Abstract

Characterizing nanoparticles in terms of size and morphology is essential to understand their physical and optical properties. Small or Ultra Small-Angle X-ray Scattering (SAXS/USAXS) is a powerful in situ technique that allows the analysis of such nanostructures exhibiting size and morphology through the Guinier and Porod regimes, which can be repeated at different scales (e.g., primary spheres and agglomerates for mass fractal agglomerates, as focused on in this study). This is the principle of the widely used Beaucage's unified model, built in reciprocal q-space (the momentum transferor scattering wave vector) in order to interpret experimental results. An alternative method based on pair correlation modeling can be used. Indeed, by definition, the scattered signal corresponds to the Fourier transform of the particles' pair correlation function. The present study compares the two approaches for fractal agglomerates of point-contact spheres. It is shown that the Beaucage's model is limited to agglomerates consisting of a large number of primary spheres and that certain destructive interferences, not taken into account in this model, can affect data inversion, potentially affecting the extraction of the primary sphere size distribution. In this work, both models are compared in the direct way applied on synthetic data, and used to invert experimental SAXS data from soot particles in a laminar ethylene diffusion flame measured at the European Synchrotron Radiation Facility (ESRF) and processed via Abel inversion. This study highlights the fundamental differences between the two models and emphasizes their respective limitations. Nevertheless, both models provide similar results except for the mass fractal dimension and primary sphere geometric standard deviation. The present study demonstrates thus the potential of the pair correlation modeling and encourages its further development.