Probing elastic properties of soft materials with AFM: Data analysis for different tip geometries

It has become increasingly common to use atomic force microscopy measurements to probe mechanical properties at the nano-micro level. The data obtained from these measurements, however, must be subjected to specific models for deconvolution of the effect of the probe's tip size and shape. While analytical models have been developed to assist in this endeavor, a thorough understanding of the limits of these models is essential to fit data accurately. In this report, we explore the relationship between three different analytical tip shape models for the AFM tip (spherical, parabolic, and conical indenters) and present an analysis of mechanical testing on selected materials. Along with this, we present a simple numerical method for computing the contact radius for true spherical contact. The role of tip size (large vs small radius) on the limitations of data analysis and the benefits and drawbacks inherent to different tip sizes is discussed. Our analysis demonstrates the ability to accurately apply multiple models to a given data set, while also showing the limitations of simple analytical models to accurately describe tip-sample interactions outside of certain indentation regimes.