Persistence Length, Mass Fractal, and Branching in the Aggregating of Vinyltriethoxysilane-Derived Organic/Silica Hybrids

The time evolution of the local chain persistence determined by small-angle X-ray scattering (SAXS) in the aggregation kinetics of vinyltriethoxysilane(VTES)-derived organic/silica hybrids has been analyzed by the classical Sharp and Bloomfield (SB) model, by a mass-fractal Unified Function (UF) with an arbitrary mass-fractal dimension D, and by a modified branching Sharp-Bloomfield (BSB) model incorporating a branching probability parameter. The SB function describes well the SAXS data, but it is restricted to stages close to the appearance of a plateau in the Kratky plots. The UF and BSB models describe well the SAXS data up to the plateau and afterward when maxima rise in the Kratky plots, the maxima increasing in intensity and shifting toward the low-q with time. The UF approach does not apply to the data at the early stages of aggregation, when D is apparently not so different from the exponent similar to 1 of the rod-like power-law regime at high-q. The values of the persistence length l(p), the contour length L, the gyration radius R-g, and the mass density per chain length M/L as determined from the different approaches were used to probe the applicability of the methods.