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Using a thermodynamic approach based upon the fluctuation-dissipation theoremwe quantify the stochastic dynamics of rectangular and V-shaped microscalecantilevers immersed in a viscous fluid. We show that the stochastic cantileverdynamics as measured by the displacement of the cantilever tip or by the angleof the cantilever tip are different. We trace this difference to contributionsfrom the higher modes of the cantilever. We find that contributions from thehigher modes are significant in the dynamics of the cantilever tip-angle. Forthe V-shaped cantilever the resulting flow field is three-dimensional andcomplex in contrast to what is found for a long and slender rectangularcantilever. Despite this complexity the stochastic dynamics can be predictedusing a two-dimensional model with an appropriately chosen length scale. Wealso quantify the increased fluid dissipation that results as a V-shapedcantilever is brought near a solid planar boundary.

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