A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.     

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.     

Correction of random surface roughness on colloidal probes in measuring adhesion

Atomic force microscopes (AFM) are commonly used to measure adhesion at nanoscale between two surfaces. To avoid uncertainties in the contact areas between the tip and the surface, colloidal probes have been used for adhesion measurements. We measured adhesion between glass spheres and silicon (100) surface using colloidal probes of different radii under controlled conditions (relative humidity of < 3%, temperature of 25 +/- 1 degrees C). Results showed that the adhesion forces did not correlate with the radii of the spheres as suggested by elastic contact mechanics theories. Surface roughness and random surface features were found on the surfaces of the colloidal probes. We evaluated various roughness parameters, Rumpf and Rabinovich models, and a load-bearing area correction model in an attempt to correct for the roughness effects on adhesion, but the results were unsatisfactory. We developed a new multiscale contact model taking into account elastic as well as plastic deformation in a successive contacting mode. The new model was able to correct for most of the surface roughness features except for surface ridges with sharp angular features, limited by the spherical asperity assumption made in the model.     

Nano‐adhesion and friction of multi‐asperity contact: a molecular dynamics simulation study

In our study, the contact and sliding processes between a flat plate and a substrate with multiple asperities are studied by molecular dynamics (MD) simulations, and how the number of asperities and asperity height influence the adhesion force and friction force are investigated thoroughly. The normal force versus the separation distance curve during contact processes is analyzed completely and from which the van der Waals (vdW) force (F_vdW) and the adhesion force (F_adh) are obtained and compared with the Katainen model. The adhesion force and the friction force increase linearly as the increase of the number of asperities (i.e. real contact area) with same asperity height. With the identical number of asperities, the adhesion force and the friction force decrease with the increase of the asperity height at first. However the reductions of the adhesion force and the friction force become less obvious, when the asperity height is larger than a critical value (20 Å for our simulation parameters). Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of the adhesion properties of inorganic materials with high surface energies

With the aim of checking the validity of methods for characterizing the adhesion between inorganic materials with high surface energies, the properties of the adhesion between an inorganic material (indium tin oxide (ITO)) and model surfaces with various surface energies (Cl-, NH2-, CH(3)-, and CF3-functionalized surfaces) were evaluated using atomic force microscopy (AFM) and the Johnson-Kendall-Roberts (JKR) apparatus. For this purpose, the AFM tip and the JKR lens were modified with ITO using radio frequency (rf) magnetron sputtering. The work of adhesion between the ITO coating and each model surface was estimated using AFM and the JKR apparatus and compared with the result obtained from contact angle measurements. The adhesion forces determined from the force-displacement curves (AFM) were found to agree with the predictions of the Derjaguin-Muller-Toporov (DMT) theory. The JKR equation used in the interpretation of the JKR experiments was modified by taking into account the differences between the surface and bulk moduli of the ITO-coated poly(dimethylsiloxane) (PDMS) lens. The ratio of the surface modulus to the bulk modulus we used in this modified JKR equation was obtained by determining the slope of the attracting part of the force-displacement curve. The values of the work of adhesion calculated using the modified JKR equation were also found to agree with the values obtained from contact angle measurements. We conclude that the two methods using AFM and the JKR apparatus can be used in the evaluation of the work of adhesion between inorganic materials with high surface energies such as metal and metal oxide surfaces.     

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.     

Modeling of ultralyophobicity: suspension of liquid drops by a single asperity

With the aim of understanding the underlying physical phenomenon associated with utlralyophobic (or super repellent) surfaces, model studies have been performed on single asperities of different size and shape. A small liquid drop was deposited on top of each model asperity, and liquid was sequentially added. If the advancing contact angle was sufficiently large, it was possible to suspend large drops atop asperities with an apparent contact angle approaching 180 degrees. If more and more liquid was added, eventually the suspended drops collapsed. Roughening the surface of the asperities further bolstered suspension. Using an analysis that accounts for both capillary forces and the influence of gravity, the critical suspension volume was correctly predicted for each liquid/asperity combination.     

