Effects of contact geometry on pull-off force measurements with a colloidal probe

This paper examines the effects of contact geometry on the pull-off (adhesion) force between a glass sphere (colloidal probe) and a silicon wafer in an environment with controlled relative humidity. An atomic force microscope is used to measure the pull-off force between the colloidal probe and the sample mounted at different tilt angles. The results show that the measured pull-off force is very sensitive to the tilt angle. Through the use of a newly developed direct scanning method, the exact contact geometry is determined for the zero-tilt angle case. The obtained digital image is then rotated to determine the contact geometry for the cases with other tilt angles. A detailed examination of the contact geometry, along with a magnitude analysis of the capillary force, suggests that the adhesion is most likely dominated by the capillary force from the meniscus formed between the probe and the sample. The strong dependence of the adhesion on the tilt angle may result from the change of meniscus dimensions associated with the probe-sample separation, which in turn is controlled by the highest peak on the probe sphere. Our observation emphasizes the combined role of microsurface shape near the contact and nanoroughness within the contact in determining the colloidal probe pull-off force and also microadhesion force in general.     

Effect of contact geometry on the pull-off force evaluated under high-vacuum and humid atmospheric conditions

The effect of condensed water on pull-off forces under high vacuum (HV) and 0 to 83% relative humidity (RH) N2 atmospheric conditions was evaluated for different contact geometries using atomic force microscopy (AFM). The pull-off force was measured using two types of contact geometry: contact between hemispherical asperities and a flat silicon probe on an AFM cantilever (called a spherical-flat contact) and between a flat silicon substrate and a flat nickel probe on an AFM cantilever (called a flat-flat contact). The hemispherical asperities were fabricated using a focused ion beam (FIB) system, and each peak had a radius of curvature of between 70 and 610 nm. The flat nickel probe was fabricated by friction-induced wear. Measurement results showed that for the spherical-flat contact the pull-off force was proportional to the radius of curvature of the asperity peak and was slightly lower in HV than in humid 14% RH N2. For the flat-flat contact in HV, with increasing contact time, the pull-off force increased in HV but decreased in humid 62 and 83% RH N2. The pull-off force in HV was lower than that in humid N2 when the contact time was less than 10 s but was higher when the contact time was longer than 30 s. The estimated adhesion force based on the Laplace pressure from the contact geometry agreed reasonably well with the measured pull-off force.     

An improved meniscus surface model for contacting rough surfaces

Based on the Extended-Maugis-Dugdale (EMD) elastic theory, a single asperity capillary meniscus model considering asperity deformation due to both contact and adhesive forces was developed. Specifically included in the single asperity meniscus model was the solid surface interaction inside the contact area. Subsequently, the single asperity model was coupled with a statistical roughness surface model to develop an improved meniscus surface model applicable to a wide-range of humidity levels and adhesion parameter values. Simulations were performed using typical surfaces found in microelectromechanical systems (MEMS) and magnetic storage hard disk drives to examine the effects of surface roughness and relative humidity. It was found that smoother surfaces give rise to higher adhesive and pull-off forces, and at higher relative humidity levels, the capillary force governs the adhesive behavior. As the humidity decreases, the solid surface interaction increases and needs to be included in the total meniscus adhesion. By integrating the adhesive force-displacement curves, the adhesion energy per unit area was calculated for MEMS surfaces and favorably compared with reported experimental data.     

Stick slip contact mechanics between dissimilar materials: effect of charging and large friction

Measurements of the contact radius as a function of applied force between a mica surface and a silica surface (mica/silica) in air are reported. The load/unload results show that the contact radius generally increases with applied force. Because of the presence of charging due to contact electrification, both a short-range van der Waals adhesion force and longer-range electrostatic adhesive interaction contribute to the measured force. The results indicate that approximately 20% of the pull-off force is due to van der Waals forces. The contact radius versus applied force results can be fit to Johnson-Kendall-Roberts (JKR) theory by considering that only the short-range van der Waals forces contribute to the work of adhesion and subtracting a constant longer-range electrostatic force. Also, an additional and unexpected step function is superimposed on the contact radius versus applied force curve. Thus, the contact diameter increases in a stepped dependence with increasing force. The stepped contact behavior is seen only for increasing force and is not observed when symmetric mica/mica or silica/silica contacts are measured. In humid conditions, the contact diameter of the mica/silica contact increases monotonically with applied force. Friction forces between the surfaces are also measured and the shear stress of a mica/silica interface is 100 times greater than the shear stress of a mica/mica interface. This large shear stress retards the increase in contact area as the force is increased and leads to the observed stepped contact mechanics behavior.     

