The truncated cone effect in AFM nanoindentation on soft materials

Atomic Force Microscopy (AFM) nanoindentation is the principal method for the characterization of soft materials at the nanoscale. In most cases, pyramidal tips are used and approximated to perfect cones. However, the extended use of the AFM tip may alter its sharpness. In many cases, a truncated cone shape is appropriate for tip modeling. In this technical note, the equation that relates the force with the indentation depth when indenting an elastic half-space using a truncated cone is derived. The nanoindentation equation for a truncated cone tip is derived using the fundamental differential equation that relates the sample’s contact stiffness with Young’s modulus. When fitting Sneddon’s equation (which is valid for a perfect cone) on data obtained using a truncated cone-shaped AFM tip, the results show a ‘pseudo-softening’ behavior. The AFM tip's sharpness in nanoindentation experiments is a crucial parameter for obtaining the correct mechanical patterns of unknown samples.