The deformation and adhesion of randomly rough and patterned surfaces

Using a surface forces apparatus (SFA) and an atomic force microscope (AFM) we have studied the effects of surface roughness (root-mean-square (RMS) roughness between 0.3 and 220 nm) on the "contact mechanics", which describes the deformations and loading and unloading adhesion forces, of various polymeric surfaces. For randomly rough, moderately stiff, elastomeric surfaces, the force-distance curves on approach and separation are nearly reversible and almost perfectly exponentially repulsive, with an adhesion on separation that decreases only slightly with increasing RMS. Additionally, the magnitude of the preload force is seen to play a large role in determining the measured adhesion. The exponential repulsion likely arises from the local compressions (fine-grained nano- or submicron-scale deformations) of the surface asperities. The resulting characteristic decay lengths of the repulsion scale with the RMS roughness and correlate very well with a simple finite element method (FEM) analysis based on actual AFM topographical images of the surfaces. For "patterned" surfaces, with a nonrandom terraced structure, no similar exponential repulsion is observed, suggesting that asperity height variability or random roughness is required for the exponential behavior. However, the adhesion force or energy between two "patterned" surfaces fell off dramatically and roughly exponentially as the RMS increased, likely owing to a significant decrease in the contact area which in turn determines their adhesion. For both types of rough surfaces, random and patterned, the coarse-grained (global, meso- or macroscopic) deformations of the initially curved surfaces appear to be Hertzian.     

On scale dependence in friction: transition from intimate to monolayer-lubricated contact

Scale dependence in friction is studied in the present paper using the newly developed mesoscale friction tester (MFT). A transition in frictional shear strength from several hundreds of MPa to several tens of MPa was observed over a very limited range of contact radii (20-30 nm) in both ambient and dry environments. Thus, a single apparatus has been able to establish these two limits which are consistent with the values previously obtained from friction experiments using atomic force microscopy (AFM) and the surface force apparatus (SFA), respectively. Consequently, it is hypothesized here that a shear strength in the hundreds of MPa results from intimate contact (solid-solid) and a shear strength in the tens of MPa results from a monolayer-lubricated contact. Furthermore, both the probe size and the normal pressure govern the interfacial conditions in the contact zone and it is these conditions, rather than the nominal environment, which in turn determine the resulting shear strengths. A continuum analysis based on the Lifshitz theory for van der Waals interactions is used to explain the quantized shear strengths which were obtained from our experiments and previous AFM and SFA friction experiments. This quantized friction behavior [J.N. Israelachvili, P.M. McGuiggan, A.M. Homola, Science 240 (1988) 189] results from the discrete separation due to the different interfacial conditions that can arise between two sliding surfaces. The consistency between the analysis and the experimental results shows that this analysis is applicable for nonwear friction with single asperity contact.     

Hamaker constants in integrated circuit metalization

A new method for determining Hamaker constants was examined for materials of interest in integrated circuit manufacture. An ultra-high vacuum atomic force microscope and an atomic force microscope operated in a nitrogen environment were used to measure the interaction forces between metals, dielectrics, and barriers used during the metalization portion of integrated circuit manufacturing. The materials studied included copper, silver, titanium nitride, silicon dioxide, poly(tetrafluoroethylene), and parylene-N. Spheres coated with a material of interest were mounted on AFM cantilevers and brought into contact with substrates of interest. The interaction force was measured as the cantilever approached the substrate but before the two surfaces came into contact, and also when the particle was pulled out of contact with the substrate. The Hamaker constant calculation from the contact measurement is based on an adhesion model that quantifies the contribution of geometrical, morphological and mechanical properties of materials to the measured adhesion force. Hamaker constants determined with this new approach were compared with values found by using the Derjaguin approximation for a sphere to describe the interaction force as the cantilever approaches the surface. Both approaches produced similar values for most of the systems studied, with variations of less than 10%.     

