Small-angle neutron-scattering investigation of long-range correlations in silica aerogels: Simulations and experiments

Numerical simulations of gel formation by off-lattice diffusion-limited cluster-cluster aggregation (DLCA) of identical spherical particles in a cubic box are performed. Both the correlation function g(r) and the small-angle scattering function S(q), which is related to the Fourier transform of g(r)-1, are calculated for the resulting gel structure which is made of connected fractal clusters. In addition to the short-range features already described in a previous paper, it is found that g(r) goes through a minimum before tending to unity for large r values. As a consequence the scattering function S(q) exhibits a maximum at small q values. After multiplying S(q) by the form factor P(q), the intensity curve I(q) is calculated and its behavior is found to be in good agreement with small-angle neutron-scattering experiments on silica aerogels of various densities. In contrast with previous approaches, the low-q maximum in the I(q) curve is here directly quantitatively accounted for, without introducing any phenomenological ad hoc term to describe the intercluster correlations.