Uncertainty evaluation in atomic force microscopy measurement of nanoparticles based on statistical mixed model in a Bayesian framework

A major bottleneck in nanoparticle sizing is the lack of data comparability between techniques and between laboratories. However, this can be overcome by making the measurements traceable to the SI together with realistic uncertainty evaluation. In the present work, a novel approach is proposed to perform measurement uncertainty evaluation in a Bayesian framework by statistically modeling appropriately selected measurement data when no comprehensive physical model is available. The method is applied to the dimensional measurement of nanoparticles by atomic force microscopy (AFM) measurement and the calibration is performed by a multiple points calibration curve. Nevertheless, the proposed method can be applied to other microscopy techniques. The experimental data used to construct the statistical model are collected so that the influence of relevant measurement parameters can be assessed. An optimized experiment is designed under the intermediate precision conditions in order to limit the number of measurements to perform. Among the different influencing parameters, it is found that the AFM operator and image analyst do not significantly affect the measurement variability while the tip tapping force, the probe nature and the tip scan speed do. The particular case of gold nanoparticle of nominal diameter 30 nm is treated as an example of the method.