Investigation of dynamics of the microcantilever in torsional resonance atomic force microscopy in liquid environments

The dynamic behavior of the microcantilever in torsional resonance atomic force microscopy (TR-AFM) operating in liquid environments is governed by a complex interplay between hydrodynamic loading and tip–sample interactions, posing challenges for the quantitative analysis of its dynamic characteristics. To address this issue, this study establishes a fluid–structure interaction model by incorporating equivalent hydrodynamic added mass and added damping. Dimensionless expressions for these parameters are derived through dimensional analysis, and their quantitative correlations are fitted via fluid–structure interaction simulations. The fitted expressions for these parameters enable a systematic investigation of the microcantilever's torsional vibration characteristics in liquids. Results show that the torsional resonance frequency in liquids is primarily governed by fluid density, while the vibration amplitude is dominantly influenced by fluid viscosity. Furthermore, the analysis of tip–sample contacts reveals that the torsional contact resonance frequency is predominantly governed by the sample shear modulus, while the vibration amplitude is significantly influenced by both the sample shear modulus and contact damping. The developed framework provides an essential approach for the quantitative characterization of sample shearing properties using TR-AFM in liquids.