A unified kinetic analysis for the hyperbranched polymerization with AB_g type monomers

The unified analytical expressions of the size distribution function and the degree of branching for the hyperbranched polymerization with AB(g) type monomers are developed by kinetic theory of polymerization, based on the AB(g) + AB(h) + B-f model. The effect of the reactant parameters, the monomers branching degree g and h, the monomers feed ratio r, the functionality f and feed ratio alpha of the core molecule B-f, on the molecular parameters of the products formed was investigated. Compared with the general polycondensation of AB(g) monomer or copolycondensation of AB(g) and AB monomer without core molecule, the presence of multifunctional core molecules makes the polydispersity index of the products go down fast when the reaction approaches completion. At the end of the reaction, the polydispersity index increases with increasing g, and decreases with increasing alpha and f. For the AB(g) + AB + B-3 polycondensation system, within the range of the feed ratio of AB(g) monomer less than 0.3, the average chain segment length significantly decreases with the increasing r, and then the change becomes moderate with its further increase. For g > 2, the average chain segment length shows a shallow minimum with increasing r. The degree of branching, fractions of terminal and branching units also show maximum value with the change of monomer feed ratio r. The information obtained in this work can help people understand the structure of AB(g) type hyperbranched polymers and carry out molecular design.