Degree of branching in hyperbranched polymers

Topological considerations concerning the ratio of linear, imperfectly branched, dendritic and terminal units in hyperbranched polymers based on AB₂, AB₃ and AB_m (m≥2) type monomers are summarized. The reaction of AB₂ monomers with a core molecule of the structure B_f is also treated. For larger hyperbranched polymers based on AB₂ monomers the fraction of terminal units has to be equal to the number of dendritic units. A general expression for the degree of branching (DB) is derived for AB₂ 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 polymers in contrast to the commonly used expression based on dendritic, linear and terminal units. DB may not exceed 0.5 in hyperbranched polymers based on AB₂ systems (0.44 in AB₃ systems). Furthermore, a general expression for DB in hyperbranched polymers based on AB_m monomers is derived. Consequences for signal ratios in NMR-spectra of hyperbranched polymers are discussed. The expressions presented allow verification of NMR-integration ratios obtained experimentally on the basis of model compounds.