An elastic-plastic hybrid adhesion model for contacting rough surfaces in the presence of molecularly thin lubricant

The study of adhesion has received considerable attention in recent years, partly due to advances in the design and fabrication of micro/nano devices. Many adhesion investigations are centered on single-spherical-contact models, which include the classic Johnson-Kendall-Roberts (JKR), improved Derjaguin-Muller-Toporov (IDMT), and Maugis-Dugdale (MD) models. Based on the IDMT single-asperity model, adhesive rough surface contact models have also been developed, which are valid for elastic and elastic-plastic contact conditions. A limitation of the IDMT-based models is that they are only valid for application cases with low adhesion parameter values. In this research, a contacting rough surface adhesion model was developed by combining an extended Maugis-Dugdale (EMD) model (which is only valid for elastic contacts) with an IDMT-based elastic-plastic adhesion model. The proposed model, termed the elastic-plastic hybrid adhesion model, is valid for the entire adhesion parameter range and also for elastic-plastic contacts. The proposed model gives results similar to the EMD rough surface model when the contact is primarily elastic. Moreover, the proposed model was compared to an IDMT-based model (ISBL model) and both gave similar results for contacts with low adhesion parameter values. With high adhesion parameter values, the ISBL model fails, whereas the proposed model correctly predicts higher adhesion. Last, based on the stiffness of the external force, the instability for adhesive rough surfaces in contact was also discussed, and it was postulated that a high peak value of the external force stiffness directly relates to the unstable contact process.     

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.     

Optimal shapes for adhesive binding between two elastic bodies

The pull-off force required to separate two elastic bodies in adhesive binding depends on the surface shapes of the corresponding binding regions on the two bodies. Given a fixed binding area A, the optimal shapes are those which give the maximum pull-off force sigma(th)A where sigma(th) is the theoretical strength of interactive forces between the two solids. Here we study closed form solutions to the optimal shapes for adhesive binding over a small circular region where slip is allowed whenever shear stress along the contact interface exceeds a critical value.     

Adhesive contact based on the Lennard-Jones potential: a correction to the value of the equilibrium distance as used in the potential

A Lennard-Jones type surface law is commonly used in adhesive contact modeling; however, one of its parameters, namely the equilibrium distance z0, is not well defined. In this paper, a self-consistent method is used to derive the Lennard-Jones surface law from the interatomic Lennard-Jones potential. The parameters of the surface law are directly related to the material lattice parameter and surface energy, and the equilibrium distance z0 values are obtained for various materials. The effect of using the z0 proposed in the present work is demonstrated via the study of adhesive contact behavior for a single sphere and a flat surface, as well as the contact between planar rough surfaces. For pull-off force prediction of the contact between a single sphere and a flat surface, the error of using the z0 suggested in previous studies could be as large as 10% at intermediate ranges of a dimensionless adhesion parameter. For the contact between planar rough surfaces, the error of using the previously proposed z0 is larger for smoother cases, and the prediction of pull-off force could be different by as much as a factor of 5.     

Oscillatory loading of a viscoelastic adhesive contact

The cycle of loading and unloading of a spherically-tipped probe against an adhesive, viscoelastic plane specimen is studied by numerical integration of the relations between crack speed and apparent surface energy previously found for a linear 3-element viscoelastic solid with a Maugis-Dugdale law of force across the crack. It is found that even when the rate of loading is so slow that the loading and unloading curves almost coincide, suggesting purely elastic behaviour, the pull-off force can be appreciably greater than the elastic (JKR) value. When the normal force is modulated with a small amplitude sinusoidal variation during unloading--in order to find the contact stiffness--the contact radius barely changes, and the stiffness is close to that for a rigid flat punch instead of having the expected JKR value.     

Origin of adhesion in humid air

The origin of adhesion in humid air is investigated by pull-off force measurements between nanoscale contacts using atomic force microscopes in controlled environments from ultrahigh vacuum through various humidity conditions to water. An equivalent work of adhesion (WOA) model with a simplified interface stress distribution is developed, combining the effects of screened van der Waals and meniscus forces, which describes adhesion in humid air and which self-consistently treats the contact stress and deformation. Although the pull-off force is found to vary significantly with humidity, the equivalent WOA is found to be invariant. Increasing humidity alters the nature of the surface adhesion from a compliant contact with a localized, intense meniscus force to a stiff contact with an extended, weak meniscus force.     

