Scaling Theory and Numerical Simulations of Aerogel Sintering

A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $\xi$, in order to conserve the total mass of the system. Scaling laws are derived which predict how $a$, $\xi$ and the specific pore surface area $\Sigma$ should depend on the density $\rho$. Following the general ideas of the theory, numerical simulations of sintering are proposed starting from computer simulations of aerogel structure based on a diffusion-limited cluster-cluster aggregation gelling process. The numerical results for $a$, $\xi$ and $\Sigma$ as a function of $\rho$ are discussed according to the initial aerogel density. The scaling theory is only fully recovered in the limit of very low density where the original values of $a$ and $\xi$ are well separated. These numerical results are compared with experiments on partially densified aerogels.