Adhesion as an interplay between particle size and surface roughness

Surface roughness plays an important role in the adhesion of small particles. In this paper we have investigated adhesion as a geometrical effect taking into account both the particle size and the size of the surface features. Adhesion is studied using blunt model particles on surfaces up to 10 nm root-mean-square (RMS) roughness. Measurements with particles both smaller and larger than surface features are presented. Results indicate different behavior in these areas. Adhesion of particles smaller than or similar in size to the asperities depend mainly on the size and shape of the asperities and only weakly on the size of the particle. For large particles also the particle size has a significant effect on the adhesion. A new model, which takes the relative size of particles and asperities into account, is also derived and compared to the experimental data. The proposed model predicts adhesion well over a wide range of particle/asperity length scales.     

Effect of surface roughness and softness on water capillary adhesion in apolar media

The roughness and softness of interacting surfaces are both important parameters affecting the capillary condensation of water in apolar media, yet are poorly understood at present. We studied the water capillary adhesion between a cellulose surface and a silica colloidal probe in hexane by AFM force measurements. Nanomechanical measurements show that the Young's modulus of the cellulose layer in water is significantly less (~7 MPa) than in hexane (~7 GPa). In addition, the cellulose surface in both water and hexane is rather rough (6-10 nm) and the silica probe has a comparable roughness. The adhesion force between cellulose and silica in water-saturated hexane shows a time-dependent increase up to a waiting time of 200 s and is much (2 orders of magnitude) lower than that expected for a capillary bridge spanning the whole silica probe surface. This suggests the formation of one or more smaller bridges between asperities on both surfaces, which is confirmed by a theoretical analysis. The overall growth rate of the condensate cannot be explained from diffusion mediated capillary condensation alone; thin film flow due to the presence of a wetting layer of water at both the surfaces seems to be the dominant contribution. The logarithmic time dependence of the force can also be explained from the model of the formation of multiple capillary bridges with a distribution of activation times. Finally, the force-distance curves upon retraction show oscillations. Capillary condensation between an atomically smooth mica surface and the silica particle show less significant oscillations and the adhesion force is independent of waiting time. The oscillations in the force-distance curves between cellulose and silica may stem from multiple bridge formation between the asperities present on both surfaces. The softness of the cellulose surface can bring in additional complexities during retraction of the silica particle, also resulting in oscillations in the force-distance curves.     

Roughness models for particle adhesion

The effects of different surface roughness models on a previously developed van der Waals adhesion model were examined. The van der Waals adhesion model represented surface roughness with a distribution of hemispherical asperities. It was found that the constraints used to define the asperity distribution on the surface, which were determined from AFM scans, varied with scan size and thus were not constant for all surfaces examined. The greatest variation in these parameters occurred with materials that had large asperities or with materials where a large fraction of the surface was covered by asperities. These rough surfaces were modeled with fractals and also with a fast Fourier transform algorithm. When the model surfaces generated using the Fourier transforms are used in the adhesion model, the model accurately predicts the experimentally observed adhesion forces measured with the AFM.     

The role of few-asperity contacts in adhesion

The surface roughness of a few asperities and their influence on the work of adhesion is of scientific interest. Macroscale and nanoscale adhesion data have seemingly given inconsistent results. Despite the importance of bridging the gap between the two regimes, little experimental work has been done, presumably due to the difficulty of the experiment needed to determine how small amounts of surface roughness might influence adhesion data lying in between the two scales. To investigate the role of few-asperity contacts in adhesion, the pull-off force was measured between different sized atomic-force microscope (AFM) tips (with different roughnesses) and sample surfaces that had well-controlled material properties. There were seventeen tips of four different types, with radii from 200 nm to 60 microm. The samples were unpatterned single crystal silicon with a chemical silicon dioxide surface resulting from a standard silicon wafer clean. Some of the samples were treated with a few angstroms of vapor deposited diphenylsiloxane. We observed that the uncorrected (for surface roughness) pull-off force was independent of the radius of the AFM tip, which was contrary to all continuum-mechanics model predictions. To explain this behavior, we assumed that the interactions between the AFM tip and sample were additive, material properties were constant, and that the AFM tip, asperities, and sample surfaces were of uniform density. Based on these assumptions, we calculated a simple correction due to the measured root mean square (RMS) surface roughness of the AFM tips. The simple correction for the RMS surface roughness resulted in the expected dependence of the pull-off force on radius, but the magnitudes were higher than expected. Commercial and heat-treated AFM tips have minimal surface roughness and result in magnitudes that are more reliable. The relative uncertainty for the pull-off force was estimated to be 10%. In this paper, we derive how the cantilever and tip parameters contribute to the measured pull-off force and show how the corrected results compare with theory. Although much work is still needed, the work presented here should advance the understanding of adhesion between the macroscale and nanoscale regimes.     

