A. Hasmy et al., SMALL-ANGLE NEUTRON-SCATTERING INVESTIGATION OF LONG-RANGE CORRELATIONS IN SILICA AEROGELS - SIMULATIONS AND EXPERIMENTS, Physical review. B, Condensed matter, 50(9), 1994, pp. 6006-6016
Numerical simulations of gel formation by off-lattice diffusion-limite
d 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 Fou
rier transform of g (r) - 1, are calculated for the resulting gel stru
cture which is made of connected fractal clusters. In addition to the
short-range features already described in a previous paper, it is foun
d 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 ma
ximum 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 experimen
ts on silica aerogels of various densities. In contrast with previous
approaches, the low-q maximum in the I (q) curve is here directly quan
titatively accounted for, without introducing any phenomenological ad
hoc term to describe the intercluster correlations.