No Access Submitted: 22 June 2018 Accepted: 17 August 2018 Published Online: 04 September 2018
Review of Scientific Instruments 89, 093701 (2018);
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  • Aleksander Labuda
  • Changhong Cao
  • Tim Walsh
  • Jieh Meinhold
  • Roger Proksch
  • Yu Sun
  • Tobin Filleter
A method for calibrating the dynamic torsional spring constant of cantilevers by directly measuring the thermally driven motion of the cantilever with an interferometer is presented. Random errors in calibration were made negligible (<1%) by averaging over multiple measurements. The errors in accuracy of ±5% or ±10% for both of the cantilevers calibrated in this study were limited only by the accuracy of the laser Doppler vibrometer (LDV) used to measure thermal fluctuations. This is a significant improvement over commonly used methods that result in large and untraceable errors resulting from assumptions made about the cantilever geometry, material properties, and/or hydrodynamic physics of the surroundings. Subsequently, the static torsional spring constant is determined from its dynamic counterpart after careful LDV measurements of the torsional mode shape, backed by finite element analysis simulations. A meticulously calibrated cantilever is used in a friction force microscopy experiment that measures the friction difference and interfacial shear strength (ISS) between graphene and a silicon dioxide AFM probe. Accurate calibration can resolve discrepancies between different experimental methods, which have contributed to a large scatter in the reported friction and ISS values in the literature to date.
We would like to thank Mark Reitsma, Ted Limpoco, John Sader, Deron Walters, Ryan Wagner, and Donna Hurley for valuable discussions.
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  1. © 2018 Author(s). Published by AIP Publishing.