Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

Abstract

Dynamical scaling properties in fractal structures were investigated from small-angle X-ray scattering (SAXS) data of the kinetics of aggregation in silica-based gelling systems. For lack of a maximum in the SAXS intensity curves, a characteristic correlation distance ξ was evaluated by fitting a particle scattering factor model valid for polydisperse coils of linear chains andf-functional branched polycondensates in solution, so the intensity atq= ξ−1,I(ξ−1,t), was considered to probe dynamical scaling properties. The following properties have been found: (i) the SAXS intensities corresponding to different timest,I(q,t), are given by a time-independent functionF(qξ) =I(q,t)ξ−D/Q, where the scattering invariantQhas been found to be time-independent; (ii) ξ exhibited a power-law behavior with time as ξ ≃tα, the exponent α being close to 1 but diminishing with temperature; (iii)I(ξ−1,t) exhibited a time dependence given byI(ξ−1,t) ≃tβ, with the exponent β found to be around 2 but diminishing with temperature, following the same behavior as the exponent α. In all cases, β/α was quite close to the fractal dimensionDat the end of the studied process. This set of findings is in notable agreement with the dynamical scaling properties.