Interplay between capillary and dispersion forces in adhesion under ambient conditions

Measurements of adhesion force between hydrophilic rough surfaces performed at controlled humidity generated controversial results at humidity below the critical one. Measurements with adhered cantilever demonstrated roughness but not humidity dependence, while measurements with atomic force microscope (AFM) showed an important role of capillary interaction. In this paper, the controversy is resolved using the contact of a deposited Au surface with Si wafer as an example. No assumption on surface roughness is made. Instead, all necessary information is extracted from large, detailed AFM scans. Using the force balance equation, not only the adhesion force but also a realistic place-to-place variation of the force is determined. Critical new elements of the analysis are the inclusion of the long-distance dispersion force and the nominal area of contact. For small roughness, the short-distance, capillary, and long-distance dispersion forces are all proportional to the nominal area of contact as usually assumed. However, for larger roughness, the short-distance and capillary forces grow with area much slower, making the role of the dispersion force more important. An additional factor that influences the relative contribution of different forces to adhesion is the average distance at contact, which is also determined from the force balance. Very different nominal areas of contact used in the adhered cantilever and AFM measurements explain the seeming contradiction between these experiments.