Volume of a nanoscale water bridge

Water bridges formed through capillary condensation at nanoscale contacts first stretch and then break during contact rupture. Atomic force microscopy (AFM) pull-off experiments performed in air with hydrophilic tips and samples show that stretched nanoscopic water bridges are in mechanical equilibrium with the external pull-off force acting at the contact but not in thermodynamic equilibrium with the water vapor in air. The experimental findings are explained by a theoretical model that considers constant water volume and decrease of water meniscus curvature during meniscus stretching. The model predicts that the water bridge breakup distance will be roughly equal to the cubic root of the water bridge volume. A thermodynamic instability was noticed for large water bridges formed at the contact of a blunt AFM tip (curvature radius of 400 nm) with a flat sample. In this case, experiments showed rise and stabilization of the volume of the water at the contact in about 1 s. For sharp AFM tips (curvature radius below 50 nm), the experiments indicated that formation of stable water bridges occurs in a much shorter time (below 5 ms).     

On the adhesion between fine particles and nanocontacts: an atomic force microscope study

In this study we measured the adhesion forces between atomic force microscope (AFM) tips or particles attached to AFM cantilevers and different solid samples. Smooth and homogeneous surfaces such as mica, silicon wafers, or highly oriented pyrolytic graphite, and more rough and heterogeneous surfaces such as iron particles or patterns of TiO2 nanoparticles on silicon were used. In the first part, we addressed the well-known issue that AFM adhesion experiments show wide distributions of adhesion forces rather than a single value. Our experiments show that variations in adhesion forces comprise fast (i.e., from one force curve to the next) random fluctuations and slower fluctuations, which occur over tens or hundreds of consecutive measurements. Slow fluctuations are not likely to be the result of variations in external factors such as lateral position, temperature, humidity, and so forth because those were kept constant. Even if two solid bodies are brought into contact under precisely the same conditions (same place, load, direction, etc.) the result of such a measurement will often not be the same as that of the previous contact. The measurement itself will induce structural changes in the contact region, which can change the value for the next adhesion force measurement. In the second part, we studied the influence of humidity on the adhesion of nanocontacts. Humidity was adjusted relatively fast to minimize tip wear during one experiment. For hydrophobic surfaces, no signification change in adhesion force with humidity was observed. Adhesion force versus humidity curves recorded with hydrophilic surfaces either showed a maximum or continuously increased. We demonstrate that the results can be interpreted with simple continuum theory of the meniscus force. The meniscus force is calculated based on a model that includes surface roughness and takes into account different AFM tip (or particle) shapes by a two-sphere model. Experimental and theoretical results show that the precise contact geometry has a critical influence on the humidity dependence of the adhesion force. Changes in tip geometry on the sub-10-nm length scale can completely change adhesion force versus humidity curves. Our model can also explain the differences between earlier AFM studies, where different dependencies of the adhesion force on humidity were observed.     

Capillary force in atomic force microscopy

Under ambient conditions, a water meniscus generally forms between a nanoscale atomic force microscope tip and a hydrophilic surface. Using a lattice gas model for water and thermodynamic integration methods, we calculate the capillary force due to the water meniscus for both hydrophobic and hydrophilic tips at various humidities. As humidity rises, the pull-off force rapidly reaches a plateau value for a hydrophobic tip but monotonically increases for a weakly hydrophilic tip. For a strongly hydrophilic tip, the force increases at low humidities (<30%) and then decreases. We show that mean-field density functional theory reproduces the simulated pull-off force very well.     

Pull-off force measurements between rough surfaces by atomic force microscopy

Direct measurements of the pull-off (adhesion) forces between pharmaceutical particles (beclomethasone dipropionate, a peptide-type material, and lactose) with irregular geometry and rough polymeric surfaces (series of polypropylene coatings, polycarbonate, and acrylonitrile-butadiene-styrene) were carried out using the atomic force microscope. These measurements showed that roughness of the interacting surfaces is the significant factor affecting experimentally measured pull-off forces. A broad distribution of pull-off force values was noted in the measurements, caused by a varying adhesive contact area for a particle located on rough substrate. The possibility of multiple points of contact between irregularly shaped pharmaceutical particles and substrate surfaces is demonstrated with nanoindentations of the particle in a fluoro-polymer film. Force-distance curves showing the "sawtooth" pattern are additional evidence that particles make contact with substrates at more than one point. Reduced adhesion of 10- to 14-microm-diameter lactose and peptide material particles to the polypropylene coatings with a roughness of 194 nm was found in this study. Similar pull-off force versus roughness relationships are also reported for the model spherical particles, silanized glass particle with a size of 10 microm and polystyrene particle with a diameter of 9 microm, in contact with polypropylene coatings of varying roughness characteristics. It was found that the model recently proposed by Rabinovich et al. (J. Colloid Interface Sci. 232, 1-16 (2000)) closely predicts the pull-off forces for glass and lactose particles. On the other hand, the adhesion of the peptide material and polystyrene particle to polypropylene is underestimated by about an order of magnitude with the theoretical model, in which the interacting substrates are treated as rigid materials. The underestimate is attributed to the deformation of the peptide material and polystyrene particles.     

