Adhesion Forces between Glass and Silicon Surfaces in Air Studied

Sep 14, 2002 - Using the atomic force microscope (AFM), the pull-off forces between flat glass or silicon surfaces and silicon AFM tips or glass micro...
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Langmuir 2002, 18, 8045-8055


Adhesion Forces between Glass and Silicon Surfaces in Air Studied by AFM: Effects of Relative Humidity, Particle Size, Roughness, and Surface Treatment Robert Jones,* Hubert M. Pollock, Jamie A. S. Cleaver,† and Christopher S. Hodges† Department of Physics, University of Lancaster, Lancaster LA1 4YB, United Kingdom, and Department of Chemical and Process Engineering, University of Surrey, Guildford GU2 7XH, United Kingdom Received May 7, 2002. In Final Form: July 26, 2002 Using the atomic force microscope (AFM), the pull-off forces between flat glass or silicon surfaces and silicon AFM tips or glass microspheres of different sizes have been extensively studied as a function of relative humidity (RH) in the range 5-90%, as model systems for the behavior of cohesive powders. The glass and silicon substrates were treated to render them either hydrophobic or hydrophilic. All the hydrophilic surfaces gave simple force curves and pull-off forces increasing uniformly with RH. Small contacts (R ∼ 20 nm) gave pull-off forces close to values predicted by simple Laplace-Kelvin theory (∼20 nN), but the values with microspheres (R ∼ 20 µm) fell well below predictions for sphere-flat or sphere-sphere geometry, due to roughness and asperity contacts. The hydrophobic silicon surfaces also exhibited simple behavior, with no significant RH dependence. The pull-off force again fell well below predicted values (JohnsonKendall-Roberts contact mechanics theory) for the larger contacts. Hydrophobic glass gave similar adhesion to silicon over most of the RH range, but against both silicon tips and glass microspheres, there was an anomalously large adhesion in the RH range 20-40%, accompanied by a long-range noncontact force. The adhesion on fully hydrophilic surfaces and its RH dependence can be mostly explained by current theories of capillary bridges, but the interpretation is complicated by the sensitivity of theoretical predictions to contact geometry (and hence to roughness effects) and by uncertainties in the thickness of adsorbed water layers. The anomalous behavior on hydrophobic glass surfaces at intermediate values of RH is not fully understood, but possible causes are (1) dipole layers in the partially formed water film, giving rise to patch charges and long-range forces, or (2) fixed charges at a reactive glass surface, involving specific bonding reactions. The results may be useful in explaining the behavior of cohesive powders with different coatings or those which show a large humidity dependence (e.g., zeolites) or show electrostatic charging effects (e.g., silica aerogels).

1. Introduction To understand the bulk cohesion behavior of industrially important powders and its dependence on relative humidity (RH), it is important to study adhesion at the singleparticle level in suitable model systems (Figure 1), where the particle geometry and surface condition can be well controlled, and then progress to the more complex behavior of cohesive powders. Our ultimate aim is to provide a quantitative link between the single-particle forces and the bulk flow and cohesion behavior, so that the singleparticle data can have real predictive value for chemical engineers. The first objective of the present work was thus the practical one of providing model systems for particulate behavior. However, this work also serves the more general purpose of providing data to understand better the fundamental nature of capillary bridges and their RH dependence. The effects of RH on single-particle adhesion and bulk powder cohesion have been reviewed by Harnby et al.,1 and more recently the single-particle work has been reviewed by Tyrrell.2 There were large variations in behavior reported between different materials and dif* To whom correspondence should be addressed. E-mail: [email protected] † University of Surrey. (1) Harnby, N.; Hawkins, A. E.; Opalinski, I. Chem. Eng. Res. Des. 1996, 74, A6, Part A, 605-615. (2) Tyrrell, J. W. G. Ph.D. Thesis, University of Surrey, Guildford, U.K., 1999.

Figure 1. Some advantages of studying simple systems as models for interparticle contacts between powders, and the types of system used in the present work.

ferent investigators. However, the general trend was that adhesion was large for clean surfaces in a vacuum (because it is then dominated by the large surface energy), low in dry air (because of the low energy of contaminated surfaces and the absence of capillary bridges), and higher again in humid air because of capillary bridges (section 2.1). In the low-RH regime, where contacts are dry and thus JohnsonKendall-Roberts (JKR) contact mechanics theory (section 2.2) can probably be applied, adhesion was usually almost constant over a wide range. There was no critical RH for

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capillary condensation, but the adhesion tended to rise steeply at RH > 60%. McFarlane and Tabor3 provided the first experimental verification of the Laplace-Kelvin theory (eq 3) for the maximum adhesive force for sphereflat geometry due to liquid bridges at high RH. Zimon4 carried out the first extensive studies on humidity dependence of adhesion and reviewed the subject. Later work by Fisher and Israelachvili5 and Christenson,6 using the surface force apparatus (SFA), confirmed the trend of a monotonic increase of adhesion with RH, which was most marked above 60%. The crossed mica cylinders in the SFA gave a good approximation to the atomically flat sphere on flat contact required by the simple theory but were of limited relevance to real particles. More recently, particles have been attached to atomic force microscope (AFM) cantilevers to supplement the AFM data on pull-off forces and adhesion already available from bare tips. Almost invariably, the adhesive force for larger contacts falls well below the predictions of theory, whether JKR theory (for dry contacts) or liquid bridge theory. As a result of an extensive AFM study on dry contacts, Schaeffer et al.7 concluded that the discrepancy was due to microasperity contacts. It is now commonly accepted that the magnitude of liquid bridge adhesion depends on a complex interplay of many effects, notably the geometry of surface asperities, meniscus radii, contact angles, and the thickness of adsorbed water films. Capillary bridge effects only approach their theoretical magnitude when meniscus radii and the thickness of adsorbed water films begin to exceed the average asperity size. Both these quantities are of the order of a few nanometers and increase with RH, but there are very large variations in experimentally determined values of film thickness. Thicknesses determined by AFM methods8,9 are often in disagreement with values obtained by other techniques such as ellipsometry,10 and the primary cause is thought to be film instability under the approaching AFM tip. Contact angles and adsorbed water layers are also very sensitive to the surface chemical condition. Thus, apart from RH, the two factors that dominate adhesion are surface chemistry and roughness. For these reasons, although Laplace-Kelvin theory correctly predicts the maximum magnitude of adhesion for smooth contacts, there is still no completely satisfactory theory for predicting the RH dependence of adhesion for practical interparticle contacts. The trend for adhesion to increase sharply with RH has been confirmed by several AFM studies (for example, Thundat et al.11 and Binggeli and Mate12), mostly on bare tips. This AFM work has been recently reviewed by Cappella and Dietler.13 However, the interpretation of such data on RH dependence is complicated by many factors (see section 2.1) of which the following are noteworthy: (1) In the simplest version (3) McFarlane, J. S.; Tabor, D. Proc. R. Soc. London 1950, A202, 224-243. (4) Zimon, A. D. Adhesion of Dust and Powder; Consultants Bureau/ Plenum Publishing: New York, 1982. (5) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981, 80, 528-541. (6) Christenson, H. K. J. Colloid Interface Sci. 1988, 121, 170-178. (7) Schaeffer, D. M.; Carpenter, M.; Gady, B.; Reifenberger, R.; Demejo, L. P.; Rimai, D. S. J. Adhes. Sci. Technol. 1995, 9, 1049-1062. (8) Dey, F. K. Ph.D. Thesis, University of Surrey, Guildford, U.K., 1998. (9) Dey, F. K.; Cleaver, J. A. S.; Zhdan, P. A. Adv. Powder Technol. 2000, 11, 401-413. (10) Mate, C. M.; Lorenz, M. R.; Novotny, V. J. IEEE Trans. Magn. 1990, 26, 1225-1228. (11) Thundat, T.; Zheng, X. Y.; Chen, G. Y.; Sharp, S. L.; Warmack, R. J.; Schowalter, L. J. Appl. Phys. Lett. 1993, 63, 2150. (12) Binggeli, M.; Mate, C. M. Appl. Phys. Lett. 1994, 65, 415. (13) Cappella, B.; Dietler, G. Surf. Sci. Rep. 1999, 34, 1-104.