Experimental investigation of the adhesion force of single and double-layer coatings on MEMS surfaces

Adhesion force is one of the most important factors in microelectromechanical systems (MEMS), especially for microassembly. It depends on operating conditions and is affected by the contact area. In this study, the adhesion force between MEMS materials and AFM tips was analysed using AFM's point-mode spectroscopy. The aim was to study the effectiveness of various coatings in MEMS adhesion surfaces. For this purpose, five silicon surfaces were used, four of which were coated, and one was noncoated. Two of them were deposited by single-layer coating (Au and Ag). The other two were deposited by double-layer coating (TiO₂/Au, TiO₂/Ag) on a Si (1 0 0) substrate. The depositing was accomplished by the thermal evaporation method. Composite materials and analysis were reviewed by observing the SEM image. The experimental results showed that the method of deposition helped to decrease the adhesion force between the probe tip and the surface of the specimens, and double-layer coating had stronger effect on decreasing the adhesion force than the single-layer coating.     

Measurement of polyamide and polystyrene adhesion with coated-tip atomic force microscopy

This work presents atomic force microscopy (AFM) measurements of adhesion forces between polyamides, polystyrene and AFM tips coated with the same materials. The polymers employed were polyamide 6 (PA6), PA66, PA12 and polystyrene (PS). All adhesion forces between the various unmodified or modified AFM tips and the polymer surfaces were in the range -1.5 to -8 nN. The weakest force was observed for an unmodified AFM tip with a PS surface and the strongest was between a PS-coated tip and PS surface. The results point to both the benefits and drawbacks of coated-tip AFM force-distance measurements. Adhesion forces between the two most dissimilar (PA6-PS and PA66-PS) materials were significantly asymmetric, e.g., the forces were different depending on the relative placement of each polymer on the AFM tip or substrate. Materials with similar chemistry and intermolecular interactions yielded forces in close agreement regardless of placement on tip or substrate. Using experimental forces, we calculated the contact radii via four models: Derjaguin, Muller, and Toporov; Johnson, Kendall, and Roberts; parametric tip-force-distance relation; and a square pyramid-flat surface (SPFS) model developed herein. The SPFS model gave the most reasonable contact tip radius estimate. Hamaker constants calculated from the SPFS model using this radius agreed in both magnitude and trends with experiment and Lifshitz theory.     

Evaluation of nanotribological behavior of amorphous polystyrene: The macromolecular weight effect

Tribological testing of polymers is of prime importance in many industrial applications. Silicon nitride AFM tips have been used to mimic the contact between amorphous polystyrene surfaces and a hard asperity, which is useful in understanding of how a multitude of asperities behave in a macroscopic contact. In this study, the adhesion force and the friction force of four PS molecular weights were measured and the average contact pressure was calculated by using the JKR contact theory. The nanotribological behavior of polystyrene showed a dependence on macromolecular weight with varying applied normal force and sliding velocity. The study indicates that the length of polymer chains noticeably influences the tribological behavior of amorphous polystyrenes. Mechanisms governing such behavior differences were ascribed to energy dissipating modes.     

Capillary forces: influence of roughness and heterogeneity

A formalism is described to calculate capillary forces between solid surfaces analytically. Assumptions are that the liquid menisci (1) have a much larger extension parallel to the gap than normal and (2) are formed by capillary condensation and are in equilibrium with the vapor. To calculate capillary forces, first the gap between the two surfaces is described by a height distribution function. Roughness is considered with an asperity distribution function. Both distributions can at least in principal be measured by light, electron, or atomic force microscopy or grazing incidence X-ray reflectivity. The total capillary force versus distance or vapor pressure is obtained by a convolution of both distributions and an integration. The formalism is applied to calculate the capillary force between rough spherical particles. In addition, a method to consider surface heterogeneity is suggested.     

