A non-destructive method to calibrate the torsional spring constant of atomic force microscope cantilevers in viscous environments

Clodomiro Cafolla,Amir F Payam,Kislon Voïtchovsky

doi:10.1063/1.5046648

Clodomiro Cafolla, Amir F Payam + Show 1 more

Open Access

https://doi.org/10.1063/1.5046648

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Abstract

Calibration of the torsional spring constant of atomic force microscopy cantilevers is fundamental to a range of applications, from nanoscale friction and lubrication measurements to the characterization of micro-electromechanical systems and the response of biomolecules to external stimuli. Existing calibration methods are either time consuming and destructive (ex situ static approaches), or rely on models using the frequency and quality factor (Q-factor) of the cantilever torsional resonance as input parameters (in situ dynamical approaches). While in situ approaches are usually preferred for their easy implementation and preservation of the cantilever, their dependence on the torsional resonance Q-factor renders calibration in highly viscous environments challenging. This is problematic, for example, in many nanoscale tribological applications. Here, we propose a calibration method that does not depend on the cantilever torsional Q-factor and show how the cantilever deflection can be converted into a lateral force. The method is tested with six cantilevers of different shapes and material composition and in six fluid media. The derived spring constants are compared with predictions from existing methods, demonstrating a higher precision, in particular, for highly viscous liquids.

Highlights

Atomic force microscopy (AFM) is a widely used tool for surface characterization, allowing both imaging at nanometer scales and measuring forces in the nano- to piconewton range
While the most common AFM operation relies on measuring the flexural bending of a rectangular cantilever4,5 that quantifies forces normal to a sample, torsional measurements are becoming increasingly popular for their ability to extract in-plane forces such as the frictional force with nanoscale lateral precision
The shear force between the tip and the sample can be accurately determined from the twisting angle of the cantilever, provided that the torsional spring constant and the inverse optical lever sensitivity (InvOLS) of the system are known

Summary

Introduction

Atomic force microscopy (AFM) is a widely used tool for surface characterization, allowing both imaging at nanometer scales and measuring forces in the nano- to piconewton range. While the most common AFM operation relies on measuring the flexural bending of a rectangular cantilever that quantifies forces normal to a sample, torsional measurements are becoming increasingly popular for their ability to extract in-plane forces such as the frictional force with nanoscale lateral precision. In torsional measurement, the sample is moved laterally with respect to the main axis of the cantilever, making the cantilever twist as the AFM tip rubs against the sample’s surface. Atomic force microscopy (AFM) is a widely used tool for surface characterization, allowing both imaging at nanometer scales and measuring forces in the nano- to piconewton range.. The sample is moved laterally with respect to the main axis of the cantilever, making the cantilever twist as the AFM tip rubs against the sample’s surface. The shear force between the tip and the sample can be accurately determined from the twisting angle of the cantilever, provided that the torsional spring constant and the inverse optical lever sensitivity (InvOLS) of the system are known. The InvOLS is a constant depending on the geometry of the system and allows conversion of the raw photodiode measurement, taken in volts, into nanometer of lateral torsion at the tip.

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