Langmuir 1992,8, 1831-1836
1831
Measurement of Forces in Liquids Using a Force Microscope William A. Ducker*!+and Tim. J. Senden Department of Applied Mathematics, Research School of Physical and Engineering Sciences, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia
Richard M. Pashley Department of Chemistry, The Faculties, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia Received January 21,1992. In Final Form: April 21, 1992
A force microscope has been used to measure surface forces between a colloidal sphere (3.5 pm radius) and a flat surface in aqueous solution. The force between silica surfaces was measured as a function of surface separation, salt concentration, and pH, and the results agree well both with earlier measurements between macroscopic surfaces and, at separations greater than 3 nm, with the force predicted by DLVO theory. The technique is simple and reproducible and could be used to measure the forces acting on other colloid particles and fibers of a variety of compositions. This is demonstrated by measurement of the force on a gold-coated sphere. Introduction In the last 20 years several new devices for measuring surface and intermolecular forces have been developed: the surface forces apparatus of Israelachvili and Adams,l12 the force balance of Derjaguin et al.,3 and the osmotic stress device of Parsegan et alS4These new devices have allowed accurate measurement of surface forces and have led to improved understanding of these forces, as well as their implications for wetting, lubrication, surfactant selfassembly, and colloid stability. However, only a relatively limited variety of materials have been investigated, and in studies of colloid stability, macroscopic substrates have been used, rather than actual colloids. In the meantime, in the field of microscopy, developments in control, manipulation, and measurement on a nanoscopic scale have led to the development of the scanning tunneling microscope by Binnig and Rohrer in 1982: the atomic force microscope (AFM),B and allied technique^.^ The invention of the AFM allowed molecular and surface forces to be measured on a near molecular scale for the first time. Forces have been measured in a i F 0and in water,11J2and the frictional forces on the tip have been investigated.l3 In these studies, the force was measured between a sharp tip and a flat surface. + Current address: Materials Department, University of California, Santa Barbara, CA 93106. (1) Israelachvili, J. N.; Adams, G. J. Chem. Soc., Faraday Trans 1 1978, 74, 975. (2) Parker, J. L.; Christenson, H. K.; Ninham, B. W. Rev. Sci.Znstrum. 1989,60, 3135. (3) Derjaguin, B. V.; Rabinovich, Y. I.; Churaev, N. V. Nature 1978, 272, 313-318. (4) LeNeveu, D. M.; Rand, R. P.; Pmegan, V. A. Nature 1976,259, 601. (5) Binnig, G.; Rohrer, H. Helu. Phys. Acta 1982,55, 726-735. (6) Binnig, G.; Quate, C.; Gerber, G. Phys. Reu. Lett. 1986,56, 930933. (7) Wickramasinghe, H. K. Sci. Am. 1989 October, 74-81. (8) Durig, U.; Gimzewski, J. K.; Pohl, D. W. Phys. Reu. Lett. 1986,57, 2403. (9) Martin, Y.; Williams, C.; Wickramasinghe, H. J. Appl. Phys. 1987, 61,4723-4729. (10) Burnham, N. N.; Dominguez, D. D.; Mowery, R. L.; Colten, R. J. Phys. Rev. Lett. 1990,64, 1931. (11) Weiwnhom, A. L.; Hansma, P. K.; Albrecht, T. R.; Quate, C. F. Appl. Phys. Lett. 1989,54,2651-2653. Ducker, W. A,; Cook, R. F. App. PhYS. Lett. 1990,56,2408.
Unfortunately, because the geometry of the tip was not simple, or more usually, was not even known, comparison with theory proved difficult. In this paper we present a technique using an AFM which can be used to measure forces on small particles or fibers having diameters between about 1and 50 pm. This technique has been described briefly e1~ewhere.l~Materials of a variety of compositions and geometries can be examined. Because of the difficulty in working with such small particles, most previous investigations of colloid forces have either used model macroscopic substrates (e.g. in the surface forces apparatus) or have used indirect methods such as sedimentation studied6or light or neutron scattering,16 although recently, total internal reflectance microscopy has been used to measure the forces on colloid particles.17J8 To demonstrate the proposed method we report here measurements of surface forces between a silica-glass sphere and a large smooth silica surface in aqueoussolution as a function of salt concentration and pH. Because both the geometry and chemistry of the substrates are relatively well characterized, we have been able to compare our results with theoretical predictions, macroscopic measurements of similar substrates, and microscopic measurements using a different technique. This technique may be used on a variety of materials as shown by measurementsof forces on a gold-coated sphere. Particles which are not smooth or spherical may also be measured (although comparison with theory is then more difficult).
