Small-angle neutron-scattering investigation of short-range correlations in fractal aerogels: Simulations and experiments

The center-to-center interparticle-distance distribution function f(r) and its Fourier transform, the scattering function S(q), are computed for simulated fractal aggregates made of identical spherical particles using several three-dimensional off-lattice cluster-cluster algorithms. As expected f(r) exhibits a {δ} peak at the particle diameter followed by a discontinuity at twice this distance as a consequence of the nonoverlapping character of the spherical particles. As a result the curve log₁₀S(q) versus log₁₀q goes through a broad minimum followed by damped oscillations at large-q values. These simulations are compared with experimental small-angle neutron-scattering results on colloidal silica aerogels. The experimental scattering function S(q) is derived from the ratio between the scattered intensity I(q) and the form factor P(q) determined from measurements on the diluted colloidal solution. The agreement between simulations and experiments is qualitatively good and the influence of aerogel density is well accounted for. The departure of the experimental curves from the theoretical S(q) curve, which is stronger for larger particle sizes, is attributed to short-wavelength corrections to the simple scattering theory.