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Research Papers

Adsorption-Induced Surface Effects on the Dynamical Characteristics of Micromechanical Resonant Sensors for In Situ Real-Time Detection

[+] Author and Article Information
Kai-Ming Hu

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China;
Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: hukaiming@sjtu.edu.cn

Wen-Ming Zhang

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: wenmingz@sjtu.edu.cn

Xi Shi

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xishi@sjtu.edu.cn

Han Yan

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: yanhan_mail@foxmail.com

Zhi-Ke Peng

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: z.peng@sjtu.edu.cn

Guang Meng

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: gmeng@sjtu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 15, 2016; final manuscript received May 18, 2016; published online June 9, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(8), 081009 (Jun 09, 2016) (11 pages) Paper No: JAM-16-1189; doi: 10.1115/1.4033684 History: Received April 15, 2016; Revised May 18, 2016

By incorporating modified Langmuir kinetic model, a novel slowly time-varying dynamical model of in situ micromechanical sensors is proposed to real-time monitor atomic or molecular adsorptions on the solid surface in a viscous fluid. First, Langmuir kinetic model is modified by the introduction of time-varying concentrations of analytes. Second, van der Waals (vdW), Coulomb, and biomolecular interactions for uncharged adsorbates, charged ones, and double-stranded DNAs (dsDNAs) are adopted, respectively, to develop the governing equation of time-varying vibrational systems with Hamilton's principle. It can be found that the adsorption-induced surface effects are incorporated into the dynamical equation of sensors due to real-time adsorptions. Third, the dynamical model is validated with the theoretical results of O atoms on Si (100) surface and the experimental data of dsDNAs interactions. The results show that the dynamical behavior is adsorption-induced slowly time-varying vibration due to the time-varying effective mass, stiffness, damping, and equilibrium positions of the microcantilevers. Moreover, comparing the modified Langmuir kinetic model with the unmodified model, the amplitude and phase hysteresis phenomena of frequency shift for resonant sensors can result in huge detection errors. In addition, the fluid effect can dramatically degrade the sensitivity and precision of real-time detection by several orders, which can provide a theoretical foundation to improve the detection sensitivity by reducing the fluid effect. The work demonstrates that it is essential to develop a time-varying dynamical model for in situ real-time label-free detection technique.

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Figures

Grahic Jump Location
Fig. 1

Schematic for a cantilever-based sensor with a uniform distribution of atoms or molecules adsorbed on the upper surface: (a) the dimensions of the cantilever and the coordinate system, (b) equilibrium positions of a cantilever before bending, where a is the spacing between an adatom and the upper surface, and (c) deflection induced by the adsorption between adatoms and substrate atoms, where R denotes the radius of curvature of the beam

Grahic Jump Location
Fig. 2

Schematic illustration of a cantilever segment with adsorbates on its upper surface: (a) Au surface adsorbed S head groups and (b) Au surface adsorbed dsDNAs

Grahic Jump Location
Fig. 3

Comparison study of (a) normalized adsorption-induced frequency shift between the present work and the results of the adsorption of O atoms on Si (100) microcantilevers' surface with respect to surface coverage [16], the upper right inset shows the normalized adsorption-induced additional mass as a function of surface coverage, and the bottom left inset is the enlarged view of the results of the present work with fluid effect, and (b) frequency shift of piezoelectric microcantilevers due to dsDNA adsorptions between the present work and Ref. [45]

Grahic Jump Location
Fig. 4

Adsorption-induced surface effects under three different step-input concentrations of alkanethiols adsorbed on the Au(111) surface: (a) normalized additional mass α1, (b) normalized additional damping C2, (c) normalized additional stiffness α4, and (d) adsorption-induced surface energy uint2 with respect to the concentrations ca and adsorption time. The insets show the adsorption-induced surface effects with respect to the concentrations of analytes.

Grahic Jump Location
Fig. 5

Adsorption-induced surface effects under three different periodically varying concentrations ca(t)=a0[1+sin (πt/10)] of alkanethiols adsorbed on the Au(111) surface: (a) normalized additional mass α1, (b) normalized additional damping C2, (c) normalized additional stiffness α4, and (d) adsorption-induced surface energy uint2

Grahic Jump Location
Fig. 6

Comparison of adsorption-induced surface effects of alkanethiols on the Au(111) surface between unmodified Langmuir model and modified Langmuir model when a0=3μM : (a) normalized additional mass α1, (b) normalized additional damping C2, (c) normalized additional stiffness α4, and (d) adsorption-induced surface energy uint2

Grahic Jump Location
Fig. 7

The normalized adsorption-induced deflections of cantilever-based sensors with respect to (a) X for different detection times under step-input concentrations, (b) t for different positions under step-input concentrations, (c) X for different detection times under periodically varying concentrations, and (d) t for different positions under periodically varying concentrations

Grahic Jump Location
Fig. 8

The fluid effect on normalized adsorption-induced resonance frequency shift under three different concentrations of analytes: (a) without the fluid effect for step-input concentrations, (b) with the fluid effect for step-input concentrations, (c) without the fluid effect for periodically varying concentrations, and (d) with the fluid effect for periodically varying concentrations

Grahic Jump Location
Fig. 9

(a) Comparison of resonance frequency shift of cantilevers due to the adsorption of alkanethiols on the Au (111) surface under unmodified Langmuir kinetic model and modified Langmuir kinetic model, where the concentration of alkanethiols is ca(t)=a0[1+sin (πt/10)] and (b) fast Fourier transformation diagrams of resonance frequency shift, where fδf denotes the charge frequency of resonance frequency shift δfads due to the time-varying concentration of analytes

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