Small Angle Neutron Scattering of Aerogels: Simulations and Experiments

TL;DR

This paper combines simulations and experiments to analyze the structure of silica aerogels using small angle neutron scattering, revealing details about intra- and inter-aggregate correlations and the effects of polydispersity.

Contribution

It introduces a comprehensive simulation approach for aerogel scattering and compares results with experimental data, highlighting the impact of polydispersity on scattering regimes.

Findings

Structure factor exhibits large-q oscillations indicating short-range correlations.

Experimental fits show maxima in scattering curves related to large-scale correlations.

Polydispersity shifts the crossover between fractal and Porod regimes to lower q-values.

Abstract

A numerical simulation of silica aerogels is performed using diffusion-limited cluster-cluster aggregation of spheres inside a cubic box (with periodic boundary conditions). The volume fraction $c$ is taken to be sufficiently large to get a gel structure at the end of the process. In the case of monodisperse spheres, the wavevector dependent scattered intensity $I(q)$ is 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 $q$-region between the fractal regime and the Porod regime and quantitative comparisons are made with experiments on colloidal aerogels. Moreover, at small-$q$ values, $S(q)$ 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 aerogel are presented. In the case of polydisperse spheres, $I(q)$ is calculated directly from a single aggregate simulation. It is shown that increasing polydispersity shifts the location of the cross-over between the fractal and Porod regimes towards low $q$-value.