Our only conclusion is that there is a strongly attractive force between a hydrophobic particle and a (also hydrophobic) bubble surface in water. That this force came in before any double-layer force could be detected further suggests that the extra attractive force is again long-ranged. Forces between a Hydrophilic and a Hydrophobic Silica Surface in Water (Figure3C). Claesson et aLZ5 and more recently Tsao et aZ.1° have demonstrated the existence of attractive non-DLVO forces in water in the interactions between a hydrophilic surface and various hydrophobic surfaces which were rendered hydrophobic by surfactant adsorption or Langmuir-Blodgett deposition. Figure 11 shows the forces measured between a hydrophilic silica surface and an OTS-coated silica surface. The principal difference between the system studied here and those measured previously is that here the surface coating is chemically bound so that there is less chance of transfer of the hydrophobizing agent to the hydrophilic surface. The results are, however, very similar, showing large attractive deviations from DLVO theory. Thus, at separations greater than 25 nm, the measured force fits the expected DLVO force for two surfaces interacting at constant surface potentials of -80 mV and a decay length of 100 nm. The extrapolated DLVO force at smaller separations is shown by the solid line in Figure 11. This calculation includes the van der Waals interaction for the asymmetric system: silicahydrocarbon layerlwaterlsilica (the effect of the thin hydrocarbon layer is to increase the van der Waals force by about 10%). Clearly, the measured force is much more attractive. Since there is no a priori reason why the potentials on both surfaces should be equal, various asymmetric potentials were tried to obtain a better fit with the measured force curve. While this procedure produced a more attractive force a t smaller separations, it made the fit worse at larger separations. We thus conclude that there is an attractive non-DLVO force operating a t a separation of a t least 25 nm. During these measurements we noted that the instability in the force curve frequently occurred at different separations, even though the remainder of the force curve was constant. The maximum separation a t which the instability occurred for the same system is shown by the dashed arrow at -75 nm in Figure 11. It is difficult to understand how any force law could exist where the gradient of the force changes so abruptly from negative to positive at such large separations. It is also difficult to understand why the onset of the attractive force varies so greatly. There has been some recent speculation about the possible role of spontaneous bubble nucleation between two hydrophobic surfaces as they approach each other.26 Spontaneous capillary condensation of a vapor or gaseous bridge between two surfaces would pull the surfaces together with a very strong force due to the Laplace (25) Claesson, P. M.; Herder, P. C.; Blom, C. E.; Ninham, B. W. J. Colloid Interface Sci. 1986,118, 68-79. (26) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. J.Phys. Chem. l99S,97,10192-10197.
3286 Langmuir, Vol. 10, No. 9, 1994
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7
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Ducker et al. is similar to that previously observed between surfactant and lipid bilayer surfaces, and believed to be due to undulation, protrusion, and steric hydration forces.33
I
I
Hydrophobic- Hydrophilic
0.41\
-I
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50
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Separation, S (nm) Figure 11. Interaction between a hydrophilic silica sphere and a solid hydrophobic surface in water. The points represent experimental data and the solid line is a continuation of the best fit of DLVO theory to the measured points at greater separations. The double-layerforce was calculatedusing a fitted constant surface potential of -80 mV for both surfaces and a decay length of 100 nm. This interactionwas unusual in that the separationsat which the jump instabilitiesoccurred varied widely, even though the rest of the force-distance curve remained constant. The arrows show the extremes of positions at which instabilities occurred. Hydrophilic-Hydrophobic in 5 mM SDS (