The effect of surface roughness on the adhesion of solid surfaces for systems with and without liquid lubricant

We present molecular dynamics results for the interaction between two solid elastic walls during pull-off for systems with and without octane (C(8)H(18)) lubricant. We used two types of substrate--flat and corrugated--and varied the lubricant coverage from approximately 1/8 to approximately 4 ML (monolayers) of octane. For the flat substrate without lubricant the maximum adhesion was found to be approximately three times larger than for the system with the corrugated substrate. As a function of the octane coverage (for the corrugated substrate) the pull-off force first increases as the coverage increases from 0 to approximately 1 ML, and then decreases as the coverage is increased beyond monolayer coverage. It is shown that at low octane coverage, the octane molecules located in the substrate corrugation wells during squeezing are pulled out of the wells during pull-off, forming a network of nanocapillary bridges around the substrate nanoasperities, thus increasing the adhesion between two surfaces. For greater lubricant coverages a single capillary bridge is formed. The adhesion force saturates for lubricant coverages greater than 3 ML. For the flat substrate, during pull-off we observe discontinuous, thermally activated changes in the number n of lubricant layers (n-1-->n layering transitions), whereas for the corrugated substrate these transitions are "averaged" by the substrate surface roughness.     

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.     

Adhesive transition from noncontacting to contacting elastic spheres: extension of the Maugis-Dugdale model

In this paper, an adhesion model for spherical noncontact is proposed based on the Maugis-Dugdale (MD) adhesive contact model. The proposed noncontact model is combined with the MD contact model, thus providing a full range adhesion model with analytical transition from noncontacting to contacting asperity geometry. The proposed model is favorably compared with the full range improved DMT model for low surface energy values. The transition process from noncontact to contact and the adhesion instability that occurs during this transition are also investigated. It is found that jump-off points are different for displacement control and force control. Moreover, under displacement control, jump-on and jump-off points are different when the adhesion parameter lambda is greater than 0.95, whereas they are identical for lambda<0.95. By curve fitting a relationship between the critical approach under displacement and force control separately and the adhesion parameter lambda, approach prediction equations for jump-on and jump-off under different adhesion levels were obtained.     

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.     

Adhesion and debonding of soft elastic films: crack patterns, metastable pathways, and forces

We study the phenomenon of debonding in a thin soft elastic film sandwiched between two rigid plates as one of the plates is brought into intimate contact and then pulled away from contact proximity by application of a normal force. Nonlinear simulations based on minimization of total energy (composed of stabilizing elastic strain energy and destabilizing adhesive interaction energy) are employed to address the problems of contact hysteresis, cavitation, crack morphology, variation of contact area, snap-off distance, pull-off force, work done, and energy loss. Below a critical distance (d(c)) upon approach, simulations show the formation of columnar structures and nonrandom, regularly arranged nanocavities at the soft interface at a length scale of approximately 3h (h being the thickness of the film). The persistence of such instability upon withdrawal (distance >d(c)) indicates a contact hysteresis, which is caused by an energy barrier that separates the metastable states of the patterned configuration and the global minimum state of the flat film. The energy and the pull-off force are found to be nonequilibrium and nonunique properties depending on the initial contact, defects, noise, etc. Three broad pathways of debonding leading to adhesive failure of the interface, depending on the stiffness of the film, step size of withdrawal, and the imposed noise, are identified: a catastrophic column collapse mode, a peeling mode involving a continuous decrease in the contact area, and a column splitting mode. The first two modes are caused by a very high stress concentration near the cavity edges. These metastable patterned configurations engender pull-off forces that are orders of magnitude smaller than that required to separate two flat surfaces from contact.     

Peeling of polydimethylsiloxane adhesives: The case of adhesive failure

The adhesion properties of high molecular weight polydimethylsiloxane adhesives are measured using 90°‐peel adhesion tests, in the high velocity range. Such adhesives undergo mainly adhesive failure in this regime. The influence of viscosity (non‐Newtonian), adhesive thickness, peeling velocity, and backing properties are studied, and new unexpected behaviors are shown. The role of rheology and peeling velocity can be explained by an extension of a model already presented for cohesive failure, by using a power‐law fluid for the adhesive. On the other hand, the influence of the backing rigidity reveals to be coupled with the adhesive elastic properties, this effect being correlated to the introduction of a new parameter in the model, the Weissenberg number for viscoelasticity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2113–2122, 2007     

