Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system

Abstract

A novel diamagnetic lateral force calibrator (D-LFC) has been developed to directly calibrate atomic force microscope (AFM) cantilever-tip or -bead assemblies. This enables an AFM to accurately measure the lateral forces encountered in friction or biomechanical-testing experiments at a small length scale. In the process of development, deformation characteristics of the AFM cantilever assemblies under frictional loading have been analyzed and four essential response variables, i.e., force constants, of the assembly have been identified. Calibration of the lateral force constant and the “crosstalk” lateral force constant, among the four, provides the capability of measuring absolute AFM lateral forces. The D-LFC is composed of four NdFeB magnets and a diamagnetic pyrolytic graphite sheet, which can calibrate the two constants with an accuracy on the order of 0.1%. Preparation of the D-LFC and the data processing required to get the force constants is significantly simpler than any other calibration methods. The most up-to-date calibration technique, known as the “wedge method,” calibrates mainly one of the two constants and, if the crosstalk effect is properly analyzed, is primarily applicable to a sharp tip. In contrast, the D-LFC can calibrate both constants simultaneously for AFM tips or beads with any radius of curvature. These capabilities can extend the applicability of AFM lateral force measurement to studies of anisotropic multiscale friction processes and biomechanical behavior of cells and molecules under combined loading. Details of the D-LFC method as well as a comparison with the wedge method are provided in this article.

Micromechanics of friction: effects of nanometre-scale roughness

“…For the tests, the normal force constant of the AFM cantilever was calibrated with the Sader's method (Sader et al 1999), by deflecting the cantilever against another rectangular cantilever of known stiffness and against a hard surface. The lateral force constant was calibrated with the newly developed diamagnetic lateral force calibrator (Li et al 2006). The experiments were carried out in air where the local temperature and relative humidity near the specimen were measured to be 28G28C and 30%, respectively.…”

Speed Dependence of Atomic Stick-Slip Friction in Optimally Matched Experiments and Molecular Dynamics Simulations

“…The normal spring constant, k n ¼ 0:13 N=m, was calibrated using Sader's method [14], and the optical sensitivity obtained from force-displacement measurements. Lateral forces were calibrated using the diamagnetic lateral force calibration method [15]. Unless otherwise noted, the normal load was kept constant at F n ¼ 0:6 nN, and the scan size at 5 nm (except for the two highest speeds where the scan sizes were 10 and 20 nm, respectively).…”

Easy and direct method for calibrating atomic force microscopy lateral force measurements

“…[20][21][22][23][24][25][26] 19,20 Here, we present an alternative experimental procedure for calibrating AFM lateral force measurements that is inexpensive, easy to make, and easy to use. This method may be used to calibrate any cantilever, regardless of its size, stiffness, shape, material, or coating.…”

“…Recently, Li et al developed a diamagnetic levitation spring system to calibrate AFM lateral force measurements. 25 In this system, a levitated, diamagnetic sheet is used to apply known forces to the AFM tip. Jeon et al 26 coated a cantilever with gold which then could be twisted by inducing a Lorentz current via an external magnetic field.…”