Nanomechanical resonators are routinely used for identification of various analytes such as biological and chemical molecules, viruses, or bacteria cells from the frequency response. This identification based on the multimode frequency shift measurement is limited to the analyte of mass that is much lighter than the resonator mass. Hence, the analyte can be modeled as a point particle and, as such, its stiffness and nontrivial binding effects such as surface stress can be neglected. For heavy analytes (>MDa), this identification, however, leads to incorrectly estimated masses. Using a well-known frequency response of the nanomechanical resonator in air, we show that the heavy analyte can be identified without a need for highly challenging analysis of the analyte position, stiffness, and/or binding effects just by monitoring changes in the quality factor (Q-factor) of a single harmonic frequency. A theory with a detailed procedure of mass extraction from the Q-factor is developed. In air, the Q-factor depends on the analyte mass and known air damping, while the impact of the intrinsic dissipation is negligibly small. We find that the highest mass sensitivity (for considered resonator dimensions ∼zg) can be achieved for the rarely measured lateral mode, whereas the commonly detected flexural mode yields the lowest sensitivity. Validity of the proposed procedure is confirmed by extracting the mass of heavy analytes (>GDa) made of protein and Escherichia coli bacteria cells, and the ragweed pollen nanoparticle adsorbed on the surface of the nanomechanical resonator(s) in air, of which the required changes in the Q-factor were previously experimentally measured. Our results open a doorway for rapid detection of viruses and bacteria cells using standard nanomechanical mass sensors.
Keywords: NEMS; mass sensor; mass spectrometry; nanomechanical resonator; nanomechanics.