The Torsional Harmonic Cantilever

We have developed the torsional harmonic cantilever (THC) to measure tip-sample forces during the oscillations of the cantilever in tapping mode. These cantilevers have their tips at an offset distance from their longitudinal axis. This way, tip-sample forces excite a torque and twist the cantilever. The torsional vibrations have much higher bandwidth than vertical vibrations (i.e. they can vibrate at much higher frequencies). Therefore they can respond to the high frequency forces in the tapping-mode.

They are also more sensitive, because they create a lot more angular deviation for a small tip displacement (torsion arm is much shorter than the length of the cantilever). The conventional AFM detectors use a quadrant photodetector, which can independently and simultaneously measure torsional vibrations and vertical vibrations. A computer program is used to analyze the vibration signals and generate the tip-sample force waveforms. An example is given in the figure where we measure tapping forces on a graphite sample. Such a curve can be obtained in a fraction of a millisecond. This curve allows to estimate local elastic modulus of the sample. It is possible to map these curves across surfaces to get a mechanical maps. That is exactly what we are doing these days.