Effect of aging and pH on the modulus of aerogels

The elastic modulus E of an aerogel is related to its density ρ{variant} by E = c(pH)ρ{variant}^3.7 for gels made at various pH values; however, the constant of proportionality c depends on pH. It is found that this relation applies regardless of whether the density is varied by lengthy aging or by increasing the concentration of tetramethoxysilane (TMOS) in the initial sol; that is, changes in aging time and [TMOS] evidently have equivalent effects on gel structure. The influence of pH on densification can be understood in terms of competition between polycondensation (P, which produces shrinkage) and dissolution/ reprecipitation (D/R, which increases the rigidity of the network). At low pH, P dominates, but at high pH D/R stiffens the network and inhibits shrinkage.