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.