Small Angle Scattering by Fractal Aggregates A Numerical Investigation of the Crossover Bet.pdf

a r X i v : c o n d - m a t / 9 5 0 4 0 5 3 v 1 1 2 A p r 1 9 9 5 Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime Anwar Hasmy, Rene? Vacher and Re?mi Jullien Laboratoire de Science des Mate?riaux Vitreux, UA 1119 CNRS, Universite? Montpellier II, Place Euge?ne Bataillon, 34095 Montpellier Cedex 5, France (February 1, 2008) 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 a0 and a standard deviation σ. 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 a0, the location qc of the crossover decreases as σ increases. The dependence of qc on σ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function. PACS numbers: 61.12.-q, 61.43.Bn, 61.43.Hv Small-angle X-ray scattering as well as small-angle neutron scattering have been widely used to study the structure of disordered systems1–8. In particular they have allowed to demonstrate that silica aerogels are made of connected fractal “blobs”3,4. In such materials, the wave vector dependent scattered intensity I(q) exhibits two crossovers related to the two characteristic lengths, mean particle diameter a0 and mean blob size ξ. The first one separates the low-q (q ξ?1) saturation, called the Guinier regime9, from the intermediate power-law behaviour3,4, called the fractal regime. The second one, on which we will focus in this letter, separates the fractal regime from the high-q (q a?10 ) q?4 behaviour, called the Porod regime9. In some previous studies, it was assumed that the crossover between the fractal regime and the