Uncertainty quantification in nanomechanical measurements using the atomic forcemicroscope**This work is a partial contribution of the USDA Forest Service and NIST, agencies of theUS government, and is not subject to copyright.

Abstract

Quantifying uncertainty in measured properties of nanomaterials is a prerequisite for themanufacture of reliable nanoengineered materials and products. Yet, rigorous uncertaintyquantification (UQ) is rarely applied for material property measurements with the atomicforce microscope (AFM), a widely used instrument that can measure properties atnanometer scale resolution of both inorganic and biological surfaces and nanomaterials. Wepresent a framework to ascribe uncertainty to local nanomechanical properties of anynanoparticle or surface measured with the AFM by taking into account the mainuncertainty sources inherent in such measurements. We demonstrate the framework byquantifying uncertainty in AFM-based measurements of the transverse elastic modulus ofcellulose nanocrystals (CNCs), an abundant, plant-derived nanomaterial whosemechanical properties are comparable to Kevlar fibers. For a single, isolated CNC thetransverse elastic modulus was found to have a mean of 8.1 GPa and a 95% confidenceinterval of 2.7–20 GPa. A key result is that multiple replicates of force–distancecurves do not sample the important sources of uncertainty, which are systematic innature. The dominant source of uncertainty is the nondimensional photodiodesensitivity calibration rather than the cantilever stiffness or Z-piezo calibrations.The results underscore the great need for, and open a path towards, quantifyingand minimizing uncertainty in AFM-based material property measurements ofnanoparticles, nanostructured surfaces, thin films, polymers and biomaterials.