Mass-fractal growth in niobia/silsesquioxane mixtures: a small-angle X-ray scattering study

The nucleation and growth of niobium pentaethoxide (NPE)-derived clusters in ethanol, through acid-catalyzed hydrolysis/condensation in the presence and absence of the silsesquioxane 1,2-bis(triethoxysilyl)ethane (BTESE), was monitored at 298-333 K by small-angle X-ray scattering. The data were analyzed with a newly derived model for polydisperse mass-fractal-like structures. At 298-313 K in the absence of BTESE the data indicated the development of relatively monodisperse NPE-derived structures with self-preserving polydispersity during growth. The growth exponent was consistent with irreversible diffusion-limited cluster agglomeration. At 333 K the growth exponent was characteristic for fast-gelling reaction-limited cluster agglomeration. The reaction yielded substantially higher degrees of polydispersity. In the presence of BTESE the growth exponents were substantially smaller. The smaller growth exponent in this case is not consistent with irreversible Smoluchowski-type agglomeration. Instead, reversible Lifshitz-Slyozov-type agglomeration seems to be more consistent with the experimental data