The hyperbranched polymers can be made by self-condensing vinyl polymerization without gelation transition. The average molecular weights, as well as the average sizes, can reach infinite values as the reaction is quantitatively completed, and the scaling forms of the molecular parameters should exist. In the paper, based on a recursion formula, the scaling form of the number fraction distribution and the number of the n-mers are given analytically as the conversion of double bonds is near 1. The mean square radius of gyration for very large hyperbranched polymers is calculated explicitly to give a scaling exponent. Finally, a scaling relation associated with the fractal dimension and the polydispersity exponent is given clearly.

Abstract Silica fume was modified by a silane coupling agent (KH-550). The modified silica fume was further investigated to reinforce polyurethane (PU) composites. Unmodified and modified silica fume reinforced PU composites were prepared. Through the comparisons of Fourier transform infrared (FT-IR) spectroscopy, transmission electron microscopy (TEM) and scanning electron microscopy (SEM) of unmodified and modified silica fume, the agglomerations of silica fume particles were effectively prevented as KH-550 was grafted. The compressive strength of the modified silica fume/PU composites was largely improved, because KH-550 could react with both silica fume and PU. Meanwhile, modified silica fume turned from hydrophilic to hydrophobic; a better dispersion was realized in the PU elastomers compared to the unmodified silica fume. The reinforcement effects were evaluated based on the results of a universal test machine in comparison with unmodified silica fume/PU composites.