Mechanical structure–property relationship of aerogels

The elastic moduli (E) of high-porosity materials (such as aerogels) exhibit power-law scaling with their relative densities (ρ), E∝ρm, where 3⩽m⩽4, but the physics responsible for this behavior is not well-understood. Computer models of aerogels were generated by diffusion-limited cluster–cluster aggregation (DLCA) algorithms, and their linear elastic properties were examined by the finite element method (FEM), assuming that the stiffness of each interparticle bond can be represented by a beam element. The simulation yields m≈3.6 for perfectly connected structures, contradicting the consensus that the dangling mass on the gel gives rise to the exponent. The results suggest that the high exponent is largely because of the reduction in the connectivity of the material with decreasing density. The open-cell foam model, which predicts m=2, is valid only when the connectivity remains unchanged upon variation of the density. The mechanical structure–property relationship in the gel can be described by the `blob-and-linkʹ model. The bonds (links) between the fractal clusters (blobs) are more sparsely distributed than those inside the clusters, and therefore the strain energy is localized at the cluster boundaries during deformation. This model is consistent with the experimental evidence.