Mass Detection in Viscous Fluid Utilizing Vibrating Micro- and Nanomechanical Mass Sensors under Applied Axial Tensile Force

Vibrating micro- and nanomechanical mass sensors are capable of quantitatively determining attached mass from only the first three (two) measured cantilever (suspended) resonant frequencies. However, in aqueous solutions that are relevant to most biological systems, the mass determination is challenging because the quality factor (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 resonances and, correspondingly, the accuracy of estimated masses. In this work, a technique capable of determining the mass for the cantilever and also the position of nanobeads attached on the vibrating micro-/nanomechanical beam under intentionally applied axial tensile force from the measured fundamental flexural resonant frequencies is proposed. The axial force can be created and controlled through an external electrostatic or magnetostatic field. Practicality of the proposed technique is confirmed on the suspended multi-walled carbon nanotube and the rectangular silicon cantilever-based mass sensors. We show that typically achievable force resolution has a negligibly small impact on the accuracy of mass measurement.