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of Laplace-Kelvin theory, for spherical geometry, RH dependence disappears in the derivation of maximum adhesion force (see below). (2) More sophisticated versions of liquid bridge theory introduce some RH dependence, but it is still usually smaller than experimentally observed variations, or even opposite in direction. (3) The exact form of the RH dependence predicted by theories is critically dependent on contact geometry and contact size, with RH effects largest for small contacts. (4) There is mounting evidence that the surface chemical condition of the contacts can have a dramatic effect on the RH behavior, and anomalous peaks of adhesion are sometimes seen at some intermediate value of RH (see, for example, Chikazawa et al.14 and Xu et al.15). Similar anomalous behavior was later reported for glass spheres by Tyrrell.2 These effects are so striking as to suggest that the RH dependence of adhesion is a reliable way of distinguishing hydrophilic and hydrophobic surfaces. The present work was motivated by the need for simple model systems (Figure 1) to help in the understanding of the more complex behavior of cohesive powders. The interparticle forces in these cohesive materials and their relation to bulk cohesion and flow will be described elsewhere. However, it soon became apparent that even the best available systems, such as AFM tips, glass ballotini, or polymeric microspheres, are imperfect in terms of particle geometry, smoothness, and controlled surface condition, the most critical parameters for determining adhesion behavior. This could explain the wide variations in reported behavior, and one of our priorities was to understand discrepancies between our early results and the parallel work of Tyrrell.2 The effects of particle size, roughness, and chemical treatment on adhesion are particularly clear in the work below, and the ease with which RH can be varied has enabled us to look at a wide range of behavior, which is useful in understanding the fundamental nature of liquid bridge contacts. 2. Theoretical Background The interparticle forces most likely to be relevant to the present work are contact forces, van der Waals forces, capillary forces, and electrostatic forces. Van der Waals forces are very significant for smooth contacts and in liquid but are likely to be small compared to other forces for the present work involving relatively rough surfaces in air. Contact forces may be masked by the larger liquid bridge effects except for hydrophobic surfaces or at low RH. Longrange (∼1 µm) electrostatic forces appear to operate only for a limited range of surfaces and RH values but then dominate all other behavior and so must be discussed. Liquid bridges provide the dominant adhesion forces above ∼40% RH. 2.1. Capillary Bridges. The theory of interparticle forces due to capillary bridges, and their dependence on relative humidity, has been summarized by Israelachvili,16 Pollock,17 and Tyrrell.2 As the RH is increased, vapor will spontaneously condense on surfaces. The meniscus curvature is related to the relative vapor pressure, p/psat (or (14) Chikazawa, M.; Kanazawa, T.; Yamaguchi, T. The role of adsorbed water on adhesion force of powder particles. KONA Powder Part. 1984, 2, 54-61. (15) Xu, L.; Lio, A.; Hu, J.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem. 1998 B102, 540. (16) Israelachvili, J. N. Intermolecular and surface forces, 2nd ed.; Academic Press: London, 1992. (17) Pollock, H. M. The forces acting between dry powder particles; IFPRI Report SAR 12-09; International Fine Particle Research Institute, 1994.

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Figure 2. Geometry of an idealized contact between a sphere and a flat in the presence of an adsorbed water film and a capillary bridge. The surfaces illustrated are wettable with a small contact angle.

RH for water), by the Kelvin equation (Orr et al.18):

(1r + 1x)


) rk )

γV RgT log(p/psat)


where rK is the Kelvin radius, γ is the surface tension of water, Rg is the gas constant, and V is the molar volume. In general for an annular meniscus, r is small and negative (concave) and x is large and positive (convex). For low humidity, the Kelvin radius is small; hence the onset of capillary condensation with increasing RH first occurs at small values of rK in cracks and pores. Fisher and Israelachvili5 have experimentally confirmed the validity of eq 1 for water down to a radius of ∼5 nm. The Laplace pressure in the liquid is


(1r + 1x) ≈ r

P ) γL

since x . r


and acts on an area πx2, pulling the surfaces together. For perfect sphere-on-flat geometry (Figure 2) where the contact radius x is small compared with the sphere radius R, the meniscus radius r (and hence the RH dependence) disappears from the final expression for the Laplace pressure contribution to the adhesion force, given by

