Nanoscale capillary interactions in dynamic atomic force microscopy

Standard models accounting for capillary interactions typically involve expressions that display a significant decay in force with separation. These forces are commonly investigated in the nanoscale with the atomic force microscope. Here we show that experimental observations are not predicted by these common expressions in dynamic interactions. Since in dynamic atomic force microscopy methods the cantilever is vibrated over the surface, the nanoscopic tip is submitted to nonlinear interactions with the sample in a periodic fashion. That is, the force dependencies involved in dynamic interactions in the nanoscale can be probed. We describe two extreme experimental scenarios in these dynamic interactions and interpret them as single and multiple asperity cases. In both extremes there is a predominantly attractive component of the net force that is relatively independent of distance and that ranges several nanometers above the surface. The distance dependence approximates that of a square well. Experimental data have been acquired for cantilevers of different stiffness and fundamental resonant frequency indicating that the distance dependencies provided here are valid for a relatively large range of frequencies. The reproducibility of our experiments and the accurate prediction of the experimental data that we present imply that future investigations should take the phenomena that we report into account to describe and interpret dynamic capillary interactions.