Abstract
Adhesion in hard-material contacts is exquisitely sensitive to roughness. Recent models suggest that large-scale adhesion depends strongly on the topography across many length scales. In this experimental investigation, micro- to millimeter-scale spheres of silica and alumina were brought into contact with silicon and nanodiamond surfaces of varying roughness. The surfaces were characterized across multiple length scales using stylus profilometry, atomic force microscopy, and, in some cases, transmission electron microscopy. Hundreds of contact tests were performed on each substrate to measure adhesion and to evaluate statistical fluctuations. Results were analyzed in light of the following three types of models: single-scale continuum elasticity (e.g. the extensions to the model of Greenwood and Williamson); single-scale rigid-body adhesion (e.g. the “modified Rumpf” model described by Rabinovich); and multi-scale elasticity (e.g. models by Persson). In all models analyzed, the simplest equations to describe the dependence of adhesion on scalar roughness parameters failed to capture the observed behavior. Yet by accounting for the spectral nature of topography, better agreement could be reached between model predictions and experimental observations.