F ) 4πRγL cos θ


where θ is the contact angle of water on the two surfaces (assumed identical). This simple derivation neglects any contribution to adhesion from the resolved surface tension around the circumference (valid for small θ) or from the solid-solid interaction across the liquid bridge. It also ignores any condensed liquid film (thickness t) present before the surfaces are brought into contact. Nevertheless, it has been verified several times for smooth contacts approximating sphere-on-flat geometry. To progress further with understanding liquid bridges at more realistic interparticle contacts, the critical importance of the relative proportions of R, r, x, and t in the schematic diagram (Figure 2) must be grasped. Thus RH dependence vanishes because r is small compared with the other dimensions (except when very close to saturation) but returns when r and x (eqs 1 and 2) are comparable in magnitude, as for small asperity contacts. Tyrrell2 has considered scale diagrams of the sphere-flat contact for (18) Orr, F. M.; Scriven, L. E.; Rivas, A. P. J. Fluid Mech. 1975, 67, 723-742.

typical particle sizes (R ∼ 20 µm), small contact angles, and typical meniscus radii (∼10 nm at 90% RH), from which it is clear that even the smallest asperities of a few nanometers in height transform the geometry of the effective contacts completely, and hence both the magnitude and RH dependence of the adhesion. Various models have attempted to improve on the basic Laplace-Kelvin theory by considering different bridge geometries, as follows: (1) Sphere-on-sphere geometry (Coughlin19) predicts adhesion forces exactly half those for sphere-on-flat geometry (Iinoya20), but the predicted RH dependence is very small and similar in both cases. (2) Pendular bridge geometry, where the contacting spheres are very small and comparable in size to the meniscus radii (R ∼ r ∼ x), may give a closer approximation to real contacts between particles involving small asperities. The surface tension component of adhesion, previously ignored in eq 3, becomes relatively important under these conditions and is given by 2πxγ, where x is the neck radius in Figure 2. (3) Cone-on-flat geometry19 may be an even better approximation to asperity contacts and predicts a dramatically increased RH dependence. This is because for these very small menisci the importance of the surface tension term increases relative to that of the Laplace pressure term, eq 2. Tyrrell2 has discussed at length the predictions of sphere-on-sphere geometry19 and sphere-on-flat geometry20 for small contacts (R ) 100 nm) and large contacts (R ) 20 µm). At large R, the predicted adhesion is constant and equal to the Laplace-Kelvin value (eq 3) until so close to 100% saturation that no AFM experiment could detect the change. At small R, the predicted variations with RH, although mostly occurring above 80% RH, would now be detectable. However, the Laplace pressure contribution (acting over the contact area πx2) is predicted to fall steeply at high RH whereas the surface tension contribution 2πxγ (acting around the circumference of the neck) rises steeply at high RH. The sum of the two contributions falls slightly at high RH, the opposite of the commonly observed behavior. However, the cone-on-flat model predicts a large increase of adhesion with RH because of the dominant effect of the surface tension term. This suggests that the cone-on-flat model is a much more realistic fit for the bulk of the published experimental work. 2.2. JKR Contact Mechanics. Contact forces will often be masked by liquid bridge forces but may be applicable for hydrophobic surfaces and at low RH. For a sphereon-flat contact between two identical solids, the so-called JKR approximation16 (applicable for highly deformable contacts or cases of high surface energy, large particles, and low elastic modulus) gives for the adhesion or pull-off force

F ) -3πRγSV


where R is the sphere radius and γ is the solid-vapor interfacial energy. At the other extreme of small deformations, the pull-off force becomes -4πRγSV, the so-called DMT approximation.16 Apart from the uncertainties of contact size that affect all other surface forces, there are large uncertainties in interfacial energy. Data are available for clean glass or silica surfaces, but under the conditions of the experiments described below, liquid bridges are most likely to be absent (and hence contact (19) Coughlin, R. W.; Elbirli, B.; Vergara-Edwards, L. J. Colloid Interface Sci. 1982, 87, 18-30. (20) Iinoya, K.; Muramoto, H. J. Soc. Mater. Jpn. 1967, 16, 352-357.


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mechanics theory applicable) for hydrophobic surfaces where γ is considerably reduced and not accurately known. Nevertheless, it is useful for setting limits or for approximate comparisons between experimental pull-off force and theory. 2.3. Long-Range Coulomb Forces. These are again very sensitive to contact geometry. Their origin in dipole layers or patch charges21,22 is not considered in detail here. For sphere-on-flat geometry, the exact form of the forcedistance curve depends on the relative values of distance D and sphere radius R.13,22 The classical inverse-square dependence is applicable only at large relative separations:

R F ) π0V2 D

for R . D




F ) π0V2


for R , D


where V is the tip-surface potential difference. Coneon-flat geometry predicts a more complex logarithmic distance dependence. In the present work, long-range forces are typically seen in the range of 1-5 µm for spheres of 20 µm radius having surface asperities of the order of 10 nm in height. Thus the sphere rather than the asperities (cone-on-flat) should determine the behavior, with R . D. 3. Experimental Details 3.1. AFM and Cantilevers. The AFM used was a TM Microscopes “Explorer” instrument, used in conjunction with the standard force spectroscopy software for obtaining force curves. Cantilevers of spring constant 0.032 N/m, 0.064 N/m (silicon nitride), and 1 and 30 N/m (silicon) were used to cover the complete range of forces measured with both bare tips and large glass ballotini, ensuring sufficient lever deflection without excessive instability and giving some overlap of data between the different ranges. This is important to avoid cantilever-generated artifacts and obtain reliable pull-off forces. Spring constants were not routinely calibrated, and the manufacturer’s stated values were assumed. A small number of 30 N/m levers were calibrated by measuring their resonant frequency, and all were found to be within 20% of the stated value. 3.2. Samples and Preparation. Glass ballotini were obtained from Potters Ballotini, Barnsley, Yorkshire, U.K., in two sizes, of approximate radius 20 and 100 µm. The larger ballotini were either uncoated (BST) or coated by the manufacturer (BMP) with unspecified organosilicon compounds and were used without further treatment. The smaller ballotini were uncoated and were soaked in isopropyl alcohol overnight and then dried before use. They were the same batch of glass microspheres as those used by Tyrrell2 and by Tyrrell and Cleaver23 in work that closely paralleled that described below. Standard contact mode AFM images of ballotini were obtained to check the surface roughness. The 20 µm radius spheres were noticeably less rough than the 100 µm spheres. The particles were attached to cantilevers with epoxy resin either by using a micromanipulator and a binocular microscope or (more usually) by using the AFM controls and its low-power video imaging facility. For studying particle-particle adhesion, the particles were attached to a glass slide with either an adhesive carbon disk or a thin film of epoxy resin, to form a thin but continuous bed of particles. For force curve work, single particles were selected to obtain an approach that was as near “head-on” as possible in the video, but more glancing approaches did not give significantly different force curve behavior. (21) Burnham, N. A.; Colton, R. J.; Pollock, H. M. Phys. Rev. Lett. 1992, 69, 144-147. (22) Burnham, N. A.; Colton, R. J.; Pollock, H. M. Nanotechnology 1993, 4, 64-80. (23) Tyrrell, J. W. G.; Cleaver, J. A. S. Adv. Powder Technol. 2001, 12, 1-15.

