Mass fractal dimension from 2D microscopy images via an aggregation model with variable compactness

Giulia Ferri (1) , Severine Humbert (1) , Jean-Marc Schweitzer (1) , Mathieu Digne (1) , Veronique Lefebvre (1) , Maxime Moreaud (1)

1 IFPEN - IFP Energies nouvelles

Microscopy-image analysis provides precious information on size and structure of colloidal aggregates and agglomerates. The structure of colloids is often characterized using the mass fractal dimension d f , which is different from the two-dimensional fractal dimension d p that can be computed from microscopy-images. In this work we propose to use a recent morphological aggregation model to find a relationship between 2D image fractal dimension and 3D mass fractal dimension of aggregates and agglomerates. Our case study is represented by scanning transmission electron microscopy-images of boehmite colloidal suspensions. The behaviour of the computed d f at different acid and base concentration shows a fair agreement with the results of Small Angle X-Ray Scattering and with the literature, enabling to use the d f vs d p relationship to study the impact of the composition of the colloidal suspension on the density of colloidal aggregates and agglomerates.

Mots clés: fractal dimension; morphological model; image analysis

Domaines: Traitement du signal et de l'image [eess.SP]; Chimie analytique

Giulia Ferri, Severine Humbert, Jean-Marc Schweitzer, Mathieu Digne, Veronique Lefebvre, et al.. Mass fractal dimension from 2D microscopy images via an aggregation model with variable compactness. Journal of Microscopy, 2022, 286 (1), pp.31-41. ⟨10.1111/jmi.13088⟩. ⟨hal-03692434⟩