Crossover from scalar to vectorial percolation in silica gelation

Abstract

We present a rheological study of the gel transition in silica gels resulting from the hydrolysis-condensation of a silicon alkoxide. The complex shear modulus is measured in a large frequency range (${10}^{\mathrm{-}2–}$ ${10}^2$ rad/s). The exponents for the viscosity s=0.7±0.1, for the elasticity t=2.0±0.1, for the dynamic crossover frequency z=2.9±0.2, and for the scaling-frequency power law Δ=0.72±0.03 are in agreement with the scalar percolation model in a restricted region around the gelation time (3%). Beyond, there is a crossover to a vectorial percolation regime characterized by a much higher elasticity exponent t’=3.6±0.1.