  We find that the jump-into-contact of the cantilever in the atomic force
microscope (AFM) is caused by an inherent instability in the motion of the AFM
cantilever. The analysis is based on a simple model of the cantilever moving in
a nonlinear force field. We show that the jump-into-contact distance can be
used to find the interaction of the cantilever tip with the surface. In the
specific context of the attractive van der Waals interaction, this method can
be realized as a new method of measuring the Hamaker constant for materials.
The Hamaker constant is determined from the deflection of the cantilever at the
jump-into-contact using the force constant of the cantilever and the tip radius
of curvature, all of which can be obtained by measurements. The results have
been verified experimentally on a sample of cleaved mica, a sample of Si wafer
with natural oxide and a silver film, using a number of cantilevers with
different spring constants. We emphasize that the method described here is
applicable only to surfaces that have van der Waals interaction as the
tip-sample interaction. We also find that the tip to sample separation at the
jump-into-contact is simply related to the cantilever deflection at this point,
and this provides a method to exactly locate the surface.
