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.
Issue Section:
Research Papers
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