For studying particle-flat adhesion, glass microscope slides and cover slips and silicon wafers (p-type, 111-orientated) were treated to make them either hydrophilic or hydrophobic as follows: The substrates were precleaned in boiling isopropyl alcohol and then immersed in either (a) baths of H2SO4/H2O2 and then NaOH/H2O2 at 40 °C for 10 min or (b) 2% Decon 90 at 40 °C for 2 h. Either procedure produced a very wettable surface, although the resultant surface chemistry was probably not identical for the two procedures. In either case, it was important that the surface was thoroughly rinsed with distilled water. The contact angle of a drop of distilled water on either surface, measured in an optical microscope, was 10-15°, decreasing further as the drop evaporated. Clean surfaces were used for force curve work within about 4 h since the contact angles increase significantly during 8 h in room air, suggesting contamination. For hydrophobic surfaces, freshly cleaned and dried hydrophilic surfaces were placed overnight in the vapor above a small dish of hexamethyldisilazane (HMDS) in a desiccator. Contact angles with water drops were approximately 70-80°, decreasing to about 40° as the drop evaporated. For well-prepared hydrophilic and hydrophobic surfaces, the meniscus retreated very uniformly on evaporation, but patchy surfaces showed less uniform behavior. HMDS-treated surfaces were stable in air for longer periods than hydrophilic surfaces. 3.3. Humidity Control. The AFM was enclosed in a Perspex glovebox (volume of about 18 L) supplied with air continuously circulated at a flow rate of up to 10 L/min by an oil-less linear diaphragm pump. The circulating air was diverted in varying proportions through a drying line containing columns of silica gel, a humidifying line containing a tank of water and a large aquarium air-stone, and a bypass line. The RH was measured close to the microscope by a Comark humidity probe covering the range 4-90% RH and in the flow line by a Panametrics humidity probe designed to cover the lower end of the RH range more accurately. The probes agreed within 5% over the range 4-50% RH. The air flow did not significantly affect AFM operation, and all the common adjustments were readily accessible via the glove ports. RH measured in the glovebox stabilized within about 5 min of making small changes, and starting from normal room air both extremes of humidity (2% and 90%) could be reached after about 30 min of continuous flow. Thus, in the course of a day it was possible to obtain up to 60 sets of force curves, going up and down in RH about twice. Prolonged operation above 80% RH was avoided because of possible damage to the high-voltage scanner. 3.4. Force Curve Collection. Normally, four pairs of force curves (4× approach and 4× retraction) were collected at the same point on the flat glass and silicon surfaces before changing the RH and randomly moving to another point. When the lower contact was a second particle, the experiment was usually confined to the same pair of particles. Standard parameters used were as follows: Z-range of 1 or 2 µm, sometimes larger when long-range forces were present; approach and retraction speeds of 1 µm/s; force limit of about 200 nN (1 N/m levers) and 3000 nN (30 N/m levers). There was no evidence that varying the speeds, the contact time, or the force limit significantly affected the subsequent pull-off force for the relatively hard materials studied here. The sensor deflection was converted to a force scale in the usual way from the spring constant (assumed to be the same for all levers of a given type) and the sensor response (slope of the hard repulsion region of the force curve) measured separately for each lever at the same time as the main experiment. The Z-piezo movement was corrected using these measurements to give a true tip-sample separation in plotted force curves. It is important to recognize that the linear portion after pull-off for curves plotted in this way is simply a straight line joining adjacent data points and has no physical significance; information is lost from this part of the curve. The random scatter of pull-off force values within a single experiment was of the order of (10% on glass surfaces and rather less on silicon surfaces. This is attributed to a combination of localized variations in surface quality and imperfect equilibration of RH values. Since many clean surfaces became significantly contaminated in room air in 8 h, experiments were a compromise to obtain sufficient RH data in this time. Additionally, there

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Table 1. Summary of Adhesion Forces (Maximum Pull-Off, in nN) between Glass and Related Surfaces

predicted pull-off, nN Laplace-Kelvin JKR spring constant, N/m measured pull-off, nN

hydrophilic glass hydrophilic silicon hydrophobic glass hydrophobic silicon


bare Si tip, R ∼ 20 nm

glass sphere, R ∼ 20 µm

glass sphere, R ∼ 20 µm

glass sphere, R ∼ 100 µm

sphere-flat 18 63 1.0 15 w 60 (Figure 3)

sphere-flat 18 000 63 000 1.0 1200

sphere-flat 18 000 63 000 30 4000 w 7000 (Figure 5)

sphere-sphere 45 000

15 w 45 (Figure 4) 10, 200a (Figure 8) 20 (Figure 9)


4000 w 9000 (Figure 6) 400, 1600a


150, (Figure 10)

30 500 w 2000 (Figure 5) uncoated ball 500 coated ball


Refers to the anomalously high values of pull-off at some intermediate value of RH (20-50%).

were systematic variations from one experiment to another, also of the order of (10%, due to uncertainties in lever calibrations.