Experimental Section a. Sample Preparation. The flat silica surfaces were prepared from polished silicon wafers. The wafers were oxidized to a depth of 30 nm by heating to 920 "C in purified oxygen. AFM (12) More recent publications include: Butt, H. Biophys. J.,in press. Weisenhorn, A. L.; Maivald, P.; Butt, H.; Hansma, P. K. Phys. Rev. B., in press. Hoh, J. H.; Revel, J.; Hansma, P. K. Nanotechnology, in prese. (13) Erlandsson, R.; Hadziioannou, G.; Mate, C. M.; McClelland, G. M.; Chiange, S. J. Phys. Chem. 1988,89,5190-5193. (14) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991,353, 239-241. (15) Zhenge, X.; Yoon, R. J. Colloid Interface Sci. 1990,134,427-434. (16) Ottewill,R. H. In Concentrateddispersions;Gocdwin,J. W.; Royal Society of Chemistry: London, 1982. (17) Brown, M. A.; Staples, E. J. 1990,6, 1260-1265. (18) Prieve, D. C.; Frej, N. A. 1990, 6, 396-403.
0743-746319212408-1831$03.00/0 0 1992 American Chemical Society
1832 Langmuir, Vol. 8, No. 7,1992
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images of the oxidized surface revealed that in 0.45 pm2areas the highest asperity was typically 0.7 nm above mean height and the standard deviation from mean was 0.2 nm. In 49 nm2scans the highest asperity was 0.3 nm above mean height and the standard deviation was 0.1 nm. The hydrophobic surfaces were prepared by exposingsome of these wafers to a 1% (w/w)solution of dichlorodimethylsilane in dry trichloroethane a t room temperature for 2 min. The roughness was unchanged by this procedure. Gold surfaces were freshly sputter-coated onto freshly cleaved mica, to a thickness of approximately 50 nm. AFM measurement showed that this surface was very rough. In a typical 0.45 pm2 area, the peak to peak roughness was about 20 nm. To avoid particulate contamination, surfaces were handled and loaded into the AFM in a laminar flow cabinet. The equipment in contact with solutions was washed in distilled ethanol, blown dry with nitrogen, and then rinsed with purified water. Deionized, particle-free water (Noble's Pureau, Sydney, Australia) was distilled once inside a laminar flow cabinet before use in each experiment. When equilibrated with the atmosphere the conductivity of this water was -1 pS cm-l and the pH 5.7 (becauseof dissolved COZ). In some experiments, the AFM fluid cell was connected to a 100-mLflask equipped with a pH meter, a liquid injection port, and nitrogen input and vent lines. In these experiments, COZ was displayed by nitrogen, and the pH could be continuously monitored. A peristaltic pump ensured exchange between the flask and cell. A thermistor placed at the entrance to the cell was used to monitor the temperature. Analytical grade NaCl, NaOH, and HC1were used without further treatment. b. Colloid Probe Preparation. The colloid probes were prepared by attaching a silica sphere to a microfabricated AFM cantilever. The spheres (Polysciences, Inc., Warrington, PA) were composed of silica glass. AFM was used to show that the maximum peak-to-peak roughness on the sphere was 3 nm over 0.45 pm2,but scanning the sample with the probe rendered the surface more smooth, as indicated by the rapid loss of lateral resolution while imaging. The cantilevers were standard Vshaped AFM single cantilever springs manufactured by Park Scientific(Mountain View, CA). Cantileverswith integrated tips could be used if the diameter of the particle was greater than the height of the tip. The colloid particles were attached to the cantilevers with an epoxy resin, Epikote 1004 (Shell). The cantilever was placed on a heating stage at a temperature above the melting point of the glue, then a thin copper wire (-40 pm diameter) attached to a three-dimensional translation stage was used to position about L of molten resin near the apex of the cantilever. Care was taken to avoid coating the reflective gold side of the cantilever. Another clean wire was used to position a colloid particle on the cantilever, then the glue was frozen by removal of the cantilever from the heating stage. This method could be used for a wide variety of solid colloid particles, provided that the particles are large enough to view with an optical microscope. For smaller particles, an appropriate electron microscopy technique could be used to select colloid probes suitable for measurement. Immediately prior to each experiment, the colloid probe was cleaned by exposure to a water plasma (25-W, 18-MHz rf source in 0.03 Torr of argon and 0.02 Torr water) for 3 min. This treatment also ensured that the silica surface contained a high density of silanol groups. Excessiveplasma