Relationship between Q-factor and sample damping for contact resonance atomic force microscope measurement of viscoelastic properties

Contact resonance AFM characterization techniques rely on the dynamics of the cantilever as it vibrates while in contact with the sample. In this article, the dependence of the quality factor of the vibration modes on the sample properties is shown to be a complex combination of beam and sample properties as well as the applied static tip force. Here the tip-sample interaction is represented as a linear spring and viscous dashpot as a model for sample (or contact) stiffness and damping. It is shown that the quality factor alone cannot be used to infer the damping directly. Experimental results for polystyrene and polypropylene are found to be in good agreement with predictions from the model developed. These results form the basis for mapping viscoelastic properties with nanoscale resolution. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3592966]