We present measurements of the thermal expansion of silica-aerogels of various densities in the two following situations: thermal expansion of evacuated samples and the additional expansion due to ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorption on the silica surface in the temperature range 2–80 K. At the same time we measured the number of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms adsorbed at the surface. To analyze the adsorption data we use a Brunauer-Emmett-Teller model, where we introduce a distribution of binding energies to take into account the surface heterogeneity. A simple model, involving the same distribution, allows us to relate the expansion to adsorption. We therefore determine some microscopic parameters for the adsorption energies and derive the elastic properties at different scales of the fractal structure.

• Received 5 June 1995

DOI:https://doi.org/10.1103/PhysRevB.52.17491