Dynamical scaling property of colloidal aggregation in a zirconia-based precursor sol during gelation

Zirconia precursor gels, prepared in the zirconium n-propoxide, n-propanol, acetylacetone and water system, are studied by small angle X-ray scattering (SAXS). The SAXS intensity pattern exhibits a pronounced maximum for a scattering vector q different from zero. The intensity maximum of the finite q-vector peak increases during gelation while its position qm moves towards smaller and smaller q-vectors. The SAXS intensity distribution is well accounted for by recent direct numerical calculations of diffusion-limited cluster aggregation (DLCA). The structural aspects of cluster growth can be described by scaling assumptions. The position q(m) of the intensity maximum and the structure function S(q/q(m),t) are shown to scale according to S(q/q(m),t) = q(m) (t)(-d) F(q/q(m)) where F(q/q(m)) is a time-independent scaling function. This scaling requires d= D-f, the fractal dimension of the clusters, instead of d= 3 for spinodal decomposition. The gel structure is made up of connected fractal clusters, around 50 nm in size, with an apparent fractal dimension of 1.7, resulting from the aggregation of very small primary particles about 2.5 nm in diameter.