Small-angle X-ray scattering intensity of multiscale models of spheroids.

The microstructure of heterogeneous catalysts often consists of multiscale aggregates of nanoparticles, some of which are highly anisotropic. Therefore, small-angle X-ray scattering, in classical or anomalous mode, is a valuable tool to characterize this kind of material. Yet, the classical exploitation of the scattered intensities through form and structure factors or by means of Boolean models of spheres is questionable. Here, it is proposed to interpret the scattered intensities through the use of multiscale Boolean models of spheroids. The numerical procedure to compute scattered intensities of such models is given and then validated on asymptotic diluted Boolean models, and its applicability is demonstrated for the characterization of alumina catalyst supports.

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

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 $d_f$ , which is different from the two-dimensional (2D) fractal dimension d p $d_p$ 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 $d_f$ 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 $d_f$ versus d p $d_p$ relationship to study the impact of the composition of the colloidal suspension on the density of colloidal aggregates and agglomerates.

Boehmite powder is often employed for the manufacturing of γ $\gamma$ -alumina catalyst carriers and absorbents. This process involves boehmite colloidal particles coagulation, the size and shape of the particles affect the porosity of the final solid. As there is a high interest in tuning the porosity via the synthesis parameters, this work is aimed at the use of microscopy analysis to evaluate the mass fractal dimension of boehmite aggregates and agglomerates formed under controlled physical chemical conditions (acid and alkaline content and Brownian motion). Since the mass fractal dimension cannot be directly computed on binary two-dimensional images, a recently developed morphological model has been used to generate three-dimensional clusters characterized by a certain mass fractal dimension d f $d_f$ , the projection of the clusters leads to the estimation on the projected fractal dimension d p $d_p$ , being related to the slope on a bi-logarithmic plot perimeter versus area. According to the morphological model, the higher the d f $d_f$ , the lower the d p $d_p$ . The relationship between d f $d_f$ and d p $d_p$ has been used to estimate the mass fractal dimension from STEM images of boehmite suspensions. The trend of d f $d_f$ with respect to the acid and alkaline content in the suspensions agrees with small angle X-ray scattering measurement and with the literature.