Multimode Brownian dynamics of a nanomechanical resonator in a viscous fluid

Gress, H. and Barbish, J. and Yanık, Cenk and Kaya, İsmet İnönü and Erdogan, R. T. and Hanay, M. S. and González, M. and Svitelskiy, O. and Paul, M. R. and Ekinci, K. L. (2023) Multimode Brownian dynamics of a nanomechanical resonator in a viscous fluid. Physical Review Applied, 20 (4). ISSN 2331-7019

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Brownian motion imposes a hard limit on the overall precision of a nanomechanical measurement. Here, we present a combined experimental and theoretical study of the Brownian dynamics of a quintessential nanomechanical system, a doubly clamped nanomechanical beam resonator, in a viscous fluid. Our theoretical approach is based on the fluctuation-dissipation theorem of statistical mechanics: we determine the dissipation from fluid dynamics; we incorporate this dissipation into the proper elastic equation to obtain the equation of motion; and the fluctuation-dissipation theorem then directly provides an analytical expression for the position-dependent power spectral density (PSD) of the displacement fluctuations of the beam. We compare our theory to experiments on nanomechanical beams immersed in air and water and obtain excellent agreement. Within our experimental parameter range, the Brownian-force noise driving the nanomechanical beam has a colored PSD due to the "memory"of the fluid; the force noise remains mode independent and uncorrelated in space. These conclusions are not only of interest for nanomechanical sensing but also provide insight into the fluctuations of elastic systems at any length scale.
Item Type: Article
Divisions: Faculty of Engineering and Natural Sciences
Sabancı University Nanotechnology Research and Application Center
Depositing User: İsmet İnönü Kaya
Date Deposited: 06 Feb 2024 12:02
Last Modified: 06 Feb 2024 12:02

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