Numerical study on the adhesion and reentrainment of nondeformable particles on surfaces: the role of surface roughness and electrostatic forces

In this paper, the reentrainment of nanosized and microsized particles from rough walls under various electrostatic conditions and various hydrodynamic conditions (either in air or aqueous media) is numerically investigated. This issue arises in the general context of particulate fouling in industrial applications, which involves (among other phenomena) particle deposition and particle reentrainment. The deposition phenomenon has been studied previously and, in the present work, we focus our attention on resuspension. Once particles are deposited on a surface, the balance between hydrodynamic forces (which tend to move particles away from the surface) and adhesion forces (which maintain particles on the surface) can lead to particle removal. Adhesion forces are generally described using van der Waals attractive forces, but the limit of these models is that any dependence of adhesion forces on electrostatic forces (due to variations in pH or ionic strength) cannot be reproduced numerically. For this purpose, we develop a model of adhesion forces that is based on the DLVO (Derjaguin and Landau, Verwey and Overbeek) theory and which includes also the effect of surface roughness through the use of hemispherical asperities on the surface. We first highlight the effect of the curvature radius on adhesion forces. Then some numerical predictions of adhesion forces or adhesion energies are compared to experimental data. Finally, the overall effects of surface roughness and electrostatic forces are demonstrated with some applications of the complete reentrainment model in some simple test cases.     

Comparison of the adhesion forces in single and double-layer coatings on the MEMS surfaces by JKR and DMT models

In many medical and industrial applications, some strategies are needed to control the adhesion forces between the materials, because surface forces can activate or hinder the function of the device. All actual surfaces present some levels of roughness and the contact between two surfaces is transferred by the asperities on the surfaces. The force of the adhesion, which depends on the operating situations, can be influenced by the contact region. The aim of the present study is to predict the adhesion force in MEMS surfaces using the JKR and DMT models. The surfaces of the coating material in this research consisted of the single-layer coating of Gold and Silver, and the double-layer coating of TiO₂/Gold and TiO₂/Silver on the silicon (100) substrates. The depositing was done by the thermal evaporation method. The results showed that the double-layer coating developed by the new deposition method helped the reduction of the adhesion forces between the probe tip and the specimen surface. The predicted adhesion forces between the probe and the specimens with DMT and JKR models were compared with the experimental results. For all specimens, the simulated data by applying the JKR theory were in a good agreement with the adhesion force experimental values.     

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.     

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.     

Analysis of Contact Interactions between a Rough Deformable Colloid and a Smooth Substrate

A model was developed for the effect of van der Waals interactions between a rough, deformable, spherical colloid and a flat, smooth, hard surface in contact. The model demonstrates the significant effect of colloid roughness on removal force. Small changes in colloid roughness produce large changes in the predicted removal force. Several authors attribute discrepancies in the observed interaction force between particles and surfaces to colloid roughness, and our model supports their hypotheses. Experimental data documenting the force required to remove colloids of polystyrene latex from silica substrates in aqueous solution were collected during AFM studies of this system. When colloid roughness exists, as is the case in this work, our model bounds the observed removal force. The predicted range of removal forces is in better quantitative agreement with our removal force data than are forces predicted by classical DLVO theory. Copyright 2000 Academic Press.     

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.     

Extended DLVO interactions between spherical particles and rough surfaces

An "extended DLVO" approach that includes Lifshitz-van der Waals, Lewis acid-base, and electrostatic double layer interactions is used to describe interaction energies between spherical particles and rough surfaces. Favorable, unfavorable, and intermediate deposition conditions are simulated using surface properties representing common aquatic colloids and polymeric membranes. The surface element integration (SEI) technique and Derjaguin's integration method are employed to calculate interaction energy. Numerical simulations using SEI demonstrate that nanometer scale surface roughness features can produce a distribution of interaction energy profiles. Local interaction energies are statistically analyzed to define representative interaction energy profiles-minimum, average, and maximum-for various combinations of simulated particles and surfaces. In all cases, the magnitude of the average interaction energy profile is reduced, but the reduction of energy depends on particle size, asperity size, and density of asperities. In some cases, a surface that is on average unfavorable for deposition (repulsive) may possess locally favorable (attractive) sites solely due to nanoscale surface roughness. A weighted average of the analytical sphere-sphere and sphere-plate expressions of Derjaguin reasonably approximates the average interaction energy profiles predicted by the SEI model, where the weighting factor is based on the fraction of interactions involving asperities.     

