On the adhesion between thin sheets and randomly rough surfaces

Thin, elastic sheets are well known to adapt to rough counterfaces, whereby adhesive interactions and pull-off stresses sigma (p) can be significant, yet no generally applicable, quantitative guideline has been suggested hitherto as to when a sheet should be considered thin enough to be sticky. Using computer simulations, we find that the dependence of sigma (p) on surface energy gamma has a high and a low-pull-off-stress regime. For randomly rough surfaces, we locate the dividing line at the point, where gamma is approximately half the elastic energy per unit area needed to make conformal contact, which is the same ratio as for semi-infinite elastic solids. This rule of thumb also applies to a certain degree for single-wavelength roughness, in which case the transition from low to high stickiness occurs when at the moment of maximum tension contact is not only broken at the height maxima but also at the saddle points.