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 $d_0\left(L\right)$ 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 $\delta d\left(L\right)$ in the separation, where the scale $L$ is related with the separation $d$ via the effective area of interaction $L^2\sim \pi Rd$. This uncertainty depends on the roughness of interacting bodies and disappears in the limit $L\to \infty$.

• Received 7 October 2009

DOI:https://doi.org/10.1103/PhysRevB.80.235401