Computer simulation of mechanical structure–property relationship of aerogels

Aerogel is a highly compliant material, whose elastic modulus scales with its relative density with an exponent between 3 and 4; however, the underlying physics is not understood. The diffusion-limited cluster–cluster aggregation (DLCA) was combined with a `dangling bond deflectionʹ algorithm to generate aerogel models with extensive loop structure. Their linear elastic properties were examined by the finite element method. Although the network models contain negligible dangling mass, the simulation yields the same empirical scaling relationship as aerogels, with an exponent of about 3.6. Therefore the consensus that `dead-endsʹ contribute to the compliance of aerogels is contradicted. The result shows that the fraction of bonds bearing the strain in the aerogel model decreases with decreasing density and this is why the network is so compliant. During gelation, particles aggregate to form primary clusters with dense cores (which we call `blobsʹ). Then the clusters percolate by interconnecting with a few tenuous chains (links) to form a gel. Stress and strain localize mostly at the weak links when the gel network is deformed, leaving the rigid blobs unloaded.