Atomic-scale roughness effect on capillary force in atomic force microscopy

We study the capillary force in atomic force microscopy by using Monte Carlo simulations. Adopting a lattice gas model for water, we simulated water menisci that form between a rough silicon-nitride tip and a mica surface. Unlike its macroscopic counterpart, the water meniscus at the nanoscale gives rise to a capillary force that responds sensitively to the tip roughness. With only a slight change in tip shape, the pull-off force significantly changes its qualitative variation with humidity.     

Experimental humidity dependency of small particle adhesion on silica and titania

The humidity present in ambient atmosphere affects the adhesion of small particles by causing capillary bridge formation between the particle and the surface. Even in moderate relative humidities this, usually attractive, force can have a significant effect on adhesion behaviour of micro and sub-micro particles. We have directly measured the pull-off forces of initially adhered oxide particles on oxide surfaces with atomic force microscope in controlled atmosphere with adjustable humidity. We demonstrate the effect of the surface roughness resulting in two different regions of capillary formation and the particle shape having a strong effect on the humidity dependency of adhesion. The experimental results are explained by theoretical framework.     

Using the Dugdale approximation to match a specific interaction in the adhesive contact of elastic objects

In the Maugis-Dugdale model of the adhesive contact of elastic spheres, the step cohesive stress sigma(0) is arbitrarily chosen to be the theoretical stress sigma(th) to match that of the Lennard-Jones potential. An alternative and more reasonable model is proposed in this paper. The Maugis model is first extended to that of arbitrary axisymmetric elastic objects with an arbitrary surface adhesive interaction and then applied to the case of a power-law shape function and a step cohesive stress. A continuous transition is found in the extended Maugis-Dugdale model for an arbitrary shape index n. A three-dimensional Johnson-Greenwood adhesion map is constructed. A relation of the identical pull-off force at the rigid limit is required for the approximate and exact models. With this requirement, the stress sigma(0) is found to be k(n)Deltagamma/z(0), where k(n) is a coefficient, Deltagamma the work of adhesion, and z(0) the equilibrium separation. Hence we have sigma(0) = 0.588Deltagamma/z(0), especially for n=2. The prediction of the pull-off forces using this new value shows surprisingly better agreement with the Muller-Yushchenko-Derjaguin transition than that using sigma(th) = 1.026Deltagamma/z(0), and this is true for other values of shape index n.     

Kinetics of liquid annulus formation and capillary forces

The dependence of the capillary adhesion force F(cap) between a silica microsphere and a flat silica surface versus a time period t of the samples' contact (i.e., dwell-in time) is experimentally investigated using atomic force microscopy (AFM). F(cap) was found to be dependent on t if the humidity was >30-35%. This dependence is exponential, with decay (characteristic) times of ～10 s. It is suggested that the kinetics of the adhesion process are related to the growth of the water annulus between surfaces. Furthermore, we propose that the growth kinetics has two components: (1) water vapor diffusion from the surrounding humid media into the gap between samples and (2) water drainage from the gap. The theory of diffusion through thin pores (i.e., gaps) is developed, and analytical formulas are obtained for the dependence of the meniscus radius r versus time t. However, the experimental dependence of F(cap) versus t and, consequently, r versus t obtained in this article disagrees with the theoretical prediction by several orders of magnitude. Similar results were obtained from the literature data for capillary forces between an AFM cantilever tip and a flat surface. Possible reasons for the deviation from diffusion theory are suggested: surface and Knudsen regimes of vapor diffusion, nonsteady state vapor flow, and tortuosity. Taking into account the viscous drainage of water from the multilayer gap can explain the experimental kinetics of bridge formation, but only if the viscosity of the adjacent multilayer of water is several orders of magnitude larger than the bulk viscosity.     

Mechanism of adhesion between polymer fibers at nanoscale contacts

Adhesive force exists between polymer nano/microfibers. An elaborate experiment was performed to investigate the adhesion between polymer nano/microfibers using a nanoforce tensile tester. Electrospun polycaprolactone (PCL) fibers with diameters ranging from 0.4-2.2 μm were studied. The response of surface property of electrospun fiber to the environmental conditions was tracked by FTIR and atomic force microscopy (AFM) measurements. The effect of temperature on molecular orientation was examined by wide angle X-ray diffraction (WAXD). The adhesive force was found to increase with temperature and pull-off speed but insensitive to the change of relative humidity, and the abrupt increase of adhesion energy with temperature accompanied by a reduced molecular orientation in the amorphous part of fiber was observed. Results show that adhesion is mainly driven by van der Waals interactions between interdiffusion chain segments across the interface.     

