Contact between rough surfaces and a criterion for macroscopic adhesion

Abstract

At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude. In all cases, the area of atomic contact is initially proportional to the load. The prefactor rises linearly with adhesive strength for weak attractions. Above a threshold adhesive strength, the prefactor changes sign, the surfaces become sticky, and a finite force is required to separate them. A parameter-free analytic theory is presented that describes changes in these numerical results over up to five orders of magnitude in load. It relates the threshold adhesive strength to roughness and material properties, explaining why most macroscopic surfaces do not stick. The numerical results are qualitatively and quantitatively inconsistent with classical theories based on the Greenwood−Williamson approach that neglect the range of adhesion and do not include asperity interactions.surface roughness | contact mechanics S urfaces are adhesive or "sticky" if breaking contact requires a finite force. At the atomic scale, surfaces are pulled together by van der Waals interactions that produce forces per unit area that are orders of magnitude larger than atmospheric pressure (1). This leads to strong adhesion of small objects, such as Gecko setae (2, 3) [capillary forces may also contribute to Gecko adhesion in humid environments (4, 5)] and engineered mimics (6), and unwanted adhesion is the main failure mechanism in microelectromechanical systems with moving parts (7). Although tape and gecko feet maintain this strong adhesion at macroscopic scales, few of the objects we encounter are sticky. Indeed, our world would come to a halt if macroscopic objects adhered with an average pressure equal to that from van der Waals interactions.The discrepancy between atomic and macroscopic forces has been dubbed the adhesion paradox (8). Experiments show that a key factor underlying this paradox is surface roughness, which reduces the fraction of surface atoms that are close enough to adhere (8-11). Quantitative calculations of this reduction are extremely challenging because of the complex topography of typical surfaces, which have bumps on top of bumps on a wide range of scales (12, 13). In many cases, they can be described as self-affine fractals from a lower wavelength λ s of order nanometers to an upper wavelength λ L in the micrometer to millimeter range (10,14).The traditional Greenwood−Williamson (GW) (15) approach for calculating nonadhesive contact of rough surfaces approximates their complex topography by a set of spherical asperities of radius R. The distribution of asperity heights is assumed to be either exponential or Gaussian, and the long-range elastic interactions between different asperities...

On the debris-level origins of adhesive wear

“…Instead, the tangential load is shown to be a good indicator of the asperity junction size. This finding is in agreement with observations in recent studies (29,30,35,36,38) that show that, although friction force is always linear with the real contact area at any length scale, the relation between the normal load and the real contact area is largely influenced by the roughness parameters and interfacial adhesion.…”

“…S9 and S10). This result is consistent with recent observations in single (29,34,35) and multiasperity (36,37) contacts that confirm a nonlinear relation between the contact area and applied normal load, where the degree of nonlinearity is a function of adhesion, material properties, and roughness parameters.…”

Shearing Nanometer-Thick Confined Hydrocarbon Films: Friction and Adhesion

“…For soft elastic solids when an adhesive interaction occur between the solids as in the case studied in this paper, the area of real contact will also increase in which case (3) with κ ≈ 2 is no longer accurate. In this case one must distinguish between two cases [24][25][26]: (a) If the adhesive interaction is not too strong, (3) is still approximately valid, but κ is larger than 2. In this case, if adhesion hysteresis is negligible, no adhesion will be observed in a pull-off experiment.…”

Contact area of rough spheres: Large scale simulations and simple scaling laws

“…Negative values are found for strongly adhesive interactions and correspond to macroscopic adhesion or stickiness. [14] At high loads, the surfaces are pushed into compliance and A = A 0 . Over the whole range of loads, the fractional area of contact f = A/A 0 approximately follows an error function [7,12,29,30],…”

“…We show results for different interfacial interactions with λ s = 4a 0 , λ L = 512a 0 and H = 0.8, but simulations with other parameters were carried out with no fundamental differences in the results. Contact area is obtained from atoms that feel a repulsive load [14]. Contact radii up to 1024 atoms were studied, corresponding to ∼ 0.3 µm.…”