treatment damaged the reflective gold layer on the back of the cantilever. A SEM image of the probe is shown in Figure 1. No resin can be detected on the top part of the sphere, either by electron microscopy or by force measurement (i.e. no hydrophobic forces present). When the surface was deliberately coated in resin, a characteiistic hydrophobic force was observed in water. c. Force Measurement. All surfaceforcemeasurementswere performed using a commercial AFM, the Nanoscope I1 atomic force microscope (Digital Instruments, Santa Barbara, CA). In this device, the force between a sample and a tip is measured as a function of the displacement of the sample. Sample displacement is achieved using a piezoelectric crystal, and in the experiments reported here the sample velocity was varied in the range 0.2 and 2 pm s-l. The force on a tip is known from the deflection of a microfabricated cantilever (0.1-0.2 mm in length)
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Figure 1. SEM image of a colloid probe. Sample Displacement (nm)
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Figure 2. (a) Example of the data produced by the Nanoscope software showing the interaction between a pyramidal Si3N4 tip (4 p m high and 4 pm along the base) and muscovite mica in aqueous 10-3 M NaCl, a t pH 5.6. The horizontal axis shows the distance over which the piezoelectricdriver has been moved, and the vertical axis records the correspondingoutput from the diode. The region of constant compliance is indicated by the arrows. (b) Data from part a converted to force (in pN) as a function of tip-sample separation (in nm).
to which the tip is attached. A laser beam reflected from the back of the cantilever is made to fall onto a split photodiode which detects small changes in the deflection of the ~anti1ever.l~ In most of the experiments reported here, a small particle has been attached to the end of the cantilever so that the force is measured between a particle and the sample. The software provided with the Nanoscope produces a screen file which records the change in photodiode output (which is proportional to spring deflection) as a function of sample displacement. The pixel coordinates from the screen file were translated to a text file so that the data could be converted into force versus surface separation curves, but it would be better to capture the data directly, avoiding this unnecessary transfer and the digitization error incurred. Figure 2a shows an example of a voltage-displacement curve. To convert the diode-voltageversus sample-displacementdata (for a probe of any geometry) to a force vs tip-sample separation curve, it is necessary to define zeros of both force and separation and to convert the diode signal to cantilever deflection and force. The zero of force was chosen where the deflection was constant (where the particle and flat were far apart), and the zero of (19) Meyer, G.; h e r , N. M. Appl. Phys. Lett. 1988,53, 1045.
Langmuir, Vol. 8, No. 7, 1992 1833
Measurement of Forces in Liquids distance was chosen to occur when the cantilever deflection was linear with respect to sample displacement at high force. As the sample is driven toward the sphere, the cantilever deflects, and this is registered by the photodiode. At some point, the output of the diode becomes a linear function of the sample displacement: the regime of constant compliance. We explain this as the region where the particle is “incontact” with the surface and thus changes in displacement of the sample are equal to changes in deflection of the cantilever. In the experiments presented here, the relationship between sample displacement and diode response in the region of constant compliance was independent of the surface force (e.g. independent of salt concentration), and was used to convert the diode response into the deflection of the cantilever. This conversion was then used to determine changes in particle-surface separation (relative surface separation was calculated by adding the displacement of the sample to the deflection of the cantilever) and also to calculate the surface force. An overestimate of surface force will be obtained if the cantilever is not significantly more compliant than the sphere, the flat surface, and the components connecting them. For compliant substrates this problem can be surmounted by an independent calibration of cantilever deflection. In contrast, determination of the sphere-flat separation is not affected by elastic deformation of the substrates or connections. It should also be noted that for any material it is