Detailed Study on the Failure of the Wedge Calibration Method at Nanonewton Setpoints for Friction Force Microscopy

Abstract

The wedge calibration method is the most popular calibration technique in friction force microcopy for converting raw lateral laser deflection signals (in volt) into forces (in newton). Recent trends in nanotribology demand the use of the method at nanonewton (nN) force ranges, however, we found that this method fails at these small forces. The objective of the present work is to identify the reason why the conventional wedge calibration method fails at nN force ranges. We found that the equation used in the model in this method amplifies experimental errors by orders of magnitude only at small setpoints purely due to its mathematical expression. In general, signal-to-noise ratio is poor at small setpoints, thus this low tolerance against experimental errors in nanonewton force ranges completely gives an inconsistent calibration. We identified that the condition, under which the method operates accurately, is adhesion << setpoint. Discovery of this operation range (adhesion << setpoint) is important, because performing the calibration under other conditions can wrongly calibrate the system by orders of magnitude. Our result imposes a warning to the field that the conventional wedge calibration method has to be conducted at setpoints much larger than adhesion forces for the accurate calibration.

Recent progress in polydiacetylene mechanochromism

“…75,76 The use of this experimental technique was partially enabled by our recent identification of an error source in the wedge calibration method over the nanonewton range. 77 Quantitative friction force microscopy combined with fluorescence microscopy confirmed that PDA reacts only to lateral forces, F ∥ , as the lateral force presents a perfect correlation with Δfluorescence, whereas the vertical force does not (Fig. 6a).…”

Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy

“…The wedge method [9], another popular AFM lateral force calibration method, uses the known angle between two facets of a strontium titanate surface, the voltage response to sliding on each facet, and quasi-static force balances to solve for the lateral force calibration constant in terms of the normal force calibration constant. The wedge method and its variants [4,[10][11][12] are considered semi-direct in that they yield the lateral force calibration constant without requiring a direct lateral force measurement. Like resonance-based methods, wedge method calibration can be accomplished without the need for external calibration standards and instruments.…”

“…The primary problems of the original wedge method were the small facet size and its incompatibility with colloidal probes. Varenberg et al developed a colloid-compatible 'improved wedge method' using larger sloped Si surfaces [4] but, as others point out, this method is susceptible to significant errors from likely sources that include adhesion and shear center offsets [11,13]. Our own 'extended wedge method' [10] aimed to resolve the sensitivity to these effects but revealed its own significant errors of yet unknown origin.…”

“…Our own 'extended wedge method' [10] aimed to resolve the sensitivity to these effects but revealed its own significant errors of yet unknown origin. While these error sources have proven difficult to trace, Ortuso and Sugihara have suggested that the method equations themselves amplify otherwise small errors [11].…”

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

“…36 This makes the common wedge calibration suspect in the low-load singleasperity regime, with recent work showing that it becomes unreliable once the load is reduced to values comparable to the adhesion. 30,34 Thus, a low-load LFM calibration method valid in a regime typically dominated by a non-linear frictional response can be of significant use for maintaining the integrity of small-diameter single-asperity scanning probe tips. The necessity of a fast and reliable low-load lateral calibration method has increased in recent years as few-layer graphene and related 2D materials have risen in prominence and LFM has proven to be effective at probing their nanoscale properties.…”