Model-Based Identification of Nanomechanical Properties in Atomic Force Microscopy: Theory and Experiments

The ability of the atomic force microscope (AFM) to resolve highly accurate interaction forces has made it an increasingly popular tool for determining nanomechanical properties of soft samples. Traditionally, elasticity is determined by gathering force-distance curves. More recently, dynamic properties such as viscoelasticity can be determined by relating the observables to sample properties, either by singlefrequency or multifrequency modulation of the cantilever. In this paper, a model-based technique for resolving nanomechanical properties is presented. Both the sample and cantilever are represented by dynamic models. A recursive least squares method is then employed to identify the unknown parameters of the sample model, thus revealing its nanomechanical properties. Two sample models are presented in this paper, demonstrating the ability to swap sample models to best suit the material being studied. The method has been experimentally implemented on a commercial AFM for online estimation of elastic moduli, spring constants, and damping coefficients. In addition, the experimental results demonstrate the capability of measuring time- or space-varying parameters using the presented approach.