difficult to measure repulsive surface forces which have gradients of magnitude much greater than the spring constant and difficult to measure attractive forces with gradient greater than the spring constant. It is also important to note the influence of the geometry of the cantilever on the measured interaction. The cantilevers used in these experiments were designed to be much more flexible in the direction perpendicular to the surface, so that the motion of the particle was confined to one degree of freedom. The forces may differ for ”free” particles or those restrained by different cantilevers. For example, after contact with the surface, the particle in our experiment is subject to shear and torsion motions. In the surface forces apparatus, the use of double cantilevers to reduce torsional movement of the sample has resulted in measurements of adhesion values larger than those measured with single cantilevers.20 d. Errors in Force Measurement. Figure 2 shows a force curve obtained with the Nanoscope 11, showing a typical noise level of *0.02 nN. (This error depends on the value of the spring constant, and in general, the technique is capable of greater resolution with other displacement measuring devices.) The sample may be displaced in increments smaller than 0.1 nm, which is more than adequate for current force measurements. However, as explained below, there are systematic errors and errors in the data analysis presented here which limit resolution. Calculation of normalized surface forces requires knowledge of the spring constant and the probe radius, which introduce systematic errors into the surface force. A scanning electron microscope was used to measured two perpendicular radii of each silica particle after each experiment. The two radii were always the same to within the 1%resolution of the microscope. The spring constant was not measured, but the manufacturer’s specifications were quoted to two significant figures (0.58 N m-l) so an error of 5% has been assumed. There is also error in calculating the deflection of the cantilever from the region of constant compliance. The least-squares fit used here has an error of about 5% giving a cumulative error of about 12%. Relative surface separation was calculated by adding the displacement of the sample to the deflection of the cantilever. At small forces, the error in surface separation is dictated by the control of the piezoelectric crystal. The crystal response was calibrated by measuring the height of the tracks on a CD stamper which had been measured by ellipsometry. The total error in calibrating the piezo expansion was about 10%. For large forces and small separations, the error in surface separation is dominated by the 5% error in the diode-voltage vs cantilever-deflection calibration described above. Errors also originate from the nonlinearity of both the piezovoltage versus distance and the diode-voltage versus cantileverdeflection responses. These were not measured independently, (20) Christenson, H.K.J. Colloid Interface Sci. 1988, 121, 170-178.
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Figure 3. Force on a silica-glass particle in aqueous solution in 5.7. For each a variety of NaCl solutions at 30 OC and pH concentration, an analog signal was digitized to 400 points, and these data were condensed by averaging sets of ten points to produce the filled circles presented in this figure. The lines were calculated from DLVO theory using an exact numerical solution to the Poisson-Boltzmann equation and a Hamaker constant of 0.8 X loTzoJ. At each concentration, the upper line represents the interaction at constant surface charge, and the lower line at constant surface potential. The relevant parameters are as follows: at 1.1 X M area per electron charge (l/uo) = -56 nm2/q,surface potential ($0) = -61 mV, Debye length ( K - ~ ) = 21 nm; at 10-3 M l/uo = -36 nm2/q, $o = -53 mV, K - ~ = 9.5 nm; at M l/uo = -21 nm/q, $0 = -34 mV, K - ~ = 3.2 nm; at 10-1 M 1/uo = -12 nmz/q, $0 = -21 mV, K -=~ 1.1nm. but in the constant compliance regime, the diode-voltage-output to piezovoltage-input response was linear to within 2%. Finally, the data collection procedure introduces some error. Because data was read from a screen file which was only 200 by 400 pixels, a digitization error of l/zWth of the maximum force and Vmth of the maximum displacement is incurred. Althovgh this error can be reduced by measuring the force curve in a series of segments of smaller range or by averaging pixel values, this is the limiting error in the low force and small displacement regimes.
