Abstract
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.
Highlights
Micro-/nanosized beams are the fundamental component used in nanotechnology for detection of various physical quantities including pressure, force [1], quantum state [2], spin [3], thin film mechanical properties [4], and molecule masses [5]
We recall the known fact that flexural oscillations of the majority of micro-/ nanosized beams, including those used as mass sensors, are realized and controlled by an external electrical or electromagnetic field, which creates a constant axial force [5,17,35,36,37,38]
In order to verify the practicality of the proposed technique, the suspended multi-walled carbon nanotube-based mass sensor (MWCNT) of density 2.1 g/cm3, elastic moduli 1.15 TPa, and of length 11.4 μm with outer and innermost diameters of 15 nm and 3 nm, respectively, which is loaded by a mass of m = 122 ag, i.e., ε ≈ 0.03, with an attachment position at h = 5.6 μm, is considered
Summary
Micro-/nanosized beams are the fundamental component used in nanotechnology for detection of various physical quantities including pressure, force [1], quantum state [2], spin [3], thin film mechanical properties [4], and molecule masses [5]. The vibrating micro-/nanomechanical mass sensors possess the ultrahigh sensitivity, excellent selectivity, and operating frequencies up to several gigahertzes with the extraordinary controllability via optomechanical or electromechanical coupling, and, they enable real-time mass measurement with the capability of reaching the ultimate limits of mass detection [6,7]. These devices usually measure shift of the flexural resonant frequencies caused by the attached molecule. This approach was successfully implemented in a single-protein real-time mass detection in a vacuum [7]
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