DEGREE OF BRANCHING IN HYPERBRANCHED POLYMERS

Topological considerations concerning the ratio of linear, imperfectly branched, dendritic and terminal units in hyperbranched polymers base d on AB(2), AB(3) and AB(m) (m greater than or equal to 12) type monom ers are summarized. The reaction of AB(2) monomers with a core molecul e of the structure B-f is also treated. For larger hyperbranched polym ers based on AB(2) monomers the fraction of terminal units has to be e qual to the number of dendritic units. A general expression for the de gree of branching (DB) is derived for AB(2) systems, which is based on the number of dendritic and linear units. The expression is valid for low molecular weight as well as high molecular weight hyperbranched p olymers in contrast to the commonly used expression based on dendritic , linear and terminal units. DB may not exceed 0.5 in hyperbranched po lymers based on AB(2) systems (0.44 in AB(3) systems). Furthermore, a general expression for DB in hyperbranched polymers based on AB(m) mon omers is derived. Consequences for signal ratios in NMR-spectra of hyp erbranched polymers are discussed. The expressions presented allow ver ification of NMR-integration ratios obtained experimentally on the bas is of model compounds.