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

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.