Indirect method for determining degree of branching in hyperbranched polymers

In an attempt to relate architecture to physical properties through a systematic study of degree of branching (DB), we recently reported the copolymerization of a series of AB/AB₂ monomers ranging from 0 to 1 mole fraction AB monomer content (x_AB). However, the DB of copolymers with 0.25 < x_AB < 1.0 were not measurable by standard ¹H NMR due to severe aggregation and lack of dispersion. To indirectly measure the DB of the whole series, a reaction scheme involving nonpolymerizable small molecules that contain the A, B, and B₂ functionalities ((A + B)/(A + B₂) model reaction), whose products represent the linear and dendritic connectivities in the AB/AB₂ copolymer products, was devised. By control of the stoichiometry and utilization of reaction conditions identical to those of the polymerizations, the products representing hyperbranched polymer units were produced and their ratios were monitored by ¹H NMR and/or HPLC to indirectly determine the DB. In all reactions the A functionality was consumed in 2.5 min or less (p_A = 1 at 2.5 min) and no detectable side products were observed in either analytical technique. Excellent agreement in DB was observed for copolymer compositions that could be measured and the corresponding model reactions, validating our indirect method for measuring DB in our AB/AB₂ ether-imide copolymers.