On the mass determination in liquid utilizing measurement of only the fundamental flexural resonances of the micro-/nanomechanical based mass sensors

TL;DR

This paper presents a method to accurately determine the mass of molecules in liquid environments using only the fundamental flexural resonances of micro-/nanomechanical sensors, overcoming damping challenges.

Contribution

The authors derive simple expressions for mass determination from fundamental resonant frequencies under axial tension, applicable in liquid conditions.

Findings

Mass can be accurately determined using only fundamental resonances.

Axial tension control enables reliable mass measurements in liquids.

Force resolution has negligible impact on mass sensitivity.

Abstract

Micro-/nanomechanical mass sensors are capable to quantitatively determine molecule mass from only first three (two) measured cantilever (bridge) resonant frequencies. However, in liquid solutions that are relevant to most of the biological systems, the mass determination is challenging because the Q-factor due to fluid damping decreases and, as a result, usually just the fundamental resonant frequencies can be correctly identified. Moreover, for higher modes the resonance coupling, noise and internal damping have been proven to strongly affect the measured resonant frequencies and, correspondingly, the accuracy of the estimated masses. Here, we derive the easy accessible expressions enabling the quantitative mass(es) determination just from the fundamental resonant frequencies of the micro/nanomechanical mass sensor under intentionally applied axial tension, which can be easily created and controlled by the electrostatic or magnetostatic forces. We also show that typically achievable force resolution has a negligible impact on the mass determination and the mass sensitivity.