Résumé
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.