Contact between rough surfaces and a criterion for macroscopic adhesion

Significance Macroscopic objects rarely stick together, yet the van der Waals interactions between surface atoms produce attractive pressures that are orders of magnitude larger than atmospheric pressure. This “adhesion paradox” has been linked to surface roughness, which reduces the area of intimate atomic contact to summits on the rough landscape. This paper presents a parameter-free theory that captures the interplay between elasticity, interatomic attraction, and surface roughness. It predicts how adhesion changes contact area and when surfaces are sticky. The results offer a simple explanation for why tape sticks to our desktops but a sheet of paper does not, and may aid in the design of adhesives and in engineering surface roughness to enhance or eliminate adhesion. 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.

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