The Stochastic Dynamics of an Array of Atomic Force Microscopes in a Viscous Fluid

TL;DR

This paper investigates the stochastic behavior of two closely spaced atomic force microscope cantilevers in a viscous fluid, highlighting fluid-mediated correlations and their potential for high-resolution biomolecule sensing.

Contribution

It introduces a thermodynamic approach to quantify hydrodynamic correlations between cantilevers in a viscous fluid, providing insights into their stochastic dynamics without external driving.

Findings

Fluid correlations reduce the force on a cantilever by over 3 times compared to Brownian force.

Displacement correlations can detect piconewton forces with microsecond resolution.

Results are based on numerical simulations of readily available AFM cantilevers.

Abstract

We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications of atomic force microscopy, and we explore the stochastic cantilever dynamics due to the constant buffeting of fluid particles by Brownian motion. The stochastic dynamics of two adjacent cantilevers are correlated due to long range effects of the viscous fluid. Using a recently proposed thermodynamic approach the hydrodynamic correlations are quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available atomic force microscope cantilevers. It is shown that the force on a cantilever due to the fluid correlations with an adjacent cantilever is more than 3 times smaller than the Brownian force on an individual cantilever. Our results indicate that measurements of the correlations in the displacement of an array of atomic force microscopes can detect piconewton forces with microsecond time resolution.