Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime

TL;DR

This study numerically investigates how particle size distribution affects the transition point in small angle scattering from fractal to Porod regimes in fractal aggregates.

Contribution

It introduces a numerical analysis of the crossover behavior in scattering intensity considering polydispersity in fractal aggregates.

Findings

Crossover point decreases with increasing size distribution width.

The shape of interparticle-distance distribution influences the crossover.

Polydispersity significantly impacts scattering behavior.

Abstract

Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussian-like distribution characterised by a mean $a_0$ and a standard deviation $\sigma$. The wave vector dependent scattered intensity $I(q)$ is computed in order to study the influence of the particle polydispersity on the crossover between the fractal regime and the Porod regime. It is shown that, given $a_0$, the location $q_c$ of the crossover decreases as $\sigma$ increases. The dependence of $q_c$ on $\sigma$ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.