Theoretical investigation of van der Waals forces between solid surfaces at nanoscales

A theoretical investigation of van der Waals forces acting between two solid silicon surfaces at separations from zero to approximately 20 nm is presented. We focused our efforts on the analysis of different factors that can cause deviations from the classical pressure–distance dependence p  1/D³. It is demonstrated that a layer (oxide or water) at any of the surfaces influences the pressure up to distances, which are an order of magnitude larger than its own thickness. A jump on the p(D) curve is expected at contact of the adsorbed liquid layers. The retardation of van der Waals forces at 5 < D < 20 nm has the similar effect on the pressure as 1 nm oxide layers. At the far end of this range the pressure decreases by 30% due to the retardation. Nanoscale roughness plays a great role when the surfaces are close-to-contact, the crucial factor is the height distribution of asperities. However, their curvature and surface density are also important, as well as the amount of adsorbed water.