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{\ensuremath{-}}2--}$${10}^{2}$ rad/s). The exponents for the viscosity s=0.7\ifmmode\pm\else\textpm\fi{}0.1, for the elasticity t=2.0\ifmmode\pm\else\textpm\fi{}0.1, for the dynamic crossover frequency z=2.9\ifmmode\pm\else\textpm\fi{}0.2, and for the scaling-frequency power law \ensuremath{\Delta}=0.72\ifmmode\pm\else\textpm\fi{}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\ifmmode\pm\else\textpm\fi{}0.1.