Intramolecular cyclization of long-chain hyperbranched polymers (HyperMacs) from A2 + Bn step-wise polymerization

Well-defined hyperbranched polymers with long-chain backbones between the branched points (HyperMacs) are an emerging issue in topological polymers. Owing to the difficult discrimination of branching points interfered with or overlapped by long-chain backbones in nuclear magnetic resonance signals, the fine identification and quantitative characterization of intramolecular cyclization and the calculation of the degree of branching for HyperMacs are always challenges. In this contribution, a convenient expression of the macro-cyclic index (m-CI) was presented and deduced as the ratio of NA/NB of HyperMacs to that of their completely intramolecular cyclized analogues. The physical meaning of m-CI is the similarity of HyperMacs to their completely cyclized analogues. Accordingly, a m-CI closer to 1 means a high degree of intramolecular cyclization, even complete cyclization. The experimental validation via model polymers indicates that m-CI is a facile parameter to analyze intramolecular cyclization of HyperMacs. The increase of the chain length of the backbones between branched points can enhance intramolecular cyclization of HyperMacs accompanied with the increase of the m-CI value. As an original contribution to polymer science, the presentation of m-CI overcomes the difficult problem of quantitative characterization of intramolecular cyclization in long-chain hyperbranched polymers, which is helpful for a good understanding of their relationship between topological structures and properties.