Results Figure 2b shows an example of a force-displacement curve. Here, the force-distance relationship differs between the approach and separation of the surface. This does not necessarily indicate that the force as a function of separation depends on the direction of sample motion. Because the gradient of the surface force is a function of tip-sample separation, different equilibrium tip-sample separations are accessible according to the separation between the undeflected end of the cantilever and the sample. The sections of the curve in Figure 2b marked J were probably recorded when the tip was not in mechanical equilibrium and have large error in the separation, so should be used as a guide only. Force Measurements between Silica Surfaces in Aqueous Solutions. The forces between a silica-glass sphere and an oxidized silicon wafer in a variety of NaCl solutions are shown in Figure 3. The forces at each concentration were independent both of the order in which concentrations were measured and of whether the measurements were performed on approach or separation of the surfaces. The measured forces decay exponentially with distance, and both the decay lengths and potentials decrease with concentration, as expected. Figure 4 shows the reproducibility of measurements using different probes and suggests that perhaps the systematic error has been overestimated. The systematic error in the spring constant is smaller here because all the cantilevers used in these experiments were manufactured
1834 Langmuir, Vol. 8,No. 7, 1992 v Experiment A
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Figure 5. Forces between a silica-glass sphere and a flat silica plate as a function of pH at 20 O C . The measurements were performed in a background of M NaC1. The data points represent measurements of the surface force, and the solid lines are the best fit to DLVO theory at constant surface potential, as in Figure 3. The following parameters were used: pH 10, l/uo = -27 nm2/q,$0 = -67 mV, K - ~= 10.7 nm; pH 7, l/uo = -26 nm2/q, $0 = -60 mV, K - ~= 86 nm; pH 4, l/uo = -34 nm2/q,$0 = -48 mV, K - ~= 80 nm; pH 3,l/uo = -37 nm2/q, $0 = -35 mV, ~ - 1 =62 nm; 1 56 nm; pH 2,l/uo pH 2.6: l/uo = -36 nm2/q,$0 = -35 mV, ~ - = = -52 nm2/q, $0 = -13 mV, K - ~ = 30 nm. on the same chip. In the future it would be better to measure the spring constant for each spring. Figure 5 shows the measured force between a silicaglass sphere and an oxidized silicon wafer as a function of pH. These measurements were performed in a background of M NaCl and the pH was altered by addition of NaOH or HC1. As the pH is reduced, the magnitude of both the force and the fitted surface charge decreases. The Force between Hydrophobic Silica Surfaces. A silica sphere was made hydrophobic by exposure to trimethylchlorosilane vapor, and the force was measured as the sphere approached a hydrophobized plate (see Experimental Section). Unfortunately, the adhesion was too large for the force to be measured on approach, but a pulloff force, FIR = 0.4 N m-l was measured by separating the surfaces with a stepper motor. This is in the range of results obtained by Pashley et al.21(FIR = 0.35 N m-l) and Claesson et al.22 (0.44 N m-1). The Force between Gold Surfaces. The forces measured between a gold-coated particle and a gold surface in aqueous lo4 M NaCl are shown in Figure 6. At large separation,the forcedecays exponentiallyas for the silicasilica interaction. However, in the last 2-3 nm, the force (21) Pashley, R. M.; McGuiggan,P. M.; Ninham, B. W.; Evans,D. F. Science 1985,229, 1088-1089. (22) Claesson,P. M.;Christeneon, H. K.J. Phys. Chem. 1988,92,1650.
Ducker et al.
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20 30 40 50 60 70 Distance / nm Figure 6. Forces between a gold-coated silica sphere and a goldcoated mica surface in aqueous lo-' M NaC1. The filled circles represent measurements taken on approach of the two surfaces and the open ones on separation. The forces have been scaled by the radius of the gold sphere (3.5 pm), but the radius of the region of the interacting may be much smaller than this.
-10
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between gold surfaces decreases, then becomes attractive. Once the probe comes into contact with the surface, a repulsive force (negative applied load) is required from the cantilever to separate the surfaces,indicatingadhesion. When a sufficient negative load is applied, the particle moves to the next stable position, which in this case is about 50 nm from the position where the surfaces were touching. This pull-off force was extremely variable, with the unstable region extending up to 300 nm from the surface in some measurements. The measured force on approach was also quite variable and the curve in Figure 6 serves only as an example. Because the adhesion is so high, it is possible that the shape of the contact region could change between measurements. It was not possible to fit the measured force to a calculated DLVO (Derjaguin, Landau, Verwey, and Overbeek) force using a Hamaker constant3 of 35 X J when the origin of the plane of charge was placed at the onset of the regime of constant compliance. There are several possible reasons for this: (1)the effective radius may be smaller than the radius of 3.5 pm obtained from SEM,(2) organic material has probably adsorbed at the gold surface, possibly producing hydrophobic interactions, and (3)some of the charge on each surface may be situated at a negative surface separation. Although most of the charge on a conducting surface would be concentrated on the asperities, charge on adsorbed material may lie beyond the point of closest approach. Also, although the film is continuous on the mica, it may not be continuous on the sphere, which could expose dissociablesilica sites. If the interaction is modeled with the plane of charge at -10 nm but with the same van der Waals force, then a reasonable fit is obtained with an effective surface potential at infinite separation of -65 mV. No reasonable fit can be obtained by lowering the Hamaker constant alone. It is clear that more smooth, better characterized gold surfaces are required for a more detailed study.