Controlling adhesion force by means of nanoscale surface roughness

Control of adhesion is a crucial aspect in the design of microelectromechanical and nanoelectromechanical devices. To understand the dependence of adhesion on nanometer-scale surface roughness, a roughness gradient has been employed. Monomodal roughness gradients were fabricated by means of silica nanoparticles (diameter ～12 nm) to produce substrates with varying nanoparticle density. Pull-off force measurements on the gradients were performed using (polyethylene) colloidal-probe microscopy under perfluorodecalin, in order to restrict interactions to van der Waals forces. The influence of normal load on pull-off forces was studied and the measured forces compared with existing Hamaker-approximation-based models. We observe that adhesion force reaches a minimum value at an optimum particle density on the gradient sample, where the mean particle spacing becomes comparable with the diameter of the contact area with the polyethylene sphere. We also observe that the effect on adhesion of increasing the normal load depends on the roughness of the surface.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

A Simple Model Incorporating the Effects of Deformation and Asperities into the van der Waals Force for Macroscopic Spherical Solid Particles

The van der Waals interaction between perfectly spherical, infinitely hard spheres is well understood. Unfortunately, real powder particles are not infinitely hard and rarely spherical. Those particles that are approximately spherical are often covered in small asperities. It is often believed that the size of these asperities dominates the cohesive force between powder particles. This paper rigorously examines this phenomenon and demonstrates the regimes over which the asperities dominate the cohesive force and when the particle size dominates. Deformation of particles is also investigated with a simple model and is shown to produce a significant increase in cohesive force. We demonstrate that previous simple models for calculating the effect of deformation are inadequate, as they ignore effects that can be as large as the correction they suggest. This can lead to an underestimation of the cohesive force by a factor of approximately 2. Copyright 2000 Academic Press.     

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.     

Effect of roughness on particle adhesion in aqueous solutions: a study of Saccharomyces cerevisiae and a silica particle

An atomic force microscope (AFM) has been used to quantify the adhesion of living cells Saccharomyces cerevisiae on three different silica surfaces with defined roughness. The effects of support roughness on the adhesion forces of a smooth silica particle were studied in addition. A living single cell was immobilized at the apex of a tipless AFM cantilever using a key-lock mechanism. Adhesion was quantified from the force-distance data measured on a smooth silica substrate and two substrates coated with hydrophilic monodisperse silica particles with 110 and 240 nm in diameter to study the effect of roughness on particle adhesion. The AFM technique gives unique insight into the primary colonization event of biofilm formation. The new knowledge helps substantially to design surface coatings relevant for biotechnology, medicine and dentistry.     

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.     

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.     

Scanning white-light interferometry as a novel technique to quantify the surface roughness of micron-sized particles for inhalation

A novel approach of measuring the surface roughness of spherical and flat micron-sized drug particles using scanning white-light interferometry was applied to investigate the surface morphology of micron-sized active pharmaceutical ingredients (APIs) and excipient particles used for inhalation aerosols. Bovine serum albumin (BSA) and alpha-lactose monohydrate particles were chosen as model API and excipient particles, respectively. Both BSA and lactose particles were prepared with different degrees of surface corrugation using either controlled spray drying (four samples of BSA) or decantation (two samples of lactose). Particle size distributions were characterized by laser diffraction, and particles were imaged by scanning electron microscopy (SEM). Surface roughness of the BSA and lactose particles was quantified by white-light optical profilometry using vertical scanning interferometry (VSI) at full resolution using a 50x objective lens with 2.0x and 0.5x fields of view for BSA and lactose, respectively. Data were analyzed using Vision software (version 32, WYKO), and surface roughness values are expressed as root-mean-square roughness ( Rrms). Furthermore, data were compared to topographical measurements made using conventional atomic force microscopy. Analysis of the optical profilometry data showed significant variation in BSA roughness ranging from 18.58 +/- 3.80 nm to 110.90 +/- 13.16 nm for the smoothest and roughest BSA particles, respectively, and from 81.20 +/- 15.90 nm to 229.20 +/- 68.20 nm for decanted and normal lactose, respectively. The Rrms values were in good agreement with the AFM-derived values. The particle morphology was similar to SEM and AFM images. In conclusion, scanning white-light interferometry provides a useful complementary tool for rapid evaluation of surface morphology and roughness in particles used for dry powder inhalation formulation.