The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary

TL;DR

This paper uses a thermodynamic approach to analyze the stochastic dynamics of rectangular and V-shaped atomic force microscope cantilevers in viscous fluids, highlighting the influence of higher modes and boundary proximity.

Contribution

It introduces a thermodynamic method to quantify stochastic cantilever dynamics, accounting for higher modes and complex flow fields in V-shaped cantilevers.

Findings

Higher modes significantly affect tip-angle dynamics.

V-shaped cantilevers exhibit complex 3D flow fields.

A 2D model can predict stochastic dynamics with proper scaling.

Abstract

Using a thermodynamic approach based upon the fluctuation-dissipation theorem we quantify the stochastic dynamics of rectangular and V-shaped microscale cantilevers immersed in a viscous fluid. We show that the stochastic cantilever dynamics as measured by the displacement of the cantilever tip or by the angle of the cantilever tip are different. We trace this difference to contributions from the higher modes of the cantilever. We find that contributions from the higher modes are significant in the dynamics of the cantilever tip-angle. For the V-shaped cantilever the resulting flow field is three-dimensional and complex in contrast to what is found for a long and slender rectangular cantilever. Despite this complexity the stochastic dynamics can be predicted using a two-dimensional model with an appropriately chosen length scale. We also quantify the increased fluid dissipation that results as a V-shaped cantilever is brought near a solid planar boundary.