Modelling mesoporous alumina microstructure with 3D random models of platelets
Résumé
This work focuses on a mesoporous material made of nanometric alumina "platelets" of unknown shape. We develop a 3D random microstructure to model the porous material , based on 2D Transmission Electron Microscopy (TEM) images, without prior knowledge on the spatial distribution of alumina inside the material. The TEM images , acquired on samples with thickness 300 nm, a scale much larger than the platelets's size, are too blurry and noisy to allow one to distinguish platelets or platelets aggregates individually. In a first step, the TEM images correlation function and integral range are estimated. The presence of long-range fluctuations, due to the TEM inhomogeneous detection , is detected and corrected by filtering. The corrected correlation function is used as a morphological descriptor for the model. After testing a Boolean model of platelets, a two-scales model of microstructure is introduced to replicate the statistical dispersion of platelets observed on TEM images. Accordingly a set of two-scales Boolean models with varying physically-admissible platelets shapes is proposed. Upon optimization, the model takes into account the dispersion of platelets in the microstructure as observed on TEM images. Comparing it to X-ray diffraction and nitrogen porosimetry data, the model is found to be in good agreement with the material in terms of specific surface area.
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