Discussion a. The Forces between Silica Surfaces. The data presented in Figure 3 are similar to previousmeasurements reported by Horn et al.23and Peschel et al." for interactions between macroscopic silica sheets and by Rabinovich et (23) Horn, R. G.; Smith, D. T.;Haller, W. Chem. Phys. Lett. 1989,162, 404-408. (24) Peschel, G.;Belouechek, P.; Muller,M. M.; Muller, M. R.; Konig, R. Colloid Polym. Sci. 1982,260, 444-451.
Measurement of Forces in Liquids Table I. Comparison of Surface Potential Measurements on Silica Obtained by Various Workers measured values of the surface potential, mV, of silica in NaCl solutions obtained by various workers concn, this work M u b HomC Pescheld Rabine Weissf lo-' -21 -35 -23 -22 1V2 -34 -43 -28 -40 lV3 -53 -58 -32 -50 -45 -67 lo-' -61 -65 -40 -57 -83 Calculated with the planeof chargesituatedat the plane of closest approach. *Calculated with the plane of charge shifted -1.5 nm relative to the position of constant compliance. For measurements u and b, the systematic error arising from the radius and spring constant correspondsto 2 mV in 10-l and 10-2 M and to 4 mV in 10-3 and lo-'M. From Horn et al., force measurementson silica23 From Peschel et al., force measurements on silica.24 e Rabinovich et ai., force measurements on silica in KC1 solution.25fWeiss et al., streaming potential on silica in KCl solutions.3
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a1.S for interactions between quartz fibers. For particle
radii, r 3.5 pm, and for the Debye lengths, K - ~ , in these experiments, r / ~ - l >35 so the Derjaguin approximation26 can be used to convert the measured values to equivalent interaction energies per unit area with an error of less than 2 95. The solid lines showthe theoretical force/radius calculated from DLVO theory using an exact numerical solution of the Poisson-Boltzmann equation and a Hamaker constant2' of 0.8 X J. For each concentration, two theoretical curves are shown: one calculated for the surfaces interacting at constant charge and the other for the interaction at constant potential. The value of the effective surface-potential-at-infinite-separation was ob-' tained from the best fit of the model to the data with the plane of charge at the onset of the regime of constant compliance. However, because the surface is not smooth, the surface charge is most likely not situated in a single plane but distributed over a layer equal in thickness to the roughness of each substrate. This means that the potentials fitted from our data are likely to underestimate the surface potential, particularly for short Debye lengths. A more realistic model may be to position the origin of charge at a negative surface separation equal to half the maximum roughness. In the present case, this places the origin of charge at -1.5 nm. (Note that a residual layer of hydration water on the silica surface in the constant compliance regime would have a similar qualitative effect of moving the origin of charge to negative values.) Table I shows the fitted surface potentials as a function of NaCl concentration in our experiments (calculated for each origin of charge) as well as values calculated by other workers. Figure 7 shows the fitted potentials plotted together with values calculated using the simple massaction modelB used by PashleyS to describe the surface potential of mica substrates. For silica surfaces above the isoelectric point, the dissociation equation is
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4 i - O H Si+- + H+ with the corresponding equilibrium constant, Ka. Iler'sm value of PKa = 6.8 f 0.2, has been used to calculate the potential in the shaded region of Figure 7. The calculated points assume (i) ion sizes are smaller than an individual (25) Rabinovich, Y. I.; Derjaguin, B. V.; Churaev, N. Adu. Colloid Interface Sci. 1982, 16,63-78. (26)Derjaguin, B. Kolloid-2. 1934,69, 155-164. (27) Hunter, R.J. Foundations of Colloid Science; Oxford University Press: Oxford, 1987; pp 222. (28)Payene, T.A. J. Philips Res. Rep. 1955,10, 425. (29)Pashley, R. M.J. Colloid Interface Sci. 1981,83,531-546. (30)Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979; p 182.