4. Results and Discussion The vast majority of force curves were of a very simple form, and the only measurable parameter of interest was the pull-off force, which was usually averaged for plotting for each set of four curves. Some typical force curves are shown as insets to the main figures. An abrupt pull-off and large-scale force curve hysteresis were nearly always present as is normal for adhesion and liquid bridge effects. In some cases, there were also interesting jump-to-contact effects, long-range noncontact forces, and more gradual pull-off effects, but these were seen only under very limited conditions and will be discussed and illustrated as appropriate. Pull-off forces showed little evidence for hysteresis with respect to cycling the RH up and down, suggesting that particles and surfaces reached equilibrium with the surrounding RH within 10 min. Table 1 summarizes all the pull-off forces measured, with some indication of their dependence on relative humidity, for bare AFM tips and glass ballotini of different sizes in contact with hydrophilic and hydrophobic glass and silicon surfaces. The theoretical maximum adhesion forces expected from Laplace-Kelvin theory and JKR contact mechanics theory are also given. Note that the data for the larger ballotini are for contact between two particles where the theoretical adhesion is exactly half that for sphere-on-flat geometry. For the smaller ballotini, data are given for cantilevers differing by a factor of 30 in spring constant to check that the cantilevers do not introduce serious errors in force measurement. We consider the simplest contacts first before discussing the more complex behavior with larger particles and hydrophobic surfaces. 4.1. Hydrophilic Substrates: Effects of Contact Geometry and RH on Adhesion and Comparison with Theory. 4.1.1. Small Contacts (R ∼ 20 nm): The Easiest To Model. In this instance, force curves are invariably simple with an abrupt pull-off and no unusual features (Figure 3). The pull-off force and its RH dependence for silicon tips in contact with glass and silicon substrates are similar, with a monotonic increase between 40 and 80% RH. There is no evidence that the adhesion behavior is significantly different when the humidity is increasing and decreasing, whereas earlier studies sometimes reported differences. The magnitude of the pull-off force and the increase with RH are similar to results reported by Fujihira et al.24 (24) Fujihira, M.; Aoki, D.; Okabe, Y.; Takano, H.; Hokari, H.; Frommer, J.; Nagatani, Y.; Sakai, F. Chem. Lett. 1996, 7, 499.

Figure 3. Dependence of pull-off force on relative humidity for small contacts between a silicon AFM tip and a hydrophilic glass surface. The behavior is relatively simple, and the forcedistance curves used to derive pull-off values (inset) are also simple.

Figure 4. Dependence of pull-off force on relative humidity for small contacts between a silicon AFM tip and a hydrophilic silicon surface. The behavior is similar to that on glass substrates and easily reversible with humidity changes. Forcedistance curves are simple and similar to those on glass.

Only two small differences between glass (Figure 3) and silicon (Figure 4) may be noted: (1) there is more scatter in the data for glass, suggesting greater difficulty of cleaning and more patchy surface chemistry; (2) the adhesion with silicon reaches a maximum at about 70% RH and declines slightly at higher values. This is rather


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Figure 5. Dependence of pull-off force on relative humidity for large contacts between glass spheres and hydrophilic glass surfaces. The RH dependence is similar to that for small contacts on hydrophilic surfaces but is less pronounced, and the magnitude of pull-off values falls well below theoretical predictions. The associated force-distance curves are generally very simple.

unexpected because all experimental studies of adsorbed water film thickness indicate an increase up to the highest RH values, and (for those theories that predict an increase of adhesion with RH, such as the cone-on-flat model of asperity contacts) the adhesion might be expected to parallel the water adsorption. This behavior has been seen elsewhere and attributed to disjoining pressure,3,4 but in these studies the contact area may have been much larger. The nominal radius of the silicon AFM tip quoted by the manufacturer is 20 nm, for which Laplace-Kelvin theory would predict a pull-off force of 18 nN at high RH, compared with the measured value of ∼60 nN. However, AFM tips are often significantly less sharp than claimed, and this is the most likely explanation for the discrepancy. The small residual pull-off at low RH (10-15 nN in this work) was not usually discussed in previously published work. It is lower than the value of 63 nN predicted by JKR theory, but there are again uncertainties of contact area and surface energies. The very marked RH dependence for small contacts with silicon and glass suggests that a cone-on-flat model is more realistic than a sphere-on-flat model. As noted earlier, most theories suggest that the RH dependence should be most marked for small contacts and least marked for contacts with large smooth spheres. 4.1.2. Larger Contacts (R ) 20-100 µm): Roughness Effects. With glass spheres of 20 µm radius against flat hydrophilic surfaces, the behavior is qualitatively similar to that of bare tips. There is a monotonic increase of adhesion with RH, and again the behavior is very similar for glass (Figure 5) and silicon (Figure 6) flats. Force curves are generally very simple in form, but occasional jumpto-contact effects and long-range pull-off effects have been seen. These are suggestive of the mobile surface films and pendular bridges discussed by Tyrrell2 and Tyrrell and Cleaver23 but were unusual in the present work, possibly due to differences in surface preparation. A comparison of all the data for hydrophilic surfaces, for small and large contacts, and for glass and silicon (Figures 3-6) reveals a number of points of interest: (1) There is no evidence, except for one set of data in Figure 5, for different behavior on increasing and decreasing the RH. Glass microspheres might be expected to equilibrate with ambient RH more slowly than AFM tips. (2) The

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Figure 6. Dependence of pull-off force on relative humidity for large contacts between glass spheres and hydrophilic silicon surfaces. The behavior is similar to that with large contacts on hydrophilic glass surfaces, and force-distance curves are generally very simple.

smaller scatter of data for silicon is again apparent (Figure 6), suggesting a more uniformly cleaned surface than for glass (Figure 5). This might also be explained by less variation in roughness in the silicon surface. (3) There is some indication that the adhesion increases uniformly over the whole RH range for silicon (Figures 4 and 6) but increases only above 40% RH for glass (Figures 3 and 5); a possible explanation is that capillary condensation is delayed if the glass surface is less perfectly wettable. (4) The RH dependence of the adhesion is more muted for the larger contacts. As noted before, this behavior would be expected for large smooth contacts, but a full interpretation would depend on whether the data for Figures 5 and 6 represent single smooth contacts or multiasperity contacts. However, the most notable feature of the data for large contacts is that the magnitude of the pull-off force now falls well below the predictions of Laplace-Kelvin theory for smooth sphere-on-flat geometry. Values obtained with 30 N/m cantilevers are about 3 times smaller than those predicted for spheres of 20 µm radius, and the discrepancy is even greater for 1 N/m levers, where the pull-off force is at the limit of the measurable range (Table 1). This strongly suggests, with the observations by Tyrrell and Cleaver,2,23 Schaeffer et al.,7 and others, that roughness and microasperity contacts are important in determining the adhesion behavior, and this is confirmed by topographic images of the glass ballotini used (Figure 7). If the Kelvin meniscus radii (eq 1), which increase from 0.2 to 5.0 nm over the RH range 10-90%, are compared to typical asperity sizes (15 nm high, 50 nm across), it is clear that a single continuous contact will not be formed and the adhesion will be reduced. Tyrrell and Cleaver2,23 have presented data for glass spheres (from the same source as those used in the present work) on a glass flat where adhesion both increases (as above) and decreases with RH, or even goes through some maximum value (see later). The results are difficult to compare with the present work because of small differences in experimental procedures. However, the main conclusions, that the adhesion is usually well below the theoretically predicted value and that surface cleaning and roughness are critical, seem inescapable. The bulk of the studies were carried out with 20 µm radius glass ballotini that had relatively smooth and clean surfaces in comparison with several other samples avail-

