Statistical approach to quantifying the elastic deformation of nanomaterials

Quantifying the mechanical properties of nanomaterials is challenged by its small size, difficulty of manipulation, lack of reliable measurement techniques, and grossly varying measurement conditions and environment. A recently proposed approach is to estimate the elastic modulus from a force-deflection physical model based on the continuous bridged-deformation of a nanobelt/nanowire using an atomic force microscope tip under different contact forces. However, the nanobelt may have some initial bending, surface roughness and imperfect physical boundary conditions during measurement, leading to large systematic errors and uncertainty in data quantification. In this article, a statistical modeling technique, sequential profile adjustment by regression (SPAR), is proposed to account for and eliminate the various experimental errors and artifacts. SPAR can automatically detect and remove the systematic errors and therefore gives more precise estimation of the elastic modulus. This research presents an innovative approach that can potentially have a broad impact in quantitative nanomechanics and nanoelectronics.