Nanoparticle flotation collectors: mechanisms behind a new technology

This is the first report describing a new technology where hydrophobic nanoparticles adsorb onto much larger, hydrophilic mineral particle surfaces to facilitate attachment to air bubbles in flotation. The adsorption of 46 nm cationic polystyrene nanoparticles onto 43 μm diameter glass beads, a mineral model, facilitates virtually complete removal of the beads by flotation. As little as 5% coverage of the bead surfaces with nanoparticles promotes high flotation efficiencies. The maximum force required to pull a glass bead from an air bubble interface into the aqueous phase was measured by micromechanics. The pull-off force was 1.9 μN for glass beads coated with nanoparticles, compared to 0.0086 μN for clean beads. The pull-off forces were modeled using Scheludko's classical expression. We propose that the bubble/bead contact area may not be dry (completely dewetted). Instead, for hydrophobic nanoparticles sitting on a hydrophilic surface, it is possible that only the nanoparticles penetrate the air/water interface to form a three-phase contact line. We present a new model for pull-off forces for such a wet contact patch between the bead and the air bubble. Contact angle measurements of both nanoparticle coated glass and smooth films from dissolved nanoparticles were performed to support the modeling.     

Determination of solid surface tension from particle-substrate pull-off forces measured with the atomic force microscope

Atomic force microscopy (AFM) is capable of solid surface characterization at the microscopic and submicroscopic scales. It can also be used for the determination of surface tension of solids (gamma) from pull-off force (F) measurements, followed by analysis of the measured F values using contact mechanics theoretical models. Although a majority of the literature gamma results was obtained using either Johnson-Kendall-Roberts (JKR) or Derjaguin-Muller-Toporov (DMT) models, re-analysis of the published experimental data presented in this paper indicates that these models are regularly misused. Additional complication in determination of gamma values using the AFM technique is that the measured pull-off forces have poor reproducibility. Reproducible and meaningful F values can be obtained with strict control over AFM experimental conditions during the pull-off force measurements (low humidity level, controlled and known loads) for high quality substrates and probes (surfaces should be free of heterogeneity, roughness, and contamination). Any probe or substrate imperfections complicate the interpretation of experimental results and often reduce the quality of the generated data. In this review, surface imperfection in terms of roughness and heterogeneity that influence the pull-off force are analyzed based upon the contact mechanics models. Simple correlations are proposed that could guide in selection and preparation of AFM probes and substrates for gamma determination and selection of loading conditions during the pull-off force measurements. Finally, the possibility of AFM measurements of solid surface tension using materials with rough surfaces is discussed.     

Chemical force microscopy study of adhesive properties of polypropylene films: influence of surface polarity and medium

The adhesive properties of untreated and corona treated polypropylene (PP) films were studied in polar (water) and nonpolar (hexadecane) liquid medium by using chemical force microscopy. A gold-coated colloidal probe was sequentially modified with self-assembled monolayers (SAMs) of omega-functionalized alkanethiols. The same colloidal probe was used for the force measurements, to avoid influence of determination accuracy of the spring constant and sphere radius on the obtained results. The thermodynamic work of adhesion was determined from the measured pull-off force using the Johnson-Kendall-Roberts (JKR) adhesion theory. Rabinovich's model was applied for the consideration of an effect of roughness when calculating the work of adhesion. It was found that the work of adhesion correlates with the hydrophilic properties of the PP surface and SAMs as well as with the polarity of the liquid medium. The observed correlations agree well with those found for the work of adhesion calculated from contact angle measurement.     

Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius

Elastic spheres in contact deform around the contact region, due to intermolecular interaction forces. The deformed contacting surfaces change the distance between interacting molecules that in turn alters the force of interaction. Thus, the contact behavior of elastic spheres constitutes a nonlinear mathematical problem that defies the traditional analytical methods for general solution. Efficient computational techniques have enabled a detailed study of adhesive contact behavior of elastically deformable spheres with self-consistent solutions of a nonlinear integral governing equation. The present work extends the previous computational analysis to the quantities of practical interests such as the pull-off force and the radius of contact area. Trends of variations in the pull-off force as physical properties change are examined. Computationally determined radial positions as stress condition indicators suggest that the concept of contact radius is not clearly defined in the literature and can be confusing. It seems that some contact mechanics models would be consistent with the definition of the edge of contact area as the radial position for the local surface stress to change from compression to tension, whereas others would rather assume the contact radius as the radial position for the local tensile stress to reach its peak. The substantial quantitative deviation of self-consistently computed contact radius from the DMT model prediction suggests that models based on the assumption of a well-defined contact area having a constant gap may not be appropriate when describing cases of small values of Tabor's parameter. Copyright 2001 Academic Press.     

General solution to two-dimensional nonslipping JKR model with a pulling force in an arbitrary direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Deltagamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.