Fluid-structure interaction in atomic force microscope cantilever dynamics and thermal response

Abstract

This paper discusses the effects of fluid loading on structures at low Reynolds numbers, a regime commonly found in the case of atomic force microscope cantilevers. In order to provide insight to the problem, the effect of fluid loading is analyzed from a feedback/systems approach, a perspective that considers the response of the fluid loaded system using the open-loop characteristics of the in vacuo cantilever and hydrodyamic effects. Increased mass ratio is shown to increase the bandwidth of the fluid-structure feedback loop with corresponding decrease in system quality for high fluid loading. The nondimensional natural frequency plays the role of a Reynolds number and determines the phase margin of the system. An analysis of the frequency response of the fluid loaded system, using the fluctuation-dissipation theorem, shows the fluctuating force is not spectrally white, but is related to the imaginary part of the hydrodynamic function. The mean potential energy of the cantilever is shown to be 12kBT, however, the kinetic energy is shown to be less than this value, decreasing with increasing fluid loading.