Analytical Modeling of Density and Young’s Modulus Identification of Adsorbate with Microcantilever Resonator

Abstract

Density and Young’s modulus are critical parameters in biological research, which can be used to characterize molecules, cells, or tissues in the diagnosis of severe diseases. Microcantilever resonators are ideal tools to measure the physical parameters of small objects at the micro/nanoscale. In this study, a mathematical model was built based on the Rayleigh–Ritz method with the consideration of the first five-order bending natural frequencies. The mathematical model can be used to detect the density and Young’s modulus of an adsorbate on a cantilever resonator with a single measurement. The influence of different order natural frequencies and the adsorbate position on the measurement accuracy and reliability was analyzed. This study revealed that the frequency pairs and the relative position of the adsorbate on the cantilever are two important factors that affect the accuracy and reliability of the measurement. Choosing appropriate frequency pairs can help to improve the accuracy and reliability of measurement. Finally, the results of finite element analysis verified the proposed method.