Criteria for ultralyophobic surfaces

Very rough surfaces can suspend small liquid drops and produce very large contact angles. This behavior often is referred to as ultralyophobicity or super repellency. It is proposed that two criteria must be met to invoke ultralyophobicity: a contact line density criterion and asperity height criterion. The proposed criteria were tested using experimental data available in the literature and were found to correctly predict suspension of small water drops on model rough surfaces with a wide variety of asperity shapes, sizes, and spacing.     

The mechanics of contact and adhesion of periodically rough surfaces

An analytical model based on the Johnson–Kendall–Roberts (JKR) theory of adhesion was used to study the contact mechanics and adhesion of periodically rough surfaces. The relation of the applied load to the contact area and the work of adhesion W was found in closed form for arbitrary surface profiles. Our analysis showed that when the parameter [where α* is a numerical constant of order one, β is the aspect ratio of a typical surface profile (or asperity), and ρ is the number of asperities per unit length], the surfaces will jump into contact with each other with no applied load, and the contact area will continue to expand until the two surfaces are in full contact. The theory was then extended to the non‐JKR regime in which the region where the surface forces act is no longer confined to a small region near the contact zone. Exact solution was also obtained for this case. An exact analysis of the effect of entrapped air on the mechanics of adhesion and contact was also enacted. The results showed that interaction between asperities should be taken into consideration in contact‐mechanics models of adhesion or friction. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1195–1214, 2001     

In situ estimation of the chemical and mechanical contributions in local adhesion force measurement with AFM: the specific case of polymers

The atomic force microscope (AFM) was used to perform surface force measurements in contact mode to investigate surface properties of model systems at the nanoscale. Two types of model systems were considered. The first one was composed of a rigid substrate (silicon plates) which was chemically modified by molecular self-assembling (SAMs) to display different surface properties (hydroxyl, amine, methyl and ester functional groups). The second system consists of model polymer networks (cross-linked polydimethylsiloxane or PDMS) of variable mechanical properties, whose surfaces were chemically modified with the same groups as before with silicon substrates. The comparison of the force curves obtained from the two model systems shows that the viscoelastic or mechanical contribution dominates in the adhesion on polymer substrates. Finally, a relationship, which expresses the separation energy at a local scale as a function of the energy dissipated within the contact zone, on one hand and the surface properties of the polymer on the other, was proposed.     

Electrostatic free energy of interacting ionizable double layers

The electrostatic contribution to the interaction free energy of charge-regulating materials, similar as well as dissimilar, contains electric work as well as chemical work and can be obtained from an integration over the diffuse part of the double layer together with a summation of the surface contribution to the free energy over the two surfaces. Examples for the surface contribution are given for acid, base, zwitterionic, and amphoteric (1-pK and 2-pK) materials for a diffuse double layer and for the Stern-Gouy-Chapman model, with and without ion adsorption. For charge-regulating materials, the electrostatic contribution to the interaction free energy at contact (adhesion force of curved surfaces, or particles) is always finite and can be obtained from a simple calculation.     

Roughness assessment and wetting behavior of fluorocarbon surfaces

The wetting behavior of fluorocarbon materials has been studied with the aim of assessing the influence of the surface chemical composition and surface roughness on the water advancing and receding contact angles. Diamond like carbon and two fluorocarbon materials with different fluorine content have been prepared by plasma enhanced chemical vapor deposition and characterized by X-ray photoemission, Raman and FT-IR spectroscopies. Very rough surfaces have been obtained by deposition of thin films of these materials on polymer substrates previously subjected to plasma etching to increase their roughness. A direct correlation has been found between roughness and water contact angles while a superhydrophobic behavior (i.e., water contact angles higher than 150° and relatively low adhesion energy) was found for the films with the highest fluorine content deposited on very rough substrates. A critical evaluation of the methods currently used to assess the roughness of these surfaces by atomic force microscopy (AFM) has evidenced that calculated RMS roughness values and actual surface areas are quite dependent on both the scale of observation and image resolution. A critical discussion is carried out about the application of the Wenzel model to account for the wetting behavior of this type of surfaces.