Abstract: This work deals with the dependence of the z-average mean-square radius of gyration (<R²> z) on the degree of branching(DB) for highly branched copolymers made from the one-pot cocondensation of AB₂ and AB monomers. A new expression of the degree of branching has been derived. The DB monotonously increases with increasing A group conversion and the fraction of AB₂ monomers. The value of DB calculated in accordance with our formula is lower than that given by Frey and coworkers. Howerver, when the reaction approaches completion, our expression of the degree of branching degenerates into the equation reported by Frey. Furthermore, the z-average mean-square of gyration of the resulting copolymer in the Θ state has been derived on the basis of the classical work developed by Stockmayer, Gordon, Li and Ba. The relationship between DB and <R²> z is illustrated by numerical results. The z-average mean-square radius of gyration of the copolymer with a certain weight-average molecular weight monotonously decreases with increasing the degree of branching.

Key words: Hyperbranched copolymers, Degree of branching, Mean-square radius of gyration