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Langmuir, Vol. 8, No. 7, 1992 1835 I
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Figure 7. Fitted surface potential at infinite separation as a function of NaCl concentration. The circles represent data from Figure 3, and the shaded region is the potential calculated from a simple mass action model assuming no binding of the Na+ ion. The range of the shaded region is due to the uncertainty in the H+binding constant, pK, = 6.8 f 0.2.30
silanol site, 0.25 nm2 (the silica is only sparsely charged), and (ii) there was no binding of the Na+ ion to the silanol sites. Returning again to Figure 3, it can be seen that the force lies between the limits of constant charge and constant potential for all but the last 2-3 nm before the regime of constant compliance. At smaller separations, the force is greater than that predicted by DLVO theory (and no adhesive minima are measured). This effect has been measured p r e v i ~ u s l y ~ and ~ -was ~ ~ attributed to the hydration of the silica. However, there are other possible explanations for this observation, and these will now be considered. The existence of a gel layer on the surface of silica has been postulated for some time,3l and compression of this gel, or the confinementof silicate chains protruding from the surface, would lead to a repulsive force. This force would be larger when the silica is more highly charged or hydrated. The measured force cannot be attributed to the compression of asperities on the surface. The gradient of force required to elastically compress an asperity of area 1 nm X 1 nm and height 3 nm is about 70 N m-l (Young's modulus for silica is about 70 X lo9 N m-2).32 This value is much greater than the spring constant (so it would be difficult to discern in the regime of "constant" compliance)and is greater than the surface forces gradients measured here. Moreover, a force of this origin should be independent of solution conditions and this was not observed here. Similarly, the deformation of the colloid sphere under Herzian conditions33 is too small (0.02 nm) to account for this force. The "additional" force could also be explained by postulating a shift in the position of the plane of surface charge. The measured force can be fitted to that predicted by double-layer theory by positioning the origin up to -3 nm relative to the zero of separation used here. This shift is somewhat larger than would be expected considering the roughness of the substrates. However, the existence of residual water at the position of closest approach and/or hydrated ions on the surface would also cause a shift in the zero of charge. The surface force was also monotonic increasing over the pH range from 2 to 10, suggesting that for silica, the additional effect prevents coagulation by van der Waals forces over this pH range. This is in contrast to previous work on mica, where it has been shown that the presence of a hydration force is critically dependent on the P H . ~ It is also apparent from comparison of Figures 4 and 5 (31) Hunter, R.J. Foundutions of Colloid Science; 1987; p 381. (32)Condon, E.U.Handbook of Physics; McGraw-Hill: New York, 1967; pp 3-12. (33) Horn,R. G.;Israelachvili, J. N.; Pribac, F. J. Colloid Interface Sci. 1987, 115, 480-492.
1836 Langmuir, Vol. 8,No. 7, 1992
that the force in the last few nanometers before contact is much smaller at pH 2 than the force at the same ionic strength at pH 5.6 M NaC1). It is thus tempting to suggest that the magnitude of the additional force is greater in the presence of charged surface groups or ions, although again, this effect could be explained by a shift in the zero of charge. This result is consistent with models of both hydration and confinement of swelled silicate groups since the swelling of a gel layer should also be reduced as the charge on surface groups is reduced. If the surface potentials of best fit to the data in Figure 7 are compared to values obtained from the same ionbinding model used for the NaCldata, a poor fit is obtained at both high and low pH. However, the fit a t high pH can be improved by introducing a finite binding constant for Na+,which is lo7times more abundant than H+ a t pH 10. In fact, a binding constant, pK(Na+) = 4 produces a good fit to the data above neutral pH. b. Comparison of the Force Microscope and Surface Forces Apparatus. Currently, one of the leading techniques for the measurement of surface forces is the surface forces apparatus (SFA)developed by Israelachvili.