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.