Adhesion Forces between Glass and Silicon

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Figure 7. AFM topographic image and line profiles of the surface of a 20 µm radius glass sphere of the type used in the adhesion studies. The surface is smooth in comparison with that of many particles, but asperity sizes are similar to Kelvin meniscus radii, explaining the large deviations from the pull-off force theoretically predicted for a smooth sphere (Table 1).

able. Uncoated 100 µm ballotini from the same supplier gave adhesion values (Table 1 and Figure 5) that fell even further below the prediction of theory (in this case, for sphere-sphere). Topographic images revealed an even rougher surface with asperities 200 nm high; the unknown surface condition may have also contributed to the low adhesion. If a single asperity contact (as seen with AFM tips) corresponds to a pull-off force of 10-40 nN, this suggests that a typical contact with glass spheres and relatively stiff cantilevers corresponds to the order of 100 asperity contacts. There is no evidence for multiple pull-off effects in force curves, so it is necessary to explain in this case how a large number of events can add to give the appearance of a single pull-off. It should be possible to obtain clues concerning the nature of the contacts, and to eliminate artifacts arising from cantilever instabilities, by studying pull-off forces for levers with a wide range of spring constants. The discrepancy between data obtained with 1 and 30 N/m levers is rather small (Table 1). However, some force curve studies with floppy cantilevers (0.032 and 0.064 N/m) and coated and uncoated glass ballotini from a different source gave pull-off values that were much smaller (∼10 nN) and very similar to those in Table 1 for bare tips. These studies formed part of an investigation of fine cohesive powders (to be reported elsewhere) where it was important to avoid large loads on a powder agglomerate. It seems very unlikely that the large difference in pull-off force compared with that for 1 N/m levers could be explained by cantilever artifacts or differences in roughness and surface condition of the samples. A more likely explanation is that some compres-

sion of asperities occurs with the stiffer levers, causing more contacts, but still well below the smooth sphere contact area. The maximum applied load during force curve acquisition varies from approximately 10 nN for floppy levers to 3000 nN for the stiffest levers. For highmodulus materials and small loads, the pull-off force is usually independent of applied load, and this also appears to be the case in the present work when load is varied over a small range with a single cantilever. Also, for perfect elasticity the modulus, although affecting contact area, does not appear in the final expression for pull-off force (JKR theory). Nevertheless, the very large increase in load between one type of cantilever and the next might be sufficient to increase the number or area of contacts and cause the observed increase in the magnitude of capillary bridge effects. 4.2. Hydrophobic Substrates: An Anomalous Effect of RH on Adhesion for Glass with No Simple Fit to Theory but Simple Behavior with Silicon. 4.2.1. Small Contacts (R ∼ 20 nm). The behavior for silicon AFM tips in contact with silicon flats is extremely simple, with force curves that were flat in the noncontact region and showed a constant small pull-off (∼20 nN) over the complete range of RH (Figure 9). Glass shows similar behavior over most of the RH range, but large anomalies occur over a limited range of RH, usually 20-40% RH. These are characterized by a greatly increased pull-off force (Figure 8), a very long-range attractive force, and significant jump-to-contact effects. The anomalous force curves are broadly similar to those shown for larger contacts in Figure 11. The pull-off force is here defined as the vertical step on retraction from the maximum negative value to the (nonzero) value of the attractive force just


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Figure 8. Dependence of pull-off force on relative humidity for small contacts between a silicon AFM tip and a hydrophobic glass surface. The pull-off force is small and constant apart from anomalous large values over a limited range of RH. The behavior is not completely reproducible but is seen on both increasing and decreasing the RH. The associated force curves show evidence for long-range forces and jump-to-contact effects and are similar in appearance to those in Figure 11, obtained with larger contacts.

Figure 9. Dependence of pull-off force on relative humidity for small contacts between a silicon AFM tip and a hydrophobic silicon surface. The large anomaly seen with glass is absent. The pull-off force is almost constant over the entire range of RH and is similar to that seen with glass outside the anomalous region.

after pull-off. The exact range of RH over which the effects are seen on glass varies somewhat from sample to sample and is usually quite narrow, so that the effects are normally seen at only 1 or 2 values of RH and are occasionally missed altogether. However, they have been seen in several experiments, under conditions of both increasing and decreasing RH (Figure 8). The small residual adhesion, constant with increasing RH and best seen with silicon (Figure 9), can probably be explained by JKR contact mechanics if we assume that the contact is dry and completely free from capillary bridge effects. However, the experimental values of 10-20 nN are much lower than that calculated (63 nN) using a surface energy of 0.35 J m-2 for clean glass or silicon. The discrepancy probably arises because this surface energy is unrealistically large for HMDS-coated surfaces, and there are also uncertainties in tip size and geometry. 4.2.2. Larger Contacts (R ) 20-100 µm): Roughness Effects. The contacts of glass spheres with silicon substrates show constant pull-off and no anomalous behavior with RH. The behavior of glass spheres on glass

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Figure 10. Dependence of pull-off force on relative humidity for large contacts between glass spheres and hydrophobic glass surfaces. The pull-off force is almost constant except for anomalous large values over a small range of RH. Only one anomalous data point is shown, but the anomaly is typical of the behavior in several experiments. The associated force curve is also anomalous (see Figure 11). The anomaly disappears with repeated measurements at the same location and is not seen in a comparable experiment with a hydrophobic silicon surface. The residual pull-off values fall well below theoretical predictions for smooth spheres (Table 1).