An approximate model for the adhesive contact of rough viscoelastic surfaces

Surface roughness is known to easily suppress the adhesion of elastic surfaces. Here, a simple model for the contact of viscoelastic rough surfaces with significant levels of adhesion is presented. This approach is derived from our previous model (Barthel, E.; Haiat, G. Langmuir 2002, 18, 9362) for the adhesive contact of viscoelastic spheres. For simplicity, a simple loading/unloading history (infinitely fast loading and constant pull-out velocity) is assumed. The model provides approximate analytical expressions for the asperity response and exhibits the full viscoelastic adhesive contact phenomenology such as stress relaxation inside the contact zone and creep at the contact edges. Combining this model with a Greenwood-Williamson statistical modeling of rough surfaces, we propose a quantitative assessment of the adhesion to rough viscoelastic surfaces. We show that moderate viscoelasticity efficiently restores adhesion on rough surfaces over a wide dynamic range.     

On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and investigating general formulas for μ arbitrary complex, a detailed discussion of , where m is a non-negative integer, is carried out. The results are applied to obtain several explicit expressions for the associated Legendre function of the second kind of integer degree and order, . In particular, we arrive at formulas which generalize to the case of (0 ≤ m ≤ n) the well-known Christoffel’s representation of the Legendre function of the second kind, Q _n (z). The derivatives and , all with m > n, are also evaluated.     

Aromaticity and electron affinity of Carbo(k)-[3]radialenes, k=0, 1, 2

Aromaticity enhancement is a possible driving force for the low reduction potentials of buta-1,3-diynediyl-expanded [N]radialenes: this hypothesis is theoretically analyzed for the expanded [3]radialene prototype. This study is undertaken within a more general prospect, namely the evaluation of the variation of aromaticity with endocyclic and peripheral carbomeric expansion of [3]radialene and its mono- and dianions. The structures, denoted as [C-H](6) (h)[C-C](3) (k)carbo-[3]radialene(q) (h=0, 1; k=0, 1, 2; q=0, -1, -2), were optimized in relevant singlet, doublet, or triplet spin states at the B3PW91/6-31G** level. They were found to be all planar. The structural aromaticity was measured through the average bond length d(av) over the [C-C](3) (k)carbo-[3]radialene core, and by the corresponding bond-length equalization parameter sigma(d), related to Krygowski's GEO. The magnetic aromaticity was measured by Schleyer's NICS values at the center of the rings. Regarding the relative variation of NICS and sigma(d), two classes of species can be distinguished according to their endocyclic expansion level. The species with a nonexpanded (k=0) or doubly expanded (k=2) ring constitute the first class: they exhibit D(3h) symmetry and a strong correlation of NICS with sigma(d). The species with a singly expanded ring (k=1) fall far from the correlation line, and constitute the second class. This class distinction is related to the degeneracy scheme of the frontier orbitals of the neutral representative. A finer appraisal of the electron (de)localization is brought by the ELF (Electron Localization Function) analysis of the electron density. It allows for a weighting of relevant resonance forms. Unsubstituted species are well described by the superimposition of two or three resonance forms. For (doublet spin state) monoanionic species, their respective weights are validated by comparison with AIM spin density. The weighted mean, n, of the formal numbers of paired pi(z) electrons in the resonance forms was calculated and compared with the closest even integer of either forms 4m+2 or 4m. A density-based continuous generalization of the orbital-based discrete Hückel rule is then heuristically proposed through an analytical correlation of NICS versus sigma(d), n, and S, the spin of the species. The frontier-orbital-degeneracy pattern of neutral species is discussed with respect to structural and magnetic aromaticity criteria. A decreasing HOMO-LUMO gap versus endocyclic expansion is obtained, but [C-C](3) (1)carbo-[3]radialene possesses the highest HOMO and LUMO energies. Vertical and adiabatic electron affinities of neutral and monoanionic species were also computed and compared with related experimental data.     

Experimental Study of Fibrin/Fibrin-Specific Molecular Interactions Using a Sphere/Plane Adhesion Model

Fibrin, the biopolymer produced in the final step of the coagulation cascade, is involved in the resistance of arterial thrombi to fragmentation under shear flow. However, the nature and strength of specific interactions between fibrin monomers are unknown. Thus, the shear-induced detachment of spherical monodispersed fibrin-coated latex particles in adhesive contact with a plane fibrin-coated glass surface has been experimentally studied, using an especially designed shear stress flow chamber. A complete series of experiments for measuring the shear stress necessary to release individual particles under various conditions (various number of fibrin layers involved in the adhesive contact, absence or presence of plasmin, the main physiological fibrinolytic enzyme) has been performed. The nonspecific DLVO interactions have been shown to be negligible compared to the interactions between fibrin monomers. A simple adhesion model based on the balance of forces and torque on particles, assuming an elastic behavior of the fibrin polymer bonds, to analyze the experimental data in terms of elastic force at rupture of an elementary intermonomeric fibrin bond has been used. The results suggested that this force (of order 400 pN) is an intrinsic quantity, independent of the number of fibrin layers involved in the adhesive contact. Copyright 2001 Academic Press.     

