Conversion dependence of the mean size of the star-branched polymers made by AB + Af type polycondensation

The statistical method was used to give the number of bonds formed for the star-branched polymer chains made by the AB + Af polymerization. On the basis of the kinetic model described by the Smoluchowski-like coagulation equation, the mean-square radii of gyration were given analytically. Furthermore, the z- and weight-average mean-square radii of gyration were investigated explicitly. The results were much different from that of the hyperbranched polymers made by the AB f type monomers, where the former had the finite values when the reaction was quantitatively completed, and the latter reached the infinite values. In principle, by varying the number of the A f type multifunctional core moieties, the average sizes, as well as the average degrees, can be controlled effectively.