Figure 11. Details of force curves between a glass sphere and a hydrophobic glass surface, showing typical anomalous behavior in the region of 10-40% relative humidity. The true tip-sample separation is plotted, after correction for the cantilever deflection. There is a large pull-off force, a longrange attractive force on both approach and retraction, and a small jump-to-contact. The anomaly declines steadily with successive measurements (curves 1-4) at the same location. The inset shows the long-range force (retraction curve 3) fitted almost perfectly to an exponential decrease with distance.

substrates is qualitatively similar to that with small contacts, with little change of pull-off force (∼200 nN) over most of the range of RH but large anomalous values of maximum adhesion (∼1000 nN) somewhere in the range of 10-40% RH (Figure 10), both with increasing and decreasing RH. The anomaly in Figure 10, although shown as an isolated point, is typical of several experiments. Details of force curves with this anomalous behavior are shown in Figure 11. Here the maximum adhesion, or maximum negative value, is the sum of the pull-off force (as defined earlier) and the long-range force just out of contact. For these larger contacts, it appears that the residual pull-off component is larger relative to the longrange attractive force and is nearly constant even over the anomalous region. In other words, for small contacts

Adhesion Forces between Glass and Silicon

the anomaly is predominantly due to an increased pulloff, plus some long-range attraction, but for large contacts the anomaly results mostly from the long-range attraction. The adhesion values measured in the “normal” regions (where the anomaly is absent) fall well below the predictions of theory for smooth contacts, as with hydrophilic surfaces (but now using JKR theory). The discrepancy is even more striking for these “dry” contacts. If we define a ratio of theoretical and experimental pull-off forces as did Schaeffer et al.,7 then the ratio for capillary bridges on hydrophilic surfaces (Laplace-Kelvin theory) varies from 3 for the smoother 20 µm spheres to as much as 20 for the larger, rougher spheres, using the data of Table 1. However, using JKR theory for dry hydrophobic contacts and 20 µm spheres, the ratio is in the region of 300. For comparison, Schaeffer et al. obtain ∼50 for dry contacts between spheres of 4 µm radius for a variety of materials. The much larger shortfall in adhesion for the dry contacts could be due to either (1) coatings reducing the interfacial energy or (2) the absence of liquid films, which can bridge the spaces between the smaller asperities and give an approximation to sphere-on-flat geometry for the smoother surfaces. Thus, whereas our wettable 20 µm spheres have in the region of 100 point contacts, the dry systems appear to have an order of magnitude fewer contacts under similar conditions. 4.2.3. The Cause of the Anomaly on Hydrophobic Surfaces. The long-range attractive force is apparent only on glass surfaces and over a limited range of RH. Figure 11 shows the detail of a set of force curves that illustrates particularly well the main properties. The attractive force has many of the characteristics expected of an electrostatic (Coulombic) effect: (1) It is never seen with silicon, a good conductor that might be expected to dissipate charges but otherwise be chemically rather similar to a glass surface (both are silica in their surface layers, to a first approximation, and both surfaces are treated with HMDS). (2) The anomaly disappears even on glass when force curves are repeated many times on the same spot, rather than adopting the usual practice of moving randomly between measurements (Figure 10). The effect reappears on moving to a new spot. In addition, the effects can sometimes be seen to decline in successive force curves of a single set, obtained over a period of less than a minute, both on approach and retraction (Figure 11). Both effects suggest a charge leaking away on repeated contact. (3) The effect is never seen at RH values greater than about 40%, where rapid discharge is possible. However, it is much more difficult to account fully for its absence at the lowest RH values also. (4) The effects generally are more striking and occur over a longer range for large glass spheres than for small contacts, as expected for more extended surfaces. The conclusion that the long-range attraction seen here is due to charging seems inescapable since no other surface forces operate over such a long range in air. It is of interest to study the exact dependence of this force on distance although, as we have seen, this is very dependent on contact geometry, and for sphere-on-flat geometry an inverse or inverse-square dependence might be expected (eqs 5 and 6). Neither is observed, and the inset to Figure 11 shows that the long-range force-separation curve in fact shows an extremely good fit to an exponential decay. We are unsure how to explain this at present. None of the force-distance relationships for different geometries given by Burnham et al.22 are of this form, but the force curves modeled were for smaller contacts and were much shorter in range than those under present consideration. Since glass is a good insulator, it seems reasonable to assume

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that the charge will be extremely localized and it might be more realistic to treat the system as a set of charged asperities or small patches rather than a uniformly charged sphere. For a full analysis, it must be remembered that the long-range force extends to separations that are 1-2 orders of magnitude larger than the average asperity heights and not very much smaller than the radii of the spheres themselves. For this reason, it would be useful to compare the behavior with that of the single-asperity contact of the bare tip, but data of comparable quality to that of Figure 11 are not available. To explain the origin of the charges and why they occur only over a small range of RH is even more problematical. It seems likely that the anomaly is linked in some way with the onset of capillary condensation at 20-40% RH. For hydrophilic surfaces, we expect patchy coverage at these intermediate humidities, with preferential condensation in cracks or pores in the glass microsphere (eq 1) or on the cleanest spots of the flat substrate. Eventually at high RH the film is continuous and the pull-off force increases. For the hydrophobic surfaces under present discussion, a continuous water film will never be formed even at high RH, so the pull-off force remains low. However, localized water films will form as favored by the surface chemistry or geometry. Lateral force AFM imaging should clearly reveal these films as low-friction areas, and thus studying the RH dependence of such images would be extremely interesting. Noncontact attractive forces may arise in a variety of ways; from van der Waals interactions, from patch charges, and from permanent dipoles or double layers.17,21,22 The first is too small and too short-range to be significant in these dry and rough systems. Either of the other mechanisms might explain the long-range forces, although in general surface charge densities from patch charges are much smaller than those from double layers. A quantitative simulation of the observed long-range forces, based on such effects in the surface water film appearing at 20-40% RH, appears to be beyond our reach at present since it would require a suitable explanation for the forcedistance dependence and a more detailed knowledge of surface chemistry and charge densities. For example, it is uncertain whether the polarity of an oriented film of pure water is sufficient to produce the effects or whether other factors such as dissolved detergents or specific chemical groups on the surface, or even direct chemical bonding between the two surfaces (see below), must necessarily be involved. The long-range anomaly is probably a dynamic balance between competing effects rather than a true equilibrium phenomenon, hence its transient and poorly reproducible appearance. For example, it might be argued that if a patch charge mechanism were responsible, its effects would be strongest at intermediate RH where the coverage is patchy rather than at high saturation where the surface condition might be more uniform in terms of surface chemistry and work function. Conversely, the development of charged or dipole layers might be greatest at high RH but be outweighed by the rapid discharging in a humid atmosphere. 4.3. Other Interpretations of the RH Dependence and Its Anomalous Behavior. The explanations given above are somewhat incomplete and are by no means the only possible ones. However, we believe that they are the most plausible ones for our particular set of experimental conditions. Tyrrell2 and Tyrrell and Cleaver23 have observed a similar RH dependence of adhesion, noted the crucial effects of roughness and surface treatment, and observed anomalous RH effects on glass surfaces. Anoma-


