The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

Abstract

The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the autocorrelation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers.

Submitted to Nanotechnology April 26, 2006

Cited by in corpus (11)

• Nanomechanical Resonators and Their Applications in Biological/Chemical Detection: Nanomechanics Principles
• Thermal noise of microcantilevers in viscous fluids
• The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary
• The Stochastic Dynamics of an Array of Atomic Force Microscopes in a Viscous Fluid
• The dynamics of an externally driven nanoscale beam that is under high tension and immersed in a viscous fluid
• Multi-mode Brownian Dynamics of a Nanomechanical Resonator in a Viscous Fluid
• Dynamics of NEMS Resonators across Dissipation Limits
• Theoretical modeling of the dynamic range of an elastic nanobeam under tension with a geometric nonlinearity
• Towards non-invasive cancer diagnostics and treatment based on electromagnetic fields, optomechanics and microtubules
• Computing the multimodal stochastic dynamics of a nanobeam in a viscous fluid
• Nanomechanical Measurement of the Brownian Force Noise in a Viscous Liquid