Distance upon contact: Determination from roughness profile

The point at which two random rough surfaces make contact takes place at the contact of the highest asperities. The distance upon contact d(0) in the limit of zero load has crucial importance for determination of dispersive forces. Using gold films as an example we demonstrate that for two parallel plates d(0) is a function of the nominal size of the contact area L and give a simple expression for d(0)(L) via the surface roughness characteristics. In the case of a sphere of fixed radius R and a plate the scale dependence manifests itself as an additional uncertainty delta d(L) in the separation, where the scale L is related with the separation d via the effective area of interaction L(2)similar to pi Rd. This uncertainty depends on the roughness of interacting bodies and disappears in the limit L ->infinity.