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lies of adhesion at some intermediate value of RH have also been seen by others,14,15 but in no case has a full explanation been given. The parallel with the work of Tyrrell and Cleaver is particularly close, and the same supply of glass microspheres was used in both studies. These authors contrasted the behavior with soda-lime glass and quartz plates, whereas we have emphasized the differences between glass and silicon plates and between hydrophilic and hydrophobic surfaces. However, there were other significant differences in both experimental conditions and the observations made: (1) Anomalous effects were seen on alcohol or detergent-cleaned glass surfaces but not on clean quartz. By contrast, we see anomalies only on glass surfaces with specifically hydrophobic coatings, not on freshly cleaned hydrophilic glass. (2) Cantilever spring constants and force curve approach speeds were generally rather higher than those we used. (3) Anomalous effects were seen with successive force curves on one spot, conditions that we found abolished the long-range forces. (4) The long-range force was repulsive and slightly shorter in range than the attractive force we describe. (5) The effects were seen only on decreasing RH, whereas we see them going both ways. (6) Force curves obtained at high RH showed evidence for persistent liquid bridges at large separations with no abrupt pull-off. The authors attributed this to a mobile surface film feeding the liquid bridge. We have only rarely seen behavior of this type; normally pull-off effects were simple. Tyrrell and Cleaver did not favor an electrostatic explanation for their anomalous repulsive force. This was supported by the observation that an R-source placed close to the particle and surface did not abolish the effect. Coating the glass with gold abolished the effect, but this result might be confusing because the treatment simultaneously alters the surface chemistry and the electrical conductivity. For the anomalous pull-off force, they favored a mechanism specific to the reactive cations on the surface of soda-lime glass, since the effects were not seen with quartz. This mechanism might involve a sintering or crystallization process in the water film. However, the mechanism appears to require that the anomalies are seen only in reducing RH after exposure to high RH. Also, explaining the very long-range (∼300 nm) repulsion was still problematical. As in the present work, Tyrrell and Cleaver, after failing to obtain a satisfactory curve fit with the more usual power laws expected for electrostatic effects, found that the repulsive force was a good exponential fit. According to Tyrrell,2 several authors have observed or predicted forces decaying exponentially with distance for a variety of particulate systems, but only for repulsive forces. The exact mechanism for the anomalous humidity effects is thus still far from clear, and different mechanisms may be operating under the rather different experimental conditions of the present work and that of Tyrrell and Cleaver. It seems certain that the onset of capillary condensation and the simultaneous presence of charged groups or dipoles on the surface must be involved in some way, but determining whether true chemical reactions at the surface are involved will require a range of further experiments with meticulous attention to the chemical state of the prepared surfaces. In general, the hydrophobic, low-energy surfaces will be more stable to modification or contamination than the hydrophilic, high-energy surfaces. Whatever the detailed mechanism, such studies are important because of the widespread occurrence of electrostatic charging or sintering effects in powder technology and commercial processes such as xerography.

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In addition, many commercially important powders such as silica aerogels (fumed silica) and titania are routinely produced in coated and uncoated forms, and there is strong evidence that the forces between such particles have much behavior in common with that of the glass ballotini and treated and untreated surfaces in the model studies described above. 5. Conclusions This work confirms the widely accepted view that in determining the magnitude of the adhesion between particles in air and its dependence on RH, the particle size, roughness, and surface chemistry are of crucial importance. In a systematic AFM study of force-distance curves, silicon AFM tips, glass microspheres of different sizes, and flat glass and silicon treated to give reproducible hydrophilic or hydrophobic surfaces have provided useful models for “real” powder particles. Small (single-asperity) contacts have the simplest behavior, larger contacts between hydrophilic surfaces give adhesion that falls below the predictions of capillary bridge theory, and large contacts between hydrophobic surfaces or rough surfaces give adhesion values even more at variance with the predictions of contact mechanics theory. This confirms that a multiasperity contact model is much more realistic than a sphere-flat or spheresphere model for all extended contacts between practical surfaces in air. The dependence of adhesion on RH reported in this work for contacts of different sizes and different surface treatments confirms trends observed many times by other workers, but in a more systematic way. Small hydrophilic contacts show a large and monotonic increase of adhesion with RH. Larger hydrophilic contacts show a similar, but less pronounced, trend. These observations are more consistent with capillary bridge theory using a cone-onflat geometry rather than a sphere-on-flat geometry and again suggest that for extended surfaces the multiasperity model is applicable. The dependence of adhesion on RH for hydrophobic surfaces is very distinctive and quite different from that for hydrophilic surfaces. This again confirms a trend noted several times in the literature, that the RH dependence of adhesion is a possible diagnostic tool for distinguishing hydrophobic and hydrophilic surfaces. The overall trend is for the adhesion to be small and constant over the complete range of RH, and it can probably be described by JKR contact mechanics after allowing for asperity contacts. Superposed on this baseline is a large and anomalous adhesion that is very restricted in appearance, occurs only over a small range of RH, and is never seen on silicon. Some effect of this type has been commented on several times in the literature, but it is by no means certain that the underlying cause is always the same. Surface water films, dipolar materials or reactive chemical groups such as in the surface of soda-lime glass, and long-range Coulombic forces all seem to be implicated. One feature that must be explained is that similar effects have been seen with both clean soda-lime glass and glass treated to render it hydrophobic, and thus careful attention to the surface chemistry will be necessary to clarify the mechanism operating. The findings are highly relevant to important commercial cohesive powders such as zeolites, aerogels (fumed silica), and titania. Many of these materials are prepared with different coatings that drastically alter their adhesion properties, such as susceptibility to humidity effects, electrostatic charging, or reactions producing sintering.

Adhesion Forces between Glass and Silicon

For example, we have found a very large RH dependence in cohesive zeolite samples and long-range charging effects in fumed silica that are not unlike the effects described above with glass. These effects will be described elsewhere. In the meantime, the model systems described here have greatly assisted in elucidating the basic surface forces and adhesion mechanisms involved. Acknowledgment. This work was supported by a 4-year grant from IFPRI (International Fine Particle

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Research Institute), No. FRR 34-04. We thank Professor D. Geldart, Dr. A. Verlinden, and others in the Department of Chemical Engineering, University of Bradford, for supplying some samples, for helpful discussions, and for advice with the design of the humidity chamber. We also thank Dr. J. Tyrrell for helpful discussions and for making material from his Ph.D. thesis available. LA0259196