‘ In this technique, surface forces are measured between two macroscopic, smooth surfaces which have cylindrical geometry of radius 2 cm. The measurements presented here demonstrate that there is considerable overlap in the force measuring capabilities of the AFM and SFA, so the two techniques will be compared briefly. The primary difference between force measurements using the SFA and the AFM is the size of the substrates. The radius of the silica particle used here was about 3 pm, and the radius of the microfabricated tip is of the order of 10-100 nm, so the substrate radii were 10e106 times smaller than those used in the SFA. Since most surface forces depend on the radius of the particle, surface forces are often manifest when the substrate dimensions are in the micrometer to nanometer range of the AFM. Studies on these macroscopic surfaces can still be related to the forces on smaller particles and can be used for measurements on thin films, adhesion, lubrication and wetting problems and the SFA has been successful in performing these measurements. Until recently, the SFA was also restricted to measurement of forces between transparent substrates, but this limitation has been removed by the adoption of new force measuring techniques such as the piezoelectric-bimorph technology of Parker.34 In fact, almost any technique which is used to measure force in an AFM may also be used in a technique using surfaces of larger area, so the ultimate F/R resolution of the SFA is about lo4times higher than for the AFM. However, to utilize this higher F/R resolution, substrates must be homogeneous (and smooth) on a much larger scale. To date this has severely limited the variety of substrates used in the SFA. The hydrodynamic force on a spherical particle approaching another surface scales with the square of the particle radius.35 Thus if one wishes to examine viscous forces, measurement on large radius substrates provides higher resolution. However, measurement may be performed at speeds lo4 times greater in the AFM while maintaining the same viscous force to surface force ratio as in the SFA, facilitating the measurement of fast phenomena such as relaxation effects, and more realistically reflecting collision speeds in many colloidal systems. Higher measuring speeds also minimize the effects of thermal or other drifts. One of the major hazards in surface force measurement
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(34)Parker, J. L.Langmuir 1992,8,551. (35)Chan, D.Y.C.; Horn, R. G. J. Chem. Phys. 1985,83,5311-5324.
Ducker et al. is contamination with particles. Since the probability of trapping a contaminating particle in the zone between the substrates is proportional to the radius of the substrate, the AFM is less subject to such contamination, and this has been borne out in experiments. Other differences between the techniques depend more on the manner in which forces and distances are measured. Because the drift in the optical distance measuring technique utilized in the SFA is negligible, the SFA is much better suited for measurement of the thicknesses of adsorbed films and is much better suited for measurements in which aconstant surface separation must be maintained. (Itis currently difficult to perform these experiments with an AFM.) However, the same optical system necessitates the use of substrates which are transparent. c. Future Developments. In our analysis we have calibrated the deflection of our cantilever by driving our colloid probe into the surface until a constant compliance is reached. We have assumed that in this regime, the separation between the substrates is constant, and there is no compression of the solid (or liquid) phases, so that the deflection of the cantilever corresponds to displacement of the driving piezo. In addition we assume that the angular deflection in this “contact” mode is the same as when the surfaces are not in contact. This procedure is necessitated because with the light-lever/diode technique there is no reference to normalize measurements of the deflection of the spring. AFMs which measure cantilever deflection using interferometry should alieviate this problem and may soon be available for use in liquids. The force could be determined directly from the spring deflection, and the compression of the substrates could be measured. Recognition of the constant compliance regime would still be required to determine the absolute position of surfaces. Finally, measurement of attractive forces would be facilitated by the use of a force balance in which the surface force is balanced by an “external force” controlled by the experimenter. Such a device has already been r e p ~ r t e d . ~ ~ ~ ~
Conclusions A force microscope can be used to measure the surface forces acting between colloidal particles in aqueous solution. The technique is simple and reproducible and can be applied to a variety of materials and geometries including particles and fibers and metal and metal oxides. Measurements of the forces between silica surfaces as a function of separation, salt concentration, and pH are consistent with earlier measurements between Si02 surfaces. At large separation (>3 nm) the measured forces agree well with classical DLVO theory, at conditions intermediate between constant charge and constant potential. An additional repulsive force at small separation prevents adhesion in a van der Waals minimum. Since the AFM-measured decay lengths of the double-layer forces are well predicted by DLVO theory, measurements of the decay provide a simple method to calibrate the expansion of AFM piezoelectric crystals perpendicular to the surface. Acknowledgment. We thank Brett Sexton for providing the calibrated CD stamper, Tommy Nylander for providing the silicon wafers, and Barry Ninham, Y. I. Rabinovich, and Calum Drummond for useful discussions. (36)Miller, G. L.;Griffith, J. E.; Wagner, E. R.; Grigg, D. A. Rev. Sci. Instrum. 1991,62,705-709. (37)Joyce, S.A.;Housten, J. E. Rev. Sci. Intrum. 1991,62,710-715. (38)Wiese, G. R.; James, R. 0.; Healy, T. W. Discuss. Faraday SOC. 1975,52,302-311.
