Precise and direct method for the measurement of the torsion spring constant of the atomic force microscopy cantilevers

Calibration of T-shaped atomic force microscope cantilevers using the thermal noise method

The tip-sample interaction force measurements in atomic force microscopy (AFM) provide information about materials' properties with nanoscale resolution. The T-shaped cantilevers used in Torsional-Harmonic AFM allow measuring the rapidly changing tip-sample interaction forces using the torsional (twisting) deflections of the cantilever due to the off-axis placement of the sharp tip. However, it has been difficult to calibrate these cantilevers using the commonly used thermal noise-based calibration method as the mechanical coupling between flexural and torsional deflections makes it challenging to determine the deflection sensitivities from force-distance curves. Here, we present thermal noise-based calibration of these T-shaped AFM cantilevers by simultaneously analyzing flexural and torsional thermal noise spectra, along with deflection signals during a force-distance curve measurement. The calibration steps remain identical to the conventional thermal noise method, but a computer performs additional calculations to account for mode coupling. We demonstrate the robustness of the calibration method by determining the sensitivity of calibration results to the laser spot position on the cantilever, to the orientation of the cantilever in the cantilever holder, and by repeated measurements. We validated the quantitative force measurements against the known unfolding force of a protein, the I91 domain of titin, which resulted in consistent unfolding force values among six independently calibrated cantilevers.

In-Liquid Lateral Force Microscopy of Micropatterned Surfaces in a Fatty Acid Solution under Boundary Lubrication

This study aims to investigate the influence of surface morphology on boundary-lubricated friction in a stearic acid solution. The surface morphology was controlled by fabricating submicrometer line-and-space patterns on Si(100) surface via photolithography. The boundary-lubricated friction on the patterns was measured by in-liquid lateral force microscopy for both transverse and longitudinal ridges, with respect to the sliding direction; the highest friction was observed on longitudinal ridges and grooves, which is in agreement with the tendency observed in our previous friction studies on steel surfaces. To further investigate this phenomenon, some additional patterns having different submicrometer morphologies were prepared and their friction characteristics were investigated. On the patterns not allowing the fluid to flow along the grooves, the frictional forces were equivalent for transverse and longitudinal grooves and ridges. Therefore, the high friction observed on the longitudinal ridges was caused by flowing out of fluid along the grooves, and it was possible to conclude that the fluidity around the submicrometer ridges and grooves influences the friction-reducing effect of stearic acid in boundary lubrication regime.

Dimensions and spring constants of rectangular AFM cantilevers determined from resonance measurements

We present a reliable numerical method that computes the spring constants of a rectangular Atomic Force Microscopy (AFM) cantilever when a small number of experimental resonance frequencies are known. By using a collection of multivariate polynomial regressions followed by an algorithm that solves a set of non-linear equations, the method finds first the values of the cantilever geometric parameters associated with the given set of resonances. The results are then used to determine the normal, longitudinal, and transversal spring constants through a second collection of regressions. Both data collections were built with finite element analysis of realistic rectangular AFM cantilevers. Experiments performed on commercial cantilevers were used to test the numerical method. The computed geometric parameters were confirmed with scanning electron microscopy, demonstrating that the method is viable, self-consistent, and accurate.

Graphene used as a lateral force microscopy calibration material in the low-load non-linear regime

A lateral force microscopy (LFM) calibration technique utilizing a random low-profile surface is proposed that is successfully employed in the low-load non-linear frictional regime using a single layer of graphene on a supporting oxide substrate. This calibration at low loads and on low friction surfaces like graphene has the benefit of helping to limit the wear of the LFM tip during the calibration procedure. Moreover, the low-profiles of the calibration surface characteristic of these layered 2D materials, on standard polished oxide substrates, result in a nearly constant frictional, adhesive, and elastic response as the tip slides over the surface, making the determination of the calibration coefficient robust. Through a detailed calibration analysis that takes into account non-linear frictional response, it is found that the adhesion is best described by a nearly constant vertical orientation, rather than the more commonly encountered normally directed adhesion, as the single asperity passes over the low-profile graphene-coated oxide surface.

Method for lateral force calibration in atomic force microscope using MEMS microforce sensor

In this paper we present a simple and direct method for the lateral force calibration constant determination. Our procedure does not require any knowledge about material or geometrical parameters of an investigated cantilever. We apply a commercially available microforce sensor with advanced electronics for direct measurement of the friction force applied by the cantilever's tip to a flat surface of the microforce sensor measuring beam. Due to the third law of dynamics, the friction force of the equal value tilts the AFM cantilever. Therefore, torsional (lateral force) signal is compared with the signal from the microforce sensor and the lateral force calibration constant is determined. The method is easy to perform and could be widely used for the lateral force calibration constant determination in many types of atomic force microscopes.