Dynamics of probes attached to quartz tuning forks for the detection of surface forces

The dynamics of force microscopy probes attached to quartz tuning fork piezoelectric sensors has been investigated, by simply modeling the tuning fork/ probe system as two coupled damped harmonic oscillators. Depending on how probes are applied to the tuning fork prong, they could show appreciable compliance along the direction of approach to the surface. In particular, buckling or bending deformation of the probe may account for unexpectedly long interaction ranges found in experimental approach curves. Some peculiar curves found in the literature in the case of lateral probe oscillation ( shear force) are well reproduced by the present model. In particular, a 'clamping' effect is observed when the probe is substantially more compliant than the tuning fork. By calculating the actual probe motion along with the tuning fork response, the correct distance control operation regimes are pointed out for the shear- force case, even when using compliant probes. The model can be readily extended to the case of normal oscillation, at least for small amplitudes. Furthermore, it could be applied to a 'mixed' case of shear- force detection performed with very compliant probes. The present analysis can help to improve data interpretation and operation conditions in dynamic force microscopy and spectroscopy.