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.

[1]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[2]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[3]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[4]  C. Misra,et al.  Industrial alumina chemicals , 1986 .

[5]  D. Trimm,et al.  The control of pore size in alumina catalyst supports: A review , 1986 .

[6]  K. Tsujii,et al.  Higher-order structure formation of ultrafine boehmite particles in sols, gels, and dried materials , 1988 .

[7]  C. Lantuéjoul,et al.  Ergodicity and integral range , 1991 .

[8]  P. Levitz,et al.  Knudsen diffusion and excitation transfer in random porous media , 1993 .

[9]  Dominique Jeulin,et al.  Random texture models for material structures , 2000, Stat. Comput..

[10]  M. Thommes,et al.  Sorption and Pore Condensation Behavior of Nitrogen, Argon, and Krypton in Mesoporous MCM-48 Silica Materials , 2000 .

[11]  A. Khodakov,et al.  Pore Size Effects in Fischer Tropsch Synthesis over Cobalt-Supported Mesoporous Silicas , 2002 .

[12]  D. Jeulin,et al.  Determination of the size of the representative volume element for random composites: statistical and numerical approach , 2003 .

[13]  J. Yi,et al.  Synthesis and Characterization of Mesoporous Alumina as a Catalyst Support for Hydrodechlorination of 1,2-Dichloropropane: Effect of Catalyst Preparation Method , 2003 .

[14]  F. Štěpánek,et al.  Effective thermal conductivity of wet particle assemblies , 2004 .

[15]  C. Márquez-Álvarez,et al.  Transmission electron microscopy combined with stochastic reconstruction methods for structural characterization of porous alumina synthesized via non-ionic surfactant-templating route , 2004 .

[16]  Philippe Sautet,et al.  Use of DFT to achieve a rational understanding of acid–basic properties of γ-alumina surfaces , 2004 .

[17]  Petr Kočí,et al.  Meso-scale modelling of CO oxidation in digitally reconstructed porous Pt/γ-Al2O3 catalyst , 2006 .

[18]  Miroslav Soos,et al.  Characterisation of porous media by the virtual capillary condensation method , 2007 .

[19]  Pore-scale modeling of non-isothermal reaction phenomena in digitally reconstructed porous catalyst , 2007 .

[20]  J. Ancheyta,et al.  Hydrotreating of Maya Crude Oil: I. Effect of Support Composition and Its Pore-diameter on Asphaltene Conversion , 2007 .

[21]  Kenneth Moreland,et al.  Parallel unstructured volume rendering in ParaView , 2007, Electronic Imaging.

[22]  Ned Djilali,et al.  Determination of the effective diffusion coefficient in porous media including Knudsen effects , 2008 .

[23]  Renaud Revel,et al.  Accurate Determination of Oxide Nanoparticle Size and Shape Based on X-Ray Powder Pattern Simulation : Application to Boehmite AlOOH , 2008 .

[24]  Lucian Roiban.  Tomographie électronique analytique : développement de la cartographie chimique 3D à l'échelle du nanomètre et applications aux catalyseurs hétérogènes , 2010 .

[25]  R. Bouchet,et al.  Influence of molecule size on its transport properties through a porous medium. , 2010, Analytical chemistry.

[26]  Johanna Fasciati-Ziegel,et al.  Estimation of surface area and surface area measure of three-dimensional sets from digitizations , 2010, Image Vis. Comput..

[27]  D. Jeulin.  Variance scaling of Boolean random varieties , 2011 .

[28]  D. Jeulin,et al.  A multiscale microstructure model of carbon black distribution in rubber , 2011, Journal of microscopy.

[29]  R. Revel,et al.  TEM image analysis and modelling: application to boehmite nanoparticles , 2012, Journal of microscopy.

[30]  Dominique Jeulin,et al.  Morphology and effective properties of multi-scale random sets: A review , 2012 .

[31]  Rémi Bardenet,et al.  Monte Carlo Methods , 2013, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[32]  D. Jeulin,et al.  Influence of the fiber geometry on the macroscopic elastic and thermal properties , 2014 .

[33]  P. D. de Jongh,et al.  Quantitative relationship between support porosity and the stability of pore-confined metal nanoparticles studied on CuZnO/SiO2 methanol synthesis catalysts. , 2014, ACS nano.

[34]  Maxime Moreaud,et al.  Inverse Problem Approach for the Alignment of Electron Tomographic Series , 2014 .

[35]  D. Jeulin,et al.  Modeling of the Multiscale Dispersion of Nanoparticles in a Hematite Coating. , 2015, Journal of nanoscience and nanotechnology.