Imaging and measurement of elasticity and friction using the TRmode

Torsional and lateral vibrations of atomic force microscope (AFM) cantilevers can be used to measure elastic and frictional properties on a nanoscale. Recently a new dynamic operation mode called Torsional Resonance mode (TRmode) has been introduced. This paper describes the physical base of the TRmode and compares it to related dynamic AFM modes. In the theoretical part the torsional equation of motion of the cantilever beam is analysed. In the experimental part the contrast of images is interpreted based on the equation of motion. The route to quantitative measurements of contact stiffness, elastic moduli and friction is laid out.