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

Abstract

By incorporating modified Langmuir kinetic model, a novel slowly timevarying dynamical model of in situ micromechanical sensors is proposed to realtime monitor atomic or molecular adsorptions on the solid surface in a viscous fluid. First, Langmuir kinetic model is modified by the introduction of timevarying concentrations of analytes. Second, van der Waals (vdW), Coulomb, and biomolecular interactions for uncharged adsorbates, charged ones, and doublestranded DNAs (dsDNAs) are adopted, respectively, to develop the governing equation of timevarying vibrational systems with Hamilton's principle. It can be found that the adsorptioninduced surface effects are incorporated into the dynamical equation of sensors due to realtime 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 adsorptioninduced slowly timevarying vibration due to the timevarying 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 realtime 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 timevarying dynamical model for in situ realtime labelfree detection technique.