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

Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material

“…The fractal dimension can be estimated from the power law behavior of the scattering function, S(q) ∼ q −D in this q-range. In our case we have obtained D ∼ 1.74 consistent with the value expected for silica aerogels in three dimensions 24,25 .…”

“…1. The radial distribution function g(r) presents a strong peak at r = σ a , associated with bonds between contacting particles, and other features corresponding to short range correlations between particles belonging to the same cluster (see references 24,25 for further details). Before reaching the asymptotic limit of 1, g(r) exhibits a minimum corresponding to distances between particles located at the boundary of the clusters.…”

“…Structures with similar fractal dimension have been generated by Monte Carlo simulations using several hierarchical cluster-cluster algorithms 24,25,26 . In particular the Diffusion Limited Cluster-Cluster Aggregation procedure (DLCA) is a gel growth process widely used in theoretical studies of aerogels 25,27 .…”

“…The fractal behavior of aerogels is associated with the irreversibility of the gel formation dy-namics, which proceed by random colloidal aggregation of silica particles. The fractal dimension of silica aerogels is about 1.80 in three dimensions 24 .…”

Fluctuating Bond Aggregation: A Model for Chemical Gel Formation

“…The log-log curves exhibit the same qualitative shape as for DLCA [12], i.e. a maximum at low-q, which is shifted to larger q as the concentration increases, an intermediate fractal linear regime, followed by damped oscillations (characteristic of the short range order between particles [14]) at larger q-values. However, for c > ∼ c g , the absolute value of the fractal slope (≃ 2.3) is significantly larger than in DLCA and decreases slowly as c increases.…”