The Stochastic Dynamics of Rectangular and Vshaped Atomic Force Microscope Cantilevers in.pdf

The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary M. T. Clark∗ and M. R. Paul Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (Dated: February 2, 2008) 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. 8 We show that the stochastic cantilever dynamics as measured by the displacement of the cantilever 0 tip or by the angle of the cantilever tip are different. We trace this difference to contributions 0 from the higher modes of the cantilever. We find that contributions from the higher modes are 2 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 n rectangular cantilever. Despite this complexity the stochastic dynamics can be predicted using a a J 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. 5 1 ] I. INTRODUCTION and to suggest simplified analytical approaches to de- l