Modelling mesoporous alumina microstructure with 3D random models of platelets.

This work focuses on a mesoporous material made up of nanometric alumina 'platelets' of unknown shape. We develope 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-scale model of microstructure is introduced to replicate the statistical dispersion of platelets observed on TEM images. Accordingly, a set of two-scale 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.