Small-angle neutron scattering of aerogels: simulations and experiments

Abstract

Numerical simulation of silica aerogels was performed using diffusion-limited cluster-cluster aggregation of spheres inside a cubic box (with periodic boundary conditions). The volume fraction, c, was taken to be sufficiently large to obtain a gel structure at the end of the process. In the case of monodisperse spheres, the wave-vector-dependent scattered intensity, I( q), was calculated from the product of the form factor, P( q), of a sphere by the structure factor, S( q), which is related to the Fourier transform of g( r)-1, where g( r) is the pair correlation function between sphere centers. The structure factor, S( q), exhibits large- q damped oscillations characteristics of the short-range (intra-aggregate) correlations between spheres. These oscillations influence the I( q) curve in the region of q between the fractal regime and the Porod regime and quantitative comparisons were made with experiments on colloidal aerogels. At small values of q, S( q) goes through a maximum characteristic of large-range (inter-aggregate) correlations. Quantitative fits of the maximum in the experimental I( q) curves of base-catalyzed aerogels are presented. In the case of polydisperse spheres, I( q) was directly calculated from a single aggregate simulation. Increasing polydispersity shifts the location of the cross-over between the fractal and Porod regimes towards lower values of q.