Degree of branching in hyperbranched polymers

TLDR

Topological considerations of the ratio of linear, imperfectly branched, dendritic, and terminal units in hyperbranched polymers derived from AB₂, AB₃, and ABₘ (m ≥ 2) monomers, including core‑initiated AB₂ reactions and the equality of terminal and dendritic units in large AB₂ systems, are summarized. A general expression for the degree of branching (DB) is derived for AB₂ systems based on dendritic and linear units, and a further general expression for DB in ABₘ‑based hyperbranched polymers is presented. The derived DB expressions, valid for both low and high molecular weight polymers, show that DB cannot exceed 0.5 for AB₂ systems (0.44 for AB₃), and they enable verification of NMR‑integration ratios and interpretation of signal ratios in hyperbranched polymer spectra.

Abstract

Abstract Topological considerations concerning the ratio of linear, imperfectly branched, dendritic and terminal units in hyperbranched polymers based on AB 2 , AB 3 and AB m (m≥2) type monomers are summarized. The reaction of AB 2 monomers with a core molecule of the structure B f is also treated. For larger hyperbranched polymers based on AB 2 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 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 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 AB 2 systems (0.44 in AB 3 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.