A new method calibrates the torsional spring constant of microcantilevers used in atomic force microscopy

Microcantilevers are routinely used in nanotechnology to apply or measure forces. In atomic force microscopy (AFM), the flexural bending of a microcantilever is used to measure forces normal to a sample in the nanonewton to piconewton range. An alternative AFM operation involves torsional measurement, which can extract in-plane forces such as friction on a molecular level. This approach is crucial for many applications, including lubrication measurements and the characterization of microelectromechanical systems.

Torsional measurement with AFM requires calibration of the torsional spring constant of the cantilever. Existing methods to this calibration either are overly time-consuming or destructive to the cantilever, or fail when it comes to highly viscous liquids. A new article by Cafolla et al. proposes a novel, nondestructive method to calibrate the torsional spring constant that remains effective even in viscous environments.

The authors first developed a mathematical model for the torsional spring constant that requires knowledge of four easily accessible parameters: the fundamental torsional resonance frequencies of a cantilever in the medium of interest and in air, as well as the cantilever’s width and length. The torsional resonance frequencies can be measured with most commercial atomic force microscopes, which means the calibration method can be carried out without additional equipment.

In addition, the model is independent of the cantilever’s quality factor (Q-factor), which means it works well even in fluids with high viscosity. The Q-factor is difficult to measure accurately in viscous environments, so other calibration methods dependent on this quantity tend to fail at this point.

Finally, the authors demonstrate the method with six cantilevers of different shapes and material composition, and in six fluid media. They compare the resulting torsional spring constants with predictions from existing methods, finding that their method has greater precision and remains significantly less sensitive to viscosity.

Source: “A non-destructive method to calibrate the torsional spring constant of atomic force microscope cantilevers in viscous environments,” by Clodomiro Cafolla, Amir F. Payam, and Kislon Voitchovsky, Journal of Applied Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5046648 .