Effect of roughness on surface force distributions measured by newly developed surface force apparatus with ultra-high accuracy

A pull-off force between a sphere and a flat plate is precisely investigated using a newly developed surface force apparatus (SFA). In this system, (1) a pull-off force between a spherical glass probe and a sample plate is measured in vacuum, (2) the probe is directly pulled off from the sample by an electromagnetic force, and (3) the pull-off force and displacement of the probe are measured with ultra-high resolution of 0.4 nN and 0.3 nm, respectively, which are electrical noise levels. The pull-off process, which appears as a part of force curve, is clearly measured by this system, and pull-off force is measured with high reproducibility and accuracy. Pull-off force distributions on flat surfaces of Si, SrTiO₃, glassy carbon, and diamond-like carbon are measured. It is shown that despite the differences between these materials, for all four for them, the distribution strongly depends on the surface roughness, such that the relative standard deviation of pull-off force is proportional to the surface roughness (R_a and R_z). The Greenwood and Williamson (GW) model is then used for the analysis of the pull-off force. Comparing with SFA experiments, it is shown that the pull-off force and separation displacement can be predicted by the GW model and that the pull-off force strongly depends on the standard deviation of surface height, causing the broad distribution of pull-off force at rough surfaces.