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Micro-/nanomechanical mass sensors are capable to quantitatively determinemolecule mass from only first three (two) measured cantilever (bridge) resonantfrequencies. However, in liquid solutions that are relevant to most of thebiological systems, the mass determination is challenging because the Q-factordue to fluid damping decreases and, as a result, usually just the fundamentalresonant frequencies can be correctly identified. Moreover, for higher modesthe resonance coupling, noise and internal damping have been proven to stronglyaffect the measured resonant frequencies and, correspondingly, the accuracy ofthe estimated masses. Here, we derive the easy accessible expressions enablingthe quantitative mass(es) determination just from the fundamental resonantfrequencies of the micro/nanomechanical mass sensor under intentionally appliedaxial tension, which can be easily created and controlled by the electrostaticor magnetostatic forces. We also show that typically achievable forceresolution has a negligible impact on the mass determination and the masssensitivity.

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