Dynamical Response of Nanomechanical Oscillators in Immiscible Viscous Fluid for in vitro Biomolecular Recognition

TL;DR

This paper investigates how nanomechanical cantilevers behave in viscous fluids, providing exact formulas for their spectral response and showing that biomolecular interactions mainly cause frequency shifts through surface stress, not mass change.

Contribution

It derives an exact spectral density expression and a linear approximation for resonance frequency shift of nanomechanical cantilevers in viscous fluids, highlighting the role of surface stress.

Findings

Frequency shift is mainly due to surface stress from biomolecular interactions.

Derived an exact spectral density expression for displacement.

Provided a linear approximation for resonance frequency shift.

Abstract

Dynamical response of nanomechanical cantilever structures immersed in a viscous fluid is important to in vitro single-molecule force spectroscopy, biomolecular recognition of disease-specific proteins, and the detection of microscopic dynamics of proteins. Here we study the stochastic response of biofunctionalized nanomechanical cantilevers beam in a viscous fluid. Using the fluctuation-dissipation theorem we derive an exact expression for the spectral density of the displacement and a linear approximation for the resonance frequency shift. We find that in a viscous solution the frequency shift of the nanoscale cantilever is determined by surface stress generated by biomolecular interaction with negligible contributions from mass loading.