Scattering of clusters of spherical particles-Modeling and inverse problem solution in the Rayleigh-Gans approximation

- A scattering model for a system of clusters is solved in inverse form.
- From the inverse solution the morphological parameters of the clusters are obtained.
- The estimation is performed in a single step without any assumption.
- Applications in light and x-ray scattering show the potential of the proposed methodology.

In this work, an exact scattering model for a system of clusters of spherical particles, based on the Rayleigh-Gans approximation, has been parameterized in such a way that it can be solved in inverse form using Thikhonov Regularization to obtain the morphological parameters of the clusters. That is to say, the average number of particles per cluster, the size of the primary spherical units that form the cluster, and the Discrete Distance Distribution Function from which the z-average square radius of gyration of the system of clusters is obtained. The methodology is validated through a series of simulated and experimental examples of x-ray and light scattering that show that the proposed methodology works satisfactorily in unideal situations such as: presence of error in the measurements, presence of error in the model, and several types of unideallities present in the experimental cases.