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Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor.

Zhang Y, Zhao YP - Sensors (Basel) (2015)

Bottom Line: Extra instruments are also required.The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed.Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. zhangyin@lnm.imech.ac.cn.

ABSTRACT
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

No MeSH data available.


(a) Schematic diagram of an adsorbate on a carbon nanotube-based resonator; (b) the first three modes of a uniform clamped-clamped beam.
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sensors-15-14871-f001: (a) Schematic diagram of an adsorbate on a carbon nanotube-based resonator; (b) the first three modes of a uniform clamped-clamped beam.

Mentions: Figure 1a is the schematic of an adsorbate on a carbon nanotube (CNT)-based resonator with a length of. The governing equation of the resonator, which is modeled as a beam, is given as follows [15,40,41]:(1)[m+Moδ(x−xo)]∂2w∂t2−T∂2w∂x2+D∂4w∂x4=0where is the resonator mass per unit length; and are the mass and position of the adsorbate, which is modeled as a concentrated mass by the Dirac delta function of; [15,40,41]. is the beam displacement; is the axial load; > 0 is tension; and < 0 is compression. can vary due to adsorption. is the beam bending stiffness, and( and are the beam’s Young’s modulus and the moment of inertia, respectively).


Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor.

Zhang Y, Zhao YP - Sensors (Basel) (2015)

(a) Schematic diagram of an adsorbate on a carbon nanotube-based resonator; (b) the first three modes of a uniform clamped-clamped beam.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4541812&req=5

sensors-15-14871-f001: (a) Schematic diagram of an adsorbate on a carbon nanotube-based resonator; (b) the first three modes of a uniform clamped-clamped beam.
Mentions: Figure 1a is the schematic of an adsorbate on a carbon nanotube (CNT)-based resonator with a length of. The governing equation of the resonator, which is modeled as a beam, is given as follows [15,40,41]:(1)[m+Moδ(x−xo)]∂2w∂t2−T∂2w∂x2+D∂4w∂x4=0where is the resonator mass per unit length; and are the mass and position of the adsorbate, which is modeled as a concentrated mass by the Dirac delta function of; [15,40,41]. is the beam displacement; is the axial load; > 0 is tension; and < 0 is compression. can vary due to adsorption. is the beam bending stiffness, and( and are the beam’s Young’s modulus and the moment of inertia, respectively).

Bottom Line: Extra instruments are also required.The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed.Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. zhangyin@lnm.imech.ac.cn.

ABSTRACT
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

No MeSH data available.