The dynamic motion of a cantilever in dynamic-mode atomic force micros
copy is investigated theoretically with an elastic oscillator model of
the cantilever interacting with the surface. For the tip-surface inte
raction, the Lennard-Jones and hard-wall models are assumed. The numer
ical integration of the equation of motion and the Poincare map method
are used for the analysis of the lip motion. Various strange features
of the tip motion are due to the extremely non-linear nature of the i
nteraction, such as quasiperiodic oscillation and fractional resonance
. In particular, the coexistence of the dynamic touching mode with the
non-touching mode is revealed. The phase-frequency relation of the dy
namic touching mode is obtained, and can be observed experimentally. (
C) 1998 Elsevier Science B.V. All rights reserved.