Reusable antifouling viscoelastic adhesive with an elastic skin

Although the viscoelasticity or tackiness of a pressure-sensitive adhesive gives it strength owing to energy dissipation during peeling, it also renders it nonreusable because of structural changes such as the formation of fibrils, cohesive failure, and fouling. However, an elastic layer has good structural integrity and cohesive strength but low adhesive energy. We demonstrate an effective composite adhesive in which a soft viscoelastic bulk layer is imbedded in a largely elastic thin skin layer. The composite layer is able to meet the conflicting demands of the high peel strength comparable to the viscoelastic core and the structural integrity, reusability, and antifouling properties of the elastic skin. Our model adhesive is made of poly(dimethylsiloxane), where its core and skin are created by varying the cross-linking percentage from 2 to 10%.     

Mapping mouse gamete interaction forces reveal several oocyte membrane regions with different mechanical and adhesive properties

This study focuses on the interaction involved in the adhesion of mouse gametes and on the mechanical properties of the oocyte membrane. The oocyte has an asymmetrical shape, and its membrane is composed of two distinct areas. One is rich in microvilli, and the other is smoother and without microvilli. With a biomembrane force probe (BFP) adapted to cell-cell measurements, we have quantified the separation forces between a spermatozoon and an oocyte. Microvillar and amicrovillar areas of the oocyte surface have been systematically probed and compared. In addition to a substantial difference in the elastic stiffness of these two regions, the experiments have revealed the presence of two types of membrane domains with different mechanical and adhesive properties, both distributed over the entire oocyte surface (i.e., in both microvillar and amicrovillar regions). If gamete contact occurs in the first type of domain, then the oocyte membrane deforms only elastically under traction. The pull-off forces in these domains are higher in the amicrovillar region. For a spermatozoon contact with the other type of domain, there can be a transition from the elastic to viscoelastic regime, and then tethers are extruded from the oocyte membrane.     

Electron exchange between alpha-Keggin tungstoaluminates and a well-defined cluster-anion probe for studies in electron transfer

Fully oxidized alpha-AlIIIW12O40(5-) (1ox), and one-electron-reduced alpha-AlIIIW12O40(6-) (1red), are well-behaved (stable and free of ion pairing) over a wide range of pH and ionic-strength values at room temperature in water. Having established this, 27Al NMR spectroscopy is used to measure rates of electron exchange between 1ox (27Al NMR: 72.2 ppm relative to Al(H2O)63+; nu(1/2) = 0.77 Hz) and 1red (74.1 ppm; nu(1/2) = 0.76 Hz). Bimolecular rate constants, k, are obtained from line broadening in 27Al NMR signals as ionic strength, mu, is increased by addition of NaCl at the slow-exchange limit of the NMR time scale. The dependence of k on is plotted using the extended Debye-Hückel equation: log k = log k0 + 2alphaz1z2mu(1/2)/(1 + betarnu(1/2)), where z1 and z2 are the charges of 1ox and 1red, alpha and beta are constants, and r, the distance of closest contact, is fixed at 1.12 nm, the crystallographic diameter of a Keggin anion. Although not derived for highly charged ions, this equation gives a straight line (R2 = 0.996), whose slope gives a charge product, z1z2, of 29 +/- 2, statistically identical to the theoretical value of 30. Extrapolation to mu = 0 gives a rate constant k11 of (6.5 +/- 1.5) x 10(-3) M(-1) s(-1), more than 7 orders of magnitude smaller than the rate constant [(1.1 +/- 0.2) x 10(5) M(-1) s(-1)] determined by 31P NMR for self-exchange between P(V)W12O40(3-) and its one-electron-reduced form, P(V)W12O40(4-). Sutin's semiclassical model reveals that this dramatic difference arises from the large negative charges of 1ox and 1red. These results, including independent verification of k11, recommend 1red as a well-behaved electron donor for investigating outer-sphere electron transfer to molecules or nanostructures in water, while addressing a larger issue, the prediction of collision rates between uniformly charged nanospheres, for which 1ox and 1red provide a working model.