The Stochastic Dynamics of an Array of Micron Scale Cantilevers in Viscous Fluid

Abstract

The stochastic dynamics of an array of closely spaced micron scale cantilevers in a viscous fluid is considered. The stochastic cantilever dynamics are due to the constant buffeting of fluid particles by Brownian motion and the dynamics of adjacent cantilevers are correlated due to long range effects of fluid dynamics. The measurement sensitivity of an experimental setup is limited by the magnitude of inherent stochastic motion. However, the magnitude of this noise can be decreased using correlated measurements allowing for improved force resolution. A correlated scheme is proposed using two atomic force microscope cantilevers for the purpose of analyzing the dynamics of single molecules in real time, a regime that is difficult to observe using current technologies. Using a recently proposed thermodynamic approach the hydrodynamic coupling of an array of cantilevers is quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available micron-scale cantilevers yielding the possible force sensitivity and time resolution of correlated measurements. This measurement scheme is capable of achieving a force resolution that is more than three fold more sensitive than that of a single cantilever when the two cantilevers are separated by 200 nm, with a time scale on the order of tens of microseconds.