Modeling and experimentation of a passive low frequency nanoforce sensor based on diamagnetic levitation

This paper is focused on the study of a new low frequency micro and nanoforce sensor based on diamagnetic levitation. The force sensitive part is a 10-cm long macroscopic capillary tube used as a levitating seismic mass. This tube presents a naturally stable equilibrium state with six degrees of freedom thanks to the combination of diamagnetic repulsive and magnetic attractive forces. It is only used as a one-direction force sensing device along its longitudinal axis. This force sensor is passive. The force measurement is based on the displacement of the capillary tube and in steady-state this displacement is proportional to the force. This sensor is characterized by an under-damped second-order linear force-displacement dynamic which remains linear on several hundred micrometers and can thus measure a wide range of microforces. Because of the magnetic springs configuration used, the capillary tube presents a horizontal mechanical stiffness that can be adjusted between 0.01 and 0.03 N/m (similar to the stiffness of a thin AFM cantilever). The measurement range typically varies between ±50 μN. Bandwidth is 4 Hz. The resolution depends on the sensor used to measure the capillary tube displacement and on noises induced by environmental conditions (ground and air vibrations). The resolution typically reached with a STIL confocal chromatic sensor is 5 nN inside a test chamber located on a anti-vibration table. This study is illustrated by a pull-off force measurement.