Lateral force calibration: accurate procedures for colloidal probe friction measurements in atomic force microscopy

The colloidal probe technique for atomic force microscopy (AFM) has allowed the investigation of an extensive range of surface force phenomena, including the measurement of frictional (lateral) forces between numerous materials. The quantitative accuracy of such friction measurements is often debated, in part due to a lack of confidence in existing calibration strategies. Here we compare three in situ AFM lateral force calibration techniques using a single colloidal probe, seeking to establish a foundation for quantitative measurement by linking these techniques to accurate force references available at the National Institute of Standards and Technology. We introduce a procedure for calibrating the AFM lateral force response to known electrostatic forces applied directly to the conductive colloidal probe. In a second procedure, we apply known force directly to the colloidal probe using a precalibrated piezo-resistive reference cantilever. We found agreement between these direct methods on the order of 2% (within random uncertainty for both measurements). In a third procedure, we performed a displacement-based calibration using the piezo-resistive reference cantilever as a stiffness reference artifact. The method demonstrated agreement on the order of 7% with the direct force methods, with the difference attributed to an expected systematic uncertainty, caused by in-plane deflection in the cantilever during loading. The comparison establishes the existing limits of instrument accuracy and sets down a basis for selection criteria for materials and methods in colloidal probe friction (lateral) force measurements via atomic force microscopy.