SI-traceable determination of the spring constant of a soft cantilever using the nanonewton force facility based on electrostatic methods

Abstract

Abstract The PTB’s (Physikalisch-Technische Bundesanstalt, Germany) nanonewton force facility, first presented in work by Nesterov (2007 Meas. Sci. Technol . 18 360–6), Nesterov (2009 Meas. Sci. Technol . 20 084012) and Nesterov et al (2009 Metrologia 46 277–82), has been significantly improved and used to measure the stiffness of a cantilever. The facility is based on a disc pendulum with electrostatic reduction of its deflection and stiffness. In this paper, we will demonstrate that the facility is able to measure horizontal forces in the range below 1 μN with a resolution below 5 pN and an uncertainty below 2.7% for a measured force of 1 nN at a measurement duration of about 20 s. We will demonstrate the possibility of using this facility as a calibration device that can accurately determine spring constants of soft cantilevers ( K ≲ 0.1 N m −1 ) with traceability to the SI units. The method and the results of measuring the spring constant of a soft cantilever ( K = 0.125 N m −1 ) in air, in a medium vacuum, in a high vacuum and in nitrogen are presented. We will show that a relative standard uncertainty of the spring constant calibration of better than 0.3% (measurement in a medium vacuum) and a repeatability of better than 0.04% are achieved.

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