Quantitative friction-force measurements by longitudinal atomic force microscope imaging

Since the first lateral force measurements by atomic force microscopy, one of the main obstacles to quantitative friction-force measurements has been the difficulty in measuring the torsional response of the probes. The influence of friction on images acquired in the usual longitudinal scanning direction has also long been recognized. However, in part due to its less favorable geometry, the longitudinal mode is not typically exploited for friction-force measurements. We show here that quantitative frictional-force measurements are possible in longitudinal imaging and provide several advantages over lateral-force imaging: for instance, topology and frictional effects are coupled in a well-defined way, and there is no need to estimate the torsional spring constant. More importantly, following frictional-force measurements by longitudinal imaging with traditional lateral-force imaging allows a convenient calibration that does not require additional equipment, cantilever preparation, or special samples.