Calculation of the dynamic stiffness of a cantilever under torsional oscillation

Atomic force microscopy using Si cantilevers provides an effective means for investigating both conservative and dissipative interactions in the vertical and lateral directions between the tip and the sample. An accurate evaluation of the dynamic stiffness of the cantilever is indispensable in the quantitative analyses of the interactions. We calculated the dynamic stiffness of cantilevers under torsional oscillation based on the strain energy. Without tips, the torsional dynamic stiffness is approximately 23% larger than the static stiffness. The modification decreases to 21-23% with tips. Applying the present correction is essential for achieving quantitatively accurate stiffness values in dynamic measurements.