Comparison of frequency response of atomic force microscopy cantilevers under tip-sample interaction in air and liquids

The frequency response behavior of atomic force microscopy (afm) cantilevers in liquids iscompletely different from that in air, due to changes in the applied hydrodynamic forces and squeezeforces. in this paper, a finite-element method is used to explore the dynamic behavior of afm cantileversin air and in liquids. furthermore, the frequency response of the tapping mode afm under acousticexcitation force is studied. in the theoretical model, hydrodynamic forces exerted by the liquid on theafm cantilever are approximated by additional mass and hydrodynamic damping. the results show thatthe microcantilever operating in liquids is an intensively damped system, with a relatively large shift inits resonant frequencies from its natural frequencies, along with a considerable reduction in vibrationamplitudes. the simulation results are compared with experimental results, showing very good agreementbetween the two. in addition, the effects of liquid viscosity and liquid density on the frequency responsefunction are studied. finally, the dynamic behavior of the afm cantilever under tip-sample interactions isanalysed in both repulsive and attractive regimes. the paper shows further that the frequency responsein liquid environments close to the surface depends on two important parameters: squeeze force andtip-sample interaction.